BM6P6(@ ......------------......////////////000000000000000000000000000000000000,,,...000000//////111333111222222333222111000///...............------,,,......---,,,++++++******---,,,,,,++++++,,,,,,---***++++++,,,,,,++++++***,,,+++++++++***)))))))))---------+++)))(((***,,,...///////////////......---,,,+++,,,...///...---,,,,,,---......//////000---***((((((***+++)))&&&---,,,***)))))))))******)))((('''(((***++++++***(((((((((((()))))))))))))))(((&&&%%%%%%&&&'''(((((((((((((((((()))******(((((((((((())))))))))))''''''''''''((((((((()))%%%%%%%%%&&&&&&'''''''''$$$""""""###&&&'''%%%###%%%%%%%%%&&&&&&&&&''''''(((((('''&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&%%%%%%$$$%%%'''))))))((('''((()))&&&&&&''''''&&&&&&%%%$$$%%%$$$$$$###$$$%%%'''(((%%%%%%%%%$$$$$$#########""""""############""""""######$$$$$$$$$%%%%%%%%%######$$$%%%%%%%%%%%%$$$''''''''''''&&&&&&%%%$$$############""""""""""""!!!!!!    !!!""""""""""""!!!!!!!!!!!!""""""""""""############""""""""""""""""""""""""$$$$$$###"""!!!!!!""""""######$$$$$$$$$$$$######)))$$$!!!###)))+++&&& ######""""""!!!!!! ###"""!!! !!!"""###!!!!!! !!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!   ------,,,,,,,,,,,,------.../////////000000000000////////////////////////---...000000//////111222111111222333222111000///...////////////...------.........---,,,+++++++++---,,,,,,++++++,,,,,,---,,,+++***))))))***+++,,,,,,,,,,,,++++++++++++++++++,,,,,,+++******,,,.........////////////.........---,,,---///000///...---------------.........,,,***((())),,,---+++***,,,,,,***)))))))))*********))))))***+++,,,,,,***))))))))))))***************)))'''&&&&&&''')))***)))))))))))))))***++++++(((((((((((()))))))))***&&&&&&&&&'''''''''((((((%%%&&&&&&&&&&&&&&&&&&'''$$$###"""$$$&&&'''%%%###%%%%%%%%%%%%&&&&&&&&&&&&(((((('''&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$%%%'''((()))((('''((()))'''''''''''''''&&&%%%%%%&&&%%%$$$$$$$$$%%%&&&'''%%%%%%%%%$$$$$$$$$######""""""############""""""############$$$$$$$$$%%%######$$$%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&%%%$$$$$$############""""""""""""!!!!!!  !!!""""""""""""!!!!!!!!!!!!""""""""""""############""""""""""""""""""""""""$$$$$$###""""""""""""""""""######$$$$$$######"""000000111111000,,,(((%%%############"""""""""!!!###"""!!! !!!"""###!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!   !!! ,,,,,,,,,++++++,,,,,,,,,....../////////000000000........................---...000000//////111222000111222222222111000/////////000000000///......//////......---,,,,,,,,,---,,,,,,++++++,,,,,,---...,,,)))''''''))),,,...,,,,,,,,,,,,,,,---------***+++,,,,,,+++,,,...000......///////////////...///...---...000111000///------------,,,,,,,,,,,,+++***)))+++---...---,,,,,,+++******)))*********,,,*********,,,---,,,+++************+++++++++++++++***)))(((((()))***+++*********+++++++++,,,,,,((((((((()))))))))******&&&&&&&&&&&&'''''''''''''''''''''&&&&&&&&&&&&&&&$$$######$$$&&&&&&%%%###$$$$$$$$$%%%%%%%%%&&&&&&((((((''''''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''&&&&&&''''''&&&&&&%%%%%%%%%&&&(((((('''''''''((('''(((((((((((('''&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$###""""""############"""""""""""""""#########$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###############""""""""""""!!!!!!!!!  !!!!!!!!!!!!!!!""""""""""""""""""""""""############""""""""""""""""""""""""$$$$$$###""""""""""""###""""""############"""""")))///444333,,,%%%###$$$$$$$$$############""""""""""""!!!!!!!!!!!!""""""!!!!!!!!!!!!!!!!!!!!!!!!""""""!!!!!!   !!!!!!  ------,,,,,,,,,,,,------........./////////000000........................---///000000//////000222///000111222222111000///000000000000000//////...//////.........------------,,,,,,++++++,,,,,,------,,,***((((((***,,,---***+++++++++,,,,,,------+++,,,------,,,,,,...///---...//////////////////...---------///000///.........---,,,++++++******++++++++++++,,,,,,,,,,,,++++++******************,,,***)))***,,,,,,+++***)))))))))*********++++++***))))))))))))***++++++)))******+++++++++++++++(((((()))))))))*********''''''''''''((((((((((((((((((''''''&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&((((((''''''&&&&&&&&&%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%###$$$$$$%%%&&&'''((((((%%%&&&&&&'''&&&&&&%%%%%%$$$&&&(((((('''&&&'''(((((((((((()))(((''''''&&&'''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$$$$######"""!!!""""""""""""############$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$###############"""""""""!!!!!!!!!!!!  !!!!!!!!!!!!!!!""""""""""""!!!"""""""""############""""""""""""""""""""""""$$$$$$###""""""#########!!!""""""######""""""!!!###((((((### ######"""""""""""""""""""""""""""!!!!!!!!!!!!""""""!!!!!!!!!""""""!!!!!!!!!"""""""""!!!     ......------------..................////////////...........................///000000//////000111//////111111222111000///000000000000000//////..................------------,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,))))))******++++++,,,,,,---...///...,,,+++,,,---------...///////////////---,,,+++,,,...///...---......---,,,+++******)))------,,,+++***)))))))))************+++*********+++***))))))***+++***(((((((((((()))))))))******((((((((())))))******+++((()))***+++++++++******))))))))))))************))))))))))))************(((((((((''''''&&&&&&&&&$$$%%%&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&((('''''''''''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((''''''$$$$$$%%%&&&&&&'''((((((%%%%%%&&&&&&'''&&&&&&%%%$$$&&&(((((('''&&&'''(((((((((((()))(((''''''&&&&&&&&&&&&&&&%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######!!!""""""""""""#########$$$$$$%%%&&&&&&&&&&&&%%%###$$$$$$%%%%%%$$$$$$$$$############"""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!! !!! !!!!!!!!!"""""""""###!!!"""""""""####################################$$$###############$$$$$$""""""############"""""" !!!!!!!!!"""$$$%%% !!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!"""######"""!!!!!!""""""!!!!!!    ///......------......///------........./////////...........................000111000///...///111...///000111111111000/////////000000000///......---------------------------,,,,,,++++++,,,,,,---***+++,,,,,,,,,,,,+++*********************++++++---...///...,,,******+++,,,---...///000000000000---,,,+++,,,.........---///......---,,,++++++***---......,,,)))''''''((())))))***++++++++++++***+++***((()))******)))((('''((((((((())))))))))))((((((((()))******++++++'''(((***+++++++++***))))))))))))*********++++++************++++++++++++((((((((('''''''''''''''$$$&&&''''''%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((())))))))))))((((((%%%%%%&&&&&&''''''((((((%%%%%%&&&&&&''''''&&&&&&$$$%%%''''''&&&&&&&&&''''''(((((((((((('''&&&&&&%%%%%%&&&&&&&&&%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%######$$$$$$$$$$$$######"""""""""#########$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&###$$$$$$%%%%%%%%%%%%%%%############"""""""""""" !!!!!!!!!!!!""""""""" !!! !!!!!!""""""######""""""""""""####################################$$$############$$$%%%%%%######$$$$$$$$$$$$######%%%""""""$$$$$$### !!!!!!!!!!!!""""""""""""!!!!!!!!!!!!############!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!   ...------,,,,,,------...---------........./////////////////////////////////000111000///...///000---...000111111111000///...////////////...------,,,,,,,,,,,,,,,------------,,,,,,++++++,,,,,,---******)))(((((()))******++++++++++++++++++*********,,,------,,,+++++++++,,,---...///000000000000...---,,,---...//////---///.........------,,,,,,,,,...///---***))))))+++((()))***+++,,,++++++***,,,+++)))***++++++)))((((((((()))))))))*********((()))***+++,,,,,,,,,,,,((()))+++,,,---,,,+++***))))))*********+++++++++))))))*********+++++++++''''''''''''((((((((((((%%%'''((((((%%%$$$$$$&&&&&&&&&'''''''''(((((((((''''''''''''((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((''''''((((((((((((''''''&&&&&&&&&'''''''''''''''$$$%%%&&&&&&''''''&&&&&&###%%%''''''&&&&&&&&&''''''''''''''''''&&&%%%%%%###$$$%%%&&&&&&&&&%%%$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###############$$$$$$$$$%%%$$$%%%&&&&&&'''&&&&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&############"""""""""""" !!!!!!!!!"""""""""""" !!! !!!"""#########""""""""""""####################################$$$#########$$$$$$%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$###!!! """###""" !!!!!!!!!""" !!!"""######"""!!! !!!###$$$$$$###!!!  !!!"""""""""     ---,,,,,,++++++,,,,,,------------.........//////000000000000000000000000///000111000///...///000---...///111111111000///...............------,,,,,,,,,,,,,,,,,,,,,,,,,,,---,,,,,,++++++,,,,,,---+++)))&&&$$$$$$&&&)))+++---------,,,,,,+++++++++'''))),,,---,,,+++,,,,,,,,,---...///000000000000///...---...000000000//////............---------,,,...///...,,,***,,,...((()))***+++,,,,,,+++***---,,,++++++,,,,,,***))))))************+++++++++)))***+++,,,---...------)))***,,,......---,,,+++)))************+++++++++))))))))))))************&&&&&&''''''(((((())))))%%%''')))(((%%%###$$$&&&'''''''''(((((((((((()))'''''''''((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))&&&&&&''''''''''''&&&&&&'''''''''''''''&&&&&&&&&$$$%%%%%%&&&'''''''''&&&###%%%''''''&&&%%%&&&'''&&&&&&''''''&&&&&&%%%$$$"""###%%%&&&'''&&&&&&%%%#########$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$######$$$$$$$$$$$$%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&$$$%%%&&&&&&''''''''''''############"""""""""""" !!!!!!!!!""""""######   !!!!!! !!!"""######$$$""""""""""""####################################$$$#########$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$ ###$$$%%%$$$###""" !!!!!!!!!""""""###### !!!"""######"""!!! """###$$$$$$###"""  !!!"""###### !!!!!!!!! !!!!!!   !!!"""---------,,,,,,,,,++++++---------.........//////,,,,,,------///000111222//////000111111111111111000000000000000111222222111000///------......///000///---,,,+++*********++++++------------++++++,,,,,,------,,,,,,+++***......---+++)))(((***,,,)))***+++,,,------------------...000111111///---***+++------------...000000000000000000000000000000000///...,,,+++******)))***+++,,,,,,,,,,,,,,,***++++++,,,,,,,,,++++++++++++******)))*********------,,,++++++,,,,,,,,,************************++++++************++++++'''((()))***************((((((((((((''''''''''''(((&&&%%%$$$$$$%%%'''(((''''''''''''''''''''''''+++***(((''''''(((((()))))))))))))))))))))))))))))))))))))))))))))))))))&&&'''''''''(((((())))))%%%%%%%%%&&&&&&&&&''''''''''''''''''(((((((((((($$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&&&&$$$###!!!######$$$$$$$$$$$$######&&&&&&%%%$$$$$$%%%&&&&&&"""###$$$%%%&&&'''''''''&&&&&&''''''''''''''''''$$$$$$$$$%%%%%%$$$$$$$$$ !!!"""######"""!!! """"""""""""""""""""""""  !!!""" !!!!!!!!!!!!!!!""""""""""""""""""""""""######$$$$$$$$$%%%%%%%%%"""###$$$%%%%%%$$$###"""""""""############""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!""""""#########$$$$$$$$$"""""""""""""""""""""""" !!!!!!!!!!!! !!! !!!""""""    ---------,,,,,,,,,,,,+++---------.........//////.........///000111222333///000000111111111000000111000000000000000111111111000///.........//////000///...,,,+++*********+++,,,------------,,,+++,,,,,,------,,,,,,+++***---------,,,***)))***+++******+++,,,------------------...000111111///,,,***,,,------------...000////////////////////////000//////---,,,+++*********++++++,,,,,,,,,++++++***++++++,,,,,,+++++++++,,,++++++*********++++++---,,,,,,++++++,,,,,,---************************+++******))))))******+++)))************))))))(((***))))))))))))((((((((($$$###""""""###%%%'''(((''''''''''''''''''''''''+++***)))'''''''''(((((())))))))))))))))))))))))))))))))))))))))))))))))''''''''''''((((((((()))%%%%%%&&&&&&''''''''''''(((((((((((((((((((((((($$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&''''''%%%$$$"""$$$$$$$$$%%%%%%$$$$$$$$$&&&%%%$$$######$$$%%%&&&$$$$$$%%%&&&''''''''''''%%%&&&&&&&&&&&&'''''''''###$$$%%%%%%%%%%%%$$$###""""""###$$$$$$###""""""""""""""""""""""""""""""  !!!  !!! !!!!!!""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!############$$$$$$$$$$$$"""##################"""""""""############""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!"""""""""#########$$$$$$!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!! !!!!!!!!!    ......---------,,,,,,,,,---............/////////////////////000222333444000000111111111000000///111111000000000000000111111000000///.../////////000///...---,,,+++++++++,,,,,,------------,,,,,,,,,,,,------,,,,,,+++***+++---...---+++************+++,,,------...------,,,,,,---///111111...,,,***,,,------,,,---...///........................//////...---,,,,,,+++++++++,,,,,,,,,,,,++++++***+++++++++,,,,,,++++++***,,,,,,++++++++++++,,,,,,,,,,,,,,,++++++,,,,,,---+++++++++++++++++++++++++++******))))))******+++++++++++++++***)))((('''************))))))))))))""""""""""""$$$&&&((()))''''''''''''''''''''''''+++***)))(((''''''''''''(((((((((((((((((((((((())))))))))))))))))))))))''''''''''''((((((((((((&&&''''''''''''(((((((((((((((((((((((((((((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''''''''&&&$$$###$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$&&&&&&''''''''''''&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&"""$$$%%%''''''%%%$$$"""######$$$%%%%%%$$$######!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!  !!!!!!""""""!!!!!! """"""""""""###############""""""!!!!!!""""""###""""""############""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""############!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!!!!!!!!!!    ............------------.............../////////////////////000111222333000111111111111000//////222111111000000000000000111111000000000/////////000///...---,,,,,,,,,,,,,,,------------------,,,,,,,,,------,,,,,,ӵ,,,+++******++++++,,,---......------,,,,,,---///111000...,,,+++,,,------,,,,,,...///------------------------.........------,,,,,,,,,------------,,,+++******++++++,,,,,,,,,+++******,,,,,,++++++,,,,,,------,,,,,,+++++++++,,,------++++++++++++++++++++++++******))))))))))))************+++++++++***))))))*********)))))))))((((((Ħ((()))***'''''''''Ħ''''''+++***)))((('''&&&&&&&&&(((((((((((((((((((((((((((ӵ((('''''''''((((((((((((((('''((((((((((((((((((((())))))((((((((((((((('''%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$######$$$$$$%%%%%%$$$$$$###########################&&&&&&''''''&&&%%%%%%$$$#########$$$$$$%%%%%%&&&"""$$$&&&''''''&&&$$$"""###$$$$$$$$$$$$$$$$$$###!!!!!!!!!Ħ  !!!"""!!! !!!""""""""""""""" !!!!!!!!!!!!""""""""""""###"""!!! !!!"""###"""######$$$$$$######"""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""""""""######!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!     /////////.........------////////////////////////............//////000111000000111111111000000///111111000000000000000111111111111111111000000000000000///...------------------------------------,,,,,,------,,,4ĉ@ӵ+++++++++,,,,,,---.........------,,,,,,---///000000...++++++---...---,,,,,,---///---------------------------------------------,,,---------------,,,+++***,,,,,,,,,,,,,,,+++***))),,,+++++++++,,,,,,---...,,,+++++++++,,,,,,---...++++++++++++++++++++++++***))))))))))))))))))***(((((()))++++++,,,,,,,,,))))))((((((((('''''''''>L''''''''''''''''''=hĦ''')))))))))((('''&&&&&&%%%((((((((((((((((((((((((4ĉ@ӵ((((((((((((((('''''''''((((((((((((((((((((('''((((((((((((''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$###""""""""""""############""""""########################%%%%%%%%%%%%%%%$$$###"""""""""######$$$%%%&&&&&&###$$$&&&''''''&&&$$$###########################!!!!!!!!!>L!!! !!!"""!!! !!!!!!""""""""""""""" !!!!!!!!!"""""""""###"""!!! !!!"""#########$$$$$$$$$$$$######!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!"""""""""       !!!!!!000////////////.........000000000////////////..................///000000//////000111111111111111000000000000000111111222111222222222222111000000000000///.....................------------......,,,,,,------,,,GG=?,,,---------............------++++++,,,...000000---+++,,,---......,,,,,,---...------------------------,,,,,,------------------,,,------------,,,,,,+++,,,,,,,,,,,,++++++***)))+++******++++++,,,---...++++++++++++,,,---......,,,,,,,,,,,,,,,,,,,,,,,,***))))))(((((())))))***'''((()))+++,,,------...((((((((((((''''''''''''HdĦ%%%$$$$$$$$$'''=Īj''''''((((((((('''&&&&&&((((((((((((((((((((((((GG=?(((((((((((('''''''''(((((((((''''''''''''&&&(((''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$#########""""""""""""!!!!!!""""""""""""!!!!!!######$$$%%%%%%$$$######$$$$$$$$$$$$$$$###""""""""""""###$$$%%%%%%&&&'''%%%%%%&&&&&&&&&&&&%%%%%%######""""""""""""######!!!!!!!!!HdĦ!!! !!!!!!!!!  !!!!!! !!!""""""######"""""" !!!!!!!!!!!!""""""""""""###""""""!!!!!!""""""#########$$$$$$$$$$$$######""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!   !!!!!!     !!!!!! 000000000ӵ000000000ĭӵ///ӵ///Ħ////////////000111333333222ӵӵ,,,,,,ĦƜ`1.׼s+++---///---Ħ------++++++,,,...000000---ӵ,,,Ħ------------------,,,,,,,,,---ĭӵ+++***Ħ------+++Ħ...Ħ,,,,,,,,,,,,))))))(((((((((((())))))------)))'''DdD'''''''''?fӵ%%%&&&'''Ħ)))))))))ӵƜ`1.׼s)))(((ĭӵ'''&&&&&&############$$$$$$$$$%%%ӵ$$$$$$$$$$$$Ħ######""""""######"""&&&%%%$$$###$$$$$$%%%Ħ""""""###$$$%%%&&&%%%Ħ############$$$%%%"""""""""DdD !!!!!! ӵӵ###ӵ!!!!!!!!!""""""Ħ###$$$ӵ"""""""""!!!ĭӵ     !!!!!!!!!      !!!000000?~4///111111g&e>&e000g&e--->hӵ......///000222444444g&e222guO>uO>&e---,,,4ff?>ߝL---gĉ@++++++...000Shӵ---++++++,,,...000///g&e...>hӵ...............+++,,,,,,fff?><z,,,g&e>&e,,,+++HL+++,,,---ShӵgL,,,,,,,,,,,,,,,))))))(((((((((((()))S?ʬ++++++3h?D%%)?''''''ZufĦ$$$%%%&&&gL'''******g&e***gĉ@))))))g&e>&e&&&@e&&&&&&??""""""""""""#########$$$g<ĉ$$$$$$$$$$$$3we<Ħ$$$$$$######3h?@e&&&&&&&&&%%%$$$$$$%%%%%%Z%%%"""######%%%&&&3h?gL&&&$$$$$$$$$$$$&&&&&&#########D%%)?!!!fff?><z!!!!!!=?Ħg&e"""g&e"""""""""S?ʬ"""4ff?>ߝL%%%@e$$$g&e###""""""3h?g&e>&e ??  !!!   !!!!!! !!!""""""      !!!...4Dӵ000//////Hƅ^Hu]Ħ---Hu]Ħ000ZuR)Ħ111000000000111222333Hu]Ħ///HŐeHŐeHu]Ħ///qIܗGIӵ---tt+++,,,,,,HGgĉ@---,,,---...000222222000Hu]Ħ111ZuR)Ħ.........//////......sߝLGdUĦ---Hƅ^Hu]Ħ---ntHdĦ+++***HGgĉ@+++HdĦ,,,,,,---------++++++++++++******Htƅ^((((((Bt=o9ĦDtfo9Ħ(((''''''g?'''&&&HdĦ&&&&&&&&&Hu]Ħ&&&tt&&&)))Hƅ^Hu]Ħ&&&H׼s&&&%%%'''&&&%%%""""""###$$$%%%%%%tQ%%%%%%######je<Ħ%%%$$$$$$Bt=o9ĦH׼s&&&%%%%%%$$$$$$$$$$$$$$$$$$HtĦ$$$###$$$&&&(((Bt=o9ĦHdĦ&&&%%%$$$###$$$%%%%%%#########Dtfo9ĦsߝLGdUĦ Ht@cӵHu]Ħ"""Hu]Ħ""""""Htƅ^"""qIܗGIӵ###H׼s######Hu]Ħ###$$$Bt=o9ĦHƅ^Hu]Ħ!!! !!!  !!!!!!   !!!!!! !!!  !!!!!!   !!!!!!...///4DuXӵ000///000DdDΦDdDĦ...DdDĦ000000t|<222111111000111222333444DdDĦ///DdDΦDdDΦDdDĦ///peƜ4DuTӵ---`eĭ,,,qet,,,,,,,,,---///111222222111DdDĦ111///t|<,,,,,,---------...//////DdDDdDĦ---DdDΦDdDĦ---q<niDdDĦ+++qet++++++DdDĦ,,,------------******))))))(((q<R)))(((qjRgdKӵHdDĦgdKӵ&&&&&&GR/f6LĭĦ&&&%%%DdDĦ&&&&&&'''DdDĦ&&&`eĭ(((DdDΦDdDĦ&&&DdDĦ'''&&&%%%$$$%%%&&&''''''%%%$$$$$$$$$%%%%%%&&&geĦ'''&&&%%%FSĦ%%%%%%qjRgdKӵDdDĦ&&&%%%%%%$$$$$$$$$$$$$$$$$$DdDĦ$$$###$$$&&&qjRgdKӵDdDĦ&&&%%%$$$$$$$$$%%%%%%#########HdDĦgdKӵDdDDdDĦ DdDĦ4DufӵDdDĦ"""DdDĦ"""q<R""""""peƜ4DuTӵ###DdDĦ######DdDĦ###qjRgdKӵDdDΦDdDĦ!!!!!! !!!    !!!  !!!!!!  ...///4DuXӵ000///000DdDΦDdDӵ...DdDĦ000000o)h111111111111111222333555666DdDĦ///DdDΦDdDΦDdDӵ...=ӊB1.uTӵ...HߝL`o9---po9wӵ,,,...///111222222111DdDĦ000000o)h,,,---------.........//////DdDΦDdDĦ---DdDΦDdDӵ---GIpӵDdDĦ***po9wӵDdDĦ,,,,,,---------***)))'''&&&&&&po9u))))))((((((GIdnuR)ĦDdDĦnuR)Ħ$$$$$$CdgĪj$$$DdDĦ'''''''''DdDĦ'''HߝL`o9'''DdDΦDdDӵ'''DdDĦ((('''&&&%%%&&&((((((((('''&&&&&&&&&&&&&&&&&&geĦ((('''sp?aĦ&&&&&&GIdnuR)ĦDdDĦ%%%%%%%%%%%%$$$$$$$$$$$$$$$DdDĦ%%%$$$%%%&&&GIdnuR)ĦDdDĦ&&&%%%$$$$$$$$$%%%%%%#########DdDĦnuR)ĦDdDΦDdDĦ!!!DdDĦnuR)ĦDdDĦ"""DdDĦ###po9u"""###""""""=ӊB1.uTӵ###DdDĦ######DdDĦ###GIdnuR)ĦDdDΦDdDӵ !!!       !!!!!!   ...0004DuXӵ000000000DdDʜ4DuTӵ///>d<Ħ000Dt///111111222333555666666>d<Ħ///>d<ʜDd<ʜ4DuTӵ...---F&uTӵ---4DufئL>e...puR)Ħ---...///111222222111>d<Ħ///Dt---.........//////......DdDΦDdDĦ,,,>d<ʜ4DuTӵ+++4DwDd<Ħ)))puR)Ħ>d<++++++,,,,,,***)))'''&&&&&&peӵ)))ĦpeӵDx<>d<ӵDd<$$$qR/ܗ?fӵ$$$>d<'''(((>d<Ħ'''4DufئL>e'''DdDʜ4DuTӵ(((DdDĦ)))((('''&&&'''((())))))'''&&&&&&&&&&&&%%%%%%geĦ'''s<v>aĦ''''''peӵDx<DdDĦ%%%%%%%%%%%%%%%%%%$$$$$$$$$DdDĦ%%%$$$%%%&&&peӵDx<>d<%%%%%%%%%$$$$$$$$$#########>d<ӵDd<DdDΦDdDĦ!!!DdDӵnd<DdDĦ""">d<Ħ###peӵ"""Ħ"""F&uTӵ###DdDĦ######>d<Ħ###peӵDx<>d<ʜ4DuTӵ !!!!!!     !!! !!!   ///0004DuXӵ111000000D&dq&ĒR000111sdKĦ000DHRRud000111333444555666666sdKĦ///D&oq<Ōq&ĒR///...--->dp&ĒR,,,---nfʜd<Φ>d<Ħ***s&dq&ĒR))))))i?ʜtd<Ħ(((HHܗDӊB'''<x*********))))))((((((B?d<'''&&&''')))***)))(((%%%%%%%%%$$$$$$$$$geĦ'''Hg8>aĦ''''''B?Ho9&&&>d<%%%%%%%%%%%%$$$$$$%%%>d<ӵ%%%&&&B?Ho9'''<x%%%%%%$$$$$$#########&ӫeʬtIӇ >d<Φ>d<Ħ!!!D&ӫetIӇ!!!DdDĦ###sdKĦ###B?dp&ĒR######>d<sdKĦ###B?Ho9"""s&dq&ĒR !!!!!!!!!    !!!!!! !!! !!!  !!!!!!  ///0004DuXӵ111000111Hu]3hh111222222ne000000=e///000222333444444444444ne111000pIƎ@t@h///......>h,,,,,,---fe...@ďD......///.........//////...ne+++,,,=e((()))))))))******++++++ege******sĪj@h(((((()))fdDĦ(((@ďD''''''Hkge******************++++++@h))))))@G((()))HĪj@IŌ)))(((Bene'''Hkge)))ne))))))fe(((Hu]3hh))))))(((se((('''&&&''')))))))))'''$$$$$$$$$$$$$$$$$$geĦja>aĦ&&&'''@G''''''se%%%%%%%%%&&&&&&$$$$$$%%%<Ō%%%%%%%%%@G&&&&&&Hkge&&&&&&%%%$$$############HĪj@IŌ ege""""""Hu]3hIŌ!!!"""DdDĦ###ne"""$$$@h"""""">h$$$######se###ne######@G!!!!!!sĪj@h !!!!!!!!!    !!!!!!!!!  !!!!!!  !!!"""///4DuXӵ111ĵD^222333333333///000000333///000222333333333222222222111000.........---------,,,,,,,,,------,,,,,,---------------------------***)))***)))))))))************+++++++++++++++)))))))))***+++DdDĦ+++***(((((((((++++++++++++((()))+++,,,---,,,***+++++++++)))))))))((())))))((())))))*********)))+++***D^((()))((((((s׼s)))'''&&&%%%&&&((()))((('''###$$$$$$$$$%%%&&&geFm8%%%>aĦ&&&&&&&&&&&&&&&'''s׼s$$$%%%%%%&&&&&&&&&$$$$$$%%%Ho(((&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$############ !!!""""""D^!!!""""""DdDĦ######"""$$$###$$$"""""""""$$$$$$######s׼s###############!!!###!!!!!! !!!!!!!!!   !!! !!!!!!!!!!!!  !!!!!!   Φ4DuXӵtvӵ>d<Ħ222333444444444333111Ħ000000000111222444444///000222222333222111000111111Ħ000...---//////......---------,,,......---------......///---------,,,,,,+++++++++((()))+++,,,---,,,,,,+++))))))*********+++++++++,,,,,,,,,,,,,,,,,,,,,,,,Ħ((()))***++++++++++++,,,,,,,,,---------,,,,,,,,,------.........------------------------******+++,,,---......///>d<Ħ---,,,,,,************************++++++,,,,,,,,,---------&&&(((+++------,,,***)))++++++++++++++++++,,,,,,******++++++++++++******((((((''''''''''''((((((************))))))))))))((()))+++,,,+++***((('''******++++++Ħ***((())))))******+++,,,,,,+++>d<Ħ(((((((((((('''Be(((((('''&&&%%%&&&(((((((((&&&$$$$$$%%%%%%&&&'''geFYĉ'''&&&>aĦ%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&Be$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%nu]ӵ(((%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''&&&%%%$$$###############"""""""""""" !!!"""""">d<Ħ!!!!!!!!!"""""">d<Ħ$$$$$$$$$Ħ$$$$$$############$$$$$$"""""""""""""""######$$$$$$$$$######Be$$$############Ħ### !!!!!!!!!""""""######!!!!!!!!!"""!!!  !!!!!!!!!!!!   !!!!!! !!!!!!!!!"""!!!  !!!!!!   ?aŖ%7uSQuR)ӵsdKĦ333222222111000///gdKĦ///000111222333444444666555333111////////////000gdKĦ000...---------,,,,,,,,,+++++++++,,,+++***)))))))))++++++)))***++++++))))))***+++,,,+++)))))))))+++---...)))***,,,......---,,,+++---------///000000---gdKĦ******+++,,,---------,,,+++,,,---...///...---,,,+++,,,...000111333111000...------------......------------......gdDĦ++++++++++++***((('''''')))+++,,,,,,,,,,,,,,,,,,,,,,,,,,,((()))***+++,,,---------*********))))))))))))(((,,,,,,,,,++++++*********(((((('''''''''(((((()))((((((((((((((()))******************************(((((((((gdKĦ(((+++++++++++++++++++++++++++sdKĦ(((''')))(((((('''''''''%%%&&&'''(((((('''&&&%%%"""$$$&&&'''&&&&&&ŶS&&&&&&&&&3we<%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%&&&&&&&&&''''''''''''((('''&&&&&&iĉ@3hR/Ō%%%&&&&&&&&&''''''$$$%%%''''''''''''%%%$$$###$$$$$$%%%%%%$$$$$$###""""""""""""!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!"""DdDĦ!!!  sdKĦ###$$$gdKĦ""""""""""""############"""###$$$%%%%%%$$$###""""""#########$$$$$$%%%%%%%%%gdKĦ###$$$$$$############$$$$$$!!!!!!!!!!!!  !!!"""!!! !!!   !!!######""""""!!!!!!!!!  !!!!!!  !!!!!! >A000ne222222222222111111ne000000000000111111111111222222111000000000111222ne000///---,,,,,,,,,,,,,,,,,,+++******+++++++++******+++,,,,,,---...///...---,,,---///...---,,,++++++,,,...///+++,,,---...///...------.........000111111ne*********+++,,,---...---,,,,,,,,,---/////////...---,,,,,,---///000111000///...------............------------...De------,,,,,,+++***(((''''''((()))***,,,,,,,,,,,,,,,,,,,,,,,,(((((()))***+++,,,,,,+++++++++*********))))))))),,,,,,,,,++++++*********((((((''''''''''''(((((('''''''''''''''(((((()))************************))))))ne))))))+++++++++++++++++++++++++++ne(((((('''))))))((((((((('''''''''&&&&&&'''(((((('''&&&&&&###%%%&&&'''&&&&&&>A&&&&&&&&&k<%%%%%%%%%$$$$$$'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''((('''&&&&&&fh%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$###"""""""""!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!"""De"""!!! ne"""###ne###""""""""""""############"""###$$$$$$$$$$$$###""""""############$$$$$$$$$$$$###ne""""""#########""""""#########!!!!!!!!!!!!     !!!!!!   ...///111000000//////000111---000000000//////...............//////000222333444......---,,,,,,++++++,,,---,,,+++***)))***+++,,,---------------...000111000///...///000000///...---------...///---------.........///////////////111222222++++++++++++,,,------......------......///000000///---,,,,,,---...///000///............//////......------------............---------+++***((('''''''''((((((,,,,,,,,,,,,,,,,,,,,,,,,'''((()))***+++++++++***,,,+++++++++************+++++++++++++++*********((((((''''''''''''((((((&&&&&&&&&&&&&&&'''((((((***************************************+++++++++++++++++++++++++++)))((((((''')))))))))(((((((((''''''&&&&&&'''(((((('''&&&&&&$$$%%%'''&&&%%%$$$&&&&&&&&&&&&&&&%%%%%%%%%%%%(((''''''&&&&&&''''''(((&&&&&&&&&''''''''''''((('''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######"""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""""""""!!!!!! !!! !!!"""""""""""""""""""""############"""###$$$$$$$$$$$$###""""""############$$$$$$$$$""""""!!! """"""""""""""""""""""""!!!!!!!!!!!!    !!! !!!  !!!  000000000//////...............///000000000000///,,,---///000000...---+++........................---......///000222333333111000///...---------...,,,---...///...---+++******,,,---/////////......,,,...///...---,,,---...111000///...------......---------,,,---...//////......///000222111///,,,++++++++++++,,,,,,------............//////000000000///...---------------............//////000000......------------..................------------,,,,,,***)))((((((((((((++++++++++++++++++++++++))))))***+++++++++++++++,,,,,,,,,+++++++++******+++++++++***************)))((((((''''''''''''(((''''''&&&&&&''''''((()))******************************************************************************))))))(((((((((((()))))))))(((((((((((('''&&&''''''''''''''''''&&&%%%&&&'''&&&$$$$$$%%%&&&%%%%%%%%%&&&'''((()))***&&&&&&&&&&&&&&&&&&%%%%%%''''''&&&&&&&&&&&&''''''&&&&&&&&&''''''''''''((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&'''''''''&&&$$$$$$$$$$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$#########"""""""""!!!!!!!!!!!!!!!""""""!!!!!!!!!!!!!!!!!!!!!"""""""""""""""!!!!!!!!!!!!!!!!!!""" !!!"""""""""""""""!!!"""""""""#####################$$$$$$#########""""""#########$$$$$$$$$!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!   !!!"""""""""""""""!!!!!!!!!"""!!!!!!"""  ---------....../////////......///000000000000000---...000111111000...------------...///000000111//////000000111111111222333222111000////////////...///000000000///...---,,,---...///000//////...+++,,,------,,,+++,,,---//////...------,,,,,,,,,,,,,,,++++++,,,,,,---...------...///111000---+++++++++,,,,,,------------........./////////////////////......------------------...//////000000000......------------......---------,,,,,,,,,,,,+++...---,,,+++******))))))++++++++++++++++++++++++++++++,,,,,,---,,,,,,,,,,,,,,,,,,+++++++++******************************))))))((('''''''''''''''((((((''''''(((((()))***))))))))))))))))))))))))************************************************)))))))))(((((((((((((((***)))))))))(((((((((((('''''''''&&&&&&'''''''''%%%&&&&&&%%%######%%%&&&%%%%%%%%%&&&'''((()))***&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''((('''&&&%%%%%%&&&'''(((%%%$$$$$$######$$$$$$%%%############""""""""""""!!!!!!"""######"""!!!!!!!!!!!!!!!!!!""""""""""""!!!""""""""""""""""""!!! !!!"""""""""""""""!!!"""""""""############$$$##################$$$""""""#########$$$$$$$$$"""""""""""""""""""""""" !!!""""""""""""!!! !!!!!!!!!"""!!!!!!     !!!!!!!!!!!!""""""""""""""""""!!!!!!"""  +++,,,---...///000000111///000111111222222111111111111333444444333333222---......///111222222333000111222222222222111111444333333222222111111000111111111000000000000000....../////////.........,,,---......---,,,---...---------,,,,,,,,,,,,,,,+++++++++,,,,,,,,,---------------///000000---+++++++++,,,---------------------...////////////..................---------------...///000000//////......------------......------,,,,,,,,,+++++++++...---------,,,,,,++++++++++++++++++++++++++++++,,,,,,---------------,,,,,,+++++++++************)))))))))******************)))(((''''''&&&''''''((((((((((((((()))******))))))))))))))))))))))))************************************************((((((((((((((((((((((((******)))))))))(((((((((((('''&&&&&&&&&&&&'''(((%%%%%%%%%$$$"""###%%%'''&&&&&&&&&&&&&&&'''((()))&&&&&&&&&&&&''''''''''''%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''((((((''''''''''''((((((&&&%%%$$$######$$$%%%&&&$$$$$$#########"""""""""!!!!!!############!!!!!!!!!!!!!!!!!!""""""""""""!!!""""""######""""""!!! !!!""""""######""""""""""""""""""############$$$$$$###""""""###$$$$$$"""############$$$$$$$$$""""""############$$$$$$!!!!!!############!!!!!!!!!!!!!!!""""""!!!!!!   !!!!!!    !!! !!!  !!!  .../////////000000111111111222333333444444333333222222222333333333444444111111111222222333333333000111222333444333333222333333444444333222000///333222000///...///000111000000///...------------,,,.........---,,,---...+++,,,,,,------------,,,++++++---.........---,,,------...000111000...++++++,,,---.........---,,,+++,,,---...///......---------..................---...///000000//////.........------------.........---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++************************,,,,,,,,,------,,,,,,+++++++++*********)))))))))((()))))))))*********+++***)))(((''''''&&&&&&&&&(((''''''''''''((())))))))))))))))))))))))))))))))))))))))))))))))))))))************************((((((((((((((((((((((((*********)))))))))((((((((('''&&&&&&&&&&&&'''((($$$$$$$$$###"""###&&&)))''''''&&&&&&&&&''''''(((&&&&&&&&&&&&'''''''''(((&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''&&&''''''''''''''''''&&&&&&%%%###""""""###%%%&&&$$$$$$$$$#########"""""" !!!###$$$$$$###!!! !!!!!!!!!!!!""""""""""""!!!"""############"""!!!!!!"""######$$$$$$######""""""""""""############$$$$$$###""""""###$$$$$$"""############$$$$$$$$$"""""""""######$$$$$$$$$!!!"""$$$%%%%%%$$$"""!!!!!!!!!""""""""""""!!!!!!  !!!""" !!!   !!! !!! 222222222111111111111111333333444555555555555444000000//////000111222222444444444333333333333222///111222444555555555444222333444555444222000...333111///---,,,...000111222000...---,,,,,,,,,---+++,,,---,,,++++++,,,---++++++,,,---.........---+++,,,...000000///...---///...///111222222///---+++,,,---.........---,,,++++++---.........---,,,,,,,,,---.../////////...---...///000000///...---.........------.........//////.........---------******+++,,,,,,,,,++++++************************++++++,,,,,,,,,++++++************))))))))))))((((((((())))))*********+++******)))''''''&&&&&&&&&'''&&&&&&&&&&&&'''(((((())))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))'''''''''(((((((((((((((************))))))))))))((('''&&&%%%%%%&&&'''(((#########""""""###''')))(((''''''&&&&&&&&&''''''&&&&&&&&&'''''''''(((((('''''''''&&&&&&'''''''''&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''$$$%%%''''''''''''%%%$$$&&&%%%###""""""###%%%&&&$$$$$$$$$############""" """###$$$$$$###""" !!!!!!!!!!!!""""""""""""!!!"""###$$$$$$###"""!!!""""""###$$$$$$$$$$$$$$$""""""""""""############%%%$$$###""""""###$$$%%%"""############$$$$$$$$$!!!!!!""""""######$$$$$$!!!###$$$%%%%%%$$$###!!!!!!!!!"""""""""""""""!!!!!! !!!""""""   !!!!!! !!!!!!!!!""""""###### !!!!!! 444333222000000000111111333222111000000111222333222222333444444444333333333333333333333333333333222222222222222222222222222333333444333222111000000000//////......------000////////////.........***+++---.........------,,,,,,,,,,,,,,,,,,,,,,,,------..................////////////////////////------,,,+++,,,---...///------------------------.........///////////////////////////////////////000000///...------,,,,,,......---,,,,,,,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++++++++++++++,,,,,,------,,,,,,+++***************)))((('''))))))(((((((((((())))))***)))(((&&&&&&&&&'''(((&&&&&&%%%&&&)))******)))******))))))((((((''''''***)))(((&&&&&&&&&'''((((((***++++++******+++,,,''''''((((((((((((''''''))))))))))))((((((((((((&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&'''((((((((((((((((((''''''&&&&&&&&&'''''''''((((((%%%%%%%%%&&&'''((())))))(((''''''''''''&&&&&&&&&'''''''''&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""""""""""""""""""""###$$$$$$$$$%%%"""""""""""""""!!! """"""############""""""######$$$$$$$$$$$$############$$$$$$$$$$$$######""""""""""""""""""""""""""""""""""""""""""""""""########################""""""""""""""""""""""""    !!!!!!"""""" 444333222111111111222333333222111000000111222333222222333333333333444444222222222222222222222222333333333333333333222222222333333333333222111000111111111000000000///////////////............---+++,,,---.........------,,,,,,,,,,,,,,,,,,,,,,,,...........................//////////////////...------,,,,,,,,,---...///------------------------////////////....................................000//////...------,,,,,,......---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++++++++++++++,,,,,,------,,,,,,++++++++++++++++++***))))))))))))(((((((((((())))))***)))((('''''''''(((((('''&&&&&&''')))***)))(((***)))))))))((((((((('''))))))((('''''''''''''''((()))+++***))))))***,,,(((((())))))))))))(((((())))))))))))(((((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&&&&'''''''''((((((%%%&&&&&&''''''((((((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############""""""""""""###############$$$$$$$$$"""############"""!!! """"""############""""""######$$$$$$$$$$$$############$$$$$$$$$$$$######""""""""""""""""""""""""""""""""""""""""""""""""########################!!!!!!!!!!!!!!!!!!!!!!!!   !!!!!!!!!""" 222222222111222222333444222222111111111111222222333333222222222333444555111111111111111111111111333333333333333333444444222222333333333222111111333222222222222111111111///............---------,,,,,,---............---,,,,,,,,,,,,,,,,,,------..............................////////////.........------------...//////------------------------000/////////...---------........................//////......---,,,,,,,,,------------,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,++++++++++++++++++++++++******))))))(((((((((((())))))******)))((((((((()))))))))((('''''')))))))))'''))))))))))))(((((((((((((((((())))))(((((('''''''''(((***)))(((((()))+++))))))************)))))))))))))))((((((((('''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&'''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&'''''''''(((((((((''''''''''''''''''''''''(((''''''''''''&&&&&&&&&%%%&&&&&&'''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$#####################$$$$$$$$$###""""""""""""############""""""######$$$$$$$$$$$$############$$$$$$$$$$$$######""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!   !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!! 000111111111222222333333222222222222222222222222444333111111111333555777222222222222222222222222333333444444444444555555222222222222222222222222222222222222222222222222............------------------..................,,,,,,,,,---------------...............---------......///000000///...................../////////.................................................................................------,,,,,,,,,------------,,,,,,++++++************************++++++++++++++++++++++++++++++,,,,,,,,,,,,+++++++++*********************))))))(((((((((((())))))*********))))))))))))******((('''((())))))((('''))))))))))))(((((((((((('''((()))******)))((('''&&&((())))))(((((()))***((())))))******))))))((())))))((((((((('''''''''((((((((((((((('''''''''''''''''''''((((((((((((&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''((((((((((((((((((((((((''''''''''''(((''''''''''''&&&&&&&&&'''''''''((((((((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###############$$$$$$%%%$$$$$$$$$###"""""""""$$$$$$$$$%%%%%%$$$$$$###"""######$$$$$$######"""######$$$$$$$$$$$$############$$$$$$$$$$$$######""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!   !!!!!!!!!!!!"""""""""""" !!!!!!!!!!!!!!! //////000111111222222222222222222333333222222222333222111000111333666777444444444444444444444444333333333444444555555555222222222222222222222333111111111111111111111111//////.........---------........................,,,,,,,,,------.........//////.........------------...///000000///...---....../////////000000000........................+++,,,,,,---...///000000........................---------------,,,,,,,,,,,,,,,---------,,,+++***************************++++++++++++++++++++++++***++++++,,,,,,++++++***))))))(((((((((((()))***))))))(((((((((((()))))))))))))))************)))***)))(((((()))***((('''(((((((((((())))))))))))'''((()))******)))((('''&&&((())))))(((((()))***'''(((((())))))(((((('''((((((((((((''''''''''''(((((((((((((((((((((((('''''''''((((((((())))))&&&''''''((((((''''''&&&%%%%%%%%%&&&&&&&&&'''''''''''''''((((((((())))))((((((((((((((((((''''''(((''''''''''''&&&&&&&&&))))))((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$$$$%%%%%%$$$$$$$$$###"""""""""###$$$%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$############$$$$$$$$$$$$############$$$$$$$$$$$$######""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!   !!!!!!!!!""""""######!!!!!!!!!!!!!!!    000000111222222222111111222222333333333333222222222111111111222444666777555555555555555555555555222222333333444444555555222222111111222222333444/////////000000000000000000////////////.........000///......---.........,,,,,,,,,---......///////////////...------,,,,,,---...///111111///...---...//////000111000000000........................++++++,,,---...//////000------------------------------,,,,,,,,,,,,,,,,,,+++,,,---------,,,***)))++++++++++++++++++++++++++++++++++++++++++++++++******++++++++++++******)))((('''&&&'''((()))***))))))(((((((((((())))))'''((()))*********))))))***(((((((((******)))((((((((((((((())))))))))))(((((())))))******))))))'''(((***)))(((((()))+++''''''((((((((((((''''''((((((((('''''''''&&&&&&'''''''''(((((((((((((((''''''''''''((((((((()))&&&'''((())))))((('''&&&%%%%%%%%%&&&''''''((((((''''''((((((((()))))))))(((((((((((((((((((((((((((''''''''''''&&&&&&&&&))))))(((((('''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$%%%%%%%%%$$$$$$$$$#####################$$$%%%%%%%%%$$$$$$######$$$$$$$$$$$$############$$$$$$$$$$$$############$$$$$$$$$$$$######""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!    !!!!!!""""""###!!!!!!!!!!!!!!!    222333444444444333222111222222333444444333222222000111111222444555555666444444444444444444444444111111222222333444444444222222111111111222333444/////////000000000111111111111000000000/////////111000///...------...///,,,,,,------.../////////000//////...------,,,,,,,,,...000111111000...,,,...///000111111111000000........................------------------------------------------------,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,------,,,***))),,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++******++++++++++++******)))((('''&&&'''(((***+++))))))(((((((((((())))))&&&'''((()))))))))(((((()))((('''(((***++++++***'''((((((((()))))))))***))))))(((((()))******+++((()))+++***))))))***,,,(((((())))))))))))(((((((((((('''''''''&&&&&&&&&&&&&&&'''''''''(((((((((&&&&&&'''''''''(((((((((&&&'''((())))))((('''&&&%%%&&&&&&'''(((((())))))'''((((((((())))))))))))''''''(((((())))))******(((''''''''''''&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$%%%&&&&&&###############$$$$$$$$$""""""###$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$$$$############$$$$$$$$$$$$######""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!    !!!!!!"""""""""!!!!!!!!!  !!!555555666777666555333222222222444444444444222222///000222333444555555555333333333333333333333333000000111222222333444444222222111111111222444555//////000000111111111222111111111111000000000000111000///...------...///,,,,,,------...///000000000000///...------,,,,,,,,,...000111111000...,,,...///000222222111111000////////////////////////000//////...,,,+++******------------------------,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,------+++***(((,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++******++++++++++++*********)))((('''((()))+++---))))))(((((((((((())))))%%%&&&''')))))))))((('''(((''''''(((+++,,,,,,+++'''((((((((())))))*********)))((((((((()))+++,,,(((***++++++******+++,,,))))))************))))))(((((('''''''''&&&&&&&&&%%%&&&&&&&&&''''''((((((&&&&&&&&&&&&'''''''''(((&&&'''(((******((('''&&&&&&&&&''''''((()))******(((((((((((())))))))))))&&&''''''((()))******+++(((((('''''''''&&&&&&&&&$$$$$$%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&""""""######$$$$$$$$$%%%!!!"""###$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$$$$############$$$$$$$$$$$$######"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" !!!  !!!   !!!!!!"""""""""!!!!!!   !!!!!!555555555555555555555555222222333222111111222444333444444555555444444333333333333333333333333333555444222111111222444555444444333333333333222222222111111000000000000000111000000///...---------,,,,,,,,,---------......,,,,,,+++***+++---000111---......///////////////////////////000000000000......///000111222222333000...---...000111111111222111000///...---,,,,,,------............------------------------------,,,,,,,,,++++++*********))))))************))))))***+++,,,,,,,,,***((('''******++++++++++++******...---+++))))))((())))))(((((())))))))))))(((((('''''''''''''''((())))))(((((()))************)))'''((()))******)))((('''(((((())))))*********+++++++++++++++++++++++++++************)))))))))))))))(((((('''&&&%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((''''''''''''((())))))''''''&&&%%%&&&'''((()))''''''((()))))))))))))))(((''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%(((&&&$$$###$$$%%%%%%%%%############""""""""""""######$$$$$$$$$%%%%%%%%%$$$%%%&&&&&&%%%$$$"""!!!$$$$$$%%%%%%%%%%%%&&&&&&########################""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!""""""""""""""""""!!! !!!!!!!!!   !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""" """###!!! !!!!!!""""""  444444444444444444444444222333333222111000222333222333333444444444333333333333333333333333333333444333111000000111333444333333222222222111111111222111111000000000000000111000000///......------,,,,,,,,,---------.........---,,,++++++---...///---......///////////////......//////000000111111/////////000111111111222000///---...///000000///111111000///...---,,,,,,------............------,,,,,,,,,,,,,,,,,,,,,,,,+++++++++*********))))))))))))************))))))++++++************************++++++++++++******---,,,***)))(((((())))))(((((())))))))))))(((((('''''''''''''''((())))))((())))))***+++*********((()))************)))((())))))))))))*********+++++++++++++++++++++++++++************))))))))))))))))))(((((('''&&&&&&%%%''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((('''''''''((()))***'''((())))))******))))))))))))((((((((('''''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%(((%%%######$$$%%%%%%$$$!!!!!!""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$%%%%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&########################""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!"""""""""###"""!!!!!! !!!!!!   !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""  """###!!! !!!!!!!!!!!!!!!  333333333333333333333333333444444222111000111333111111222222333333333333444444444333333222222222333222111000000111222333222222222111111111000000222111111000000000000000111000000//////......---,,,,,,,,,---------......000///---,,,,,,,,,---...---......///////////////---......///000111111222000000000000000000000000111///------/////////...111111000///...------,,,------............------++++++++++++++++++++++++************))))))))))))))))))************)))))),,,+++)))((((((***,,,---******++++++++++++******+++***)))(((((((((((((((((())))))******))))))((('''''''''''''''((())))))))))))***++++++++++++***)))******++++++******))))))))))))***************++++++++++++++++++++++++************))))))))))))******))))))((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&((()))))))))(((''')))(((((((((((()))******(((((()))******************)))))))))((((((((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%###"""###$$$$$$### !!!"""###$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!"""""""""######"""!!!  !!!!!!!!!   !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""!!! """"""!!! !!!!!!!!!!!!!!! 222222222222222222222222333444444222000000111222000000000111111222333333555444444333333222222111333333222111111222333333222222222222111111111111222111111000000000000000000000000000//////......,,,,,,,,,---------......///...------------......---......///////////////------...///000111222222000000000000000/////////111000...---...///...---111000000///......------,,,------......------,,,++++++++++++++++++++++++++++++******************)))******++++++******)))******)))))))))***,,,---******++++++++++++******)))))))))((((((((((((((()))))))))******)))))))))'''''''''''''''((()))))))))******+++++++++++++++++++++++++++++++++++++++************************++++++++++++++++++++++++************)))))))))(((************))))))((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&(((******)))'''&&&((((((((((((((()))))))))((())))))***************)))))))))(((((((((''''''%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&%%%%%%$$$$$$###%%%$$$""""""###$$$###"""!!!!!!"""######$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$###%%%$$$######$$$%%%'''((($$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""""""""#########"""!!!  !!!!!!!!!!!! !!!!!!!!!!!!  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""!!!!!!!!!""""""!!!!!!""""""!!!!!! 222222222222222222222222333444444222111000111333111000000000000111222333444444444333333222222222444444444333333444444444444333333333333222222222222111111000000000000000000000000000000/////////,,,,,,,,,---------......,,,,,,------...///000000---......///////////////---......///000111111111000000000///////////////222000.........///...---000000//////......------,,,,,,------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,******++++++++++++******((()))***+++,,,,,,+++*********++++++++++++******((((((((()))))))))))))))))))))************))))))'''''''''''''''((())))))))))))***++++++++++++***,,,,,,++++++++++++,,,,,,+++++++++***************++++++++++++++++++++++++************)))))))))(((***************)))))))))((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&(((******)))'''&&&&&&&&&'''''''''((((((((((((((()))***************((((((((('''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$######$$$$$$###!!!$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###$$$%%%'''((($$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""############""""""!!! !!!""""""!!!!!!!!! !!!"""!!!!!!  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""""""""!!!!!!""""""""""""!!!!!! 222222222222222222222222222333333222111111222444333222111000000111222333333333333333333333333333444444555555555555444444444444444333333333222222222111111000000000000000000000000000000000000000,,,,,,,,,---------......+++,,,---...///000111111---......///////////////////////////000000000000////////////////////////222000......000000000///000000//////............,,,,,,------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------------******++++++++++++******''')))+++,,,---,,,***)))******++++++++++++******'''((())))))************)))******++++++******)))'''''''''''''''((())))))(((((()))************))),,,++++++******++++++,,,+++++++++++++++*********++++++++++++++++++++++++************))))))))))))*********)))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&((()))))))))((('''%%%&&&&&&'''((('''''''''''''''((()))))))))))))))''''''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$%%%%%%###!!!%%%%%%$$$$$$$$$###############$$$$$$$$$%%%%%%%%%&&&%%%%%%%%%%%%&&&&&&'''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%########################"""""""""""""""""""""""""""""""""#########$$$$$$$$$###""""""!!!!!!"""""""""""""""!!!!!!!!! !!!!!!!!!!!!!!!  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""######!!!!!!"""###!!!!!!!!!!!!!!!  333333333333333333333333000111222222111222333555555444222000000000111222111222222333333444444555333444444444444444444333333333333333222222222111222111111000000000000000000000000000000000000000,,,,,,,,,---------......------...///////////////---......///////////////000000000000////////////---.........///000000000222000//////111222222111////////////............+++,,,,,,------,,,,,,++++++++++++++++++++++++++++++++++++,,,,,,---------***++++++,,,,,,++++++******++++++++++++******)))******++++++++++++******'''((()))+++++++++++++++)))******++++++******)))'''''''''''''''((())))))''''''((())))))))))))(((,,,+++***))))))***+++,,,,,,,,,,,,++++++*********++++++++++++++++++++++++************))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''((((((((((((%%%&&&'''((()))(((((('''&&&&&&'''(((((((((((((((((((((((((((''''''''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$%%%%%%&&&&&&'''%%%%%%$$$%%%&&&&&&$$$!!!###$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%########################""""""""""""""""""""""""""""""#########$$$$$$$$$%%%$$$$$$###############""""""""""""!!!!!!!!! !!!!!!!!!!!!  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!###$$$###!!! """$$$ !!!!!!!!!!!!!!! !!! 333333333333333333333333///000222222111222444666777555333111000000111222000111222333444444555666222333333444444333333222222222222111111111111000222111111000000000000000000000000000000111111111,,,,,,,,,---------....../////////000//////...------......///////////////111111000000//////......,,,------...///000111111222000///000222333333222///////////////.........+++,,,,,,------,,,,,,+++))))))))))))))))))))))))*********++++++,,,,,,,,,***++++++,,,,,,++++++***...,,,***)))((()))***+++******++++++++++++******'''(((***+++,,,,,,,,,+++******++++++++++++******'''''''''''''''((())))))&&&''''''(((((((((((((((,,,+++***))))))***+++,,,,,,,,,,,,++++++*********++++++++++++++++++++++++************))))))))))))((((((((((((((()))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((((((''''''''''''((())))))&&&''')))*********)))(((%%%&&&&&&'''''''''''''''))))))))))))((((((((((((%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&"""###$$$%%%&&&&&&'''(((&&&%%%%%%&&&'''&&&$$$"""""""""###$$$%%%&&&&&&'''!!!!!!"""###%%%&&&'''(((&&&&&&'''((('''&&&$$$###$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%########################"""""""""""""""""""""""""""############$$$$$$$$$&&&%%%$$$$$$######$$$$$$""""""""""""!!!!!!!!!!!! !!!!!!!!!!!!!!!  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!###%%%$$$!!! """$$$ !!!!!!"""""" !!! 444444333333333222222222111333444444333222222333222222111111111111222222555444444333333444444555444444444444444444444444444555444222000///000111333333222111000///......---...///000000000000000000///...------------------.........//////000000---------.........//////...///000111111000///...000000000000////////////111///...,,,,,,...///111///////////////////////////...---,,,,,,,,,,,,,,,---,,,,,,++++++************************)))(((((((((((((((((()))***+++,,,,,,---,,,,,,+++***)))((())))))************))))))(((((()))***************((()))***+++++++++++++++(((((((((((((((((((((((((((((((((((())))))))))))++++++,,,,,,,,,,,,------+++++++++*********))))))******))))))))))))******+++*********))))))((((((((((((((((((((((((((((((************)))(((&&&&&&&&&'''''''''(((((())))))))))))(((((('''''''''&&&((((((((((((((('''''''''((((((((((((''''''''''''%%%%%%'''((())))))))))))))))))))))))((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$######$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$############$$$$$$##############################$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$###""""""######""""""!!!!!!   !!!"""""""""!!!!!!!!!!!!!!!!!!!!!!!!######""""""!!!!!! """"""""""""!!!!!!!!!!!! """!!!  444444444444333333333333111333444444333222222333333333222222222222333333333333222222222222333333444444444444444444444444666777666555222111222333222222111111000/////////---...//////000000000///000///...------------.............../////////000.........//////000000000///000111333333111000///000000000000/////////...111000///......///000111..............................---,,,,,,,,,,,,,,,------,,,++++++***))))))+++++++++++++++***))))))((((((((())))))***+++,,,***++++++,,,,,,+++++++++))))))************))))))((())))))***************))))))***+++++++++******))))))))))))))))))))))))(((((((((((())))))))))))*********+++++++++,,,,,,+++++++++*********))))))******))))))))))))******++++++++++++******))))))((((((((((((((((((((((((************)))((('''&&&''''''''''''((((((((())))))(((((((((''''''''''''((((((((((((((((((((('''((((((((((((''''''''''''&&&'''(((((())))))))))))))))))))))))((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$############$$$$$$####################################$$$$$$%%%%%%&&&&&&%%%$$$$$$###""""""###"""""""""!!!!!!!!! !!!!!!!!!   !!!"""""""""!!!!!!!!!!!!!!!!!!!!!!!!###"""""""""!!!!!!!!! """""""""!!!!!!!!! !!!!!!  !!!!!!!!!555555555444444444444333111333444444333222222333444444333333333333444444111111000000000000111111444444444444333333333333555666666555222111111222000000000000000000000000......////////////////////////......------..................//////////////////000000000000111111///111222333333222111///000000000/////////......000000000000000000000000...........................------,,,,,,,,,,,,,,,...---,,,+++***)))((((((+++,,,,,,,,,,,,+++******((((((((()))******++++++((()))***+++,,,,,,,,,,,,))))))************))))))((()))******++++++************+++++++++******)))************************(((((((((((()))))))))))))))))))))************++++++++++++*********************))))))))))))******,,,,,,++++++++++++******)))))))))))))))))))))))))))******))))))((('''&&&''''''''''''((((((((((((((((((((((((''''''''''''''''''((((((((((((((((((((((((((((((''''''''''''(((((())))))***))))))))))))))))))(((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$%%%&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$############$$$$$$"""""""""""""""""""""""""""""""""############$$$%%%%%%%%%$$$######""""""""""""""""""!!!!!!!!!!!!"""""""""!!!!!!!!!  !!!"""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!! !!! !!!###$$$%%%666666555555555444444444111333444444333222222333444444333333333333444444111111000000000000111111444444444333333333333333222444444333000///////////////000000111111111111000000000///000000000000//////............//////.........///////////////000000000000000000000000///000222333333222000///000000/////////...............///000000///......------------------------------,,,,,,+++,,,,,,---...---,,,+++***)))((('''***++++++,,,++++++******(((((()))***************((()))***++++++,,,,,,+++))))))************))))))))))))***++++++++++++***+++++++++++++++***)))((())))))))))))))))))))))))(((((((((((()))))))))))))))))))))*********++++++************************+++******))))))******+++************************)))))))))))))))))))))))))))))))))))))))((('''''''''''''''(((((((((((((((((((((((((((((('''''''''''''''''''''(((((((((((((((((((((((('''''''''''')))************))))))((())))))((((((((('''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''(((((('''&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%###$$$%%%'''((()))))))))''''''&&&&&&%%%%%%%%%$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$############$$$$$$"""""""""""""""""""""""""""""""""""""""""""""###%%%$$$$$$$$$######""""""""""""""""""!!!!!!!!!!!!"""""""""!!!!!!!!!  !!!"""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!  !!!  """$$$&&&666666555555555444444444111333444444333222222333333333222222222222333333222222111111111111222222444444333333333222222222222333444333111///....../////////000111111222222222222111000000111111222//////.........//////000///////////////.........////////////////////////...///111222222111///...////////////............,,,,,,---......---,,,,,,------------------------,,,,,,+++++++++,,,,,,------,,,,,,+++)))(((((('''))))))***************)))(((((()))************))))))******++++++******)))))))))************))))))))))))***++++++++++++++++++++++++++++++***)))((((((((((((((((((((((((((((((((((((((())))))))))))************+++++++++,,,************************++++++************++++++((((((((()))))))))))))))))))))))))))))))))))))))((())))))))))))(((((('''(((((((((((((((''''''''''''''''''(((((((((((((((&&&'''''''''(((((())))))(((((((((((('''''''''''')))************))))))(((((((((((((((''''''''''''&&&&&&&&&''''''(((((((((''''''''''''''''''''''''&&&&&&%%%%%%$$$###""""""$$$$$$$$$%%%%%%&&&&&&&&&###$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%###$$$%%%'''((()))******'''''''''&&&&&&%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$############$$$$$$""""""""""""""""""""""""###"""""""""""""""""""""$$$$$$###############"""!!!!!!!!!!!!""""""""""""!!!!!!!!!  !!!"""""""""""""""""""""""""""""""""!!!!!!!!!!!!""""""""""""!!!     !!!555555555444444444444333111333444444333222222333333333222222222222333333333333222222222222333333444444333333222222111111333555666555333111000000//////000000111111111222333222111000///000111222//////......//////000000///////////////.........000000////////////......---///000111111000///---/////////.........------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++,,,,,,---+++++++++***))))))(((((((((((()))************)))((()))***++++++***)))((()))***************))))))))))))************)))))))))***++++++,,,+++++++++******+++++++++******)))''''''''''''''''''''''''(((((((((((())))))))))))*********+++++++++,,,,,,***************+++++++++++++++************++++++'''''''''(((((((((((()))))))))))))))))))))))))))(((((())))))))))))(((((((((((((((((((((''''''''''''''''''(((((((((((((((&&&&&&''''''((()))))))))((((((((((((''''''''''''(((((())))))***)))))))))((((((((('''''''''&&&&&&&&&&&&&&&'''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$######""""""###$$$$$$%%%%%%&&&&&&'''###$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%###$$$%%%'''((()))))))))'''''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$############$$$$$$########################$$$############"""""""""########################!!!!!!!!!!!!""""""""""""!!!!!!!!!  !!!"""""""""""""""""""""""""""""""""!!!!!!!!!!!!""""""""""""!!!!!!!!!     444444444444333333333333111333444444333222222333444444333333333333444444333333222222222222333333444444333333222111111000222444666555333000//////000000000000000111111111222111///...---...///000///////////////000111111000/////////............111111111000000/////////...///111222222111///...//////.........---------------,,,++++++,,,------++++++++++++++++++++++++++++++******+++,,,,,,---************))))))))))))((()))******+++++++++***((()))***++++++***)))''''''((()))******++++++***))))))************)))))))))***++++++,,,,,,++++++))))))***+++++++++******(((((((((((((((((((((((((((((((((((()))))))))))))))))))))************+++))))))*********+++++++++,,,++++++******++++++,,,'''((((((((())))))))))))(((((((((((((((((((((((((((((())))))))))))(((((()))(((((((((''''''''''''''''''''''''((((((((()))&&&&&&''''''((())))))***((((((((((((''''''''''''&&&'''(((((())))))))))))(((((('''''''''&&&&&&&&&&&&&&&&&&'''((()))))))))%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''###$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%###$$$%%%&&&'''(((((((((&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$############""""""""""""############ !!!!!!!!!"""""""""###"""""""""!!!!!!!!!   !!!"""""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!"""""""""###"""""""""!!!!!!!!!   !!!!!!444444333333333222222222111333555444333222333333555555555444444555555555333333222222222222333333444444333333222111000000000222444333111...------111111000000000000000000111000...,,,+++,,,---...///////////////000111111000000//////.........---222222222222111111000000///000222333333222000/////////.........---------///...,,,++++++,,,...///+++++++++++++++++++++++++++*********+++,,,,,,---))))))))))))************)))***+++,,,,,,,,,,,,,,,((()))***++++++***((('''%%%&&&((()))+++,,,,,,,,,))))))************))))))******+++,,,,,,,,,,,,+++((()))***+++++++++++++++))))))))))))))))))))))))(((((((((((())))))))))))(((((((((((())))))))))))))))))******++++++++++++,,,++++++******++++++,,,(((((())))))*********+++(((((((((((((((((((((((((((((()))))))))))))))((())))))(((((('''''''''&&&&&&'''''''''(((((())))))&&&&&&&&&'''((())))))***)))(((((((((''''''''''''%%%%%%'''((())))))))))))(((((('''''''''&&&&&&&&&&&&&&&&&&'''((())))))***%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&######$$$%%%%%%&&&''''''###$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$%%%&&&''''''''''''%%%&&&&&&&&&'''((((((((('''&&&&&&%%%%%%&&&&&&'''$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######"""""""""""""""######### !!!!!!!!!""""""##################""""""""""""   !!!"""""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!""""""######""""""""""""!!!!!!!!!!!!    !!!!!! 555444222000000111222333///111333555666666666666333444444444444444444444555555555555555555555555444444444333333222222222222222222222222222222222111111111111000///---,,,........................000000000///.........---------...//////...------///000111222222222222222000000000111222222000...444222000---,,,,,,---------,,,,,,+++,,,---...///++++++++++++++++++++++++***+++,,,+++******,,,---)))))))))))))))*********(((((())))))******************))))))(((((('''''')))))))))))))))******+++,,,,,,,,,+++)))((()))***,,,+++***))))))***+++,,,++++++,,,,,,,,,,,,------++++++)))((('''''''''''''''(((((()))))))))))))))***)))'''&&&'''(((***+++******+++,,,,,,---......******,,,,,,,,,,,,******))))))))))))))))))))))))))))))))))))))))))))))))(((((('''''''''&&&&&&&&&))))))((((((''''''&&&&&&%%%%%%&&&'''((()))******''')))******))))))***+++))))))(((((('''''''''&&&''''''''''''(((((((((((((((((((((((((((((((((((($$$%%%&&&'''((((((((((((((('''&&&%%%%%%&&&'''((($$$$$$%%%&&&&&&''''''(((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%$$$###"""!!!!!!"""$$$%%%%%%$$$"""!!!######$$$$$$$$$%%%%%%%%%"""###$$$&&&'''((())))))((('''&&&%%%%%%&&&'''((('''''''''&&&&&&%%%%%%%%%'''&&&$$$#########$$$$$$$$$$$$$$$############"""%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############"""!!!!!!!!!!!!  !!!!!!  !!!!!!!!!  !!!!!! !!!!!!!!! !!!"""###"""!!!   !!!!!!!!!555444222111000111222333000111333444555666555555444444444333333333333333444444444444444444444444444444444333333222222222333333222222222222222222111111000000//////....../////////////////////////////////.......................................000000111111111000///////////////111222222000...333111///---,,,,,,---...,,,,,,+++++++++,,,---...------------------------***++++++***)))(((***+++((((((((((((((())))))))))))))))))))))))***************))))))(((((((((((()))))))))))))))******+++++++++,,,***)))(((***+++,,,+++***))))))***+++,,,++++++,,,,,,,,,,,,------++++++)))((((((''''''''''''(((((()))))))))))))))***)))'''''''''(((***+++))))))******+++,,,,,,---***+++,,,,,,,,,,,,+++***************************(((((((((((((((((((((((((((((('''''''''&&&&&&&&&((((((((((((((('''''''''&&&&&&''''''((()))))))))''')))******))))))***+++)))))))))(((((((((''''''''''''((((((((()))))))))(((((((((((((((((((((((($$$%%%&&&'''((((((((((((((('''&&&&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%###"""""""""###$$$%%%%%%$$$###"""###$$$$$$$$$$$$%%%%%%%%%###$$$%%%&&&'''(((((((((((('''&&&&&&&&&&&&'''(((''''''&&&&&&&&&%%%%%%%%%&&&%%%$$$#########$$$$$$$$$$$$$$$$$$############%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############"""!!!!!!!!!!!!  !!!!!!  !!!!!!!!!  !!!!!! !!!!!!!!!  !!!"""###"""!!!   555444333222111222333444222222333444444444444444444444333333222222111111333333333333333333333333444444333333333333222222333333333222222111111111111111000/////////000111////////////////////////---------...............//////...------...//////000000000000///...------.........000222222000...111000///---------...///,,,++++++++++++,,,------------------------------***++++++***((('''((()))((((((((((((((((((((((((*********)))))))))))))))***))))))))))))((((((((()))))))))))))))******+++)))***+++***))))))+++---,,,++++++******++++++,,,++++++,,,,,,,,,,,,------+++***))))))(((((((((((('''((())))))******))))))))))))((('''((()))***+++(((((())))))***+++++++++++++++,,,,,,,,,,,,++++++************************(((((((((((((((((((((((((((((((((''''''''''''&&&'''''''''(((((((((((((((((((((((((((((((((((((((''')))******(((((()))+++***)))))))))))))))((((((((((((((()))))))))******((((((((((((((((((((((((%%%%%%&&&'''((((((((((((((('''&&&&&&&&&&&&'''((((((((('''&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&%%%%%%$$$###""""""###$$$%%%%%%$$$###"""$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&'''''''''''''''((('''&&&&&&&&&&&&'''((('''&&&&&&&&&&&&%%%%%%%%%&&&%%%$$$#########$$$$$$%%%$$$$$$$$$############$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############"""!!!!!!!!!!!!  !!!!!!  !!!!!!  !!!!!!!!! !!!!!!!!! !!!""""""""""""!!! 555444333333333333444444333333333333444333333333444444333222222111000000222222222222222222222222333333333333333333333333444333333222222111111111222111///......000222333////////////////////////,,,,,,------......//////111///...,,,,,,...///111//////000000000///......------...000222222000...//////............///000---------,,,------------,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,***((('''((()))))))))))))))((((((((((((************)))))))))))))))))))))))))))))))))))))))))))))))))))******+++((()))******)))***,,,...,,,,,,,,,++++++,,,,,,,,,+++++++++,,,,,,,,,------+++******)))(((((())))))(((((()))************)))))))))((((((((()))***+++)))))))))*********++++++++++++,,,,,,,,,,,,++++++************************((((((((((((((((((((((((((((((((('''''''''''''''&&&&&&''''''(((((())))))))))))(((((('''''''''''''''((())))))(((((()))+++************))))))))))))))))))))))))************((((((((((((((((((((((((%%%&&&&&&'''(((((('''''''''''''''&&&&&&'''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&'''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""!!!!!!!!!!!!  !!!!!!  !!!!!!  !!!!!!!!!!!! !!!!!! !!!!!!!!!"""""""""!!!!!! 444444444444444444555555333333222222333333333333444444333222222111000000222222222222222222222222333333333333333333333333333333333222222111111111222111///......000222333........................,,,------....../////////111000...------...000111---...///000111111111111.........000222222000..................//////000//////////////////......,,,,,,,,,,,,,,,,,,,,,,,,---------+++)))((()))***+++++++++******)))))))))*********)))))))))))))))))))))))))))************)))))))))))))))******+++''')))******)))***,,,...,,,,,,,,,------,,,,,,,,,+++++++++,,,,,,,,,------+++******))))))))))))***((())))))***************)))))))))))))))******+++*********+++++++++++++++++++++++++++++++++++++++************************''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&''''''(((((()))))))))))))))(((''''''&&&&&&&&&((())))))(((((()))***))))))))))))************))))))))))))************((((((((((((((((((((((((%%%&&&''''''((('''''''''&&&''''''''''''''''''&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''((((((''''''&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$######$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""!!!!!!!!!!!!  !!!!!!  !!! !!!!!!!!!!!! !!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 444444555555555555555555222222222222222333444444444444333333222222111111222222222222222222222222222222333333333333444444222222222222222222222222222222111000000000111222////////////////////////.........///////////////000000///......///000000,,,---...000111222333333000000000111222222000............///////////////000000000111000000///...........................,,,------,,,***)))***,,,,,,,,,,,,++++++******)))((()))))))))************)))))))))************+++)))))))))))))))******+++((()))******)))***,,,...,,,------......------,,,++++++,,,,,,,,,,,,------+++******))))))*********((()))******++++++******)))))))))*********++++++++++++++++++++++++++++++******))))))))))))******++++++++++++++++++++++++'''''''''''''''''''''''''''(((((((((((()))))))))'''''''''((((((((((((((())))))(((((('''''''''&&&&&&((())))))''''''(((***(((((()))))))))))))))***((((((((()))))))))******((((((((((((((((((((((((&&&&&&'''''''''''''''&&&&&&&&&'''(((((('''&&&&&&$$$$$$%%%%%%&&&'''((((((%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''(((((((((''''''&&&&&&&&&'''(((((('''&&&&&&%%%%%%%%%&&&&&&&&&&&&'''######$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############"""!!!!!!!!!!!!  !!!!!!   !!!"""!!!!!! !!!!!! !!!"""!!!!!!!!! !!!!!!!!!  444444555666666666666666111111000111222333555666444444444333333333333333333333333333333333333333222222222333333444444444111111111222222333333444333222222111111000000000111111111111111111111111000000000000000/////////////////////////////////,,,---...///000111111111333222222222333222000...//////////////////......///000000111000///...---////////////////////////***+++,,,+++))))))***,,,,,,,,,++++++***))))))(((''''''((()))***++++++,,,))))))*********+++++++++)))))))))))))))******+++)))*********)))***+++---,,,---...//////...---,,,++++++,,,,,,,,,,,,------+++******))))))***++++++))))))***++++++++++++***))))))******+++++++++******************************)))(((''''''((()))***++++++++++++++++++++++++'''''''''''''''''''''''''''((((((((())))))))))))((((((((((((((('''''''''((((((((((((((('''''''''&&&'''((((((''''''(((***''''''((((((((()))))))))''''''((((((((()))))))))((((((((((((((((((((((((&&&'''''''''''''''&&&&&&&&&&&&'''(((((('''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&'''((((((((((((((('''&&&&&&'''(((((('''&&&&&&%%%%%%%%%&&&&&&&&&''''''"""###$$$%%%%%%%%%%%%$$$&&&&&&%%%%%%%%%$$$$$$$$$"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############"""!!!!!!!!!!!!  !!!!!! !!!!!!!!!!!! !!!""""""!!!!!! !!!!!!!!!"""""""""!!!  !!! !!!   444444555666777777666666000000000000111333555777444444444444444444444444333333333333333333333333222222222333333444444444000000111222333444444555333333333333222000///...333333333333333333333333222222111111000000////////////000000000000//////------......///.........555444333333444333000---//////000000///...------...///000000000///---,,,------------------------))))))***)))((((((***,,,+++++++++***)))(((((('''&&&&&&''')))***+++,,,---))))))******++++++++++++)))))))))))))))******+++)))***+++***))))))+++---,,,---...//////...---,,,++++++,,,,,,,,,---------+++***************++++++))))))***++++++++++++***))))))***++++++++++++***))))))))))))(((((((((((()))((('''&&&&&&'''((()))++++++++++++++++++++++++'''''''''''''''''''''''''''((((((((())))))******))))))(((((('''''''''&&&((((((((((((((((((((((((&&&'''((((((''''''(((***&&&'''''''''(((((())))))''''''''''''((((((((((((((((((((((((((((((((((((&&&'''''''''''''''&&&&&&%%%&&&'''(((((('''&&&%%%(((''''''&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&'''&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''&&&''''''(((((((((((((((%%%&&&'''(((((('''&&&%%%%%%%%%%%%&&&&&&'''''''''"""###$$$%%%&&&%%%%%%$$$&&&&&&&&&%%%%%%%%%$$$$$$"""###$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############""""""!!!!!!!!!  !!!!!! !!!!!!!!!!!!!!!  !!!"""###!!!!!! !!!!!!!!!"""""""""!!!  """!!! !!!!!!!!!  222222222333333333444444111000000000111333555666444333333222222333333444333222222111111222222333222222222222222222222222555444222111000111111222111111000000//////......222222444555555444222222333333333333333333333333...///000111111000///...------......//////000000222222222222111///...---,,,,,,,,,---------......,,,,,,,,,,,,,,,,,,,,,,,,......---,,,,,,+++************++++++++++++******))))))))))))))))))************+++++++++,,,,,,,,,++++++******************+++***)))))))))***,,,---,,,,,,,,,,,,++++++***))),,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,,,,,,,+++***))),,,,,,+++***))))))******''''''''''''((()))++++++++++++***)))(((((())))))++++++************++++++))))))))))))***+++,,,---***++++++++++++***))))))(((((((((((((((((((((((()))&&&%%%&&&)))***)))'''&&&&&&&&&'''''''''''''''******))))))((((((((('''''''''((((((''''''&&&%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%&&&&&&%%%%%%$$$###'''&&&%%%%%%$$$$$$$$$$$$''''''''''''''''''&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&))))))((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$'''***+++***)))))))))''''''&&&&&&&&&%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%$$$######"""############$$$$$$$$$"""######$$$$$$######""""""""""""""""""######### !!!!!!!!!!!!  !!!  """ !!!!!!!!!!!!!!!!!!!!!!!!""""""!!!!!!  !!!!!!!!!  333333333333444444444444222222222222222333333444555555555555555555555555444333333333333333333444333333333333333333333333444444333222111111111111111111111111000000000000111111222222222222111111111111111111111111111111/////////000000//////............//////000000000111111222222111000...---,,,---------............,,,,,,,,,,,,,,,,,,,,,,,,......------,,,++++++*********++++++++++++******************))))))))))))************+++++++++,,,******************************))))))******+++,,,++++++,,,,,,,,,+++******,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++*********,,,++++++***))))))******(((((('''(((((()))***+++++++++***)))))))))))))))******))))))))))))******))))))))))))***+++,,,---++++++++++++******)))(((((((((((((((((((((((((((((('''%%%''')))***)))'''''''''''''''''''''''''''))))))((((((((('''''''''&&&&&&&&&&&&&&&%%%$$$$$$&&&&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$$$$%%%&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$$$$%%%''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''')))******)))))))))''''''&&&&&&&&&%%%%%%%%%'''''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%$$$$$$######"""############$$$$$$$$$######$$$$$$$$$$$$###############""""""""""""""" !!!!!!!!!!!!   """ """!!!!!!!!!   333444444444444555555555444444444444333222222111444555555666666555555444555444444333333444444555333333333333333333333333333333333333222111000///111111111111222222222222000000////////////000000///////////////////////////...............//////////////////000000000000///000111111111000//////------........./////////------------------------......------,,,+++++++++******++++++++++++******++++++*********))))))))))))))))))*********++++++************************))))))***+++++++++++++++******+++,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,---,,,+++***)))***++++++,,,+++******)))*********))))))(((((((((((())))))+++***))))))))))))))))))))))))(((((((((((())))))))))))))))))******+++,,,++++++++++++***)))((('''((((((((((((((((((((((((((('''&&&''')))***)))((()))((((((''''''&&&&&&&&&(((''''''''''''&&&&&&&&&$$$$$$%%%%%%$$$$$$###"""%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&'''(((((((((&&&&&&%%%$$$$$$$$$%%%%%%''''''''''''''''''''''''%%%%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''(((((())))))((((((''''''&&&&&&&&&%%%%%%%%%'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$######"""############$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$######""""""!!!!!! !!!!!!!!!!!!  !!!!!!!!! !!!  """ !!!!!!!!! 444444444555555555666666333444555555555444222111222222333444444333222222444444333333333333444444444444444444444444444444222222333333333111///...//////000111111222333333000000...------...000000........................///...---,,,,,,---///000000000000000000000000000---...000111111111000///.........////////////000------------------------......------,,,,,,,,,,,,***++++++,,,,,,++++++***,,,++++++******))))))(((((())))))))))))************************+++++++++((()))***,,,,,,+++******)))***++++++,,,,,,,,,,,,++++++++++++++++++++++++---,,,***(((((()))+++,,,++++++***************+++***))))))(((((((((((()))******)))))))))))))))*********))))))))))))******)))))))))))))))***++++++++++++++++++***((('''&&&(((((((((((((((((((((((((((''''''((())))))))))))***))))))((('''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%$$$######%%%&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''((((((((((((&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&'''''''''''''''%%%&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&&&&%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%(((''''''((()))))))))(((''''''&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$######""""""#########$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$###"""!!! !!!!!!!!!!!! !!!!!!!!!!!!""" !!!  !!! 444444444555555555666666222333444666666555444444222333333333333333333222333333222222222222333333444444444444444444444444111222333333222111///...---......///000111222222111000///......///000111////////////////////////...---,,,,,,,,,...///000000000000///////////////,,,---///000111111000000.........////////////000..............................------------,,,,,,++++++,,,,,,,,,,,,++++++,,,+++++++++******))))))((())))))))))))*********))))))*********+++++++++((()))***,,,,,,+++******)))***++++++,,,,,,,,,,,,++++++++++++++++++++++++,,,+++)))(((((()))+++,,,+++***************++++++***))))))(((((((((((()))***)))))))))))))))******,,,++++++******++++++,,,)))))))))((())))))******+++++++++***)))(((''''''(((((((((((((((((((((((('''((()))))))))))))))*********)))(((''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%&&&''''''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((''''''&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&'''''''''((((((%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&(((+++,,,***(((''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$######""""""#########$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$###"""!!! !!!!!!!!!!!! !!!!!!!!!!!!""" !!!!!!   333444444444444555555555333444444555666666666666666555555444444555555666333222222111111222222333333333333333333333333333222222222222111000///...---......///000111111111111111000000000000111111////////////////////////------------...///000000////////////............,,,---///000111000000///------........./////////////////////////////////......------------------++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++)))))))))*********++++++)))))))))***++++++,,,,,,))))))***+++++++++++++++******+++,,,,,,,,,++++++++++++++++++++++++++++++******)))((()))***+++,,,*********)))******+++,,,))))))(((((((((((()))))))))))))))))))))******+++,,,,,,,,,++++++,,,,,,,,,)))))))))(((((())))))***))))))******))))))((('''((((((((((((((((((((((((''')))******(((((()))+++***))))))(((((('''''''''%%%%%%%%%&&&&&&&&&&&&'''''''''((((((''''''&&&%%%%%%&&&'''(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''&&&%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%&&&&&&'''(((((((((&&&&&&'''(((((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&***...///,,,)))''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$######"""############$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$######""""""!!!!!! !!!!!!!!!!!!  !!!!!!!!! !!!!!!    333333333333444444444444777666555555555555555555777666444222222444666777333333333222222333333333333333333333333333333333333222111000000//////////////////000000111111111000000111111111111000000////////////////////////------...///000000000000///.........---------,,,---...///000000000///...,,,---------............////////////////////////------..................+++,,,,,,------,,,,,,+++)))******++++++,,,,,,---************+++++++++,,,((())))))***++++++,,,,,,******))))))******+++,,,++++++,,,,,,,,,+++******************************))))))))))))*********+++******))))))***++++++,,,(((((('''(((((()))***+++)))))))))))))))***++++++,,,++++++++++++++++++,,,))))))(((((((((((())))))'''(((((()))))))))))))))((((((((((((((((((((((((''')))+++***((((((***,,,)))))))))(((((((((((((((%%%&&&&&&&&&'''''''''''''''(((((((((((('''&&&&&&%%%&&&'''((())))))))))))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&'''%%%%%%&&&&&&'''(((((()))&&&&&&'''(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''',,,222333///***''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&##################$$$$$$"""############$$$$$$$$$######$$$$$$$$$$$$###############""""""""""""""" !!!!!!!!!!!!   !!!"""    222222222333333333444444:::999777555444333444444666444111//////111444666555444444333333444444555222222222222222222222222444222111/////////000000111111111111111222222222...///000111111000///...........................,,,---///111222111111000......---------,,,,,,,,,......///000000///...---,,,,,,,,,---------......000000000000000000000000------..................+++,,,,,,------,,,,,,+++))))))***+++,,,------...***++++++++++++,,,,,,,,,((())))))***++++++,,,,,,+++***)))))))))***,,,---,,,,,,,,,,,,,,,+++***)))************************'''((()))*********************))))))***+++,,,,,,''''''''''''(((***++++++))))))((())))))***++++++++++++************++++++***)))(((((((((((())))))&&&'''((()))************((((((((((((((((((((((((''')))+++***((((((***,,,(((((((((((())))))))))))&&&&&&&&&''''''(((((((((''''''((((((''''''&&&%%%%%%&&&'''((())))))))))))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&'''''''''$$$$$$$$$$$$%%%%%%&&&'''%%%%%%&&&&&&'''((())))))&&&''''''(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$'''...444555000+++''''''&&&&&&&&&%%%%%%%%%#########$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&##################$$$$$$"""############$$$$$$$$$#########$$$$$$#########"""""""""""""""######### !!!!!!!!!!!!  """"""   333444555555666666555555555444333444666777666555333333222222222333444444222222333333333222111111111111000000222444777999222222222222222111000//////000111222222111000///111000///......///000111222111000//////...////////////000000000000000///000...,,,++++++,,,---///---...000111000///---,,,///...---,,,+++,,,,,,---111111000///...---,,,,,,***+++---.........------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,------+++***(((++++++++++++++++++++++++---,,,+++)))((((((''''''------,,,,,,+++,,,,,,,,,******))))))(((((('''''')))))))))***+++++++++,,,((((((((()))******++++++''''''(((((())))))*********)))))))))***+++,,,,,,***************)))(((((((((((((((((((((((((((((('''((()))******)))((('''''''''''''''''''''&&&&&&((()))***+++***)))'''%%%************)))((('''&&&((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&%%%&&&'''((()))((('''&&&%%%%%%&&&'''((('''%%%$$$%%%(((***(((&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$""" !!!###%%%'''((((((((((((((((((''''''''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%%%%&&&'''))))))))))))((((((((('''''''''&&&&&&&&&'''&&&%%%%%%%%%%%%&&&'''%%%&&&&&&&&&%%%%%%$$$#########""""""######$$$%%%%%%%%%$$$###"""""""""#########$$$$$$$$$$$$######"""""""""""""""""""""""" !!!!!!  !!!!!! !!!!!!!!!!!! 333444555555666666555555444333222333555666555444444444333333333333333444000111222333333333333333333222222222222333444555111111222222222111111111///000111222222111000//////......------......///111000////////////////////////000000000000//////...---,,,+++,,,,,,......***,,,...///000///...---///...---,,,,,,,,,------000000//////......------+++,,,---.........------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,------+++***(((************************,,,+++***)))((((((((((((,,,,,,++++++++++++,,,,,,***)))))))))((((((((('''***************+++++++++*********)))))))))))))))(((((((((((())))))))))))******************++++++***************)))(((((((((((((((((((((((((((((('''((()))******)))((('''''''''''''''''''''''''''((()))***+++***)))'''&&&&&&&&&'''((())))))))))))'''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%&&&'''((()))((('''&&&&&&&&&&&&'''((('''%%%$$$%%%((()))(((&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$"""!!!!!!###%%%''''''''''''''''''''''''''''''''''''&&&&&&'''''''''(((((('''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&$$$%%%'''((())))))(((''''''''''''&&&&&&&&&&&&%%%'''&&&%%%%%%%%%%%%&&&'''%%%&&&&&&&&&%%%$$$$$$#########""""""######$$$%%%%%%$$$######""""""############$$$$$$$$$$$$######!!!!!!!!!!!!!!!!!!!!!!!! !!!!!! !!!!!!!!!!!! 333444555555666666555555333222111222444555444333666666555444444333333333///000111222333444444444444444444333333222111000000000111222222222222111000000111111111111000000......//////000//////.../////////...//////000000/////////000000//////...++++++,,,,,,------......(((***,,,...//////............---,,,,,,,,,------........................+++,,,---.........------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,---,,,+++***)))))))))))))))))))))))))))******))))))))))))******+++***************++++++))))))))))))((((((((((((+++++++++***************++++++******)))(((((('''))))))))))))((((((((((((+++++++++******************************)))(((((((((((((((((((((((((((((((((((())))))))))))((((((''''''''''''''''''''''''(((((()))******)))'''&&&$$$%%%&&&'''(((((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&'''((((((((('''&&&&&&&&&&&&'''((('''&&&%%%&&&'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$###"""!!!!!!###%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%&&&'''((('''''''''''''''&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%&&&''''''''''''&&&###$$$&&&'''(((''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%$$$$$$$$$######""""""######$$$%%%$$$$$$###"""""""""############$$$$$$$$$$$$######  !!!!!! !!!!!!!!! 333444555555666555555555222111000111333444333222777777666666555444333222000111222222333333333333222333444444444222000///111111222222222111111000000000000111111000000000///000222333333222111111...............///000111/////////000//////......)))***+++------.........)))+++---/////////...------------------------------------....../////////,,,---------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,+++***)))************************))))))(((((()))***++++++)))))))))))))))******+++))))))))))))((((((((((((,,,+++++++++***)))))))))************))))))((((((******))))))((((((''''''++++++++++++******))))))***************)))(((((((((((((((((((((((((((((((((((())))))))))))((((((&&&&&&&&&'''''''''''''''(((((())))))))))))((('''''''''''''''&&&%%%$$$$$$''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''(((((('''''''''&&&&&&'''''''''&&&&&&%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""!!!"""###%%%&&&$$$%%%%%%%%%%%%%%%&&&&&&)))'''&&&%%%%%%&&&''')))''''''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&''''''((((((''''''"""###%%%&&&''''''&&&%%%&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$######""""""######$$$%%%######""""""""""""############$$$$$$$$$$$$######   !!!!!! 333444555555666555555555222111000111333444333222666666666666555444333222333333333333222222111000///000333444444333111000333333333222111000///...111000000000000000000111///000111333333333222111......---......///000000///////////////...------)))***+++,,,---------------...///000000///---,,,,,,---------------------,,,,,,------......//////------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++******++++++++++++++++++++++++(((((((((((()))***+++,,,)))((((((((())))))***+++(((((((((((()))))))))))),,,+++++++++***)))))))))(((((())))))******************))))))((((((''''''+++++++++++++++***)))(((***************)))(((((())))))))))))))))))))))))))))))(((((((((((())))))&&&&&&&&&'''''''''(((((((((((()))))))))))))))(((''''''''''''&&&%%%$$$###''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''&&&''''''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%######"""""""""###$$$%%%$$$$$$$$$$$$%%%%%%&&&&&&((('''&&&&&&&&&&&&'''(((&&&'''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&''''''((((((''''''"""###$$$&&&&&&&&&&&&%%%&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$#########$$$%%%%%%######""""""######$$$%%%###""""""!!!""""""############$$$$$$$$$$$$######  !!!!!!  333444555555666666555555222111000111333444333222444555666666555444222111444444444333222111000///---///111333444444333222222333333222222111//////111111000000000000111111------...///000000000000.........---......//////////////////......---,,,******++++++,,,,,,------...///000111111///---,,,+++,,,---.........------,,,,,,------.........///......---,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++******++++++++++++++++++++++++))))))(((((()))***++++++(((((((((((()))***+++,,,(((((((((((())))))))))))+++++++++***************'''(((((()))******++++++))))))))))))(((((((((((()))***+++,,,,,,+++)))(((***************)))(((((())))))))))))))))))))))))))))))(((((((((((())))))%%%%%%&&&&&&'''((((((((((((((((((((())))))))))))###$$$%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''&&&&&&'''(((((('''&&&&&&%%%&&&'''&&&%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###############$$$$$$%%%###$$$$$$%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%&&&''''''''''''&&&"""###%%%&&&'''&&&&&&%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$###""""""###%%%&&&######""""""######$$$%%%""""""!!!!!!!!!"""############$$$$$$$$$$$$######  !!!!!!!!!  333444555555666666555555333222111222444444444333222333444555555444222111333333333333333222111000...///111222333333222222///000111222222222222222222111000//////000111222------------...///000111//////...---------......////////////...---,,,+++,,,,,,+++******+++,,,---,,,---...000000///...,,,+++,,,---.........------------------------------///...---,,,,,,,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++******++++++***************************)))))))))))))))******))))))))))))***+++,,,,,,'''((((((((()))))))))******************+++++++++)))))))))))))))*********(((((((((((())))))))))))((()))+++,,,,,,+++***)))***************)))(((((())))))))))))))))))))))))***)))(((''''''((()))***%%%%%%&&&&&&'''(((((()))((((((((((((((()))******$$$%%%&&&''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''((((((((('''&&&&&&&&&'''(((((('''&&&&&&%%%&&&(((&&&$$$###$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$%%%&&&'''''''''%%%&&&'''))))))'''&&&%%%&&&&&&&&&'''''''''((((((&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&###$$$%%%'''''''''&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%&&&''''''&&&%%%%%%$$$###"""!!!"""###%%%&&&######""""""######$$$%%%!!!!!!!!!!!!!!!"""############$$$$$$$$$$$$######!!!!!!!!!!!!!!!!!!!!!!!! !!!"""!!!  333444555555666666555555333222111222444555444333000222333555555444333111111222222333333333222222000111111222222222222111,,,---///111333444555555222111000//////000111222///............000222333000///...---------------////////////...---,,,+++...,,,+++))))))***,,,---(((***,,,...//////...---***+++---...///...------------------------------///...---,,,+++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---,,,++++++******++++++))))))))))))))))))))))))******))))))))))))******))))))))))))***+++,,,---'''((((((((())))))******))))))******+++++++++,,,++++++******)))(((((((((''''''(((((())))))******'''(((***,,,---,,,+++******************)))(((((())))))))))))))))))))))))***)))(((''''''((()))***%%%%%%&&&&&&'''((())))))((((((((((((((()))******(((((((((((('''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%'''((((((((('''&&&%%%&&&'''(((((('''&&&%%%$$$&&&((('''$$$"""$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$"""#########$$$$$$$$$$$$$$$$$$%%%&&&&&&'''(((((($$$&&&(((******(((&&&$$$&&&&&&&&&'''''''''((((((&&&&&&&&&%%%%%%$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%###$$$&&&'''(((((('''&&&(((((('''''''''&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%$$$###"""!!!"""###%%%&&&#########"""###$$$$$$%%%!!!!!!!!!!!!!!!"""############$$$$$$$$$$$$######"""""""""""""""""""""""" """"""!!!  333444555666666666555444111000///000222333333111222222333333333222222111111111000000000000000000111222333333333333222111111111222222222222111111000000///......///000111...//////000000000000000222000...---------///000------............------///---++++++------+++)))---.........------,,,+++...------,,,,,,------...,,,,,,.../////////...---,,,---...//////...---,,,------,,,+++************...+++***+++...000///---,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++******++++++,,,******))))))***+++,,,,,,---,,,+++******+++,,,,,,)))'''&&&''')))************)))((((((((()))+++,,,******))))))((((((''''''(((((()))***+++,,,,,,,,,,,,,,,+++++++++++++++,,,---------,,,***((('''&&&))))))))))))))))))))))))(((***+++***)))((()))***((((((''''''''''''(((((())))))))))))))))))))))))***)))((('''''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&%%%$$$###"""########################%%%%%%%%%&&&&&&&&&''''''&&&&&&'''''''''&&&$$$###$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!! !!!  !!!  !!!  !!!  """  333444555555555555444333111000000111222333222111222222333333333222222111000111111222222111111000111222333333333333222111111111111222222111111111333222111111111222333333......///000000000000///111000...---,,,---...///------............------///---++++++------,,,)))---------------,,,++++++------,,,,,,,,,,,,------++++++---.........---,,,------...//////...------...---,,,,,,,,,,,,,,,,,,111...,,,,,,...///...---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,******))))))***++++++,,,******(((((((((((()))******)))((((((******)))((()))(((((((((((()))******+++*********))))))))))))(((((()))++++++,,,,,,+++++++++************++++++******+++++++++******)))))))))))))))))))))))))))(((***+++***)))((()))***((((((''''''''''''(((((()))))))))))))))))))))))))))(((((('''&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&'''''''''&&&%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%%%%$$$$$$'''&&&&&&%%%%%%&&&&&&'''%%%%%%&&&&&&'''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!   !!!   !!! !!!  333333444444444444333333222111000111222333222111222222333333333333222222000111333444444333111000111222222333333222222111111111111111111111111111333222222111111222222333---......///////////////000///---,,,,,,,,,---...------............------...,,,++++++------,,,***,,,,,,,,,,,,,,,+++++++++------,,,,,,,,,,,,------***+++,,,,,,------,,,,,,------...//////...---------------------......///222000.........///...,,,------------------------------,,,,,,,,,,,,------*********)))******+++,,,))))))(((''''''((()))******))))))***++++++)))''''''((())))))***)))))))))++++++++++++************((()))***+++++++++++++++******)))))))))******+++)))******+++++++++******))))))))))))))))))))))))(((***+++***)))((()))***((((((''''''''''''(((((())))))))))))))))))))))))(((((('''&&&&&&&&&&&&'''((('''''''''&&&%%%%%%%%%'''''''''&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&'''''''''&&&%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!  !!!!!!  !!! !!! !!!!!!!!!!!! !!!!!!!!!!!! !!!"""  333333333333333333222222333111111111333333222111222222333333444333333333000111444666666444222111222222222222222222222222111111000000000000111111000000//////////////////------...//////////////////...---,,,,,,,,,,,,---,,,------......------,,,---,,,,,,,,,,,,,,,,,,+++,,,+++++++++++++++++++++---,,,,,,,,,,,,,,,,,,---++++++,,,,,,---------------..................---,,,,,,,,,,,,---...///000000///.............................................------,,,,,,------...+++***************+++++++++***)))))))))***+++,,,))))))***,,,...---***((('''(((***+++++++++***)))************************((()))***+++++++++++++++)))))))))((())))))***+++,,,,,,,,,+++***)))((('''(((((((((((((((((((((((((((***+++***)))((()))***((((((''''''''''''((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&'''''')))(((((('''&&&%%%%%%$$$'''''''''''''''&&&&&&&&&&&&&&&''''''''''''&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%$$$$$$###$$$%%%%%%&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%'''&&&&&&%%%%%%&&&&&&'''###$$$%%%&&&''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&%%%%%%$$$######""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!! !!!""""""!!! !!!""" !!! !!!"""!!!!!!!!!!!!!!!!!!!!! """###!!!444444333333222222222222444222111222333333222111111222333444444444444444///111444666666555333222222222222222222222222222111111000//////000111111/////////......------,,,---......///000/////////......------,,,,,,,,,,,,,,,,,,------------,,,,,,+++,,,,,,,,,,,,,,,,,,---,,,+++*********+++,,,,,,,,,,,,,,,++++++,,,,,,,,,---------------......///.........------.........++++++++++++,,,...///000,,,---------,,,---...///...........................------,,,,,,------...++++++***************++++++***)))))))))+++,,,---((()))***---//////---+++)))***+++,,,---,,,+++***))))))))))))))))))))))))))))))***+++++++++******))))))(((((()))******+++,,,,,,,,,+++***)))((('''(((((((((((((((((((((((((((***+++***)))((()))***((((((''''''''''''((((((((((((((((((((((((((((((''''''&&&&&&&&&''''''((())))))((('''&&&&&&%%%%%%''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&%%%%%%$$$$$$$$$######$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''###$$$%%%&&&''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&%%%%%%$$$######""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!! !!!""""""!!! !!!""" !!! !!!"""!!!!!!!!!!!!!!!!!!!!! """###!!!666555444333222222222333444333222222333333222111111222333444444555555444000111333555555555444333333222222111111222222333111000///......///000111111111111111000///.........//////000000000000000............---------,,,,,,,,,------------,,,,,,***,,,------++++++,,,...,,,,,,+++******+++---...,,,,,,++++++++++++,,,,,,...------------...///000///...------------...///++++++++++++,,,---...///***,,,---,,,,,,,,,...000------------------------------,,,,,,,,,,,,------,,,+++******)))*********))))))(((((((((***+++,,,+++***+++---//////...,,,)))***++++++,,,,,,++++++((((((((((((((())))))))))))******+++++++++******))))))))))))******+++,,,((()))***+++++++++++++++))))))))))))))))))))))))(((***+++***)))((()))***((((((''''''''''''(((((())))))))))))))))))))))))(((''''''''''''((()))))))))((((((((('''&&&&&&&&&'''''''''''''''(((((((((&&&&&&''''''''''''&&&&&&'''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%$$$$$$######$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%&&&''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%&&&''''''''''''###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!  !!!!!!  !!! !!! !!!!!!!!!!!! !!!!!!!!!!!! !!!"""  777666555444333333333444555333222222333333222111111222333444555555555555000111222333444444444444333333222111111222333333111000///......///000111222333333333222111/////////000000111111111111111////////////......------+++,,,,,,------,,,,,,+++))),,,------++++++---///---,,,+++***+++,,,...///,,,,,,++++++++++++,,,,,,------,,,,,,,,,---...//////...------------...///------,,,,,,---...//////,,,...///...,,,,,,...000,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,,,,++++++***))))))*********))))))))))))+++---...000...------......---+++))))))(((((())))))***+++(((((()))))))))***************+++++++++******))))))))))))******+++------(((((()))++++++,,,,,,+++))))))))))))))))))))))))(((***+++***)))((()))***((((((''''''''''''(((((())))))))))))))))))))))))((((((((((((((()))******((((((((((((''''''''''''&&&'''''''''((((((((()))&&&&&&''''''''''''&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''&&&%%%%%%$$$######$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&'''(((&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&'''''''''((('''&&&&&&%%%%%%&&&&&&'''%%%%%%&&&&&&'''&&&&&&&&&######$$$%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!   !!!   !!! !!! 888777555444333333444444555444222333333444222111111222333444555555555555000000111111222333444444444333222111111222333444222000///......///000222222222333333222111///...000000111222222222222222//////000000//////...---+++,,,,,,------,,,,,,+++)))+++...---++++++---///...---+++++++++---///000,,,++++++++++++++++++,,,---,,,+++***+++,,,---...///...---,,,,,,---...//////............///000000///111111000,,,+++---000,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++******++++++,,,,,,,,,+++***))))))******,,,,,,++++++,,,...///000444111///------,,,+++)))((('''&&&&&&&&&''')))***))))))******+++++++++,,,******+++++++++******)))************+++,,,---...+++++++++++++++***)))((())))))))))))))))))))))))(((***+++***)))((()))***((((((''''''''''''(((((()))))))))))))))))))))))))))))))))))))))***++++++'''''''''(((((((((((((((&&&'''''''''(((((())))))&&&''''''''''''''''''&&&'''&&&&&&%%%%%%&&&&&&'''''''''&&&%%%%%%$$$######%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$%%%&&&'''(((&&&&&&''''''''''''&&&&&&&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&'''&&&&&&%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%&&&"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!! !!!  !!!  !!!!!!  !!! !!!  """ 444555777888777555222000111222222333444555666666222333555666666555333222111222222333333222222111222333333444444333333222666222...---000222333222...000111222111000111222000000////////////000000111...,,,///333444000,,,)))***++++++------...///.........------,,,,,,,,,+++,,,------......------,,,,,,,,,---------......---------.........//////...............///000000......////////////............------------......,,,------......------,,,///...,,,+++***)))))))))---,,,++++++,,,,,,+++)))))))))***+++,,,...000111222111...,,,+++******+++))))))))))))************++++++***************+++++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,---***+++,,,+++)))((()))+++---+++)))***,,,,,,)))'''))))))(((((((((((())))))************))))))))))))+++******)))(((''''''&&&)))************+++++++++((((((((((((((((((((((((''''''''''''''''''''''''''''''((((((((((((''''''(((((('''&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%''''''''''''''''''''''''((((((''''''''''''(((((((((((('''&&&'''((()))***''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$$$$%%%%%%######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''%%%%%%$$$###""""""###############"""!!! """""""""""""""""""""""" !!!!!!""""""!!!!!!  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!######"""!!! """!!!  !!! !!!"""!!!  !!!  """%%%'''333444666777666555222000333333333444555555666666222333555666666555333222222222333333333333222222222333333444444333333222555222///...111222222111...000222222111000111222111111000000000000111111111...---///222333000,,,+++++++++,,,,,,------...------------------,,,,,,+++,,,------......------++++++,,,---...///000000------------.........///...............///000000......////////////......000//////......//////000---------......------------,,,,,,+++++++++++++++---+++******+++,,,***)))***************+++,,,,,,///...---,,,+++*********))))))))))))*********+++++++++************++++++++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,(((***++++++)))(((((())),,,+++)))***,,,,,,***'''((((((''''''''''''((((((************)))))))))))))))))))))(((''''''&&&&&&))))))*********+++++++++((((((((((((((((((((((((''''''''''''''''''''''''''''''((((((((((((''''''(((''''''&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((''''''''''''''''''(((((('''&&&&&&&&&'''))))))((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''%%%$$$$$$###""""""######$$$$$$###""""""!!! """""""""""""""""""""""" !!!!!!!!!!!!!!!!!!!!!  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""""""""!!! !!!!!!  !!! !!!!!!"""!!!!!!  """###333444666777777555333222555555555555555555555555333444555666666555444333222222333333333333222222222333333444444333333222222111000000222222222000...000222222111000111222222222111111111111222222111///---///222222000,,,,,,,,,,,,,,,,,,,,,,,,---,,,,,,------------------,,,,,,---............---)))******,,,---...///000------------...........................///000000........................111000000//////000000111------------------------+++++++++++++++,,,---...,,,+++******++++++***(((+++***)))(((((((((((((((++++++,,,,,,++++++******))))))*********+++++++++++++++************++++++++++++,,,,,,,,,,,,------......------,,,,,,++++++(((+++------+++***)))))),,,+++***+++,,,,,,***(((((((((''''''''''''((((((************)))))))))))))))((((((''''''&&&&&&%%%)))))))))*********++++++((((((((((((((((((((((((''''''''''''''''''''''''''''''(((((((((((('''''''''''''''&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&'''''''''&&&&&&&&&&&&'''(((((()))))))))((((((((('''''''''''''''''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''%%%$$$######"""#########$$$$$$$$$###""""""!!!!!!""""""""""""""""""""""""!!!!!!!!!!!!!!!   !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!     !!!!!!""""""!!! 444555666777888777666555666666666555555444444444444444555555555555444444222333333333333333333222222333333444444333333222000111111222333222111000///000222222111111111222222111111000000111111222111000...///111111///---......------,,,,,,,,,,,,,,,,,,,,,------.........,,,------...............)))******++++++,,,,,,,,,------------------------...............///000000......------------......111000000//////000000111......------------......,,,,,,,,,,,,,,,---......,,,***))))))***+++)))(((+++***)))((((((((((((((()))***,,,---------,,,+++*********+++++++++,,,,,,++++++*********+++,,,,,,+++++++++,,,,,,,,,------//////...---,,,++++++***+++---000111000---++++++++++++++++++,,,,,,+++***))))))(((((((((((())))))************)))))))))((())))))((((((''''''''''''))))))))))))************((((((((((((((((((((((((''''''''''''''''''''''''''''''((((((((((((''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&''''''((()))))))))(((((((((''''''(((((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$###############$$$$$$$$$$$$$$$######""""""!!!!!!!!!!!!!!!!!!!!!!!!""""""!!!!!! !!!!!! !!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!""""""!!!     !!!!!!!!! !!!""" 666777888888888888777777666666666555444444333333555555555555555555555555333333333444444333333333222333333444444333333222///111222333333222000000///111222333222111222333000000////////////000000222000/////////000///...///......------,,,,,,+++,,,,,,,,,------.........,,,---......//////...............---,,,,,,++++++------------------,,,,,,...............///000000///...------------...///000//////......//////000///......------......//////...------,,,,,,------,,,+++******++++++***(((******)))))))))***++++++)))***,,,............---++++++++++++,,,,,,,,,,,,++++++******+++,,,,,,---+++++++++,,,,,,,,,------//////...------,,,+++++++++...111222000...,,,,,,***+++,,,,,,,,,+++++++++++++++************++++++************)))))))))(((*********)))))))))))))))(((((()))))))))*********((((((((((((((((((((((((((((((((((((((((((((((((''''''((((((((((((''''''&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&'''''''''''''''((((((((('''''''''&&&&&&(((((())))))(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$###############$$$$$$$$$$$$$$$###############!!!!!!!!!!!!!!!!!!!!!!!!""""""!!!!!! """!!!!!! !!!!!!""" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!"""""""""  !!!  ###$$$"""777888888888888888777777555555555444444333333333555555555555555555555555333333444444444444333333222333333444444333333222///111333333222111000111///111333333222111222333000000////////////000000222111000///....../////////.........------,,,,,,,,,,,,------------------------...////////////...444333222111000///...---------------,,,,,,,,,,,,...............///000000000///...------...///000000//////......//////000000///...------...///000000///...------------------,,,***+++,,,,,,+++))))))))))))***+++,,,---...++++++,,,---............++++++,,,,,,,,,---------++++++***++++++,,,---...++++++,,,,,,,,,,,,------//////......------,,,,,,***---//////---+++++++++)))+++------,,,+++,,,---,,,,,,++++++++++++,,,,,,************))))))))))))************************((((((((()))))))))******((((((((((((((((((((((((((((((((((((((((((((((((''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''&&&'''(((((())))))((((((((((((((('''''''''&&&&&&(((((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########"""######$$$%%%########################""""""""""""""""""""""""!!!!!!!!!!!!!!! !!!!!! !!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!""""""  !!!!!! !!!!!!  ######"""777777777777666555555555333333333333333222222222666666555555555555666666333333444444444444333333222333333444444333333222///111333333111000111222///111333333222222222333111000000000000000000111222222111///...---...///...............---------------------------,,,,,,------...///////////////333333222111000//////...---------,,,,,,,,,++++++...............///000000222111///......///111222111000000//////000000111000///...------...///000..................///000...---,,,,,,------,,,***************+++,,,------++++++++++++,,,---......,,,,,,,,,,,,------------++++++++++++,,,---......++++++,,,,,,,,,,,,------...............---------+++---......,,,++++++,,,)))+++------,,,+++,,,...,,,++++++******++++++,,,************)))))))))))))))))))))))))))*********(((((((((((()))))))))***((((((((((((((((((((((((((((((((((((((((((((((((''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((''''''''''''''''''((('''((()))*********)))((()))))))))((((((((('''''''''(((((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))((('''%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######""""""###$$$$$$%%%"""""""""""""""""""""""""""""""""""""""""""""""" !!!!!!!!!!!!!!!!!!  !!! !!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!! !!!!!! !!!!!! !!!!!!777777666555444333333222222222222222222222222222666666555555555555666666333444444555555444444333222333333444444333333222000222333222000///111333000111333333222222222333222222111111111111222222222222111///------...000.................................------,,,,,,,,,---......///////////////////////////............---------,,,,,,+++++++++...............///000000222111000......000111222222222111111111111222222111///...------...///111,,,---------///000111222///---,,,,,,---...,,,+++******************+++,,,,,,+++***)))***+++---...,,,,,,,,,---------......++++++++++++,,,---...///++++++,,,,,,,,,------------------..................//////...---,,,---...(((+++......,,,+++,,,...++++++************++++++************))))))))))))(((((((((((())))))))))))(((((((((((())))))))))))(((((((((((((((((((((((())))))))))))))))))))))))''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((()))''''''''''''''''''''''''((((((''''''''''''(((((('''(((***+++++++++***)))************))))))))))))'''''''''''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))'''%%%$$$######$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######""""""###$$$%%%%%%!!!!!!!!!!!!!!!""""""""""""""""""""""""""""""""" !!!!!!""""""   !!!!!! !!!!!!!!!"""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!"""!!!!!!!!! !!! 444444444444333222111000444444444444444444444444555444444333333444444555333333333444444444555555888666444222111000111111222222222222222222222222333333222222333333444555555444333222111111111111000000000000000//////...,,,---------....../////////............---------***++++++,,,,,,------...,,,------......------,,,,,,,,,+++***+++,,,---...111...++++++,,,...000000000111111///......///111000000000000////////////000000//////.........---//////.........---------******+++,,,,,,***)))(((******)))))))))))))))***************************,,,,,,,,,,,,,,,,,,,,,,,,...---,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---......///.........000///---,,,,,,---...///...---,,,,,,++++++++++++++++++************++++++)))))))))))))))******+++((()))*********)))'''&&&))))))))))))))))))))))))******))))))))))))))))))************************((((((((('''&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''&&&&&&&&&''''''''''''((())))))))))))))))))))))))(((''''''''''''(((((()))------,,,+++***)))((((((&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%(((((('''&&&%%%%%%$$$$$$############$$$%%%&&&'''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""""""""!!!!!!!!!!!!""""""###############"""!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!  !!!!!! !!!!!!!!!!!!!!!!!!  !!!!!!!!!!!!!!!!!!!!!!!!""""""!!!!!!    777777777777666555444333555444444444444444444555555444444333333444444555444444444444555555666666777666444222111111111222333333333333333333333333333333222222333333444555555444333222222111111111000000000000000//////...,,,,,,---------.........///............---------......---,,,,,,++++++***+++,,,,,,------,,,,,,+++------,,,++++++,,,---...///...,,,+++,,,,,,+++***+++---//////......///000000000000000////////////000/////////............//////.........---------+++++++++++++++******)))+++******))))))*********+++++++++,,,,,,,,,---------------,,,,,,,,,,,,,,,------,,,+++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,+++,,,---...////////////000///---,,,,,,---...///...---,,,,,,++++++,,,,,,++++++************++++++)))))))))))))))******+++''''''((()))******))))))))))))))))))))))))))))))************************************************''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''(((''''''''''''((())))))+++++++++***))))))((((((&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&%%%$$$###############$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""######""""""""""""######"""############"""!!!!!! !!!!!!!!!!!!!!! !!!"""!!!  !!!!!! !!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""!!!!!!!!!    888888888888777666555555666555444333333444555666555444444333333444444555333333333444444444444555555444333222222222222333333333333333333333333333333333222222333333444555555555444444333222222222000000111111000000///...------------............///............---------......------,,,+++++++++++++++,,,,,,,,,,,,++++++......------,,,------.........---------***%%%"""$$$(((---///000///......////////////000000000000////////////............/////////............------,,,++++++******++++++,,,++++++******++++++,,,+++,,,,,,---...//////000------------------------,,,,,,+++************+++------------------------***+++,,,......////////////...---,,,,,,---...///...---,,,,,,,,,,,,,,,,,,++++++************++++++)))))))))))))))******+++'''''''''((()))***,,,,,,))))))))))))))))))))))))************************************************''''''''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''&&&&&&&&&''''''''''''((('''''''''''''''''''''''''''''''''''''''((())))))))))))))))))))))))((((((&&&&&&&&&'''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&(((((('''&&&$$$"""$$$$$$$$$###$$$$$$%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""$$$######""""""######$$$""""""######""""""!!!  !!!!!!"""""" !!!"""!!!  !!!!!!!!! !!!!!!!!!!!!!!!!!!""""""!!!!!! """"""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!! 777777777777777666555444777666555444444555666777555444444333333444444555222222222222222222222333333333333333333333333444444444444444444444444444333333222222333333444555555555555555444333333222000111111111111000/////////////////////////////////............---------++++++,,,,,,---.........+++,,,,,,------,,,,,,+++//////......------------...//////000...)))""" %%%,,,111222000///...////////////000000000000///////////////........./////////..................---,,,******+++,,,,,,,,,,,,+++++++++,,,------***+++,,,---...///000111---------...............,,,+++******))))))******------------------------,,,,,,---.........------......---------...//////...------,,,,,,,,,------,,,++++++******++++++,,,)))))))))))))))******+++)))(((''''''(((***+++---))))))))))))))))))))))))************++++++++++++************************&&&&&&''''''(((((())))))''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&''''''((('''''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''&&&''''''((()))***''''''''''''(((((())))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&((()))(((&&&$$$"""%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""######""""""""""""######"""""""""""""""!!!!!!  !!!"""###### !!!"""!!! !!! !!!!!!!!!!!! !!!!!!!!!!!! !!!"""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!  !!! !!!!!!!!! 777777777888777777666666777666555555555555666777555444444333333444444555444444444444333333333333222222333333333444333333444444444444444444444444333333222222333333444555444444555555555444333222111111111111111000000///111111000000000000000000///............---------+++,,,,,,------...//////------............------.....................---///000111222000+++###!!!&&&---222333222111000.../////////000000000111.........//////////////////////////////////////////...,,,+++++++++,,,---,,,,,,++++++,,,------...)))***+++,,,---...//////---------.........//////,,,+++******))))))******------------------------............---,,,+++***------------......//////---------,,,,,,---......,,,,,,++++++++++++,,,,,,)))))))))))))))******++++++***)))(((((()))***+++))))))))))))))))))))))))))))))*********+++++++++))))))))))))))))))))))))&&&''''''(((((()))))))))''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&''''''((('''''''''&&&&&&&&&''''''''''''(((((((((((((((((((((((((((&&&&&&&&&''''''(((******&&&&&&&&&'''(((((())))))'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%'''))))))'''$$$"""%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""!!!!!! !!!!!!"""""""""""""""!!!  !!!"""######!!!"""""""""  !!! !!!!!!!!!"""""" !!!!!!!!!"""""" !!!"""""""""""""""!!! !!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!  888999999::::::999888888666777777777777777777666555444444333333444444555777666666666666666555555222222333444444444333333333333333333333333333333333333222222333333444555222333444555555444333222111111222222111111000///111111111111000000000000///............---------//////......---,,,,,,,,,......////////////......,,,,,,---...............//////000111000---'''"""%%%)))...111222111111222......//////000000111111.........///////////////...////////////000000000......------,,,,,,------++++++++++++,,,---......))))))***+++,,,------...,,,,,,,,,---......//////,,,,,,+++************+++,,,,,,,,,,,,,,,,,,,,,,,,------...------,,,+++***,,,,,,---....../////////------------------...///,,,,,,++++++++++++,,,,,,)))))))))))))))******+++,,,+++***)))))))))))))))))))))))))))))))))))))))((((((((()))******++++++))))))))))))))))))))))))(((((((((((((((((())))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''&&&&&&&&&''''''''''''((())))))))))))))))))))))))&&&&&&&&&'''''')))***+++&&&'''''''''(((((())))))'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%'''(((((('''%%%$$$$$$$$$$$$###$$$$$$%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""!!!  !!!!!!!!!""""""!!!!!!  !!!!!!""""""!!!"""###"""  !!! !!!!!!!!!""""""""" !!!!!!!!!"""""""""!!!!!!!!!""""""!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!!!!!!! 888888999999999999888888555666888999999888666555555444444333333444444555666666666555555444444444222333444444444333222111333333333333333333333333333333222222333333444555111222333444444333222111111222222222222111000000000000000/////////......///............---------/////////...------,,,,,,---..................---)))***,,,---...............------...///...+++((()))+++.../////////111222.........///000111111111............/////////000.../////////000000000000...............---,,,,,,************+++,,,---...******++++++,,,,,,,,,---+++++++++,,,---.........------,,,+++++++++++++++++++++++++++++++++++++++***+++,,,---------------+++,,,---...////////////---------------...//////---,,,,,,++++++,,,,,,---)))))))))))))))******+++))))))***+++++++++******))))))))))))))))))))))))&&&''''''((())))))******)))))))))))))))))))))))))))))))))(((((((((((((((''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''&&&&&&&&&''''''''''''(((((((((((((((((((((((((((&&&&&&&&&&&&((()))***+++(((((((((((((((((())))))(((((('''''''''&&&&&&&&&''''''''''''''''''''''''%%%%%%&&&''''''&&&&&&%%%############$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""!!!!!! !!!!!!!!!!!!""""""!!!!!!  !!!!!!!!!!!!!!!!!!"""###""" """ !!!!!!!!!"""""""""""" !!!!!!!!!""""""""""""!!!!!!!!!!!!!!!  !!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!!!!!!!  !!!!!!!!!!!!!!!!!!  555666666777777777666666555666999::::::999666555555444444333333444444555333333333222222111111111333333444555444333222111222222222222222222222222333333222222333333444555000111333444444333111000111222222222222111000000//////......---------,,,//////.........---------,,,,,,------...//////000,,,------......------,,,'''(((+++---............,,,++++++,,,---...---+++,,,---...---------000222---......///000111111222---.........//////000000.../////////000000111111---.../////////...,,,+++************+++,,,---...,,,,,,,,,,,,,,,,,,,,,,,,******+++,,,,,,---.........---,,,,,,++++++,,,,,,************************((((((***,,,---...//////+++,,,---...////////////---------------...///000---,,,,,,++++++,,,,,,---)))))))))))))))******+++&&&((()))+++,,,,,,,,,+++))))))))))))))))))))))))%%%&&&&&&'''((())))))***))))))))))))))))))))))))******))))))((((((''''''((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''%%%%%%&&&&&&((()))***+++)))))))))))))))))))))((((((((('''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&############$$$%%%&&&'''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""""""""!!!!!!!!!!!!""""""!!!!!!!!!!!!!!! !!!!!!!!!!!!!!! !!!"""###"""!!! !!!"""!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!""""""""""""!!!!!!!!!!!! """"""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!""""""""""""""""""!!!   777777888888777666444333999888888888999999888666666666555555555444444444444333222222111111111111111222444555555444333111333333333333333333333333000222444555555222000...111111111111111222222222222111111111333333333222000000////////////000000111000000///...,,,+++***..................------......---,,,,,,,,,------000...,,,---000000---+++.........///////////////////////////////////////------...///000111222222000000000000111111111111000///...///000111000///***+++---//////...---,,,---,,,+++***+++---000111.........------,,,,,,,,,,,,,,,------...////////////...---,,,,,,,,,,,,,,,***)))((('''&&&&&&'''(((((()))***+++,,,------------------............//////////////////......---...------,,,,,,++++++***)))))))))))))))*********((()))***++++++***)))((())))))******)))((('''&&&'''&&&&&&&&&'''(((***+++***))))))((((((((((((((())))))(((((('''''''''&&&************)))))))))))))))((('''&&&%%%&&&&&&'''''''''''''''''''''''''''(((''''''''''''&&&&&&&&&))))))((('''''''''''''''''''''((()))******))))))))))))))))))(((((((((((())))))((('''''''''''''''''''''''''''''''''''''''###%%%&&&&&&%%%$$$%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&%%%%%%$$$###&&&$$$"""!!! !!!"""###""""""""""""""""""""""""$$$#########""""""!!!!!!######""""""!!!!!! """""""""""""""""""""""""""""""""""""""""""""""" !!!""""""######"""  !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!! !!!!!!""""""""""""!!!!!!""""""!!!   777888888999888777555444888888888888999999888777666666666555555555444444555444333222222222222333222333444555555444222111333333333333333333333333333444555666555444222111000000111111222222333333222111111111222222222111000000////////////000000111111000000///...,,,,,,..................------,,,,,,,,,,,,---......///---,,,+++---///000///,,,.............../////////////////////////////////......//////000000111111/////////000000000111111111000//////000000///...+++,,,---.........------++++++******+++,,,...///------------,,,,,,,,,+++,,,,,,------...////////////...---,,,,,,,,,,,,---+++***)))'''''''''''''''((()))***+++,,,------------------............//////////////////......---......---,,,,,,++++++***************))))))))))))((()))***++++++***)))((())))))))))))(((((((((((()))(((((('''((()))++++++++++++***)))))))))))))))))))))(((((((((''''''''')))))))))((((((((((((''')))((('''&&&&&&&&&''''''''''''''''''''''''''''''(((''''''''''''&&&&&&&&&))))))((('''''''''''''''''''''((()))))))))(((((((((((((((((())))))))))))))))))((('''''''''''''''''''''''''''''''''''''''###%%%'''&&&%%%$$$%%%&&&###$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$###%%%$$$""" !!!"""###""""""""""""""""""""""""############"""""""""!!!###"""""""""!!!!!!!!! """"""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!"""###"""!!!  !!!!!!!!!!!!!!!!!!!!! !!!!!!""""""""""""!!!!!!"""!!!!!!  888999999999999777666555777777888888999888888777666666666666555555555555555555444444333444444444333444555555555333222111333333333333333333333333555555555555555555444444000000111222222333444444111111111111111111111111000000000000000000000000000000111111000//////...------------------......+++++++++,,,---...000111*********,,,///000///...---------.........//////////////////////////////////////////000000000000....../////////000000000222000//////000000///---,,,------------.........*********+++,,,,,,------,,,,,,,,,,,,++++++++++++,,,,,,,,,---......//////......---,,,,,,,,,---------,,,+++)))((('''''''''((()))***,,,---------------------............//////////////////......---......------,,,++++++++++++++++++***)))))))))((())))))************))))))))))))(((''''''(((************)))))))))***++++++,,,++++++***************))))))((((((((((((''''''(((((((((((('''''''''''')))(((''''''&&&&&&''''''''''''''''''''''''''''''(((''''''''''''&&&&&&&&&)))((((((''''''''''''(((''''''((((((((('''&&&&&&''''''(((((())))))******))))))((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%''''''%%%$$$%%%&&&$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$###!!! !!!"""""""""""""""""""""""""""############""""""""""""""""""""""""!!!!!!!!!!!!""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!  !!!""""""!!!   !!!!!!!!!"""""""""!!!!!!!!! !!!!!!""""""!!!!!! !!!!!!!!!  999999::::::999888666555666777888999888777888888777777777666666666555555666666555555555555555666555555555555444333111111333333333333333333333333666555444444333444555666000111111222333444555555333333444333111111111111000000000111111000000000...//////000000000//////,,,,,,------------......---------------...///000***++++++---............,,,,,,------......//////////////////////////////111000000000/////////...............////////////222111//////000000...---...------------...//////***+++,,,------------,,,+++++++++++++++++++++++++++,,,,,,------...//////...------,,,,,,,,,------///...---+++)))(((''''''))))))+++,,,---.........---------............//////////////////......---.........---,,,,,,++++++,,,,,,++++++***)))(((((()))))))))******))))))))))))((('''&&&'''(((+++,,,+++*********))))))******++++++***))))))))))))***))))))(((((((((((((((((())))))((((((((('''''''''((((((''''''''''''''''''''''''''''''''''''''''''(((''''''''''''&&&&&&&&&)))(((''''''''''''(((((('''((((((((('''&&&%%%%%%&&&&&&'''((()))***++++++))))))((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&''''''&&&%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$""""""!!! !!!!!!"""""""""""""""""""""""""""#########"""""""""""""""""""""""""""!!!!!!!!!!!!""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!!!!   !!!!!!""""""""""""!!!!!!!!!!!! !!!!!!!!!!!!!!!!!! !!!!!!   999999::::::999888666555444666888999777666888999888888777777777666666666666666666555555666777777666666555555444333222111333333333333333333333333555444222111111333444555111222222333444444555555555666777555333111222333000000111111111111000000------.../////////......,,,,,,,,,,,,------......000///......------------,,,---......------,,,,,,,,,,,,------...//////000////////////////////////111111000000//////..................////////////222000//////000000///---......---------...///000,,,---......///......---++++++++++++++++++++++++++++++,,,,,,---.........------,,,,,,,,,------...//////...---+++***(((((()))***+++,,,---.........---------............//////////////////......---//////...------,,,,,,+++---,,,,,,+++***))))))(((***))))))))))))))))))***)))((('''&&&'''(((+++,,,))))))))))))))))))((((((******)))(((((((((((()))(((((())))))))))))))))))*********)))))))))((((((''''''(((((((((((((((((((((((((((((((((((((((((((((''''''''''''&&&&&&&&&((((((''''''''''''(((((('''((((((((('''&&&%%%%%%%%%&&&'''((()))***+++,,,))))))((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&((('''&&&%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%%%%""""""!!!!!!!!!"""""""""""""""""""""""""""""""""""""""""""""""""""######!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!   """"""""""""!!!!!!!!!!!! !!!!!!!!!!!! !!!  !!! 888999999999999777666555333666999999666666777:::888888888888777777777777666666555555666666777777666666555555444444333333333333333333333333333333333222111000111222333444333333444444444444555555666888999777333111222444///000111222222111000///------...............---++++++,,,,,,------......111111///...------,,,,,,---///000///...,,,,,,---,,,------...///000111111////////////////////////111111000000//////............/////////000000000000///...///000111000///------........./////////.............../////////++++++++++++,,,,,,,,,,,,+++++++++,,,------......------,,,,,,,,,---......////////////---,,,***))))))***+++---............---------............//////////////////......---//////......---,,,,,,,,,,,,,,,,,,+++*********)))******))))))))))))******))))))(((''''''(((******(((((()))******))))))(((***))))))((((((((((((((((((((())))))))))))******************))))))))))))''''''((()))))))))(((((((((((((((((((((((((((((((((''''''''''''&&&&&&&&&(((''''''''''''(((((()))''''''((((((((('''&&&&&&&&&&&&'''((()))***++++++))))))((('''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&((((((&&&%%%&&&'''%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''$$$$$$%%%&&&&&&&&&%%%%%%""""""""""""############""""""""""""""""""""""""""""""""""""############!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!  !!!    """""""""!!!!!!!!!  !!!!!!    777888888999888777555444222555999999666555777:::999999888888888777777777555555555555555666777777555555555444444444555555333333333333333333333333111111111111111222333333555555555555444444444444666888:::777222///111333///000222333333222000///....../////////......---***++++++,,,------......111000///......---......,,,///111000///...///000------...///000111222333////////////////////////000000000000/////////////////////000000000111111///...---...000222111000,,,---///000000//////...///...------------...///+++,,,,,,,,,------------***++++++,,,,,,---......,,,,,,,,,,,,,,,---.../////////000000///---,,,+++)))***,,,---......//////---------............//////////////////......---/////////...------,,,,,,+++++++++++++++++++++++++++***)))(((((()))***+++))))))))))))(((((((((((('''(((***++++++++++++***+++***))))))(((((())))))(((((()))))))))************))))))))))))(((((((((&&&'''((()))***))))))((((((((((((((((((((((((((((((''''''''''''&&&&&&&&&'''''''''''''''((())))))''''''((()))))))))((((((&&&''''''((()))******+++))))))((('''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%'''(((((('''&&&&&&'''%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&'''''''''(((###$$$%%%%%%&&&&&&&&&%%%""""""###$$$$$$$$$$$$$$$""""""""""""""""""""""""!!!"""""""""############ !!!!!!!!!"""""""""###!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!  !!!!!!  !!!!!!!!!  !!!!!!      777777888888777666444333111555999999666555777;;;999999999888888888888777555555555555555666777777555555444444444555555666333333333333333333333333111111111222222333333333666666666555444444333333555888:::777111...000333///000222333333222000///000000000000000///......******+++,,,,,,---......//////.........//////000+++...111111000///111333......///000111222333333////////////////////////////////////000000000000000000000000111111111111...------...111222222111,,,---///111111000...---///...,,,++++++,,,---///,,,,,,,,,------.........***++++++,,,,,,---......,,,,,,,,,,,,,,,---.../////////000000000...---,,,******,,,---.../////////---------........./////////////////////......---/////////...------,,,,,,++++++++++++++++++,,,,,,+++***)))(((((()))***+++))))))******)))((('''&&&((()))***,,,------,,,,,,,,,++++++***)))*********(((((())))))*********+++)))(((((((((''''''''''''&&&'''(((*********)))((())))))))))))))))))))))))(((((('''''''''&&&&&&&&&'''''''''''''''((()))***''''''((()))*********)))''''''(((((())))))******))))))((('''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%'''(((((('''&&&&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((###$$$%%%%%%&&&&&&&&&&&&"""###$$$%%%%%%%%%%%%%%%""""""""""""""""""""""""!!!!!!""""""#########$$$ !!!!!!!!!""""""######!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!! !!!!!!"""  !!!     !!!!!!!!!  !!!!!!   !!!!!! 777777777777777666555555888;;;>>>>>><<<999777666777777888999999999999888555666777888888777666666777777777777888888888888888888777777666444333222444444333222222222333333555666888888777666666777555444444333333222222111111222222333333222222111000000111222333111---***,,,,,,---.../////////...---------------------,,,000///...------...///000+++,,,...///000000000000111000...------...///000000111111000//////000222//////------...000222444///000111222222111000///////////////............------------------------,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,++++++,,,,,,***,,,...///000///...---------,,,,,,,,,,,,------...---------...///111222///...,,,++++++,,,---///------............------,,,------......------,,,///...---,,,++++++++++++(((((()))***++++++,,,,,,******))))))))))))******(((((()))***++++++,,,,,,************************''')))******))))))***+++((())))))(((&&&&&&'''((())))))))))))(((((((((((()))******)))(((''''''(((***)))'''&&&&&&&&&'''(((***)))'''&&&'''(((***,,,************************((()))***++++++,,,+++++++++***((('''&&&&&&&&&'''***)))((('''%%%$$$###"""%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%(((''''''''''''&&&&&&&&&%%%$$$$$$######$$$$$$%%%############""""""!!!!!!$$$$$$$$$###"""!!!!!! ######""""""!!!!!! !!!"""""""""!!!  !!!    """"""""""""""""""""""""!!!!!!     !!!!!!!!!   888888999999888777777666888:::======;;;888777666777777888999999999999999777777888999999888777666666666666777777777888888777777777777666555444333333333333222222333444444555666888777666555555666555555444333333222222111222222333333333333222222111000000111222111...+++------.../////////......------..................000///...------...///000.........//////////////////000000//////......---000111111111//////000222//////...---...000222333///000111111111111000///////////////............------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,------...+++---...///000///------......------------......---------......///000111///...,,,++++++,,,.../////////000000000000//////++++++,,,,,,,,,,,,++++++///...---,,,++++++++++++)))))))))***++++++,,,,,,******))))))))))))******)))******+++,,,,,,------+++******************+++''')))******))))))***+++))))))***((('''&&&((()))))))))))))))(((((((((((()))******)))((('''''')))***)))((((((''''''(((((()))((('''''''''(((***+++************************(((((()))***+++++++++++++++***((('''&&&&&&'''''''''''''''&&&&&&%%%%%%$$$%%%&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$######"""""""""$$$$$$######"""!!!!!! ###"""""""""!!!!!!!!! !!!"""""""""!!!  !!! !!!!!!  !!!!!!!!!!!!!!!!!!!!!!!!   !!!!!!!!!!!!!!!    999999999:::999999888777777999<<<<<<:::777666666777888888999999999999999999999:::::::::999777666555555555666666666666777555555666666666666555555222222222222333444444555555666777777555444444444555555444444333222222222222222333333333333222222222111000000000000///---...////////////......------------...//////000000//////............//////111000///........./////////000111222111///,,,***///111222111000///000222//////.........000111222///000000111111000000///////////////............------------------------,,,,,,,,,,,,,,,,,,,,,,,,******++++++,,,...///000---.../////////...---,,,///..................///,,,---...///000000000000......---,,,,,,---.../////////000000000000////////////000000000000//////......---,,,++++++++++++))))))******+++,,,,,,,,,******))))))))))))************++++++,,,---------+++***)))(((((()))***+++''')))******))))))***+++***++++++***(((''')))***(((((((((((())))))))))))((()))***)))((('''((()))))))))******))))))((('''(((((((((((())))))))))))************************'''((()))***++++++++++++******)))(((''''''''''''%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$$$$$$$######$$$$$$######"""!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!"""!!!   !!! !!!!!!""""""  !!!!!!!!!!!!!!!!!!!!!!!!     !!!!!!!!!"""""""""!!!!!!!!!  888999999999999999888888777999;;;;;;999777666666777888999999::::::999999:::::::::::::::888666555444444444555555555666666444444555666666777666666111111111222333444555666555666777666444333333333555555555444333333222222222333333333333333333222444111/////////000000///000000000000000///...---,,,,,,------...///000000/////////....../////////222000///------...000111111111222111000...,,,+++///000222111000///000111//////......///000111222///000000000000000000///////////////....................................------,,,,,,,,,,,,+++++++++++++++,,,,,,...//////.../////////...---,,,+++//////............//////,,,---///000000000///......------------......///------............------000111111222222111111000...---,,,,,,+++++++++,,,*********++++++,,,,,,,,,+++******))))))******+++*********++++++,,,,,,,,,+++***)))(((((()))***+++''')))******))))))***+++++++++,,,***)))((()))+++(((((((((((())))))))))))((()))***)))((('''((())))))***+++++++++***((('''''''''((()))***)))))))))************************'''((()))***++++++++++++***))))))(((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&'''((((((&&&&&&&&&%%%%%%%%%%%%$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%############""""""!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!   !!! !!!""""""""" !!!!!!!!!!!!!!!  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!    !!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!  !!!!!! 777777888888999888888777777888::::::888777777777888888999::::::::::::999999999::::::999777555444444444444444555555555555333444555666777777777777111111111222333444555666444666777666444333333444666666555444444333333222333333333444444333333333444222///...///111111111111111111111000///......++++++,,,---...//////000...//////////////////...000///...---...000222444444333111///...---.........000222222111000000000///////////////000000000000//////////////////000////////////....................................---------,,,,,,+++++++++...------,,,,,,---------/////////......---,,,,,,//////............//////,,,---///000000000///...------------......//////------............------,,,,,,------------,,,,,,------,,,+++++++++,,,,,,+++++++++++++++,,,,,,,,,++++++************++++++))))))))))))******************)))(((((()))******''')))******))))))***++++++,,,,,,+++))))))***+++'''((((((((()))))))))***''')))***)))((('''(((***)))***+++++++++***((('''''''''((()))***)))))))))))))))))))))))))))))))))''''''((()))************)))))))))))))))((((((((((((''''''&&&&&&%%%$$$$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))''''''''''''&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&#########"""""""""""""""!!!!!!!!!!!!"""""""""""""""!!!!!!!!!  !!! !!!"""""""""!!!!!!!!!!!!!!!!!!!!!!!! """"""""""""""""""######!!!!!!!!!!!!!!!!!!!!!!!!     !!!!!!!!!!!!""""""""""""!!!!!!"""""""""!!!  666777888888888888888888777999::::::999888888999888999999:::::::::::::::888888999999999777666555444444444555555555555666444444555666777777666666222222222222333444444555333555777777555444555666666666555555444333333333333333444444444444333333333111//////000111222111000111111111111000000///---------......//////000......////////////..................///111333444555333000...---...///000...000222222111000000000/////////000000000000000000//////......//////000////////////.......................................------,,,,,,++++++***//////...---------------...............---------///..................///......///////////////...---------...//////000000//////000000000000//////,,,,,,------------,,,,,,---,,,,,,++++++,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,++++++************++++++))))))))))))))))))))))))))))))))))))))))))))))))''')))******))))))***++++++,,,,,,***)))(((***+++''''''(((((())))))******'''((())))))(((((()))***))))))******))))))((('''(((((((((((())))))))))))))))))))))))))))))))))))&&&'''((()))************((())))))******))))))((((((((('''&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''(((((((((((('''''''''&&&&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&######""""""""""""""""""!!!!!!!!!!!!""""""""""""""""""!!! !!!  !!!  !!!!!!""""""!!!!!!!!!!!!!!!  !!!!!!!!!!!!  """"""""""""############!!!!!!!!!!!!!!!!!!!!!!!!  !!!  !!!  !!!!!!!!!"""""""""!!!!!!"""###"""!!! 777888888999::::::999999888:::;;;:::999888999;;;888999::::::;;;;;;::::::888888999::::::999888777444555555555555666666666555555666666666666666555333333333222222333444444333555777777666666777888666666666555444444333333333333444444444444333333333111000000111222222111000000111111222222111111000000000000000000111111---...///000000///...---//////000000000111111222222111111000000//////000...000222333111000///000//////000000000000//////000///............///000////////////..........................................---,,,,,,+++******...------------......///...------------......///......------------......//////............//////,,,---...//////000000000//////000000000000//////...//////000000//////...,,,,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++******++++++,,,))))))))))))))))))))))))'''((()))******)))((('''''')))******))))))***+++***++++++***(((((()))+++'''''''''((()))*********&&&((())))))(((((()))+++***)))((((((''''''(((((()))((('''''''''(((***+++))))))))))))))))))))))))&&&'''((()))************((()))************)))(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%&&&'''((('''''''''&&&&&&&&&%%%%%%%%%$$$$$$######$$$$$$%%%###$$$$$$$$$%%%%%%%%%%%%"""""""""""""""""""""### !!!!!!!!!"""""""""######"""!!!  !!!  !!! !!!!!!!!!!!!!!!  !!!""""""!!!  !!!!!!!!!""""""""" !!!!!! !!!!!!  !!!!!!!!! !!!#########""" 888999::::::;;;;;;;;;;;;999:::;;;;;;999999:::<<<888999::::::;;;;;;::::::888999:::;;;;;;;;;:::999555555555666666666666777555666666666666666555555444444333222222222333333222444777777777777888:::666666666555444444333333333444444555555444444333222111000111222333222000///000111222222222222222333333333222222222222222---...///000000///...---000111111111111000/////////000111222222111///...---000222333222000/////////000000000000000///...000///...------...///000000/////////............////////////////////////......---,,,,,,+++******,,,,,,,,,---...///000111---------------...///000---------,,,,,,---------000000...------...///000,,,---...///000000000000------............------,,,,,,------------,,,,,,,,,,,,,,,++++++,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++******++++++,,,++++++******************&&&'''***++++++***'''&&&((()))******))))))***+++***++++++)))(((''')))***&&&''''''((()))******+++&&&((())))))(((((()))+++***)))'''&&&&&&&&&'''(((***)))'''&&&'''(((***,,,))))))))))))))))))))))))&&&'''((()))************((()))***++++++***)))((($$$$$$%%%&&&&&&'''(((((($$$$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$######$$$%%%&&&'''(((&&&&&&&&&%%%%%%%%%$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%#########$$$$$$%%%%%%%%%"""""""""""""""######### !!!!!!!!!""""""#########"""!!! !!!  !!!!!! !!!!!!!!!  !!!""""""!!!   !!!!!!   !!!!!! !!!!!!  !!! !!!###$$$###""" 999999999999999888777666999::::::;;;;;;::::::999<<<<<<<<<<<<;;;999777666999999999999999888777777444555666777999999::::::;;;999666444444555777888:::888666333222222333444555666888777555444444555;;;:::888666555444444555333333444444333333222111111111222333333111000///111111000000111111222333222222222111111111111000.........///////////////---...000111111111000///......//////000000111111///000000000111111111111111111111///------///111333222000///...///000222000000000000////////////------------------------///...---,,,,,,,,,,,,,,,------------------------,,,,,,------...///000000............////////////////////////////////////000000//////.........---......////////////......000000///////////////000...,,,***)))))),,,...000------,,,,,,,,,,,,++++++,,,+++++++++***)))))))))++++++******************+++******+++---,,,)))%%%***************)))(((((((((+++---,,,'''%%%(((+++))))))))))))))))))))))))((('''&&&(((,,,---+++)))***)))(((''''''((()))***))))))))))))))))))))))))***++++++******)))((('''))))))((((((''''''&&&&&&+++******)))(((''''''&&&&&&&&&''''''&&&&&&%%%$$$$$$&&&((((((&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################!!!!!!!!!!!!"""""""""""""""!!!  !!!"""!!!!!! !!!!!!!!!!!!### !!!!!!!!!!!!  !!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!    !!!!!!  !!! 999999999999999888777777999::::::;;;;;;::::::999:::;;;;;;;;;:::888777666888888888888888777777666777888888888888777666666999888666444444555666777777666555333333444555666555666888777666444555555:::999777555444444444444444444444444444333333222222222222222222111000000111111000000111111222333222222222111111111111000////////////////////////......///000000000000///////////////000000111111111111111111222222222222222333222111//////111333333222000///...///000111111111000000000/////////------------------------...------,,,,,,,,,------------------------------,,,,,,------...//////000............////////////........................000000000000/////////.........////////////......000000///////////////000---,,,+++***+++,,,...///------,,,,,,,,,+++++++++++++++******************************************,,,+++***,,,------***&&&***************))))))((((((+++---+++(((&&&(((+++))))))))))))))))))))))))((('''''')))+++---+++)))***)))(((((((((((()))***)))))))))))))))))))))))))))************)))((((((((((((((((((((('''''''''******))))))(((''''''&&&&&&&&&''''''&&&&&&%%%$$$$$$&&&((((((&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################!!!!!!!!!!!!""""""""""""!!!!!! !!!!!!"""!!!  !!!"""!!!!!! !!!!!!  """ !!!!!!!!!!!!  !!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!      999999:::::::::999888888::::::;;;;;;;;;;;;:::::::::;;;;;;<<<;;;:::999888888888888777777777666666888888888888888777666666666666666555555555555555555555444333444555777888555777888888666555555666888777666444333333333444555555555555555444444333333333222222222111111111111111000000111111222333222222222111111111111000////////////////////////...............///000000/////////000000000000111111222222222222333333333444444444222111000222444333222000/////////000111111111111111000000000000---------------------------,,,,,,,,,,,,------...------------------------,,,,,,------.../////////---............/////////........................000000000000000/////////......////////////......//////.........//////000,,,,,,,,,,,,,,,---------,,,,,,,,,,,,++++++++++++))))))******************************************,,,,,,,,,---...---+++)))******++++++******)))((((((+++---+++(((''')))+++))))))))))))))))))))))))((((((((()))+++,,,+++)))***))))))(((((())))))***))))))))))))))))))))))))(((((()))************)))'''((((((((((((((())))))***))))))(((((('''''''''&&&''''''''''''&&&%%%%%%$$$&&&((((((&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$################################################!!!!!!!!!!!!""""""""""""######""""""""""""######!!!!!! !!!!!!!!!!!! !!!!!! !!!!!!!!!!!!  !!!"""!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!      !!!!!!!!!!!!!!!!!!!!!!!!999:::::::::::::::999999::::::;;;;;;;;;;;;::::::;;;;;;<<<======<<<;;;:::888777777666666666666666555555777888888999999999444444555666666555444333666555555444555666777777555777888888666555555666777666444333222333333444666666666666666555555444444444333222222222222222111111000000111111222333222222222111111111000000000000000//////////////////...---------...000111000000000000000000000000111111111222222222333333444444444222111111222444222111000000//////000000222111111111000000000000........................++++++++++++,,,---......,,,,,,---------------------------.........//////---------.........//////........................//////////////////............////////////............------......//////+++,,,---......---,,,,,,,,,,,,,,,++++++++++++***(((((())))))******++++++***************+++++++++,,,------......---,,,+++***++++++++++++***)))))))))+++,,,+++)))(((***+++))))))))))))))))))))))))(((((()))******+++***)))))))))))))))))))))))))))(((((((((((((((((((((((('''''')))******+++++++++''''''(((((()))))))))***))))))(((((((((''''''''''''''''''''''''&&&&&&%%%$$$&&&((((((&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&'''''''''&&&&&&'''''''''&&&&&&%%%%%%%%%$$$$$$$$$""""""""""""""""""""""""########################!!!!!!!!!!!!""""""""""""$$$######""""""######$$$!!!!!!!!! !!!!!!!!!!!!  !!!  !!!!!!!!!!!! !!!!!!"""!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!      !!!!!!!!!!!!!!!!!!!!!!!!999::::::;;;;;;;;;:::::::::;;;;;;<<<<<<;;;;;;:::999:::;;;<<<<<<;;;:::999888888777666555666666666555666777888888888888888333444555666666666444333777777666666555555555555666777999888666555555666555444333222222333444555666666777777666666555444444444444444333333333222111111000000111111222333222222222111111111000000111111000000//////////////////...------///000111111111111111000000000000000000000000111111111222333333333111//////111333222111111000000000000000111111111000000000000///........................+++++++++++++++,,,---...,,,,,,,,,---------......---------...............------------....................................------------------------......////////////......------,,,------...//////,,,---...//////...,,,+++,,,,,,+++++++++*********((((((((())))))******+++))))))*********+++++++++,,,---......------------+++++++++++++++***))))))******++++++*********+++))))))))))))))))))))))))((()))******************))))))************))))))((((((((((((((((((((((((&&&'''(((***++++++++++++'''((((((((())))))******((((((((((((''''''''''''''''''((((((''''''&&&%%%$$$&&&((((((&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&'''''''''&&&&&&'''''''''&&&&&&%%%%%%%%%$$$$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!""""""""""""###""""""!!!!!!""""""### !!!!!!!!!!!!!!!!!!   !!!  !!!!!!!!!!!!!!! !!!""""""!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!     !!!!!!!!!!!!!!!!!!!!!!!!::::::;;;<<<<<<<<<;;;;;;;;;;;;<<<<<<<<<<<<;;;;;;888888999999999888666555999888777666555666777888999999999999888666555444333444555666777666555555777777777666666555555555666888999888777666666666555444333222333444555666666666666666666555555444333444555666555444333222111111000000111111222333222222222111111111111000222111111000000//////...///////////////000111111222111111111111000000000//////000000000111111111222222222000......000222111111111111000000000///000000000000////////////........................,,,++++++++++++,,,,,,---+++,,,,,,------.................................,,,------------.........------------------------+++++++++,,,,,,,,,,,,,,,......////////////......,,,,,,,,,,,,,,,---...///------...//////...,,,+++++++++++++++************(((((()))))))))))))))))))))))))))***++++++,,,,,,+++---...---,,,,,,---///+++++++++,,,++++++***)))*********+++++++++++++++))))))))))))))))))))))))''')))++++++)))))))))***)))******++++++******)))))))))))))))))))))))))))''''''(((******+++++++++((())))))))))))))))))***'''''''''''''''''''''''''''(((((((((((('''&&&&&&$$$&&&((((((&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$########################""""""""""""""""""""""""!!!!!!!!!!!!""""""""""""""""""!!!!!!!!!!!!"""""" !!!!!!!!!!!!    !!!!!!!!!!!!!!!!!! !!!!!!"""###!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!    !!!!!!   ::::::;;;<<<<<<<<<<<<<<<;;;;;;<<<<<<<<<<<<;;;;;;::::::;;;;;;:::888666555:::999888666666777888999999999999999777666555444444555666666777777777777555666666777777777777666666888999999777666666777555444333333333555666777555666666666666555444444222444666888777555222111111111000000111111222333222222222111111111111000222222111111000//////...///000000111111111111111222222222111111111000000000000111111111222222222222222222000......000222111111111111111000//////////////////.........---........................,,,,,,++++++***+++++++++++++++,,,,,,---......///........................,,,,,,---------.........------------------------+++++++++,,,,,,---------......////////////......++++++++++++,,,---...///...............------,,,++++++++++++************)))))))))))))))(((((((((((())))))***++++++,,,,,,***,,,------++++++---///++++++,,,,,,++++++***)))+++*********,,,,,,,,,+++))))))))))))))))))))))))'''***,,,+++)))((()))***)))***++++++++++++***)))))))))))))))))))))))))))'''((()))************************)))))))))))))))''''''''''''''''''''''''((((((((((((((('''&&&&&&$$$&&&((((((&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""!!!!!!!!!!!!""""""""""""""""""!!!!!!!!!!!!"""""" !!!""""""!!!     !!!!!!!!!!!!!!!!!!!!!!!!!!!""""""###!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!       ::::::;;;<<<=========<<<;;;;;;<<<<<<<<<<<<;;;;;;>>>>>>>>>>>>===;;;999888;;;:::888777666777888:::666777777888888888888777666666666666777777888888333444555777888888999999777888999999777666666777555444333333444555777888555555555555555444444333111444777999999666222000111111111000111222222333222222222111111111111000222222222111000//////...///000111333333222111111222222222222111111000000111111222222222333333333222333222111//////111333111111111111111000/////////.........------------////////////////////////------,,,+++************++++++,,,,,,---...//////.....................---,,,,,,,,,---------......------------------------,,,,,,,,,------...............////////////......++++++++++++,,,---.../////////......------------+++++++++************)))******))))))((((((''''''((())))))***++++++,,,,,,***,,,---,,,******---000+++,,,,,,,,,,,,+++******+++*********,,,---,,,,,,))))))))))))))))))))))))'''***,,,+++)))'''(((***)))***+++,,,,,,+++***)))))))))))))))))))))))))))((())))))************)))++++++******))))))((((((&&&'''''''''''''''''''''(((((((((((((((''''''&&&$$$&&&(((((('''%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""!!!!!!!!!!!!""""""""""""######""""""""""""###### !!!""""""!!!   !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!"""!!!!!!!!!!!!!!!"""######!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!     !!!!!!  <<<<<<======<<<;;;::::::999:::;;;<<<============>>>===;;;888777888999999<<<<<<<<<<<<;;;:::999888;;;:::999888777777777777333333444444555444444444333444666888999999888777666666777888888888888888777777777777777666666555111111111222222333333333333444555666666666555444444444444333333222222222222333555555555333111000000222222222111000111222222111000//////000111222444222111//////000222333000111111111222222222222333222111/////////000111222222222222111111111000111000000000000/////////------------------------++++++++++++++++++++++++------------------------,,,,,,------------------,,,,,,++++++,,,,,,---............////////////000...///000111111000///......///////////////...---***+++,,,,,,------------------------------------,,,,,,,,,+++++++++************)))((('''(((+++---,,,,,,,,,++++++*********+++++++++*********))))))))))))******++++++++++++*********++++++,,,,,,,,,))))))))))))))))))))))))))))))*********))))))((())))))))))))))))))))))))((('''&&&%%%%%%&&&'''((())))))))))))))))))))))))***)))(((''''''((()))***))))))(((((((((((())))))&&&'''((((((((('''%%%$$$%%%%%%&&&&&&%%%%%%$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$############$$$%%%%%%&&&&&&%%%%%%&&&&&&%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%""""""""""""""""""""""""######$$$$$$$$$$$$############""""""""""""######""""""!!!!!!  !!!"""!!!  !!!"""""" !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!"""!!!!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!!!!!!!!!!!!!!!!!!!!!!  !!!"""  !!!"""   !!!!!!!!!!!!   <<<============<<<;;;:::999:::;;;<<<============>>>===;;;999888999:::;;;>>>>>>>>>>>>===<<<;;;:::::::::999888777777777777444444444555555444333333222444666777888888777666444444555666666666666666666666666666666555555444444444444444444555555555333444555666666555444333444444444333333222222222222333444555444333111000000222333222111000111222222111000//////000111222555444222000/////////000000000000111111111222222333222111000//////000111222222111111111000000000.........---------,,,,,,---------------------------------,,,,,,,,,,,,,,,------,,,,,,,,,,,,------------------------------,,,,,,++++++,,,,,,---...,,,,,,---------............///000111111000///...------...............---***+++,,,---------------........................,,,,,,,,,+++++++++******)))***)))((('''(((+++------,,,,,,,,,++++++++++++------,,,,,,,,,+++++++++)))*********++++++++++++++++++++++++++++++,,,,,,++++++++++++++++++++++++))))))************))))))))))))))))))))))))))))))***)))(((''''''((()))***))))))))))))))))))))))))***)))(((''''''((())))))))))))(((((((((((())))))''''''(((((('''&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$#########$$$%%%%%%&&&&&&%%%%%%&&&%%%$$$######$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%"""""""""""""""""""""""""""""""""######"""""""""######""""""""""""######""""""!!!!!!!!!  !!!"""!!!  !!!"""""" !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!""""""!!!!!!!!!!!!!!!!!!!!!!!!"""!!!  !!!"""!!!!!!!!!!!!!!!!!!!!!!!!  !!!"""  !!!"""  !!!!!!!!!  ==================<<<;;;999:::;;;<<<<<<======<<<===<<<;;;::::::;;;<<<===>>>>>>>>>>>>===<<<;;;;;;999888888777777777888888555555555555555444333222222333555666777777666555444444555666666666666666555555666666555555444333555555555555555444444444333333444555555444333222444444333333333333222222222333444444444333111111111222333222111000111333222111000000000000111222999777555222000////////////000000000111111111111222222111000000000111111111111000000000/////////------------,,,,,,,,,+++........................//////......------,,,,,,------++++++++++++------........................,,,,,,++++++,,,,,,---...++++++++++++,,,,,,,,,,,,...///000000000000///...++++++,,,---.........---+++,,,,,,------------,,,........................,,,,,,,,,+++++++++******)))******)))((((((+++---------------,,,,,,,,,,,,............------------************++++++++++++,,,,,,++++++++++++++++++++++++++++++++++++++++++))))))***************)))))))))))))))))))))))))))++++++************++++++))))))))))))))))))))))))))))))(((((((((((())))))))))))(((((((((((())))))(((((('''&&&&&&&&&&&&'''%%%%%%&&&&&&%%%%%%$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$######$$$%%%%%%&&&&&&%%%%%%$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""""""""""""""""""""!!!!!!""""""""""""!!!!!!""""""""""""""""""""""""""""""!!!!!!!!!!!!  !!!!!!!!!  !!!"""""" !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!"""""""""!!!!!!!!!!!!!!!!!!!!!!!!""""""!!!!!!!!!!!!""""""!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!  !!!!!!  !!!!!!  <<<======>>>======<<<<<<999999:::;;;<<<<<<<<<<<<<<<;;;;;;;;;;;;<<<===>>>;;;;;;<<<<<<;;;::::::999888777777777777888888999666666666666555444222222333333444555666666555555666666777888888888888888666666666777666555555444555555444444333333222222333444555555555444333222333333333333333333333333222222333333333333222111111222333333111111222333111111111111111111111111999888666555333222222222//////000000000111111111222111111111111111111111000000000000//////////////////.........---------........................//////......---,,,,,,,,,---,,,+++******+++,,,---//////............------,,,,,,++++++,,,,,,---...***++++++++++++,,,,,,,,,---...///000000///...---***+++,,,---.../////////,,,,,,---------------,,,........................,,,,,,,,,+++++++++******)))*********))))))+++---------------------------............------------++++++++++++++++++++++++,,,,,,,,,++++++*********))))))))))))))))))))))))))))))***+++++++++******))))))))))))))))))))))))++++++++++++++++++++++++))))))))))))))))))))))))((((((((((((((()))))))))(((((())))))))))))((((((((((((&&&%%%%%%&&&'''(((%%%%%%&&&&&&%%%%%%$$$#########$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""!!!!!!""""""""""""!!!!!!""""""############""""""""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!  !!!"""""" !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!"""""""""!!!!!!!!!!!!!!!!!!!!!!!!###""""""""""""""""""###!!!!!!!!!!!!!!!!!!!!!!!! !!!!!! !!!!!!  !!!!!!  <<<<<<============<<<<<<888999:::;;;<<<<<<<<<<<<;;;;;;;;;;;;<<<======>>>;;;;;;;;;<<<;;;;;;:::999777777777666777777888888666777666666555444333222444444444555555555555555666666777888888888888888777888888888888777666666555555555444444333333333444444555555555444222222333333333333333333333333111222222222222222222222111333333333222111222333111111222222222222111111555444444333333333333333000000000000111111111111111111111222222222222111000000000000//////////////////.........---------...........................---------,,,,,,,,,+++------,,,++++++,,,------//////......------------,,,,,,++++++,,,,,,---...,,,,,,,,,,,,---------------...///000000///...---+++,,,---//////000000000---------......------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++******)))***++++++******+++---------------------------------------,,,,,,,,,,,,,,,+++++++++++++++++++++,,,,,,,,,++++++*********))))))))))))))))))))))))))))))***+++++++++++++++************************************************))))))))))))))))))))))))''''''((()))))))))))))))(((((())))))))))))((((((((('''&&&%%%%%%&&&((((((%%%%%%&&&&&&%%%%%%$$$#########$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$########################"""######$$$$$$######"""!!!"""############"""!!!!!!!!!"""""""""""""""""""""!!!!!! !!!!!!!!!  !!!"""""" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""""""""###"""""""""""""""""""""""""""##################"""!!!!!!!!!!!!!!!!!!!!!!!!     !!!!!!!!!  :::;;;<<<<<<<<<<<<<<<<<<888999:::;;;;;;<<<<<<;;;::::::;;;;;;<<<<<<<<<<<<<<<===============<<<<<<888777777666666666777777666666666666666555444333555555555555555555555666444444555666666666666666888888999999999888777777777777777777777666666666555666666666666555333222222222333333333333444444111111111111222222222222222333444333222111222444111111222333333222111111/////////000111222222222000111111111222222222222000111222222333222222222111111000000000/////////------------,,,,,,,,,+++------------------------,,,,,,,,,,,,,,,,,,,,,,,,------------------------.........---,,,,,,++++++,,,,,,++++++,,,,,,---...------------............---...////////////...---------...///000000000000---............------,,,++++++++++++++++++++++++,,,,,,,,,+++++++++******)))***,,,+++******+++---,,,,,,,,,,,,------------,,,,,,,,,,,,+++++++++***,,,,,,,,,,,,++++++++++++,,,,,,++++++++++++++++++++++++++++++++++++++++++))))))***+++,,,,,,,,,,,,************************((()))************)))((())))))))))))))))))))))))&&&'''((()))*********)))'''((()))******)))(((''''''&&&&&&&&&&&&'''((((((%%%%%%&&&&&&%%%%%%$$$#########$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%######$$$%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$$$$######!!!"""###$$$$$$###"""!!!!!!!!!""""""""""""######""""""!!!!!! !!!!!!!!!  !!!"""""" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""""""""######""""""""""""""""""""""""""""""############""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!  !!!!!!   !!!!!!  !!!"""!!!!!!  999999:::;;;;;;;;;;;;;;;888888999:::;;;;;;;;;;;;:::::::::;;;;;;;;;;;;:::<<<<<<===============<<<999888777666666666666666555555666666666666555555777666666666555666666666444444555666666666666666888888888888888777666666777777777777777888888888666777888888777555444333222222222333333444444444111111111111111222222333222333444444222222333444111222222333333222222111......000111111222222222222222222222333333333333000111222333333333222222222222111111111000000000.........---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------......//////,,,---///000000///---,,,...------,,,++++++******,,,,,,++++++,,,,,,---...------------............------...//////...------------...//////........................---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++******)))***,,,,,,+++***+++,,,++++++++++++,,,,,,,,,---,,,,,,,,,,,,++++++++++++------,,,,,,,,,+++++++++++++++++++++++++++,,,,,,++++++++++++++++++++++++((()))***+++,,,,,,,,,,,,************************((()))***++++++***)))((())))))))))))))))))))))))%%%&&&((()))*********)))'''((()))******)))((('''%%%&&&&&&'''((((((''''''%%%%%%&&&&&&%%%%%%$$$#########$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%###$$$%%%&&&&&&%%%$$$###################################################""""""############""""""!!!"""###$$$$$$###"""!!!!!!!!!"""""""""###############"""!!!!!!!!!!!!!!!!!!  !!!"""""" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""""""""#########""""""""""""""""""""""""!!!!!!"""######"""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!  !!!!!!!!!   !!!!!!!!!!!! !!!"""###!!!!!!  888999::::::;;;;;;;;;:::888888999:::;;;;;;;;;;;;999::::::;;;;;;:::999999::::::;;;;;;;;;;;;;;;:::999999888666555555555555444555666666666666666555888777777666666666777777666777777888888888888888777777777777777666666555444444555555666666777777777888888888888666444333222222222333333444444444111111000000111222333333222333444444222222333444111222333444444333222111111222333444444444444444222222333333333444444444000111222333444333333222222222222222111111111111111000000000000/////////++++++++++++++++++++++++,,,,,,---...///000111111,,,...000222222000...,,,------,,,++++++***)))))),,,,,,++++++,,,,,,---...,,,,,,------------......,,,---...//////...---,,,---------...------,,,,,,.../////////...---,,,,,,------------------------,,,,,,,,,+++++++++******)))***,,,,,,+++++++++,,,*********++++++,,,,,,,,,------,,,,,,,,,+++++++++---------,,,,,,+++++++++*********++++++,,,,,,---))))))))))))))))))))))))((()))***+++,,,---------************************)))***+++,,,,,,+++***)))))))))))))))))))))))))))%%%&&&((()))*********)))'''((()))++++++)))((('''$$$%%%'''((()))((('''&&&%%%%%%&&&&&&&&&%%%$$$$$$######$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$%%%&&&&&&&&&&&&%%%$$$################################################!!!!!!""""""""""""!!!!!! """###$$$$$$###""" !!!!!!""""""#########$$$######"""!!!!!!!!!!!!!!!!!!  """"""""" !!!!!!!!!!!!!!!!!!!!!!!!""""""""""""############"""""""""""""""""""""""" !!!"""######"""!!! !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!  !!!!!!!!!   !!!!!!""""""!!!  !!!######!!!!!!  :::::::::;;;======;;;999<<<;;;999888999<<>>???<<<999:::999777666666666777888<<<;;;;;;:::999888777777999999888888777777666666::::::999888777777888888888888777777666555555555888888888888888888888888666666666666666666666666555555555666666666666666333111000222444333000---000111111222444555666666333444555666555444333222000111222333444333222222222222222222222222222222111222222222222333333333555444222111000111222333......//////000000111111---------.........//////////////////////////////000000000000000/////////...------------,,,,,,,,,,,,,,,,,,---------......---------...------,,,,,,((())),,,...////////////------,,,+++,,,---...////////////...------,,,,,,------......------,,,+++)))))))))))))))))))))))),,,,,,,,,,,,,,,,,,,,,,,,++++++,,,------......///,,,++++++******++++++,,,,,,,,,,,,,,,,,,+++***))),,,,,,------,,,,,,+++***************+++,,,---...))))))))))))))))))))))))++++++++++++++++++,,,,,,))))))*********+++++++++---,,,++++++,,,,,,***)))************************************))))))))))))(((''''''''''''&&&&&&&&&&&&((()))(((%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&#########$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$#########$$$$$$$$$%%%%%%%%%"""###$$$%%%$$$######$$$!!!!!!!!!!!!"""""""""""" !!!"""""""""""""""""""""""""""############!!!!!!!!!!!!""""""""""""!!!!!! !!!!!!!!!!!! !!!!!!"""###############""""""""""""""""""""""""!!! """"""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!! """!!!!!!  """"""!!!   888888888:::<<<===;;;:::===<<<;;;:::;;;<<<>>>???<<<<<<;;;;;;;;;;;;;;;<<<<<<::::::;;;===>>>;;;999999888777666666777888888::::::999999888888777777888888888777777777777777999888888777666666777777999999888777777666666555777777777777777777777777666666666666666666666666555666666666666666666666333222111222444444111...///000111222333444555555333333444444333333222111000000222333333333222111222222222222222222222222222222222111111000000000444333333222111111111111.../////////000000000111---------.........//////------------------------////////////////////////.........------,,,,,,,,,,,,,,,,,,---------......,,,------.........------***+++,,,---//////000000...---,,,,,,,,,---//////------..................,,,,,,------,,,,,,+++***************************,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,------......///,,,,,,++++++++++++,,,,,,---------------,,,++++++---------------,,,++++++************+++,,,---...***************************++++++++++++,,,,,,,,,*********+++++++++,,,,,,---,,,***+++,,,,,,+++)))************************************))))))))))))(((''''''''''''&&&&&&&&&&&&'''((((((%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%&&&%%%&&&&&&&&&%%%%%%$$$######$$$$$$$$$$$$%%%%%%%%%"""###$$$$$$###""""""""" !!!!!!!!!""""""""" !!!"""""""""""""""""""""""""""############!!!!!!!!!!!!"""""""""###!!!!!! !!!!!!!!!!!!!!! !!!""""""###############""""""""""""""""""""""""!!!!!!!!!!!! """"""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!!!!!!! !!!!!!  """!!!!!! 777777777999;;;<<<;;;:::====================================<<<<<<;;;:::;;;::::::;;;<<<<<<:::888888888777777777888888999888888888777777777777777777777777777888888888888888888777666666666666777::::::999999888777777666777777777777777777777777666666666666666666666666666666666666666666555555444333222333444444222000///000000111222333444444444333333222222222222222000111222222333333222222333333333333333333333333555444333222111000//////333333333333222111000///////////////000000000000---------...............,,,,,,,,,,,,,,,,,,,,,,,,........................//////...---,,,,,,++++++,,,,,,,,,---------......,,,------....../////////------------...///000111......------......///000,,,,,,------...//////000++++++,,,,,,++++++***)))++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,------......///,,,,,,++++++++++++,,,,,,---............------,,,---............---,,,,,,************+++,,,---...++++++++++++++++++++++++******+++++++++,,,,,,,,,+++++++++,,,,,,,,,---------+++***+++,,,,,,+++)))************************************))))))))))))(((''''''''''''&&&&&&&&&&&&'''((((((&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%###############"""!!! !!!!!!!!!!!! !!!!!!"""""""""""""""""""""""""""############!!!!!!!!!"""""""""######"""!!!!!! !!!!!!"""!!!!!!!!!!!! !!!"""######$$$$$$######""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!   !!!!!!!!!!!!!!!  !!!!!!!!! :::999999:::;;;<<<;;;999======>>>??????>>>===<<<===>>>??????>>><<<:::999;;;:::::::::::::::999999888888888888888888999999555666666666777777888888666666777777888888999999888888777777777777888888;;;;;;:::999999888888777777777777777777777777777666666666666666666666666666666666666555555555555444444444444444444444333111111222333333444555555555444333222111222333444222222333333444444444444333333333333333333333333555555444333333222111111222222333333333111///...////////////000000000000........................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------------...//////...---,,,++++++***,,,,,,,,,---------......,,,,,,------...///000111///...------...///000222............//////000000---------.........//////,,,,,,,,,,,,,,,+++******,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++,,,------......///,,,,,,,,,++++++,,,,,,,,,------.........------,,,......//////......---,,,************+++,,,------,,,,,,,,,,,,,,,,,,,,,,,,*********++++++,,,,,,---,,,,,,,,,---------......,,,+++******,,,,,,+++***************************************)))))))))((((((''''''''''''&&&&&&&&&%%%'''((('''&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$###"""######"""!!! !!!!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!"""""""""############!!!!!!"""""""""#########""""""!!!!!!!!!!!!""""""!!!!!!!!!!!!!!!!!!!!!!!!""""""###$$$$$$$$$$$$###""""""""""""""""""""""""#########""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!   !!!!!!!!!!!!!!!!!!  !!!!!! >>>===;;;;;;<<<<<<;;;999<<<===?????????>>><<<;;;===>>>??????>>><<<:::999;;;;;;;;;:::999999999999888888888999999999999888555555555666777777888888666666777777888888999999999999999888888999999:::;;;;;;::::::999888888888999999999999999999999999777777777777777777777777777777666666555555555444444444444444444444444555333444444444555666666666777666555333333444555555444444444444555555666666333333333333333333333333111111111111222222222222000111222333222111000///000000000000////////////.....................---------------------------+++,,,,,,,,,------......//////...---,,,,,,++++++,,,,,,,,,---------......,,,,,,,,,,,,---///000111000///...------...000111........./////////////////////.........------------------------,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++,,,------......///---,,,,,,,,,,,,,,,,,,---,,,,,,------------,,,,,,......//////......---,,,************+++,,,------,,,,,,,,,,,,,,,,,,,,,,,,))))))***+++,,,,,,------,,,,,,---------.........,,,+++******,,,,,,,,,***************************************)))))))))((((((''''''''''''&&&&&&&&&%%%&&&((('''&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$###""""""$$$$$$""" !!!!!!!!!!!!"""!!!!!!""""""""""""!!!!!!!!!"""""""""############""""""""""""############""""""!!!!!!!!!!!!""""""""""""""""""""""""""""""""""""###$$$$$$$$$$$$$$$########################$$$#########""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!!!!!!!!!!  @@@>>><<<;;;<<<<<<<<<;;;;;;<<<===>>>>>>>>>===<<<============<<<<<<;;;:::<<<<<<<<<;;;999888999;;;999999::::::999999888777555555666666777777888888777777777777888888888888:::999999999999:::;;;;;;;;;;;;:::999999888888777::::::::::::::::::::::::777777777777777777777777777777777666555555444444333444444444333333555666555555555666666666777777777666666555555555555555555555444444444555666777333333333333333333333333............//////000000///000111111222111111111000000000000////////////...............---------------------------------+++,,,,,,------...............---------,,,,,,,,,,,,,,,,,,---------......---,,,++++++,,,---///000//////......---.........------...////////////...000//////...------,,,,,,---............---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++,,,------......///------,,,,,,,,,,,,------++++++,,,------------,,,---............---,,,,,,************+++,,,---...,,,,,,,,,,,,,,,,,,,,,,,,))))))***+++,,,------...,,,,,,,,,---------......+++*********,,,---,,,+++************************************))))))))))))(((''''''''''''&&&&&&&&&$$$&&&''''''&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%###!!!###%%%&&&$$$!!!!!!!!!!!!!!!"""""""""""""""""""""""""""!!!!!! """"""""""""############"""""""""#########$$$$$$###""""""!!!!!!""""""###""""""""""""############"""###$$$$$$%%%$$$$$$$$$####################################""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!  !!!""""""""""""  ===;;;::::::<<<=========:::;;;<<<<<<============<<<<<<;;;;;;;;;;;;;;;<<<===>>>>>><<<999888:::<<<:::;;;;;;;;;:::888666555777777777777777777777888888888888777777777777777999999888888999999:::;;;:::::::::999888888777777999999999999999999999999777777777777777777777777888777777666555555444444222333444333111222444777555555555555666666666666555555666666555555444333444333333222333444555666444444444444444444444444000000000///////////////////////////000222333444111000000000/////////...//////.........---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---......//////,,,,,,,,,------------...,,,,,,,,,---------......---,,,+++******+++---..................---,,,,,,+++,,,---...///......---..................------,,,------------,,,++++++++++++++++++++++++++++++************************++++++,,,------......///------,,,,,,,,,,,,------,,,,,,---...............---------------,,,++++++************+++,,,---...++++++++++++++++++++++++((()))***+++,,,------...+++,,,,,,,,,------------+++***)))***,,,---,,,+++************************************))))))))))))(((''''''''''''&&&&&&&&&$$$&&&''''''&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$###$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''%%%"""!!!###''')))&&&###""""""""""""#########$$$"""""""""""""""!!! """"""""""""############""""""#########$$$$$$$$$######""""""""""""######"""""""""######$$$$$$$$$"""###$$$$$$%%%%%%$$$$$$##############################"""""""""!!!!!!!!!""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!""""""!!!  !!!""""""""""""!!!!!!  999888777888;;;>>>??????:::::::::;;;<<<===>>>>>><<<;;;:::999999:::<<<======??????<<<999888:::===;;;;;;<<<;;;:::888666444888888888888777777777777999999888888777777666666888888777777888999::::::::::::999999888777777666888888888888888888888888777777777777777777777777888777777666555444444444111333444333111111444777444444444555555555555555333444555666555444333222333222111000111222333444444444444444444444444444555444444333222111000000............000222444666111111000000/////////...//////.........---------++++++++++++++++++++++++,,,,,,------...///000000++++++,,,------......///,,,,,,,,,---------.........,,,***))))))***+++---------...///...---+++***++++++---.........---,,,,,,,,,------.../////////+++,,,,,,,,,,,,+++******++++++++++++++++++++++++************************++++++,,,------......///...------,,,,,,------...------...///000000//////,,,,,,------,,,,,,+++***************+++,,,---...++++++++++++++++++++++++((())))))+++,,,---......+++++++++,,,,,,,,,------+++***)))***,,,---,,,+++************************************))))))))))))(((((('''''''''&&&&&&&&&$$$&&&''''''&&&%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$############$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%"""!!!###(((***((($$$"""#########$$$$$$$$$$$$"""""""""""""""!!! """"""""""""############"""############$$$$$$$$$######""""""""""""######""""""######$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$########################""""""""""""!!!!!!!!!!!!""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!""""""!!!  !!!"""""""""""""""!!!!!!   999:::::::::;;;<<<<<<<<<<<<;;;<<<===??????===;;;999999::::::;;;<<<<<<<<<<<<<<<;;;;;;;;;;;;<<<<<<999999888888777777666666444666999<<<<<<:::777555999999999888777666666555444444555666777888999999888666444666999;;;;;;999999:::;;;:::888777888999666777888999:::;;;;;;;;;666777777777777666666555444666777666555555666777777666666444333222111111777666444333222222333444555333111000111333333222444333222222222444666888222222222222222222222222444333111000000000111111333333333222111000///.........////////////......,,,,,,---....../////////...,,,++++++---......---000000//////.........------------,,,,,,+++++++++000///...---,,,+++******...///...---,,,,,,...000111000///...............////////////////////////111000...---,,,,,,------++++++***************+++))))))***++++++,,,------...------,,,,,,------......------,,,,,,...///000000///...---------------...------,,,,,,++++++***************************++++++++++++++++++++++++++++++******++++++,,,---+++***)))***,,,---,,,+++***+++,,,,,,---------,,,))))))))))))))))))))))))------,,,,,,+++***))))))((((((((((((((((((((((((%%%&&&''''''&&&&&&((()))&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%%%%%%%&&&'''&&&&&&%%%$$$%%%&&&'''(((((((((((('''&&&&&&&&&%%%''''''''''''''''''&&&&&&$$$%%%&&&''''''&&&%%%$$$########################!!!!!!!!!!!!!!!!!!!!!!!!##############################""""""""""""###############""""""""""""!!!#########"""""""""""""""#########$$$$$$%%%%%%%%%"""###%%%%%%###"""###$$$""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""""""""""""""  !!!""""""  !!!!!!""" !!!!!!!!!!!!""";;;;;;;;;<<<<<<<<<<<<<<<<<<;;;;;;===>>>???===;;;;;;;;;;;;;;;;;;<<<<<<<<<;;;;;;::::::::::::;;;;;;888888888888777777777777444555888:::;;;;;;999888999999999888777666666666777777777777777888888888:::888777888:::<<<<<<::::::;;;<<<;;;999888999:::888888999999999999999888888888888888777777666555444555666555444444555666777666666555444333222111666555444333333333444444555333111000222333333333555444333222222444555666222222222222222222222222444333111000000000111222444444444444333222222111//////000000000000//////------------...///000000...,,,+++,,,---///......000/////////............---------,,,,,,,,,++++++............------------.........---,,,,,,...000000/////////............////////////////////////111000...---,,,,,,------++++++************++++++******++++++,,,---------------,,,,,,,,,,,,------......---------...///000//////...---------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++******++++++,,,---+++***)))***,,,---,,,+++++++++,,,------,,,,,,,,,************************,,,,,,+++******)))(((((((((((((((((((((((((((((($$$%%%'''&&&%%%%%%'''(((&&&&&&%%%%%%%%%%%%&&&&&&'''&&&%%%%%%%%%%%%&&&'''&&&&&&%%%%%%%%%&&&'''(((''''''''''''&&&&&&&&&&&&''''''''''''''''''&&&&&&$$$%%%%%%%%%%%%%%%%%%$$$########################""""""""""""""""""""""""##############################""""""""""""######$$$############""""""""""""""""""!!!!!!!!!!!!!!!######$$$$$$$$$%%%%%%%%%"""###%%%%%%###"""###$$$""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!"""  !!!!!!!!! !!!!!!!!!;;;;;;;;;;;;;;;;;;::::::;;;;;;;;;<<<>>>>>>===;;;=========<<<<<<<<<<<<;;;::::::999999999999::::::777777777888888888888888444555777999:::;;;;;;;;;999999999888777777666666:::999999999888888888777===;;;999:::;;;<<<<<<;;;;;;<<<===<<<:::999:::;;;999999::::::999999888777:::::::::999888777666555444555666555444333444555777777666555444333333222666555444444333444444555555333111111222444444333666555444333222333444555222222222222222222222222333333222111111111111222333333333444444333333222000000111111111111000000...------,,,---///000111...---,,,,,,...//////...////////////............---------------,,,,,,,,,,,,,,,---...///000111111---...///...,,,,,,...000...///000000000///...---////////////////////////000///...---------------++++++************++++++++++++,,,,,,------......------,,,,,,,,,,,,------///............///000000///.........------------******+++,,,,,,---......,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++++++++++++++************+++,,,,,,+++***)))***,,,---,,,+++,,,,,,,,,------,,,++++++++++++++++++++++++++++++++++++******)))((((((((((((((((((((((((((((((((($$$%%%&&&&&&%%%%%%&&&'''''''''&&&&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&''''''%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######################################################""""""""""""######$$$$$$$$$############"""!!!!!!!!!!!!!!!!!!!!!!!!###$$$$$$$$$$$$%%%%%%%%%"""###%%%%%%###"""###$$$""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!!!!  !!!!!!!!!!!! ;;;:::::::::999999888888;;;::::::;;;===>>>===<<>>>>>===<<<<<<;;;;;;::::::999999999999::::::777777777888888999999999777777777888999:::;;;<<<999999999888888777777777::::::::::::::::::::::::===<<<;;;::::::::::::::::::;;;<<<;;;:::999:::;;;::::::;;;;;;;;;::::::999;;;;;;;;;:::999888777666555666777666555444555666777777666666555444444333444444444444444555555555555333111111333555555444777666555333333222333333222222222222222222222222222222222222222222222222///000111222222222222222111111111222222111111111......---,,,---///111222///...,,,---...000000//////////////////..................---------------------...///000111222222---...///...---,,,...///---...000111111///...,,,//////////////////////////////......------------++++++*********+++,,,,,,,,,,,,,,,------.........---,,,,,,,,,,,,,,,,,,---............//////000000..................------+++++++++,,,,,,---------************************++++++++++++++++++++++++***************++++++,,,+++***)))***,,,---,,,+++,,,,,,------,,,,,,++++++++++++++++++++++++++++++++++++******))))))))))))((((((((((((((((((((((((%%%'''((('''&&&&&&'''((('''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''%%%%%%%%%&&&&&&'''''''''%%%%%%&&&&&&&&&&&&''''''&&&%%%$$$######$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$######""""""######$$$$$$$$$$$$$$$############!!!!!!!!!!!!""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$"""###%%%%%%###"""###$$$!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!  !!!""""""!!!!!! <<<<<<;;;;;;::::::999999;;;:::999:::<<<>>>>>>===??????>>>===<<<;;;;;;:::;;;;;;::::::::::::;;;;;;777777888888999999::::::;;;:::999888888999999:::999999999999888888888888888999999:::;;;<<<<<<<<<;;;;;;:::999888888888999888999::::::999888999;;;999:::;;;<<<============;;;;;;;;;::::::999777777777999999888777666666777777777777666666555555444333444444555555666666666555444222222444555666666777666555444333222222222222222222222222222222222222222222333333333222222//////000111222222222222111111222222222222111111......------...///111222000...------///000000///.........///////////////........................000000000000000000000000,,,...//////---------...,,,...///111111000...---////////////////////////...............---------++++++******+++,,,,,,---,,,,,,------------......,,,,,,,,,++++++,,,,,,,,,---......///////////////------...//////......------------,,,,,,+++++++++************************++++++++++++++++++++++++******))))))******+++,,,+++***)))***,,,---,,,+++,,,,,,,,,------,,,,,,++++++++++++++++++++++++++++++++++++++++++*********((((((((((((((((((((((((((()))***)))((('''((()))'''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&$$$%%%%%%%%%&&&&&&''''''%%%%%%%%%%%%&&&&&&'''''''''&&&%%%$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$############$$$$$$$$$$$$$$$#########"""""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###%%%%%%###"""###$$$!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!    """###""""""!!! ==================<<<<<<;;;999888999<<<>>>>>>===>>>>>>======<<<;;;::::::;;;;;;::::::::::::;;;;;;888888888999999999999999<<<;;;:::999999888888999999999999999999999999999888888999:::;;;<<<======999::::::888666666777888777999::::::888888999;;;888999;;;<<<===>>>>>>>>>999::::::::::::999888888999:::;;;:::888666777888888888777777666666666666222333444666666777777777666444222333555666777777666666555444444333222222222222222222222222222222111222333333444333333333111222333444444444444444111111222222222222111111---......///000000111111000///......000111111000.........///////////////.........///////////////111111000000//////......,,,...//////...------...---...///000000000///...////////////////////////---......///......------++++++***++++++,,,---...,,,,,,,,,,,,,,,---------,,,,,,++++++++++++,,,,,,,,,------...///.........,,,---.../////////...---......---,,,,,,+++******,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++***))))))))))))***+++++++++***)))***,,,---,,,+++***+++,,,,,,---------,,,++++++++++++++++++++++++++++++++++++++++++++++++(((((((((((((((((((((((()))***+++***)))((()))***''''''&&&&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$############$$$$$$#########""""""""""""!!!"""######$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###"""###%%%%%%###"""###$$$""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!   !!!###$$$###"""!!! <<<<<<<<<<<<<<<<<<======:::999888999;;;===>>>>>>===<<<<<<<<<;;;;;;::::::::::::999999999999:::::::::999999999999999999888::::::::::::::::::999999999999999999999999999999999999999::::::;;;;;;;;;777999:::888666555777:::888999::::::999999:::<<<999999:::;;;;;;<<<;;;;;;777888888999999999999999999::::::999777666666777888888777777777777666666111333444666777888777777666444333333555777888888555555555555444333333222222222222222222222222222111222333444444444333333222222333444444444333333000000111111111111000000,,,---///111111111000///111///...///000222111111............/////////000....../////////000000000000000/////////.........,,,...///000...------.............../////////000////////////////////////,,,---...//////...------++++++++++++,,,---......,,,,,,,,,,,,,,,,,,++++++,,,,,,++++++++++++,,,,,,++++++---.........---,,,+++,,,...///000///...---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++)))))))))))))))***+++++++++***)))***,,,---,,,+++)))***+++,,,---.........***************************************+++++++++(((((((((((((((((((((((()))***+++***((((((((()))&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%&&&''''''&&&%%%%%%$$$%%%&&&'''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&&&&''''''%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$$$$######$$$$$$%%%"""""""""!!!!!!!!! !!!""""""###$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$######"""###%%%%%%###"""###$$$""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!   !!!###$$$###"""!!! !!!!!!!!!888888888999999::::::::::::999777888;;;===>>>>>><<<;;;;;;;;;;;;:::::::::999999888888888888999999;;;::::::999999888888888888999:::;;;;;;;;;;;;;;;999999999999999999999999;;;;;;:::::::::999999999777999:::999666666888;;;999:::;;;;;;::::::<<<===999999:::::::::999888888666666777888999999999999888999:::888666555555666888888888888777777777777111222444666888888888888666444333333555777888888444444555555444444333222222222222222222222222222000111333444555444333333111111222222222111111000000000111111111111000000+++---000222333222000...111000...///111222222111---.........//////000000.../////////000000111111............////////////+++---000000...---------...............///000111////////////////////////,,,---.../////////------++++++++++++,,,---...///++++++++++++++++++++++++,,,++++++++++++++++++,,,***+++,,,---------,,,++++++,,,...000000///...---***++++++,,,,,,------...************************++++++++++++++++++++++++)))))))))))))))******++++++***)))***,,,---,,,+++((()))***,,,---...//////)))))))))))))))))))))))))))))))))))))))*********(((((((((((((((((((((((()))******)))(((''''''(((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&''''''&&&%%%%%%$$$%%%&&&'''''''''&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$######$$$%%%%%%&&&''''''###$$$%%%&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%################################################%%%$$$$$$######$$$$$$%%%!!!!!!!!!!!! !!!!!!"""###$$$$$$$$$%%%%%%%%%$$$$$$#########"""###%%%%%%###"""###$$$""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!   """$$$%%%$$$"""!!! !!!!!!!!!!!!""";;;::::::999:::;;;===>>>>>>===<<<;;;;;;;;;;;;;;;<<<<<<;;;:::;;;<<<===>>>::::::999999::::::;;;<<<<<<;;;:::999888888888888;;;:::888888888888:::;;;999999888888888888999999:::;;;<<<<<<<<<:::888666999999999::::::;;;;;;;;;>>>>>>===<<<;;;::::::999??????>>>===<<<:::888777:::999888777777777888888:::::::::999999888888888999:::<<<======<<<:::999888888888888777777777777555555666666777777888888666666666666666666666666444444555555444444333222333333333222222222111111333444555444222111222333333222222111111222222333222222222111///...///000000000//////000111222222//////............//////...000111222222111000...////////////////////////...//////000000000000000,,,...000000///000111333000///------.........---------...//////...------***+++,,,,,,------,,,,,,------------------------,,,------......------,,,((()))***+++,,,------------......///000/////////---------------------------,,,,,,++++++*********,,,,,,,,,+++++++++******)))+++,,,+++)))''''''(((++++++,,,,,,,,,,,,+++++++++)))))))))+++,,,+++***((()))+++,,,,,,+++)))(((,,,,,,,,,+++++++++******))))))(((((()))***++++++)))+++,,,+++)))&&&%%%%%%$$$$$$%%%%%%&&&'''((((((%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&%%%%%%&&&&&&'''((('''&&&%%%$$$%%%%%%&&&&&&&&&&&&'''''''''(((((('''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################!!!!!!!!!!!!!!!"""""""""##############################"""!!!!!!!!!!!!!!!!!!!!!"""###$$$$$$%%%%%%$$$$$$$$$######"""""""""###$$$%%%$$$"""""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############!!!!!!""""""!!!  """###"""!!! !!!###!!!  !!! !!!!!!!!!!!! !!!"""######"""!!!  !!!"""""""""""""""!!! ;;;;;;:::999999999::::::<<<<<<;;;;;;;;;<<<<<<===<<<;;;;;;:::;;;<<<===>>>999999888888999999:::;;;<<<;;;:::999888888888888999999888888888888999999999999888888888888999999999:::;;;<<<<<<;;;999888999999:::::::::;;;;;;;;;=========<<<;;;;;;::::::============<<<;;;::::::<<<;;;;;;:::::::::::::::;;;:::999999888888888999999:::;;;======;;;:::999888888888888777777777777555666666666777777777888666666666666666666666666555555666666555555444333444333333333333222222222333444555444222111222333333222222111111222222333111222222111//////000111111000000000000111111222111000000//////000000111...///111222222111///...////////////////////////......///000000000000///---...////////////000111000///------.........,,,,,,---...//////...---,,,++++++,,,------------,,,------------------------,,,------......------,,,******+++,,,------------------...////////////...------------------------++++++++++++++++++++++++,,,,,,++++++***************+++,,,+++)))(((((((((***++++++++++++++++++******)))((()))+++,,,,,,+++)))***+++,,,,,,+++***))),,,,,,,,,+++++++++******))))))(((((()))******+++)))+++,,,+++(((&&&%%%&&&$$$$$$%%%&&&&&&'''((((((%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&%%%%%%&&&&&&'''((('''&&&%%%%%%%%%&&&&&&%%%&&&&&&&&&&&&''''''''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################""""""""""""""""""""""""##############################"""!!!!!!!!!!!!!!!!!!""""""###$$$$$$%%%%%%%%%%%%$$$$$$$$$############$$$%%%$$$"""""""""###$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###############!!!!!!!!!!!!!!!  """###"""!!! !!!"""!!!  !!! !!!!!!!!!!!! !!!"""######"""!!!  !!! !!!!!!!!!!!! ;;;;;;:::999888888888888:::::::::;;;<<<<<<======<<<;;;;;;;;;;;;<<<======999888888888888999::::::;;;;;;:::999888888888888888888999999999999888888999999888888888888999999999:::;;;<<<<<<<<<;;;::::::::::::;;;;;;;;;;;;;;;<<<<<<<<<<<<<<<<<<<<<<<<;;;;;;<<<<<<<<<<<<<<<;;;<<<<<<;;;;;;;;;:::::::::;;;:::999888888888999:::999:::;;;<<<<<<;;;:::999999999888888888777777777666666666666777777777777666666666666666666666666555666666666666555444444555555444444444333333333333444555444222111222333333222222111111222222333000111111111000000111333222222111000000000111111222111111000000111111222//////111111111111//////////////////////////////---......///////////////---...//////...---...000000///------//////...,,,,,,,,,---......---,,,,,,++++++,,,---------------------------------------,,,------......------,,,,,,,,,------...------,,,,,,,,,---...............------------------------***++++++++++++,,,,,,,,,+++************)))))))))***+++,,,+++)))(((((((((******++++++++++++******)))(((((()))+++---,,,+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++******))))))((((((((()))******)))***+++***(((&&&&&&&&&%%%%%%%%%&&&''''''((((((%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###################################################""""""!!!!!!!!!!!!!!!"""""""""###$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$%%%$$$"""""""""########################### !!!!!!""""""######!!!!!!!!!!!!!!!  !!!"""""" !!!"""!!!  !!! !!!!!!!!!!!! !!!""""""""""""!!!  !!! :::::::::999999999999999::::::;;;;;;<<<<<<<<<<<<;;;;;;;;;;;;<<<<<<======:::999999999999:::;;;;;;;;;:::999999888888888999888999:::;;;;;;:::999888:::999999888888999999:::888999;;;<<<=========<<<;;;;;;;;;;;;;;;<<<<<<<<<;;;;;;;;;<<<<<<<<<======;;;;;;<<<<<<<<<<<<;;;;;;::::::::::::999999888888;;;:::999777777888:::;;;999:::;;;;;;;;;;;;:::999999999999888888888777777666666666666777777777777666666666666666666666666555555666666555555444333666555555555444444444444222333444444222222333444333222222111111222222333///000111111000111333555333222222111000000000000111111111000000111111111//////000111111000//////////////////////////////------...///////////////---...///...---,,,---...000///......//////...,,,+++,,,---......---,,,++++++,,,,,,---...---------------------------------,,,------......------,,,..................------+++,,,------......------------------------------,,,,,,++++++++++++++++++***)))))))))))))))))))))***,,,---,,,***(((((())))))******++++++******))))))(((((()))+++------,,,---,,,,,,++++++,,,,,,---,,,,,,,,,+++++++++******))))))((((((((())))))***)))***+++***(((&&&&&&'''%%%&&&&&&&&&''''''((((((%%%%%%%%%%%%%%%&&&'''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#######################################""""""!!!!!!!!!!!!""""""""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%$$$"""""""""########################### !!!"""###### !!!!!!!!!!!!!!!  !!!"""!!! !!!"""  !!!!!!!!!!!! !!!""""""!!!  !!! 888999999:::;;;<<<<<<<<<;;;;;;<<<<<<;;;:::999999;;;;;;;;;<<<<<<<<<<<<<<<<<<;;;;;;;;;;;;<<<======::::::999999888888999999999:::;;;<<<<<<;;;:::999::::::999999999999::::::999:::;;;<<<===>>>>>>>>><<<<<<<<<<<<<<<<<<<<<<<<::::::;;;;;;<<<=====================<<<;;;:::999999999:::::::::999888777:::999888888888999:::;;;999::::::::::::::::::999999999999999888888888888777777777777666666666666777777777777777777777777555555555555555444333333666666666555555555444444222333444444222222333444333222222111111222222333///000111111111111444666333333222111000000111111111000000//////000000111/////////000000/////////000000000000000000000000---......///000/////////---...///...---,,,---...000///...///000000...,,,,,,,,,---......---,,,,,,,,,,,,---.........------------------------------,,,------......------,,,....../////////...------+++,,,------......------------------------------------,,,,,,+++***)))))))))))))))))))))))))))******,,,---,,,***(((((()))******++++++++++++******)))(((((()))+++---,,,+++---,,,,,,++++++,,,,,,---,,,,,,,,,+++++++++******))))))((((((((((((((())))))******)))'''&&&'''(((&&&&&&'''''''''''''''(((&&&&&&%%%%%%&&&&&&'''((('''&&&&&&%%%%%%&&&&&&'''%%%&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!""""""###############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%$$$"""""""""###"""""""""""""""""""""""" !!!""""""### !!!!!!!!!!!!!!! !!!"""!!!  !!!  !!!!!!!!!!!! !!!""""""!!!  !!! !!!!!!!!!!!! 777888999;;;======>>>>>>;;;;;;<<<<<<;;;:::888777:::;;;<<<<<<======<<<<<<===<<<<<<<<<<<<===>>>>>>::::::999999888999999:::::::::;;;;;;;;;;;;::::::::::::999999999999::::::;;;;;;;;;<<<===>>>??????===============<<<<<<<<<;;;;;;;;;<<<<<<<<<==================<<<;;;:::999999:::;;;<<<;;;:::999888888999999999999:::::::::::::::999999999999:::::::::999999999999888888888777777777777666666666666777777777777777777777777555666666666666555444444666666555555555444444444111333444444222222333555333222222111111222222333///000111111111111444666333222222111111111222222000000000//////000000000////////////////////////000000000000000000000000...//////000000000000000---...//////...---...000000//////000111000...,,,------...//////...------,,,,,,---...............------------------------,,,------......------,,,------...............---,,,,,,---...............------------------------------,,,,,,+++******))))))))))))************++++++,,,---,,,***)))))))))+++++++++,,,,,,++++++++++++)))))))))+++,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++******))))))((((((''''''(((((()))******)))'''&&&((()))''''''''''''''''''''''''&&&&&&&&&&&&&&&''''''((('''&&&&&&%%%%%%&&&&&&'''$$$%%%&&&'''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###""""""!!!!!!""""""""""""""""""""""""!!!!!!!!!!!!!!!""""""###########################$$$$$$$$$$$$%%%%%%%%%%%%###$$$%%%$$$"""""""""###!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!"""""" !!!!!!!!!!!!!!!!!! !!!!!! !!! !!!!!!  !!!!!!!!!!!! !!!!!!!!!!!!  !!!!!!!!!!!!!!!!!! 777888999;;;<<<<<<<<<;;;999:::;;;<<<<<<;;;999888:::;;;<<<=========<<<;;;<<<<<<<<<<<<<<<===>>>>>>:::999999888999999:::::::::999999888888999999:::;;;::::::999999::::::;;;<<<<<<<<<<<<===>>>??????>>>>>>>>>=========<<<<<<;;;;;;;;;<<<<<<<<<<<<<<<;;;<<<<<<<<<<<<<<<;;;;;;888999:::;;;;;;999777666666888999;;;;;;:::999888:::999999999999999999:::::::::999999999888888888888777777777666666666555777777777777777777777777888888888888888777666666555555555444444444333333111222444333333222444555333222222111111222222333000111222222111111333555222222111111111222333333222111111000000111111222/////////....../////////000000000000000000000000///000000111111111111111---...////////////000111/////////111222111...,,,......///000000///......,,,------...............------------------------,,,------......------,,,+++,,,---...............------...////////////...------------------------*********++++++,,,,,,,,,************++++++,,,,,,+++,,,------+++))))))***,,,,,,------------,,,,,,,,,+++)))***++++++***((()))***+++,,,,,,+++***))),,,,,,,,,+++++++++******))))))(((''''''''''''''')))******((('''&&&(((***((((((((((((''''''''''''&&&&&&&&&&&&&&&'''(((((('''&&&&&&%%%%%%&&&&&&'''$$$%%%&&&'''''''''&&&&&&%%%&&&&&&&&&&&&''''''''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###""""""!!! """"""""""""""""""""""""!!!!!!!!!!!!!!!"""#######################################$$$$$$$$$%%%%%%###$$$%%%$$$"""""""""###!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!! !!!!!! !!! !!!!!!  !!!!!!!!!!!! !!!!!!  !!! 777888999:::;;;:::999888666888:::<<<<<<<<<;;;:::::::::<<<=========<<<;;;<<<;;;;;;;;;;;;<<<======999999999888999999::::::999888777666666777888999;;;::::::999999::::::;;;>>>============>>>>>>?????????>>>>>>=========<<<<<<<<<<<<<<<<<<<<<<<<<<<999:::;;;<<<============555666888888888777555333555777:::<<<<<<;;;999888:::999999888888999999::::::::::::999999999888888888888777777666666666555777777777777777777777777999::::::::::::999888888555555444444444333333333111222444333333333444555333222222222222222222333111222333222111111333555111111111111222333444444333222222222222222222333//////............//////000000000000000000000000000000111222222222222222,,,...000000///000111333//////000111222111...,,,...///000111111000///...,,,---......//////......------------------------,,,------......------,,,***+++,,,---............---...//////000000//////------------------------'''((()))***,,,...//////******+++++++++,,,,,,,,,+++---...---+++))))))***,,,------......------,,,---+++******++++++)))(((((()))+++,,,,,,+++)))(((,,,,,,,,,+++++++++*********)))(((''''''''''''''')))***)))(((&&&&&&(((***(((((((((((((((''''''''''''&&&&&&&&&&&&'''(((((('''&&&&&&%%%%%%&&&&&&'''###$$$&&&'''((('''&&&&&&&&&&&&&&&'''''''''(((((('''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########"""!!! """"""""""""""""""""""""!!!!!!!!!!!!!!!"""######$$$$$$##################"""""""""######$$$$$$$$$###$$$%%%$$$"""""""""###!!!!!!!!!!!!!!!!!!!!!!!!"""""""""""""""!!!!!!!!! !!!""""""!!!!!! !!!  !!! !!!!!!  !!!!!!!!!""" !!!!!!  !!!!!!  555777999::::::999:::;;;;;;;;;;;;<<<<<<;;;::::::999999::::::::::::;;;;;;:::;;;;;;<<<======<<<<<<;;;:::999999:::;;;>>>???999999999999:::;;;<<<===<<<;;;::::::999999999999=========>>>???>>>;;;888???@@@AAAAAA@@@???@@@AAA======>>>>>>===<<<;;;;;;<<<<<<<<<<<<<<<<<<<<<<<<888888888888888888888888=========<<<;;;:::888888888999;;;<<<<<<<<<;;;;;;===<<<:::999888999999:::777777777777777777777777888888888888888888888888:::::::::999888777666666333333333444444555555555222222222222222222222222333333333333333333333333000000000000000111111111111111222333444444444444444444333333222111000000///000111222222111000///000000000000////////////000000000000111111111111111111000000000000111111555444111///...///111333000000//////.........---////////////////////////------------------------------............---------...............------////////////////////////......//////...,,,+++)))***+++---......---+++***---------,,,,,,+++++++++///...,,,,,,,,,,,,***)))000///...---------------...---+++*********++++++******+++++++++,,,,,,,,,,,,,,,------,,,,,,++++++---,,,,,,+++***)))((((((******+++,,,,,,***)))(((&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((('''''''''&&&&&&&&&)))(((&&&%%%%%%&&&((())))))(((((('''&&&$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%""""""""""""""""""""""""!!!###$$$###"""!!!"""###""""""""""""""""""""""""#########"""""""""""""""""""""""""""""""""""""""###$$$%%%%%%$$$###"""!!!!!!!!!""""""#########$$$"""""""""""""""""""""""" !!!"""  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!!!!! !!!!!!!!!!!!!!!  !!!!!! 888999;;;;;;::::::<<<===;;;;;;;;;;;;;;;;;;;;;:::999:::::::::;;;<<<<<<<<<;;;;;;<<<<<<<<<<<<<<<<<<999999:::;;;;;;<<<<<<<<<888888999999:::;;;<<<=========<<<;;;;;;;;;;;;;;;======<<<===???>>><<<:::???@@@AAA@@@???>>>???AAA>>>>>>>>>>>>>>>>>>===<<<<<<<<<<<<<<<<<<<<<<<<<<<999999999999999999999999;;;<<<<<<===<<<;;;999888:::;;;<<<=========<<<;;;<<<;;;:::999999999:::;;;888888888888888888888888888888888888888888888888999999999999888777666666333333333444444555555555333222222222222222222333333333333333333333333333000000000000111111111111111111222333444444444444444444333333222111111000///000111222222111000///000000000000000000000/////////000000111111222222111111000000000000111111333222111//////000111222111111000000000/////////////////////////////////------------------------------............---------...............------........................///////////////---,,,++++++,,,---......---,,,+++.........------,,,,,,,,,///---,,,,,,,,,,,,***)))---------,,,,,,,,,,,,,,,---,,,+++*********++++++*********+++++++++,,,,,,,,,---------,,,+++******,,,++++++******)))))))))******++++++******)))(((&&&''''''((((((''''''&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((('''''''''&&&&&&&&&&&&((('''&&&%%%%%%&&&'''(((((((((((('''&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%########################!!!###$$$###"""!!!"""###"""""""""""""""""""""""""""""""""""""""#########"""""""""""""""""""""""""""###$$$$$$$$$###"""!!!!!!"""""""""############!!!!!!!!!!!!!!!!!!!!!!!!  !!!  !!!!!!""""""""""""!!!!!! !!!!!!!!!!!!!!!  !!!!!!;;;;;;<<<;;;:::;;;>>>@@@;;;;;;;;;;;;;;;;;;;;;;;;::::::;;;<<<<<<===>>>>>>;;;<<<<<<<<<<<<<<<;;;;;;777999;;;<<<<<<;;;999888888888999999:::<<<===>>><<<<<<;;;:::::::::;;;;;;===<<<;;;<<<>>>???>>>===>>>???@@@@@@>>>>>>???@@@===>>>???????????????>>>========================999999999999999999999999999;;;<<<======<<<:::999=========>>>======<<<;;;::::::999999999:::;;;;;;999999::::::::::::999999888888888888888888888888999999999999888777666666444444444444444555555555444333222111111222333444333333333333333333333333111111111111111111111111111111222333444444444444444333333222222111111111000000111111111111000000000000000000000000000000//////000000111222333333111111000000000000111111000000000111111111111222111111111111000000000000////////////////////////------------------------------............------------...............---........................//////000//////...---,,,+++,,,---......---,,,+++............------------...---++++++,,,,,,+++)))++++++++++++++++++,,,,,,---,,,+++*********++++++*********++++++++++++,,,---------,,,+++***)))(((******************************))))))((((((((()))&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&((('''&&&%%%%%%&&&'''(((''''''(((((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%########################!!!###$$$###"""!!!"""###""""""""""""""""""""""""!!!!!!""""""######$$$$$$""""""""""""""""""""""""!!!!!!"""#########""""""""""""""""""############!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!    !!!!!!""""""!!!!!!  !!!!!!!!!!!!   <<<<<<;;;:::999:::===@@@;;;:::::::::;;;;;;<<<<<<;;;;;;<<<===>>>??????@@@<<<<<<<<<===<<<<<<;;;:::999:::;;;;;;;;;:::999888999999999:::;;;<<<===>>>:::999999888888888999999===<<<;;;;;;>>>???@@@???===?????????>>>===>>>???<<<===>>>>>>????????????>>>>>>>>>>>>>>>>>>>>>>>>::::::::::::::::::::::::888:::<<<>>>>>>===<<<:::============<<<<<<;;;;;;999999999999:::;;;;;;<<<::::::;;;<<<<<<;;;::::::888888888888888888888888888888888888888777666666444444444555555555555555555444222111111222444555333333333333333333333333222222111111111111111000111111222333444444444444333333333222222111111111000000000111111000000000000000000000000111111111//////000111222222333444111111000000000000111111...///000222222222111111000000000000000000000000////////////////////////------------------------------............------,,,---......///................................................------,,,,,,---............---,,,---------------------------,,,++++++,,,,,,+++))))))******+++,,,,,,,,,,,,,,,+++++++++++++++++++++************++++++++++++,,,,,,,,,,,,+++)))((('''((()))))))))*********++++++***((('''''''''((()))''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&''''''(((((('''''''''$$$$$$$$$$$$$$$$$$$$$$$$########################!!!###$$$###"""!!!"""###"""""""""""""""""""""""" !!!"""###$$$$$$%%%"""""""""""""""""""""""" !!!!!!"""""""""""""""""""""""""""#########!!!!!!!!!!!!!!!!!!!!!!!!"""!!!    !!!!!!!!!!!!!!!!!!  !!!!!!!!!   ;;;;;;:::999888888;;;>>>;;;::::::::::::;;;<<<===<<<<<<===>>>>>>???@@@@@@;;;<<<<<<<<<<<<<<<;;;;;;<<<;;;:::999999999:::;;;::::::::::::;;;<<<======999999999888888999::::::===<<<;;;<<<>>>@@@@@@@@@===?????????>>>===>>>???;;;;;;<<<===>>>>>>>>>>>>????????????????????????::::::::::::::::::::::::888:::<<<===>>>>>><<<<<<===<<<<<<;;;;;;:::::::::888999999:::;;;;;;;;;;;;:::;;;<<<======<<<;;;:::888888888888888888888888777777888888888777666666555555555555555555555555444444333222222333444444333333333333333333333333333222222222111111000000111111222333444444444444333333222222222222222111111000000000000000000111///000000000111111111222///000000111222333333333111111000000000000111111---...000222222222111000////////////////////////////////////////////////------------------------------............------,,,------...//////..............................------,,,,,,,,,,,,,,,,,,,,,------------------,,,++++++++++++++++++++++++---+++******+++,,,+++))))))***+++,,,------,,,,,,++++++++++++++++++++++++))))))*********+++++++++++++++++++++***)))((('''((((((((()))******+++++++++***((('''''''''((()))'''(((((((((((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%&&&''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$########################!!!###$$$###"""!!!"""###"""""""""""""""""""""""" !!!"""###$$$$$$%%%"""""""""""""""""""""""" !!!!!!!!!"""############"""""""""""""""""" """!!!    !!!!!!!!!!!!  !!!   999999999888777777999;;;;;;:::999999:::;;;===>>>======>>>>>>>>>>>>??????:::;;;;;;<<<======<<<<<<===<<<:::999999:::<<<>>><<<<<<;;;;;;;;;;;;<<<<<<<<<<<<;;;;;;;;;<<<=========<<<<<<===???@@@@@@???>>>???@@@@@@>>>>>>???@@@;;;<<<<<<============<<<>>>>>>>>>>>>>>>>>>>>>>>>;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;<<<===============<<<<<<;;;:::::::::;;;;;;999999:::;;;;;;;;;::::::999;;;<<<======<<<;;;999888888888888888888888888666777777888888777666666666666666555555555555555333333444444444444333333333333333333333333333333333333333222111111000000111111222333444444444444222222222222222222222222111111000000000000111111///000000111111222222222111111111222222222222222111111000000000000111111...///000111111111000///............////////////////////////////////////------------------------------............------,,,,,,---...////////////------------------------,,,,,,+++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,************++++++++++++,,,+++******+++,,,+++))))))***+++,,,---,,,+++*********+++,,,,,,,,,++++++)))))))))************+++)))************)))((((((((((((((())))))***************))))))((((((((()))'''(((((())))))(((((('''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$###"""!!!"""###""""""""""""""""""""""""!!!!!!""""""######$$$$$$""""""""""""""""""""""""""""""!!!!!!!!!"""##################"""""""""""" !!!!!!    !!!!!!  !!!    888999:::999888777888:::;;;:::999999999;;;===???>>>>>>>>>>>>>>>=========999999;;;<<<======>>>>>>;;;;;;;;;;;;<<<======>>>>>>===<<<;;;;;;::::::;;;===<<<<<<<<<======>>>???===<<<===???@@@AAA???===???@@@AAA@@@???>>>???AAA======>>>>>>>>>======<<<>>>>>>>>>>>>>>>>>>>>>>>>;;;;;;;;;;;;;;;;;;;;;;;;======<<<;;;;;;<<<===>>><<<<<<;;;:::;;;;;;<<<===999:::;;;;;;;;;:::999888999:::<<<>>>>>><<<:::999888888888888888888888888666666777777777777777666777666666666555555555444222333444555555444333222333333333333333333333333444444333222222111000000111111222333444444444444222222222222222222222222222111000//////000111222///000000111111222333333333333222222222222111111111111000000000000111111000000000000000000//////......//////000000000000////////////////////////------------------------------............------+++,,,---...////////////---------------------------,,,+++++++++,,,------+++++++++******+++++++++*********++++++,,,,,,,,,+++***)))***+++,,,+++***)))***+++,,,,,,***)))''')))***+++,,,,,,,,,,,,+++))))))))))))************'''((())))))***)))))))))((((((((()))))))))))))))******++++++******)))((((((((())))))))))))((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$###"""!!!"""###"""""""""""""""""""""""""""""""""""""""#########""""""""""""""""""""""""%%%$$$###"""""""""##################"""""""""!!!  !!!   !!!!!!  !!! !!!!!!  888999;;;;;;999888888999;;;:::999888999;;;===?????????>>>>>>===<<<<<<<<<888999:::<<<===>>>>>>???999:::<<<>>>??????>>>===???>>>===<<<;;;:::::::::;;;;;;;;;;;;;;;<<<===>>>======>>>@@@AAAAAA>>><<>>===<<<========================<<<<<<<<<<<<<<<<<<<<<<<>><<<::::::<<<===???===<<<;;;;;;<<<===>>>???:::;;;;;;<<<;;;:::888777888:::<<<======<<<:::888888888888888888888888888666666777777777777777666777777666666555555555444111333555777777555333111333333333333333333333333444444333333222111000000111111222333444444444444222222222222222222222222222111000//////000111222///000000111222222333333444444333222222111111000111111000000000000111111111111000000//////......//////000000111111111222////////////////////////---------------------------..................---+++,,,---...////////////------------------------...---,,,,,,,,,---...///+++******))))))******++++++++++++,,,,,,---------+++***)))***+++,,,+++***((()))***+++***)))'''%%%)))***+++,,,---,,,,,,+++))))))))))))************&&&'''((()))************)))))))))))))))(((((((((***++++++,,,,,,+++)))((((((((())))))))))))((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%$$$###"""########################$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$###"""!!!"""###""""""""""""""""""""""""#########"""""""""""""""""""""""""""""""""""""""&&&%%%$$$"""""""""######$$$#########""""""!!!!!!  !!!"""    !!!!!! !!!!!!  !!!!!! ;;;;;;;;;::::::999999999999999::::::::::::;;;;;;>>>===<<<:::::::::;;;<<<;;;:::888888:::===@@@BBB???>>>;;;999999:::<<<>>>>>>>>>===<<<;;;::::::999<<<<<<<<<============>>>===<<<<<<<<<<<<>>>@@@AAAAAABBBCCCCCCCCCCCCBBBAAA>>>>>>======<<<<<<;;;;;;;;;===??????>>>======>>>>>>>>>======<<<<<<<<<;;;=========;;;888777888999999999:::;;;<<<===>>>???::::::;;;;;;;;;:::999888:::;;;<<<======;;;999888::::::999999999999888888777888888999999777666555666666555555555444444444444444555555444444333222222222333333333444444444333333333333333333333333333333222222111222222222333222222111000///......111111222222222222111111222222222222222111000///...///000222222111111000000000000000000//////...///000000///...------............///////////////........./////////////////////...------------...000///...---------------+++,,,---.........---,,,---------------------------------...------,,,,,,,,,,,,+++***))))))******,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++++++++++++++*********))))))(((((()))))))))***+++++++++,,,)))))))))))))))******++++++++++++************)))+++++++++***)))((((((''')))+++,,,+++)))''''''(((((((((((((((((((((((((((''''''&&&%%%&&&'''((()))''''''''''''''''''''''''$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&'''((()))%%%$$$$$$######$$$$$$%%%$$$$$$############$$$$$$"""""""""###$$$$$$$$$%%%""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!"""###$$$%%%&&&%%%###!!!!!!"""###$$$""""""#########$$$$$$$$$$$$$$$$$$###"""!!!!!!   !!!!!!  !!!!!!   ;;;;;;;;;::::::999999999999999::::::::::::;;;;;;<<<<<<;;;:::::::::::::::::::::999999;;;===@@@AAA@@@>>>===;;;;;;<<<===>>>>>>>>>>>>======<<<;;;;;;<<<<<<=========>>>>>>>>>>>>===============>>>>>>??????@@@AAAAAA@@@??????AAA@@@@@@@@@????????????===???@@@@@@>>>===>>>???>>>=========<<<<<<<<<<<<===>>>>>><<<999888999::::::::::::;;;;;;;;;;;;;;;::::::;;;<<<;;;:::999888:::;;;<<<===<<<;;;999888;;;;;;;;;::::::999999999777888888999888777666555666666555555555444444444444444555555444444333222222222222222333333333444333333333333333333333333333333222222222222222333333222222111111000000///111111222222222222111111222222222222222111000000...///111222222222111000000000000000000//////...111222222222000///000111...////////////////////////////////////.........///......---,,,---------......---,,,,,,,,,,,,,,,,,,---.........---,,,+++------------------------,,,------...------,,,,,,,,,,,,+++***************,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++************)))))))))(((******************++++++)))))))))))))))******++++++++++++*********))))))++++++******)))((((((''')))+++,,,+++)))''''''((('''''''''''''''''''''''''''&&&&&&%%%&&&'''((()))''''''''''''''''''''''''$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((((((%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$############$$$$$$##################$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!"""###$$$%%%&&&%%%###"""!!!"""###$$$""""""#########$$$$$$$$$$$$$$$######"""!!!!!!   !!!!!!  !!!  ;;;;;;::::::::::::999999999999::::::::::::;;;;;;:::::::::;;;::::::999999999999:::;;;===>>>???@@@??????>>>>>>>>>>>>======>>>>>>>>>>>>>>>>>>>>>>>><<<<<<<<<=========>>>>>>>>>>>>>>>>>>>>>======<<<<<<======>>>>>>======<<>>>>>>>>============<<<<<<<<<<<<>>>>>>>>><<<:::999:::;;;;;;;;;;;;::::::999999999:::;;;;;;<<<<<<:::999888::::::;;;<<<<<<;;;999888===<<<<<<;;;:::999999999777888888888888777666666666666666555555555444444444444555555444444333222111111222222222333333333222222222333333444444444333333222222222222333333222222222222222222222222111111222222222222111111222222222222222222111000//////111222222222111000000000111111000000///...111222222222000///000111//////////////////......000000//////......------...------,,,,,,,,,,,,,,,------,,,+++++++++,,,,,,............---,,,++++++------------------------,,,,,,------...------,,,,,,++++++************+++,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++************))))))))))))******************)))))))))))))))))))))******+++++++++*********)))))))))+++******))))))((((((''')))***++++++)))''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''(((%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$############$$$$$$##################""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!"""###$$$%%%%%%$$$###"""""""""###$$$"""""""""############$$$$$$######""""""!!!!!! !!!!!!!!!    ::::::::::::::::::::::::999999999:::::::::;;;;;;999:::;;;<<<<<<;;;999999888:::;;;===>>>???>>>>>>>>>>>>?????????>>>===<<<<<<<<<=========>>>>>>>>>;;;;;;;;;;;;<<<<<<<<<<<<<<<===>>>??????>>>===<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>???AAABBBAAA>>>========================<<<<<<<<<===>>>>>><<<:::999:::;;;;;;;;;;;;::::::::::::999:::;;;<<<<<<<<<;;;999999999:::;;;;;;;;;::::::999<<<<<<;;;:::999888888777888888888888777777777666666666666666555555555555444444555555444444333222111111111222222222333333111111222333333444555555333333222222222333444444222222222333333444444444111222222333333222222111222222222333333222111111///000111222333222111111000111111111111000//////...000111000......///000////////////............111111000///...------,,,------,,,++++++++++++,,,------,,,,,,,,,,,,,,,---//////......---,,,+++***------------------------,,,,,,------...---------,,,++++++******+++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++*********)))))))))))))))++++++******))))))(((((()))))))))))))))******+++************))))))))))))******))))))(((((((((((()))***+++***((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&''''''%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$######""""""!!!!!!""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!"""###$$$$$$$$$$$$###""""""######$$$""""""""""""##################""""""!!!!!!!!!!!!"""""""""!!!     ::::::::::::::::::::::::999999999:::::::::;;;;;;:::;;;<<<======<<<;;;:::999:::<<<>>>??????>>>===<<<===>>>??????===<<<::::::;;;;;;<<<<<<======>>>999999::::::::::::;;;;;;999:::<<<>>>@@@@@@??????================================================>>>@@@AAA@@@===<<<;;;<<<<<<<<<<<<===============;;;<<<<<<;;;999888999:::;;;;;;;;;;;;<<<<<<<<<<<<;;;;;;<<<===<<<;;;:::999999999::::::::::::::::::::::::999999888777777666888888888777777777777777777777666666666555555555444444555555444444333222111111222222222333333333111111222333333444555555333222222222333444444555222222222333444444555555222222333333333333222222111222222333333333222222///000111333333222222111111111111111111000000///...000111000///...///111000000//////.........---111111000///...------,,,------,,,++++++++++++,,,......------------......//////...---,,,+++++++++------------------------+++,,,,,,---.........---,,,+++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++))))))))))))))))))******+++******))))))((((((((()))))))))))))))******+++*********)))))))))(((((()))))))))((((((((((((((((((***+++***(((&&&&&&'''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$############$$$$$$$$$######""""""!!!!!!!!!""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""###$$$##################$$$$$$"""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!###""""""!!!!!!    !!! !!!!!! !!! 999999::::::::::::;;;;;;999999::::::::::::;;;;;;;;;;;;<<<<<<======<<<<<<:::;;;===>>>??????>>>>>><<<===>>>???>>>===<<<;;;:::;;;;;;;;;<<<<<<======999999999:::::::::;;;;;;999:::;;;===???@@@AAAAAA???>>>>>>======>>>>>>???>>>>>>>>>>>>>>>?????????===???@@@???===<<<<<<<<<<<<<<<<<<===============;;;;;;;;;:::888888999:::;;;;;;;;;<<<<<<=========;;;<<<<<<===<<<;;;:::999999999999999::::::::::::888888888888777777777777999888888777666777777777777777777666666666555555444444555555444444333222222222333333333444444444222222222333333444444444333222222333333444555666222222222333333444444444222222333333333333222222111222333333333333333333000000222333333333222111111111222222111111000///000222333222111111222444000000000///......------000000//////......------...------,,,,,,,,,,,,,,,......---------.../////////...---,,,,,,,,,,,,,,,------------------------++++++,,,---............,,,++++++++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++))))))))))))************))))))))))))))))))(((((()))))))))))))))******+++******)))))))))(((((((((((((((((((((((((((((((((((()))******(((&&&&&&'''(((((((((((((((((((((((($$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$############$$$$$$""""""""""""""""""!!!!!!""""""""""""""""""""""""""""""""""""""""""""""""###"""""""""""""""######"""#########$$$$$$$$$$$$###"""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""""""""!!!    !!!""" !!!!!!!!! !!!!!!!!!!!!!!! 999999999::::::;;;;;;;;;999999::::::::::::;;;;;;;;;:::::::::;;;;;;<<<===;;;<<<===>>>>>>>>>>>>>>>>>>?????????>>>>>>======<<<<<<<<<<<<============::::::;;;;;;;;;<<<<<<<<<;;;;;;;;;<<<===???@@@AAA@@@???>>>======>>>???@@@>>>>>>?????????@@@@@@@@@===>>>@@@@@@>>>======>>><<<<<<<<<<<<=========>>>;;;<<<<<<;;;999999:::<<<<<<<<<;;;;;;;;;;;;;;;:::;;;<<<=========<<<:::999999999888999999::::::;;;777888888888888999999999999999777666666666777888777777777777666666666555444444555555444444333222333333444444444555555555333333333333333333333333222222222333333555666666222222222222333333333333222333333444444333333222111222333333444444333333000111222333333333222222111222222222222111000000000111333333222111333444111000000///......------///////////////.........///......---,,,------------,,,,,,,,,------...///......---,,,,,,,,,---...------------------------***+++,,,---............+++++++++++++++,,,---...,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++((()))))))))************((((((((())))))))))))))))))))))))))))))******+++***)))))))))((((((((((((((((((((((((((((((((((((((()))***)))'''&&&&&&&&&''''''''''''''''''''''''###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&'''''''''((((((((('''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$############$$$$$$!!!!!!!!!"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""######""""""""""""######""""""###$$$$$$$$$$$$$$$######""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""!!!  !!!  !!!!!!!!!  !!!### !!!!!!!!!!!! !!!!!!!!!"""""""""    999999999::::::;;;;;;;;;999999:::::::::;;;;;;;;;::::::999888999:::<<<===<<<<<<======>>>>>>??????@@@@@@@@@???????????????>>>>>>>>>>>>>>>=========<<<<<<<<<=========>>>>>>>>>===<<<<<<<<<>>>???@@@@@@???>>>======>>>???@@@======>>>>>>?????????@@@===???@@@AAA?????????@@@;;;<<<<<<<<<======>>>>>><<<======<<<::::::;;;======<<<<<<;;;999888888777;;;<<<=========<<<::::::999888888888999::::::;;;777888888999::::::;;;;;;:::999777666666666777888777777777777666666666666444444555555444444333222444444444555555555666666444333333333333333333333222222222333444555666777222222222222222222222222222333333444444333333222111222333333444444444444000111222333444333222222111222222222222111000000...///111111000000111222111000000///...---------........./////////////////////...------------...++++++++++++,,,,,,---......---,,,+++,,,---...///------------------------***+++,,,---............++++++++++++,,,,,,---...,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++(((((())))))*********+++''''''(((((())))))******)))))))))))))))******+++))))))))))))(((((((((((('''''''''(((((((((((((((((()))***)))'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&'''''''''(((((((((((()))'''&&&%%%%%%$$$$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''$$$$$$############$$$$$$ !!!!!!""""""######""""""""""""""""""""""""""""""""""""""""""""""""######"""""""""""""""###!!!"""###$$$$$$$$$$$$$$$######""""""!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!  !!!!!!!!!  """### !!!!!!!!!""" !!!!!!!!!""""""######!!!!!!!!!!!!!!!!!!!!!!!! !!!   ::::::::::::::::::::::::::::::;;;;;;;;;;;;;;;;;;;;;:::999999:::===???AAA?????????@@@BBBBBBAAA???;;;===?????????>>>???@@@@@@@@@???>>>======>>>>>>>>>>>>>>>===>>>>>>?????????????????????@@@@@@AAA??????>>>>>>======<<<<<<========================<<<<<<;;;;;;;;;<<<<<<===>>>>>>>>>>>>>>>=========;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;<<<<<<============<<<<<<:::::::::888777777:::<<<;;;999777888:::;;;:::777777888999::::::999888777777777666666555555555444555555555555444333222222777777777666555555555444444555555666555444222111222333444444333333555777777666555444333222111111222222222222222222222222111111111222222333333444444333111000000111333444222333333444333222000///222222222111111111000000111111111000000000000000111//////000111222111000000000//////.........---+++******)))))))))))))))---------,,,,,,+++++++++,,,...//////---,,,,,,---'''((()))***+++,,,,,,,,,............---,,,+++***------------------------,,,,,,***)))))))))***+++***++++++++++++***))))))''''''''''''''''''''''''))))))(((((('''''''''&&&))))))))))))))))))))))))******************************))))))((((((''''''''''''&&&&&&&&&&&&''''''&&&&&&'''(((((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''(((((((((''''''$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$&&&''''''&&&$$$$$$%%%%%%&&&&&&'''&&&&&&%%%########################$$$$$$##################"""############$$$$$$$$$$$$#########""""""!!!!!!""""""""""""##########################################""""""!!!!!! !!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!   ######""""""!!!!!! """!!! !!!###$$$!!!!!! !!!!!! ::::::::::::::::::::::::::::::;;;;;;;;;;;;<<<<<<::::::999999:::<<<>>>@@@@@@??????@@@AAABBB@@@???<<<>>>@@@@@@>>>>>>>>>???@@@??????>>>======>>>>>>@@@??????>>>>>>>>>??????>>>>>>>>>>>>>>>???@@@@@@???>>>>>>>>>=========<<>>;;;999777888:::;;;:::888777888999::::::999888777777666666666555555555555444444555555555444333333666555555555555555555444444444555555444444333333333444555444333333555666555444444444444444333333222222222222222222222222222222222222222333333333333222000//////000222333111222333333333222111000222222222111111111000000111111111111000000000000111//////000111222111000000/////////............,,,,,,+++************+++---------,,,,,,,,,++++++***,,,------+++******+++((()))***++++++,,,++++++,,,,,,---------------,,,------------------------,,,+++***)))))))))***++++++++++++++++++******)))(((((((((((((((((((((((()))(((((((((''''''''''''******************************************************))))))((((((''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''((('''&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%################################################"""############$$$$$$$$$############"""""""""!!!!!!!!!"""""""""####################################"""""""""!!!!!!!!! !!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!   ###"""""""""!!!!!!!!! !!!!!!!!!!!!!!!""""""###!!!!!! !!!!!! ::::::::::::::::::::::::::::::;;;;;;;;;<<<<<<<<<::::::999999:::<<<>>>???@@@@@@???@@@AAAAAA???>>>===???@@@@@@>>>======>>>??????>>>=========>>>>>>AAAAAA@@@??????>>>>>>>>>===============>>>??????>>>>>>>>>>>>============@@@@@@@@@@@@@@@@@@@@@@@@>>>======<<<<<<=========;;;;;;;;;;;;;;;;;;;;;;;;<<<<<<<<<<<<<<<<<<<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;:::;;;;;;<<<<<<;;;;;;:::::::::888666555777;;;???:::999888888::::::999888777888999::::::999888777666666666666555555555555333444444555555555444444333444444444444444444555444333333333333444555555555666666555333333444666333333333444444555555555333333333333333333333333333333333333222222222222222111000//////000111222000111222222333222222222222222222111111111111111111111111111111111111111111//////000111222111000////////////...............---,,,,,,++++++,,,,,,------------,,,,,,,,,,,,***,,,------+++******+++******++++++++++++************,,,---............------------------------,,,+++******))))))******+++,,,,,,,,,,,,+++******))))))))))))))))))))))))((((((((((((''''''''''''******************************************************))))))((((((''''''''''''&&&&&&&&&&&&''''''((('''&&&%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$################################################"""############$$$$$$$$$############""""""""""""!!!!!!!!!!!!""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!   """"""""""""!!!!!!!!!!!! !!!!!!"""""""""""""""!!!!!! !!!!!! 999999::::::::::::;;;;;;::::::;;;;;;<<<<<<======;;;;;;;;;;;;<<<===>>>???AAA@@@???@@@AAA@@@???===>>>???AAA@@@>>>=========???>>>>>>=========>>>>>>AAAAAAAAA@@@???>>>======<<<<<<<<<<<<<<<===>>>>>>>>>>>>>>>>>>============???????????????????????????>>>>>>============>>><<<<<<===============>>>========================;;;;;;;;;;;;;;;;;;;;;;;;999::::::;;;;;;::::::999===<<<999666555666:::===999999999999999:::999999777888999::::::999888777666666666666666555555555333333444555555666555555222222222333333444444444333333222222333444666777666777777555333333444555333333333444444444555555333333333333333333333333444444444333333222222111222222111000000111222222000000111111222222222333111111111111111111111111000111111111111111222222111/////////111222111000///////////////............---,,,,,,++++++,,,,,,------------------,,,,,,,,,...///...---,,,,,,,,,+++,,,,,,,,,++++++***)))******+++,,,------------,,,,,,,,,,,,,,,,,,,,,,,,+++++++++***************,,,,,,,,,,,,,,,+++******((((((((((((((((((((((((((((((((((((((('''''''''******************************************************))))))((((((''''''''''''&&&&&&&&&&&&''''''((('''%%%$$$$$$%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&'''&&&&&&&&&&&&%%%%%%$$$##########################################$$$$$$$$$""""""#########$$$$$$$$$#########""""""""""""""" !!!!!!!!!"""""""""!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!    """"""""""""!!!!!!!!!!!! """#########"""!!!!!!!!! !!!!!! 999999999::::::;;;;;;;;;::::::;;;<<<<<<===>>>>>>======>>>>>>??????@@@@@@@@@???>>>???@@@@@@???===>>>???AAA@@@>>>=========>>>===============>>>>>>@@@AAAAAAAAA@@@>>>===<<<<<<<<<<<<<<<<<<======>>>============>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>??????>>>===============;;;<<<<<<<<<======>>>>>>========================;;;;;;;;;;;;;;;;;;;;;;;;999999::::::::::::999999???>>>;;;777555555777:::999999:::999999999999999777888999::::::999888777555555555666666666666666333333444555666666666666111222222222333333444444333222222222333555777888666666666555333222444555555555444444444333333333333333333333333333333333555444444333333222222222333333333222222333333333000000000111111222222333111111111111111111111111000000111111222222222333111/////////111222111000.........///////////////------,,,++++++++++++,,,------------------------,,,...///...---,,,,,,,,,,,,,,,,,,,,,,,,+++***)))+++,,,,,,,,,,,,,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++******))))))+++,,,,,,,,,,,,+++******'''''''''''''''''''''''''''''''''((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))******))))))((((((''''''''''''&&&&&&&&&&&&''''''((('''%%%$$$$$$%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%%%%%%%%%%'''(((%%%%%%&&&&&&%%%$$$$$$###########################""""""#########$$$$$$$$$""""""#########$$$$$$$$$""""""""""""""""""######!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!    !!!!!!   !!!!!!!!!!!!"""""""""""" """#########"""!!!!!!!!! !!!!!!  888999999::::::;;;;;;<<<::::::;;;<<<===>>>>>>????????????@@@@@@AAAAAAAAA>>>======???@@@AAA@@@>>>===???@@@@@@>>>======>>>======<<<<<<======>>>>>>>>>???@@@@@@???>>>===;;;<<<<<<<<<<<<<<<===>>>>>>============>>>>>>>>>>>><<<<<<<<<<<<<<<<<<<<<<<>>===<<<<<<<<<<<<999999999:::;;;;;;<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;999::::::;;;;;;::::::999>>>>>><<<999666555666888888999::::::888888999:::777888999::::::999888777555555555666666666666666444444555666666666555555222333333333333333333444222222222333444555666777444555555444222222333555555555555444444333333333333333333333333333333333444444444444333333333333444444444444444444444444111111000000000111222222111111111111111222222222000000111111222333333333111//////000111222111000.........///////////////------,,,++++++++++++,,,------------............***,,,------+++******+++,,,,,,------,,,+++******+++,,,,,,,,,,,,,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,***++++++++++++***))))))***++++++++++++***))))))'''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))******))))))((((((''''''''''''&&&&&&&&&&&&'''''''''&&&%%%$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%$$$$$$########################"""""""""###$$$$$$%%%%%%"""############$$$$$$$$$""""""""""""############""""""""""""############""""""""""""""""""""""""!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!    !!!!!!!!!!!!   !!!!!!!!!!!!"""""""""""" !!!!!!"""""""""""""""!!!!!! !!!!!!  888888999::::::;;;<<<<<<::::::;;;<<<===>>>????????????@@@@@@AAAAAA@@@@@@<<<<<<<<<>>>@@@AAAAAA???<<<>>>@@@@@@>>>>>>>>>???<<<<<<<<<<<<<<<===>>>>>><<<===>>>??????>>><<<;;;======<<<<<<======>>>???<<<=========>>>>>>>>>???;;;;;;;;;;;;;;;;;;;;;;;;???>>>===<<<;;;;;;;;;;;;888888999::::::;;;<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;::::::;;;;;;;;;;;;:::::::::;;;;;;:::888777888999888999;;;:::888777999;;;777888999::::::999888777555555555555666666666777555666666666666555555444444444444444333333333333222222333444555555555555222333333333222222333555333333444444444444444555444444444444444444444444333333333444444444444444333333333444444333333333222111000//////000111111000000111111111222222222000000111222222333444444111//////000111222111000............/////////000///...------,,,---------------------.........///***,,,------+++******+++,,,,,,,,,---,,,,,,++++++)))***+++,,,,,,,,,,,,,,,++++++++++++++++++++++++***++++++,,,+++***)))((()))************)))((((((''''''''''''''''''''''''''''''''''''((((((((()))''''''''''''''''''''''''))))))))))))))))))))))))******))))))((((((''''''''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&''')))***((('''''''''&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&"""###$$$%%%%%%%%%%%%%%%########################!!!""""""###$$$$$$%%%%%%"""############$$$$$$$$$!!!"""""""""########################$$$$$$$$$$$$######################## !!!!!!!!!"""""""""###!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!    !!!!!!!!!!!!!!!  !!!!!!!!!"""""""""###!!!!!!!!!!!!!!!""""""###!!!!!! !!!!!!  888888999::::::;;;<<<<<<::::::;;;<<<===>>>???@@@>>>??????@@@@@@@@@??????;;;;;;<<<>>>@@@BBBAAA@@@;;;===?????????>>>???@@@<<<<<<<<<<<<<<<===>>>???:::;;;===>>>???>>><<<;;;===============>>>??????<<<=========>>>>>>??????<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>===;;;;;;:::::::::::::::;;;;;;<<<===>>>>>>;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;:::;;;;;;<<<<<<;;;;;;:::666888:::;;;:::999999:::777:::;;;:::888777999;;;777888999::::::999888777444555555555666666777777666777777777666555444444555555555444444333333333222333444555666555444333000111222222111111333555111222222333444666666777444444444444444444444444333333333444444555555555111222222333333222222111333222111/////////000000000000111111222222222222000000111222333333444444111//////000111222111000---.........//////000000000000///...............---------.........//////,,,...//////---,,,,,,---+++,,,,,,------,,,,,,,,,'''((()))+++---.........++++++++++++++++++++++++******+++,,,+++***)))((()))))))))))))))(((''''''))))))))))))))))))))))))&&&'''''''''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))*********)))(((((('''''''''''''''&&&&&&'''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&(((***,,,(((((('''''''''&&&&&&&&&%%%&&&'''(((((('''&&&%%%!!!"""###$$$%%%&&&&&&&&&########################!!!""""""###$$$$$$%%%%%%"""############$$$$$$$$$!!!!!!""""""#########$$$######$$$$$$$$$%%%%%%%%%######################## !!!!!!!!!""""""######!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!   !!!!!! !!!""""""!!!!!! !!!!!!  !!!!!!!!!""""""######"""!!! !!!###$$$!!!!!! !!!!!!  ===;;;888666777999<<<>>>>>>===<<<;;;;;;<<<===>>>???>>>>>>>>>???@@@AAAAAABBBAAAAAA@@@???>>>======;;;<<<>>>???>>>===>>>???@@@???>>>======>>>???@@@===???AAA>>>:::888:::>>>;;;;;;;;;<<>>??????>>>===;;;:::888999:::;;;============<<<>>>>>>>>>>>>>>>======<<<>>>===<<<;;;;;;<<<===>>>@@@===::::::<<<;;;999666;;;;;;;;;::::::999999999;;;::::::::::::;;;<<<<<<===<<<;;;;;;999999888777999999999999999999999999:::::::::::::::999888777666777777666444222333444555444444333333333444444666666666666666666666666222444555555444222222222...111555666555444333333444333333333333222222222222333444444555555444444555555444333333333444444333333333333333333333333333333333333333333333333000000000000000111111222111111222222222222111111111111000000000000111111///////////////////////////...---,,,,,,,,,,,,,,,---,,,,,,++++++,,,,,,---,,,---...---+++***+++,,,,,,,,,---......---,,,,,,---,,,++++++,,,---///000,,,,,,------,,,,,,+++***))))))))))))))))))))))))***)))(((&&&&&&''''''((())))))))))))))))))))))))''''''''''''''''''''''''&&&&&&&&&''''''''''''((((((((((((((())))))))))))+++---,,,(((&&&((('''###***)))'''%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%&&&''''''((((((''''''''''''((()))))))))))))))'''((()))))))))(((&&&%%%###$$$$$$%%%%%%$$$$$$###&&&&&&%%%%%%%%%%%%$$$$$$%%%$$$###"""""""""$$$$$$$$$$$$############$$$$$$###$$$$$$###""""""###%%%$$$###"""""""""###%%%%%%$$$$$$$$$$$$$$$###"""!!!""""""!!!!!! !!!!!!!!!!!!""""""""""""""""""!!! !!!!!!!!!!!!!!!!!!""""""""""""!!!!!!""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!""""""""""""######"""""""""""""""###""""""""""""""""""""""""   !!!<<<;;;999888888:::<<<>>>===<<<;;;;;;;;;;;;<<<===>>>>>>>>>>>>>>>>>>??????@@@??????>>>>>>>>>??????;;;===??????>>>===>>>?????????>>>>>>>>>>>>??????;;;>>>???===888777999===<<<;;;;;;<<<>>>@@@???>>>??????@@@???>>>===;;;:::888999;;;<<<============>>>>>>>>>>>>===<<<;;;;;;======<<<;;;;;;<<<=========;;;999:::<<<<<<;;;999<<<<<<;;;;;;;;;;;;;;;;;;;;;::::::::::::;;;<<<<<<<<<;;;;;;::::::999999888::::::999999999999999999::::::::::::999888666666555666777666444333333444555555444444444444444555555555555555555555555555111333444444111/////////---000444666555444333444555444444444333333222222444555666666777777666666222222222222222333444555333333333333333333333333333333333333333333333333111111111111111222222333111111222222222222111111111111000000000000111111////////////////////////......---,,,,,,,,,---------,,,,,,++++++,,,,,,---+++,,,---,,,*********,,,,,,,,,---......---,,,,,,...---,,,++++++,,,------,,,,,,------,,,,,,+++***))))))))))))))))))))))))***)))((('''&&&''''''(((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''((((((((())))))))))))+++---,,,(((&&&((('''$$$)))((('''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''''''''((()))))))))))))))'''((()))))))))(((&&&%%%$$$$$$%%%%%%%%%%%%$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$############$$$$$$$$$$$$############$$$$$$###$$$$$$###""""""###%%%$$$###"""""""""###$$$%%%$$$$$$$$$$$$$$$###""""""""""""!!!!!!!!! !!!!!!!!!!!!""""""""""""""""""!!! !!! !!!!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!""""""""""""######""""""""""""######""""""""""""""""""""""""   ;;;::::::::::::;;;<<<<<<<<<<<<;;;;;;;;;;;;<<<<<<>>>>>>>>>>>>============???>>>===<<<<<<>>>@@@AAA<<<===??????>>>===>>>???>>>>>>????????????>>>>>><<<>>>???===:::888:::======<<<;;;<<<>>>???>>>===???@@@@@@@@@???===<<<:::888999:::<<<======>>>>>>============<<<;;;:::999<<<<<<;;;;;;;;;;;;<<<<<<;;;:::999:::<<<===<<<;;;;;;;;;<<<<<<<<<<<<<<<<<<;;;::::::::::::;;;<<<<<<:::::::::::::::::::::::::::::::::999999888888888::::::999999888666555444444555666555444333444555555555444444444555555666444444444444444444444444111222333111...+++******---000333555555444555555666666555444333333222222444555666666777777666666000000000111222333555555222222222222222222222222444444333333222222111111222222222111222333333444111111222222222222111111000000000000000000000000////////////////////////------,,,,,,,,,---......---,,,,,,++++++,,,,,,---)))***++++++******+++,,,,,,------......------,,,......,,,+++************,,,,,,,,,,,,,,,++++++***))))))))))))))))))))))))))))))(((''''''''''''(((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''((((((((()))))))))***---,,,(((&&&((('''$$$(((((('''&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((((((((((((''''''(((((()))))))))))))))((((((((()))(((((('''&&&%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$###$$$$$$############$$$$$$###$$$%%%$$$""""""$$$%%%######""""""######$$$%%%###$$$$$$$$$$$$###""""""""""""!!!!!!!!!!!! !!!!!!!!!!!!""""""""""""###"""!!!!!! !!!!!! !!!!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!""""""""""""###"""""""""""""""######""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!! ::::::;;;<<<<<<<<<<<<<<<======<<<<<<<<<<<<======???????????????>>>======@@@>>><<<;;;;;;<<>>@@@???>>>===>>>???===>>>???@@@@@@???>>>===???@@@AAA???===<<<>>>@@@===<<<;;;;;;===>>>===;;;>>>?????????>>>===;;;:::777888999;;;<<<===>>>>>>=========<<<;;;:::999888;;;;;;;;;;;;;;;;;;;;;;;;::::::::::::;;;<<<<<<;;;::::::;;;;;;<<<<<<======;;;::::::::::::;;;<<<<<<999999999::::::;;;;;;;;;;;;::::::999999888888888999999999888777555333333333444555555333333444666555555444444444555666666333333333333333333333333111111111...***'''&&&''',,,///333444555555555666777666666555444333222222222333444444555444444444111111111111222333444555111111111111111111111111555444444333222111000000222111111111111222333333111111222222222222111111000000111111111111000000////////////////////////,,,,,,,,,,,,,,,---...///---,,,,,,++++++,,,,,,---)))***,,,,,,++++++,,,...------------------------,,,,,,,,,++++++*********+++,,,,,,,,,,,,+++******)))))))))))))))))))))))))))(((((((((''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''''''''((((((((())))))***,,,+++((('''((('''$$$''''''''''''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((((((((((((((((((((())))))))))))((((((((((((((((((((((((''''''&&&&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$"""###$$$%%%&&&%%%$$$###%%%$$$$$$######$$$$$$%%%$$$$$$%%%$$$###"""$$$&&&###############$$$$$$$$$######$$$$$$$$$######"""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""###""""""!!! !!!!!!!!! !!!!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!""""""""""""""""""""""""""""""###$$$!!!!!!!!!!!!!!!!!!!!!!!!"""""""""""""""""""""""" :::;;;<<<=========<<<<<<>>>>>>????????????>>>>>>@@@AAAAAAAAAAAA@@@>>>>>>BBB@@@===;;;:::;;;===>>>===???@@@@@@>>>===>>>???===>>>???@@@@@@???>>>===???@@@??????======>>>???<<<;;;:::;;;<<<===<<<;;;<<<============<<<:::999888888999:::;;;<<<===>>><<<<<<<<<<<<;;;:::999888:::;;;;;;;;;;;;;;;;;;:::;;;<<<<<<;;;::::::::::::999999::::::;;;;;;;;;<<<;;;::::::::::::;;;<<<<<<888999999::::::;;;;;;<<<:::::::::999999888888888888888888777666555444333222444555444333333444555444444444444444555666666333333333333333333333333111111000---)))&&&&&&&&&---///222444444444666777666555555444333333222222222333444444555444444444444444333333333333444444111111111111111111111111444444333222111111000000000000000000000111222222111111222222222222111111///000111111111111000///000000000000000000000000,,,,,,,,,,,,,,,---...///---,,,,,,++++++,,,,,,---***,,,------,,,,,,...///------------------------******++++++,,,,,,,,,,,,++++++,,,,,,++++++***)))(((((((((((((((((((((((((((((((((((((((''''''&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''''''''(((((((((((())),,,+++(((''')))(((%%%&&&&&&'''(((((()))))))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((())))))(((((((((((())))))))))))(((((((((((('''''''''(((((((((&&&''''''((((((''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$"""###$$$&&&&&&&&&%%%$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$%%%%%%$$$######$$$&&&""""""######$$$$$$$$$$$$"""######$$$$$$$$$######!!!!!!""""""""""""""""""!!!!!!!!!!!!""""""""""""######"""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!""""""""""""!!!!!! !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!""""""""""""""""""!!!!!!"""###$$$$$$!!!!!!!!!!!!!!!!!!!!!!!!"""""""""""""""""""""""" ;;;<<<======>>>>>>======??????@@@@@@@@@@@@??????@@@AAABBBBBBBBBAAA@@@???CCCAAA???===;;;<<<<<<===>>>???AAA@@@???>>>>>>???>>>>>>????????????>>>>>>===<<<<<<;;;;;;<<<<<<<<<;;;:::999:::<<<===<<<;;;;;;;;;<<<===<<<;;;:::999:::999999999:::;;;<<<===;;;;;;<<<<<<;;;;;;:::999;;;;;;<<<<<<<<<<<<;;;;;;;;;<<<===<<<:::999:::;;;999999::::::::::::::::::;;;::::::::::::;;;<<<<<<999999999::::::;;;;;;;;;999999999999999999999999777888888777777666555444333444555444333222333444333333333333333444555666333333333333333333333333111111000---***((()))***...000333444333444555777444444333333333333222222444555666666777777666666666555444444333333333444222222222222222222222222333333222222111111000000000000//////000000111222111111222222222222111111///000111222222111000///000000000000000000000000------,,,,,,,,,---......---,,,,,,++++++,,,,,,---,,,---......------...///...------,,,,,,------...)))***+++,,,------------+++++++++++++++******)))((((((((((((((((((((((((((((((((()))(((''''''&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&'''''''''((((((((())),,,+++(((''')))(((%%%%%%&&&'''(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''((())))))))))))((()))))))))))))))(((((('''(((''''''''''''((())))))&&&&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$"""###$$$%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$%%%&&&%%%######%%%&&&""""""###$$$$$$$$$$$$###""""""###$$$$$$$$$$$$###!!!!!!""""""""""""######!!!!!!!!!!!!""""""""""""$$$###""""""!!!!!!""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!""""""""""""!!!!!! !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!"""###$$$%%%""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!! <<<============>>>>>>>>>>>>???@@@@@@@@@@@@???>>>>>>???AAABBBBBBAAA@@@???AAA@@@???>>>>>>>>>>>>>>>>>>@@@AAAAAA???>>>>>>>>>??????>>>>>>>>>>>>??????<<<;;;::::::;;;<<<<<<<<<999888888999;;;===<<<<<<;;;<<<=========<<<;;;:::;;;::::::999999:::;;;;;;:::;;;;;;<<<<<<<<<<<<;;;;;;<<<============<<<;;;999;;;<<<<<<:::999;;;===;;;;;;;;;;;;;;;:::::::::;;;::::::::::::;;;<<<<<<::::::::::::::::::::::::888888888999999::::::;;;777777777888888777777666444555555444222111222333111111111222222444555555444444444444444444444444111111000...,,,+++---...000111333333333333444666111111111222222222222333444555666666777777666666333333333222333333444444333333333333333333333333222222222111111111111111111111000000111111222333111111222222222222111111///000111222222111000///000000000000000000000000......---,,,,,,,,,---------,,,,,,++++++,,,,,,---,,,.........,,,+++,,,---...---,,,,,,,,,,,,---...+++,,,------...---,,,,,,+++++++++++++++***))))))(((((((((((((((((((((((('''((()))))))))(((&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''(((((()))++++++''''''))))))&&&%%%%%%''''''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((())))))))))))))))))))))))))))))(((''''''(((''''''&&&'''((()))***&&&&&&&&&''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%&&&%%%$$$###%%%'''!!!"""###$$$%%%$$$$$$###""""""###$$$$$$$$$$$$$$$!!!!!!"""""""""#########!!!!!!!!!!!!""""""""""""$$$###""""""!!!!!!""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!""""""""""""!!!!!! !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!"""###$$$%%%""""""""""""""""""""""""  ===============>>>??????===>>>???@@@@@@???>>>===<<<===???AAABBBAAA@@@???>>>?????????@@@@@@@@@@@@???@@@AAAAAA???>>>>>>>>>@@@???>>>======>>>???@@@>>><<<;;;;;;===>>>======888777777999;;;======<<<<<<===>>>>>>>>>===<<<;;;<<<;;;:::999999999:::;;;::::::;;;<<<============;;;<<<===>>>>>>===<<<;;;666999;;;<<<::::::===@@@=========<<<<<<;;;;;;:::;;;::::::::::::;;;<<<<<<::::::::::::::::::::::::777777888999:::;;;;;;<<<666777777888888888888888444555666444222111111222111111111111222333444555444444444444444444444444111111111///......000111111222444333333222444555///000000111222222333333222333444444555555444444000000000111222333555555333333333333333333333333111111111111111222222222222222111111222222333444111111222222222222111111...000111222222111000...000000000000000000000000///...------,,,,,,,,,,,,---,,,,,,++++++,,,,,,---,,,---...---+++***+++,,,...---,,,,,,,,,,,,---...---......///...---+++******++++++++++++***))))))(((((((((((((((((((((((('''((()))))))))(((&&&%%%''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&&&&'''''''''(((((()))++++++''''''))))))&&&%%%%%%&&&''''''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''(((((())))))))))))))))))))))))))))))(((''''''((('''&&&&&&'''((()))***%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$######$$$&&&''')))&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&%%%$$$$$$%%%'''!!!"""###$$$%%%$$$######!!!"""###$$$$$$$$$$$$$$$!!!!!!""""""#########$$$!!!!!!!!!!!!""""""""""""$$$######""""""""""""""""""""""""""""""""""""""" !!!!!!!!!"""!!!!!!""""""""""""!!!!!! !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!"""!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!"""###$$$%%%""""""""""""""""""""""""   @@@???>>>>>>>>>???@@@AAA????????????????????????AAA>>><<<===@@@BBBBBB@@@AAAAAAAAAAAAAAAAAAAAAAAA??????@@@@@@@@@??????>>>??????>>>===============;;;;;;;;;<<<<<<<<<<<<<<<999999::::::;;;<<<======<<<<<<<<<<<<<<<<<<<<<<<<;;;<<<<<<;;;999999:::<<<<<<;;;::::::999999::::::;;;>>>@@@AAA???===<<<<<<999::::::;;;<<<<<<<<<;;;;;;;;;;;;::::::;;;;;;<<<===;;;::::::;;;<<<;;;:::999999999::::::;;;;;;;;;888888888777888888999999999888888777777777777777555555444333333333333444222222333333444555666666333333333444444444555555333222222111000000000111333444555666666666555444666555555444444555555666666555444333333333444555555555444333333333444444222222222222222222222222222222222333444555777888666555444333222222222222///......///111111000///111222333333444444444444444444333222111000///...........................,,,---......,,,,,,---...000///...---,,,+++++++++,,,,,,------------,,,,,,/////////......---------------...---,,,***(((&&&***)))))))))))))))***+++***)))(((''''''''''''''''''((()))******)))((('''%%%%%%&&&'''((((((''''''&&&&&&&&&''''''''''''(((&&&&&&'''''''''''''''''')))++++++'''''')))(((%%%''''''''''''(((((((((((()))((('''&&&%%%&&&&&&'''((('''&&&%%%%%%&&&'''(((&&&'''((('''&&&'''(((***(((((())))))))))))((((((&&&''''''(((((((((((((((******))))))((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""$$$$$$$$$#########""""""###"""!!! !!!"""###!!!!!!""""""""""""!!!!!!######""""""!!!!!! !!!!!!!!!!!!  !!!""""""#########""""""!!!!!! """"""""""""############""""""""""""""""""""""""""""""############"""""""""""""""""""""""""""""" !!!!!!   ??????>>>>>>>>>???AAABBB>>>>>>>>>>>>>>>>>>>>>>>>@@@>>>;;;<<<>>>@@@???>>>@@@@@@AAAAAAAAAAAA@@@@@@===>>>>>>>>>???>>>>>>>>>======<<<<<<<<<<<<======<<<<<<<<<<<<;;;;;;;;;;;;999999::::::;;;<<<<<<===========================<<<======<<<;;;;;;<<<>>><<<;;;::::::999999::::::999;;;======;;;999888888999:::;;;;;;<<<<<<;;;;;;<<<;;;:::::::::::::::;;;:::999777777999::::::999999::::::::::::::::::;;;999999888888777888888888999888777777666666777777555555444333333333333444222222333333444555555666333333333444444444555555444333222111111111111111222333444555666555555444555555444444444444555555555444333222222333444555555444333333222333333333222222222222222222222222111111111222333444666777555444333222111111111111000//////000222222111///111222333333444444333333333222222111///......---...............---------,,,---......,,,,,,---...//////...---,,,,,,,,,,,,------............------.........---------,,,,,,---------,,,+++***)))(((******)))))))))))))))***))))))((('''''''''(((((('''((()))******)))((('''%%%&&&&&&'''((((((''''''&&&&&&&&&''''''''''''(((((((((((('''&&&&&&&&&%%%)))++++++'''''')))(((%%%&&&&&&&&&&&&'''''''''''')))((('''&&&%%%&&&&&&'''((('''&&&&&&&&&&&&'''(((&&&'''((('''&&&'''(((***(((((())))))))))))((((((&&&''''''((((((((((((((())))))((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""$$$$$$$$$#########""""""###"""!!! !!!"""###!!!!!!""""""""""""!!!!!!###"""""""""!!!!!!!!! !!!!!!!!!!!!  !!!""""""#########""""""!!!!!!!!!!!!""""""""""""############""""""""""""""""""""""""""""""############""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!"""!!!  >>>>>>>>>>>>???@@@BBBBBB>>>>>>>>>>>>>>>>>>>>>>>>???===<<<;;;=========<<<>>>???AAABBBBBBAAA???>>>;;;<<<<<<======>>>>>>>>><<<;;;;;;;;;;;;<<<<<<===<<<<<<<<<;;;;;;:::::::::999::::::;;;;;;<<<<<<<<<========================>>>>>>???>>>======>>>@@@<<<;;;;;;:::::::::::::::888:::;;;;;;999777666666::::::;;;;;;<<<<<<;;;;;;;;;;;;:::999999999999999999777666777999:::::::::;;;::::::::::::::::::999:::999888888777777777777999888777777666666777777555555444333333333333444222333333444444555555555333333333444444444555555444444333222222222333333222222333444444444444444555444444333333444444555444333333222222333333444444333222222111111222222222222222222222222222222000000000111222333444555444333222111000000000000111000000111333333222000111222222333333333333333111111000///......------//////.........---------,,,---......,,,,,,---...///...------,,,,,,,,,,,,.........//////.........------,,,,,,,,,,,,,,,+++---,,,++++++******++++++++++++***)))((((((((()))(((((('''''''''((())))))'''(((((())))))(((((('''%%%&&&''''''((('''''''''&&&&&&&&&''''''''''''((())))))((('''&&&%%%%%%$$$)))++++++'''''')))(((%%%%%%%%%%%%&&&&&&&&&&&&'''(((((('''&&&&&&&&&&&&'''((('''&&&&&&&&&&&&'''(((&&&'''((('''&&&'''(((***(((((())))))))))))((((((&&&''''''((((((((((((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&'''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""$$$$$$$$$###############""""""!!!!!!!!!!!!""""""!!!""""""######""""""!!!""""""""""""!!!!!!!!!!!! !!!!!!""""""!!!!!!  !!!!!!""""""######""""""""""""!!!!!!!!!""""""""""""############""""""""""""""""""""""""!!!""""""######""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!######""""""!!!<<<======>>>@@@AAABBBCCC>>>>>>>>>>>>>>>>>>>>>>>>??????>>>=========<<<<<<<<<>>>@@@BBBBBB@@@>>><<<;;;;;;<<<<<<===>>>???@@@>>>===<<<<<<;;;;;;;;;<<<===<<<<<<;;;:::999888888:::::::::;;;;;;;;;<<<<<<===========================>>>???>>>======???AAA<<<<<<;;;:::::::::::::::;;;<<<===<<<:::888888888::::::;;;;;;<<<;;;;;;:::;;;;;;:::999888888888888:::888888999;;;<<<===<<<;;;;;;;;;::::::999999999::::::999777666666666666888888777666666666666666555555444333333333333444333333333444444444555555333333333444444444555555555444444333333333444444222222333333333333444333444444333333333333444444222222222222333333333444333222222111000111111111111111111111111111111111/////////000000111333333222222111000000000000000222111111222444444333111111222222333333333222222111111000//////...------/////////...------,,,,,,,,,---......,,,,,,---...///...---,,,,,,,,,,,,,,,......////////////......++++++++++++++++++++++++,,,,,,*********+++,,,---,,,,,,***)))((((((((((((((('''''''''((()))******((((((((((((((((((((((((&&&&&&'''''''''''''''&&&&&&&&&&&&''''''''''''(((((((((''''''&&&&&&&&&%%%)))++++++'''''')))(((%%%%%%%%%&&&&&&&&&'''''''''''''''''''''&&&&&&'''''''''''''''&&&&&&'''''''''&&&'''((('''&&&'''(((***(((((())))))))))))((((((&&&''''''(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&'''(((((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""########################""""""!!!!!!!!!!!!"""""""""""""""######"""""""""""""""""""""!!!!!!!!!!!!!!!!!!""""""""""""!!!!!! !!!!!!""""""""""""""""""""""""""""""""""""!!!"""""""""############""""""""""""""""""""""""!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""""""""!!!!!!  <<<===>>>???@@@AAABBBBBB@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@AAA@@@???>>>>>>>>><<<>>>@@@BBBBBB@@@>>><<<===<<<<<<======???@@@AAAAAA@@@???===<<<;;;;;;;;;<<<<<<;;;:::999888888777:::::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;<<<=========<<<<<<>>>@@@===<<<;;;;;;::::::;;;;;;<<<===>>>===;;;999999::::::;;;;;;<<<;;;;;;::::::;;;:::999999888888888999999888777888:::<<<<<<<<<;;;;;;;;;::::::999999999:::999888777666666666666888777777666555666666666555555444333333333333444333333333444444444444444333333333444444444555555555444444333444444555555222222222222333333444444555444444333333444444555222222333333444444444444222222111000000000111111111111111111111111111111////////////000000111222111111000000//////000000222111111222444444333222222222222333333222111111111111111000000//////...//////.........---------,,,---......,,,,,,---.........---,,,,,,,,,------......////////////......++++++++++++++++++++++++,,,+++***)))***+++,,,---,,,,,,***)))((((((((((((((((((((((((((()))***+++((((((''''''''''''((((((&&&'''''''''''''''&&&&&&&&&&&&&&&''''''''''''(((%%%&&&&&&&&&''''''(((((()))++++++'''''')))(((%%%&&&'''''''''((((((((((((&&&&&&''''''''''''''''''&&&''''''''''''''''''&&&&&&'''((('''&&&'''(((***(((((())))))))))))((((((&&&''''''(((((((((((((((%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((())))))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""########################!!!!!!""""""""""""!!!!!!""""""############""""""!!!!!!!!!!!!""""""""""""!!!!!!""""""""""""!!!!!!!!!!!!!!!"""""""""""""""""""""""""""############!!!"""""""""############""""""""""""""""""""""""!!!!!!""""""""""""!!!!!!  !!!!!!""""""   <<<===>>>@@@AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA@@@AAACCCBBBAAA@@@@@@AAA>>>???AAABBBBBBAAA???>>>>>>======<<<===>>>@@@AAABBBAAA???>>><<<<<<;;;;;;:::::::::999999888888888;;;;;;;;;;;;;;;;;;;;;;;;:::::::::::::::::::::::::::;;;<<<<<<;;;;;;===???===<<<<<<;;;;;;;;;;;;;;;:::;;;<<<;;;:::999:::;;;;;;;;;<<<<<<;;;;;;::::::::::::999999999999::::::888666555666888999999999;;;::::::::::::::::::999999888777777666666666666888777666666555555666666555555444333333333333444444444444444444444444444333333333444444444555555444444333333333444555555333333333333333444555555555555555444444555555555222222333444555555555555333222111111000000111111111111111111111111111111///////////////000111222111111000000000000000111222111111222444444333111222222222222222222111000111111111000000/////////........................,,,---......,,,,,,---......------,,,,,,---------.........//////.........***++++++++++++,,,,,,,,,+++++++++***++++++,,,,,,++++++***)))((((((((()))))))))((((((((()))******(((''''''&&&&&&''''''((('''''''''(((''''''&&&%%%&&&&&&&&&''''''''''''((($$$%%%%%%&&&'''((()))))))))++++++'''''')))(((%%%'''''''''((((((((())))))%%%&&&''''''((('''''''''&&&&&&'''(((((('''&&&&&&&&&'''((('''&&&'''(((***(((((())))))))))))((((((&&&''''''(((((((((((((((%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((((((((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""###############$$$$$$$$$!!!!!!""""""""""""!!!!!!"""######$$$$$$######"""!!!!!!!!!!!!""""""""""""!!!""""""######""""""!!!"""""""""""""""""""""""""""""""""############$$$""""""""""""############"""""""""""""""""""""""" !!!!!!""""""!!!!!! !!!"""###   ===>>>???@@@AAA@@@@@@???@@@@@@@@@@@@@@@@@@@@@@@@>>>AAACCCCCCBBB@@@AAABBB@@@@@@AAAAAAAAAAAA@@@@@@>>>===<<<;;;;;;<<<>>>???>>>>>>===<<<<<<<<<======999999999999888888888888;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;:::;;;<<<<<<;;;<<<>>>@@@======<<<;;;;;;;;;;;;;;;999:::;;;;;;999999;;;===;;;;;;<<<<<<;;;;;;:::999999999999999:::;;;<<<===999777666666777888888777999::::::::::::::::::;;;888777777666666666777777777777666555555555555666555555444333333333333444444444444444444444444444333333333444444444555555333333222222333444444555555444333333333444666666777666666555555666666777222333444666777777666666333333222111111111111222111111111111111111111111000000000///000000111222111111111000000111111222111000000111333444222111222222222222222111000000000000////////////......,,,,,,------.../////////,,,---......,,,,,,---...---------,,,,,,------...------............------++++++++++++,,,,,,------++++++,,,,,,,,,++++++*********)))))))))))))))*********))))))((()))))))))((('''&&&&&&&&&&&&'''(((''''''(((((('''&&&&&&%%%&&&&&&&&&''''''''''''(((%%%&&&&&&&&&'''((((((((()))++++++'''''')))(((%%%&&&&&&&&&'''''''''((((((%%%%%%'''(((((((((''''''&&&&&&'''(((((('''&&&&&&&&&'''((('''&&&'''(((***(((((())))))))))))((((((&&&''''''(((((((((((((((%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""""""""#########$$$$$$$$$ !!!"""######"""!!! """######$$$$$$######""" !!!!!!!!!"""""""""###""""""############""""""""""""""""""""""""""""""""""""#########$$$$$$$$$""""""""""""############"""""""""""""""""""""""" !!!!!!!!!!!!  !!! !!! !!! !!!!!!!!!>>>>>>@@@AAAAAA@@@???>>>????????????????????????===@@@CCCCCCBBB@@@AAACCCAAAAAAAAAAAAAAAAAAAAAAAA>>>===;;;::::::;;;<<<===:::::::::;;;<<<===>>>???888888888888888999999999;;;;;;;;;;;;;;;;;;;;;;;;<<<<<<<<<<<<<<<<<<<<<<<<:::;;;<<<<<<<<<<<<>>>@@@======<<<;;;;;;;;;;;;<<<:::;;;<<<<<<;;;;;;===???;;;<<<<<<<<<;;;::::::999999999999:::;;;<<<===>>>;;;:::888888999:::999888999999999::::::;;;;;;;;;777666666666666777777888777777666555555555555555555555444333333333333444444444444444444444444444333333333444444444555555222222222222333333444555555555444333444555666777777777666666666666777777222333555777888777777666444333222222111111222222000000000000000000000000111000000000000111111222222111111111111111222222111000000111333333222000222222222222222111000///...............---------+++,,,,,,---...///000000,,,---......,,,,,,---...------,,,,,,,,,------...,,,------------------,,,+++++++++,,,,,,---------++++++,,,---,,,+++***)))***)))))))))))))))***+++++++++***)))(((((())))))((('''&&&%%%%%%&&&'''((('''((((((((('''&&&%%%%%%&&&&&&&&&'''''''''((((((''''''''''''''''''&&&&&&)))++++++(((''')))(((%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%'''(((((((((''''''%%%&&&'''(((((('''&&&%%%&&&'''((((((&&&'''(((***(((((())))))))))))((((((&&&''''''(((((((((((((((&&&&&&&&&''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((('''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""""""""######$$$$$$$$$$$$ !!!"""######"""!!! ######$$$$$$$$$$$$###### !!!!!!!!!""""""######""""""############""""""#########"""""""""""""""""""""######$$$$$$$$$$$$""""""""""""############"""""""""""""""""""""""" !!!!!!!!!!!!   !!!!!! !!!!!! !!!!!!!!!""""""??????>>>>>>>>>>>>>>>???BBBBBBBBBCCCBBBBBBAAAAAA>>>???@@@AAAAAA@@@???>>>>>>???@@@AAAAAAAAAAAAAAA>>>>>>======<<<<<<<<<;;;;;;;;;<<<<<<;;;;;;:::999999999999999999999999999;;;;;;:::::::::;;;<<<<<<;;;<<<======;;;:::;;;<<<>>>===<<<;;;;;;<<<===>>>>>><<<999777777888:::<<<;;;::::::999:::;;;===>>><<<=========<<<;;;;;;:::888888999::::::;;;<<<<<<;;;:::999888777555444444;;;:::999888777777777777777777666666666666777777777777666555444333333333666555444222222111111222333444444333222333555888333333333333333333333333444222111000000111333555333333444444444444444444333444555666777777777666777777666666555555555444333333333333333333333333555333111///...000222333000000000000111222333444333111000.........//////222222111111111111111111444444333333222111000000111111000000000000111111....................................---,,,+++***,,,------......------,,,+++++++++,,,,,,---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++*********))))))))))))))))))))))))+++******)))))))))))))))(((((())))))))))))((((((((('''&&&&&&'''((('''&&&%%%%%%&&&&&&'''((())))))%%%&&&'''((()))))))))))),,,,,,+++***)))))))))******)))(((''''''((()))***&&&''''''(((((((((((((((''''''''''''''''''''''''(((((((((((())))))))))))(((((((((((())))))))))))''''''''''''((((((((()))'''(((((((((((((((''''''%%%%%%&&&'''((((((((('''''''''''''''''''''''''''%%%&&&&&&&&&'''(((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$###!!! !!!!!!""""""#########$$$##############################$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$###"""!!!########################""""""""""""""""""""""""""""""""""""############ !!!!!!"""###$$$$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""$$$###""" !!!"""  !!!!!!!!!!!! !!!!!!  AAA@@@@@@?????????@@@@@@@@@AAABBBCCCCCCBBBAAAAAA>>>???@@@AAAAAA@@@???>>>???@@@@@@AAAAAAAAA@@@@@@??????>>>>>>>>>=========<<<<<<======<<<<<<;;;;;;999999999999999999999999;;;::::::999999999::::::;;;<<<<<<;;;::::::;;;===>>>===<<<;;;;;;<<<===>>>===<<<:::999999999;;;<<<;;;;;;:::999::::::<<<<<<<<<<<<<<<<<<<<<;;;:::999999999::::::;;;<<<<<<===;;;::::::999777666666555::::::999888777777777777999999999888888999999999777777666444444333333444555555555444333222222222333333444333222222555777333333333333333333333333444333222111111222444555555555444444333333222222444444444555555666666666777666666666555555555444333333333333333333333333444333111000///000111222000000000000111222333444111111///......//////000111111111111111111111111444333333222111111000000111111000000000000111111........................////////////...---,,,+++------------,,,,,,,,,,,,,,,,,,,,,,,,---------...,,,,,,,,,,,,,,,,,,,,,,,,---,,,,,,,,,++++++++++++************************+++******)))))))))))))))(((((())))))))))))((((((((('''&&&&&&'''((('''&&&%%%%%%&&&''''''(((((()))&&&&&&''''''((())))))***,,,,,,+++***))))))))))))))))))''''''''''''((()))&&&''''''((((((((((((((('''''''''''''''''''''''''''((((((((())))))))))))(((((((((((())))))))))))'''''''''((((((((())))))'''(((((((((((((((''''''%%%&&&''''''((((((''''''((((((((((((((((((((((((&&&&&&&&&'''''''''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$###"""!!! """"""""""""#########$$$##############################$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$###""""""########################""""""""""""""""""""""""""""""""""""############ !!!!!!"""######$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""######"""!!!!!!!!!!!!!!!   !!!!!!!!!!!! BBBAAAAAA@@@@@@AAAAAABBB>>>???AAACCCCCCCCCAAA@@@???@@@@@@AAAAAA@@@@@@???@@@AAAAAAAAAAAA@@@@@@???????????????>>>>>>>>>>>>>>>============<<<<<<<<<888888888888888888888888;;;:::999888888888888888:::;;;;;;999888888;;;===>>>===<<<;;;;;;<<<===>>>===<<<<<<<<<;;;;;;;;;;;;;;;;;;:::999999999::::::::::::;;;;;;;;;:::999999999999::::::;;;<<<<<<<<<;;;;;;:::999999888777777999999888888888888888999::::::999999999999::::::777666555444444444444444555555666666555444222111222333333222111111333666333333333333333333333333444333333222333444555666666666555444333222111111555444333333333444555666666666666555555555555555444444444333333222222222222222222111111111111111000000000000111111222333000////////////000000111111111111111111111111111222222222111111000000///111111000000000000111111///////////////////////////000000//////...---,,,......,,,+++***++++++,,,---------...............++++++++++++++++++++++++------------,,,,,,,,,,,,************************+++******)))))))))))))))(((((())))))))))))((((((((('''&&&&&&'''((('''&&&&&&&&&&&&''''''(((((()))(((''''''&&&'''(((***+++---,,,+++***))))))))))))((('''&&&%%%&&&&&&((((((&&&''''''(((((((((((((((''''''''''''''''''''''''''''''((((((((()))))))))(((((((((((())))))))))))''''''((((((((()))))))))'''(((((())))))(((((((((&&&&&&'''(((((((((''''''))))))))))))))))))))))))'''''''''''''''&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$###""""""!!!"""""""""#############################################$$$$$$$$$%%%%%%%%%###########################$$$$$$$$$$$$###""""""########################""""""""""""""""""""""""""""""""""""############!!!!!!!!!"""######$$$$$$"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!    !!!!!!!!!!!! AAAAAAAAA@@@AAAAAABBBCCC<<<>>>@@@CCCDDDCCCBBBAAA@@@AAAAAAAAAAAAAAAAAA@@@BBBBBBBBBBBBAAA@@@??????>>>>>>>>>>>>>>>>>>>>>>>>>>>======<<<<<<<<<<<<<<<888888888888888888888888<<<;;;:::888888777777777999:::999888777888:::======<<<;;;;;;;;;;;;<<<===<<<===>>>>>>>>>===;;;:::;;;;;;::::::999999999999999999:::::::::999999888999999999999::::::;;;;;;;;;;;;;;;::::::999999999888888888777888888999999999888888888888888888999777666555444444444444444444555666777777555333222222333333111000000333555333333333333333333333333444444333333444555666777666666666555555444444444666444222111111222444555555555555555555555555555555555444333333222111111111111222333222111000///000000000000000111222222.........///000111111222000000000000111111111111111111111000000000//////111111000000000000111111000000000000000000000000000000000000000///......///...,,,***)))***+++,,,.........///////////////************************------------------------************************+++******)))))))))))))))(((((())))))))))))(((((((((&&&&&&&&&'''((('''&&&&&&&&&''''''((((((((())))))(((&&&&&&'''(((+++,,,------+++***))))))))))))'''&&&%%%%%%%%%&&&'''(((&&&''''''((((((((((((((('''''''''''''''''''''''''''''''''((((((((())))))(((((((((((())))))))))))'''(((((((((((()))))))))'''(((((())))))))))))(((''''''((((((((((((''''''((((((((((((((((((((((((((((((((('''&&&&&&&&&%%%''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$###############################################################$$$$$$$$$%%%%%%%%%##############################$$$$$$$$$######"""########################!!!!!!!!!!!!!!!!!!!!!!!!!!!"""""""""############!!!!!!""""""############!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!"""######"""!!!     !!!!!!  @@@@@@@@@@@@@@@AAABBBBBB===>>>AAABBBCCCCCCBBBAAABBBAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBBBBAAA@@@???===========================<<<;;;:::::::::;;;;;;888888888888888888888888<<<<<<;;;999888888888888888999999888777888:::<<<===<<<;;;::::::;;;<<<===<<<===>>>???>>>===;;;:::;;;;;;;;;;;;:::999999888888888999999:::999999888888888888888999999999999;;;;;;::::::::::::::::::888888888777888888999999999888888888888888888999666666555444444444444555333444666777777555333222333333333111000000222444333333333333333333333333333444444444555666777777555555666666777777888888666555333111000111222444444444444555555555555555555555444333333222111111000111222333333111000///000000000///000000111111------...///000111111222//////000000000111111111111111111000000000000000111111000000000000111111000000000000000000000000000000000111000000///...///...,,,******+++,,,---////////////////////////************************------------------------************************+++******)))))))))))))))(((((())))))))))))(((((((((&&&&&&&&&'''((('''&&&'''''''''((((((((((((((()))((('''&&&''')))+++---...---,,,***)))(((((((((&&&%%%$$$$$$%%%&&&'''(((&&&''''''(((((((((((((((''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((())))))))))))(((((((((((()))))))))***''''''((()))******))))))'''(((((((((((((((''''''''''''''''''''''''''''''((((((((('''&&&&&&&&&%%%''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$#############################################$$$$$$$$$%%%%%%%%%########################"""######$$$$$$$$$##############################!!!!!!!!!!!!!!!!!!!!!!!!!!!"""""""""############"""""""""""""""#########!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!"""######"""!!!     @@@@@@@@@@@@AAABBBCCCCCC@@@AAAAAABBBCCCCCCCCCCCCCCCBBBBBBAAAAAABBBBBBCCCAAABBBBBBBBBBBBAAAAAA@@@<<<<<<<<<<<<===============<<<;;;999999:::;;;;;;999999999999999999999999<<<;;;:::999999999999999666888::::::999999:::<<<===<<<;;;::::::;;;<<<===<<<===>>>>>>>>>===;;;:::;;;;;;<<<<<<<<<;;;::::::888888999:::::::::999999888888888999999999999999:::::::::::::::::::::;;;999999888888888888888999::::::999999999999::::::666555555444444444555555333444555666666555444333444444444222000000222444333333333333333333333333222333333444555666777777444444555666777888999999666555444222111111222222444444444444444555555555444444444333333222222222111111222333222111000///000000000//////000000111------///000111111111111...//////000000111111111111111111111111111111111111111000000000000111111//////////////////////////////000000000000//////...---,,,,,,,,,---......///////////////.........++++++++++++++++++++++++,,,,,,,,,,,,------------+++++++++++++++++++++++++++******)))))))))))))))(((((())))))))))))((((((((('''&&&&&&'''((('''&&&(((((((((((((((((((((((()))(((''''''((()))+++,,,...---,,,***)))(((((((((&&&%%%$$$$$$%%%&&&((()))&&&''''''(((((((((((((((''''''''''''''''''''''''&&&&&&'''''''''((((((((((((((((((((())))))))))))((((((((()))))))))******''''''((()))************(((((()))))))))((('''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$#######################################$$$$$$$$$%%%%%%%%%########################""""""###$$$$$$$$$$$$###########################""""""""""""""""""""""""""""""""""""############""""""""""""""""""######"""""""""""""""""""""""""""""""""""""""""""""""" !!!!!!"""""""""""""""    AAAAAAAAAAAABBBCCCDDDEEEDDDCCCBBBBBBBBBCCCDDDDDDDDDCCCBBBAAAAAABBBCCCDDDAAAAAABBBBBBBBBBBBBBBBBB<<<<<<======>>>>>>>>>>>>>>>===;;;:::::::::<<<<<<:::::::::::::::::::::::::::999888888888888999999555888;;;<<<;;;::::::;;;<<<<<<::::::::::::<<<<<<<<<=========<<<<<<;;;;;;:::;;;<<<=========<<<;;;888999999:::;;;;;;::::::::::::::::::::::::::::::888888999999:::::::::;;;::::::999888777777777777999999999888888999999999555555444444444555555666333333333333444444444444555555555333111111333555333333333333333333333333111222333444555666666666444444444555666666666777666666555444333222111111333333333444444555555555333333333333333333333333222222222222222111000000000000////////////000000---...///000111111000000......//////000111111222111222222222222222222222111111000000000000111111...........................//////000000//////...,,,------......//////000/////////.........------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,,,,---+++++++++++++++++++++++++++******)))))))))))))))(((((())))))))))))((((((((('''&&&&&&'''((('''&&&)))(((((((((((((((((((((((((((((()))******++++++///...,,,***)))(((''''''&&&%%%%%%%%%%%%''')))***&&&''''''(((((((((((((((''''''''''''''''''''''''&&&&&&&&&'''''''''(((((((((((((((((())))))))))))(((((()))))))))*********''''''(((******++++++***)))))))))))))))(((''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$#######################################$$$$$$$$$%%%%%%%%%########################""""""###$$$$$$$$$$$$$$$########################""""""""""""""""""""""""""""""""""""###############"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!"""######    BBBBBBBBBCCCCCCEEEFFFFFFFFFEEECCCBBBAAACCCDDDEEEDDDCCCBBBAAAAAABBBCCCDDD@@@@@@AAABBBCCCCCCCCCCCC======>>>>>>?????????@@@@@@>>><<<;;;:::;;;===>>>;;;;;;;;;;;;;;;;;;;;;;;;888777777777777777888999444777;;;======;;;::::::<<<;;;::::::::::::;;;<<<===<<<<<<<<<;;;;;;;;;;;;:::;;;===>>>>>>>>>======888999:::;;;;;;;;;;;;;;;<<<<<<<<<<<<<<<<<<<<<<<<777888888999999::::::;;;;;;:::999888777777777777777777666666666666777777555555444444444555555666333333222222222333444444555666555444222222333555333333333333333333333333000111222444555666666666444444444444444444333333666666666666444333111000333333333444444555555555333333333333333333333444222222222111111111111111111000////////////000000---...000111111000000///---......///000111111222222222222222222222333333111111000000000000111111..............................///////////////...+++,,,...///000111111000//////......---------,,,,,,,,,,,,,,,,,,,,,,,,,,,*********++++++,,,,,,,,,+++++++++++++++++++++++++++******)))))))))))))))(((((())))))))))))((((((((('''&&&&&&'''((('''&&&))))))))))))(((((((((((('''((()))***+++++++++***///...,,,***)))(((''''''&&&&&&%%%%%%&&&((()))***&&&''''''(((((((((((((((''''''''''''''''''''''''&&&&&&&&&'''''''''(((((((((((((((((())))))))))))))))))))))))************''''''(((******+++++++++)))))))))))))))(((''''''))))))))))))))))))))))))%%%&&&&&&''''''(((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%$$$$$$#######################################$$$$$$$$$%%%%%%%%%########################!!!"""###$$$$$$$$$$$$$$$########################""""""""""""""""""""""""""""""""""""#####################""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!! """###$$$!!!!!!!!!!!!!!!!!!!!!!!!   CCCCCCCCCCCCDDDDDDDDDEEECCCCCCBBBBBBBBBAAAAAAAAAAAAAAABBBCCCDDDDDDCCCCCCAAAAAABBBBBBBBBAAA@@@???>>>===<<<<<<===???AAACCC======<<<;;;;;;;;;;;;;;;999999999;;;<<<<<<:::888777777777777888888888888999::::::999888999;;;>>>;;;;;;;;;<<<<<<<<<<<<<<<>>>============<<<<<<<<<===;;;999:::===>>>===;;;======<<<;;;999888777777999:::<<<======<<<:::999888777666555666777999;;;999999888888888888888888777777777777666666555555666666555555555444444444444444333333222111000000333333222111222333555666555444333333222222222222222333555666666666555444777666555555555666888999444444333333333444555555444444444555555555555666333333444444333333222111333222111000000000111222222222111000//////000000/////////000111111222222000000000000000111111222444222000111444555333111333222111000000111222333222111000//////000111222222111111000000000000000///000111111111000...---.........///////////////,,,,,,---------,,,++++++)))***,,,---...------,,,+++))))))***---...,,,***---+++)))((('''((()))***,,,***))))))******)))'''))))))(((((('''''''''&&&&&&&&&''''''((()))))))))''''''(((((())))))******---///...***)))++++++(((''''''&&&&&&&&&%%%%%%%%%''''''''''''''''''&&&&&&(((''''''''''''&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&((((((((((((((()))******))))))************))))))***)))))))))((((((''''''***)))(((&&&&&&''''''(((''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''(((((('''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&''''''&&&%%%$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""############""""""%%%$$$$$$$$$###"""""""""$$$$$$########################""""""""""""#####################"""!!!!!!!!!!!!""""""######$$$$$$###############"""!!!!!!!!!!!!""""""######$$$$$$!!!  """###!!!   CCCCCCCCCDDDDDDDDDDDDDDDCCCCCCCCCCCCBBBBBBAAAAAAAAABBBBBBCCCDDDDDDCCCCCCBBBBBBBBBAAAAAAAAA@@@@@@AAA@@@>>><<<;;;<<<<<<=========<<<<<<;;;<<<<<<<<<999888888999;;;;;;:::999666666777777777888888888999::::::999888999;;;===;;;;;;;;;<<<<<<<<<<<<<<<>>>>>>>>>=========<<<<<<;;;:::888999<<<===<<<:::::::::::::::::::::::::::999:::;;;<<<<<<;;;:::999777666555444555666888999888888888888888888888888999999999888888888888888666666555555555444444444444333333333222111111111333333222222222333444555444444333222222222333333444444555666666666666555777666666555666777888999555444444333333333444444444444444444555555555555444555555555555444333333444333111000000000111111111111000000000000000000/////////000111111222222000000//////000111222222111///...///111222000///222111000000000000111222222111000//////000111222333222111000000000000000///000111111111000...---........................,,,,,,---------,,,++++++***+++,,,---------,,,++++++))))))***------,,,))),,,+++)))(((((((((***++++++***))))))******)))''')))((((((((('''''''''''')))(((((((((((('''''''''''''''(((((())))))******---///...***)))++++++((('''''''''&&&&&&&&&%%%%%%''''''''''''''''''''''''(((''''''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&&&&'''''''''''''''((())))))))))))))))))))))))))))))*********))))))(((((((((***)))((('''&&&'''((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''(((((('''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''&&&%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!""""""######""""""!!!$$$$$$$$$#############################################""""""""""""#####################"""!!!!!!"""""""""""""""########################"""!!!!!!"""""""""""""""#########!!!  """###!!! DDDDDDDDDDDDDDDCCCCCCCCCDDDDDDDDDCCCCCCCCCCCCBBBAAABBBCCCCCCDDDCCCCCCCCCCCCBBBAAA@@@@@@@@@AAAAAAAAA@@@>>><<<;;;:::;;;;;;=========<<<<<<===>>>>>>:::888777777999::::::999666666666777777777888888888999:::999888888:::<<<;;;;;;;;;<<<<<<<<<======>>>>>>>>>============<<<:::999888999;;;<<<;;;:::888888999:::;;;;;;<<<===::::::::::::::::::::::::777666555444555666777888888888888888888888888888888888888888888999999999555555555555555444444444333333333333222222222222333333222222222333444444333222222222222333333444444444444444444555666666777777666666666777888999666555444333333222333333444444444444555555555555555555666666555555444333444444222111000000000000000000000000000000111111...//////000000111111222////////////000111222333111///...///000000///...111111000000000000111111111111000000000000111111333333222000000////////////000111111111000...---//////......------,,,,,,---------------,,,+++++++++,,,---------,,,+++******))))))***+++,,,***)))+++***)))(((((()))+++,,,+++***))))))******)))(((((((((((((((''''''''''''++++++***)))'''&&&%%%%%%''''''(((((())))))******---///...***)))++++++((('''''''''&&&&&&&&&&&&%%%''''''''''''''''''''''''(((''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&'''((((((+++***)))(((((()))***+++***************)))))))))***)))((('''''''''((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&'''''''''''''''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''(((((('''&&&&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!""""""""""""!!!!!!###############$$$$$$$$$##############################""""""""""""#####################"""!!!!!!############"""""""""""""""############""""""!!!############""""""""""""!!!  !!!"""!!!  DDDDDDDDDDDDCCCCCCCCCCCCDDDDDDDDDDDDDDDDDDDDDCCCBBBBBBCCCCCCCCCCCCCCCBBBCCCBBBAAA@@@@@@@@@AAAAAA???>>>>>>=========>>>>>>>>>============>>>>>>???:::888666666888999:::999666666666777777777888888888999:::999888888999:::::::::;;;;;;<<<==================<<<<<<<<<;;;;;;:::999999:::;;;;;;;;;;;;888888999::::::;;;<<<<<<:::999999888888999999:::777777666666666666777888888888888888888999999999666666666666777777777777555555555555555555555555222222333333333333333333333333333333333333333444222111111111222333444444444333222111222333444555666666666666777777888888666555444333222222222222333333444444444555555555555555555555555444333333555444333222000//////.........///000000111111111......//////000111111111////////////000222333333222222111111111111111000000000000000000000000000111000000000000000000111222222000///......------///000111111111000...---//////...---,,,+++++++++............---,,,++++++,,,------...---,,,***))))))))))))*********)))(((***))))))))))))***,,,,,,+++)))((()))******)))(((((((((((((((((('''''''''++++++***)))((('''&&&&&&''''''(((((())))))******---///...***)))++++++(((''''''''''''&&&&&&&&&&&&&&&&&&&&&'''''''''''''''(((''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''(((''''''''''''((()))))),,,***(((''''''(((***,,,++++++******************)))))))))(((((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''((((((''''''''''''(((((('''&&&%%%%%%$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!!!!""""""!!!!!!!!!"""""""""###$$$$$$$$$%%%###############$$$$$$$$$######""""""""""""#####################"""!!!!!!$$$$$$######""""""!!!!!!""""""############"""!!!$$$$$$######""""""!!!!!!!!!!!!  !!!"""!!! !!!!!!!!!!!!!!!!!!!!!!!!DDDDDDDDDDDDDDDCCCCCCCCCCCCDDDDDDDDDDDDDDDDDDDDDBBBCCCCCCCCCCCCCCCBBBBBBBBBBBBAAAAAA@@@@@@@@@AAA@@@@@@??????????????????>>>>>>============>>>>>>:::888666666888999:::999777777777777888888888888888:::;;;:::999888999:::::::::;;;;;;<<<======>>><<<<<<<<<;;;;;;;;;:::::::::;;;;;;<<<;;;<<<<<<===:::::::::::::::::::::::::::999999888888999999:::999888888888888888888888777777888888888999999999666666666666666777777777444555555555555555555555333333333333333333444444333333333333333333333222111111111111222222333444222111000///000111222333555555666666777777777777666555444333222111111111333333333444444444444555333444444444444333222222444444333222111000///...---...///000111000000000.........///000000111111////////////000111222333222222222222111000000111000000111111111111000000000000000111111000000000000000///------,,,,,,,,,///000111111111000...---//////...---,,,+++++++++............---,,,+++***,,,------...---,,,***)))((()))*********))))))))))))))))))******+++,,,,,,***)))((()))***+++***)))'''''''''((((((((((((((())))))))))))))))))))))))''''''(((((())))))******---///...***)))++++++((((((((('''''''''&&&&&&&&&&&&&&&&&&'''''''''(((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&'''((())))))(((((())))))***+++,,,***(((''''''(((***,,,******************++++++)))))))))))))))(((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''(((((('''''''''(((((()))'''&&&%%%%%%$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!""""""""""""!!!!!!"""""""""###$$$$$$$$$%%%""""""#########$$$$$$$$$######""""""""""""#####################"""!!!!!!$$$$$$######""""""!!!!!!!!!""""""#########""""""$$$$$$######""""""!!!!!!!!!!!!!!! !!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!CCCCCCCCCCCCDDDDDDDDDEEEBBBCCCCCCCCCCCCDDDDDDDDDCCCCCCCCCDDDCCCCCCBBBAAAAAAAAABBBBBBBBBAAA@@@???CCCCCCBBBAAA???>>>======???>>>======<<<<<<<<<===:::888777777999::::::999888888888999999999::::::999;;;<<<<<<:::999999:::999::::::;;;<<<===>>>>>><<<<<<<<<;;;;;;;;;:::::::::;;;===<<<;;;;;;<<<>>>;;;;;;;;;::::::999999999::::::::::::::::::::::::999999999999999999888888777777777888999999::::::999999999999888888888777444444444555555555555555444444444444333333333333333333444444444333222222222111111111111222222333000000000000000111222222333444555666666666555555555444333222222111222222333333333333444444444444333333444444333333222111333333333333222000///...---...///000111000///...---......//////000000111000000000000000111111222111222222111///...///000111111222222222222111111000000111111111111000000///......---------------///000111111111000...---//////......------,,,,,,////////////...,,,+++***+++,,,---------,,,+++***)))***,,,+++***))))))************+++++++++++++++***)))((()))***+++***)))'''''''''(((((((((((((((''''''((())))))***++++++''''''(((((())))))******---///...***)))++++++(((((((((((('''''''''&&&&&&%%%%%%&&&&&&'''((((((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&''''''(((******))))))******+++,,,+++***)))(((((()))***+++)))))))))***************))))))*********)))((('''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&''''''''''''''''''&&&&&&%%%%%%&&&&&&'''(((''''''''''''((())))))'''&&&%%%%%%$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""############""""""###############$$$$$$$$$"""""""""###$$$$$$%%%%%%######""""""""""""#####################"""!!!!!!############""""""""""""!!!""""""############"""############"""""""""""""""""""""!!!!!!!!! !!!  AAABBBBBBCCCDDDEEEFFFFFFAAAAAABBBBBBCCCCCCCCCCCCCCCCCCDDDDDDCCCBBBBBBAAA???AAABBBDDDCCCBBB???>>>AAAAAAAAA@@@???>>>======??????===<<<;;;;;;::::::999888888999;;;;;;:::999999999:::::::::;;;;;;;;;:::<<<======;;;:::::::::999999:::;;;<<<===>>>>>>>>>>>>=========<<<<<<<<<999;;;<<<<<<::::::;;;===;;;;;;;;;::::::999999999999:::;;;<<<<<<;;;:::999999999999999999888777777666777777888999999::::::;;;::::::999888777666666444444444555555555666666555555555444333333333222333333444444444333222111333222111111111111111111000111111222333222222222222333444555555555444333333333222222222222222333222222333333333444444444444444444444444333333222111222222333222111000///......000111000///...,,,------......///000000000222111111000000000000000222333444333000...///111111222333444444333222111///000111222222111000/////////.........///000000///000111111111000...---........................000000//////...,,,+++******+++,,,---------,,,+++))),,,------***))))))++++++++++++,,,++++++******)))(((((((((***+++***)))''''''''''''((((((((()))'''(((((()))******++++++''''''(((((())))))******---///...***)))++++++(((((((((((((((''''''''''''%%%%%%&&&&&&'''(((((()))(((''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&'''(((((()))))))))))))))******+++))))))))))))))))))))))))((((((((())))))*********))))))***+++***)))((('''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%&&&&&&''''''&&&&&&&&&''''''((()))'''&&&%%%%%%$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$###############!!!""""""###$$$$$$%%%%%%######""""""""""""#####################"""!!!!!!"""""""""""""""#########!!!!!!"""###############"""""""""""""""#########"""""""""""""""!!! !!!  @@@AAABBBCCCDDDFFFGGGGGGAAAAAAAAABBBBBBBBBCCCCCCCCCDDDDDDDDDCCCBBBAAAAAA>>>@@@CCCEEEDDDBBB???===;;;<<<===???@@@@@@@@@@@@@@@???===<<<:::999999999999999999;;;<<<<<<:::888:::::::::;;;;;;;;;<<<<<<;;;===>>>>>><<<;;;::::::999999:::;;;<<<===>>>???????????????>>>>>>>>>>>>777:::<<<;;;999888:::===::::::::::::::::::::::::999:::<<<======<<<:::999888888888888888777666555666777777888999999:::::::::999888777666444333333444444444555555555666666666666555444333333222222333333444555444333111000333333222111000000000111111222333444555444333333111222333444444444333222222222222111222222333333222222333333333444444444555555666666555555444333000111222333333222000000...///000111000///---+++------......///000000000333222111000////////////444666777666222111222444222333444444444444333222///000111222222111000////////////000000111222333///000111111111000...---.........///////////////000000000///...,,,+++***)))***,,,---...------,,,***,,,...---***)))***+++,,,,,,,,,,,,,,,+++***))))))(((((((((***++++++***&&&'''''''''(((((())))))((()))))))))************''''''(((((()))*********---///...***)))++++++((()))(((((((((''''''''''''%%%%%%&&&&&&'''((())))))(((((('''''''''&&&&&&&&&$$$$$$$$$%%%&&&'''((()))((((((((((((((()))******))))))************))))))''''''(((((()))))))))***)))******++++++)))(((''''''''''''''''''''''''''''''''''''&&&&&&'''''''''&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&'''((()))'''&&&%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%$$$$$$$$$######""""""!!!""""""###$$$$$$%%%%%%######""""""""""""#####################"""!!!!!!!!!!!!""""""######$$$$$$!!!!!!"""###############!!!!!!""""""######$$$$$$"""""""""""""""!!! !!!!!!  CCCCCCBBBBBBBBBCCCCCCDDDEEEEEEEEEDDDDDDDDDDDDDDDEEEFFFGGGHHHGGGEEECCCAAA@@@AAACCCDDDEEEDDDCCCCCC@@@???===<<<<<<>>>@@@AAA????????????>>>===;;;;;;999:::;;;<<<<<<<<<;;;:::;;;;;;;;;<<<<<<<<<==============================>>>>>>======<<<<<<<<<;;;::::::<<<<<<<<<<<<::::::<<<<<<<<<<<<<<<<<<<<<<<<888888888888888888888888::::::;;;<<<=========<<<888999999::::::999999888777777888888888999999999::::::999888888777666666777777555555444555666777777666555444222111000///111111222222222333333333444222111//////000222333333333333222222222111111333333222111222333444555333333333333333333333333444444444333333222222222777666666555444444333333000111111111111000//////111111111111000000000000---......///......------000000000000000111111222444333333222222333333444333333222222222222222222111000///......///000111000000////////////000000111111111000//////......000000000000111111111111222222111111000...---,,,,,,,,,,,,,,,,,,,,,,,,,,,///......------,,,++++++***++++++++++++***)))))),,,,,,+++***))))))******((((((((((((((((((((((((''''''(((((())))))******))))))))))))***+++,,,---,,,...---))))))++++++)))******)))(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&''''''((()))******+++++++++++++++++++++++++++*********)))))))))))))))(((((((((((((((''''''&&&''''''''''''''''''''''''(((''''''&&&&&&&&&''''''&&&'''((())))))((('''&&&''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&&&&''''''&&&$$$$$$%%%'''######""""""###$$$%%%%%%&&&%%%$$$$$$######$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%%%%$$$######""""""############$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$"""""""""""""""""""""""""""""""""""""""""""""""" !!!""""""###"""""""""""""""""""""""""""""" !!!!!!!!!!!! !!!!!!     CCCCCCCCCCCCCCCDDDDDDEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEFFFGGGHHHGGGEEECCCBBBBBBBBBCCCCCCDDDCCCCCCCCCAAA@@@>>>======>>>???@@@????????????>>>===<<<;;;:::;;;<<<<<<<<<<<<;;;:::;;;;;;;;;<<<<<<<<<====================================<<<<<<;;;;;;;;;;;;::::::;;;;;;;;;;;;::::::;;;;;;;;;;;;;;;;;;;;;;;;888888888888888888888888;;;;;;;;;;;;;;;;;;:::999888999999::::::999999888777777888888888999999999999999999888777777666666777666555333333444666777888777666555333222111111111222222222222333333333333222111000111111333333333333333333222222222222333333222222222333444555333333333333333333333333444444333333222222222222666666555444444333333222111111222222111111000///111111111000000000//////.....................---000000000000000111111222444333333222222333333444222222222222222222222222111000////////////000111111111000000000000111111//////////////////000000/////////000000000111111222222111111000...---,,,------------------------.........---,,,,,,+++++++++++++++++++++******)))++++++***)))))))))))))))(((((((((((((((((((((((('''((((((((()))))))))***))))))))))))***+++,,,------///...+++***,,,,,,*********)))(((((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%''''''&&&&&&&&&&&&''''''''''''(((((())))))******++++++++++++++++++++++++))))))))))))))))))))))))(((((((((((((((''''''&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&'''&&&'''(((((((((((('''&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&''''''&&&$$$$$$%%%'''###############$$$%%%%%%&&&%%%$$$$$$######$$$$$$$$$$$$############$$$$$$%%%$$$######""""""############$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$"""""""""""""""""""""""""""""""""""""""""""""""" !!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!! !!!!!!     CCCCCCCCCCCCCCCDDDEEEFFFFFFFFFFFFFFFFFFFFFFFFFFFEEEFFFGGGGGGFFFEEECCCBBBDDDDDDCCCCCCBBBCCCCCCCCCBBBAAA???>>>===>>>???????????????>>>>>>======<<<;;;;;;<<<<<<<<<<<<;;;;;;;;;;;;<<<<<<<<<=========>>>>>>>>>>>>>>>>>>>>>>>><<<<<<;;;;;;;;;;;;;;;:::;;;::::::999999::::::;;;::::::::::::;;;;;;;;;;;;888888888888888888888888;;;;;;;;;;;;:::999888777888999999::::::999999888888888888888888999999999999999999888888777666666777666333222222444666888999888777666555333333222222222222222333333333333111111222222333333444444444444444444333333333333333333222222222333444555333333333333333333333333333333222222222222222111555555444333333222222111222222222222222111111000111111000000000000//////........................000000000000000111111222333333222222222222333333111111111222222333333444111111000//////000111111222222111111111111222222------......///000000111....../////////000000000111111111111000...---,,,..............................------,,,,,,+++++++++,,,,,,,,,,,,+++************)))((((((((())))))(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))***+++,,,---...000///++++++------+++***))))))(((((((((((((((((((((((((((((((((((((((&&&&&&&&&%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&''''''&&&$$$$$$%%%'''$$$############$$$$$$%%%&&&%%%$$$$$$######$$$$$$######"""""""""######$$$%%%$$$######""""""############$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""!!!""""""""""""!!!!!! !!!!!!!!!!!! !!!!!!     BBBBBBBBBBBBBBBCCCDDDEEEFFFFFFFFFFFFFFFGGGGGGGGGFFFFFFFFFGGGFFFEEEDDDCCCFFFEEEDDDBBBBBBBBBCCCDDDCCCBBBAAA???>>>>>>>>>>>>@@@??????>>>>>>=====================<<<<<<<<<;;;<<<<<<<<<<<<============????????????????????????<<<<<<<<<<<<<<<<<<<<<<<<;;;:::999888888999:::;;;999999:::::::::::::::;;;999999999999999999999999::::::;;;;;;;;;::::::999888999999::::::999999888888888888888888888888888999999::::::999888777666777555333111222444666888888888777666555444333222222222222333333333444444000111222333444555555444555555444444444333333333222222222333333333444444222222333333333333444444222222222222222222222222444444333333222111111000222333333333333222111111111000000000////////////.............../////////000000000000000111111222333333222222222222333333000000111222333333444444111111111111111111111111222111111000000111111222------......////////////............////////////111111111111000///...---////////////////////////......------,,,++++++***,,,,,,,,,,,,,,,+++******))))))((((((((((((((()))(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))***+++,,,---...000///+++***------***))))))(((((((((((())))))((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''((((((((((((((((((''''''))))))))))))))))))))))))((((((((()))))))))))))))(((((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&''''''&&&$$$$$$%%%'''$$$$$$$$$######$$$$$$%%%&&&%%%$$$$$$######$$$$$$"""""""""!!!""""""###$$$%%%$$$######""""""############$$$$$$$$$$$$##############################""""""""""""""""""""""""""""""""""""""""""""""""""""""###""""""!!!  !!!!!!!!!!!! !!!     @@@@@@@@@@@@AAABBBCCCDDDEEEEEEFFFFFFGGGGGGGGGGGGFFFFFFFFFFFFFFFEEEEEEDDDGGGFFFDDDCCCBBBBBBCCCDDDCCCCCCBBBAAA@@@?????????@@@??????>>>===>>>>>>???>>>>>>======<<<<<<<<<<<<<<<<<<<<<=========>>>>>>@@@@@@@@@@@@@@@@@@@@@@@@===============>>>>>>>>><<<;;;999999999999;;;<<<999999999::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;999999:::<<<============888999999::::::999999888888888888888888888888888999:::;;;<<<;;;:::999888666555333222222444777888777666666555444333222222222222333333333444444444000111222333444555555444555555444444444333333333222222333333333444444444222222222333333444444444222222222222222222222222444333333222111111000000222333333333333222111111000000000////////////...///............///000111000000000000000111111222333222222111111222222333000000111222333333444444111111222222222222111111000000////////////000000000000//////........................////////////000000111000000///...---////////////////////////...------,,,++++++******+++,,,,,,,,,,,,+++******)))((((((((((((((())))))(((((((((((((((((((((((())))))))))))(((((((((((())))))))))))***+++,,,---,,,///---***))),,,,,,)))))))))(((((((((((())))))''''''''''''''''''''''''''''''''''''((((((((((((''''''&&&&&&&&&&&&''''''((((((((((((''''''''''''((((((((((((((((((((((((''''''(((((())))))))))))(((((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%&&&'''%%%%%%%%%$$$$$$%%%%%%%%%''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&&&&''''''&&&$$$$$$%%%'''%%%%%%$$$$$$$$$$$$$$$%%%&&&%%%$$$$$$######$$$$$$""""""!!!!!!"""######$$$%%%$$$######""""""############$$$$$$$$$$$$##############################""""""""""""""""""""""""""""""""""""""""""""""""""""""###""""""!!!  !!!!!!!!!!!! !!!  >>>>>>>>>???@@@AAABBBCCCDDDDDDEEEEEEFFFGGGGGGGGGFFFFFFEEEEEEEEEEEEEEEEEEEEEEEEDDDDDDCCCDDDDDDDDDBBBBBBBBBBBBAAA@@@@@@@@@@@@@@@>>>======>>>???@@@@@@???>>>======<<<======<<<<<<=========>>>>>>>>>????????????????????????===>>>>>>>>>>>>?????????<<<;;;;;;::::::;;;;;;<<<999999::::::;;;;;;<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;888999:::<<<===>>>??????888999999::::::999999888999999999888888888888888888999;;;<<<<<<:::999777555555444444555666888888666666555555444333333222333333333333444444444444111111222222333333444444444444444444333333333333111222333444444444333333111222222333333444444555222333333333333333444444444444333222222111111000222222222222222111111000000000////////////......///......---...///111222000000000000000111111222222222111111111111222222111111111222222333333444111222333333333333222111000000////////////000000222111111000//////............/////////000000000000000000000000///......////////////////////////------,,,,,,++++++*********++++++++++++***))))))))))))((((((((()))******(((((((((((((((((((((((())))))))))))(((((((((((())))))))))))***+++,,,---,,,...---))))))++++++(((((((((((((((((())))))***''''''''''''''''''''''''((((((((((((((()))))))))''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''((((((((((((((((((((((((&&&''''''(((((())))))***(((((((((((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''(((&&&%%%%%%$$$$$$%%%%%%&&&(((''''''&&&&&&''''''(((&&&&&&''''''''''''&&&&&&&&&''''''&&&$$$$$$%%%'''&&&%%%%%%$$$$$$$$$$$$%%%&&&%%%$$$$$$######$$$$$$""""""""""""######$$$%%%%%%$$$######""""""############$$$$$$$$$$$$##############################""""""""""""""""""""""""""""""""""""""""""""""""!!!""""""""""""!!!!!! !!!!!!!!!!!! !!!!!!  >>>>>>>>>???@@@AAACCCDDDCCCCCCDDDEEEEEEFFFGGGGGGFFFEEEEEEEEEEEEEEEFFFFFFCCCDDDDDDEEEEEEEEEEEEDDDAAABBBBBBBBBBBBBBBAAAAAAAAA@@@>>>======>>>@@@AAAAAA@@@???===============<<<=========>>>>>>>>>>>>????????????????????????============>>>>>>>>>???;;;<<<<<<======<<<<<<;;;999::::::;;;<<<<<<======::::::::::::::::::::::::888999:::;;;<<<=========888999999::::::999999888999999999888888888777777555777999:::;;;999777666444555666777888888888888777777666666555444444444333333333444444444444555333222111000111111333333333333333333222222222222111222333444444444333333111111222333333444555555333333444444444555555555444444444333222222111111111111222222111111000///000000/////////.........//////...---...000222333000000000000000111111222222222111111111111222222222222222222222222222222222222333444444333222222111000000000000000000111111111111111111000000000/////////000000000111111000000000000000//////...........................------,,,,,,+++*********)))************)))(((((()))))))))))))))***++++++((((((((((((((((((((((((***)))))))))((((((((('''))))))))))))***+++,,,------///...***))),,,,,,)))((((((((((((((()))******((((((((((((((((((((((((''''''''''''(((((())))))''''''&&&&&&&&&&&&''''''%%%&&&&&&''''''((((((((())))))))))))))))))))))))&&&&&&''''''((())))))***(((((((((((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((()))'''&&&%%%$$$$$$%%%&&&''''''&&&&&&%%%%%%&&&&&&'''&&&&&&''''''''''''&&&&&&&&&''''''&&&$$$$$$%%%''''''&&&%%%$$$$$$$$$$$$$$$&&&%%%$$$$$$######$$$$$$"""""""""######$$$&&&&&&%%%$$$######""""""############$$$$$$$$$$$$##############################"""""""""""""""""""""""""""""""""""""""""""""""" !!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!! !!!!!!  ?????????@@@AAABBBDDDEEEBBBCCCCCCDDDEEEFFFFFFFFFFFFEEEEEEEEEEEEEEEFFFFFFBBBCCCDDDFFFFFFFFFEEEDDDAAAAAABBBBBBCCCBBBBBBBBBAAA@@@>>>======???@@@BBBBBBAAA???============>>>============>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>;;;<<<<<<<<<======>>>>>>;;;<<<===>>>>>>===<<<;;;::::::;;;;;;<<<===>>>>>>888888888888888888888888999999:::;;;;;;;;;::::::999999999::::::999999999999999999999888888777777333555777999999888666444444555777999999999999888888888777777666666555555333333333444444444555555444222111//////000222333333333333222222222111111111222333444555444333333111111222333333444555555444444444555555666666666555555444333333222222111111111111111111000//////000/////////............//////...---...000222444000000000000000111111222222222111111111111222222333333222222222222222222222222444444444444222222222222111111111111222222000000000111222222333333000000000000111111111111///000000000000000///...........................------,,,,,,+++******))))))))))))))))))(((''''''******))))))***+++,,,,,,((((((((((((((((((((((((******))))))((((((((('''))))))))))))***+++,,,---...000///++++++------***((((((((((((((()))******))))))))))))))))))))))))&&&&&&&&&'''''''''(((((('''''''''&&&&&&'''''''''%%%%%%&&&&&&'''((())))))************************&&&&&&&&&'''((())))))***(((((((((((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((()))***''''''%%%%%%%%%%%%''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&''''''''''''''''''&&&&&&''''''&&&$$$$$$%%%''''''&&&%%%%%%$$$$$$$$$$$$&&&%%%$$$$$$######$$$$$$############$$$%%%&&&'''%%%$$$$$$###"""###############$$$$$$$$$$$$######"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" !!!""""""###"""""""""""""""""""""""""""""" !!!!!!!!!!!! !!!!!!  BBBAAA@@@???@@@AAABBBCCCBBBBBBBBBCCCDDDEEEEEEFFFDDDDDDDDDEEEFFFFFFGGGGGGFFFFFFFFFEEEEEEEEEEEEEEECCCCCCBBBAAAAAA@@@@@@???>>>??????>>>======???@@@>>>>>>>>>>>>????????????:::999:::<<<>>>>>>===;;;????????????>>>>>>>>>>>><<<;;;;;;:::::::::;;;;;;;;;===>>>>>><<<;;;<<<<<>><<<;;;<<<<<<<<<;;;<<<:::777777888999::::::888999;;;<<<<<<;;;999888999::::::;;;;;;::::::999<<<;;;;;;:::999888777777777777777777777777777777666666666666666555555555888777777777777777888888333444666888888777666444444222000000111333333222222222222111222222333333222111//////000111444555555555444444444555555666444444555555555444222111222222222222222111000///111222333444444444333222000000///...............///...,,,++++++,,,---..................///000000333333222222111222222222111111222333333333222222111222333333333333222111000000000000000000111111111111111111111111111111//////000000000000//////000000////////////000000000000000000///...---,,,,,,------,,,******+++---************))))))))))))))))))))))))))))))))))))(((((('''(((((()))******((((((((((((((((((((((((((((((((()))******++++++//////...---,,,,,,,,,,,,))))))))))))))))))))))))*********)))))))))))))))(((((('''''''''&&&&&&&&&%%%&&&'''(((((('''&&&%%%%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&(((((((((((()))***+++,,,))))))))))))((('''&&&%%%$$$%%%%%%&&&&&&'''''''''$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&(((((('''&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&'''%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%$$$$$$###############$$$################################################""""""############"""""""""""""""""""""""""""""""""""""""""""""""""""""" """#########"""!!!!!!!!!!!!!!!!!!  !!!!!!AAAAAA@@@@@@@@@AAABBBCCCBBBBBBBBBCCCDDDEEEEEEEEECCCCCCDDDEEEEEEFFFFFFGGGFFFFFFFFFEEEEEEEEEEEEEEECCCBBBBBBAAA@@@@@@??????>>>???@@@???======???AAA@@@??????>>>>>>=========::::::;;;===@@@AAA@@@>>>>>>>>>>>>>>>>>>>>>>>>>>><<<<<<<<<<<<<<<<<<======<<<===???>>><<<;;;<<<<<<>>><<<::::::;;;<<<<<<;;;<<<:::888888999:::;;;;;;999:::<<<======<<<:::999999999::::::::::::999999999999999888777666666555888888888888888888888888777777666666555555555555555555444444444444555555333444555666666666555555555333111111222333444333333333222222222222222333222111000///000222444555555444444444444444555555444444555555555444222222222222333333222222111000222333444444444333222111111000//////....../////////...---,,,,,,---///000...............///000000222222222111222222333333111111222333333333222222111222333333333333222111111111111000000000000000111111111111111111111111//////000000000000//////000000////////////000000000000000000///...---,,,,,,------,,,******+++---************)))))))))))))))))))))))))))))))))))))))((((((((())))))***+++(((((((((((((((((((((((((((((())))))******++++++//////---,,,++++++++++++))))))))))))))))))))))))***)))))))))))))))))))))(((((('''''''''&&&&&&&&&&&&'''(((((((((((('''&&&&&&&&&'''''''''((((((((((((((('''''''''&&&&&&&&&(((((((((((()))***+++,,,))))))))))))((('''&&&%%%'''((((((((((((((())))))$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''))))))((((((''''''''''''(((''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%&&&'''%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%$$$$$$###############$$$################################################""""""############"""""""""""""""""""""""""""""""""""""""""""""""""""""" !!!"""###""""""!!!!!!!!!!!!!!! AAAAAAAAA@@@AAABBBBBBCCCBBBBBBBBBCCCDDDDDDEEEEEEBBBCCCCCCDDDDDDEEEFFFFFFFFFFFFFFFEEEEEEDDDDDDDDDBBBBBBAAAAAA@@@@@@?????????@@@@@@???>>>>>>???AAA@@@@@@???>>>===<<<<<<;;;;;;;;;<<<>>>AAACCCBBBAAA========================<<<<<<<<<======>>>>>>???<<<===???>>><<<;;;;;;<<<<<<:::999999:::;;;:::888999999999999999:::;;;<<<:::;;;<<<======<<<;;;:::888888999999999999888888999999888888777777666666888888888888888888888888777777666666555555555666444444333333333333444444444444444444444555555666666444222222333444555444555444333222222111222222222111000000111222444555444444333333333333444444333444555555555444333222333333444444333333222222333444444444444333222111222111111000///000000000///......---...///111222//////.........///000000111111111111222333444444000111222333333333333333111222222333333222222111222111111111000000//////111111111111111111111111///000000111111000000///000000////////////000000000000000000///...---,,,,,,------,,,******+++---++++++*********)))))))))))))))))))))))))))))))))***))))))))))))***++++++(((((((((((((((((((((((((((((())))))***+++++++++///...---,,,******))))))))))))))))))))))))))))))))))))))))))))))))******(((((((((''''''''''''&&&'''(((((())))))(((((('''''''''((((((((()))))))))(((((((((''''''''''''&&&(((((((((((()))***++++++((((((((((((((('''&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&)))))))))((((((((((((((('''''''''&&&&&&%%%%%%$$$%%%$$$$$$$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$###############$$$$$$################################################""""""############"""""""""""""""""""""""""""""""""""""""""""""""""""""" !!!"""""""""""""""  AAAAAAAAAAAABBBBBBCCCCCCBBBBBBBBBCCCCCCDDDDDDDDDBBBBBBCCCCCCDDDDDDEEEEEEFFFFFFFFFEEEDDDDDDCCCCCCBBBBBBBBBAAA@@@@@@??????@@@AAAAAA@@@>>>>>>???AAA?????????>>>>>>==================>>>AAABBBAAA@@@<<<<<<<<<<<<============;;;<<<<<<===>>>>>>>>>>>><<<>>>???>>><<<;;;;;;<<<<<<:::999999888777444222555666888888999999;;;<<<999:::;;;<<<<<<;;;;;;:::777888888999999888888777:::::::::::::::::::::999999999999999999999999999888777666555555555666666777777666555555555666666555444222222222333555777777555333333444555555555666555444333222111111111222222111111222333444555444444333222222222333333333444555555555444333222333444444444444444333333444444444444333222222111333222111111000000111111//////...///000111222333000///////////////000000111111111111222333444555000111222222333333333333222222222222222222222222222222111111000/////////111111111111111111111111000000000111111000000000//////000000000000////////////000//////...------,,,------,,,******+++---+++++++++*********))))))))))))))))))))))))))))))+++***************++++++((((((((((((((((((((((((((())))))******+++,,,,,,///...---+++***)))(((((((((((((((((((((((((((((()))))))))))))))*********((((((((('''''''''''''''(((((())))))))))))((((((''''''((((((((()))))))))((((((((('''''''''''''''((((((((((((((()))******'''(((((((((''''''&&&%%%$$$$$$######""""""!!!!!!&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$#########"""######$$$%%%################################################""""""############""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!""""""""""""""" !!!   AAAAAABBBBBBBBBCCCCCCCCCBBBBBBBBBBBBCCCCCCCCCCCCBBBBBBCCCCCCDDDDDDEEEEEEFFFFFFEEEEEEDDDCCCCCCBBBCCCCCCBBBBBBAAA@@@@@@@@@AAABBBBBBAAA???>>>@@@AAA======>>>>>>??????@@@@@@@@@>>>======>>>???>>><<<;;;<<<<<<<<<=========>>>:::;;;<<<============<<<===>>>???>>><<<;;;:::;;;===;;;:::888666333...***///333666888777777999;;;888888999999::::::::::::777888888999999888888777:::::::::::::::;;;;;;;;;999999999999999999999999999888666555555555777777999888888777666666777777555444222111222333555777777555333333444666666555666555444333222222222222222222222333333444555555555444333222222222222222222333444555555555444333333444444555555555444444444444444333222222222222333333222111111111111111/////////000111222333333111000000/////////000000111111111111222333444555///000111222333333444333222222222222222222222222111111111111000000//////111111111111111111111111000000111111111111000000//////000000000000////////////////////////...---,,,------,,,******+++---++++++++++++************************************++++++***************+++)))))))))))))))))))))))))))))))))***++++++,,,,,,///...,,,+++***)))))))))(((((((((((((((((((((((((((((())))))************(((((((((((((((((((((((())))))(((((((((((())))))&&&&&&'''''''''((((((((((((((((((((((((((((((((((((((((((((((((((()))***'''''''''''''''&&&&&&%%%''''''&&&&&&%%%%%%$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$######""""""######$$$######""""""###$$$$$$%%%################################################""""""############""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""### !!!!!!  AAAAAABBBCCCCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBCCCCCCDDDDDDEEEFFFFFFFFFFFFEEEEEEDDDCCCBBBBBBDDDDDDCCCCCCBBBAAAAAAAAABBBCCCCCCAAA??????@@@AAA===>>>>>>???@@@AAABBBBBBAAA???===<<<<<<<<<;;;:::<<<<<<<<<======>>>>>>???;;;<<<===>>>======;;;;;;===??????>>><<<::::::;;;===;;;999777444///((($$$+++000555777777666888:::777777888888999999::::::888888999999999999888888777777888888999999:::::::::::::::::::::::::::::::::999777555555666777888888777666555555555555555666444333222222444666777777555333333444555666555666555444333333222333333222222333444444555555666666555444333333222222333222333444555555555444333333333444444555555444444444333333222222333333444333222111111000111111111///000000111111222222222111111000/////////000000111111111111222333444444///000111222333444444444333222222111111222222333000000000000000000000111111111111111111111111111000111111222222111111000...///000111111000///......///////////////......,,,------,,,******+++---,,,++++++++++++*********************************++++++***))))))))))))***))))))))))))))))))))))))))))))******+++,,,,,,,,,...---,,,++++++***++++++))))))))))))))))))))))))((((((((()))******++++++'''(((((((((((())))))))))))((((((''''''(((((()))&&&&&&'''''''''((((((((('''(((((((((((()))))))))(((((((((''''''(((((()))&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$############$$$###$$$%%%&&&&&&%%%$$$#########""""""""""""######""""""""""""###$$$%%%%%%################################################""""""############""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!"""###### !!!!!! AAAAAACCCDDDDDDDDDCCCBBBBBBBBBBBBBBBBBBBBBBBBBBBCCCCCCDDDEEEEEEFFFFFFGGGGGGFFFEEEDDDCCCBBBAAAAAAEEEEEEEEEDDDCCCCCCBBBBBBCCCDDDDDDBBB@@@???@@@AAA@@@@@@@@@AAAAAABBBBBBCCCAAA>>><<<;;;<<<===<<<;;;<<<<<<===>>>>>>???@@@@@@===>>>?????????===;;;:::>>>???@@@???<<<::::::::::::999888777333...&&&!!!)))///666888777777999;;;888888888888999:::;;;;;;999999::::::::::::999999777777888888999:::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;999777555555666888999777777666555444333444444555555444444444555666777777555222222444555555444555444444333333333444444222333444555555666666666777666555444333333333333222222444555555555444444222222333444444444444444333222222222222333555666222222111000000000000000000000111111111111111000222111111000//////000000222222222111222222333333///000111222333444444444333333222111111222333333/////////000111111222222111111111111111111111111000111111222222111111000...///000111111000///.........////////////......,,,------,,,******+++---,,,,,,+++++++++*********************************+++***))))))((((((((())))))))))))))))))))))))))))))******++++++,,,,,,---------,,,,,,,,,,,,------))))))))))))))))))))))))'''(((((()))******++++++'''((((((((())))))))))))(((((('''&&&&&&'''((((((''''''((((((((()))))))))'''((((((((()))))))))))))))(((((('''''''''((((((%%%&&&&&&''''''&&&&&&&&&"""""""""###############$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$###############"""###%%%&&&&&&%%%###"""######""""""""""""######""""""""""""###$$$%%%&&&################################################""""""############"""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!!!! !!!"""###$$$ !!!!!!  AAAAAACCCDDDDDDDDDCCCBBBBBBBBBBBBBBBBBBBBBBBBBBBDDDDDDEEEEEEFFFFFFGGGGGGGGGFFFEEEDDDCCCBBBAAAAAAFFFFFFFFFEEEDDDDDDCCCCCCDDDDDDDDDBBB@@@???@@@BBBBBBBBBBBBBBBBBBBBBBBBBBB@@@>>><<<;;;===>>>>>>>>><<<======>>>???@@@@@@AAA???@@@AAAAAA@@@>>>;;;:::>>>???@@@???<<<:::::::::888777777666333---&&&!!!(((///666:::999888:::<<<999999999999:::;;;<<<===999::::::;;;;;;::::::999999999:::;;;<<<<<<======;;;;;;;;;;;;;;;;;;;;;;;;;;;999777555555666888999999888777666555444444444555555555555555666777777666444222222333444555444444444333333333444555555222333444555666666666666888777666555444333333333111222444555555555444444111222333333444444444333222111111111222444666777222111111000///000000000000000111111111000000///222222111000000///000000333333222222111222222222//////111222333444444444444333222111111222333444......///000111222333333111111111111111111111111111111222222222222111111...///000222222000///.........///////////////...---------,,,+++***+++---,,,,,,,,,+++++++++************************************)))(((((('''(((((()))))))))))))))))))))))))))******++++++,,,------------,,,,,,------......))))))))))))))))))))))))'''(((((()))***+++++++++'''((((((((())))))******((('''&&&%%%%%%&&&'''((())))))))))))************'''((((((((())))))******)))(((((('''''''''((((((%%%%%%&&&&&&'''&&&&&&&&&%%%%%%%%%&&&&&&''''''((($$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$###""""""######"""###%%%&&&&&&%%%###"""######""""""""""""######""""""""""""###$$$%%%&&&################################################""""""############"""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!! !!!###$$$ !!!!!!   !!!!!!BBBCCCDDDDDDBBBAAABBBCCCCCCBBBBBBBBBBBBCCCDDDDDDHHHHHHGGGFFFEEEDDDCCCCCCEEEDDDCCCBBBBBBBBBBBBBBBCCCCCCCCCDDDDDDEEEGGGGGGCCCDDDDDDCCCAAA???@@@AAACCCDDDDDDDDDCCCAAA???===@@@@@@???>>>======>>>>>><<<<<<<<<<<<===???@@@AAA>>>>>>????????????>>>>>><<<<<<;;;::::::::::::;;;>>>;;;999666444111---***///222666:::<<<===<<<<<<666888:::<<<<<<:::888666666666777777888888888888<<<<<<<<<<<<============<<<<<<<<<;;;;;;::::::999666777888888888888888777666666666555444444333333888555333333555666555333333333444444333333222111444111000111444666444222444555666777777666555444444666666666444333444555555333111000222333333222222222111111222222333444111222333333444444333333222111111111111111111111333222000///.........///000111111///---,,,---///111111111111111111111111222222222222222222222222555444333222111111111111000000000000////////////000000000000000000000000000111222333333222111000000000111111111111000000//////000000000000//////,,,,,,------.../////////***++++++***((()))+++---*********)))))))))))))))'''(((((()))))))))))))))******))))))((((((''''''*********))))))))))))(((------------------,,,,,,,,,+++)))((((((((()))***((((((((((((((((((((((((***)))((('''&&&&&&'''(((''''''&&&%%%&&&'''((()))))))))))))))))))))))))))((('''&&&%%%&&&''')))+++)))((('''&&&&&&'''((()))(((((('''&&&&&&&&&&&&'''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((())))))))))))((((((%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######"""""""""""""""&&&&&&%%%%%%$$$###""""""$$$%%%%%%&&&%%%$$$###"""$$$$$$$$$$$$######""""""""""""############""""""########################$$$#########""""""!!!!!!###"""!!!  !!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!! !!!!!!  !!!CCCDDDDDDCCCAAA???@@@@@@CCCBBBBBBBBBBBBCCCDDDDDDGGGGGGFFFFFFEEEDDDDDDDDDFFFEEEDDDCCCCCCCCCCCCCCCDDDCCCBBBBBBBBBBBBCCCCCCCCCDDDDDDCCCAAA@@@@@@AAACCCCCCDDDDDDCCCAAA???===AAA@@@??????>>>>>>>>>???=========>>>>>>@@@AAAAAA>>>>>>????????????>>>>>>===<<<;;;;;;::::::;;;;;;>>><<<999888666333000---111333777:::<<<===<<<<<<777888:::<<<<<<:::888777888888999999999999999999<<<<<<<<<<<<==================<<<;;;:::999999999555666777777888888888888777666666555555444333333666444222333555777666555555555555555555444444333444222111222555666555333555555666666666666555555555666777666444333333444444222000000111222222222222222111111222222333444111222333333444444333333000000111111111222222222333222000///......//////000111111000......///111111111111111111111111111222222222222222222222222444444333222111000000111111000000000////////////000000000000000000000000000111222222222222111000///000000111111000000/////////000000000000//////,,,,,,,,,---------------)))******((('''''')))+++)))))))))))))))*********'''(((((()))))))))))))))+++*********))))))))))))******++++++,,,,,,,,,---...------------,,,,,,,,,,,,+++***)))((())))))******************************)))((('''&&&''''''(((''''''&&&&&&&&&'''((())))))))))))))))))))))))))))))(((&&&&&&&&&((()))+++)))((('''&&&&&&'''((()))((((((''''''&&&&&&&&&'''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((())))))(((((('''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###############&&&%%%%%%$$$$$$#########$$$$$$%%%%%%%%%$$$###"""$$$$$$$$$$$$#########"""""""""############""""""####################################"""""""""!!!###"""!!!  !!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!! !!!!!!  !!!CCCDDDDDDBBB???>>>>>>>>>CCCBBBBBBBBBBBBCCCDDDDDDEEEEEEEEEEEEEEEEEEEEEEEEFFFFFFEEEDDDDDDDDDDDDEEEEEEEEEDDDBBBBBBAAAAAAAAACCCDDDDDDCCCAAA@@@AAABBBCCCCCCDDDDDDCCCAAA???>>>AAAAAA@@@@@@??????@@@@@@???????????????@@@AAABBB>>>>>>????????????>>>>>>===<<<;;;;;;:::;;;;;;;;;>>><<<:::999999777444222444666999;;;======<<<;;;777999:::<<<<<<:::999777::::::::::::::::::::::::;;;<<<<<<<<<<<<===============<<<;;;:::999888888444444555777888888888888777777666555555444444333444222222333555777888777666777777777777666555555555333333333555666555444666666555555555555666666555666777555333222222333333111//////111222222222222222111111222222333444111222333333444444333333000000000111222222222333333222111000////////////000111111111000000222333111111111111111111111111222222222222222222222222333333222111000000000000111111000000000/////////000000000000000000000000000111111222222111111000...//////000000//////...//////000000000000//////---,,,,,,,,,,,,+++++++++)))))))))'''%%%%%%'''((((((((())))))******++++++'''((())))))******))))))++++++++++++************))))))***+++,,,---............---------,,,,,,,,,++++++***))))))))))))***************************))))))((('''''''''((((((''''''&&&&&&''''''((())))))))))))))))))))))))))))))((('''&&&'''((()))***((((((''''''''''''((((((((((((((('''''''''&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###"""$$$$$$$$$$$$############""""""############""""""####################################""""""""""""""""""!!! !!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!   !!!BBBCCCDDDBBB@@@??????@@@CCCBBBBBBBBBBBBCCCDDDDDDDDDDDDDDDDDDEEEEEEFFFFFFEEEEEEDDDDDDDDDDDDDDDEEEGGGFFFEEEDDDDDDCCCCCCDDDCCCDDDDDDCCCBBBAAAAAABBBCCCCCCCCCCCCBBBAAA@@@???BBBAAAAAA@@@@@@AAAAAAAAA@@@@@@?????????@@@@@@AAA>>>>>>????????????>>>>>>======<<<;;;;;;;;;;;;;;;===<<<;;;;;;;;;;;;999777777999:::<<<===<<<<<<;;;888999:::;;;;;;:::999888;;;;;;;;;:::::::::::::::;;;;;;;;;<<<<<<<<<============<<<;;;999888777777222333555666777888999999777777666666555444444444444333333333555666777777777777777777777666555555555555444555555555555555666666444333333444666666555666777555333111222333333111//////000222222222222222111111222222333444111222333333444444333333222111111111111111111111222222111111000000000000...000111000000000222444111111111111111111111111222222222222222222222222333222111111000000000111111111111000000000//////000000000000000000000000000000111111111111000000......////////////......//////000000000000//////......------,,,++++++************'''%%%%%%&&&(((''''''((()))***++++++,,,(((((()))************)))************************(((((()))******+++,,,,,,.........------,,,,,,+++++++++*********)))))))))************************))))))(((((((((((((((((('''''''''''''''(((((())))))))))))))))))))))))))))))((((((''''''((())))))(((((((((''''''((((((((((((((((((((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%###$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$$$$######"""#################################"""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!  !!!  !!!AAABBBCCCCCCBBBAAACCCDDDCCCBBBBBBBBBBBBCCCDDDDDDCCCCCCCCCDDDEEEEEEFFFFFFCCCCCCCCCBBBBBBCCCCCCDDDEEEEEEDDDDDDDDDDDDEEEEEEBBBDDDDDDDDDBBBAAABBBCCCCCCCCCCCCCCCBBBAAA@@@@@@BBBAAAAAAAAAAAAAAABBBBBB@@@??????>>>>>>>>>??????>>>>>>????????????>>>>>>======<<<;;;;;;;;;;;;<<<<<<;;;;;;<<<======;;;:::999:::;;;<<<<<<<<<;;;;;;999:::;;;;;;;;;;;;:::999:::::::::::::::::::::999;;;;;;;;;;;;<<<<<<<<<<<<===<<<;;;:::999888777777333444555777888999999999888777777666555555444444555555555444444444555666555666666666666555444444555555555555555444555555666555444333333444555666555666666555333111222333333111//////111333333333222222111111222222333444111222333333444444333333444333333222111000//////222222222222222111111111---.../////////000222444111111111111111111111111222222222222222222222222333222111111111111111111111111111111000000000000000000000000000000000000000000000000000000000000......////////////......//////000000000000//////000000///...---,,,++++++,,,,,,+++)))'''&&&((()))''''''((()))***++++++,,,((())))))***************))))))))))))))))))))))))+++*********************//////...---,,,,,,++++++++++++++++++*********)))))))))))))))))))))))))))(((((())))))))))))))))))'''''''''(((((((((((((((************************)))))))))((((((((())))))'''(((((((((((((((((('''(((((()))))))))((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$###############$$$$$$$$$$$$$$$$$$%%%%%%#####################$$$$$$$$$$$$$$$$$$$$$$$$%%%######$$$$$$$$$$$$##############################""""""""""""""""""######!!!!!!""""""""""""""""""!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!  !!!!!!!!!  !!!@@@BBBCCCCCCCCCCCCDDDFFFCCCBBBBBBBBBBBBCCCDDDDDDCCCCCCCCCDDDDDDEEEEEEEEECCCBBBBBBBBBBBBCCCCCCDDDCCCCCCBBBBBBBBBCCCCCCDDDBBBDDDEEEDDDCCCBBBCCCDDDCCCCCCBBBBBBBBBAAAAAAAAAAAAAAA@@@@@@AAAAAABBBBBBAAA@@@???>>>>>>>>>>>>>>>>>>>>>????????????>>>>>>>>>===<<<<<<;;;;;;<<<<<<;;;::::::;;;======<<<:::::::::;;;;;;<<<<<<;;;;;;::::::;;;;;;;;;;;;::::::999999999::::::;;;;;;;;;:::;;;;;;;;;;;;<<<<<<<<<;;;;;;::::::999999888888555555666888999999999999888888777666666555555444555666666555333333444555444555555555555444333333444555666555333333333555555555444444444444555555333444555444333222333444333111000000222444444444222222111111222222333444111222333333444444333333444333333222111000//////222222333333333222222111---///000//////000222444111111111111111111111111222222222222222222222222333333222222222222222333222222111111111000000000000000000000000000000000111000000//////000000111...//////000000//////...//////000000000000//////000000///...------,,,,,,,,,---,,,***((((((***+++(((((())))))******++++++((()))******++++++******((((((((((((((()))))))))...---------,,,,,,,,,,,,//////...---,,,,,,+++***++++++,,,,,,++++++***)))(((((((((((((((((((((((((((((()))*********))))))&&&'''((())))))))))))(((******************************))))))))))))((((((''''''((((((((((((''''''(((((()))***)))((('''&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%###$$$$$$%%%%%%&&&&&&'''%%%%%%$$$###############$$$$$$$$$$$$$$$$$$$$$$$$######"""""""""###$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%######$$$$$$$$$$$$##############################""""""""""""############!!!!!!"""#########""""""!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!  !!!!!!  !!!AAABBBCCCCCCAAAAAABBBDDDCCCBBBBBBBBBBBBCCCDDDDDDCCCCCCDDDDDDDDDDDDDDDDDDCCCCCCCCCCCCCCCDDDEEEEEEEEEDDDCCCBBBBBBAAABBBBBBBBBDDDEEEDDDCCCBBBCCCEEECCCCCCBBBBBBAAAAAAAAABBB@@@@@@@@@@@@@@@AAABBBBBBBBBBBBAAA@@@???>>>>>>>>>>>>>>>????????????>>>>>>>>>======<<<<<<<<<<<<<<<:::999999:::<<<===;;;:::999999::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;999999:::;;;<<<======>>>::::::;;;;;;;;;<<<<<<<<<999999999999999999999999777777888999999999999999888888777777666555555555333555666555333333555777444555555555555444333333333555666555222111222444333444444555555444444333111333444444333222444555444222000111333555666555222222111111222222333444111222333333444444333333111111111111111111111111111222333444444333222222///000111111000000222444111111111111111111111111222222222222222222222222444333333333333333444444222222222111111111000000000000000000000000000000111000///......///000111///000000111111000000/////////000000000000//////.........------,,,,,,,,,+++,,,,,,***))))))+++---)))))))))))))))*********))))))***++++++++++++***(((((()))))))))*********,,,,,,------------------000///...---,,,++++++***++++++,,,,,,,,,+++***)))))))))))))))))))))))))))'''((()))***+++******)))&&&'''((()))***))))))(((***************************************)))((((((&&&'''((())))))((('''&&&'''(((*********)))'''&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%######$$$%%%%%%&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$############"""!!!!!!"""###$$$%%%$$$$$$$$$%%%%%%%%%&&&&&&###$$$$$$%%%%%%$$$$$$###########################!!!"""""""""############ !!!"""###$$$######"""!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!   !!!!!! !!!AAABBBCCCBBB@@@???@@@AAACCCBBBBBBBBBBBBCCCDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDEEEFFFFFFIIIHHHFFFEEECCCBBBBBBBBBBBBDDDEEEDDDCCCCCCDDDEEECCCCCCBBBAAAAAAAAABBBBBB????????????@@@@@@AAABBBDDDCCCBBBAAA@@@?????????>>>>>>????????????>>>>>>>>>>>>===<<<<<<<<<<<<<<<999999888:::;;;<<<:::999888999999::::::;;;;;;<<<;;;;;;;;;;;;;;;;;;;;;;;;999:::;;;<<<===???@@@@@@:::::::::;;;;;;;;;<<<<<<888888999999999:::::::::888999999:::::::::999999888888777777666666555555111333555555333444777:::555555555666555444444333222444666444111000111444222333555555555555333222000222333333333333444666444333111222444666777666222222111111222222333444222222333444444444333333...///000111222333444444111222333444444444333222111222333222111111333555111111111111111111111111222222222222222222222222444444444333333444555555222222222111111111111000000000000000000000000000111000///......///000111000000111111111111000000//////000000000000//////------,,,,,,,,,,,,++++++***++++++***((()))+++---*********)))))))))))))))))))))***++++++++++++***))))))******+++++++++,,,))))))***+++,,,,,,---...000//////---,,,+++******++++++,,,---,,,+++***)))************************'''((()))+++++++++***)))&&&''')))*********)))(((***************************************)))((('''&&&'''((())))))((('''&&&'''(((***+++***)))'''&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((''''''&&&%%%&&&&&&''''''&&&&&&%%%######$$$%%%%%%&&&''''''''''''&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$###""""""###"""!!!!!!!!!###$$$%%%$$$$$$$$$%%%%%%&&&&&&&&&###$$$$$$%%%%%%$$$$$$###########################!!!!!!""""""#########$$$ !!!"""$$$$$$$$$###"""!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!    !!!!!! !!!!!!AAA@@@@@@??????@@@@@@AAACCCDDDEEEDDDBBBAAAAAABBBCCCCCCCCCCCCDDDDDDEEEEEEEEEDDDCCCCCCCCCDDDFFFGGGGGGEEEDDDCCCDDDCCCBBB@@@EEECCCBBBAAAAAA@@@???===EEEFFFFFFDDDBBB@@@@@@AAA@@@@@@???>>>===>>>BBBEEEGGGFFFEEEDDDAAA???===<<<999;;;>>>>>>>>>>>>???@@@===>>>>>>>>>>>>======<<<;;;;;;;;;<<<>>>===:::777::::::999999999:::;;;<<<:::::::::;;;;;;;;;<<<<<<:::::::::;;;;;;;;;<<<<<<<<<<<<;;;::::::::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;666555444333444555777999888888777666666666666666444444444444444555666777999555222222555888888777666555333222222333555666444444444333333222222222222222222333333444444444555444333444555555333222333333333333333333333333444333333222222333333444333333333444444555555555222222222222333333444555222222222222222222222222111222222222222111000000333333333333333333333333444333333222222333333444555444222000///000000111222111000//////000111111222000///......///000222222111111000000000000000000000000000000000000000000000///...------,,,,,,*********)))******+++,,,+++++++++************)))))))))*********))))))(((******+++,,,,,,,,,,,,+++,,,,,,++++++,,,...///111//////...---,,,++++++***,,,,,,,,,+++++++++******+++***)))'''''')))***+++))))))))))))((((((((((((''''''''''''((((((((())))))***+++,,,,,,,,,,,,,,,******))))))((((((''''''''''''(((((())))))************)))''''''&&&&&&&&&######$$$$$$%%%&&&''''''&&&%%%%%%$$$#########$$$###$$$%%%%%%&&&&&&&&&&&&((('''&&&%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''%%%$$$$$$$$$###"""""""""%%%%%%%%%$$$$$$#########%%%%%%$$$###""""""######$$$$$$##################""""""""""""""""""""""""""""""""""""""""""""""""$$$$$$###"""!!!!!!""""""""""""""""""""""""""""""""""""############""""""    @@@@@@@@@@@@@@@@@@@@@@@@BBBDDDEEEDDDBBBAAAAAABBBBBBBBBCCCCCCCCCDDDDDDDDDDDDCCCBBBBBBBBBCCCEEEEEEEEEDDDBBBCCCDDDDDDCCCBBBDDDCCCBBBBBBCCCCCCBBBAAADDDEEEEEECCCAAA@@@AAABBBAAAAAA@@@???>>>???BBBEEEEEEDDDDDDCCCAAA@@@>>>===<<<>>>??????======>>>???????????????>>>===<<<<<<;;;:::;;;<<<===<<<999777999999999999::::::;;;;;;:::::::::;;;;;;;;;;;;<<<:::::::::;;;;;;;;;;;;<<<<<<<<<;;;:::::::::::::::::::::::::::::::::::::::777666555444555666888999888888777666666666666666555555555444555555666666888555222222444666777666666555333222222333555666555444444444333333333333222222333333333444444444333222222444555666555444333333333333333333333333444333333222222333333444444444444555555666666666333333222222222333444444222222222222222222222222222222222222222111000000333333333333333333333333444333333222222333333444444333222000000000000111444333111000////////////111000///......///000111222111111000000000000000////////////////////////000//////...------,,,,,,***************++++++,,,+++++++++************)))******++++++++++++************+++,,,,,,,,,,,,+++,,,,,,++++++,,,---...///000//////......------,,,,,,,,,,,,++++++++++++******)))(((''''''((()))******)))))))))(((((((((((('''''''''((((((((()))))))))******+++,,,,,,++++++******))))))(((((((((((((((((((((((())))))))))))***)))((('''&&&&&&&&&&&&$$$$$$$$$%%%&&&'''''''''&&&%%%%%%$$$######$$$$$$###$$$%%%%%%&&&&&&&&&%%%''''''&&&%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$###############%%%%%%%%%$$$$$$$$$######%%%$$$$$$###""""""##############################""""""""""""""""""""""""""""""""""""""""""""""""$$$$$$###"""""""""""""""""""""""""""""""""""""""!!!""""""######""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!  !!!  !!!???@@@AAABBBBBBAAA@@@???AAACCCDDDDDDBBBAAAAAABBBBBBBBBBBBBBBBBBCCCCCCCCCBBBBBBBBBBBBBBBCCCDDDDDDCCCBBBAAABBBDDDEEEDDDCCCAAAAAAAAABBBBBBCCCCCCCCCDDDDDDDDDBBB@@@@@@BBBDDDCCCCCCBBB@@@??????BBBDDDAAABBBBBBBBBAAA@@@??????@@@@@@@@@???======>>>???@@@@@@@@@??????===<<<<<<:::::::::;;;<<<;;;999777999999999999:::::::::;;;::::::::::::;;;;;;;;;;;;::::::::::::;;;;;;;;;;;;<<<;;;::::::999999::::::999999999999999999999999888777666666666777888999888888777666666666666666777777666555555555666666777555333222444555555444666555444333333444555666555555555555555444444444333333333333444444444444222111111333666777666555333333333333333333333333444333333222222333333444555555555666666666666666444444333222222222333333222222222222222222222222222222222222222111111000333333333333333333333333333333222222222222333333444333222111000000000000555444222000///.........111000///......///000111222111111000000000000000//////////////////////////////......---,,,,,,,,,***************+++,,,,,,+++++++++************)))***++++++,,,,,,,,,++++++******+++,,,,,,,,,,,,+++,,,,,,++++++++++++,,,---////////////////////////,,,,,,,,,,,,++++++++++++***)))(((''''''((()))*********)))))))))(((((((((''''''((((((((()))))))))))))))******++++++*********))))))))))))((((((((())))))))))))(((((((((((((((((('''&&&%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%'''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&###############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###%%%$$$######"""#################################""""""""""""""""""""""""""""""""""""""""""""""""$$$###"""""""""""""""""""""""""""""""""""""""""" !!!!!!""""""!!!!!! """"""!!!!!!!!!!!!""""""  !!!!!!  !!!???@@@BBBCCCCCCBBB@@@???@@@BBBCCCCCCBBBAAABBBCCCBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBCCCCCCCCCDDDDDDCCCBBBAAAAAACCCDDDCCCAAA>>>???@@@@@@??????@@@AAACCCCCCCCCAAA@@@@@@BBBDDDDDDDDDCCCAAA??????AAACCC>>>???@@@@@@AAA@@@@@@@@@@@@@@@@@@???>>>>>>???AAA@@@@@@@@@@@@???>>><<<<<<;;;:::999:::;;;;;;999777888888999999::::::::::::999999:::::::::;;;;;;;;;999999:::::::::;;;;;;;;;;;;::::::999999999999999888888888888888888888888999888888777777888999999888777777666666666666666999888777666666666666666666555333333333333444444555555444444444444555555666666666666666555555555333333444444444444444444333222222444555666555444333333333333333333333333444333333222222333333444555555555555555555666666555444333333222222222222222222222222222222222222222222333333222222111000333333333333333333333333333333222222222222333333333222222111111000000000333222111111000//////...111111000//////000111111222111111000000000000000////////////////////////.........------,,,,,,,,,+++************+++,,,,,,+++++++++*********))))))******++++++,,,+++++++++******+++,,,,,,,,,,,,+++,,,,,,++++++++++++++++++------......////////////------,,,,,,,,,+++++++++******)))(((((()))***************)))))))))(((((('''(((((((((((()))))))))((())))))*********))))))))))))))))))))))))))))))*********)))(((''''''''''''&&&%%%%%%$$$$$$$$$%%%&&&&&&&&&'''''''''((((((&&&%%%%%%$$$$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""""""""###$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$###############$$$$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""######"""""""""""""""###"""""""""""""""""""""""" !!!!!!!!!!!! """!!!  !!!"""  !!!!!!!!!!!!!!! !!!!!!!!!???@@@BBBCCCCCCBBB@@@??????AAABBBCCCBBBBBBBBBCCCBBBBBBBBBBBBBBBBBBBBBBBBCCCCCCDDDDDDEEEEEEEEEEEEEEECCCAAAAAABBBBBB@@@???@@@AAABBBAAA???>>>???AAABBBCCCCCCAAA@@@@@@BBBDDDCCCDDDDDDBBB@@@@@@AAACCC======>>>???@@@@@@??????===>>>??????>>>???AAACCC@@@@@@@@@??????===<<<<<<<<<:::999:::;;;;;;999888777888999:::::::::999999999999999:::::::::;;;;;;999999999:::::::::;;;;;;::::::999888888888888999888888888888888888888888999999888888888888888999888777777666666666666666999888777666666666666666444444444444333333444444555555555555555555555555666666666666666666666666444444444444444444444444666444444444555555333111333333333333333333333333444333333222222333333444444444444444444444444444555444333333222222222222222222222222222222222222222333333333333222111111333333333333333333333333333222222111111222222333222222222222111111111000000000000111111111111111111111000000000000111111222111111000000000000000........................---------------,,,,,,,,,+++++++++***+++,,,,,,---+++++++++*********))))))(((((()))***++++++************+++,,,,,,,,,,,,+++++++++++++++++++++******,,,,,,,,,------...//////---------,,,,,,,,,++++++,,,++++++++++++++++++,,,************))))))))))))(((((((((((()))))))))***))))))*********))))))((())))))))))))************++++++***)))((('''&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&&&&'''''''''''''''&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""""""""###$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$""""""#########$$$$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""###"""""""""""""""############################## !!!!!!!!!!!! !!!  !!!  !!! !!!!!!!!!!!!!!!!!! @@@AAABBBCCCCCCBBBAAA@@@===???BBBBBBBBBBBBCCCDDDCCCCCCCCCBBBBBBBBBBBBBBBCCCDDDDDDEEEFFFEEEEEEEEEEEECCCAAAAAAAAAAAA???===BBBEEEFFFEEEAAA@@@AAADDDAAACCCCCCBBBAAA@@@@@@AAAAAABBBCCCBBB@@@@@@AAABBB======>>>>>>>>>>>>>>>===:::<<>>>>>>>>>>>>>>======<<<===<<<::::::;;;<<<;;;999666777999:::::::::999888999999999999::::::::::::999999999999:::::::::::::::999888888777777888888888888888888888888888888999999999999888888888777888888777666666666666666777777666555555555666666222444555555444444555666555555555555555555555555555555555666666666666666555555555555444444444444777666444444555444222000333333333333333333333333444333333222222333333444444444444444444333333333444444333222222222333333222222222222222222222222333333333333333222222111333333333333333333333333222222111111111111222222111111222222222111111000...///000111111222222111111111111111111111111111222111111000000000000000........................------,,,,,,,,,,,,,,,,,,+++++++++++++++,,,------+++++++++************)))'''((()))*********************+++,,,,,,,,,,,,+++++++++,,,,,,,,,,,,,,,++++++,,,,,,,,,------......------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++*********)))))))))((((((((()))))))))************++++++******)))))))))))))))************++++++******)))(((''''''&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&'''%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###############$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%#########"""######$$$%%%"""""""""###$$$$$$%%%%%%"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""######$$$######################## !!!!!!""""""!!!!!!    !!!!!!  BBBBBBBBBBBBBBBBBBBBBBBB===???AAABBBBBBBBBCCCDDDDDDDDDDDDCCCCCCCCCBBBBBBBBBCCCDDDEEEEEEEEEDDDDDDCCCAAA@@@@@@AAAAAA@@@>>>AAADDDGGGFFFBBBAAADDDGGGAAACCCDDDDDDBBB???>>>>>>???@@@AAAAAA@@@@@@AAABBB>>>>>>>>>>>>===<<<;;;;;;999<<>>>>>>>>;;;;;;<<<============<<<>>>===;;;;;;<<<===<<<;;;666777999:::::::::888777888999999999999:::::::::888999999999999:::::::::999999888777777777777777999999999999999999999999888888888888888777777666888888777666666666666666555555555444555555666666111333666666555555777999555555666666666666555555444444555555555666666666666555555555444444444444666555444444555555333111333333333333333333333333444333333222222333333444666555555555444444444444333333222222222333444444222222222222222222222222333333444444333333222111333333333333333333333333222222111111111111222222000111222222222222111000//////111111222111000000111111111222222111111111222111111000000000000000........................,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++,,,------+++++++++************)))'''((()))***++++++++++++******+++,,,,,,,,,,,,+++***+++,,,---......------------------...............------------,,,,,,,,,+++,,,,,,,,,,,,,,,,,,++++++++++++*********))))))(((((()))))))))*********++++++,,,,,,+++******)))))))))*********+++++++++******))))))((((((''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''%%%&&&&&&&&&%%%%%%$$$###$$$$$$######$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$#####################$$$$$$$$$%%%%%%%%%######""""""###$$$$$$%%%!!!""""""###$$$$$$%%%%%%"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""###$$$$$$########################!!!""""""######""""""!!!!!!  !!!   !!!!!! CCCBBBBBBAAAAAABBBBBBCCC<<<>>>AAABBBBBBBBBCCCEEEEEEEEEDDDDDDDDDCCCCCCCCCAAAAAACCCDDDDDDDDDCCCBBB@@@?????????AAABBBAAA@@@===AAAEEEDDDAAAAAADDDHHH@@@CCCEEEEEECCC???===<<<>>>???AAAAAA@@@@@@AAABBB?????????>>>===;;;:::999:::===AAABBB@@@===;;;:::999:::;;;<<<============???>>><<<<<<=========<<<555777999:::::::::888777888888999999999:::::::::888888999999999:::::::::999888888777777777777777999999999999999999999999888888888888888777666555888888777666666666666666444444444444444555666777000333666777666666888:::555555666666666666555555333444444444555555666666666666555555555444444444444333333444555666444333333333333333333333333333444333333222222333333444777777666666555555555444222222222222333444444555222222222222222222222222333333444444333333222111333333333333333333333333222222111111111111222222000000222333333222111000000111222222222000///...111111222222222222111111222111111000000000000000........................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---...+++++++++************)))((()))***+++,,,---------******+++,,,,,,,,,,,,+++)))+++,,,...//////......////////////////////////......---------,,,,,,,,,***++++++,,,,,,++++++***+++++++++************)))))))))))))))************,,,,,,,,,,,,,,,+++***)))))))))******++++++++++++))))))))))))((((((((((((&&&&&&&&&%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&%%%%%%$$$###$$$#########$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%$$$$$$$$$######""""""#########$$$$$$%%%%%%%%%######""""""###$$$%%%%%%!!!""""""###$$$$$$%%%%%%""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!""""""###$$$$$$########################""""""############"""""""""!!!!!!""" !!!!!!!!!!!!!!!!!!!!!!!!  BBBBBBBBBBBBBBBBBBBBBBBBCCCCCCCCCBBBAAAAAA@@@@@@DDDCCCBBBAAA@@@AAABBBBBBBBBCCCDDDEEEDDDAAA???===EEEDDDCCCBBBBBBBBBBBBBBBCCCDDDEEEEEEDDDBBBCCCDDD???@@@BBBBBBBBB@@@>>>===???@@@BBBBBBAAAAAABBBCCCAAA@@@>>>===<<<<<<<<<===>>>???@@@@@@@@@>>>===<<<>>>===<<<===>>>??????===>>>===;;;:::999999:::::::::;;;;;;;;;:::888666555999:::;;;;;;;;;999777555888999:::;;;;;;;;;:::999999888888888999:::;;;;;;999999888888888888999999888888888888777777777777777777777777666666666666555555555555555555555555777777777777777666666666777777777777777777777777666444222111111333666777666555444333333333333333444444444555555555555666777666444222111222444555555555555444444333333333666666555555444444333333555555444333333333333444444444444444444444444444222222222222222222222222111111111111111111111111444333333222222111111111000000000000///////////////000000000...------...///000111222222111///...000000000000000///............------------............---------,,,,,,,,,//////---,,,+++*********++++++++++++++++++++++++******))))))******+++,,,+++,,,,,,------,,,,,,+++***+++,,,---............000000///...---,,,,,,,,,...---,,,+++***+++,,,---++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++*********))))))((((((***)))((((((((()))+++,,,))))))))))))(((((((((((('''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$#########$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$############$$$$$$############""""""""""""######""""""""""""######%%%$$$$$$$$$######"""""""""############$$$$$$$$$%%%$$$###"""!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!############"""""""""""""""""""""!!!!!!!!!!!!!!!###########################"""!!! !!! !!!!!!"""""" !!!!!! !!!!!! !!!!!!  !!!!!!!!!!!!""" !!!!!!!!!!!!  !!!!!!!!!!!!!!! !!!   !!!!!!BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBCCCCCCCCCEEEDDDBBBAAA@@@AAAAAABBBBBBCCCCCCCCCCCCBBB@@@???EEEEEEDDDCCCBBBBBBBBBBBBBBBDDDEEEDDDCCCBBBBBBCCC@@@AAABBBBBBBBBAAA???>>><<<===??????>>>===???@@@@@@???>>>===<<<<<<======???????????????>>>======<<<;;;:::;;;===>>>===<<<>>>===;;;:::999999::::::::::::;;;;;;:::999888777888999:::;;;;;;:::888777999:::;;;;;;;;;:::999888888888888888888999::::::999888888777777888888999888888777777777666666666777777777777666666666555444444444444444444444444666666666666666666666666555555555555555555555555555444222111222333666777555444444444444444555555444444444555555555555666777666444333333333444555555444444444444444444333666666555555555555555555666666555444333333333444444444444444444444444444222222222222222222222222111111111111111111111111222222333333222222111111000000000000////////////000111111000///......000///000000111111111000000000000000000000///............------------......------,,,,,,,,,+++++++++------,,,+++++++++,,,,,,+++++++++++++++++++++++++++++++++++++++,,,,,,---+++,,,,,,------,,,,,,+++++++++,,,---............000000///------,,,,,,---------,,,,,,,,,+++,,,,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++*********)))***))))))((()))***+++,,,***)))))))))(((((((((((('''&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$############$$$$$$############""""""""""""######""""""""""""######$$$$$$#########""""""""""""############$$$$$$$$$%%%$$$###"""!!!!!!!!!!!!"""""""""""""""""""""!!!############""""""""""""""""""""""""""""""""""""##############################!!! !!!!!! !!!!!!!!!"""""" !!!!!! !!!!!! !!!!!!  !!!!!!!!! !!!!!!!!!!!!  !!!!!!!!!!!!!!! !!!   !!!AAAAAAAAAAAABBBBBBBBBBBBAAABBBBBBCCCDDDDDDEEEEEEEEEDDDCCCAAA@@@@@@AAAAAABBBBBBBBBBBBBBBBBBBBBBBBFFFEEEDDDCCCBBBBBBBBBBBBAAACCCDDDCCCBBB@@@AAAAAA@@@AAABBBCCCBBBAAA@@@???;;;===>>>>>>===<<<>>>??????>>>>>>=========>>>>>>??????>>>>>>======>>>>>>:::999999999;;;<<<;;;:::======;;;:::::::::::::::::::::;;;;;;;;;;;;::::::777888:::;;;;;;;;;:::999::::::;;;;;;:::999888888888888888888888999999999999888888777777888888999777777777666666666555555777777777666666666555555333333333333333333333333333444444555555666666666444444444444444444444444555444333222222333555777555555444444444555555666444444444555555555555666666666666555555555555555444444444444444555555555555555555666666666666666888777666555444333333333444444444444444444444444333333333333333333333333111111111111111111111111000111222333333333222111000000000000////////////000111222111/////////111////////////000111111222000000000000000//////.........------------......,,,,,,+++++++++*********+++++++++++++++,,,---...,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---...,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,------.........000///...---------------,,,------...---,,,+++***++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,************************,,,,,,,,,+++++++++++++++***))))))))))))***++++++******)))))))))(((((((((''''''&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########"""""""""######""""""""""""############""""""""""""!!!!!!"""############$$$$$$$$$%%%$$$###"""!!!!!!!!!!!!""""""""""""""""""""""""############""""""""""""################################################$$$###""""""!!!""""""""" !!!!!!!!!!!!"""""" !!!!!!!!!!!! !!!!!!!!! !!!!!!!!!  !!!!!!!!!!!!  !!!!!!!!!!!!""""""!!!!!! !!!  !!!""" AAAAAAAAAAAAAAABBBBBBBBBCCCCCCCCCDDDDDDDDDEEEEEEFFFDDDCCCAAA@@@@@@@@@AAABBBAAAAAAAAAAAABBBCCCDDDDDDCCCBBBAAAAAA@@@@@@@@@AAABBBCCCCCCAAA??????@@@AAAAAABBBBBBBBBBBBAAA@@@>>>@@@AAA@@@??????@@@AAA>>>>>>>>>>>>>>>>>>?????????>>>===<<<<<<===>>>???:::999888999;;;<<<;;;:::<<<<<<;;;;;;:::::::::::::::::::::;;;;;;<<<<<<<<<777888999:::;;;;;;;;;;;;;;;;;;::::::999999888777777888888888888888888888888888777777777777888888666666666666555555555555777777666666666555555555333333333333333333333333222222333333444555666666444444444444444444444444555444333222222444555666777666555555444444444555444444444555555555555666555666666777777666555555333333444444555555666666555555555666666777777777888777666555444333333333333333444444444444444444333333333333333333333333111111111111111111111111...000111333333333222111000000000000///////////////000111000///...///000///.........///000222333//////000000000000//////......------------......,,,,,,,,,,,,+++++++++++++++++++++***++++++,,,---,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---......///000///...---------------+++,,,...//////---+++)))***+++++++++++++++,,,,,,++++++++++++++++++++++++)))))))))))))))*********++++++++++++++++++++++++)))))))))*********++++++*********)))))))))((((((''''''&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""######""""""""""""######"""""""""!!!!!!!!!!!!!!!""""""#########$$$$$$$$$$$$$$$###"""!!!!!!"""""""""""""""""""""#####################"""""""""!!!###$$$$$$$$$$$$$$$%%%%%%########################$$$#####################!!!!!!!!!!!!!!!!!!""""""!!!!!!!!!!!!!!!  !!!!!!!!!!!!   !!!!!!!!!!!!  !!!!!!!!!!!!""""""""""""!!!!!! !!!  !!!###  @@@@@@@@@AAAAAAAAABBBBBBEEEEEEDDDDDDDDDCCCCCCCCCEEEDDDBBBAAA@@@@@@AAAAAAAAAAAAAAAAAAAAABBBDDDDDDBBBAAA@@@@@@??????@@@@@@AAABBBCCCBBB@@@?????????@@@AAAAAAAAAAAAAAAAAAAAA@@@AAABBBBBB@@@???@@@BBB>>>>>>>>>??????????????????>>>===<<<<<<===>>>???<<<:::::::::<<<===<<<;;;;;;;;;;;;;;;;;;;;;::::::::::::::::::;;;<<<<<<===777888999:::;;;<<<<<<<<<::::::999999888888888888888888999999999999888777888777777777777777777888666666666666555555555555666666666666555555555555333333333333333333333333111222222333444555555666555555555555555555555555444444333333333444555666999888666555333333222222444444444555555555555666555555666777777666666555444444444555555666666666444444555555666666777777777777666444444333333333333333333444444444555555333333333333333333333333111111111111111111111111...///111222333222222111000000000000////////////---...///...------...//////...------...000222333//////000000000000//////......------------......------------,,,,,,,,,,,,,,,,,,+++************+++,,,,,,,,,,,,,,,,,,,,,,,,***************+++,,,,,,---,,,,,,++++++,,,,,,---,,,,,,+++,,,,,,---///000//////...------------...+++,,,///000000...+++)))*********++++++,,,,,,,,,++++++++++++++++++++++++(((((()))))))))*********))))))******************)))*********++++++++++++************))))))))))))(((''''''&&&&&&''''''((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''&&&%%%$$$######$$$%%%%%%%%%%%%$$$###$$$$$$$$$$$$##################""""""""""""######!!!!!!!!!!!!!!!"""""""""""""""#########$$$$$$$$$$$$###""""""""""""""""""!!!"""""""""#########$$$############"""""""""!!!######$$$$$$%%%%%%%%%%%%#################################$$$$$$$$$$$$###""""""""""""""""""!!!!!!!!!!!!""""""!!!!!!  !!!""""""!!!   !!!!!!!!!!!! !!!!!!!!!""""""""""""######"""!!! !!!  !!! """ ??????@@@@@@AAAAAABBBBBBEEEEEEDDDDDDCCCBBBBBBAAADDDCCCBBBAAA@@@AAABBBBBBAAAAAAAAABBBBBBCCCCCCCCC@@@@@@?????????@@@AAAAAABBBCCCDDDCCC@@@???>>>??????@@@@@@@@@@@@@@@AAAAAA???@@@AAA@@@>>>>>>>>>@@@>>>??????@@@@@@???>>>>>>======<<<<<<======>>>>>>===;;;;;;<<<===>>>===<<<:::;;;;;;<<<<<<;;;::::::::::::999999:::;;;<<<<<<888999999:::;;;<<<<<<===999999888888888888999:::888999:::;;;:::999888777888777777666666777777888777777777666666666555555666666666555555555444444333333333333333333333333222333333444444555555555555555555555555555555555444333333333444444555555888777555444222222111111444444444555555555555666555555555555555666666666555555555555555666666666444444444555555555555555555555444333333333333444222333333444444555555555333333333333333333333333111111111111111111111111000000000111111111111111000000000000////////////+++---......---,,,---///............///000000111...//////000000000000000......------------...............---------,,,,,,---,,,+++***************++++++++++++++++++++++++******))))))******+++,,,------++++++++++++---------,,,++++++,,,---///000///......---------......,,,---///000000...,,,************++++++,,,,,,---++++++++++++++++++++++++((())))))******+++++++++)))))))))))))))*********)))***++++++,,,,,,++++++++++++*********)))))))))((((((''''''''''''((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''''''''&&&&&&&&&$$$%%%&&&''''''%%%###"""###$$$%%%&&&&&&%%%$$$###%%%$$$$$$$$$$$$###############""""""""""""######!!!!!!""""""""""""######"""############$$$$$$$$$######"""""""""""""""###!!!""""""######$$$$$$$$$############""""""""""""#########$$$$$$%%%%%%&&&########################""""""###$$$$$$$$$$$$#########""""""""""""!!!!!!!!!""""""""""""!!!  !!!""""""!!!    !!!!!!!!!!!! !!!!!!!!!!!!""""""""""""############"""!!! !!! !!!  """ >>>??????@@@AAAAAABBBBBBCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBAAA@@@AAABBBCCCDDD@@@AAABBBCCCCCCCCCBBBAAA??????@@@@@@AAACCCDDDEEECCCDDDEEECCCAAA?????????>>>>>>>>>>>>??????@@@@@@>>>@@@@@@???>>>======>>>???@@@@@@AAA@@@???======;;;<<<<<<===>>>>>>=========;;;;;;;;;===>>>===<<<::::::;;;<<<<<<;;;;;;:::::::::999888999999:::;;;:::::::::::::::;;;<<<===888888777777888999:::;;;999:::<<<<<<<<<:::999777777777666666666666777777888888777777777666666666666666555555555444444444444444444444444444444444444444444444444555555555444444444444444444444444333333333444444444555555444444333222222222222333444444444555555555555666555444333333333444666777666666666666555555555555444444444444444333333333333222222222222333444444222222333333444555555666444444444444444444444444111111111111111111111111333222000/////////111222000000000000////////////,,,---......------...000......///////////////.........///000000000000000......------------......---------,,,,,,,,,++++++******************+++,,,************************+++************+++,,,,,,...---+++******+++---...---,,,+++++++++---///000......---------......///---...///000///...,,,+++)))******+++,,,,,,------************************))))))******+++,,,,,,---)))))))))******+++++++++)))***+++,,,,,,,,,+++++++++++++++*********))))))((((((''''''''''''((((((((((((((((((''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&'''''''''(((((((((((((((''''''&&&&&&###%%%'''((('''&&&###"""###$$$&&&''''''&&&$$$###%%%%%%$$$$$$$$$###############""""""""""""######"""""""""#########$$$$$$"""############$$$$$$$$$######""""""""""""######!!!""""""######$$$%%%%%%############""""""""""""""""""######$$$%%%%%%%%%########################!!!!!!###$$$$$$$$$###############"""""""""!!!!!!"""""""""""""""!!!  !!!""""""!!!  !!!  !!!!!!!!! !!!!!!!!!!!! !!!!!!"""""""""############$$$$$$######!!! !!! !!!  """ >>>>>>???@@@AAAAAABBBBBB@@@@@@AAAAAABBBCCCCCCCCCBBBAAA@@@@@@AAABBBDDDEEE@@@AAACCCDDDDDDCCCAAA@@@@@@@@@@@@BBBCCCEEEFFFGGGCCCDDDEEEDDDAAA?????????>>>>>>======>>>???@@@@@@@@@AAAAAA@@@>>>>>>>>>???@@@AAAAAAAAA@@@???===<<<:::;;;===>>>>>>>>>===<<<<<<;;;:::;;;===>>>===<<<999:::;;;<<<<<<<<<;;;:::;;;:::999888888888999:::;;;;;;:::::::::;;;<<<<<<777777666666777999;;;<<<:::;;;=========;;;999888777777666666666666777777888888888888777777777777666666555555555444444444555555555555555555555555555555555555555555444444333333333333333333333333333333333444444444555555111111111111222333444555444444444555555555666666555444222111222444666777777777666666555555444444444444444333333222222222111111111111222333444444222222333333444555666666444444444444444444444444111111111111111111111111555333000...---...000222000000000000////////////,,,...//////......///111......000000000///...---......///000000000000000.........------.........,,,,,,,,,+++++++++******((((((((()))***,,,---...)))))))))))))))))))))))),,,,,,++++++,,,,,,---......---+++******+++---...---,,,+++++++++---///111......---------......///---.../////////...---,,,))))))***+++,,,,,,------************************))))))***+++,,,,,,------*********++++++,,,,,,,,,)))***+++,,,---,,,+++++++++++++++************)))((((((''''''''''''(((((()))(((((((((''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''(((((())))))(((((('''''''''&&&###%%%'''((((((&&&###!!!###$$$&&&''''''&&&$$$###%%%%%%%%%$$$$$$$$$############""""""""""""######""""""######$$$$$$$$$%%%"""############$$$$$$$$$###"""""""""""""""######!!!""""""###$$$$$$%%%%%%############""""""""""""!!!!!!"""###$$$$$$%%%%%%######################## !!!"""###$$$$$$###"""$$$#########""""""!!!!!!"""""""""""""""!!!!!!  !!!######!!!  !!!""" !!!!!!!!!!!!""" !!!!!!!!!!!! """"""""""""############$$$$$$$$$######!!! !!!!!! !!! !!!###  !!!!!!!!!AAAAAAAAAAAAAAA@@@???>>>BBBBBBCCCCCCBBBBBBAAA@@@AAA@@@AAAAAABBBCCCDDDEEECCCCCCCCCCCCCCCCCCBBBBBBCCCBBBAAA@@@@@@BBBCCCEEECCC@@@???@@@CCCEEECCCAAAAAA@@@@@@@@@@@@@@@@@@AAA>>>????????????>>>============<<<<<<<<<;;;;;;;;;888:::<<<<<<<<<<<<===???:::;;;<<<<<<::::::;;;<<<:::::::::;;;;;;<<<<<<<<<888888999999999:::::::::===<<<;;;:::::::::::::::777777888999::::::;;;;;;999999999888888888888777666666666666666555555555::::::999888777666555555777777777777666666666666666666666666666555555555444444444333333222222222777666555444333444444555555555666444222222333444555555444444444555555666222222222333333333444444555444333333444555444333333333333333333444555666777555444444666666444111333333333333333333333333222222444444444444222222333333333333333333333333333333222111000000111111111222444555444222000///333222111000////////////000//////........./////////000000///---,,,---///000000000000////////////------......//////000000///...---,,,+++,,,,,,---(((((()))++++++,,,,,,,,,,,,,,,---...---,,,***)))(((((()))***+++,,,,,,---+++,,,------++++++,,,------------...///000111222///...---,,,,,,---...//////000111111111///...---......---------,,,,,,,,,,,,,,,,,,+++++++++******''''''(((((())))))******,,,+++***))))))***+++,,,))))))))))))***************)))(((((()))+++---...((((((''''''''''''(((((((((((())))))((('''&&&&&&''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$######""""""######!!!"""###$$$$$$###"""!!!""""""""""""""""""""""""""""""""""""############""""""#########$$$$$$$$$######""""""""""""######$$$$$$############$$$$$$################################################'''&&&$$$#########$$$$$$$$$$$$########################"""!!!!!!!!!!!!!!!###"""!!! !!!"""###""""""""""""""""""""""""    !!!!!!!!!!!!!!! !!!!!! ###############"""!!!!!! !!!   !!! AAAAAAAAAAAAAAA@@@??????@@@@@@AAABBBCCCCCCCCCBBB@@@@@@@@@@@@AAABBBCCCDDDCCCCCCCCCCCCCCCCCCBBBBBBCCCBBBAAA@@@@@@BBBCCCEEEBBBAAA???AAACCCDDDCCCAAABBBAAAAAA@@@@@@AAAAAABBB@@@@@@?????????>>>>>>>>>======<<<<<<<<<;;;;;;;;;999;;;<<<<<<;;;;;;===>>><<<======<<<999888999999:::::::::;;;;;;;;;<<<<<<888999999999999:::::::::===<<<;;;::::::::::::;;;888888888999999::::::;;;999999999888888888888777555555555666666666777777999999888888777666666666777777777777666666666666555555555666666666666666444444444333333333222222777666444333333333444555555555555444222222333555444444333333333444444444444444444444555555555555555444333333444555444333222222333444555666888999888666555666777777555222333333333333333333333333222333333444444333333222444444444444444444444444333333222111111111111111222222333333333222000000333222111000//////////////////............//////222333333111000///000222000000000000/////////.........///////////////000///...---,,,,,,,,,------((()))***+++,,,,,,,,,,,,,,,---------,,,,,,+++***)))))))))***++++++,,,,,,+++,,,------++++++,,,---------------......///000///...---,,,,,,---.../////////000000000///------------------,,,,,,,,,,,,,,,,,,++++++************'''((((((((()))))))))***+++***))))))))))))***+++))))))))))))***************)))((('''(((***,,,---''''''&&&&&&&&&&&&'''''''''((((((((((((''''''&&&&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$######""""""######!!!"""###$$$$$$###"""!!!""""""""""""""""""""""""""""""""""""#####################$$$$$$$$$$$$%%%######""""""""""""######$$$$$$############$$$$$$################################################&&&%%%$$$#########$$$$$$##############################"""!!!!!!!!!!!!!!!###"""!!!!!!!!!!!!"""###""""""""""""""""""""""""    !!!!!!!!!!!!!!!!!!!!! !!!!!! """"""######"""!!!!!!     !!! !!!AAAAAAAAAAAAAAA@@@@@@???>>>???@@@BBBCCCCCCDDDDDD@@@@@@???@@@@@@AAABBBCCCBBBBBBBBBBBBBBBBBBCCCCCCBBBBBBAAA@@@AAABBBCCCDDDBBBAAA@@@AAABBBCCCBBBAAABBBAAAAAAAAAAAAAAAAAABBBBBBAAA@@@???>>>??????@@@=========<<<<<<<<<;;;;;;:::<<<===<<<;;;;;;<<<============;;;999777777777::::::::::::;;;;;;;;;;;;999999999999::::::::::::<<<<<<;;;:::::::::;;;;;;999999999999999999999999999999999888888888888777555555555666666777777777777777777777777777777777777777777777666666666666444444555555666666777777444444444444333333333333555555333222222333333444444555555444222222333555444333333222222222333333555555555666666666777777444333222333444555444333222222333444666888999:::777666666666777777666444333333333333333333333333444333333222222333333444555555555555555555555555333222222111111111111222222222222111111111111111222222111000//////////////////............/////////000000///------...000000000000/////////......000000000000////////////......---,,,,,,,,,------))))))***+++,,,,,,,,,,,,------,,,,,,++++++,,,,,,************************+++,,,---,,,+++***+++---------,,,,,,,,,,,,---.........------------......---.../////////...---,,,,,,,,,,,,,,,+++++++++++++++************)))))))))(((((((((((())))))))))))))))))(((((((((((())))))))))))))))))************((((((''''''''')))***,,,&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''(((((((((''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$######""""""######""""""############""""""""""""""""""""""""""""""""""""""""""############$$$$$$$$$$$$%%%%%%%%%%%%######""""""""""""######$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################&&&%%%$$$#########$$$$$$##############################"""!!!!!!!!!!!!"""###""""""!!!!!!""""""###""""""""""""""""""""""""     !!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!     !!! !!! @@@AAAAAABBBAAAAAA@@@@@@??????@@@AAABBBCCCCCCBBB@@@?????????@@@@@@AAABBBAAAAAABBBBBBBBBBBBCCCCCCBBBBBBAAAAAAAAABBBCCCDDDAAAAAAAAAAAAAAABBBAAAAAAAAAAAA@@@@@@@@@@@@AAAAAACCCBBB@@@>>>>>>???@@@BBB============<<<<<<<<<<<<;;;<<<======;;;:::;;;<<<<<<<<<===;;;888777777888::::::::::::::::::::::::999999999:::::::::;;;;;;<<<;;;;;;:::::::::;;;;;;::::::999999999999999999999999999888888888777777777777666666666666666666666666777777888888888888777777777777666666666666333444444555666777888888444444444444444444333333444444222222222222333444444555555444222222444555555444333333222333333333555555555555666666666666444222222222444555444333222222333333555666777888555555555666666666555444333333333333333333333333444444222222222222444444444444444444444444444444333222222111111222222222222222111000000000111222111111000//////////////////............//////000---......---,,,,,,---///000000/////////.........111111111000000//////...------------------------******+++,,,------,,,,,,...---,,,+++***+++,,,---+++++++++*********))))))***,,,,,,,,,+++***+++,,,---,,,+++++++++++++++,,,------------------------,,,---.........---,,,+++,,,,,,,,,+++++++++*********)))))))))))))))))))))(((((((((((())))))))))))(((((((((''''''(((((((((((()))))))))************(((''''''''''''((()))***'''&&&&&&%%%%%%&&&&&&'''%%%%%%&&&'''(((((((((((($$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######""""""######"""""""""######"""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!"""""""""############$$$$$$%%%%%%%%%&&&&&&&&&$$$######""""""######$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$###""""""!!!!!!""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!    !!!!!!!!!!!!!!!!!!!!!!!!  !!!     !!! !!!!!! @@@AAAAAABBBBBBBBBAAAAAA@@@AAAAAABBBAAAAAA@@@@@@@@@@@@?????????@@@AAAAAAAAAAAAAAAAAABBBBBBCCCCCCAAAAAAAAAAAABBBBBBCCCCCCAAAAAAAAAAAAAAA@@@AAAAAA@@@@@@????????????@@@@@@CCCBBB@@@>>>>>>???@@@BBB>>>>>>=========<<<<<<<<<;;;<<<======;;;:::;;;<<<:::;;;<<<;;;999888999:::::::::::::::::::::::::::999999:::::::::;;;;;;;;;;;;;;;:::::::::;;;;;;<<<::::::999999999999999999999999999888888888777777999999888777666555555444666666666777888888999999777777777777666666666666333444444555666777888888444444444444444444444444444333222222222222444444333444555444333333444666666666555444444444444444333333444444444555555555333222111222444555444333333333333222333333444444333444555555444444444444333333333333333333333333444444222222222222444444333333333333333333333333333222222222222222333333222111111000111111222222111000//////////////////...............///000000///000111000//////000222////////////............111111000000//////......,,,---------------------+++,,,,,,------------,,,---,,,+++***+++,,,---...,,,,,,++++++***)))))))))***+++,,,,,,******+++,,,,,,++++++*********++++++,,,------------------,,,+++,,,---......---,,,,,,,,,,,,,,,+++++++++******)))))))))))))))))))))***))))))))))))(((((((((((('''''''''(((((('''''''''((()))))))))************'''''''''''''''(((((((((((((((''''''''''''((((((%%%%%%&&&''''''(((''''''$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######""""""#########""""""""""""""""""###!!!!!!!!!!!!!!!!!!!!!!!!!!!"""""""""############$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$############$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$###"""""""""""""""""""""############""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!  !!!   !!!!!!""""""""""""!!!!!!!!!      !!!  !!!!!! !!!!!!!!!!!! @@@AAAAAABBBBBBBBBBBBBBBAAAAAAAAAAAAAAA@@@??????AAAAAA@@@@@@@@@@@@AAAAAA@@@@@@AAAAAABBBBBBCCCCCCAAAAAAAAABBBBBBBBBCCCCCC@@@AAABBBAAA@@@???@@@AAAAAA@@@@@@??????@@@@@@AAABBBAAA@@@???>>>??????@@@>>>>>>>>>=========<<<<<<:::<<<===<<<;;;;;;<<<===:::;;;<<<<<<::::::;;;<<<::::::::::::999999999999::::::::::::;;;;;;;;;;;;;;;;;;:::::::::;;;<<<<<<999999999999999999999999999999999888888888888777999999888777777666555555666666777777888888888999777777777777666666666666444444555555666666777777444444444444555555555555444333333222222333555555333444444444333333444666777666666555444444444444222222222333333333333444222111000222444555444333444333333222222222222222111333444444333333333444333333333333333333333333444333333222222333333444333333333333333333333333333222222222222333333444222222222222222333333333000//////....../////////......---......///000111---...///...------///111/////////.........------////////////............+++,,,---.........------,,,------......---------,,,,,,++++++,,,,,,------,,,+++++++++******))))))***+++,,,+++***)))***,,,++++++*********++++++,,,,,,,,,------------,,,,,,+++,,,---.........---,,,,,,,,,,,,,,,++++++++++++)))))))))************+++))))))))))))((((((((((((''''''((((((((((((''''''))))))))))))************''''''(((((((((((((((((((((((((((''''''(((((((((%%%&&&&&&'''''''''&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######""""""############""""""""""""######""""""""""""""""""""""""""""""""""""############$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$############$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%##############################$$$%%%%%%%%%$$$$$$"""""""""###$$$$$$%%%%%%$$$$$$###""""""""""""###"""######$$$$$$######"""""""""""""""""""""""""""!!!!!! !!!!!!   !!!""""""""""""""""""!!!!!!!!!  !!!     !!!  !!!"""!!!!!!!!!"""!!!!!! @@@AAAAAABBBCCCCCCBBBBBB???@@@@@@AAAAAAAAA@@@@@@BBBBBBAAAAAAAAAAAABBBBBB???@@@@@@AAABBBBBBCCCCCCAAAAAABBBBBBCCCCCCBBBBBB@@@AAACCCBBB???>>>???AAACCCBBBBBBAAAAAABBBBBBCCC@@@@@@?????????>>>>>>>>>>>>>>>>>>>>>=========<<<999;;;<<<<<<;;;;;;===>>><<<===>>>===;;;:::;;;<<<:::::::::999999999888888:::::::::;;;;;;;;;;;;<<<:::::::::::::::;;;<<<===888888888999999::::::;;;999999999888888888888777777777777777777777777777777777777777777888888888777777777777666666666666555555555666666666666666444444444444555555555666555444333333333444666777222444444444333333555777777666555444333333333333222222222222333333333333111000000111333555444333333333222222222333333444111333555555444333444666333333333333333333333333222333333444444333333222444444444444444444444444222222222222222333444555111222333444555444444333//////.........//////000---------......///000111+++,,,,,,,,,++++++---/////////.........---------------------............+++,,,---.........------------............------***+++,,,,,,---------,,,+++++++++***************)))+++,,,+++***)))***+++************++++++,,,---+++,,,------------,,,++++++,,,---/////////...---------------,,,,,,,,,,,,************++++++,,,,,,***)))))))))(((((((((''''''((())))))))))))((('''))))))))))))************((((((((())))))((((((((((((''''''&&&&&&''''''(((&&&&&&'''''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######""""""######$$$###"""!!!!!!"""###$$$""""""""""""""""""""""""""""""""""""#####################$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%########################"""###$$$%%%%%%%%%%%%$$$!!!""""""###$$$$$$%%%%%%%%%$$$######""""""######"""###$$$$$$$$$$$$###"""""""""""""""""""""""""""!!!!!! !!!!!!   !!!""""""###""""""""""""!!!!!!!!!  !!!!!!!!!!!!!!!!!!!!!    !!! !!!!!!"""!!!""""""""""""!!! @@@AAAAAABBBCCCCCCCCCBBB===>>>???@@@AAABBBBBBBBBCCCCCCBBBAAAAAABBBBBBBBB??????@@@AAAAAABBBCCCCCC@@@AAABBBBBBCCCCCCBBBBBB@@@BBBCCCBBB???===???AAADDDDDDCCCCCCCCCCCCDDDDDD>>>????????????>>>======>>>>>>>>>>>>============999:::<<<<<<<<<<<<===??????@@@@@@>>>;;;::::::::::::::::::999999888888888:::::::::;;;;;;;;;<<<<<<:::::::::::::::;;;<<<===777777888999::::::;;;;;;999999999888888888888777444555666777888999::::::888888777777777777777777777777777777666666666666666666666666666555555555444444444555555555666666555444444333444555666777222333444444333333555777666555444333222222222222222222222333333333444444111000000111333555444333222222222333444555666777111444777666444444555777333333333333333333333333222222444555555444222222555555555555555555555555222222222222333333444555111222444666666666444333//////.........//////000---------......000111111---...//////......000222//////.........---------+++,,,,,,------.........***+++---...///...---------...............------)))***,,,---...---,,,,,,************************)))+++++++++***)))***+++************+++,,,---...++++++------------+++++++++,,,.../////////............------------,,,,,,******+++++++++,,,,,,,,,******))))))(((((((((''''''((()))******)))((('''))))))))))))************((()))))))))))))))(((((('''&&&&&&%%%%%%&&&&&&'''''''''''''''&&&%%%$$$$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###"""#########$$$###"""!!!!!!"""###$$$""""""""""""""""""""""""""""""""""""############""""""#########$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%########################"""###$$$%%%&&&%%%%%%$$$!!!""""""###$$$$$$%%%%%%%%%$$$######"""#########"""###$$$%%%%%%$$$###"""""""""""""""""""""""""""!!!!!! !!!!!!  !!!!!!!!!!!!!!!!!!!!!!!! !!!""""""###""""""""""""!!!!!!!!!!!! !!!"""""""""!!!!!!!!!!!!   !!!!!! !!!"""""""""""""""""""""!!!!!! @@@AAAAAA@@@???>>>???AAA??????@@@AAABBBBBBCCCCCC@@@@@@AAAAAAAAAAAABBBBBBDDDCCCCCCBBBCCCDDDFFFGGGCCCBBBBBBAAAAAABBBBBBCCCAAAAAA@@@???===>>>AAADDDDDDDDDCCCCCCCCCBBBBBBBBB@@@@@@@@@??????????????????@@@AAA???<<<:::;;;<<<999999999::::::;;;;;;;;;999999:::;;;===???AAABBB999999999999:::;;;<<<===<<<;;;999777777888999:::;;;;;;:::::::::;;;<<<<<<@@@<<<888999;;;<<<888444999999888888888888888888555555666666777777888888777777777777777666666555777777777777666666666666666666666666666555555444666666777777666555444444555555555333222222333555666666555444444444444555000111222222333333333333555555444444444444555555888777555333333333555666444444333333333444555555444444444444555555555666777666555444444444444444444333333222222333333444444444555555555555555555111111111222333444555666444555555555444333333222////////////............//////...------------...//////.........---------///...------...///000111////////////000000000000/////////...------,,,,,,---------------+++***)))((()))+++---...---+++******++++++,,,,,,++++++***))))))***+++,,,,,,------)))***++++++***+++---///...,,,++++++,,,------,,,,,,,,,,,,---------......---,,,++++++******++++++***))))))))))))+++,,,---++++++)))(((''''''''''''(((((())))))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((('''((()))(((&&&&&&((()))''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######""""""######$$$$$$$$$$$$$$$###"""!!!!!!!!!""""""######$$$$$$#########"""""""""""""""%%%%%%%%%$$$$$$#########%%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###"""###$$$&&&'''########################%%%%%%$$$###""""""######""""""""""""""""""""""""!!!!!!""""""""""""!!!!!!!!!!!!    !!! !!!!!!!!!!!!""""""""""""###""" !!!"""###!!! """"""""""""""""""""""""   !!!!!!!!!!!!!!!!!! !!!""""""###""""""!!! BBBBBBBBBAAA???>>>???AAA??????@@@@@@AAABBBBBBCCC?????????@@@@@@AAAAAAAAAAAA@@@@@@??????@@@AAABBBBBBBBBAAAAAAAAAAAABBBBBBAAAAAAAAA@@@>>>>>>@@@BBBCCCCCCCCCBBBBBBBBBBBBAAA@@@@@@?????????>>>>>>>>>???@@@AAA???<<<:::;;;<<<:::::::::::::::;;;;;;;;;>>>===<<<;;;;;;;;;;;;;;;::::::999999999::::::;;;<<<<<<:::999999999:::;;;;;;:::::::::::::::;;;;;;===999777888;;;<<<999666888888888888888888888888777777777888888888999999777777777777777666666555888888777777666666555555666666777777666666555444666666666666666555444444555555555444222222444555444444444444444555666777222222333333333333333333555555444444444444555555777666444333222333444555444333333333333444555555444444555555555666666666666666555555444444444444444333333222222333333444666666666555444444444333111111111222333444555666444444555555444333333222111111111111000000000/////////...---------------//////.........---------//////...---......000000....../////////000000000///............---------......------,,,+++++++++)))***+++,,,---,,,,,,+++++++++,,,,,,,,,,,,++++++*********++++++,,,,,,---)))***++++++***+++---///...,,,++++++,,,------,,,,,,,,,,,,---------......---,,,++++++******++++++***))))))))))))+++,,,---+++***)))(((''''''''''''(((((())))))))))))((((((''''''''''''''''''''''''(((((((((((((((((((((((('''((()))(((&&&&&&((()))((('''&&&&&&%%%%%%&&&&&&%%%%%%&&&&&&&&&'''''''''''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######""""""######$$$$$$$$$$$$$$$###"""""""""""""""""""""#####################""""""""""""%%%%%%%%%$$$$$$$$$######%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###$$$$$$%%%%%%########################%%%$$$$$$###""""""######""""""""""""""""""""""""!!!!!!""""""""""""!!!!!!!!!!!!    !!! !!!!!!!!!!!!""""""""""""###!!! !!!"""###""" !!!!!!!!!!!!!!!!!!!!!!!!    !!!!!!!!!!!! !!!!!!""""""""""""!!! CCCDDDDDDBBB@@@???@@@AAA?????????@@@@@@AAAAAABBB===>>>>>>???@@@AAAAAABBBCCCCCCBBBAAAAAAAAABBBBBBBBBAAAAAA@@@@@@AAAAAABBBAAABBBCCCAAA@@@>>>???@@@BBBBBBBBBBBBAAAAAAAAAAAA@@@@@@???>>>>>>===<<<<<<>>>???@@@>>><<<;;;;;;<<<;;;;;;;;;;;;;;;;;;::::::>>>===<<<:::999999888888;;;:::999999888888999999<<<<<<<<<<<<<<<;;;::::::::::::::::::999999999:::999777555777:::;;;:::888888888888888888888888888888888888999999999999999777777888888777777666555999999888777666666555555777777777777777666666555666666666666666555555444555666666444333222444555333333333444555666777888444444444555444444333333444444444444444444444444666555333222222222333444333333333333333444555555555555666666666777777777666666555555555555555555444444333333333333444444777777666555444333333222222222222222222333444555444444444444444333333222333333333222222222111111///...------,,,,,,------/////////............---000//////............///............////////////------........./////////000///---,,,++++++,,,,,,++++++++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++)))+++++++++++++++---///...,,,++++++,,,------,,,,,,,,,,,,---------......---,,,++++++******++++++)))))))))))))))+++,,,,,,+++***)))((((((''''''((((((((())))))))))))((((((''''''''''''''''''''''''(((((((((((((((((((((((('''((()))(((&&&&&&((()))((('''&&&&&&%%%&&&&&&&&&%%%&&&&&&&&&&&&'''''''''''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######""""""#########$$$$$$$$$$$$###""""""############""""""""""""########################%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$##############################%%%$$$######"""#########""""""""""""""""""""""""!!!!!!""""""""""""!!!!!!!!!!!!!!!    !!! !!!!!!!!!!!!"""""""""""""""!!! !!!"""###"""!!!  !!!!!!!!!   !!!!!!!!!  !!!!!!!!!""""""!!!!!! DDDEEEDDDBBB@@@???@@@AAA?????????@@@@@@@@@AAAAAA>>>>>>???@@@AAABBBBBBCCCDDDDDDCCCCCCBBBBBBAAAAAAAAAAAA@@@@@@@@@@@@AAAAAAAAACCCDDDCCCAAA???>>>???BBBBBBAAAAAAAAA@@@@@@@@@@@@@@@???>>>===<<<;;;:::>>>???>>>===<<<;;;;;;;;;===<<<<<<;;;;;;:::::::::999888888888999:::;;;<<<999999888888888999999::::::;;;=========<<<:::999999999::::::999999888888888666555666999:::888777888888888888888999999999888888999999999999999999777888888888888777666666:::999999888777666555555777777888888777777666555555666666666666666555555555666666555333333444555333333333444444666777777555666666666555444333333444444444444444444444444444333333222222222333444222222222222333444555555666666666666777777777777555555666666666555555555444444333333333333444444666666555555444444444333222222222222222222333333333333444444444333333222444333333333222222222222///......---,,,---------/////////...............000000//////............---.........////////////,,,------...///000000000111000---,,,+++,,,---...,,,,,,+++++++++,,,,,,---+++,,,,,,,,,,,,,,,,,,+++,,,,,,++++++++++++++++++***+++,,,,,,++++++---///...,,,++++++,,,---,,,,,,,,,,,,,,,---------......---,,,++++++******++++++((((((((()))******+++,,,******)))((((((((((((((((((((())))))))))))((((((''''''''''''''''''''''''(((((((((((((((((((((((('''((()))(((&&&&&&((()))(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$######""""""############$$$$$$$$$######"""$$$$$$######""""""!!!!!!"""###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&%%%$$$"""!!!########################$$$$$$###############$$$""""""""""""""""""""""""!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!    !!! !!!!!!!!!!!!"""""""""""""""!!! !!!"""###"""!!!  !!!""""""  !!!!!!  !!! !!!!!!!!! DDDDDDDDDBBB@@@???@@@BBB@@@@@@@@@@@@@@@AAAAAAAAA@@@@@@AAAAAABBBCCCCCCDDD@@@@@@@@@@@@??????>>>>>>BBBAAAAAA@@@@@@AAAAAABBBBBBCCCDDDCCCAAA?????????BBBBBBAAAAAAAAA@@@@@@@@@@@@@@@???>>>===<<<;;;:::>>>>>>===<<<<<<<<<;;;;;;<<<<<<<<<;;;;;;::::::999666666666777999;;;<<<===777777777888999;;;<<<===999:::<<<======;;;999777999::::::::::::999888777999888777777777777777666777777888888888999999999888888888888888888888888888888888888888777777666:::999999888777666666666777777777777777666555555555555666666666666666555444666777666444333444555666555555444444444555555666666666666555555444333333333444555555444333333333333333222333333333444111111111222333444555555666666666666777777777777555555666777777666666555555444444333333444444555333444444444555555666666333333222111111111222222222222333333444333333222333333222222222111111111000///......------......////////////////////////000000000//////...------.........////////////000,,,------...///000111111222000...,,,,,,,,,......------,,,++++++,,,,,,---,,,,,,,,,------,,,,,,,,,,,,,,,++++++++++++++++++***+++,,,,,,+++,,,...000...,,,++++++,,,---,,,,,,,,,,,,,,,---------......---,,,++++++******++++++'''(((((()))******++++++***))))))(((((((((((()))(((((())))))))))))((((((''''''''''''''''''''''''(((((((((((((((((((((((('''((()))(((&&&&&&((()))(((((('''&&&&&&&&&&&&'''&&&&&&&&&'''''''''((((((''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$######""""""######"""######$$$$$$$$$######$$$$$$######""""""!!!!!!""""""######$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&%%%$$$"""!!!########################$$$###############$$$$$$""""""""""""""""""""""""!!!!!!""""""""""""!!!!!!!!!!!!"""""""""!!!   !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!! !!!"""######"""  !!!"""""" !!!!!!   !!!  BBBCCCCCCBBB@@@@@@AAABBBAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCCAAAAAABBBBBBBBBAAA@@@@@@CCCBBBBBBAAAAAABBBBBBCCCBBBCCCCCCBBB@@@???@@@AAABBBBBBBBBBBBAAAAAAAAAAAA@@@@@@???>>>>>>===<<<<<<>>>===<<<<<<======;;;:::::::::::::::::::::999999888888888888888999::::::666777777999:::<<<>>>???999:::<<<===<<<;;;999777::::::;;;;;;;;;999888777999888888888777777666666777777777888999999::::::888888888888888777777777888888999999888888777666999999888888888777777777666666666666666555555444444555666666666666666666444666777777555444444555666666555444444444444444555555555666555555444444222333444555555444333222333333333333444444444444111111111111222444555666555555666666666777777777444555666777888777666555555555444444444444555555222333333444555666777777444333222111111111111111111222222333333333333333222222222111111111000000111000//////......//////...////////////000000000...//////000//////...---////////////000000000000------...///000000111111222111///...------......------------,,,,,,,,,,,,,,,,,,------------,,,,,,++++++++++++++++++++++++***,,,,,,,,,+++,,,...000...,,,++++++,,,------,,,,,,,,,,,,---------......---,,,++++++******++++++&&&'''((()))************))))))(((((((((((())))))(((((())))))))))))((((((&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((('''((()))(((&&&&&&((())))))(((''''''&&&&&&''''''&&&&&&'''''''''(((((((((''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&&&&'''%%%$$$######""""""######""""""###$$$$$$$$$$$$###############""""""""""""""""""######$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$#######################################"""######$$$%%%""""""""""""""""""""""""!!!!!!""""""""""""!!!!!!!!!!!!"""###"""!!!   !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!! !!!###$$$###"""  !!!!!!!!! !!!!!!!!!!!!  !!!!!! !!!!!! ???@@@AAA@@@???@@@AAACCCBBBBBBBBBBBBBBBBBBBBBBBBCCCCCCBBBBBBBBBBBBAAAAAABBBCCCDDDEEEEEEEEEDDDDDDDDDCCCCCCBBBBBBCCCCCCDDDBBBCCCCCCAAA@@@@@@BBBDDDCCCCCCCCCBBBBBBBBBBBBAAA@@@@@@?????????>>>>>>>>>>>><<<:::;;;======<<<:::888888999999999999999999::::::999888888888999999999999999:::;;;===>>>???;;;<<<<<<===<<<;;;:::999:::;;;<<<===<<<:::888777777888888888888888888999666777777888999999::::::::::::999999999888888888888999999999999888777777777888888888888999999999555555555555555444333333444444555666666666666666444666888777666444444444555555444444444555555666333333444555555555444444111222444555555444222111333333444555555555555555000000000111222444555666444444555555555666666666444555777888888888666666555555444444444444555555333444444444555666666666444333222111000000000000111111222333333333333333222222222222111111111000222222111000000000000000.../////////000000000000---...///000000//////...000000000000111111111222......//////000000000111111111000000///.........,,,---.........---+++***,,,,,,------------,,,,,,*********++++++,,,,,,---+++,,,---,,,,,,,,,...000...,,,++++++,,,------,,,,,,,,,,,,---------......---,,,++++++******++++++&&&'''((()))*********)))))))))(((((((((((())))))(((((())))))))))))((((((&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((('''((()))(((&&&&&&((())))))(((((('''''''''''''''''''''''''''((((((((((((''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%&&&''''''%%%$$$######""""""######""""""###$$$$$$$$$$$$$$$"""""""""""""""#########""""""###$$$$$$%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###$$$$$$%%%%%%##############################""""""###$$$$$$%%%""""""""""""""""""""""""!!!!!!""""""""""""!!!!!! !!!#########"""    !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!!  ###$$$###"""!!!!!!!!!!!!!!!!!!!!!!!!    !!!!!!!!!!!!!!! !!!!!!!!!"""""" !!!!!! >>>???@@@@@@???@@@BBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCBBBBBBAAAAAA@@@@@@??????@@@BBBCCCCCCCCCBBBBBBDDDDDDCCCCCCCCCCCCDDDDDDCCCCCCBBB@@@???@@@CCCFFFDDDDDDCCCCCCCCCBBBBBBBBB@@@@@@@@@???????????????>>><<<:::;;;===>>><<<999777777777888888999999:::999999888888999::::::;;;;;;;;;;;;;;;;;;<<<===>>>===============<<<<<<;;;;;;<<<=========;;;888777555666888888888999;;;<<<666777777888999999::::::;;;;;;;;;::::::999999999888999999999999888777777777777777888999999::::::444444555555444444333222444444555666777777666666444666888888666444444444333333333444555666777888222222333444555555555444111222444555555444222111333444444555666666666555000000000111222444555666444444444444555555555666333555777888999888777666555555444444444444555555555555555555555555444444444444222111000000000000000111222333333333333333333333333222222222111111333222222111111111111111.../////////000000111111,,,---...000000000//////000111111111222222222222////////////000000000000000111111111000///...---,,,---...//////---+++***,,,------......------,,,))))))***+++,,,,,,------+++,,,------,,,,,,...000...,,,++++++,,,------,,,,,,,,,,,,---------......---,,,++++++******++++++%%%&&&(((*********))))))))))))(((((((((((()))***(((((())))))))))))((((((&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((('''((()))(((&&&&&&((()))))))))((('''''''''''''''''''''''''''((((((((()))''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%&&&''''''%%%$$$$$$###"""#########!!!"""###$$$$$$$$$$$$$$$!!!!!!""""""######$$$$$$""""""###$$$%%%%%%&&&&&&#########$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&'''''''''######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((('''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###"""###$$$&&&'''##############################""""""###$$$%%%%%%""""""""""""""""""""""""!!!!!!""""""""""""!!!!!! !!!###$$$###"""  """""""""""""""""""""""" !!!!!!""""""""""""""""""""""""!!!!!!!!!!!!""""""""""""  ###$$$$$$###""""""""""""""""""""""""  !!!!!!""""""###### !!!!!!!!!!!!!!!!!!!!!!!!!!!"""""""""""" !!!!!! AAAAAAAAA???>>>???BBBEEEAAACCCDDDCCCBBB@@@AAAAAACCCAAA@@@@@@AAABBBAAA@@@DDDCCCBBBAAA@@@AAAAAABBBDDDCCCBBBAAA@@@@@@AAABBBBBBCCCCCCCCCBBBAAA@@@@@@DDDDDDDDDCCCBBB???===;;;@@@@@@@@@????????????>>>>>>>>>>>>>>>>>>===<<<<<<888888999:::::::::999999888888888:::<<<<<<;;;999<<<;;;;;;::::::;;;;;;<<<===>>>>>>===<<<;;;;;;===;;;;;;<<<;;;:::888666444777888999999::::::999999;;;;;;::::::999888888777999999999999999888777666::::::999999888888777777888888888888777777777777888888777666555444444333333333333444444444555555333333444555555444333333555555555666555555444444444444444444444444444333333444555555666666555555333444444444555555666666333222222111111222222333777666666555555555666666666888888666333222555888999666444555777777555222444555666666666444111000333333333333222...((($$$+++---000222222222333444555555444333222222111111222222111000000000000000111111111000000///......////////////000000000000---...000111111111000///000000000000000000000000000000///.....................////////////......---,,,,,,+++***)))((((((***++++++,,,,,,++++++***+++******)))***,,,---...///---++++++,,,,,,+++***---------...------,,,,,,---,,,***(((((((((((()))'''(((((())))))))))))((())))))((('''&&&&&&%%%%%%))))))((('''&&&%%%%%%$$$''''''''''''''''''''''''''''''''''''''''''''''''(((((())))))))))))((((((&&&'''((('''&&&&&&'''(((''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$###"""######$$$$$$$$$%%%%%%%%%%%%$$$$$$###"""""""""###""""""""""""""""""""""""""""""""""""############$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$######%%%'''(((&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######""""""""""""""""""""""""""""""""""""""""""""""""$$$######"""!!! !!!!!!""""""!!!  !!!!!!!!!!!!"""""""""""""""""""""""""""""""""""" !!!""""""""""""""" !!!""""""###""""""""""""""""""""""""""""""""""""""""""""""""   !!!!!! !!!!!! !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!  @@@AAA@@@???>>>???BBBDDD@@@BBBCCCBBBAAA@@@@@@@@@BBBAAA???@@@AAABBBBBBAAADDDCCCBBBAAAAAAAAABBBBBBDDDCCCBBBAAAAAAAAABBBCCCCCCCCCCCCCCCCCCBBBAAAAAAAAAAAABBBBBBBBBAAA???????????????>>>>>>>>>======>>>>>>>>>>>>>>>===<<<<<<;;;;;;;;;;;;:::999888888:::999999;;;<<<<<<;;;999<<<;;;;;;;;;;;;;;;;;;<<<<<<>>>???>>><<<;;;;;;<<<;;;;;;<<<<<<;;;999777666888999999:::::::::::::::;;;;;;;;;:::999999888888999999999999999888777777:::999888888777777777777888888888888777777777777777777666666555444444444333444444444555555555555333333444555555444333333666666666666666555444333333333333333333333444444333333444555555555555444555555555555555444444444333333222222222222333333666666666555555555666666666777888666444333555777888666444555777777666444555555666666555444222111333333444444222,,,$$$&&&***...111222222333444666555555444333333222222111111000000//////000000000//////............///....../////////000000000---...///000111000000///000000000000000000000000//////...---------------......////////////......++++++++++++++++++*********++++++,,,,,,++++++***++++++*********+++---......,,,******+++++++++***,,,---------------,,,,,,---,,,***)))((((((((()))'''(((((())))))))))))))))))((((((''''''&&&%%%%%%(((((((((''''''&&&&&&%%%''''''''''''''''''''''''''''''''''''''''''''''''(((((())))))))))))((((((&&&'''((((((&&&&&&'''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$#########$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$#######################################""""""""""""############$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$######%%%&&&(((&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!!!!!!!"""""""""""""""""""""""""""""""""""" !!!""""""""""""""" !!!!!!""""""###""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!  !!!  !!!!!!""""""!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!  @@@@@@@@@???>>>???AAADDD@@@AAABBBBBB@@@??????@@@AAA@@@??????AAACCCCCCBBBCCCCCCBBBAAAAAAAAABBBBBBDDDCCCBBBAAABBBCCCDDDEEECCCCCCDDDDDDDDDCCCBBBBBB>>>???@@@AAABBBBBBBBBBBB>>>>>>>>>>>>=========<<<>>>>>>>>>>>>>>>===<<<<<<======<<<;;;:::999999888<<<;;;;;;;;;===<<<;;;999;;;;;;;;;;;;;;;;;;;;;;;;;;;===??????===<<<;;;<<<:::;;;<<<<<<<<<;;;999888999999:::;;;;;;;;;;;;;;;;;;;;;;;;:::999999888888888999999999999888777777999888777666666666888888999999888888888777777777555555555555555555555555444444555555555666666666333444444555555444444333777777777666555444333222111111111222333333333444222222333444444444444444666666666555444444333333444333333222222333333444666666555555666666666666555666777777555444555555666555444555666777666555777666555444444444444444333444555555222*** """&&&,,,000222333444555666666666555444444333333000000000000////////////...---,,,++++++---...000............////////////......///000000000000000000000000000000000000000......------,,,,,,------...//////000000//////...+++++++++,,,,,,---------***++++++,,,,,,++++++***,,,+++*********+++,,,------+++))))))***+++***))),,,,,,------------,,,,,,,,,+++***)))))))))))))))'''((((((((()))))))))))))))((((((''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((())))))))))))((((((&&&'''((((((&&&&&&'''(((((((((((((((((((((((((((((('''''''''&&&%%%%%%%%%&&&&&&'''&&&&&&%%%$$$###$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%$$$$$$$$$$$$$$$########################"""""""""#########$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$###$$$%%%&&&'''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!""""""#########!!!!!!!!!!!!!!!  !!!!!!!!!!!!"""""""""""""""""""""""""""""""""""" !!!""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" !!!  !!! !!!"""""""""""""""""" !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!  @@@AAABBBAAA@@@@@@BBBDDD@@@BBBCCCCCCAAA@@@@@@AAA@@@???>>>???AAACCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBCCCBBBBBBAAABBBCCCEEEFFFCCCDDDDDDDDDDDDDDDCCCCCC>>>>>>???@@@AAABBBBBBBBB??????>>>>>>>>>=========>>>>>>>>>>>>>>>===<<<<<<======<<<<<<;;;;;;;;;;;;>>>===<<<<<<===<<<;;;999;;;;;;<<<<<<<<<<<<;;;;;;:::<<>><<<;;;<<<:::;;;<<<======<<<;;;;;;999:::;;;;;;<<<<<<;;;;;;:::::::::999888888777777888888999999999888888777888777666555555777888999999999999888888888777777333444444444555555555666555555555666666666666777444444444444444444444444666666666555444222111000//////000111222333333444111222333333444444333333555555555555555444444444444444333333333333444444555555555666666666666666444555777777777666555444555444444555666777777777888777555444333444555666666555555444111+++######'''---111333444444555777666666666555555555444000000000000//////......---+++))))))))),,,///111---.........////////////...//////000000000000000000000000000000000000000///......---------......//////000000000000//////------------------------***++++++,,,,,,++++++***,,,,,,+++******+++,,,------+++******+++,,,,,,+++++++++,,,---------,,,,,,+++++++++******)))))))))'''''''''(((((()))******)))(((((((((''''''&&&&&&&&&'''''''''((((((((()))''''''''''''''''''''''''))))))))))))))))))))))))(((((())))))))))))((((((&&&((()))((('''&&&'''((()))))))))))))))))))))))))))(((((('''&&&%%%%%%$$$&&&&&&''''''&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$%%%%%%&&&########################""""""#########$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" !!!!!!!!!!!!!!! !!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!"""""""""""""""############"""""""""""""""""""""""""""""""""""" !!!!!! !!!!!! !!!!!!"""""""""!!!!!! !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!  AAABBBCCCCCCBBBBBBCCCEEEBBBCCCEEEDDDBBBAAAAAABBB@@@???>>>???AAACCCCCCCCCAAABBBBBBBBBBBBBBBBBBBBBCCCBBBAAAAAABBBCCCDDDEEECCCCCCDDDDDDDDDDDDDDDCCC@@@@@@@@@@@@@@@@@@@@@AAA@@@@@@?????????>>>>>>>>>>>>>>>>>>>>>>>>===<<<<<<<<<;;;;;;;;;;;;<<<>>>>>>>>>===;;;;;;<<<<<<;;;:::;;;<<<<<<======<<<<<<;;;:::<<<>>>>>>===<<<<<<===:::;;;<<<=========<<<;;;999:::;;;;;;<<<<<<;;;;;;999999999888777777666666777888888999999999888888777777666666666888999:::999999999999888888888888333333444444555666666666555555555666666666666777444444444444444444444444555444444333222111///...//////000111111222333333111222333333444444333333333333333444555666777777555444444444444444444555444444555666777777666666444555666777777777555444444555555666666666777777999777555444333555666888888666444222111...+++((())),,,111444444444555555777666666666666666555555///000000111000///......,,,+++)))((())),,,///111.........////////////000///////////////000000111111111111111111111111111000///////////////000000//////000000000000////////////......---,,,++++++***++++++,,,,,,++++++***,,,+++*********+++,,,---...---++++++---...------***++++++,,,------,,,,,,+++++++++++++++*********''''''''''''((()))++++++((((((((((((((('''''''''&&&&&&''''''((()))))))))((((((((((((((((((((((((************************(((((())))))))))))(((((('''((()))(((''''''((()))))))))))))))))))))))))))))))))((('''&&&&&&%%%%%%&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$%%%&&&&&&####################################$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######""""""""""""""""""""""""""""""""""""""""""""""""######""""""!!!  !!!!!!!!!!!!!!! !!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!"""""""""""""""############""""""""""""######################## !!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!  !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!  @@@BBBCCCCCCBBBBBBCCCDDDCCCDDDEEEEEECCCBBBBBBCCCAAA@@@??????AAACCCCCCBBB@@@AAABBBCCCCCCCCCBBBBBBCCCBBBAAA@@@AAABBBCCCDDDBBBBBBCCCDDDDDDDDDCCCCCCAAAAAA@@@????????????@@@@@@@@@@@@@@@????????????>>>>>>>>>>>>>>>===<<<<<<;;;:::::::::;;;===???@@@>>><<<::::::;;;<<<;;;:::;;;<<<===>>>>>>===<<<;;;;;;<<<======<<<<<<===???:::;;;<<<=========<<<;;;999999:::;;;;;;;;;;;;;;;999999999888777777666666777777888999999999999888666666777888999::::::::::::999999999999888888888444555555555666666777777444444555555555666666666555444444333333444444555444444444333222111000///000000000111222222222333222222333444444444444444111222333444555777888888666555555444444555555666333444555777777777666666555555444555777888666555444555777666555555666777999888666555555666777888888555333222222222222111...000333555444444555666666666666666666666555555000111222222222111///...---,,,+++++++++---000111////////////000000000000///////////////000111111111111111111111111111111000000000///000000111111///000000111111000000///000///...---,,,++++++******++++++,,,,,,++++++***+++******)))***,,,---...///---,,,,,,...//////...)))***+++,,,,,,------,,,***++++++,,,++++++******((('''''''''((()))+++,,,(((((((((((((((((((((((('''''''''(((((()))))))))(((((((((((((((((((((((())))))))))))))))))))))))(((((())))))))))))(((((('''((())))))''''''((()))(((((((((((((((((((((((()))((((((((('''&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######""""""""""""""""""""""""""""""""""""""""""""""""###""""""!!! !!!!!!!!!!!!!!!!!! !!!!!!!!!!!!"""""""""""""""""""""""""""""""""""" !!!"""""""""""""""""""""""""""""""""""""""######################## """!!!!!! !!!!!!"""!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!  >>>@@@BBBBBBAAA@@@AAABBBBBBDDDEEEDDDCCCAAABBBBBBBBBAAA???@@@AAABBBBBBAAA@@@AAABBBCCCCCCCCCBBBBBBCCCBBBAAA@@@???@@@AAAAAAAAAAAABBBCCCCCCCCCCCCCCC@@@@@@???>>>>>>???@@@AAA????????????>>>>>>>>>>>>>>>>>>>>>>>>>>>===<<<<<<<<<;;;:::999:::;;;===>>><<<:::888999:::<<<<<<;;;;;;<<<===>>>>>>===<<<;;;<<<======;;;:::;;;>>>@@@:::;;;<<<===<<<<<<:::999888999999:::::::::::::::;;;;;;::::::999888888888777777888999999999999999555666888;;;<<<<<<;;;;;;::::::999999999888888888666666777777777777777777333444444444555555555555555444333333333333444555444444444444444333222222111222222222222222222222333333444555555555555444222333333444555666777777666666555555555555666666222333555777888777666666777555333444666888777666555666888777444333555777888777777666666777888888666444333333444555444333000222333444444444777999555555555555555555555555111111333333333222000///...............///000111000000000000111111111222000//////...///000111222111111111111111111111111///////////////000111111000000111111111111000000...---------,,,,,,++++++***++++++,,,,,,++++++***))))))))))))***,,,...000...,,,++++++---.........))))))***,,,,,,------,,,******+++,,,,,,,,,+++***((('''&&&&&&'''))),,,---((((((((((((((((((((()))((((((((((((((()))))))))(((((((((((((((((((((((())))))))))))))))))))))))(((((())))))))))))((((((''')))***)))((('''((()))''''''''''''''''''''''''((((((((((((''''''''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&'''###############$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%&&&&&&&&&%%%&&&&&&&&&&&&'''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''%%%%%%%%%$$$$$$$$$######""""""""""""""""""""""""""""""""""""""""""""""""  !!!!!!!!!!!!!!! !!!!!!!!!!!!"""""""""""""""""""""""""""""""""""" !!!""""""""""""""" !!!!!!""""""###########################!!!!!!!!!!!!!!!!!!!!!!!!""""""!!!!!!!!!!!!""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!  ===>>>@@@@@@?????????@@@AAACCCDDDCCCBBB@@@AAAAAACCCAAA@@@@@@AAABBBAAA@@@???@@@BBBCCCDDDCCCBBBBBBCCCBBB@@@???>>>??????@@@@@@AAAAAABBBCCCCCCCCCBBB??????>>>>>>>>>@@@AAABBB>>>>>>>>>>>>============>>>>>>>>>>>>>>>======<<<===<<<:::999999:::;;;<<<;;;999777888:::;;;<<<<<<;;;<<<===??????===<<<;;;======<<<:::999;;;???BBB:::;;;<<<<<<<<<;;;999888888888999::::::::::::999===<<<<<<;;;;;;::::::999666777888999999999999999444666999<<<>>>===<<<;;;:::::::::999999999888888888888888888777777777777333333333444444444555555555444333333333333444555555555555666555555444444333333333222222222222222333444555555666666555555444444555555555555555555666666555555555555666666222333555777888888777666888555222333666888888777555777999777444333444666888777777777777777888888333333444555666666333111000111222222333555888;;;444444444555555555555555111222444444444333111////////////000000000000000000111111111222222222222000///.........///111222111111111111111111111111...............///000000000000111111111111000000+++++++++,,,,,,,,,------+++++++++,,,,,,+++++++++((((((((()))+++---///111,,,+++******,,,......---((()))***+++,,,---------)))***,,,,,,---,,,+++***((('''&&&&&&'''))),,,---(((((((((((())))))))))))))))))))))))(((((((((((())))))))))))))))))))))))(((((((((((((((((((((((((((((())))))))))))((((((''')))***)))((('''(((***'''''''''''''''''''''''''''''''''(((((((((((((((&&&&&&'''''''''''''''&&&%%%%%%%%%&&&&&&&&&''''''###"""""""""###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&###$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%$$$$$$$$$######"""""""""""""""""""""""""""""""""""""""""""""""" !!!""""""!!!!!! !!!!!!!!!!!!"""""""""""""""""""""""""""""""""""" !!!!!!""""""""""""""" !!!""""""###########################""""""""""""""""""""""""""""""!!!!!!!!!!!!""""""""""""""""""""""""""""""""""""###""""""!!!  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!  >>>>>>?????????@@@@@@@@@EEEFFFEEECCC@@@>>>???@@@AAA@@@@@@AAABBBBBBAAA???AAA@@@???@@@AAAAAA@@@??????@@@@@@AAA@@@???===<<<@@@AAACCCDDDCCCAAA???===CCC@@@>>>???AAABBB@@@===>>>???@@@AAAAAA@@@???>>>;;;;;;<<<<<<<<<<<<<<<<<<::::::<<<<<<<<<<<<::::::;;;;;;;;;<<<<<<<<<=====================<<<<<<<<<;;;<<<===============<<<>>>>>>?????????===<<<;;;???>>><<<:::999888777777===<<<;;;:::999888888888777888999:::;;;::::::999999999:::;;;;;;;;;;;;:::;;;:::999888777888999:::888888888888888777666666444555555555666666777777666555444333333333333333222222222333333444444444444333222222111111222222111111222333333333333222777777666666555555555444555555555666666666666777666777888888888666555444555555666666777888888888777666555444444555777888:::999999888777666666555444444444444444444444444555555555555555666777888555666666666555555444333444444333333222111000000...............---------111///------...//////...000000000000000000000000111111111000000000000000222111///.........///000000000000000000000000000......---------,,,,,,,,,+++++++++******))))))))))))))))))***+++,,,---......,,,)))(((***+++,,,,,,+++,,,,,,------,,,,,,+++,,,,,,,,,+++***)))((('''))))))************)))))))))************+++++++++((((((((((((((((((((((((''''''''''''(((***++++++,,,,,,++++++***)))))))))))))))))))))((((((((((((''')))***)))((('''(((***''''''''''''''''''''''''''''''''''''(((((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''''''''(((((('''&&&%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$"""""""""###$$$%%%""""""############"""""" !!!"""######"""""""""""""""""""""""""""!!!!!! !!!!!!""""""""""""""""""""""""""""""""""""""""""""""""$$$$$$###"""!!!!!!""""""############""""""""""""""""""""""""""""""""""""######""""""!!!!!! !!!!!!""""""""""""!!!!!! !!!!!!!!!!!! !!!!!!""""""""""""!!!!!!  !!!!!!!!!!!! !!!!!!  ?????????@@@@@@@@@AAAAAACCCDDDDDDBBB@@@@@@AAABBBBBBAAA@@@AAACCCCCCAAA@@@@@@@@@??????@@@@@@@@@??????@@@AAAAAAAAA@@@???>>>>>>@@@AAABBBBBB@@@>>><<>>>>>>>>???@@@@@@???>>>>>>=========<<<<<<;;;;;;;;;::::::;;;;;;;;;;;;::::::;;;;;;;;;<<<<<<<<<======<<<<<<==================<<<===============<<<<<<======>>>???>>>===<<<;;;===<<<<<<;;;;;;:::;;;;;;===<<<;;;::::::999999999777888999:::;;;::::::999888999999:::::::::::::::;;;:::999999888888999999999999999999999888777777555555555666666666777777666555444444333333333444333333333333333333444444333333222222111111222222222222333444444444444333777666666666555555555444444444555555555666666666666777888888777666555444777777666666666666666666:::888666444333444444555999999888777777666555555555444333222222333444555666555555555555555666777666555555555444444444444555555444444333222222111............////////////111///......000000000///111111111111111111000000111000000000000000000000222111000///...//////000..............................---------,,,,,,,,,,,,,,,+++++++++*********************+++---...//////,,,***)))***,,,,,,,,,+++,,,,,,------,,,,,,+++++++++++++++++++++******))))))************)))))))))************+++++++++))))))))))))))))))))))))((((((((((((((()))***++++++++++++************************)))))))))((((((''')))***)))((('''(((***''''''''''''''''''''''''''''''''''''(((((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''''''''(((((('''&&&&&&%%%''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$###""""""###$$$%%%""""""############"""""" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!""""""""""""""""""""""""""""""""""""""""""""""""%%%%%%$$$###########################""""""""""""""""""""""""""""""""""""###"""""""""!!!!!!!!! !!!!!!""""""""""""!!!!!! !!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!! !!!!!!  @@@@@@@@@AAAAAAAAABBBBBBAAABBBCCCBBBAAAAAABBBDDDBBBAAAAAABBBCCCCCCBBB@@@@@@@@@@@@@@@@@@@@@@@@@@@???@@@AAABBBBBBBBBAAA@@@???AAABBBCCCCCCAAA???>>>BBBAAA???@@@AAAAAA@@@>>>===>>>>>>??????>>>>>>===???>>>>>>===<<<;;;::::::;;;::::::999999::::::;;;;;;;;;<<<<<<<<<=========<<<<<<<<<======>>>>>>>>>>>>>>>>>>>>>===<<<<<<;;;<<<===>>>>>>>>>===;;;;;;;;;;;;;;;<<<======>>>>>>>>>===<<<;;;;;;;;;;;;;;;888999999::::::::::::999777888888999:::999999999999::::::::::::999888888999::::::::::::999888888555555666666666666777777555555555444444444444444444444444444333333333333333333333222222222111111333333444555555555555444666666666555555555555555333444444444555555555555666777777777777666666555888777777666555555444444888777666444444444555666888777777666666555555555666444222111111222444666666666555555444555555555666555444333333333444555666666555555444444333333...//////000000111111111222000///000111222111000333333222222111111111000000000000000000000111111222111000////////////000..............................---------,,,,,,,,,,,,,,,,,,,,,++++++++++++******++++++,,,...///000///---******,,,---------+++,,,,,,------,,,,,,+++******+++,,,,,,,,,,,,,,,))))))************)))))))))************+++++++++************************))))))((((((((())))))***)))************++++++++++++++++++*********))))))''')))***)))((('''(((***''''''''''''''''''''''''''''''''''''(((((((((((('''''''''''''''&&&&&&&&&%%%&&&&&&'''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$((((((''''''&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''(((''''''&&&%%%''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$######"""######$$$""""""############"""""" !!! !!!!!! !!!!!!""""""""""""""""""""""""""""""""""""""""""""""""&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$#########"""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!""""""""""""!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!! !!!!!!!!!!!!  AAAAAAAAABBBBBBBBBCCCCCCBBBBBBCCCBBBAAA@@@BBBDDDCCCBBBAAABBBCCCDDDBBB@@@@@@AAABBBBBBAAAAAABBBCCC???@@@BBBCCCCCCCCCBBBBBBBBBCCCDDDEEEEEEDDDCCCBBBAAAAAA@@@@@@@@@@@@??????======>>>>>>>>>>>>======>>>>>>======<<<<<<;;;;;;;;;:::999888888999:::;;;<<<<<<<<<<<<============;;;;;;<<<===>>>??????@@@?????????>>>>>><<<;;;:::;;;<<<===>>>>>>===<<<;;;:::;;;;;;<<<============>>>>>>===<<<<<<<<<<<<<<<999:::::::::::::::::::::777777888999999999999888888999:::;;;:::999888777888999999:::999999888888666666666666666666777777444555555555555555444444555555444444333333333222333333333333222222111111222333333444444444444444555555555555555555555555333333333444444444555555666777777777777666666666666666666666555555444444333333333444555777999:::777666666666555555555444777555222000000222555777777777666555444444444444777555444222222333555666555555555555444444333333//////000111111222333333222111000111333444222111444444333333222111111111000000000000000111111111111111111000000000000000..............................---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,---...///000...---++++++---......---+++,,,,,,------,,,,,,++++++,,,,,,------,,,,,,,,,))))))************))))))))))))*********+++++++++******************************))))))((()))))))))((())))))***++++++,,,,,,,,,,,,,,,+++++++++******''')))***)))((('''(((***''''''''''''''''''''''''''''''''''''((((((((((((''''''''''''''''''''''''%%%&&&&&&'''''''''''''''%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''''''''&&&%%%%%%$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''&&&'''''''''''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$##################""""""############"""""" !!!!!!"""""""""### !!! !!!!!!"""""""""""""""""""""""""""""""""""""""""""""""""""%%%$$$$$$#########$$$$$$$$$$$$$$$#########""""""!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!""""""""""""!!!!!! !!!!!!!!!!!!""""""!!!!!!  !!!!!!"""""" !!!!!!!!!!!!  AAAAAABBBBBBBBBCCCCCCCCCCCCDDDDDDBBB@@@???@@@BBBBBBAAAAAABBBCCCCCCBBB@@@@@@BBBDDDCCCBBBBBBCCCEEE???@@@BBBCCCDDDCCCCCCBBBCCCCCCDDDEEEEEEEEEDDDCCCAAAAAAAAAAAA@@@??????@@@>>>>>>============>>>>>>;;;<<<<<<======>>>>>>>>><<<;;;999999999999;;;<<<<<<<<<<<<=========>>>>>>;;;<<<<<<===>>>???@@@@@@????????????>>>===<<<;;;;;;<<<===>>>>>>===<<<<<<;;;;;;<<<<<<<<<;;;::::::>>>>>>===<<<<<<<<<======;;;:::::::::::::::::::::777777888999999999999888888999:::;;;:::999888777777777888888888888888777777777777777777777666666444444555666666555555444555555555444444333333333222222333333333222111000111111222333333333333333444444444555555555555555333333333444444444555555777666666666666777777777555555555555666666777777333333444555666777888999666666666666555555555555888666333111111333666888888777666555555555555555777666444333333444666777444444444444333333333333///000000111222333444444222111111333444555333222333333333222222222111111//////000000111111111111111111111111111000000///////////////////////////......---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,---...///000---,,,+++,,,---///...---+++,,,,,,------,,,,,,+++------------,,,+++***)))))))))************))))))))))))*********+++++++++))))))))))))))))))))))))+++******))))))))))))***(((((()))***+++,,,,,,---,,,,,,,,,,,,++++++++++++''')))***)))((('''(((***((((((((((((((((((((((((''''''''''''((((((((((((&&&'''''''''''''''''''''%%%&&&''''''((((((((('''%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&'''''''''''''''&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""""""""############""""""!!!!!!!!!""""""""""""""" !!!""""""""""""""""""""""""""""""""""""""""""""""""""""""######""""""""""""###$$$$$$$$$$$$$$$############!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!!!!!""""""""""""!!!!!! !!!!!!!!!!!!""""""!!!!!!  !!!!!!"""""" !!!!!!!!!!!!   AAAAAAAAABBBBBBBBBCCCCCCDDDDDDDDDBBB@@@???@@@AAAAAA@@@@@@AAABBBBBBAAA??????BBBEEEDDDBBBAAADDDGGG@@@AAABBBCCCCCCCCCBBBAAAAAAAAABBBBBBBBBBBBBBBBBB@@@AAABBBAAA???>>>???@@@???>>>>>>======>>>>>>???;;;;;;<<<===>>>??????@@@<<<;;;;;;::::::;;;;;;<<<<<<<<<=========>>>>>>>>>=========>>>>>>?????????????????????>>>======<<<<<<<<<>>>?????????>>>===<<<=========<<<;;;999888======<<<<<<<<<<<<======<<<;;;;;;::::::::::::;;;777888888999:::999999999999::::::::::::999888888666666777888888888888777888888777777777777666666333444555777777666555555555555555444444444444444222222333444333222111000000111222222333333222222444444444444444555555555333444444444555555555555777666666666666777777888555555666666777888888999777777666666666555555444666666666666666666666666888666444333333444666888888888777777666666777777777666555555555666777888444333333333333333333333000111111111222333333333111111111333555555444222222222222222222222222222/////////000111111222222111111222222111111000///000000000000000000000000......---------,,,,,,,,,++++++++++++,,,,,,,,,,,,******++++++,,,...///000,,,+++***,,,...///...---+++,,,,,,------,,,,,,+++......------,,,***)))((())))))************)))))))))************+++++++++))))))))))))))))))))))))******)))))))))******+++(((((()))***++++++,,,,,,,,,,,,,,,+++++++++******''')))***)))((('''(((***((((((((((((((((((((((((''''''''''''((((((((((((&&&&&&&&&'''''''''''''''%%%&&&'''(((((((((((((((%%%&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%&&&''''''((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!""""""############""""""  !!!"""###"""""""""""""""""""""""""""""""""""""""""""""""""""""""""!!!""""""###$$$%%%$$$$$$$$$$$$#########""""""""""""""""""""""""!!!!!!!!!!!!""""""""""""!!!!!!""""""""""""!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!! !!!!!!!!!!!!   @@@AAAAAAAAABBBBBBBBBBBBBBBCCCCCCBBB@@@@@@BBBCCC@@@??????@@@AAAAAA@@@>>>===AAADDDCCC@@@@@@CCCFFFAAAAAABBBCCCCCCBBB@@@???@@@@@@AAAAAABBBBBBBBBBBB???AAABBBAAA???>>>???AAA@@@???>>>>>>>>>>>>???@@@<<<<<<======>>>>>>??????;;;<<<<<<======<<<<<<;;;<<<=========>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>???>>>>>>?????????>>>>>>===<<<===???@@@@@@@@@???>>><<<===>>>>>>>>><<<:::999===<<<<<<;;;;;;<<<<<<======<<<;;;:::999::::::;;;888999999:::::::::::::::;;;:::999999888888999999666777888888999999999888888888888777777777666666333444666777777777666555444444444444555555555555111222333444444222111///111222333333444444333333333333333444444555555555444444555555555666666666777666555555666777888999777777777888888888888888777777777777666555333333777777777777777777777777888777666555555666777888888888888888888888999:::666777777777888888888999444444444444444444555555111111111111222222222222000000111333555555333111///000000111111222222222...//////000111111222222111111222222222111000///////////////////////////......---------,,,,,,,,,*********+++++++++,,,,,,************+++---...///*********+++---...---,,,+++,,,,,,------,,,,,,++++++,,,,,,,,,+++***))))))))))))************)))))))))************+++++++++************************))))))))))))***+++,,,,,,)))))))))***+++++++++,,,++++++++++++************''')))***)))((('''(((***((((((((((((((((((((((((''''''''''''((((((((((((&&&&&&&&&'''''''''((((((%%%&&&'''((())))))))))))&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$$$$%%%%%%&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%&&&&&&'''((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""#########$$$$$$$$$$$$$$$$$$%%%%%%$$$###!!! """"""############""""""!!!  !!! !!!!!!!!!!!!!!!!!!!!!!!! !!!"""###""""""""""""""""""""""""""""""""""""""""""""""""###"""""""""######$$$%%%%%%%%%$$$$$$$$$#########"""""""""""""""""""""""" !!!!!!!!!"""""""""###!!!!!!""""""""""""!!!!!! !!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!  !!!!!! @@@@@@@@@AAAAAAAAABBBBBB@@@AAABBBBBBAAABBBDDDFFF@@@???>>>???AAAAAA???===;;;???BBBBBB???>>>AAAEEEAAABBBBBBBBBBBBAAA???>>>BBBBBBBBBBBBCCCCCCDDDDDD???AAACCCBBB???===???AAAAAA@@@???>>>>>>???@@@AAA>>>>>>>>>>>>============;;;<<<===>>>>>>===<<<;;;============>>>>>>>>>>>>?????????>>>>>>>>>>>>>>>===>>>>>>????????????>>>===>>>???@@@AAAAAA@@@???<<<===???@@@???>>><<<;;;<<<<<<;;;;;;;;;<<<<<<======<<<;;;:::999::::::;;;999999:::;;;;;;;;;;;;:::<<<;;;999888777888999:::777888999:::::::::::::::999888888888777777666666222444666777888777666555333444444444555666666666111222333444444222111///222333444444555555444444333333333444444555555555555555555666666666666777777666555555555777888999::::::999999888777777777555555666666666666666555777777777777888888888888888888777777777777888888999888888888999:::;;;;;;666777888999999999999999555555555666666666666666222222111111111111111111//////000333555555333111......///000111222222333...//////000111222222222111111222333222111000///..............................---------,,,,,,,,,)))))))))******+++++++++)))))))))***+++,,,......)))))))))+++---...---++++++,,,,,,------,,,,,,+++))))))***++++++++++++***))))))************)))))))))************+++++++++++++++++++++++++++++++++))))))))))))***+++,,,---***************++++++++++++++++++*********))))))((()))***)))((('''(((***))))))))))))))))))))))))''''''''''''((((((((()))&&&&&&&&&'''''''''((((((%%%&&&'''((())))))))))))&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&''''''(((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%&&&'''((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$$$$$$$$$$$$$$$$%%%%%%$$$###!!! """"""############""""""###"""!!!  !!!!!!############"""""""""""""""""""""""""""""""""""" """######""""""""""""""""""""""""""""""""""""""""""""""""$$$#########$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$######"""""""""""""""""""""""" !!!!!!!!!""""""######!!!!!!""""""""""""!!!!!! !!!!!!!!!""" !!!!!!""""""""""""!!!!!!  !!!!!!!!!!!!  !!!!!! CCCDDDDDDDDDCCCAAA>>>===BBBAAA@@@??????AAACCCDDDEEEDDDBBB@@@@@@@@@BBBCCC@@@AAAAAABBBBBBAAAAAA@@@CCCCCCCCCCCCCCCBBBBBBBBBAAA@@@???BBBEEEGGGEEECCCDDDCCCCCCBBBBBBAAA@@@@@@>>>AAABBBAAA???>>>@@@BBBAAAAAABBB@@@???>>>???AAA@@@@@@@@@??????===<<<<<<>>>>>>===<<<<<<===>>>??????>>><<<;;;<<<===???@@@??????@@@@@@@@@AAAAAAAAA@@@@@@@@@@@@??????>>>===BBBAAA@@@???>>><<<;;;;;;;;;;;;;;;<<<<<<<<<<<<=========<<<<<<<<<;;;;;;;;;::::::999888999:::;;;<<<>>>===<<<;;;;;;;;;;;;;;;>>>;;;999888888999888777999999999888777666666555888777666444444555555666222222333444555555555444444555555444222111111222///000222444555555555444666555555444444444444555666666555555555555666666888777666666666666666777999888777666777888;;;<<<777777666666555555555444777888999::::::999777666888888888777777777777666777777777888999:::;;;<<<:::999777555555666777888666666555444444444555555333333222111000000000111000111333222222111333444111111111222222333333333111222333333111111222333111111111111111000///...111000///...------......------------,,,+++***)))******)))))))))***,,,---,,,---,,,++++++,,,///222...---,,,,,,------+++)))---......---+++******+++...---,,,,,,++++++,,,,,,)))***,,,------,,,***)))******+++++++++,,,,,,,,,***))))))***,,,,,,+++*********+++++++++,,,,,,,,,++++++***)))(((((())))))******))))))))))))******)))))))))))))))******+++))))))))))))))))))))))))'''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&''''''(((((()))))))))((('''&&&&&&'''((()))&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$%%%&&&'''(((&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''(((''''''''''''(((((((((((())))))((('''''''''''''''&&&&&&''''''''''''&&&&&&((('''&&&%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$###"""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!######$$$$$$$$$$$$######"""!!!  !!!"""!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""""""""""""""######""""""###$$$%%%%%%$$$#########""""""!!!!!!%%%$$$###"""""""""$$$$$$$$$$$$############$$$$$$$$$$$$$$$#########""""""!!!"""###$$$$$$###"""!!!""""""""""""############!!!!!!!!!!!!!!!"""######""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""!!!!!!""" !!!!!!!!!!!! !!!!!!!!!!!! @@@AAACCCDDDDDDCCCAAA@@@CCCBBBAAA@@@@@@BBBCCCEEEDDDCCCAAA@@@@@@@@@AAABBB@@@@@@AAAAAAAAAAAA@@@@@@CCCCCCCCCCCCCCCCCCCCCCCCCCCAAA@@@AAADDDEEEDDDCCCEEEEEEDDDCCCAAA@@@??????AAABBBCCCBBBAAAAAAAAACCC@@@AAAAAA@@@???>>>@@@AAA@@@@@@@@@??????>>>===<<<======<<<<<<<<<>>>???@@@???>>><<<<<<<<<===???@@@??????????????????@@@@@@AAAAAAAAAAAA@@@???>>>===AAAAAA@@@???>>>===<<<<<<>>>>>>>>>======<<<<<<<<<===<<<<<<<<<;;;;;;;;;;;;::::::999999999:::;;;<<<======<<<;;;;;;;;;;;;;;;<<<999777777777888888777888888888777666555555555888777666555444555555666333444444555555555555444444555555444222111111222000111222444555666555555666555555555555555666666666666555555555555666666666666555555555666666777888777555555555666888999666555555555444444444444555666888999999888777666888888777777777666666666999888888888999:::;;;;;;>>><<<:::888666666666777666666555444333333333444222222111111000111111111000222333333222222333555111222222222222222222333111222333333111111222333111111222222111111000///000000000/////////......------------,,,+++******+++***)))))))))***,,,---***++++++***)))***---000---,,,,,,,,,------+++))),,,---...---+++***+++,,,...---,,,,,,++++++,,,,,,***+++,,,,,,,,,,,,+++***************++++++,,,,,,))))))(((***+++,,,***)))******+++++++++,,,,,,,,,,,,+++******)))))))))************))))))*********)))))))))))))))******+++************************'''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((()))((('''&&&&&&'''((()))&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&'''(((&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''(((''''''''''''(((((((((((())))))(((''''''''''''''''''''''''(((((('''''''''((('''&&&&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$###"""!!!""""""""""""""""""""""""######$$$$$$$$$$$$############"""!!!!!!"""######!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""""""""""""""""""""!!!!!!""""""###$$$############"""""""""!!!$$$$$$###############$$$$$$$$$############$$$$$$$$$$$$$$$#########""""""!!!"""###$$$$$$###"""!!!""""""""""""############!!!!!!!!!!!!!!!"""######""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""!!!!!!""" !!!!!!!!!!!! !!!!!!!!!!!! >>>???AAACCCDDDDDDCCCCCCCCCBBBAAAAAAAAABBBDDDEEECCCBBBAAA@@@???@@@AAABBB@@@@@@AAAAAAAAAAAA@@@@@@DDDDDDDDDDDDDDDDDDDDDDDDEEECCCAAAAAABBBDDDDDDCCCFFFEEEDDDCCCAAA@@@>>>>>>DDDCCCBBBCCCDDDDDDDDDBBB???@@@AAA@@@??????@@@BBB??????@@@??????>>>===<<<<<<;;;<<<<<<===>>>???@@@>>>>>>===<<<===>>>???@@@???????????????>>>>>>>>>CCCCCCCCCBBBAAA???>>>===@@@@@@?????????>>>>>>>>>AAA@@@@@@???===<<<<<<;;;<<<<<<<<<<<<;;;;;;;;;;;;::::::999999999:::;;;<<<===<<<;;;;;;;;;;;;;;;;;;999888666666777888888777777777777666666555555444777777666555555555555666555555666666666555444444444555555444222111222333111222333555666666666666555555555555666777888888777666666555555666666777555555555555555666777888777666555333333444555555444444444444444333333333444555777888999999888777888777777777777666666666::::::999999999::::::;;;AAA???<<<:::777666666555666666444333222222222222111111111000111111222222111333444444222222333555222222222222222111111111111222333222111111222333222222222222222222111000///000111111111000///...------...------,,,+++***+++************+++,,,,,,((()))))))))((()))+++...---,,,+++,,,------+++******,,,------++++++,,,......---,,,,,,++++++,,,,,,++++++++++++++++++++++++)))))))))************+++((((((((()))***+++***(((******+++++++++,,,,,,,,,,,,,,,++++++******++++++++++++************++++++)))))))))))))))******+++************************''''''''''''''''''''''''&&&&&&&&&''''''(((((()))((((((((((((((('''''''''((((((''''''''''''((()))&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''(((&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''(((''''''''''''(((((((((((()))((((((''''''''''''((('''(((((())))))(((((('''((('''&&&&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$###"""!!!##############################$$$$$$$$$$$$######%%%%%%$$$######$$$%%%%%%""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!"""###############"""""""""""""""######$$$$$$$$$######$$$$$$############$$$$$$$$$$$$$$$###############""""""############""""""""""""""""""############!!!!!!!!!!!!!!!""""""###!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!"""!!!  !!!""" !!!!!!!!!!!! !!!!!!!!!!!! >>>???AAABBBCCCDDDDDDCCCBBBAAAAAAAAAAAABBBCCCDDDBBBAAA@@@@@@@@@@@@AAAAAAAAAAAABBBBBBBBBBBBAAAAAADDDDDDDDDDDDEEEEEEEEEEEEFFFEEEBBBAAAAAABBBCCCCCCDDDDDDCCCBBBAAA@@@@@@???FFFCCCAAABBBEEEFFFDDDAAA???@@@AAA@@@??????AAACCC???????????????>>>======::::::;;;<<<===>>>@@@@@@>>>>>>=========>>>???@@@@@@@@@@@@???????????????DDDDDDDDDCCCBBB@@@???>>>????????????????????????@@@@@@???>>>>>>===<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;999999999:::::::::;;;;;;<<<<<<;;;::::::;;;;;;;;;888777666777888999888777888888777777666666666555777666666666555555555555666777777777666555444444444555666555333222333444333333444555666666666777555555555666666888999999777777666666666666777777555555555666777888999:::777666555444333333333333444444444444444444444444555666777888999:::999999999888888888888777777777;;;::::::999999999999:::???>>><<<999777666555555666555444333222111111111111000000000111222333333222333444444333222333555333333222222111111000000000222333222111000111222222222333333333222222111///000222333333111///...------......---,,,++++++++++++++++++++++++++++++((()))))))))((()))+++------,,,+++,,,------,,,***)))+++,,,,,,,,,,,,---///...---,,,,,,++++++,,,,,,,,,++++++******++++++,,,)))))))))))))))))))))***(((''''''(((******)))(((******+++++++++,,,,,,,,,---,,,,,,++++++,,,,,,,,,,,,++++++++++++++++++,,,)))))))))))))))******+++++++++++++++++++++++++++''''''''''''''''''''''''%%%&&&&&&'''((())))))***))))))((((((''''''&&&&&&'''''''''''''''(((((()))&&&&&&%%%%%%%%%%%%&&&&&&###$$$$$$%%%&&&'''((((((&&&&&&&&&&&&&&&''''''(((&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''(((''''''''''''(((((((((((()))(((''''''''''''(((((((((((())))))))))))(((((('''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######%%%%%%%%%$$$$$$%%%%%%%%%########################""""""""""""""""""""""""""""""!!!!!!!!!""""""############"""""""""""""""!!!"""$$$%%%%%%$$$###"""$$$$$$############$$$$$$########################"""""""""######"""""""""!!!"""""""""############""""""!!!!!!!!!!!!""""""!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!! !!!!!!!!!!!! !!!!!!!!!!!! AAAAAABBBBBBBBBBBBBBBBBB@@@@@@@@@@@@@@@AAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBCCCCCCCCCCCCBBBBBBCCCDDDDDDDDDEEEEEEFFFFFFFFFEEECCCAAA@@@AAABBBDDDAAAAAAAAABBBBBBBBBBBBCCCDDDBBB@@@AAADDDEEECCC@@@???@@@AAA@@@??????@@@BBB>>>????????????>>>>>>===999:::;;;<<<===>>>??????>>>>>>>>>>>>>>>??????@@@AAAAAAAAAAAAAAAAAAAAAAAADDDDDDDDDCCCBBBAAA??????????????????@@@@@@@@@@@@========================::::::;;;;;;;;;;;;;;;;;;999999:::::::::;;;;;;;;;;;;;;;:::::::::;;;;;;<<<999888777888::::::999888999999888888888888888777666666666666666555555444666777777777666555444444444555666555333222333444444444444444555666666777555555555666666888999999777777666666666666777777666666777777888999:::;;;888777666555444333333333555555555555555555666666666777888999:::::::::;;;::::::999999999888888888::::::999888888888999999::::::999888777666555555666555444333222111111222111000000000111222333333222333444444222222222444222222222111111000000000000111222222000000111222111222222333333333222222...///111333333111000///------.........---,,,,,,++++++,,,,,,,,,+++++++++(((***++++++******,,,...,,,++++++,,,---...,,,+++(((***,,,,,,,,,,,,...///...---,,,,,,++++++,,,,,,,,,++++++******++++++,,,***)))))))))))))))))))))(((''''''(((******)))(((******+++++++++,,,,,,,,,---,,,,,,,,,,,,,,,------,,,++++++++++++++++++,,,)))))))))))))))******+++************************((((((((((((((((((((((((&&&&&&''''''((()))******))))))((((((''''''&&&&&&&&&''''''((((((((((((((('''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%&&&&&&'''((((((&&&&&&'''''''''(((((('''&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''(((''''''''''''((((((((((((((((((''''''''''''(((((((((((())))))))))))((((((&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$######""""""#########""""""""""""""""""######!!!"""###%%%%%%$$$$$$###$$$$$$############$$$$$$###########################""""""""""""""""""###!!!"""""""""############""""""!!!!!!!!!!!!"""""" !!!!!!!!!"""""""""###""""""""""""""""""""""""!!!!!!!!! !!!!!!!!! !!!!!!!!!!!! !!!!!!!!!!!! CCCCCCCCCBBBBBBAAAAAAAAA>>>?????????@@@@@@@@@@@@AAAAAABBBBBBBBBBBBBBBCCCBBBBBBCCCCCCCCCCCCBBBBBBBBBCCCCCCDDDDDDEEEEEEFFFDDDEEEDDDBBBAAA@@@BBBDDD???@@@AAAAAABBBCCCDDDDDDBBBAAA@@@AAABBBBBBAAA@@@AAAAAABBB@@@???>>>???AAA>>>>>>????????????>>>>>>999:::;;;<<<===>>>>>>>>>>>>>>>>>>?????????@@@@@@AAAAAAAAAAAABBBBBBCCCCCCCCCCCCCCCCCCBBBAAA@@@@@@??????@@@@@@@@@@@@@@@@@@<<<<<<<<<======>>>>>>>>>::::::::::::;;;;;;;;;;;;888999:::;;;;;;;;;:::::::::::::::::::::;;;;;;<<<:::999999999;;;;;;999777999999999999999999999999666666666777666555555444555555666666666555444444444555666555444333444555444444333333444555666666555555555555666777888888888777777666666777777888777777777777888888999:::888888777666555555444444555555555666666666666666777777777888888999::::::::::::999999999888888888888888777777777888888999666666666666666555555555555444444333333333333333111111111000111111222222222333444333111000111222111111111111111000000000000111222111000000111222000111222222222222222222...///000111111111000///------............------,,,,,,,,,---,,,,,,+++***)))***,,,,,,,,,,,,---...,,,++++++,,,---...---+++)))***,,,,,,,,,,,,...///...---,,,,,,++++++,,,,,,+++++++++++++++++++++++++++************)))))))))((((((((()))***+++***(((******+++++++++,,,,,,,,,,,,,,,++++++,,,,,,------++++++************++++++)))))))))))))))******+++))))))))))))))))))))))))(((((((((((((((((((((((('''''''''(((((())))))***((((((((((((((('''''''''%%%&&&'''((()))))))))(((''''''&&&&&&&&&&&&''''''%%%%%%&&&&&&''''''((((((&&&&&&'''(((((((((((('''&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''(((''''''''''''(((((((((((((((''''''''''''(((((()))'''(((((())))))(((((('''&&&&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######"""######$$$$$$######"""################################################%%%$$$$$$###############""""""""""""############!!!"""###$$$$$$$$$$$$$$$$$$$$$############$$$$$$###############$$$$$$$$$######""""""""""""######""""""""""""###############""""""!!!!!!!!!!!!!!! !!!!!!""""""######""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!! !!!!!!!!!!!! CCCCCCBBBBBBAAAAAAAAAAAA??????@@@@@@AAAAAAAAA@@@AAABBBCCCCCCDDDDDDDDDDDD@@@AAAAAAAAAAAAAAAAAA@@@AAABBBBBBCCCDDDDDDEEEEEEBBBDDDEEEDDDBBBAAABBBDDD@@@AAAAAABBBBBBCCCCCCCCC@@@AAABBBBBBAAA@@@AAABBBBBBCCCBBBAAA>>>===>>>???>>>>>>????????????>>>>>>::::::<<<=========<<<<<<>>>>>>??????@@@@@@@@@?????????@@@AAABBBBBBCCCDDDAAAAAABBBBBBBBBBBBAAAAAA@@@@@@@@@@@@@@@@@@@@@@@@???>>>>>>>>>>>>>>>>>>>>>999999:::::::::;;;;;;;;;888999:::;;;;;;;;;::::::::::::999999::::::;;;<<<:::999999999:::999777555888888888888888888888888555666777777777666444444333444444555555555555444333555666555444333555666444333333222222333555555666555555555555555666666888888777777777777888888777666666666666666777777666666666666666555444444444444444555555666666666777666666666666666777777888888888777777777666666666555555555666777888888555666666666666555555444444444444333444444555666222222111111000111111111111222333222000///000111000000000000111111111111///111222111000///000222///000111111222222111111....../////////000000000------............------,,,,,,---------,,,+++***(((***,,,---,,,,,,---...++++++***,,,......---+++***+++,,,,,,,,,,,,---......---,,,,,,++++++,,,,,,***+++,,,,,,,,,,,,+++***,,,,,,++++++************))))))(((***+++,,,***)))******+++++++++,,,,,,,,,+++++++++++++++,,,------*********))))))*********)))))))))))))))******+++((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((()))))))))'''''''''(((((((((((((((%%%&&&'''((()))))))))(((''''''&&&&&&&&&&&&''''''&&&&&&&&&'''''''''''''''%%%&&&'''((()))(((((('''&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''(((''''''''''''(((((((((((('''''''''''''''((())))))'''''''''(((((('''''''''&&&&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######"""###$$$%%%%%%$$$###"""################################################$$$$$$###"""""""""""""""!!!"""""""""############""""""""""""###$$$%%%&&&$$$$$$############$$$$$$""""""#########$$$$$$$$$$$$###"""!!!!!!"""###$$$""""""""""""##################"""!!!!!!!!!!!!!!! !!!"""#########""""""""""""""""""""""""!!!!!!""""""""""""!!!!!! !!!!!!!!!!!! !!!!!!!!!!!! BBBBBBAAAAAAAAABBBBBBCCC???@@@AAABBBBBBBBBAAAAAABBBBBBCCCDDDEEEEEEDDDDDD?????????@@@@@@?????????AAAAAAAAABBBCCCDDDDDDEEE@@@CCCEEEEEEBBBAAABBBDDDBBBBBBBBBBBBBBBBBBBBBBBB@@@BBBDDDCCC@@@???AAADDDCCCDDDCCCAAA>>>======>>>===>>>>>>?????????>>>>>>:::;;;<<<=========<<<;;;>>>>>>???@@@@@@@@@@@@???======>>>???AAABBBCCCDDD???@@@AAAAAABBBBBBAAAAAAAAAAAAAAA@@@@@@@@@??????BBBAAAAAA@@@???>>>======999999999::::::;;;;;;;;;888999:::;;;<<<;;;::::::999999999999::::::;;;<<<999888888999999888555333777777777777777888888888555666777777777666444333222222333444555555555555333555666555444444555666444333222111222333444555666555555444444444555555888888777777777777888888666555555444444444555555555555666666555555444333333333333444444555555555666555555444444444555555666666666666555555555555444444444444555777888888777777777777666555444333444444444444555666777777333333222111000000000111000222222111///...///000//////000000111111222222///111222111000///000111...///000111111111111111.........---...///000111------...............---,,,,,,---...---,,,***)))(((***,,,,,,,,,+++,,,---++++++***,,,......---,,,***,,,------++++++,,,......---,,,,,,++++++,,,,,,)))***,,,------,,,***))),,,,,,,,,+++++++++*********))))))***,,,,,,+++*********+++++++++,,,,,,,,,************++++++,,,---******))))))))))))******)))))))))))))))******+++(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))((((((((((((&&&'''''''''(((((())))))$$$%%%'''))))))))))))(((''''''&&&&&&&&&&&&'''''''''''''''''''''&&&&&&&&&%%%&&&((()))))))))((('''&&&&&&&&&'''''''''((((((&&&&&&&&&'''''''''((((((''''''''''''((((((((()))'''''''''''''''((()))***&&&&&&''''''''''''&&&&&&%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&%%%%%%%%%##############################$$$$$$$$$$$$############%%%%%%%%%%%%######""""""""""""""""""""""""##############################"""!!!!!!!!!!!!!!!!!!!!!""""""#########$$$###"""!!!!!!"""$$$&&&'''$$$$$$############$$$$$$""""""######$$$$$$$$$$$$$$$###"""!!!!!!"""###$$$""""""""""""##################"""!!!!!!!!!!!!!!! !!!"""######$$$""""""""""""""""""""""""!!!!!!""""""""""""!!!!!! !!!!!!!!!!!! !!!!!!!!!""" CCCCCCBBBBBBBBBBBBCCCCCCCCCBBBBBBBBBBBBAAAAAAAAAAAAAAA@@@@@@@@@AAABBBCCCCCCCCCBBBBBBBBBBBBCCCCCCBBBBBBBBBCCCCCCCCCCCCCCCCCCEEEEEECCC@@@AAADDDHHHEEEEEEDDDDDDDDDDDDEEEEEEDDDDDDCCCAAA@@@AAACCCEEEDDDCCCBBBAAA@@@@@@@@@@@@AAA@@@>>>===<<<<<<=========>>>>>>>>>>>>?????????>>>=========>>>@@@BBBDDDAAA@@@@@@@@@AAAAAABBBCCC@@@AAAAAA@@@???@@@CCCEEEBBBBBBBBBAAAAAAAAA@@@@@@@@@???>>><<<<<<<<<===>>>;;;;;;;;;<<<>>>>>>;;;999::::::;;;<<<;;;:::888777777777777777888999:::;;;<<<;;;999888666555555555777888999999999999888777777777777777666666666666666555555444444444555555555666666666777777888888555555555555555555444444888777555444444555777888666666555555555555666666888888777777666666555555777555333444666888777555333444555555444444666888:::888666666777888888888666666777777666555444444555555555666666666666666999999999999999999999999666444333444777777555333000000111222333333444444555444444333222111000000555222//////111333222000222222222111111111111000000000000000000000000000...///000111111000///...------------------------............---,,,+++***+++++++++,,,---...000111......------------......------------------------...---+++))))))***+++,,,)))))))))))))))*********,,,+++******)))*********************)))))))))))),,,,,,,,,,,,,,,,,,,,,,,,*********,,,------,,,***)))***+++,,,,,,,,,,,,,,,+++++++++*********))))))))))))************))))))************************))))))(((((((((((())))))))))))))))))))))))))))))(((((((((((((((((((((((()))((('''&&&%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''((())))))))))))''''''''''''''''''&&&&&&&&&'''((('''%%%%%%'''(((''''''''''''(((((((((((((((((((((((())))))))))))((((((((((((((((((((((((''''''''''''''''''''''''((('''&&&%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%$$$###"""!!! """"""""""""""""""""""""################################################%%%$$$$$$$$$######""""""########################"""############$$$$$$$$$""""""""""""############$$$###"""""""""###%%%%%%'''&&&$$$""""""""""""###!!!!!!!!!!!!""""""""""""""""""""""""""""""""""""$$$#########""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! CCCCCCBBBBBBBBBBBBCCCCCCCCCCCCCCCBBBBBBAAAAAAAAABBBAAA@@@??????AAABBBDDDCCCCCCBBBBBBBBBBBBCCCCCCBBBBBBCCCCCCCCCDDDDDDDDDEEEFFFEEECCC@@@@@@CCCEEEDDDDDDDDDCCCCCCDDDDDDDDDDDDDDDCCCBBB@@@AAACCCEEEEEEDDDCCCBBBAAAAAAAAAAAAAAA@@@>>>===<<<<<<===============>>>>>>>>>??????===<<<<<<===>>>???AAABBBAAAAAAAAA@@@AAAAAABBBBBB@@@AAAAAA@@@??????AAACCCAAAAAAAAA@@@@@@@@@@@@@@@@@@???>>>===<<<<<<===>>>;;;;;;;;;<<<======;;;999::::::;;;<<<;;;:::999888888888777888888999::::::::::::888777666666555555888888888888888888888888666666666555555555555555555444444444444444555666444444444555555666666666555555555555555555555555777666555444444555666777666666666666666666666666888777777777666666666555666333222222555666666444333444555555444444666777666444222222333444444444666666666666666555444444222333444555666777888999888888888888888888888888555444333444666777555333111111111222222333333444333333222222222222222222333111///000222333222111222222222111111111000000111111111111111111111111//////000000000000//////------------------------............---,,,+++*********++++++,,,...///000......------------......,,,,,,,,,,,,,,,,,,,,,,,,...---+++***)))***+++,,,******++++++++++++++++++***)))))))))***+++,,,,,,************)))))))))))),,,,,,,,,,,,,,,,,,,,,,,,*********,,,------,,,************+++++++++,,,,,,,,,++++++++++++*********))))))************))))))************************))))))(((((((((((())))))))))))))))))))))))))))))'''''''''''''''''''''''')))((('''&&&%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''(((((((((((((((''''''''''''''''''''''''&&&'''((('''%%%%%%'''(((''''''''''''(((((((((((('''((((((((())))))))))))((((((((((((((((((((((((''''''''''''''''''''''''((('''&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$""""""""""""""""""""""""$$$$$$$$$###########################""""""""""""""""""""""""""""""""""""################################################$$$$$$#########"""""""""########################"""############$$$$$$$$$""""""""""""###############"""!!!!!!!!!"""$$$$$$%%%$$$"""!!! !!!!!!!!!!!!!!!!!!"""""""""###""""""""""""""""""""""""############"""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! CCCCCCBBBBBBBBBBBBCCCCCCDDDDDDCCCBBBAAAAAA@@@@@@CCCAAA???>>>>>>@@@CCCEEEBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBCCCDDDDDDEEEFFFFFFFFFFFFEEECCCAAA@@@AAACCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCBBB@@@AAACCCEEEEEEEEEDDDCCCBBBBBBBBBBBB@@@@@@???=====================>>>>>>>>>?????????<<<<<<<<<<<<===???@@@AAABBBBBBAAAAAAAAAAAAAAABBBAAAAAAAAA???>>>>>>@@@AAA???????????????@@@@@@@@@???>>>>>>============>>><<<;;;:::;;;======;;;:::999:::;;;;;;;;;:::999888999999999999999999999999888888777666666666666777:::999888777777888999:::666666555444444444444444333333333333333444555666333333333333333444444444555555555555555555555555666555444333333444555666666666777888888777666666777777777777666666666666444222111111333444444333444555555555444444555777666555333333444555555444555666666666666555444444444444444555666777777888777777777777777777777777555444444444666666444222222222222222222222222222111111222222222333333333000000///111333444222111222222111111111000000000111111111111111111111111000000////////////000000........................---......------,,,+++***************+++---...///......------------......,,,,,,,,,,,,,,,,,,,,,,,,...---+++******+++,,,,,,,,,,,,,,,,,,,,,,,,,,,+++((((((((()))***,,,---...++++++*********)))))))))+++++++++++++++++++++++++++******+++---...,,,++++++***)))))))))***+++,,,,,,,,,,,,,,,++++++++++++))))))************))))))************************))))))(((((((((((())))))))))))))))))))))))))))))''''''''''''''''''''''''***)))(((&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''''''''&&&&&&''''''''''''''''''''''''&&&'''((('''%%%%%%'''(((''''''''''''((((((((((((''''''((((((((()))))))))((((((((((((((((((((((((''''''''''''''''''''''''''''''&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$#########""""""""""""""""""""""""$$$$$$$$$$$$######""""""!!!!!!""""""#########$$$""""""""""""""""""""""""######################################################""""""""""""!!!!!!########################"""############$$$$$$$$$"""""""""#########$$$$$$"""!!!!!!!!!!!!"""#########"""!!!  !!!!!!!!!"""""""""######""""""""""""""""""""""""############""""""""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!CCCCCCBBBBBBBBBBBBCCCCCCDDDDDDCCCBBBAAA@@@@@@???CCCBBB???>>>>>>@@@CCCEEEBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBCCCDDDEEEFFFGGGHHHEEEEEEDDDCCCAAAAAABBBCCCBBBBBBBBBBBBBBBBBBBBBBBBAAABBBCCCBBBAAAAAACCCEEEDDDDDDCCCBBBBBBBBBBBBBBB@@@@@@???>>>>>>=========????????????@@@@@@@@@@@@=========>>>??????@@@AAACCCCCCBBBAAAAAAAAAAAABBBAAAAAAAAA???======>>>@@@>>>>>>>>>>>>????????????>>>>>>>>>============>>><<<;;;:::;;;<<<<<<;;;:::999:::;;;;;;;;;:::999888::::::::::::::::::999999777777777666666777777888:::999777666666777999:::777666555444444444555555333333222333333444555666333333333333333333333333444444444555555555555555555555444444444444555555555777888::::::888777555777777777777666666666666333222222222333444444444444555666555333333555777777666555555666777666555555555555666666555444444888777777666555444444333777777777777777777777777444444444555555444333222333333222222222222222222222222222222222222222222...///000222333444333222111111111111000000000000222222222222222222222222111000///......///000111////////////////////////---------------,,,+++***************+++,,,---......------,,,,,,------...++++++++++++++++++++++++---,,,,,,+++++++++,,,,,,,,,,,,,,,,,,++++++++++++))))))))))))***+++,,,---+++++++++*********))))))*********+++++++++++++++,,,+++***+++---...---+++,,,+++)))(((((()))+++,,,---------,,,,,,,,,++++++)))******++++++******)))************************))))))(((((((((((())))))((((((((((((((((((((((((''''''''''''''''''''''''))))))((('''&&&%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&&&&'''''''''''''''&&&'''((('''%%%%%%'''(((''''''''''''(((((((((((('''''''''((((((((())))))(((((((((((((((((((((((('''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###"""""""""""""""""""""############""""""""""""""""""""""""################################################"""""""""!!!!!!!!!!!!!!!########################""""""#########$$$$$$$$$""""""#########$$$$$$$$$"""""""""""""""######$$$""""""!!!!!! !!!!!!"""""""""#########""""""""""""""""""""""""#########"""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!CCCCCCBBBBBBBBBBBBCCCCCCDDDDDDCCCBBBAAAAAA@@@@@@CCCAAA???>>>???@@@CCCDDDAAAAAABBBCCCCCCBBBAAAAAABBBBBBCCCDDDEEEFFFGGGHHHBBBBBBAAABBBCCCDDDDDDDDDAAAAAABBBCCCCCCBBBAAAAAA@@@AAABBBBBBAAAAAACCCDDDCCCBBBAAAAAA@@@AAAAAAAAA@@@@@@@@@???>>>>>>======@@@@@@@@@AAAAAAAAABBBBBB>>>??????@@@AAAAAAAAAAAACCCCCCBBBAAAAAABBBBBBBBBAAAAAAAAA???======>>>@@@>>>>>>>>>>>>>>>>>>>>>>>>=========>>>>>>>>>>>>===<<<;;;999:::;;;<<<;;;:::888999:::;;;;;;;;;:::999::::::;;;;;;;;;::::::999888777777777777888888999:::999777666666777999:::999888666555444555666777333333333333444444555666555555444444444444444444444444444555555555666666555555555444444555555555555777888::::::888777555666666666666777777777777444444444444444444555666555555666555333333555666444333222333444555444222444444555555555555444444888777777666555444444333888888888888888888888888444444555555444333222222333333222222222222222222444444333333222111000000---///111333333333222222111111111000000000//////111111111111111111111111111000///......///000111////////////////////////,,,,,,,,,---,,,,,,++++++************+++,,,------------,,,,,,,,,,,,------++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,------,,,,,,++++++************++++++***************+++++++++++++++******************+++++++++,,,,,,,,,---+++***+++---...---,,,---+++***(((((()))+++,,,---------,,,,,,,,,++++++******++++++++++++******))))))))))))))))))))))))))))))(((((((((((())))))((((((((((((((((((((((((''''''''''''''''''''''''(((((((((''''''&&&%%%$$$''''''''''''''''''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&&&&'''''''''((((((&&&'''((('''%%%%%%'''(((''''''''''''((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""############""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""########################!!!!!!!!!!!!!!!"""""""""########################""""""#########$$$$$$$$$############$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%############"""""""""!!!""""""""""""############""""""""""""""""""""""""""""""""""""""""""######"""""""""""""""""""""""" !!!!!!""""""CCCCCCBBBBBBBBBBBBCCCCCCCCCCCCBBBBBBBBBAAAAAAAAAAAAAAA@@@@@@@@@AAABBBCCC@@@AAABBBCCCCCCBBBAAA@@@BBBBBBCCCDDDDDDEEEFFFFFFAAA@@@@@@AAADDDEEEEEEDDD@@@AAABBBCCCCCCBBBAAA@@@???@@@BBBBBBAAAAAABBBDDDBBBAAAAAA@@@@@@@@@AAAAAA@@@@@@@@@@@@???>>>===<<<@@@@@@AAAAAAAAABBBBBBBBB???@@@AAAAAABBBBBBAAAAAABBBBBBBBBBBBBBBCCCCCCDDDAAAAAAAAA???>>>>>>@@@AAA????????????>>>>>>>>>===<<<======>>>>>>>>>>>>===<<<:::999999:::;;;;;;:::888999:::;;;;;;;;;:::999999:::;;;<<<<<<<<<;;;:::999999888888888999999::::::999888777777888999::::::888666555444555777888666555555444444555555555666666666666555555555555333333444444555666666666666666666666666666666666666666777888888777666666666666666666777777777777555666666666555555777888555666666555333333444666555444444555666666555333333333444555555555555444444444444555666777777888888888888888888888888888333555666555333222222222222222222222222222222222555444444333222111000///...000222222111111222333111111000000000/////////000000000000000000000000000000////////////000000........................++++++,,,,,,,,,,,,+++++++++++++++++++++,,,------------,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------,,,,,,++++++******)))))),,,++++++***))))))******,,,++++++++++++*********+++++++++,,,,,,------...---,,,***+++---......------,,,+++*********+++,,,,,,,,,,,,,,,++++++++++++******++++++++++++******))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((''''''&&&%%%''''''''''''''''''''''''%%%&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''(((((((((&&&'''((('''%%%%%%'''(((''''''''''''((((((((((((&&&&&&'''''''''(((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$$$$$$$$$$#########""""""""""""""""""""""""########################$$$#########""""""!!!!!!""""""""""""""""""""""""""""""""""""""""""""""""########################!!!!!!""""""""""""##############################"""############$$$$$$$$$#########$$$$$$$$$$$$%%%###$$$%%%%%%&&&&&&%%%%%%######$$$$$$$$$$$$######"""""""""#########$$$$$$""""""""""""""""""""""""""""""""""""############"""""""""""""""""""""""" !!!"""""""""CCCCCCBBBBBBBBBBBBCCCCCCAAAAAAAAABBBBBBBBBBBBCCC@@@@@@AAAAAABBBBBBBBBAAA???@@@BBBCCCCCCBBB@@@???BBBBBBCCCCCCCCCDDDDDDDDDBBB@@@@@@AAADDDEEECCCAAAAAABBBCCCDDDDDDCCCBBBAAA>>>@@@AAABBBAAAAAABBBDDDBBBBBBAAAAAAAAAAAABBBBBB@@@@@@AAAAAA@@@???===<<>>???@@@AAAAAAAAA@@@@@@AAAAAAAAAAAABBBDDDEEEFFF@@@AAAAAA@@@??????AAACCCAAAAAA@@@???>>>>>>===<<<;;;<<<===>>>??????>>>===<<<:::888888:::;;;;;;:::888999:::;;;<<<;;;::::::888:::;;;===>>>===<<<;;;;;;;;;::::::999:::::::::888888888888888888888888999888555444333444666777888888777666555555555555666666666666555555555444333333444444555666666777666777777777777777777666666666666666666666666666555666666666777777777888444666777666555444777999555666666555333333444555666555555777888888666444222333444444555555555444222333444555666777888999777777777777777777777777333555666555222000111222111111111222222333333444333333333222222111111111000222333222000///111444111000000000//////////////////////////////////////////000000000000//////------------------------***++++++,,,,,,,,,++++++,,,,,,,,,,,,,,,------...---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,------...------...------,,,++++++***************)))******++++++,,,,,,+++++++++*********+++,,,,,,---......//////...,,,++++++,,,.........---------,,,,,,,,,++++++,,,++++++++++++************++++++,,,,,,++++++***))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''((((((((('''&&&''''''''''''''''''''''''%%%&&&'''(((((((((((((((%%%%%%&&&&&&'''(((((()))&&&'''((('''%%%%%%'''(((''''''''''''((((((((((((&&&&&&&&&'''''''''((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%%%%%%%%%%&&&'''((($$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$"""""""""""""""""""""""""""""""""###$$$$$$%%%%%%""""""""""""############""""""""""""""""""""""""""""""""""""""""""""""""########################"""""""""#########$$$$$$########################"""############$$$$$$$$$#########$$$$$$$$$%%%%%%"""###$$$%%%&&&%%%$$$$$$"""###$$$%%%%%%$$$######""""""#########$$$$$$$$$""""""""""""""""""""""""!!!"""""""""############"""""""""""""""""""""""" !!!""""""###CCCCCCCCCBBBBBBCCCCCCCCC@@@@@@AAABBBBBBCCCCCCDDD???@@@AAABBBCCCBBBAAA@@@???@@@BBBCCCCCCBBB@@@???BBBBBBBBBCCCCCCCCCCCCCCCCCCBBB@@@AAADDDDDDBBB???AAABBBDDDEEEEEEDDDBBBAAA===???AAABBBAAAAAABBBCCCCCCCCCBBBBBBBBBCCCCCCDDD@@@@@@AAAAAA@@@???===<<<===>>>>>>>>>>>>?????????===>>>@@@AAAAAA@@@???>>>@@@@@@AAAAAACCCDDDFFFGGG@@@AAAAAA@@@???@@@CCCEEECCCBBBAAA@@@???===<<<<<<;;;<<<===?????????>>>===<<<:::888888999;;;;;;:::888888:::;;;<<<;;;;;;:::888999;;;===>>>>>>===<<<===<<<;;;;;;:::::::::;;;777888999999999999888777888777444222222333555777:::999888666555555555555666666666555555444444444333333444444555666777777777777888888888888777777666666555555555555666666555666666666777777888888444666777666444444666999666666666555333333444555222111111333444444222000222333444444555555555444555555555666666666666666666666666666666666666666333555777555222000111222000000111222333333444444111222222222222333333333111333333111......111444000000000000////////////////////////////////////...///000111111000///...------------------------***++++++,,,,,,,,,++++++------,,,,,,,,,---......---,,,,,,++++++,,,,,,---------------------------+++,,,------.........---//////...---,,,,,,++++++(((((())))))***+++------,,,,,,,,,+++++++++******,,,,,,------...///000000...,,,++++++,,,.........---............---,,,++++++++++++*********))))))***++++++,,,,,,++++++***))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&(((((((((((('''((((((((((((((((((((((((%%%&&&'''((())))))))))))%%%%%%&&&&&&'''((())))))&&&'''((('''%%%%%%'''(((''''''''''''((((((((()))&&&&&&&&&'''''''''((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%%%%%%%%%%&&&'''((($$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""###$$$%%%%%%&&& !!!"""###$$$%%%%%%""""""""""""""""""""""""""""""""""""""""""""""""########################""""""######$$$$$$$$$%%%########################"""############$$$$$$$$$######$$$$$$$$$%%%%%%%%%!!!"""###$$$%%%$$$######"""###$$$%%%%%%$$$###""""""############$$$$$$$$$""""""""""""""""""""""""!!!!!!""""""#########$$$"""""""""""""""""""""""" !!!""""""###@@@AAABBBBBBBBBCCCEEEGGGCCCCCCBBBBBBBBBAAAAAAAAACCCCCCDDDDDDCCCCCCBBBAAA???@@@AAABBBBBBBBBAAAAAAFFFFFFDDDAAA???>>>@@@BBBAAA@@@@@@@@@AAAAAABBBCCCDDDBBBAAACCCFFFFFFDDDBBBEEEBBB???>>>??????===;;;<<<===>>>???AAABBBCCCDDDEEECCCAAA>>><<<<<<======@@@???@@@BBBCCCBBB???===@@@AAAAAABBBBBBAAAAAA@@@CCC@@@>>>???BBBCCCCCCAAABBBAAAAAA@@@@@@AAAAAABBB===>>>??????<<<;;;:::;;;>>>>>>>>>>>>===============<<<:::888888999:::;;;;;;;;;;;;<<<<<<<<<<<<===:::999999888999;;;<<<===:::;;;<<<<<<<<<:::777666777777888888888999999999999888666555444444444555666777777666444444555777777777666666666666777777555555555555555555555555888888777777777777888888999888777666666555555666555666777888888777666666666555555666888888777666555777999999777555555555666666555555555444444444666555555555555444444444555555555555555555444444555555555555666777888999333444444333111111222444000000000111222222222333222222222111111111111111111111111111000000000000000000000000111111111111---...///000000///......---...000111111111000///000///---,,,++++++,,,---++++++++++++++++++++++++---------.........//////+++,,,---.........------.........------,,,,,,,,,------------------------+++,,,,,,------,,,,,,+++++++++++++++++++++++++++++++++,,,,,,,,,,,,------,,,,,,---......---,,,,,,++++++++++++++++++++++++,,,------......------,,,******))))))))))))************************************))))))(((((('''''''''((()))++++++******)))''')))***)))((('''(((***((('''''''''&&&&&&&&&&&&&&&''''''(((((((((((((((+++******)))(((''''''&&&''''''((()))))))))))))))$$$%%%&&&&&&''''''&&&&&&((((((''''''''''''((((((&&&'''((('''&&&&&&'''(((((('''&&&%%%$$$%%%&&&&&&******))))))((((((''''''((('''&&&%%%%%%&&&'''((('''''''''''''''''''''''''''''''''(((''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$###""""""''''''&&&%%%%%%$$$######%%%$$$$$$######$$$$$$%%%################################################""""""############""""""""""""""""""############""""""""""""""""""""""""%%%%%%$$$######$$$%%%%%%######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$###"""!!!######$$$%%%%%%%%%%%%$$$$$$$$$$$$#########""""""""""""""""""############$$$$$$%%%%%%$$$###!!! !!!"""$$$$$$######""" !!!"""###############???@@@AAAAAAAAAAAACCCEEECCCCCCBBBAAA@@@??????>>>CCCCCCCCCCCCCCCBBBBBBAAA???@@@AAABBBCCCBBBAAAAAAEEEEEEDDDAAA???>>>@@@BBB@@@@@@@@@@@@AAABBBCCCCCCBBBAAA@@@BBBDDDEEEDDDBBBCCC@@@>>>>>>@@@@@@???===@@@@@@@@@AAAAAABBBBBBCCCDDDBBB@@@>>>======>>>>>>?????????AAACCCBBB@@@>>>@@@AAAAAABBBBBBAAAAAA@@@BBB@@@???@@@BBBCCCBBB@@@AAA@@@@@@??????@@@@@@AAA>>>??????>>><<<;;;;;;<<>>>>>>>>===============<<<:::999888999:::;;;;;;;;;;;;;;;<<<<<<<<<<<<999999888888999:::<<<===:::;;;<<<<<<;;;:::888666777777888888888999999999999888666555444444555555444555555444222222333555666666555555555555666666555555555555555555555555888888777777777777888888666666666555555666777777777666666555555666777777666666666777777777777666555777999888777555555555666666555555555444444444555555555555444444444444555555555555555555444444999888777666555555555555333444444333111111222444111111111111222222222222111111111111111222222222222111111111000000000000000000000000111111111111000000111111111///...------...//////000000//////000///...,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------.........//////,,,,,,------------...............------,,,,,,,,,------------------------+++,,,,,,------,,,,,,+++++++++++++++++++++++++++++++++,,,,,,,,,,,,------,,,,,,---......---,,,,,,++++++++++++++++++++++++,,,------......------,,,******))))))))))))******++++++++++++++++++++++++***)))))))))(((((((((''''''((()))++++++******)))''')))***)))((('''(((***((((((((('''''''''&&&&&&&&&''''''(((((((((((((((******))))))((((((''''''''''''((()))))))))))))))%%%%%%&&&''''''''''''&&&(((''''''''''''''''''(((&&&'''((((((&&&&&&'''(((((((((&&&%%%%%%%%%&&&'''((((((((((((''''''''''''((('''&&&&&&&&&&&&'''(((''''''''''''''''''''''''&&&&&&'''''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$######"""''''''&&&%%%%%%$$$######%%%$$$$$$######$$$$$$%%%################################################""""""############""""""""""""""""""############""""""""""""""""""""""""%%%%%%$$$######$$$%%%%%%######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$###""""""######$$$%%%%%%%%%%%%$$$$$$$$$$$$#########""""""""""""""""""############$$$$$$%%%%%%$$$###!!! !!!"""###$$$######"""!!!""""""############"""???@@@AAA@@@???@@@BBBCCCCCCCCCBBBAAA???>>>======CCCCCCCCCCCCCCCBBBAAAAAA???@@@AAACCCCCCBBBBBBAAADDDDDDCCCAAA>>>>>>???AAA@@@@@@AAAAAABBBCCCCCCDDD@@@??????@@@CCCDDDCCCBBBAAA???>>>>>>@@@AAA@@@???BBBBBBBBBBBBBBBAAAAAAAAAAAAAAA???>>>>>>>>>???@@@>>>>>>???AAACCCCCCAAA???@@@@@@AAAAAAAAAAAA@@@@@@@@@???@@@AAACCCCCCAAA@@@@@@??????>>>>>>??????@@@?????????===;;;;;;<<<>>>??????>>>>>>>>>============<<<;;;:::999:::;;;;;;;;;;;;;;;;;;<<<<<<<<<<<<999888888777888:::;;;<<<:::;;;;;;<<<;;;:::888777888888888888888999999999888888777666555555555555555555666444333222333555666555555444444555555666666666666666666666666666888888777777777777888888444444444444555666777888888777555333333555777888666666777777777666666555555777888888666555555666555555555555555444444444555555555555444444444444444444444444444444555555888777666555555444555555333444444333111111222444222222222222222111111111000000111111222222333333222222222111111111000000000000000000111111111111111222222222111///---,,,...------------...//////000///...---,,,,,,,,,,,,------------------------------........./////////...---,,,,,,,,,---//////.........---------------........................+++,,,,,,------,,,,,,+++++++++++++++++++++++++++++++++,,,,,,,,,,,,------,,,,,,------------,,,,,,++++++++++++++++++++++++,,,------......------,,,******))))))))))))******,,,,,,,,,,,,,,,,,,,,,,,,))))))))))))(((((((((((('''((()))++++++******)))''')))***)))((('''(((***)))))))))(((((((((''''''&&&''''''((((((((((((((())))))))))))((((((((((((''''''((())))))))))))(((%%%&&&&&&'''''''''''''''''''''&&&&&&&&&&&&''''''&&&'''((((((&&&&&&'''((()))(((''''''&&&&&&''''''&&&&&&&&&&&&''''''''''''((('''&&&&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$######'''&&&&&&%%%%%%$$$$$$###%%%$$$$$$######$$$$$$%%%################################################""""""############""""""""""""""""""############""""""""""""""""""""""""%%%$$$$$$######$$$$$$%%%######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$###"""######$$$%%%%%%%%%%%%$$$$$$$$$$$$###############""""""""""""############$$$$$$$$$$$$###"""!!!!!!!!!!!!"""############""""""############""""""!!!@@@AAAAAAAAA??????AAACCCBBBBBBAAAAAA@@@@@@??????BBBBBBCCCCCCCCCBBBAAAAAA@@@@@@BBBCCCCCCCCCBBBAAACCCCCCCCCAAA???>>>???AAA@@@AAABBBBBBCCCDDDDDDDDD@@@??????@@@BBBCCCDDDDDDBBBAAA@@@??????@@@@@@@@@AAAAAAAAAAAAAAAAAAAAAAAA??????>>>>>>??????@@@AAA>>>>>>>>>@@@BBBCCCBBB@@@@@@@@@AAAAAAAAAAAA@@@@@@>>>???AAACCCDDDCCCAAA???@@@@@@????????????@@@@@@@@@@@@???===;;;;;;>>>@@@?????????>>>>>>>>>============<<<;;;:::;;;;;;;;;::::::;;;;;;;;;<<<<<<<<<888888777777888999;;;<<<:::;;;;;;;;;;;;:::999888888888888888888888888888888777777666666666555555777888888777555444666777666666555555555555666666666666666666666666666666888888777777777777888888444444444444444555666666777666555444444444555555555666777777666555555555555777888777555444555666555555555555555555555555555555555444444444333333333333444444444444555555444444444444555666777777333444444333111111222444333333333222222111111111000000111111222333444444333333222222222111111111///000000000111111111111///000111111000///...---...---,,,+++,,,---...///000///......---,,,,,,,,,---------...........................///////////////...,,,+++,,,---///111...............---------////////////////////////+++,,,,,,------,,,,,,++++++++++++++++++++++++++++++++++++,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++,,,------......------,,,+++******))))))******+++,,,,,,,,,,,,,,,,,,,,,,,,))))))))))))(((((((((((('''((()))***+++******)))''')))***)))((('''(((***))))))))))))((((((((((((&&&''''''((((((((((((((((((((((((((())))))))))))&&&'''(((((())))))((((((&&&&&&'''(((((((((((('''&&&&&&%%%%%%%%%%%%&&&&&&&&&((()))((('''&&&'''((())))))((((((''''''''''''&&&&&&&&&''''''((((((((('''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$$$$######$$$$$$%%%################################################""""""############""""""!!!"""""""""############""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""$$$$$$$$$%%%%%%$$$############$$$%%%%%%%%%%%%$$$########################!!!"""""""""###########################"""!!!!!!!!!"""""""""###########################"""!!! AAABBBCCCBBB@@@@@@AAACCC@@@@@@AAAAAABBBBBBCCCCCCBBBBBBBBBCCCBBBAAAAAA@@@@@@AAABBBCCCDDDCCCBBBBBBBBBCCCCCCBBB@@@???@@@AAAAAABBBCCCDDDDDDDDDCCCCCCAAAAAAAAAAAABBBCCCDDDFFFCCCCCCBBB@@@???>>>>>>>>>>>>>>>>>>???@@@@@@AAAAAA>>>>>>>>>>>>???@@@AAAAAA???>>>>>>???BBBCCCBBBAAA???@@@@@@AAAAAA@@@@@@???>>>???BBBCCCCCCBBBAAA@@@AAAAAA@@@@@@@@@@@@AAAAAA@@@@@@???===<<<<<>>>>>>>>>>>======<<<<<<<<<;;;<<<<<<:::::::::;;;;;;;;;;;;<<<999888888888888:::;;;<<<::::::::::::::::::999999888888888888888888888888777777777777777666666666777888888777555555666888888888777777777777888888777777777777777777777777888888777777777777888888666666555444444444444444333444666777666555333111444666777777555444555666666777777666444444555666444555555555555555555555555444444444444333333333333333333333444444555555333333333333444555666777333444444333111111222444444333333333222222111111000000111222333444444555333333333333222222222222///000000000111111111111+++,,,.../////////......---,,,+++++++++,,,...///////////////...---,,,,,,---------....../////////........./////////000000///...---,,,,,,...000111........................////////////////////////+++,,,,,,------,,,,,,++++++++++++++++++++++++++++++++++++,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++,,,------......------,,,++++++************++++++,,,,,,,,,,,,,,,,,,,,,,,,(((((((((((())))))))))))'''((()))***+++******)))''')))***)))((('''(((***))))))))))))((((((((((((&&&''''''((((((((((((((((((((((((((())))))))))))&&&&&&'''(((((((((((((((&&&'''(((((())))))((((((&&&&&&%%%%%%%%%%%%&&&&&&'''((()))(((''''''((()))(((((((((((((((''''''''''''''''''(((((())))))***&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%$$$$$$######$$$$$$%%%########################""""""""""""""""""""""""""""""############""""""!!!"""""""""############""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""###$$$$$$%%%%%%%%%$$$$$$######$$$%%%%%%%%%%%%$$$########################!!!"""""""""##################"""""""""""""""""""""""""""""""""########################"""!!! CCCCCCCCCBBB@@@???@@@BBB??????@@@AAACCCDDDEEEEEEBBBBBBBBBBBBBBBAAA@@@@@@@@@AAABBBCCCDDDCCCCCCBBBBBBCCCDDDCCCAAA@@@AAABBBCCCDDDEEEEEEEEEDDDBBBBBBBBBCCCCCCBBB@@@AAACCCFFFDDDDDDDDDAAA???===>>>???<<<======>>>???@@@@@@AAA===>>>>>>???@@@@@@AAAAAA@@@???>>>???AAABBBBBBAAA??????@@@@@@@@@@@@??????>>>@@@BBBCCCBBBAAAAAABBBBBBAAAAAAAAAAAAAAAAAABBB@@@@@@@@@???===>>>???AAA@@@@@@?????????>>>>>>>>>===============<<<<<<<<<::::::::::::;;;;;;;;;;;;:::999999888999;;;<<<===::::::::::::::::::::::::999999999888888888888888666777777888888777777666666666777555444333444666999888888777777888888999777777777777777777777777888888777777777777888888888777666555444444444444222444666888777444111///111555777777555444555888666666777555444333444666444444444555555555555555444444444444333333333333222222333333444444555555666666444333333333333333333444444333111111222444333333333333333222222222111111222222333333444444444444444333333333222222000000000000111111111111)))***,,,.../////////...---,,,,,,,,,,,,---......//////000//////...,,,,,,,,,,,,------.../////////....../////////000000000///...---------...000000.............../////////........................+++,,,,,,------,,,,,,+++++++++++++++++++++++++++++++++,,,,,,,,,,,,------,,,,,,++++++++++++,,,,,,++++++++++++++++++++++++,,,------......------,,,++++++************++++++,,,,,,,,,,,,,,,,,,,,,,,,(((((((((((())))))))))))'''((()))++++++******)))''')))***)))((('''(((***)))))))))(((((((((''''''&&&''''''((((((((((((((())))))))))))((((((((((((&&&&&&'''((((((((((((''''''(((((()))))))))))))))''''''&&&&&&&&&&&&'''''''''((())))))''''''((()))'''(((((((((((('''&&&&&&((((((((()))))))))))))))&&&&&&'''(((((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%########################""""""""""""""""""""""""""""""############""""""""""""""""""############""""""""""""""""""""""""###$$$$$$%%%%%%$$$$$$#########""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$###############$$$$$$$$$""""""""""""###############""""""!!!!!!!!!"""""""""""""""!!!"""######$$$"""############""""""!!!BBBCCCCCCAAA???>>>???@@@??????@@@AAABBBCCCCCCDDDAAABBBBBBBBBBBBAAA@@@@@@@@@AAACCCDDDDDDDDDCCCBBBBBBDDDEEEDDDCCCBBBBBBCCCEEEFFFFFFGGGEEECCCAAA@@@BBBCCCCCCAAA>>>>>>AAADDDBBBCCCDDDBBB???>>>???AAA????????????????????????===>>>??????@@@@@@@@@@@@AAA@@@??????@@@AAAAAA@@@??????@@@@@@@@@@@@?????????AAABBBBBB@@@@@@AAACCCAAAAAA@@@@@@@@@@@@AAAAAA???@@@AAA@@@??????@@@AAA@@@@@@@@@?????????>>>>>>>>>>>>>>>>>>>>>===<<<<<<999999:::::::::;;;;;;;;;;;;::::::999:::<<<===>>>:::::::::999:::::::::;;;999999999888888888777777666777888888888888777666666777777666444333555666888888777777777777888888888888888888888888888888888888777777777777888888777777666555555666666666333444555666555333111//////333777777444444666999666666666555333333444666444444444555555555666666444444444333333333222222111222222333444444555555666555444333222222222222333444444333111111222444222222333333333333333333333333333333333333333333444444444444333333333333000000000000111111111111+++,,,---/////////......,,,,,,---...............//////000000///...---,,,+++,,,,,,---......//////.../////////000000000000............////////////---........./////////000------------------------+++,,,,,,------,,,,,,+++++++++++++++++++++++++++++++++,,,,,,,,,,,,------,,,,,,+++******+++,,,,,,++++++++++++++++++++++++,,,------......------,,,,,,++++++******++++++,,,++++++++++++++++++++++++'''((((((((()))))))))***'''((()))++++++******)))''')))***)))((('''(((***((((((((('''''''''&&&&&&&&&''''''(((((((((((((((******))))))((((((''''''%%%&&&''''''((((((''''''(((((()))************)))(((''''''''''''''''''(((''')))***)))((('''((()))&&&''''''((('''&&&%%%$$$((((((((((((((((((''''''&&&&&&'''(((((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%########################""""""""""""""""""""""""""""""############""""""""""""""""""############""""""""""""""""""""""""###$$$%%%%%%%%%%%%$$$#########""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%######$$$%%%%%%%%%%%%$$$""""""#########$$$$$$$$$""""""""""""###############"""!!! !!!!!!"""######"""!!!!!!!!!"""$$$$$$!!!""""""############"""AAABBBBBB@@@===<<<===?????????@@@@@@@@@AAAAAAAAAAAAAAABBBBBBBBBAAA@@@@@@AAAAAACCCDDDDDDDDDCCCBBBCCCDDDFFFEEEDDDCCCCCCDDDFFFGGGGGGGGGFFFCCC@@@???BBBCCCBBB@@@===<<>>>>>>>>???@@@@@@@@@@@@@@@BBBAAA??????@@@AAA@@@?????????@@@@@@@@@@@@?????????AAABBBAAA??????BBBEEE@@@@@@????????????@@@@@@>>>@@@AAABBB@@@???@@@AAA@@@@@@@@@????????????>>>>>>>>>>>>>>>>>>===<<<<<<999999:::::::::;;;;;;;;;;;;;;;::::::;;;<<<>>>???:::::::::999999:::;;;;;;999999999999888888777777666777888999999888777666888999999888666666777888777777666666666666777777888888888888888888888888888888777777777777888888666666555666666777888999555555444444333222111111...222666777444444777:::666666666444333333444666444444444555555555666666444444444333333333222222111111222333333444555555222222222222333444555555444444444333222111222444222222222333333444444444444333333333333333333333555555444444444333333333000000000000111111111111......///000000///...---,,,---...///000///...---///000000000000...---,,,++++++,,,,,,---...//////////////////000000000000---......///000/////////---.........//////000000------------------------+++,,,,,,------,,,,,,+++++++++++++++++++++++++++++++++,,,,,,,,,------------,,,+++******+++,,,---++++++++++++++++++++++++,,,------......------,,,,,,++++++******++++++,,,************************'''((((((((())))))******'''((()))++++++******)))((()))***)))((('''(((***((('''''''''&&&&&&&&&&&&&&&''''''(((((((((((((((+++******)))(((''''''&&&%%%&&&''''''((((((''''''(((((()))***************((((((''''''''''''((((((''')))***)))((('''(((***%%%&&&'''''''''&&&$$$$$$(((((((((''''''&&&&&&%%%%%%&&&'''(((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%########################""""""""""""""""""""""""""""""############""""""""""""""""""############""""""""""""""""""""""""###$$$%%%&&&&&&%%%$$$############"""###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&&&&&&&######$$$%%%%%%%%%%%%$$$""""""######$$$$$$$$$$$$""""""""""""###############"""!!! !!!"""######"""!!!!!!!!!"""$$$%%% !!!"""###############DDDCCCBBBAAA@@@?????????AAA@@@@@@??????@@@@@@AAABBBBBBBBBBBBAAA???===<<<@@@BBBCCCDDDDDDBBB@@@???===>>>@@@BBBDDDDDDDDDDDDDDDDDDDDDDDDCCCBBBAAA@@@???BBBDDDCCC@@@???@@@BBB@@@AAAAAAAAAAAA@@@??????@@@AAAAAABBBBBBAAAAAA@@@>>>>>>>>>>>>>>>>>>??????>>>>>>???>>><<<===???BBB@@@@@@@@@@@@@@@???>>>===@@@???>>>======>>>???@@@CCCBBB@@@?????????@@@@@@AAABBBCCCCCCCCCAAA>>>===@@@@@@???>>>>>>???@@@AAA???>>>======>>>>>>===<<<888999:::;;;<<<<<<<<<<<<::::::::::::;;;<<<======;;;<<<<<<;;;999999;;;<<<:::999888888777888888888:::::::::999999777666555777777666666666666666777888777666555555666777888::::::999888777777777888666666666666666777888888999888666555555555666777555666666666444333111000333555777777555444444444666666666666555444333222444444444333333444444555333333333222222333444444222222222222222222222222...///222444555444333222333333333333333333333333444555666555333222333444555555444444444333333333222333333333333222111111111222333222000000000111111000///------......///000000000000111111111111000000000000////////////---,,,,,,++++++,,,,,,------------...000111000///,,,---...//////...---,,,---------------...///000------------------------,,,+++***))))))***+++,,,,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,,,,------,,,,,,---,,,+++******+++,,,---,,,,,,,,,++++++*********---------,,,,,,+++++++++((()))+++,,,---.........,,,,,,++++++***)))((((((''')))******))))))***,,,))))))))))))))))))))))))************))))))(((((()))'''%%%&&&)))***(((&&&&&&&&&&&&'''''''''((((((((((((((((((((()))******''''''''''''''''''''''''''''''((()))))))))))))))))))))))))))))))))))))))(((((())))))))))))((((((''''''((((((((((((''''''$$$%%%'''((((((((('''&&&''''''(((((('''&&&%%%%%%'''&&&%%%$$$%%%&&&'''(((''''''''''''''''''&&&&&&%%%%%%$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&'''''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$############"""!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""""""""""""""######""""""""""""######!!!"""###$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$########################""""""""""""##################""""""!!!!!!!!! !!!!!!!!!!!!!!!"""######""""""""""""""""""""""""CCCCCCCCCBBBAAA@@@@@@???AAAAAA@@@@@@@@@@@@AAAAAABBBBBBBBBAAA@@@???>>>===???@@@BBBCCCCCCCCCBBBBBB>>>???AAACCCDDDDDDDDDDDDBBBBBBCCCCCCCCCCCCBBBAAA???AAABBBBBBAAA@@@@@@AAA@@@AAAAAAAAAAAA@@@??????@@@@@@AAAAAAAAAAAA@@@@@@========================??????@@@???>>>>>>@@@CCC@@@@@@@@@@@@@@@???>>>>>>@@@???>>>>>>>>>>>>???@@@CCCCCCAAA@@@@@@@@@AAAAAAAAABBBCCCCCCBBBAAA???===AAA@@@???>>>>>>>>>???@@@???>>><<<===>>>>>>===;;;999:::;;;<<<<<<=========;;;;;;::::::;;;;;;<<<<<<;;;<<<<<<;;;:::999;;;<<<;;;:::999888888888888888:::::::::999888777666666999888888777777777888888888777666666666666777888999999888777777777888888666666666666666777888888999888777666555666666777555666666777777666444444333555777777666555555555666666555555444444444444555444444333333333333444555444444333333444444555333333333333333333333333000111222333444444333222333333333333333333333333444555666555333222333444555555444444444333333333222333333333333222111111111222333222000000000111222111000/////////000000//////000000000111111111000000000000////////////---,,,,,,++++++,,,,,,------,,,,,,...000111000...------............---------------...............,,,,,,------------------,,,+++************+++,,,,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,,,,------,,,,,,++++++***))))))***++++++,,,,,,,,,+++++++++******,,,,,,,,,,,,,,,,,,,,,,,,)))***+++,,,---.........,,,,,,++++++***))))))(((''')))******))))))***+++))))))))))))))))))))))))++++++*********))))))))))))'''&&&'''))))))(((&&&&&&&&&&&&'''''''''((((((((((((((((((((())))))***''''''''''''''''''''''''''''''((()))))))))))))))))))))))))))))))))))))))(((((())))))))))))((((((''''''((((((((((((''''''%%%&&&''''''((((((''''''''''''(((((('''&&&&&&%%%'''&&&%%%%%%%%%%%%&&&'''''''''''''''''''''''''''%%%%%%$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$############""""""""""""""""""""""""""""""""""""""""""""""""######""""""""""""######""""""###$$$$$$$$$######"""######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$########################""""""""""""##################"""""""""!!!!!!!!!"""!!!!!!!!!!!!"""##############################BBBCCCDDDDDDCCCBBBAAA@@@BBBAAAAAA@@@@@@AAAAAABBBBBBBBBAAA@@@@@@@@@@@@@@@???@@@@@@AAABBBCCCDDDEEE@@@AAABBBCCCDDDDDDDDDDDD@@@AAABBBBBBCCCCCCBBBBBB@@@??????@@@AAAAAA@@@>>>@@@AAAAAAAAAAAA@@@?????????@@@@@@AAAAAA@@@@@@?????????>>>>>>>>>=========???@@@AAA@@@??????AAACCC@@@@@@@@@@@@@@@@@@???>>>@@@@@@????????????@@@@@@DDDCCCBBBAAAAAAAAABBBBBBAAAAAABBBBBBBBB@@@???>>>AAA@@@???>>>===>>>>>>??????===<<<<<<======<<<;;;:::;;;<<<===>>>>>>>>>>>>===<<<;;;;;;:::;;;;;;;;;:::;;;<<<;;;:::999;;;===<<<;;;:::999888888888888::::::999999888777777777999999888888888999999:::888888777666666777888888777777777777777777888999777666666666666777888888999888777666666666666777555666777999999999888777444666888888777666666777777666444444333444555666555444333333222222222222666555555444444555555555444444444444444444444444222222222222333333333333333333333333333333333333444555555555333222333444555555444444444333333333222333333333333222111111111222333222000000000111333222111000000000111111//////000000000000111111000000000000////////////------,,,,,,,,,,,,------,,,,,,,,,---///000///............------.........---.../////////...---,,,,,,,,,,,,------.........---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,***++++++,,,,,,,,,,,,,,,******))))))))))))******,,,,,,,,,++++++++++++***,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,,,,------------,,,,,,++++++***)))))))))((()))******))))))***+++))))))))))))))))))))))))+++++++++***************)))'''&&&'''((()))((('''&&&&&&'''''''''((((((((((((((((((((())))))))))))''''''''''''''''''''''''''''''((()))))))))))))))))))))))))))))))))))))))(((((())))))))))))((((((''''''((((((((((((''''''''''''&&&&&&''''''((()))'''''''''(((''''''&&&%%%'''&&&&&&%%%%%%%%%&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%&&&&&&'''%%%%%%%%%%%%&&&&&&&&&&&&((((((((('''&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$####################################""""""""""""""""""""""""######""""""""""""############$$$$$$$$$######"""!!!"""###$$$$$$$$$###"""$$$$$$############$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################"""""""""#########$$$$$$#########""""""""""""""""""""""""!!!""""""###$$$########################AAABBBDDDEEEEEECCCBBB@@@BBBBBBAAAAAAAAAAAABBBBBBCCCBBB@@@??????@@@AAABBBAAAAAA@@@AAAAAACCCDDDEEEAAABBBBBBCCCDDDDDDDDDDDDAAAAAABBBBBBBBBAAAAAA@@@@@@>>>===>>>AAABBB@@@===@@@AAAAAAAAAAAA@@@??????@@@@@@AAAAAAAAAAAA@@@@@@BBBBBBAAAAAA@@@?????????>>>???@@@@@@??????@@@BBB@@@@@@@@@AAAAAA@@@??????AAAAAA@@@@@@@@@@@@AAAAAABBBBBBBBBAAAAAAAAABBBBBB@@@AAAAAAAAAAAA@@@???>>>AAA@@@???>>>======>>>>>>>>>===;;;<<<======<<<:::;;;<<<===>>>>>>?????????>>>>>><<<;;;;;;::::::::::::;;;;;;;;;::::::;;;======<<<;;;999999888888888:::999999888888777777888999888888888888999999:::888888888888888888888888666666666666777888999999777777666666777777888999888888888777777777777777666777888999999999888777555777888888777777777999777666444333333444666777555444333222222222222222666555555444444444444444444444444444444444444444444444333222222222333333333333333333333333333333333444555555333333333555555555444444444333333333222333333333333222111111111222333222000000000111222222111111000000000000////////////000000000111000000000000////////////------,,,,,,,,,,,,------,,,+++,,,---///000///...///...---,,,,,,---...///---...///000000...,,,***+++,,,,,,------.........------------------------++++++++++++++++++++++++******+++,,,,,,,,,,,,++++++******************+++++++++++++++++++++++++++++++++,,,,,,,,,,,,------++++++,,,------,,,,,,,,,+++++++++*********))))))((()))******)))((()))+++((((((((((((((((((((((((++++++++++++************((((((''''''((((((((('''''''''''''''(((((((((((('''(((((()))))))))))))))''''''''''''''''''''''''''''''((()))))))))))))))(((((((((((((((((((((((((((((())))))))))))((((((''''''((((((((((((''''''((('''&&&&&&&&&''')))***&&&'''''''''''''''&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&'''''''''''''''%%%%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&&&&'''))))))((('''&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""######""""""""""""######$$$$$$$$$$$$$$$###"""!!! !!!"""$$$$$$###"""!!!$$$######""""""######$$$&&&&&&&&&&&&&&&&&&&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""#########$$$$$$$$$###########################""""""""""""###$$$$$$########################@@@BBBCCCEEEEEEDDDBBBAAABBBAAAAAA@@@@@@AAAAAABBBCCCBBBAAA@@@@@@@@@AAABBBCCCBBBBBBAAAAAAAAABBBBBBCCCBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCBBBAAA???>>>===???===<<<>>>AAACCC@@@===@@@AAAAAAAAAAAA@@@??????AAAAAABBBBBBBBBBBBAAAAAAAAAAAAAAAAAA@@@@@@??????<<<>>>??????>>>>>>???@@@???@@@@@@AAAAAAAAA@@@@@@AAAAAABBBBBBBBBBBBAAAAAA@@@@@@@@@AAAAAAAAA@@@@@@@@@@@@@@@@@@@@@@@@??????AAA@@@>>>=========>>>>>>===<<<;;;;;;<<<<<<;;;999;;;<<<===>>>???????????????>>>===<<<;;;:::::::::999:::;;;;;;::::::<<<>>>===<<<;;;:::999999999999:::999888777777777888999777777777777777888999:::888888999999999999888888777777666777777888999999777777777777777888999999888888888888888777777666777777888999888777666555666777888888777777888:::777666444333222333555666555444333333222222222333555444444333222222333333222222222222222222222222444444333222222333333444333333333333333333333333333444555444333333444555555555444444444333333333222333333333333222111111111222333222000000000111111111111000000000//////...////////////000000000000000000000////////////...------,,,,,,------...,,,,,,,,,---///000///...///...---,,,,,,---...///---...///000000...,,,***,,,,,,,,,------.........------------------------++++++++++++++++++++++++)))***++++++,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,------,,,,,,,,,+++++++++***************)))***+++***)))((()))***((((((((((((((((((((((((************************'''(((((((((''''''(((((('''''''''((((((((())))))''''''((()))***))))))(((((((((((((((((((((((((((''''''((()))))))))))))))(((((((((((((((((((((((((((((())))))))))))((((((''''''((((((((((((''''''(((((('''&&&&&&((()))***&&&&&&'''''''''''''''&&&'''''''''&&&&&&%%%%%%$$$&&&&&&&&&'''''''''((((((&&&&&&%%%%%%&&&&&&'''(((%%%%%%&&&&&&&&&'''''''''))))))((('''&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$##############################""""""""""""######$$$$$$$$$$$$$$$###"""!!! !!!"""###$$$###""""""$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$####################################$$$$$$$$$$$$#########$$$$$$$$$$$$$$$###############$$$%%%%%%########################@@@AAABBBCCCDDDDDDCCCBBBAAA@@@@@@??????@@@@@@AAACCCCCCBBBAAAAAAAAAAAAAAACCCCCCBBBBBBBBBAAAAAAAAACCCCCCBBBAAAAAAAAABBBBBBDDDCCCCCCBBB@@@>>><<<;;;>>>>>>>>>???AAABBBAAA@@@@@@AAAAAAAAAAAA@@@??????@@@AAAAAABBBBBBAAAAAA@@@>>>>>>>>>>>>>>>>>>>>>>>><<<===??????>>>>>>>>>??????@@@AAAAAAAAAAAAAAAAAABBBBBBCCCCCCCCCCCCBBBBBB??????@@@AAAAAAAAA@@@@@@@@@@@@@@@@@@??????@@@@@@???>>>============??????===;;;::::::;;;;;;:::999;;;<<<===>>>???????????????>>>===<<<;;;;;;;;;;;;999:::;;;;;;::::::<<<>>><<<<<<;;;;;;::::::;;;;;;:::999888777777888999:::777777777777777888999:::888999::::::::::::999888888888888888888888999:::888777777777777888999999888888999999888888777666666777888888777666555444666777777777666777999;;;888777555444333333444444444444444333333444444555555444333222222222222222222222222222222222222222333333333333444444444444333333333333333333333333222444555444333333444666555555444444444333333333222333333333333222111111111222333222000000000111000000111111000000///.........////////////000000000000000000////////////......------------......---------...000111000///.........------.........---.../////////...---,,,------------------------,,,------......------,,,++++++++++++++++++++++++)))******+++++++++++++++,,,,,,------------,,,,,,***++++++++++++,,,,,,,,,---------,,,,,,+++++++++***+++,,,,,,------------************************)))***+++***)))((()))***)))))))))))))))))))))))))))))))))))))))*********'''((()))((('''&&&''')))''''''((((((((()))))))))&&&''')))*********)))(((((((((((((((((((((((((((''''''((()))))))))))))))))))))))))))))))))))))))(((((())))))))))))((((((''''''((((((((((((''''''((((((''''''(((((()))***%%%&&&''''''((('''''''''''''''''''''&&&%%%$$$$$$%%%%%%&&&&&&'''(((((((((&&&&&&&&&&&&&&&''''''(((%%%&&&&&&&&&''''''''''''((((((((('''&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################""""""""""""############$$$$$$$$$######""""""""""""#########$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#################################$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$???@@@@@@AAABBBCCCCCCCCC@@@??????>>>>>>??????@@@CCCCCCCCCCCCBBBAAA@@@???@@@AAABBBCCCCCCCCCBBBAAACCCBBBAAA@@@???@@@@@@AAABBBBBBBBBAAA@@@>>>===<<<===???AAAAAAAAAAAABBBCCC@@@AAAAAAAAAAAA@@@???????????????@@@@@@?????????;;;<<<<<<======>>>>>>???<<<>>>@@@AAA@@@??????@@@???@@@AAAAAABBBBBBAAAAAABBBCCCDDDDDDDDDDDDCCCBBB??????AAABBBBBBBBBAAAAAA@@@???????????????@@@@@@======<<<<<<===>>>@@@AAA<<<;;;::::::;;;;;;:::888;;;;;;<<<===>>>>>>>>>>>>>>>>>>===<<<<<<;;;<<<<<<999:::;;;;;;::::::<<<>>>;;;;;;;;;;;;;;;<<<<<<===:::999777666666888999:::888777777888999:::;;;;;;999999:::;;;;;;:::999999;;;:::999999999999999999888888777777888888999:::888888999999999888777666555666777888888888777666555666777666555666999;;;888888777555444333222111444444444444555666777777666666444333333222222222333333333333333333333333111222333555555555444444333333333333333333333333222333555444333333444666555555444444444333333333222333333333333222111111111222333222000000000111111111222222222111000///........./////////000000000000000000////////////......------------...............///111222111000------............---------------........................------,,,,,,++++++,,,------------,,,+++************************))))))***++++++++++++++++++,,,------------,,,+++******+++++++++,,,,,,,,,......---,,,++++++******)))***+++,,,---.........************************)))***+++***((((((((()))))))))))))))))))))))))))''''''((((((((()))))))))&&&((())))))'''&&&''')))'''((((((((())))))))))))&&&''')))*********((((((((((((((((((((((((((((((''''''((()))))))))))))))))))))))))))))))))))))))(((((())))))))))))((((((''''''((((((((((((''''''''''''((()))))))))))))))%%%&&&&&&'''(((((('''''''''''''''''''''%%%$$$###%%%%%%&&&&&&'''(((((()))&&&&&&&&&&&&&&&'''((((((&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################""""""""""""######""""""###$$$$$$$$$######%%%$$$"""""""""###%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#################################$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$?????????@@@AAABBBCCCDDD??????>>>>>>>>>>>>??????CCCDDDDDDDDDCCCAAA???======???AAADDDEEEDDDCCCBBBCCCBBB@@@???>>>??????@@@@@@@@@@@@@@@@@@???>>>===<<<@@@CCCCCCAAA@@@BBBEEE@@@AAAAAAAAAAAA@@@??????======>>>>>>>>>>>>======<<<<<<===>>>???@@@AAAAAA===???AAABBBAAA@@@@@@AAA???@@@AAAAAABBBBBBBBBBBBBBBCCCDDDEEEEEEDDDCCCBBB???@@@BBBCCCDDDCCCBBBBBB@@@???????????????@@@@@@<<<<<<<<<<<<===>>>@@@AAA<<<;;;999:::;;;;;;:::888:::;;;<<<===>>>>>>>>>>>>>>>>>>===<<<<<<<<<<<<===888:::;;;;;;:::;;;===???;;;;;;;;;;;;;;;<<<===>>>:::999777666666888999;;;999999999999:::;;;<<<===999999;;;;;;;;;;;;999999<<<<<<;;;:::999999999999888888888777888888999:::888888999:::999888777666333444666888999999999999555555666555555666888;;;888888888666555333111000444444444555666777888999888777666555444333333333444444444444444444444444000111444666666666555444333333333333333333333333222333444444333333555666555555444444444333333333222333333333333222111111111222333222000000000111222222333444333222111000............/////////000000000000000////////////......------------....../////////000222333222111,,,---...//////...---,,,---------------...///000//////...---,,,++++++***++++++,,,------,,,++++++************************))))))***++++++++++++******+++,,,------,,,+++************++++++,,,,,,,,,//////...---+++***))))))((()))+++,,,---.........******************++++++***++++++***((((((((()))))))))))))))))))))))))))&&&'''''''''(((((())))))&&&(((***)))&&&%%%''')))(((((((((((())))))))))))&&&''')))***+++***((('''))))))))))))))))))))))))'''(((((()))))))))))))))))))))))))))))))))))))))(((((())))))))))))((((((''''''((((((((((((''''''&&&''')))*********)))(((%%%%%%&&&'''((((((((('''''''''(((((('''%%%$$$"""%%%%%%&&&&&&'''((())))))'''&&&&&&&&&&&&'''((((((&&&&&&&&&'''''''''((((((&&&&&&&&&'''''''''''''''$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$######################################################""""""""""""######!!!"""###$$$$$$$$$$$$$$$&&&%%%###!!!"""$$$&&&((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$CCCCCCBBBAAAAAA@@@?????????@@@AAA@@@??????AAACCCGGGFFFDDDBBB@@@??????>>>===???@@@BBBCCCCCCBBBBBBAAAAAABBBBBBAAA???>>>===BBBBBBBBBCCCBBBBBBAAAAAA===>>>@@@AAABBBAAAAAA@@@>>>>>>?????????@@@@@@@@@??????@@@@@@@@@@@@?????????>>>>>>>>>???@@@AAAAAA===>>>???@@@AAA@@@??????===>>>???@@@AAAAAAAAAAAADDDDDDCCCCCCCCCDDDDDDEEEEEEDDDDDDCCCCCCCCCCCCDDD@@@???===>>>???@@@@@@???>>>>>>============>>>>>><<<;;;;;;:::::::::;;;;;;;;;<<<===<<<;;;;;;<<<===999;;;<<<<<<<<<<<<===???;;;<<<<<<<<<;;;:::999999;;;:::888777777888:::;;;>>><<<:::888666555666666666666888999:::;;;;;;;;;:::::::::::::::::::::999::::::888888888999:::;;;;;;:::::::::::::::;;;;;;777888:::;;;;;;:::888777333444666777777777666555444555666777777666555444666777888777555333444555333444555777777777666555555555666666666666555555555555444444444333333333333333333333333333333333000000000111111222222333000111333333333333555666666555444333333333333333222333444555555444333222666333222333555666444222555444222000///000000111000000000000////////////111111000///////////////////////////////////////...000///...000333222---///000111111111///...---***+++,,,---............---------.........//////------------------------***,,,------++++++,,,...***+++,,,,,,------,,,,,,))))))***++++++++++++***)))******+++---...//////111000///...---,,,++++++*********++++++,,,,,,---))))))))))))))))))))))))((((((***++++++,,,+++++++++***)))'''''''''((()))((((((((((((((((((((((((*********)))))))))))))))******))))))))))))******+++***)))((('''''''''((())))))))))))))))))))))))&&&&&&&&&'''''')))******))))))))))))))))))))))))((((((''''''''''''((()))''')))***)))'''&&&&&&'''&&&&&&&&&'''''''''((((((&&&&&&''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&'''''''''(((((('''&&&&&&&&&&&&'''((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''((('''''''''&&&&&&%%%%%%%%%$$$%%%%%%&&&%%%$$$"""!!!########################""""""#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&'''''''''&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$###""""""###$$$%%%###$$$$$$%%%%%%$$$$$$###%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$CCCCCCBBBAAAAAA@@@?????????@@@AAA@@@??????AAACCCEEEDDDCCCAAA@@@?????????>>>???AAABBBCCCBBBBBBAAACCCCCCDDDDDDCCCBBB@@@???AAABBBBBBCCCBBBBBBAAAAAA>>>???@@@AAAAAAAAA@@@@@@>>>>>>?????????@@@@@@@@@??????@@@@@@@@@@@@??????>>>>>>>>>>>>>>>???@@@AAA??????AAABBBBBBBBBAAA@@@>>>???@@@AAAAAABBBBBBBBBCCCCCCCCCCCCCCCDDDEEEEEEEEEEEECCCBBBBBBCCCCCCDDDBBB@@@>>>???@@@AAA@@@???>>>>>>============>>>>>>===<<<;;;;;;::::::::::::;;;<<<===<<<;;;;;;<<<======>>>>>>===:::999999:::<<<<<<<<<<<<<<<;;;::::::;;;:::999888888999::::::===<<<:::888777666666555666666888999:::;;;;;;;;;999999::::::::::::::::::;;;:::999888888888999::::::999999999999999::::::777888:::;;;;;;:::888777444555666777888777777666666666777888888777666666666777888777555333444555444555666888888888777666555555666666666666555555555555444444444333333333333333333333333333333333111111222222222222222222000222333333333333444666666555444333333333333444333444444444444444444333444222111222555666555333444333222000000000000111/////////000000000000000111111000///////////////////////////////////////...000000...000333222...//////000000000///...---++++++,,,---............---------.........//////------------------------+++,,,------++++++,,,---***+++,,,,,,------,,,,,,))))))***+++++++++++++++)))***+++,,,---......///111000///...---,,,+++++++++++++++++++++,,,,,,,,,++++++++++++++++++++++++)))))))))))))))*********+++***)))((('''(((((()))((((((((((((((((((((((((***)))))))))))))))))))))******))))))))))))******+++******)))((((((((()))************************(((((((((((()))***++++++)))))))))))))))))))))))))))((((((''''''(((((()))''')))***)))(((&&&&&&'''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''(((((((((''''''''''''((())))))((((((((((((((((((((((((''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&'''(((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""########################""""""#########$$$$$$$$$""""""############$$$$$$%%%$$$$$$######$$$$$$%%%&&&&&&''''''&&&&&&%%%$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$###""""""###$$$%%%###$$$$$$%%%%%%$$$$$$###%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$CCCBBBBBBAAAAAA@@@@@@???@@@AAAAAAAAA@@@@@@BBBCCCCCCBBBAAA@@@@@@?????????@@@AAABBBCCCCCCBBBAAA@@@CCCCCCDDDDDDCCCBBBAAA@@@AAAAAABBBBBBCCCBBBBBBAAA@@@@@@AAAAAAAAA@@@?????????????????????@@@@@@@@@??????@@@@@@@@@@@@??????============>>>???@@@AAA@@@AAABBBCCCCCCCCCBBBBBB@@@@@@AAAAAABBBBBBCCCCCCBBBBBBBBBCCCCCCEEEFFFGGGFFFEEECCCAAAAAABBBCCCDDDCCCBBB@@@@@@AAAAAA@@@>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>===<<<;;;::::::::::::;;;<<<===<<<;;;;;;<<<======>>>>>><<<:::888888999===============<<<<<<;;;;;;;;;;;;::::::999999999;;;;;;;;;:::999777666555666666888999::::::;;;;;;888888888999:::::::::;;;;;;;;;:::999888888888999999999888888888888888999777888999::::::999888777666777777888999888888888777777888888888888777777666777888777555333444555666666777888888888777777555555666666666666555555555555444444444333333333333333333333333333333333333333333333333333222222000222333333333333444666555555444333333333444444555444444333333444444555333222222333444555555444444333222111000000000000...//////000000111111111111111000/////////000000////////////////////////...000000///000444222........./////////...------+++,,,---...////////////------........./////////........................---......---+++******+++***+++,,,,,,------,,,,,,)))******+++++++++++++++******+++,,,---......///000000///...---,,,,,,+++,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,+++***)))((('''((())))))******)))((((((((())))))(((((((((((((((((((((((())))))))))))))))))************))))))))))))******++++++******)))*********++++++++++++++++++++++++))))))))))))***+++,,,,,,))))))))))))))))))))))))***))))))(((((()))))))))''')))***)))(((''''''(((&&&''''''''''''(((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&''''''''''''(((((((((((((((((((((((()))******((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$#######################################$$$$$$$$$"""#########$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$###""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$BBBBBBBBBAAAAAA@@@@@@@@@@@@AAABBBAAA@@@AAABBBDDDAAAAAA@@@?????????@@@@@@AAABBBCCCCCCCCCBBBAAA@@@@@@AAABBBBBBBBBAAA???>>>AAAAAABBBBBBCCCBBBBBBBBBAAAAAAAAAAAA@@@??????>>>??????????????????????????????@@@@@@@@@@@@??????<<<<<<<<<<<<===>>>@@@@@@AAAAAAAAABBBBBBBBBBBBBBBAAAAAAAAAAAABBBBBBCCCCCCAAAAAABBBBBBDDDEEEGGGGGGGGGEEECCCAAA@@@AAACCCDDDDDDCCCAAAAAABBBAAA???===>>>>>>>>>??????>>>>>>>>>???>>>===<<<::::::999999;;;<<<===<<<;;;;;;;;;===999;;;<<<;;;:::999:::<<<======>>>>>>>>>>>>======;;;<<<<<<<<<;;;:::999888:::;;;;;;;;;:::888666555666666888999999:::::::::666777777888999::::::;;;;;;;;;:::999999888888888999888888777777777777888777888888999999888888777888888888999999999:::999777777777777777777777777666777888777555333444555666666666777777777666666555555666666666666555555555555444444444333333333444444444444444444444444555555555444444333333222111222444333333222444555555444444333333333444444555444333222222333444555444444333333333333222222333222222111111000000000......///000111111222222111111000000///000000111///////////////////////////111111///111444333///..................------------...///////////////............////////////////////////////////////...//////---+++))))))******+++,,,,,,------,,,,,,)))***++++++,,,,,,++++++++++++,,,,,,---......///000//////...------,,,,,,---------,,,,,,++++++***,,,,,,,,,,,,,,,,,,,,,,,,...,,,***((('''''')))*********))))))))))))))))))(((((((((((((((((((((((()))))))))))))))***************))))))))))))******+++++++++******+++,,,,,,++++++++++++++++++++++++)))))))))))))))***+++,,,))))))))))))))))))))))))+++******))))))))))))***'''(((******((('''(((((('''''''''''''''((((((((('''''''''''''''&&&&&&&&&''''''''''''(((((((((((('''''''''''''''(((((((((((((((''''''(((((()))***((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&%%%%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$#########%%%%%%#########################################################$$$%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%%%%&&&&&&'''&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###!!! """$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$BBBBBBAAAAAAAAAAAA@@@@@@AAABBBCCCBBBAAAAAACCCEEEAAA@@@@@@??????@@@@@@AAAAAABBBCCCCCCCCCBBBAAA@@@@@@AAABBBBBBBBBAAA@@@???@@@AAAAAABBBCCCCCCCCCBBBBBBAAAAAA@@@@@@???????????????????????????????????????@@@@@@@@@@@@??????;;;;;;<<<<<<===???@@@AAA@@@@@@@@@@@@@@@AAAAAAAAABBBBBBAAAAAAAAABBBCCCDDDAAAAAABBBBBBDDDEEEGGGGGGFFFEEECCCAAA@@@AAABBBBBBCCCBBBBBBBBBBBBAAA???===>>>>>>????????????>>>>>>@@@???===<<<;;;::::::999;;;<<<===<<<;;;;;;;;;===999;;;<<<;;;::::::;;;=========>>>>>>>>>>>>>>>===;;;<<<<<<<<<<<<;;;:::999:::;;;;;;;;;:::999777555666777777888999999999999666666777777888999::::::::::::::::::999999888888::::::999888888777888888888888888999999888888888999999999999999::::::;;;666666666666666666666666666777888777555333444555555555555555555555555555555555666666666666555555555555444444444333333333444444444444444444444444666555555444444333333333111333444444222222333555444444333333333444444555555444333222222333444555666666555444222000000000222222222222111111111000...//////000111222222333111111000000000000111111000000000000000000000000000222222000222555444///......---------...............//////000000//////........./////////000000////////////////////////...//////---+++))))))******+++,,,,,,------,,,,,,******+++,,,,,,,,,,,,+++,,,,,,,,,------......////////////...------,,,,,,...------,,,,,,+++++++++++++++++++++++++++++++++000...,,,)))((()))***+++))))))******************))))))))))))))))))))))))(((((())))))******************))))))))))))******++++++******+++,,,------************************))))))((((((((()))******))))))))))))))))))))))))++++++***)))))))))))))))'''(((******)))(((((()))(((((((((((((((((((((((((((((('''''''''&&&&&&&&&'''''''''((((((((())))))((((((((((((((((((((((((''''''&&&&&&''''''((()))(((((((((((((((((((((((('''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$%%%&&&""""""""""""""""""""""""######################## !!!!!!"""###$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$###$$$$$$%%%%%%$$$$$$###"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!! """$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$AAAAAAAAAAAAAAAAAAAAAAAABBBCCCCCCCCCBBBBBBDDDEEEBBBAAAAAA@@@@@@@@@@@@AAAAAABBBCCCDDDDDDCCCBBBAAABBBCCCDDDEEEEEEDDDCCCBBB@@@@@@AAABBBCCCCCCCCCCCCAAAAAA@@@??????@@@@@@@@@@@@@@@@@@?????????????????????@@@@@@@@@@@@??????;;;;;;<<<===>>>@@@AAABBB??????>>>>>>>>>???@@@AAACCCBBBAAA@@@@@@AAABBBCCCBBBBBBBBBCCCCCCEEEFFFGGGEEEEEECCCBBBAAAAAA@@@@@@BBBAAAAAABBBBBBBBB???======>>>???@@@@@@???>>>===???>>>===<<<;;;;;;;;;;;;;;;<<<===<<<;;;;;;<<<===<<<===>>>===;;;::::::;;;<<<======>>>>>>>>>>>>>>><<<<<<<<<<<<<<<<<<<<<<<<;;;;;;;;;;;;:::999888777666777777888999999888888666666666777888888888999888999999:::::::::999888<<<<<<;;;:::999999999999999999999999999999999999:::999999999999:::;;;;;;666666555555555555666666666777888777555333444555666555444333333333444444555555666666666666555555555555444444444333333333444444444444444444444444444444444444444444333333222333444444222222333444444444333333333444555555555444444333333444444555666666666444111//////000111111222222222111111000///000000111111222222222111111000000000111222222000000000000000000000000000222222111222666444000.........---......///000//////000000000000//////....../////////000000000...........................//////---+++))))))******+++,,,,,,------,,,,,,***++++++,,,,,,,,,,,,,,,,,,,,,------............//////.........---------------------,,,,,,,,,,,,++++++++++++++++++++++++///...,,,+++******++++++((()))***+++++++++******))))))))))))))))))))))))((((((((()))******++++++******))))))))))))******************+++,,,---...))))))))))))))))))))))))))))))((((((((())))))***))))))))))))))))))))))))+++******)))(((((((((((('''(((******)))((()))***)))))))))(((((((((((('''((((((((('''&&&&&&%%%%%%'''''''''(((((())))))***)))))))))(((((((((((('''&&&&&&&&&&&&&&&'''((((((((((((((((((((((((((((((''''''''''''''''''''''''''''''&&&%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%""""""""""""""""""""""""$$$$$$$$$############### !!!!!!"""%%%$$$$$$######$$$$$$%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$###!!!"""$$$%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!!!!"""###%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$AAAAAAAAAAAAAAAAAAAAAAAABBBCCCDDDCCCBBBBBBDDDFFFCCCCCCBBBAAAAAA@@@AAAAAA@@@AAABBBDDDDDDDDDCCCCCCBBBCCCDDDEEEEEEDDDCCCBBB???@@@AAABBBCCCCCCCCCCCCAAA@@@?????????@@@AAABBB@@@@@@@@@?????????>>>>>>??????@@@@@@@@@@@@??????<<<<<<<<<===???AAABBBCCC??????>>>===>>>???@@@AAACCCAAA@@@??????@@@AAABBBCCCCCCCCCCCCCCCDDDEEEEEEDDDDDDDDDDDDCCCAAA???>>>?????????AAABBBBBB???======>>>@@@AAAAAA@@@>>>===>>>>>>===<<<<<<<<<<<<<<<;;;<<<===<<<;;;;;;<<<===<<<===>>>>>><<<<<<===>>>;;;<<<======>>>>>>>>>===<<<<<<;;;;;;;;;===>>>???<<<;;;::::::999999999999666777777888888888888888666777777777777777777777666777999:::;;;;;;::::::???>>>===<<<;;;;;;;;;;;;;;;::::::::::::::::::;;;:::999888888888999;;;;;;777777666555555666777777666777888777555333444555777666555444333444444555555555666666666666555555555555444444444333333333555555555555555555555555333333333333333444444444222333444444222222333444333333333333333444555666333444444444444444444333222444555444111///000222000111222222222222111000111111111111111111111111111111000000111111222333000000000000000000000000111333333111333666555111//////.........///000111000000000111111000000///.../////////000000000000---------------------------......---+++******+++***+++,,,,,,------,,,,,,***+++,,,,,,------,,,,,,------------...........................---------,,,,,,,,,---------------,,,,,,,,,,,,,,,,,,,,,,,,---,,,,,,++++++*********((()))***++++++++++++***))))))))))))))))))))))))'''(((((()))******++++++******))))))))))))******(((((())))))+++,,,---...************************+++******))))))*********))))))))))))))))))))))))+++***)))((('''''''''''''''(((******))))))***+++))))))))))))(((((((((''')))(((((('''&&&&&&%%%%%%&&&''''''((())))))******))))))))))))(((((((((''''''''''''''''''(((((()))((((((((((((((((((((((((((((((((((((((((((((((((((('''&&&%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%"""###$$$%%%%%%%%%%%%%%%""""""""""""""""""""""""$$$$$$$$$#########"""""" !!!""""""%%%$$$$$$######$$$$$$%%%$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$%%%&&&&&&%%%$$$$$$###$$$$$$%%%%%%$$$$$$### """$$$&&&&&&&&&%%%$$$########################""""""######$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$AAAAAAAAAAAAAAAAAAAAAAAABBBCCCDDDDDDBBBCCCDDDFFFEEEDDDCCCBBBAAAAAAAAAAAA???@@@BBBDDDEEEEEEDDDDDD@@@AAABBBCCCCCCCCCBBBAAA???@@@AAABBBCCCCCCCCCCCC@@@@@@?????????@@@BBBCCC@@@@@@@@@@@@??????>>>>>>??????@@@@@@@@@@@@??????<<<<<<===>>>???AAACCCDDD@@@???>>>>>>>>>???@@@AAABBBAAA???>>>>>>???AAABBBDDDDDDCCCCCCCCCDDDDDDEEECCCCCCDDDEEEDDDAAA???===>>>>>>???@@@BBBAAA???======>>>@@@AAAAAA@@@>>>===>>>======<<<<<<<<<======;;;<<<===<<<;;;;;;<<<===888:::<<<===>>>???AAACCC;;;;;;<<<===============<<<;;;::::::;;;===@@@AAA===<<<:::999888999999:::666777777888888888888777777777777777666666666666555666888:::;;;;;;;;;:::@@@@@@???======<<<<<<<<<<<<;;;;;;::::::;;;;;;<<<:::999888777888999:::;;;999888777666666777888999666777888777555333444555888777666555444444555666555555666666666666555555555555444444444333333333555555555555555555555555222222222333333444444444222444444444222222333444333333333333333444555666222333555555555555333222///222444333111111333555000000222333333222111000222222222111111111111111111111000000111222333333000000000000000000000000111333333111333666555111000///......///000111222000000111111111000000///////////////000000000000---------------------------......---+++******+++++++++,,,---------,,,,,,***+++,,,,,,------,,,,,,---------..............................---------,,,,,,,,,------.........------------------------***++++++++++++***))))))((()))***+++,,,,,,+++***))))))))))))))))))))))))'''(((((()))***+++++++++******))))))))))))******((((((((()))***,,,---...++++++++++++++++++++++++,,,,,,++++++***+++++++++))))))))))))))))))))))))******((('''&&&&&&&&&&&&'''(((*********)))***+++******))))))((((((((('''))))))((('''&&&&&&%%%%%%&&&''''''((()))******+++******))))))((((((((('''((((((((((((((()))******(((((((((((((((((((((((())))))))))))))))))))))))((('''&&&%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%!!!###$$$%%%&&&%%%%%%$$$""""""""""""""""""""""""$$$$$$$$$$$$######"""""" !!!"""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$%%%%%%&&&'''''''''&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$ """$$$&&&'''&&&%%%$$$########################!!!"""###%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$BBBAAAAAA@@@@@@AAAAAABBB???@@@@@@AAABBBCCCDDDDDDHHHGGGFFFDDDCCCCCCCCCCCCCCC???<<<<<>>???BBBDDDCCCAAADDDCCCAAA@@@???@@@@@@AAA@@@@@@AAABBBBBBBBBAAAAAA===>>>???AAAAAAAAA@@@???BBBBBBAAA@@@???>>>>>>===??????@@@@@@AAABBBCCCCCCEEEEEEDDDCCCCCCCCCCCCCCCCCCDDDEEEFFFFFFEEEDDDCCCBBBBBBBBBBBBAAA@@@???>>>:::;;;;;;;;;<<<<<<======??????@@@@@@@@@>>>===;;;<<<<<<============<<<<<<===<<<;;;:::;;;===???@@@;;;;;;;;;;;;<<<>>>???AAA<<<;;;;;;:::;;;<<<===>>>???>>><<<:::999777777777888888999999999999888888999999999888888888888888999999999999::::::;;;<<<:::::::::;;;;;;<<<<<<<<<>>><<<::::::;;;;;;888555777777666666777888999999777888999:::999777555333777666666555555555666666777777666666666666777777444555555555666666777777777555333555777777444111222333444555666666666666333444555555666666555555555555555555555555555555333333333333333333333333222111222333555555333111444444444444333333222111444444222222222222444444333333444555555444333333111111000000000000111111000000000000000000000000000222222000222666555000///////////////......---111111111111111111111111////////////..................---------,,,,,,,,,+++++++++++++++++++++,,,((()))+++---------+++***+++,,,------......------,,,---......//////......//////000000///...------...---,,,+++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***)))(((((((((((()))***+++,,,,,,+++***)))))))))***++++++++++++******************++++++,,,******))))))))))))******,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,+++******+++---,,,++++++++++++++++++,,,+++*********))))))(((((())))))((('''''''''''''''&&&&&&&&&'''((())))))***))))))************))))))(((((('''''''''&&&&&&&&&''''''''''''''''''''''''************))))))))))))))))))))))))((((((((((((&&&'''''''''''''''&&&&&&((((((((((((''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$#########$$$$$$$$$$$$###""""""!!!!!!!!!!!!"""###%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###"""############$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBCCCCCCEEEEEEDDDCCCCCCCCCDDDDDDCCC@@@>>>>>>AAACCCBBBAAABBBAAA@@@AAACCCDDDCCCBBBAAAAAA@@@@@@@@@@@@AAAAAABBB???>>>>>>AAABBBAAA@@@CCCBBBAAA@@@@@@@@@AAABBBAAAAAAAAABBBBBBAAA@@@@@@======>>>???????????????DDDDDDCCCCCCBBBAAAAAAAAAAAAAAAAAABBBBBBBBBBBBBBBEEEDDDDDDCCCCCCCCCCCCCCCAAAAAABBBCCCCCCCCCCCCCCCCCCBBBBBBAAA@@@@@@??????<<<=========>>>>>>>>>>>>>>>?????????>>>======<<<======>>>>>>>>>>>>======>>>===<<<;;;;;;<<<>>>???>>>===<<<;;;;;;<<<===>>>;;;::::::999:::;;;<<<===>>>===<<<:::999888777777888888999999999999888888999999999888888888888888999999999999999:::;;;<<<:::::::::::::::;;;;;;;;;<<<999777888:::;;;:::999777777777777777888999999999:::::::::999888666555888777777666666777777777777777666666666666777777666666666777777777888888777555444444666666555222333444555555666555555555333444555555666666555555555555555555555555555555333333333333333333333333222222222333555555333222444444444444444333222111444333333222222333333444222333444555555444333222111111000000000000000111000000000000000000000000///111111000222666555111000000000000//////...---111111111111111111111111////////////////////////......---------,,,,,,,,,---,,,,,,,,,+++*********)))***,,,---...---,,,++++++,,,------......------,,,------...............///////////////...------......---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---,,,+++***)))))))))))))))***++++++++++++***)))))))))***+++++++++++++++***))))))))))))***++++++******))))))))))))******,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,+++******+++---++++++************++++++************)))))))))((())))))((('''''''''''''''&&&&&&''''''((())))))***))))))************))))))(((((('''''''''&&&&&&&&&''''''''''''''''''''''''))))))))))))))))))))))))))))))))))))((((((((((((''''''((((((((((((''''''((((((((((((''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$#########$$$$$$$$$$$$###""""""""""""!!!""""""###$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###"""############$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%BBBCCCDDDEEEEEEDDDCCCBBBDDDDDDCCCCCCBBBBBBBBBBBBCCCCCCBBBBBBCCCDDDDDDEEEBBBAAA@@@AAACCCCCCCCCAAABBB@@@@@@AAACCCCCCCCCBBBBBBBBBBBBAAAAAABBBBBBBBBBBB@@@>>>>>>???@@@@@@???BBBAAA@@@@@@@@@AAABBBCCCBBBBBBBBBBBBAAA@@@@@@?????????>>>>>>>>>???@@@@@@CCCCCCCCCCCCCCCCCCCCCCCCBBBBBBCCCCCCCCCCCCCCCBBBEEEDDDCCCCCCBBBBBBCCCCCCBBBAAAAAAAAABBBCCCDDDDDDDDDCCCAAA@@@??????@@@@@@???????????????@@@@@@@@@>>>>>>======<<<=========>>>>>>????????????>>>>>>???>>>===<<<;;;<<<===>>>@@@???>>><<<;;;;;;;;;;;;;;;:::999999999:::;;;<<<>>>===;;;:::999888888888888888999999999999888888888888888999999999999999:::999999999999::::::;;;:::::::::::::::999999999999777555666888:::<<<<<<888777777777777888999999;;;;;;::::::999888888888888888888777777888888999888777777666666777777888777777888888888888999999888666444333444555555555555555555666555555444333333444555555666666555555555555555555555555555555333333333333333333333333222222222333555555444222333444444444444333333222444333333222222333333444222333444555555444333222222222111000//////000000000000000000000000000000...000111000333777666222222222111000000///......111111111111111111111111////////////000000000000......---------,,,,,,,,,......---,,,+++***))))))***+++---......---,,,,,,+++,,,------......------,,,,,,---........................///......---,,,//////...------------...,,,,,,,,,,,,,,,,,,,,,,,,------,,,+++************)))***++++++++++++***)))))))))******++++++++++++))))))((((((((()))************))))))))))))******,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,+++******+++---*********))))))*********************))))))))))))))))))((('''''''''''''''&&&&&&''''''((()))))))))((())))))******))))))((('''''''''''''''&&&&&&&&&''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))(((((())))))))))))((((((((((((((((((''''''''''''&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$#########$$$$$$$$$$$$###""""""######"""""""""######$$$&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###"""############$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%BBBCCCEEEFFFFFFEEECCCBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCBBBBBBBBBBBBCCCDDDBBBBBBBBBCCCDDDDDDCCCBBBBBBAAAAAABBBDDDEEEDDDCCCEEEDDDDDDCCCCCCDDDDDDEEECCCBBB@@@@@@@@@@@@??????AAA@@@@@@???@@@AAACCCDDDCCCCCCCCCBBBAAA@@@???>>>AAAAAA?????????@@@AAABBB@@@@@@AAAAAAAAABBBBBBBBBAAAAAACCCDDDEEEEEEEEEEEEDDDDDDCCCBBBBBBBBBBBBCCCFFFEEECCCBBBBBBCCCDDDEEEDDDCCC@@@>>>>>>>>>@@@AAA@@@@@@@@@@@@@@@@@@@@@@@@>>>===<<<;;;;;;<<<===>>>?????????@@@@@@?????????@@@???>>>===<<<<<<======???>>>>>>===<<<;;;;;;;;;<<<;;;:::::::::;;;<<<======<<<;;;:::999888888888888888999999999999888888888888888999999::::::::::::999999999999999::::::::::::999999999999888888999888666555666888;;;<<<888888888777777888999999;;;:::999888888888888999888888777777777888999999888777777777777777777888888888888888888888888888999777555333333555666666666666666666555444333222333444555555666555555555444444444444444444444444444444444444444444444444333222111222444555444333333444444444444444333333333333333333333333333333222333444444444444333222333222111000////////////////////////////////////---000000000333777777333333333222111000//////...111111111111111111111111/////////000000000000000......---------,,,,,,,,,---------,,,,,,++++++***,,,,,,---......------,,,+++,,,------......------,,,,,,---.........------------............------//////............//////,,,,,,,,,,,,,,,,,,,,,,,,---,,,+++************************++++++************************+++++++++((((((((((((((())))))***+++******))))))******+++,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,+++******+++---******))))))))))))***************)))))))))))))))))))))((('''''''''''''''''''''''''''(((((())))))(((((())))))))))))((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''(((((((((((())))))))))))(((((()))************)))((((((((((((''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$$$$$$$###""""""$$$$$$######"""#########&&&''''''''''''''''''&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###""""""#########$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%AAABBBDDDFFFFFFDDDBBBAAABBBBBBCCCDDDDDDEEEFFFFFFEEEEEECCCBBBBBBAAAAAAAAABBBCCCDDDDDDDDDCCCBBBBBBDDDCCCBBBCCCFFFGGGFFFEEEDDDDDDCCCCCCCCCCCCDDDDDDCCCCCCCCCBBBAAA@@@AAAAAAAAA@@@@@@???@@@AAACCCDDDCCCCCCCCCBBBAAA@@@???>>>@@@???>>>======>>>???@@@??????@@@@@@AAABBBBBBBBB>>>@@@BBBEEEFFFGGGGGGFFFDDDDDDCCCBBBBBBBBBBBBBBBHHHFFFDDDCCCBBBBBBBBBCCCDDDBBB@@@>>>===>>>???@@@????????????????????????===<<<;;;;;;;;;===>>>?????????@@@@@@@@@@@@????????????>>>>>>============;;;<<<<<<===============>>>===<<<;;;;;;<<<===>>><<<;;;::::::999999999999888888999999999999888888777777888999:::;;;;;;;;;:::999999888888999999999999999999999999999999999;;;:::888666555666888:::999999888888888888888999999999888777777777777888666666666666777777888999888888777777777777888888777777777777777777777777888777666444333444666777777777666666555444222222333444555555666555555555333333333333333333333333444444444444444444444444333222111222444555444333333444444555555444444444333333333333333333333333222222333444444333222222222222111000//////000000////////////////////////---000000000333777777333333333111000////////////000000000000000000000000......//////000000000111......---------,,,,,,,,,+++++++++,,,,,,------------------------------,,,+++,,,------......------+++,,,,,,---...---------------......///......---//////.........//////000,,,,,,,,,,,,,,,,,,,,,,,,+++******))))))))))))***+++******************+++******)))))))))***+++,,,((((((((((((((())))))***++++++************++++++,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,+++******+++---******))))))))))))******))))))))))))))))))******))))))((('''''''''''''''''''''''''''(((((((((((((((((())))))))))))((((((&&&'''''''''''''''''''''''''''''''''''''''''''''%%%&&&&&&&&&'''''''''((('''((((((((()))))))))***(((((()))***++++++******((((((((((((''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$###$$$$$$$$$$$$###""""""%%%$$$###############$$$&&&''''''''''''''''''&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###""""""#########$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%BBBCCCDDDEEEEEEDDDCCCBBBBBBBBBCCCDDDEEEFFFGGGGGGGGGFFFEEECCCBBBAAAAAAAAABBBDDDDDDDDDBBBAAABBBCCCDDDCCCCCCDDDGGGHHHHHHGGGBBBBBBAAAAAAAAAAAABBBBBBCCCDDDDDDCCCAAAAAABBBDDDBBBAAA@@@@@@@@@AAABBBCCCBBBBBBBBBBBBAAA@@@@@@???======<<<;;;;;;;;;<<<<<>>>>>???????????????>>>>>>>>>>>>>>>;;;;;;<<<<<<===>>>???@@@??????@@@@@@@@@@@@??????>>>>>>>>>>>>>>>>>>======999:::;;;===>>>????????????>>>===<<<<<<<<<===>>>;;;;;;:::999999:::::::::888888999999999999888888777777888999:::;;;<<<===:::999999888888888888999999999999999:::::::::;;;===<<<;;;888666555777999::::::999888888888888999777777777777777777777777666666666666666777888999999888888777777888888999888777777777777666666666777888777666444444666888666666666666555444333222333444555555666666555555333333333333333333333333444444444444444444444444444222111111333444444444333444444555555555555444222333333444444333333222111222333444444333222111111111000000000000111111000000000000000000000000...000111000333777666222222111000///...///000111000000000000000000000000------......//////000000......---------,,,,,,,,,******+++,,,---...//////---------,,,,,,,,,,,,,,,+++,,,------......------++++++,,,------------------...//////000////////////............///000000,,,,,,,,,,,,,,,,,,,,,,,,******)))))))))))))))***++++++***))))))***+++++++++***)))))))))***,,,---))))))((((((((()))******++++++************++++++,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,+++******+++---*********))))))*********))))))))))))************))))))((('''''''''''''''''''''(((((((((((((((((('''(((((())))))(((((('''&&&&&&&&&'''''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&'''(((((((((''''''(((((())))))******'''((()))******+++******((((((((((((''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%$$$$$$###$$$$$$$$$$$$###""""""$$$$$$#########$$$$$$%%%&&&&&&''''''''''''&&&&&&%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###"""############$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%EEEEEEEEEEEEEEEEEEEEEEEEDDDDDDDDDEEEEEEFFFFFFFFFFFFEEEDDDDDDCCCCCCCCCCCCCCCDDDDDDBBB@@@???AAADDDDDDCCCCCCDDDGGGHHHHHHGGGDDDCCCCCCBBBBBBCCCCCCDDD@@@BBBCCCBBB@@@@@@BBBEEECCCBBBAAA@@@@@@@@@AAABBBAAAAAAAAABBBBBBAAA@@@@@@===============<<<;;;;;;@@@@@@AAAAAAAAAAAAAAAAAA???AAACCCEEEFFFEEECCCBBBDDDCCCBBBBBBAAAAAABBBBBB@@@AAAAAABBBBBBAAAAAAAAAAAAAAA@@@@@@???>>>>>>>>>@@@?????????>>>>>>>>>===:::;;;===>>>???@@@@@@@@@>>>>>>????????????>>>>>>===>>>>>>?????????>>>>>>999:::;;;===>>>??????>>>???>>>===<<<;;;<<<<<<===:::::::::999999:::;;;;;;888888999999999999888888666777888999;;;<<<===>>>::::::999888888888888888888888999:::;;;<<<<<<===;;;======:::777666777999;;;:::999999888888888999777777888999999999888777777777777777888999::::::999888888777777888888999999999888888888777777777666777999888555444555777555666666666555444333333333444555555666666555555555555555555555555555555555555555555555555555555444333111111333444444444333333444555555555555555222333333444444333333222111222333444444333222111////////////000111222333000000000000000000000000///111111000222666555111000///...------///000222000000000000000000000000,,,,,,,,,---.../////////......---------,,,,,,,,,+++,,,,,,,,,---.........------,,,++++++++++++++++++,,,------......------++++++,,,------------,,,...//////000111111000000...---------......///000,,,,,,,,,,,,,,,,,,,,,,,,+++******))))))******+++++++++***))))))***+++++++++***)))((()))***,,,---***))))))))))))***++++++,,,++++++******++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,+++******+++---++++++************++++++((()))))))))************))))))((('''''''''''''''((((((((((((((((((((('''''''''((((((((((((''''''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''%%%&&&&&&'''(((((())))))'''''''''((()))*********&&&'''((()))************((((((((((((''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&%%%%%%$$$######$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$###""""""############$$$%%%%%%&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###"""############$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%GGGGGGFFFEEEEEEFFFGGGGGGFFFFFFFFFFFFEEEEEEEEEEEEEEEDDDDDDDDDDDDEEEFFFFFFCCCDDDDDDAAA>>>>>>AAAEEECCCBBBBBBCCCFFFGGGGGGFFFGGGGGGFFFFFFFFFFFFGGGGGG>>>AAABBBAAA??????BBBEEEDDDCCCAAA@@@???@@@@@@AAA@@@@@@AAABBBBBBBBBAAAAAA???@@@AAAAAAAAA???>>>===>>>>>>>>>>>>>>>>>>>>>>>>AAACCCDDDFFFEEECCC@@@???CCCCCCBBBAAAAAAAAAAAABBB>>>@@@BBBDDDEEEEEEEEEDDD@@@@@@AAA@@@@@@???======@@@@@@@@@?????????>>>>>>:::;;;===???AAAAAAAAA@@@>>>>>>????????????>>>>>><<<===>>>???????????????:::;;;<<<>>>>>>>>>>>>===>>>===<<<;;;:::;;;;;;<<<::::::999999::::::;;;;;;888888999999999999888888666777888999;;;<<<>>>>>>::::::999888777777888888888888999:::<<<===>>>>>>:::<<<===<<<999777888:::;;;::::::999888888888999777888:::;;;;;;:::999777888888888888999:::;;;<<<999999888888888888999999:::::::::999999888888888555777:::999666444555777555555555666555555444333333444555555666666555555777777777777777777777777555555555555555555555555555333111111333444555444333333444555666666666555222222444444444444222222111222333333333333222111.../////////000222333444000000000000000000000000000222222000222666555000///...---,,,---///111222000000000000000000000000++++++,,,,,,---...//////......---------,,,,,,,,,---------------------,,,---,,,++++++*********++++++,,,------......------++++++,,,---------,,,,,,//////000111111111111111---------------...///000,,,,,,,,,,,,,,,,,,,,,,,,+++++++++***++++++,,,,,,,,,+++***))))))***+++,,,+++***)))((((((***,,,---***************++++++,,,,,,++++++******++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,+++******+++---,,,,,,++++++++++++,,,,,,(((((())))))*********+++))))))((('''''''''''''''((((((((((((((('''''''''''''''((((((((((((''''''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&&&&''''''((()))******&&&''''''((()))******+++&&&&&&((())))))*********)))(((((((((''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&'''''''''((((((''''''&&&%%%%%%$$$######$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$###""""""############$$$%%%&&&'''$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&'''''''''((((((''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$"""############$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%GGGGGGFFFFFFFFFFFFGGGGGGIIIHHHGGGEEEDDDDDDDDDDDDHHHHHHHHHHHHGGGEEEDDDCCCEEEEEEEEEEEEEEEDDDDDDDDDEEEDDDCCCCCCCCCEEEFFFGGGHHHGGGFFFEEEEEEDDDBBB@@@CCCCCCCCCCCCCCCDDDEEEFFFBBBBBBBBBBBBBBBBBBBBBBBBCCCCCCAAAAAAAAAAAACCCCCC@@@??????>>>===<<<<<<;;;??????>>>===============??????@@@AAABBBBBBBBBBBBEEEEEEDDDCCCBBBAAAAAA@@@@@@AAABBBCCCCCCCCCBBBAAACCCBBBAAA@@@@@@@@@AAABBBBBBAAA???===<<<======>>>AAA@@@@@@@@@@@@@@@@@@@@@===>>>??????>>>===???@@@======<<<<<<<<<<<<======AAA@@@>>>=========>>>???<<<<<<<<<<<<<<<<<<;;;;;;999888888888999;;;===>>>===:::666666888::::::999888888:::;;;;;;:::888888999::::::888777777:::<<<888888888999:::;;;===>>>CCC@@@<<<999888888:::<<<999888888888888888888999<<<999666666999;;;:::999777777777777888999:::;;;:::999888777777777999999;;;;;;:::999999888888777666666666666777777777777777666666666555555555555888888777666666666666666888888777666666666666666444444444333333222222222444444444555555555555666222222111111111222444555444444444333333222222222222222222111111111111000......//////000000111111000000000000000000000000000......111444555333000111000...------...///000222111111111000000//////,,,,,,------------,,,,,,...---,,,+++,,,---.../////////.........---------+++***))))))***,,,...///,,,,,,,,,,,,,,,,,,,,,,,,******+++,,,,,,---......///////////////////////////...------------...///,,,,,,,,,---------......,,,+++******))))))******...---,,,+++++++++,,,---******+++,,,,,,,,,+++++++++******))))))******+++))))))))))))************+++++++++,,,,,,---------,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,,,,,,,,,,+++***&&&&&&&&&'''((())))))******))))))((('''&&&&&&&&&&&&&&&''''''(((((())))))''''''''''''((((((((((((((('''&&&%%%%%%&&&'''((((((((((((((((((((((((((('''(((((((((((((((''''''&&&&&&'''((())))))(((((('''''''''(((***+++***)))))))))(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((())))))))))))((((((%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%%%%$$$###%%%&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%GGGGGGFFFFFFFFFFFFGGGGGGIIIHHHGGGFFFEEEEEEEEEEEEFFFFFFFFFFFFFFFFFFEEEEEEBBBBBBCCCCCCDDDDDDEEEEEEDDDDDDCCCCCCCCCDDDEEEFFFGGGGGGFFFEEEEEEDDDBBB@@@BBBAAAAAAAAAAAABBBCCCDDDDDDDDDDDDDDDDDDDDDDDDDDDCCCBBBAAA@@@@@@AAABBBCCC?????????>>>=========<<>>==================>>>???AAABBBCCCDDDDDDDDDDDDDDDCCCBBBBBBAAAAAA@@@AAABBBCCCCCCCCCBBBBBBBBBAAA@@@@@@@@@AAABBBBBBBBBAAA???>>>======>>>>>>AAAAAAAAA@@@@@@@@@@@@@@@===>>>??????>>>===???@@@======<<<<<<<<<<<<======???>>>===<<<<<<<<<======<<<<<<<<<<<<<<<<<<<<<<<<::::::999999:::;;;<<<===<<<:::777666888::::::999999999999999999999999999:::::::::999777777999;;;888888888888:::;;;<<<===AAA???===:::999:::;;;<<<:::999999888888999999:::===:::888888:::;;;:::999888888888777888888999::::::999888777777888999999:::::::::999999999999888777777777777777666666666777777666666666555555555888777666666555555666666888777777666666666666666555444444444333333333222444444444555555555555666222222111111111222444444444444444333333222222222222222222111111111111000/////////000000000000000000000000000000000000000111//////111444555222///000///...------...000111111111111111000000000///------............------......---,,,,,,---...............---------,,,,,,******))))))***+++---...,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,------...///////////////////////////...---,,,,,,---...///,,,,,,,,,---------......---,,,,,,+++++++++++++++,,,+++***)))))))))************+++,,,,,,,,,++++++++++++************++++++))))))))))))************+++++++++,,,,,,---------,,,,,,,,,,,,,,,,,,,,,,,,+++,,,------------,,,+++&&&&&&''''''((())))))******))))))(((''''''&&&&&&'''''''''(((((((((((((((''''''''''''((((((((((((((('''&&&&&&&&&&&&'''(((''''''''''''''''''''''''''''''((((((((((((''''''&&&''''''((((((((((((((('''''''''(((***+++***))))))(((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((((())))))(((((((((%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%%%%$$$###%%%&&&%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%GGGGGGFFFFFFFFFFFFGGGGGGHHHGGGGGGFFFEEEEEEEEEEEECCCDDDDDDDDDEEEEEEEEEFFF???@@@@@@AAACCCDDDDDDEEECCCCCCCCCBBBCCCCCCDDDEEEFFFFFFFFFFFFEEEDDDBBBBBBBBBBBBAAAAAABBBBBBCCCCCCDDDDDDDDDDDDDDDDDDDDDDDDBBBAAA@@@??????@@@AAABBB??????>>>>>>>>>>>>>>>>>>??????>>>=========>>>>>><<<===???AAABBBDDDDDDEEECCCCCCCCCCCCCCCCCCCCCCCCAAAAAABBBCCCCCCCCCCCCBBB@@@@@@@@@@@@@@@AAABBBCCCBBBAAA@@@??????>>>??????@@@@@@@@@@@@@@@@@@@@@@@@<<<===???>>>>>>===???@@@>>>======<<<<<<======>>>>>>===<<<;;;;;;;;;<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<;;;:::;;;;;;<<<<<<<<<999777777888::::::::::::999888888888888999::::::;;;;;;999777777888:::777777777888999:::;;;<<<>>>===<<<;;;;;;;;;<<<<<<;;;::::::999999::::::;;;>>><<<:::::::::;;;:::999:::999888888777888888888999888888777888888999999888888999999999:::::::::888888888777777666666555777777777666666666555555777666666555555555555666888777666666555555666666555555555444444444444444444444444555555555555666333222222222222333333444444444333333333333222222222222222111111111111000000000000000000000//////000000000000000000000000222000///111444444111...///...---------///000111111111111111000000000000......////////////......///...------------......---------,,,,,,,,,++++++))))))))))))***+++,,,---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------////////////////////////...------,,,,,,------...,,,,,,,,,---------.........---,,,,,,++++++,,,,,,,,,+++******))))))******)))***+++,,,,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,)))))))))*********++++++++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------,,,,,,&&&''''''(((((())))))******))))))((((((''''''&&&((((((((((((((('''''''''''''''''''''((((((((((((((('''&&&&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((((((((((((''''''''''''((((((((((((((('''''''''(((***+++***)))((((((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""$$$%%%%%%$$$###%%%&&&%%%&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%FFFEEEEEEEEEEEEEEEEEEFFFFFFFFFEEEDDDDDDDDDEEEEEEDDDDDDCCCCCCCCCDDDDDDDDD??????@@@@@@AAABBBBBBCCCCCCCCCBBBBBBBBBCCCCCCCCCEEEFFFFFFFFFDDDCCCCCCCCCEEEEEEDDDDDDDDDDDDEEEEEEBBBBBBBBBBBBBBBBBBBBBBBBAAAAAA????????????AAAAAA>>>>>>????????????????????????>>>>>>===>>>>>>???>>>???@@@AAABBBCCCCCCCCCBBBBBBBBBCCCCCCCCCDDDDDDAAABBBBBBCCCCCCCCCCCCCCC?????????@@@@@@AAABBBBBBBBBAAAAAA@@@@@@?????????>>>>>>>>>>>>>>>?????????;;;===>>>>>>======???@@@>>>>>>============>>>>>>=========<<<<<<<<<<<<<<<;;;;;;;;;<<<<<<<<<<<<<<<======<<<<<<;;;;;;;;;;;;:::999888888888999::::::;;;999777666666777999;;;:::;;;;;;:::888777888999888777777888999:::;;;;;;::::::;;;;;;;;;;;;;;;:::;;;;;;;;;::::::;;;;;;;;;>>>===<<<;;;;;;;;;;;;:::;;;:::999888777777777777888888888888888888999999777777888999::::::;;;;;;999999888888777666555555777777777666666666666555666666555555555555555666777777666555555555555666555555555555555555555555444444444555555555555666333333333333333333333333333333333333333333333333222222222111111111000000222111111000000/////////////////////////////////222111000111444444111---------------...000111222111111111000000000000000000000////////////000000/////////...............,,,,,,,,,+++++++++******))))))))))))******++++++,,,,,,,,,,,,,,,,,,,,,,,,---------------,,,,,,,,,////////////////////////------,,,,,,,,,,,,------,,,,,,,,,---------......------,,,+++++++++++++++------,,,,,,,,,,,,+++,,,)))***++++++,,,,,,,,,,,,---,,,,,,++++++,,,,,,---))))))*********+++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,''''''(((((())))))))))))))))))))))))((((((''''''))))))((((((''''''&&&&&&''''''''''''(((((((((((('''''''''&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((((((((((((((((((((('''''''''((((((((('''''''''(((***+++***)))((((((((((((((('''''''''''''''''''''''''''''''''&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""$$$%%%%%%$$$###%%%&&&&&&&&&&&&&&&'''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%DDDDDDCCCCCCCCCCCCDDDDDDDDDDDDCCCCCCCCCDDDDDDEEEFFFEEEDDDCCCBBBBBBBBBBBBAAAAAAAAAAAAAAAAAAAAAAAACCCCCCCCCCCCCCCCCCBBBBBBCCCEEEGGGFFFDDDCCCDDDEEEFFFEEEEEEDDDDDDDDDEEEEEEBBBBBBBBBBBBBBBBBBBBBBBBAAAAAA????????????AAAAAA????????????@@@@@@@@@@@@??????>>>>>>>>>>>>??????AAAAAABBBBBBAAAAAA@@@@@@AAAAAABBBBBBCCCDDDDDDDDDBBBBBBBBBBBBCCCCCCDDDDDD?????????@@@@@@AAAAAAAAAAAAAAAAAAAAA@@@@@@@@@???;;;<<<<<<<<<=========>>>:::<<<===>>>======???@@@>>>>>>============>>>>>>>>>>>>>>>=========<<<<<<;;;;;;;;;<<<<<<<<<===============<<<<<<;;;::::::999999999999888999999:::;;;999777555555777999;;;999:::;;;:::888777888999888888888888999:::;;;;;;777888999:::::::::999999<<<;;;;;;::::::;;;;;;<<<============<<<;;;;;;;;;;;;;;;999888777777666666777777888888999999999999777777888999:::;;;;;;<<<:::999999888777666666555888777777777666666666666666666555555555666666777777666666555555555555555555555555555555555555555444444444555555555555666333333333333333333333333333333333333333333333333222222222111111111000000222222111111000000//////////////////////////////222111000111444444111------------...///000111111000000000000000000111111111000////////////000111000000000//////.........,,,,,,+++++++++*********)))*********++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,...---------------------////////////////////////------------------------,,,,,,,,,---------......,,,,,,+++***************------------,,,,,,++++++((()))***+++,,,,,,---,,,---,,,,,,++++++,,,,,,---************++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,---------+++******************+++((((((((())))))))))))))))))))))))))))))((((((((())))))((((((''''''&&&&&&''''''''''''((((((((((((&&&''''''''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((((((((((((((()))(((''''''''''''(((((('''''''''(((***+++***)))'''''''''(((((((((((((((''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""$$$%%%%%%$$$###%%%&&&&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%DDDDDDCCCCCCCCCCCCDDDDDDCCCCCCCCCCCCDDDDDDEEEFFFHHHGGGEEECCCBBBAAABBBBBBCCCCCCCCCBBBBBBAAAAAAAAACCCCCCDDDDDDDDDCCCBBBBBBAAADDDGGGFFFDDDCCCDDDFFFDDDDDDCCCCCCBBBBBBCCCCCCDDDDDDDDDDDDDDDDDDDDDDDDBBBAAA@@@??????@@@AAABBBAAAAAA@@@@@@@@@@@@@@@@@@??????>>>>>>>>>???@@@@@@CCCCCCCCCBBBAAA@@@???>>>BBBBBBBBBCCCCCCCCCDDDDDDCCCCCCBBBBBBCCCCCCDDDEEE??????@@@@@@@@@@@@?????????@@@@@@@@@@@@@@@??????:::;;;;;;<<<<<<=========:::;;;============???@@@???>>>>>>======>>>>>>???===>>>>>>>>>>>>===<<<<<<::::::;;;;;;<<<=========<<<<<<<<<<<<<<<;;;:::999888999::::::999888999::::::999777555555777999:::777999;;;;;;999888999::::::999999999::::::;;;<<<888888999::::::999999999<<<;;;;;;::::::;;;;;;<<<:::<<<======<<<;;;;;;<<<;;;:::999888777777777777666777888999999999999999777777888999::::::;;;;;;999999999888888777777666888888777777777666666666777666666666666777777888777666555555444444555555444444444444444555555555444444444555555555555666333444444444444333333222222222333333333333444444222222222111111111111000111111111111111111000000000000000000000000000000222000///111444444111...------......///000000000000000000000111111111111111000///......///000111000111111111000///...---,,,,,,,,,+++++++++*********++++++,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,---------------.........////////////////////////---......//////......---,,,,,,,,,---------......,,,+++******))))))*********++++++++++++***)))(((((()))***+++,,,---------,,,,,,++++++++++++,,,,,,*********++++++++++++,,,------,,,,,,,,,,,,++++++***++++++,,,,,,------...******))))))))))))******))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((('''''''''''''''''''''((((((((((((&&&&&&'''(((((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((())))))))))))***)))'''&&&&&&'''(((((('''''''''(((***+++***)))'''''''''(((((((((((((((''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""$$$%%%%%%$$$###%%%&&&&&&&&&'''''''''((((((((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%EEEEEEEEEDDDDDDEEEEEEEEEDDDDDDDDDEEEEEEFFFHHHHHHGGGFFFDDDCCCBBBCCCDDDEEECCCCCCCCCCCCDDDDDDDDDDDDDDDDDDEEEEEEEEEDDDCCCBBB@@@DDDGGGGGGDDDBBBEEEHHHEEEEEEDDDCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDDDDDDDDDDCCCBBBAAA@@@@@@AAABBBCCCBBBBBBBBBAAA@@@@@@????????????>>>>>>??????@@@AAABBBBBBBBBBBBAAA@@@??????BBBBBBBBBCCCCCCCCCCCCCCCDDDCCCCCCBBBCCCCCCEEEEEE@@@@@@AAAAAA@@@???>>>===>>>>>>???@@@@@@???>>>>>>;;;<<<<<<======>>>??????999;;;<<<=========???AAA??????>>>>>>>>>>>>??????<<<<<<=========<<<;;;:::::::::;;;;;;<<<======>>>::::::;;;<<<<<<;;;:::999777999;;;;;;999777999:::999888777666666777888999555888:::;;;:::999:::;;;;;;;;;::::::;;;;;;<<<<<<;;;;;;;;;:::::::::::::::;;;;;;::::::::::::;;;;;;777:::======<<<;;;<<<===::::::999888777777777888555666888999::::::999999888888888999999:::::::::888888888888888888888888888888888777777777666666777777777777777888999999666666555444444444444555222333333333444444444444444444444555555555555666444444555555555444222222222222222333333444444444222222222111111111111000111111111111111111222222000000000000000000000000111//////111444555222///......///////////////...///000000000111111111111111000...------...000111111111222222111///...------,,,,,,,,,+++++++++++++++,,,------------,,,+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------......//////////////////////////////......///000000///......,,,,,,,,,---------......,,,,,,+++************+++******+++++++++***)))(((((()))***+++,,,---------++++++************++++++*********+++++++++,,,,,,---------,,,,,,+++++++++******+++,,,,,,---......++++++***))))))***++++++))))))))))))))))))))))))))))))))))))))))))))))))'''''''''(((((((((((((((''''''''''''((((((((((((&&&&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''((())))))))))))***)))'''&&&&&&&&&(((((('''''''''(((***+++***)))''''''''''''((((((((()))''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&"""$$$%%%%%%$$$###%%%&&&''''''''''''(((((((((((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%GGGGGGFFFFFFFFFFFFGGGGGGFFFEEEFFFFFFGGGHHHJJJJJJFFFEEECCCBBBCCCDDDFFFGGGBBBCCCCCCDDDEEEFFFGGGGGGDDDEEEFFFFFFFFFEEECCCBBB???DDDGGGGGGDDDBBBEEEHHHGGGGGGFFFEEEEEEEEEEEEEEEBBBBBBBBBBBBBBBBBBBBBBBBCCCCCCAAAAAAAAAAAACCCCCCCCCCCCBBBAAAAAA@@@????????????>>>>>>???@@@AAAAAA@@@AAAAAABBBBBBAAAAAA@@@CCCCCCCCCCCCCCCCCCCCCCCCDDDCCCCCCBBBBBBDDDEEEFFF@@@AAAAAAAAA@@@>>>===;;;======???@@@@@@???>>>===<<<======>>>???@@@@@@AAA999:::<<<=========???AAA??????>>>>>>>>>>>>??????:::;;;<<<<<<<<<;;;:::999::::::;;;;;;<<<===>>>>>>888999:::;;;;;;;;;:::999777999<<<;;;999777888:::999888777666666777888999444777999;;;::::::;;;;;;<<<<<<;;;;;;;;;<<<======>>>===<<<;;;;;;;;;;;;<<<;;;::::::999999::::::;;;555888<<<===;;;;;;<<<>>>:::999888888777888888888555666888999::::::999999888999999999999:::::::::888888888888888999999999888888888888777777777777888888777777888999::::::666666555444444444444555222222222333333444444444444444444555555555666666444444555666555444222111222222222333333444444444222222222111111111111000000000000111222222222333000000000000000000000000000......111444666333000...///////////////...---//////000000111111111222111///...------...///111111222222222111000...------------,,,,,,,,,++++++,,,---.........---,,,+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---...///000000////////////////////////...///000111111000///...,,,,,,,,,---------.........---,,,,,,++++++,,,,,,,,,,,,---...---,,,+++***((((((***+++,,,---------+++******************+++******+++++++++,,,,,,,,,---------,,,,,,+++++++++******+++,,,,,,---......---,,,+++******+++,,,---*********))))))))))))))))))))))))))))))*********&&&'''''''''(((((())))))''''''''''''((((((((()))%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''((())))))))))))+++***'''&&&%%%&&&'''((('''''''''(((***+++***)))&&&'''''''''(((((())))))(((((((((((((((((((((((($$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&"""$$$%%%%%%$$$###%%%&&&''''''''''''((((((((()))'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%EEEEEEDDDDDDEEEFFFGGGGGGCCCDDDEEEGGGHHHHHHHHHHHHFFFFFFEEEDDDDDDDDDDDDDDDDDDDDDEEEDDDCCCCCCEEEHHHFFFCCCBBBEEEIIIJJJFFFBBBCCCDDDEEEFFFFFFEEEDDDCCCGGGFFFEEEDDDDDDEEEFFFFFFEEEEEEEEEBBBAAAAAACCCFFFEEEDDDCCCAAAAAABBBCCCCCCBBBBBBAAA@@@@@@@@@AAAAAA@@@@@@@@@@@@@@@@@@@@@???AAAAAA@@@@@@@@@@@@??????@@@@@@@@@@@@AAABBBCCCDDDEEEDDDBBBAAAAAABBBCCCDDDBBBBBBAAAAAAAAAAAA@@@@@@???>>>>>>>>>>>>>>>?????????>>>======>>>@@@BBBCCC======<<<<<<===>>>???@@@??????>>>===<<<;;;;;;:::;;;;;;;;;;;;:::::::::999======<<<;;;::::::999999:::999999888888999999:::<<<;;;:::999888999:::;;;::::::999888777777888888::::::999888999:::<<<===;;;;;;;;;;;;;;;;;;;;;:::;;;;;;<<<<<<;;;999888777555777999:::999999:::;;;:::::::::;;;;;;;;;<<<<<<;;;;;;;;;;;;::::::999888:::777555666999;;;:::888999999999999999999999999<<<;;;999777777888999:::888888777777777777888888888999::::::::::::999888888888777777666666555555111111111222333444555666555555444444444333333333666555555444444333222222222222222222222222222222111222333333222111000/////////............///////////////////////////////////////111333333111///111111000000000000111111111111111000000000000000000//////............///000/////////..................//////......---,,,------.........---+++*********+++,,,,,,---......,,,---......//////......///......---------......---------------...//////...------,,,,,,------...,,,,,,,,,,,,,,,,,,,,,,,,***++++++++++++***))))))++++++,,,,,,,,,,,,---------------,,,)))((()))+++++++++,,,,,,,,,,,,------///...---,,,,,,,,,,,,,,,++++++++++++,,,,,,---......+++)))***---...---,,,+++*********))))))(((((('''((()))***************''''''((()))))))))))))))((((((((((((((('''''''''(((((((((((((((''''''&&&(((((((((((((((''''''''')))))))))))))))))))))))),,,***)))'''''''''((((((&&&''''''((()))******+++((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&'''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$&&&''')))&&&&&&%%%%%%$$$###""""""########################&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$$$$######$$$$$$%%%EEEEEEEEEEEEEEEEEEFFFFFFDDDDDDEEEEEEFFFGGGGGGGGGFFFEEEDDDDDDCCCCCCDDDDDDEEEEEEFFFEEEDDDDDDFFFIIIGGGDDDBBBDDDHHHIIIGGGCCCDDDEEEEEEEEEEEEEEEEEEDDDGGGGGGFFFDDDCCCCCCCCCCCCFFFFFFEEECCCAAAAAADDDFFFEEEDDDDDDCCCCCCCCCCCCCCCDDDCCCCCCBBBAAAAAAAAAAAA@@@@@@@@@@@@@@@@@@AAAAAACCCCCCBBBAAA@@@??????>>>@@@@@@??????@@@AAACCCDDDDDDCCCBBBAAAAAABBBDDDEEEBBBBBBBBBAAAAAA@@@@@@@@@@@@??????>>>>>>???@@@@@@???>>>=========???AAACCC<<<===>>>>>>???>>>>>>==================<<<<<<<<<::::::999888777777888888======<<<;;;;;;:::999999::::::999999999999::::::999888777777666666777777999999888777777777777777;;;:::999999:::;;;<<<===;;;;;;;;;;;;;;;<<<<<<<<<::::::;;;;;;;;;:::999888666888:::;;;::::::;;;<<<::::::;;;;;;;;;<<<<<<<<<;;;;;;;;;;;;;;;:::999888:::777666777999;;;:::888::::::::::::::::::::::::<<<:::999777777777999:::888888777777777777888888888999::::::::::::999888777777777666555555444444555444444444444444555666555555444444444333333333555444444444444333333333222222222222222222222222111111222333222111000000//////............///////////////////////////////////////111333333111///000000////////////000000///000000000111222222222000000/////////000000111000000/////////.........---------------,,,,,,+++------.........---++++++******+++,,,,,,---......,,,------...............///......------...............------......///000------,,,,,,,,,,,,------++++++++++++++++++++++++))))))***+++,,,,,,,,,++++++++++++,,,,,,,,,---------------,,,))))))***++++++++++++,,,,,,,,,------......---,,,,,,,,,,,,,,,***************+++,,,,,,---+++)))***,,,...---,,,************)))))))))(((((())))))************)))''''''((()))))))))))))))(((((((((((((((((((((((((((((((((((((((''''''&&&'''''''''''''''&&&&&&&&&))))))))))))))))))))))))******(((''''''(((((()))''''''(((((())))))******((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$######%%%&&&'''&&&&&&%%%%%%$$$######"""########################&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$$$$######$$$$$$%%%FFFFFFFFFEEEEEEEEEEEEEEEFFFEEEDDDCCCCCCDDDEEEFFFEEEEEEDDDCCCCCCCCCCCCCCCDDDEEEEEEEEEDDDDDDFFFHHHHHHEEECCCDDDGGGHHHGGGEEEFFFFFFEEEEEEEEEEEEFFFFFFGGGGGGFFFFFFDDDCCCAAA@@@FFFFFFEEEDDDBBBBBBDDDFFFEEEEEEEEEEEEEEEDDDCCCCCCEEEEEEDDDCCCBBBBBBAAAAAA@@@??????>>>???@@@BBBCCCEEEDDDCCCBBBAAA@@@???>>>AAA@@@???>>>???AAACCCDDDCCCBBBAAAAAABBBCCCEEEFFFCCCCCCBBBAAAAAA@@@??????AAAAAA@@@@@@@@@@@@AAAAAA>>>>>>=========???@@@AAA<<<===???@@@@@@>>><<<;;;<<<<<<<<<======>>>>>>>>>;;;999777555444555666666======<<<<<<;;;:::::::::::::::999999999999::::::777777777777777666666555888888777666666666777777:::::::::999::::::;;;<<<:::::::::;;;;;;<<<<<<===::::::;;;;;;;;;:::999999777999;;;;;;;;;:::;;;<<<;;;;;;;;;<<<<<<<<<======:::;;;;;;;;;;;;::::::999:::888777777999::::::999;;;;;;;;;;;;;;;;;;;;;;;;:::999888777777777888999888888777777777777888888888999999::::::999999888777666666555555444333333888777666555555555555555555555444444444333333333333333333444444444555555333333333333333333333333000000111222222222111111000//////......//////000////////////////////////000///000111333333111/////////............////////////000111222333333444000000///000000111222333000000000/////////......,,,,,,------,,,,,,+++***,,,---.........---,,,+++***++++++,,,,,,------...,,,,,,---.......................................//////......//////000111------,,,,,,,,,,,,------************************((()))***,,,------......++++++++++++,,,,,,,,,,,,,,,------+++))))))***+++++++++++++++,,,,,,,,,,,,...------,,,,,,,,,,,,,,,***))))))))))))***++++++,,,+++******,,,------,,,************)))))))))))))))************))))))(((''''''((()))))))))))))))(((((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&)))))))))))))))))))))))))))(((((((((((())))))***))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$###"""###$$$%%%&&&&&&%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%$$$$$$######$$$$$$%%%FFFFFFFFFFFFFFFEEEEEEDDDGGGFFFCCCBBBAAABBBDDDEEEEEEDDDDDDCCCCCCCCCCCCCCCBBBCCCDDDDDDCCCCCCDDDFFFHHHFFFCCCCCCFFFHHHHHHGGGGGGGGGEEEDDDDDDEEEGGGGGGFFFGGGGGGGGGFFFEEECCCBBBFFFFFFFFFEEECCCCCCDDDFFFEEEEEEFFFGGGGGGEEEDDDCCCEEEDDDDDDCCCBBBAAA@@@@@@@@@???>>>>>>???AAACCCDDDDDDCCCCCCBBBBBBAAAAAA@@@BBBAAA???>>>>>>@@@BBBDDDAAAAAAAAAAAABBBDDDEEEFFFCCCCCCBBBAAA@@@@@@??????CCCBBBBBBAAAAAAAAAAAABBB>>>>>>=========>>>???@@@>>>>>>??????>>>===<<<;;;=====================>>><<<:::777555444444666777======<<<<<<;;;;;;;;;::::::::::::999999:::::::::999999:::;;;;;;999888777777777666666666666666777999999999999999999999999888888999999:::;;;<<<<<<<<<<<<;;;;;;:::999888888888:::<<<<<<;;;;;;;;;<<<;;;;;;<<<<<<<<<=========:::;;;;;;;;;;;;;;;:::::::::999888888999999:::999;;;;;;;;;;;;;;;;;;;;;;;;999999888777777777888999999888888777777888888999999999999999999999999999777777777666555555444444666666555555555555666666555555444444444333333333222222333333444555666666333333333333333333333333000000111111222222222222000000////////////000000////////////////////////000000000222333333111000000//////......//////000000000111111222222333333///...//////000111222333000000000////////////...,,,------------,,,++++++,,,---.........---,,,++++++++++++,,,,,,---------,,,,,,---.........---------......//////////////////////////////000111111---,,,,,,,,,,,,,,,,,,---++++++++++++++++++++++++)))***+++,,,------------***++++++++++++,,,,,,,,,,,,------+++***)))***,,,***++++++++++++,,,,,,,,,------,,,,,,+++,,,,,,---******)))))))))******+++++++++******+++,,,,,,,,,*********)))))))))))))))***************)))((('''''''''((()))))))))))))))((((((((((((((()))))))))(((((((((((((((''''''&&&&&&&&&&&&&&&&&&'''''''''(((((((((((((((((((((((('''''''''((()))******+++******))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&%%%$$$######$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###$$$%%%&&&&&&%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%EEEEEEFFFFFFFFFFFFEEEDDDGGGFFFCCCBBBAAABBBCCCDDDEEEEEEDDDCCCCCCCCCCCCCCCCCCEEEFFFFFFEEEEEEEEEGGGHHHFFFEEEDDDFFFGGGHHHHHHHHHGGGFFFEEEEEEFFFGGGHHHEEEFFFHHHIIIIIIHHHGGGFFFFFFGGGGGGFFFDDDDDDEEEFFFEEEFFFGGGGGGGGGFFFDDDCCCBBBCCCCCCCCCBBBAAA???>>>??????>>>>>>???AAACCCDDD@@@AAAAAABBBBBBCCCCCCDDDBBBAAA@@@??????AAACCCDDDAAAAAAAAABBBCCCDDDEEEEEECCCCCCBBBAAAAAA@@@??????DDDDDDCCCBBBAAAAAABBBBBB>>>>>>>>>>>>>>>?????????AAA@@@===<<<;;;<<<===>>>@@@??????>>>======<<<<<<>>><<<999777666777999:::===<<<<<<<<<<<<<<<;;;;;;;;;::::::::::::::::::;;;:::;;;<<<===<<<;;;:::999777666666666666666777777777777888888888777777777666666777888999:::::::::>>>>>><<<;;;999888777666999:::<<<<<<;;;:::;;;<<<;;;;;;;;;;;;<<<<<<<<<===:::;;;;;;<<<<<<;;;;;;;;;:::::::::999888888999:::999999999999999999999999888888888888888888999999999999888888888888999999999999999999999999999999999999888888777666666666333333333333444555666777555555444444444333333333111222222333444555666666333333333333333333333333000000000111111222333333000000////////////000000////////////////////////000000000222444444222000111000000//////000000111333222222111111000000000---------...///000111222111000000000////////////...............---,,,,,,+++,,,---.........---,,,++++++,,,,,,,,,,,,------+++,,,,,,---...---------------//////000000/////////////////////000111111,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,+++*********+++++++++,,,,,,+++,,,,,,+++***)))+++,,,*********+++++++++,,,,,,,,,,,,+++++++++,,,,,,---,,,++++++*********++++++***++++++******+++,,,---))))))))))))))))))*********************)))((('''''''''((()))))))))))))))(((((((((((())))))******(((((((((((((((''''''&&&&&&&&&''''''((((((((((((((((((((((((((((((((((((&&&&&&'''((()))******+++************))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((''''''''''''''''''''''''%%%&&&&&&&&&&&&%%%$$$###$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%&&&'''$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''%%%%%%$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%CCCDDDEEEGGGGGGGGGFFFEEEFFFEEEDDDCCCBBBBBBCCCDDDFFFFFFEEEDDDDDDDDDDDDDDDEEEGGGIIIIIIHHHGGGHHHIIIGGGFFFFFFFFFFFFGGGHHHHHHHHHHHHGGGGGGGGGGGGHHHHHHFFFGGGHHHIIIIIIJJJIIIIIIFFFGGGHHHGGGFFFEEEEEEFFFFFFFFFFFFFFFFFFEEEDDDDDD@@@AAABBBBBBBBBAAA@@@????????????@@@AAAAAAAAAAAA>>>???@@@AAABBBCCCDDDEEECCCCCCBBBBBBBBBBBBCCCCCCAAABBBBBBCCCCCCDDDDDDDDDBBBBBBAAAAAAAAAAAA@@@@@@EEEDDDCCCBBBAAAAAAAAABBB???????????????@@@??????BBB@@@<<<::::::<<>>===;;;:::::::::<<<===<<<<<<<<<<<<<<<<<<<<<<<<;;;;;;::::::::::::;;;;;;:::::::::::::::999999888777777666666666777888888777777888888888777666666777777777888888999999999???>>><<<:::888777777777999:::<<<<<<:::::::::;;;:::::::::;;;;;;;;;<<<<<<:::;;;;;;<<<<<<<<<<<<;;;:::;;;;;;:::888888999;;;999999999999999999999999888999999999999:::::::::999999888888888888999999:::999999888888999999:::::::::999888888777777666111111111222333444555666555555444444444333333333222222333333444555666666333333333333333333333333111111111000111111222333111000000//////000000111////////////////////////111000111222444444222000111111000000000000111111333333222111000///............---......///000111111111000000000/////////......//////......---,,,+++,,,---.........---,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,---------------,,,---///000111111000/////////......//////000111,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++******************+++++++++++++++,,,,,,+++******+++---************+++++++++++++++++++++++++++,,,,,,---,,,,,,+++************+++)))***++++++)))***+++---))))))))))))************)))************))))))(((''''''((()))))))))))))))'''(((((())))))******+++(((((((((((((((''''''&&&&&&&&&''''''((()))))))))))))))))))))))))))))))))&&&&&&((()))************************************))))))))))))))))))))))))((((((((((((((((((((((((''''''''''''''''''''''''###$$$&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%AAACCCEEEGGGHHHHHHGGGFFFEEEEEEDDDDDDDDDDDDDDDDDDGGGGGGFFFEEEEEEEEEEEEEEEDDDFFFIIIIIIHHHGGGGGGHHHEEEFFFGGGHHHGGGGGGGGGHHHGGGGGGHHHHHHHHHHHHGGGGGGHHHHHHGGGGGGGGGHHHIIIIIIFFFHHHIIIHHHFFFEEEFFFGGGFFFFFFEEEDDDDDDDDDDDDEEE???@@@BBBCCCDDDCCCBBBAAA>>>???AAABBBBBBAAA@@@???>>>??????@@@AAABBBCCCCCCCCCCCCDDDEEEEEEDDDCCCBBBBBBBBBCCCCCCCCCCCCCCCCCC@@@@@@AAAAAAAAAAAABBBBBBEEEDDDCCCBBBAAAAAAAAAAAA@@@@@@AAAAAAAAAAAA@@@@@@???>>><<<;;;;;;===???@@@?????????>>>>>>>>>===============<<<======>>>???<<<<<<<<<<<<============;;;;;;::::::::::::;;;;;;;;;:::999999888888999999777777777777777888999999888999:::::::::888777666999999999999::::::::::::===<<<:::999999999999:::888:::;;;;;;:::999999:::999999999::::::::::::;;;::::::;;;<<<<<<<<<<<<<<<:::;;;<<<:::888777999;;;::::::::::::::::::::::::999999:::;;;;;;;;;;;;;;;:::999999888888999999:::::::::999888888999::::::999999888888777666666666222222222222222333444444555555444444444333333333333333333444444555555555444444444444444444444444333222111000000000111222111111000000000000111111////////////////////////111000111222444444222111000000////////////000000111000000000///.........000///////////////000000111111111000000000//////---............---,,,,,,++++++---.........------,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,------------,,,,,,---///111222111000///......------......///000,,,,,,++++++++++++,,,,,,++++++++++++++++++++++++******++++++++++++++++++************+++++++++++++++,,,,,,+++******+++---************++++++++++++++++++******+++,,,,,,---++++++***))))))))))))))))))***++++++))))))+++---((()))))))))************((())))))************)))''''''((()))))))))))))))'''(((((()))******++++++(((((((((((((((''''''&&&%%%%%%&&&''''''((())))))))))))))))))))))))))))))&&&'''((()))******)))))))))))))))******++++++,,,))))))))))))))))))))))))((((((((((((((((((((((((''''''''''''''''''''''''"""###%%%&&&''''''&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$######$$$$$$%%%@@@BBBDDDGGGHHHHHHGGGGGGDDDDDDEEEEEEFFFEEEDDDDDDHHHGGGGGGFFFFFFFFFFFFFFFAAACCCFFFFFFEEEDDDDDDEEEDDDFFFHHHIIIHHHGGGGGGGGGGGGGGGIIIJJJJJJIIIGGGGGGJJJIIIGGGFFFEEEFFFGGGGGGFFFHHHIIIIIIGGGFFFFFFGGGGGGFFFDDDCCCCCCCCCDDDEEE???AAACCCDDDEEEEEECCCBBB>>>???BBBCCCCCCAAA???===??????@@@@@@@@@@@@AAAAAACCCDDDFFFGGGGGGEEECCCBBBCCCCCCCCCDDDCCCCCCBBBBBB???@@@@@@AAAAAABBBBBBCCCEEEDDDCCCBBBAAA@@@@@@@@@AAAAAABBBBBBBBBAAAAAA@@@<<<<<<======>>>>>>??????>>>>>>>>>>>>????????????<<<<<<===>>>>>>?????????<<<<<<<<<===============<<<;;;;;;::::::;;;;;;<<<<<<;;;:::999888999:::;;;888888777777888999:::::::::;;;;;;<<<;;;:::999888<<<;;;;;;;;;;;;;;;;;;;;;::::::999888999:::<<<===888999;;;:::999888888999888888999999999:::::::::::::::;;;<<<=========<<<:::<<<===;;;888777999;;;;;;;;;;;;;;;;;;;;;;;;;;;999:::;;;;;;<<<<<<<<<;;;:::999999888888999999:::;;;:::999888888999:::;;;888888777777666666555555444444333222222222333333555555444444444333333333333333333444444444555555444444444444444444444444444333111000000000111111111111000000000000111111////////////////////////111111111333444444333111//////............//////............////////////222111000000000000000111111111111111000000000000,,,,,,---------,,,++++++***+++---.........------,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,---------,,,,,,+++---///111222222000000---------------...//////,,,++++++++++++++++++,,,************************'''((()))***+++,,,,,,,,,)))************+++++++++***+++,,,+++******+++---)))************++++++++++++*********+++,,,,,,---******)))((((((((((((((((((***,,,+++)))(((+++...(((((())))))*********+++'''((()))***************'''(((((()))))))))))))))'''(((((()))***+++++++++(((((((((((((((''''''&&&$$$$$$%%%%%%&&&'''(((((())))))))))))))))))))))))&&&''')))******))))))((((((((()))***+++,,,,,,,,,))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((( """$$$'''((('''&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&%%%$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%DDDCCCDDDEEEGGGFFFDDDBBB@@@DDDGGGIIIHHHFFFEEEEEEFFFFFFFFFFFFEEEEEEEEEEEEDDDEEEFFFFFFEEEEEEFFFGGGEEEEEEEEEFFFGGGGGGHHHHHHEEEEEEEEEDDDCCCDDDGGGJJJGGGHHHIIIIIIJJJJJJIIIIIIGGGHHHJJJKKKKKKIIIHHHFFFFFFDDDBBBAAA@@@AAABBBCCCGGGHHHHHHHHHGGGDDDAAA@@@EEEEEEEEEDDDCCCCCCBBBBBB>>>>>>??????@@@AAABBBCCCCCCDDDFFFGGGHHHGGGEEEDDDDDDDDDDDDDDDDDDDDDCCCCCCCCCCCCDDDDDDCCCCCCBBBAAA@@@@@@AAAAAAAAAAAABBBBBBBBBBBBAAA@@@@@@?????????BBB@@@???>>>???@@@???>>>>>>>>>>>>>>>>>>?????????;;;<<<===>>>>>>===<<<;;;>>>===============>>>>>><<<<<<<<<<<<;;;:::999888999:::;;;<<<<<<<<<;;;;;;999999999888888888777777888:::;;;;;;:::999:::;;;<<<<<<;;;:::::::::;;;;;;:::999888777777888999:::===<<<999777777999;;;<<<999;;;;;;;;;999999999;;;:::::::::;;;;;;<<<<<<<<<>>><<<:::888777888:::<<<:::;;;<<<<<<<<<;;;:::999::::::999999888999999999888888888888888777666555555888;;;<<<<<<;;;:::;;;:::999888666555555444444555333000000222444555555555555666666666555333222111222333444555555555555555444444444555555333222333333222111000000111111//////000111222333333444000000////////////000000///000222333333222000///222111///.........///000444333222111000000000000000111111111000111222444222222111000///...------+++,,,---.........---,,,------------------------,,,,,,------,,,,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,+++---//////...---...////////////...---------,,,......------------......---,,,,,,+++*********+++******+++++++++,,,,,,,,,---,,,+++*********+++,,,,,,+++++++++++++++,,,,,,++++++************++++++++++++++++++++++++++++++************************,,,,,,+++***)))(((''''''(((((((((((())))))))))))******))))))))))))******))))))(((((('''''''''&&&''''''((()))))))))))))))(((''''''&&&&&&&&&'''''''''''''''(((((((((((((((&&&''')))***+++++++++***++++++******))))))(((((((((((()))***+++,,,,,,,,,---+++***,,,------***'''))))))))))))))))))))))))))))))))))))((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$"""###$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$######%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%$$$######EEEDDDDDDFFFHHHIIIHHHGGGBBBEEEGGGHHHGGGEEEEEEEEEFFFFFFFFFEEEEEEDDDDDDDDDDDDFFFGGGGGGFFFFFFGGGHHHGGGFFFFFFFFFFFFFFFFFFFFFEEEFFFEEEEEEDDDEEEHHHKKKGGGHHHIIIIIIJJJJJJIIIIIIHHHIIIJJJKKKJJJIIIGGGFFFGGGFFFDDDCCCBBBCCCDDDEEECCCDDDFFFGGGGGGFFFDDDCCCDDDDDDDDDDDDCCCCCCCCCCCC@@@@@@@@@@@@AAAAAABBBCCCAAABBBDDDEEEFFFEEEDDDCCCCCCCCCCCCDDDDDDDDDDDDDDDCCCCCCCCCCCCCCCBBBAAA@@@CCCBBBBBBAAAAAA@@@@@@@@@@@@@@@@@@@@@@@@@@@AAAAAAAAA???======>>>>>>===<<<>>>>>>==================<<<===>>>>>>>>>===<<<<<<>>>>>>============>>>>>><<<<<<<<<<<<;;;:::999888999999:::;;;;;;;;;;;;;;;999999999888888888777777888:::<<<;;;:::999999:::;;;;;;:::::::::;;;;;;<<<::::::999999999999::::::;;;:::999888888999;;;<<<:::;;;<<<<<<::::::;;;<<<::::::;;;;;;;;;;;;;;;;;;;;;:::888777666777888999888999;;;<<<<<<<<<;;;;;;::::::999999999999999:::888888999999999888777777666999<<<<<<;;;:::::::::999888666555444333333333555333111000222444555555444555666666666555333222111222333444555555555555444444444444555444333222333333222111111111111111000000000111222222333333000000////////////000000///000222333333222000///222111000///...//////000222222111111000000111111000111222111000000222333222222111000///...---------------......---,,,,,,---------------------------------------,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,...000000///...///000...............---------......------------......---,,,++++++******++++++******+++++++++,,,,,,,,,,,,,,,+++******++++++,,,++++++************++++++++++++************++++++++++++++++++++++++++++++************************++++++******)))((((((((((((((((((((()))))))))******))))))(((((())))))***)))(((((((((''''''''''''''''''((()))))))))))))))((('''''''''&&&''''''''''''''''''((((((((((((((('''((()))***++++++***************))))))((((((((()))))))))***+++++++++,,,---+++***+++------***'''))))))))))))))))))))))))))))))))))))((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$%%%&&&'''&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%$$$######DDDCCCCCCDDDGGGIIIJJJJJJEEEFFFGGGFFFEEEDDDEEEFFFGGGFFFFFFEEEDDDCCCCCCBBBDDDFFFHHHIIIHHHGGGGGGGGGHHHHHHGGGFFFFFFEEEDDDDDDFFFFFFGGGFFFEEEFFFIIIKKKGGGHHHIIIIIIJJJJJJIIIIIIHHHIIIJJJJJJJJJHHHGGGFFFHHHHHHFFFEEEEEEEEEFFFGGGCCCDDDEEEFFFFFFEEEDDDCCCBBBCCCCCCCCCCCCDDDDDDDDDCCCBBBBBBAAABBBBBBCCCCCC@@@AAABBBCCCDDDCCCBBBBBBBBBCCCCCCCCCDDDDDDEEEEEEDDDCCCCCCBBBBBBAAA@@@@@@EEEDDDCCCAAA@@@@@@???????????????@@@AAABBBBBBBBB???===;;;;;;<<<===<<<;;;>>>>>>======<<<<<<;;;;;;======>>>??????>>>>>>===>>>>>>============>>>>>><<<<<<<<<<<<;;;:::999999888888999999999:::::::::999999999888888888888888999;;;<<<;;;999888888999::::::::::::;;;<<<<<<<<<:::::::::;;;;;;:::::::::999999999::::::;;;;;;<<<;;;<<<======;;;;;;<<<===;;;;;;;;;;;;;;;;;;::::::999999999999888888888888777888:::;;;<<<=========::::::999999999999::::::888999999::::::::::::999888:::<<<<<<;;;999999999999888777666555444444444555333111111333444555555444555555555555444333333111222333444555555555555444444444444444333222222333222222111111111111222111111111111111111111111000000////////////000000///000222333333222000///111111000///////////////111111000000000111222222111222333111000///111222222222111000///...------//////...---,,,,,,,,,,,,---------------------------............---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---///111111000///000111---------.....................------------......,,,,,,++++++******++++++******+++++++++,,,,,,,,,,,,++++++******+++,,,,,,+++******)))))))))******++++++************++++++++++++++++++++++++++++++************************))))))))))))))))))))))))((((((((()))))))))******)))((((((''''''(((((()))((((((((((((''''''''''''''''''((()))))))))))))))'''''''''''''''((((((((('''''''''(((((()))))))))))))))******+++******)))))))))))))))((((((((((((******************++++++,,,+++++++++,,,,,,***)))))))))))))))))))))))))))))))))))))))((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%$$$$$$%%%$$$$$$######$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%&&&'''((('''%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&%%%%%%$$$$$$###DDDBBBAAABBBDDDGGGHHHHHHFFFGGGFFFEEECCCCCCEEEGGGGGGGGGFFFEEEDDDBBBBBBAAABBBEEEHHHHHHGGGFFFFFFFFFGGGFFFFFFFFFEEEEEEEEEDDDFFFGGGHHHGGGGGGGGGJJJLLLGGGHHHIIIIIIJJJJJJIIIIIIIIIIIIIIIIIIIIIHHHGGGFFFHHHGGGGGGFFFFFFFFFGGGGGGFFFFFFFFFEEEDDDCCCAAA@@@AAAAAABBBCCCCCCDDDEEEEEEEEEDDDCCCCCCCCCCCCCCCDDD@@@AAABBBCCCCCCCCCBBBBBBBBBBBBCCCCCCDDDEEEEEEEEEDDDCCCBBBBBBAAA@@@@@@@@@EEEDDDBBBAAA@@@@@@@@@AAA@@@@@@@@@AAAAAAAAABBBBBB???===;;;;;;=========<<>>===<<<<<<;;;;;;>>>>>>>>>??????????????????>>>>>>============>>>;;;<<<<<<<<<;;;;;;:::999888888888888888999999:::888888888888888888888888:::;;;<<<;;;999777777777888999:::;;;<<<<<<======888999:::;;;;;;:::999888777888999;;;<<<<<<;;;;;;:::;;;<<<<<<;;;;;;<<<===<<<<<<<<<;;;;;;::::::::::::;;;;;;<<<<<<;;;:::999999999:::;;;<<<<<<<<<===::::::999999999:::;;;;;;999999:::;;;<<<<<<<<<;;;:::<<<===<<<:::888888888;;;:::999888777777777777555333222222444555555444444444444444444444444444111222333444555555555555333444555444333222222222333222222111111222222222222222222111111111000000000000////////////000000///000222333333222000///111000000///////////////////////////000111222333222333333222000///000222222222111000///...------111000...---,,,,,,,,,---------------------------......//////......---,,,++++++,,,,,,,,,,,,---------...000000/////////000,,,---------.../////////......------------......,,,,,,++++++***++++++,,,******+++++++++,,,,,,,,,++++++++++++++++++,,,,,,+++***))))))((()))))))))++++++************++++++************************************************(((((())))))************(((((()))))))))*********((((((''''''''''''((((((((((((((((((((('''''''''''''''((()))))))))))))))''''''(((((()))))))))((('''''''''((())))))***************************)))((((((((((((((((((((((((+++++++++***************++++++++++++,,,,,,+++***))))))))))))))))))))))))))))))))))))((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%#########$$$&&&((($$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&'''&&&%%%&&&'''''''''%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$FFFDDDBBBBBBDDDEEEFFFEEEFFFGGGFFFDDDCCCCCCFFFHHHHHHGGGFFFEEEDDDCCCBBBAAAAAADDDFFFFFFEEEDDDEEEEEEDDDDDDEEEEEEEEEFFFFFFFFFFFFGGGHHHHHHHHHHHHJJJKKKGGGHHHIIIIIIJJJJJJIIIIIIIIIIIIIIIIIIHHHGGGFFFEEEFFFFFFFFFEEEFFFFFFFFFGGGEEEEEEEEEDDDCCCBBBAAAAAA@@@@@@AAABBBCCCDDDEEEEEEEEEEEEDDDDDDCCCDDDDDDDDDBBBBBBCCCCCCDDDDDDDDDDDDBBBCCCCCCCCCDDDDDDEEEEEEDDDCCCBBBAAAAAAAAABBBBBBCCCBBBAAA@@@@@@AAACCCDDDBBBBBBBBBAAAAAAAAA@@@@@@@@@>>>======>>>??????>>>@@@@@@??????>>>===<<<<<<>>>>>>>>>>>>>>>???@@@@@@??????>>>===============;;;;;;;;;<<<;;;;;;::::::888888777777777888999:::888888888888888888888888999;;;<<<;;;888777777777888999:::;;;<<<===<<<<<<777888999::::::999888777666777999;;;<<<<<<;;;:::888:::;;;;;;::::::;;;<<<<<<<<<<<<;;;;;;:::::::::999:::<<<======<<<;;;:::;;;;;;;;;;;;;;;;;;;;;;;;:::999999999:::;;;;;;<<<999:::;;;<<<<<<<<<<<<<<<;;;<<<===<<<999888888888;;;:::999888888777777888555333222333555666555444444444333333333444444444111222333444555555555555222444555555222111111333333222222222222222333333333333222222111000000000000000////////////000000///000222333333222000///000000000000000//////.........//////000111333333222333333222000///000222222222111000///...------222000///---,,,,,,------------------------------......//////......---,,,+++++++++,,,,,,---------+++---//////.........///,,,---------.../////////......------------......,,,++++++***++++++,,,,,,******+++++++++,,,,,,,,,******++++++,,,,,,,,,,,,+++******)))(((((())))))++++++************++++++************************************************((((((((()))******++++++))))))))))))************((((((''''''''''''(((((('''''''''(((((((((((((((''''''((()))))))))))))))'''((()))*********))))))''''''(((((()))******++++++++++++***************((((((((()))))))))))))))+++++++++***************+++++++++++++++++++++,,,************************))))))))))))((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######%%%'''((($$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&%%%$$$%%%&&&'''&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$HHHGGGEEEEEEFFFGGGGGGFFFEEEEEEEEEDDDDDDDDDGGGIIIHHHGGGGGGFFFEEEDDDDDDCCCBBBCCCEEEDDDCCCCCCDDDFFFCCCCCCDDDEEEEEEFFFGGGGGGEEEGGGHHHHHHHHHHHHIIIKKKGGGHHHIIIIIIJJJJJJIIIIIIJJJJJJIIIHHHGGGFFFFFFEEEDDDEEEEEEEEEEEEFFFFFFFFFAAAAAABBBBBBCCCCCCDDDDDD@@@@@@AAABBBCCCCCCDDDDDDDDDDDDDDDCCCDDDDDDEEEEEEDDDDDDDDDDDDDDDEEEEEEEEEDDDDDDDDDDDDDDDDDDDDDDDDCCCCCCBBBAAABBBCCCDDDEEECCCBBBAAA@@@AAABBBDDDFFFCCCCCCCCCBBBAAA@@@@@@@@@AAA???>>>>>>@@@AAAAAA@@@@@@@@@??????>>>>>>=====================>>>@@@@@@@@@???>>>======<<<<<<===:::;;;;;;<<<;;;;;;::::::999888777777777888:::;;;888888888888888999999999888:::;;;:::888777777888888999;;;<<<===<<<<<<;;;777888888999999888888777777888:::;;;<<<;;;;;;:::777999::::::999999;;;<<<;;;;;;;;;;;;;;;;;;::::::777888:::;;;;;;::::::999===<<<;;;::::::::::::;;;:::999999::::::;;;<<<===:::;;;;;;<<<<<<<<<<<<;;;;;;<<<<<<;;;999888888999888777666555555555555666444333333444555666555444333333333222333333444555111222333444555555555555111333666555222000111333333222222222222333333444333222222222111111000000000000////////////000000///000222333333222000///000000000000000///...............///000111222333111222333111000///111222222222111000///...------000000///...---------------------------------------............---,,,,,,***++++++,,,,,,------...+++---//////...---...///---------.....................------------......++++++******++++++,,,,,,******+++++++++,,,,,,,,,))))))+++,,,,,,,,,,,,,,,,,,+++******))))))))))))++++++************++++++************************************************(((((())))))*********+++)))))))))*********++++++)))((((((''''''(((((()))'''''''''(((((((((((((((''''''((()))))))))))))))'''((()))+++++++++******''''''((())))))***++++++++++++*********++++++,,,))))))))))))******************************++++++***+++,,,+++******,,,...************************))))))))))))((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$%%%'''(((###$$$$$$%%%%%%&&&&&&'''$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''$$$%%%%%%&&&&&&'''''''''&&&%%%$$$%%%&&&'''&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%EEEEEEEEEFFFHHHIIIGGGFFFBBBDDDEEEEEEEEEEEEGGGIIIHHHHHHGGGGGGFFFFFFFFFEEEDDDEEEDDDCCCBBBCCCFFFHHHDDDDDDDDDEEEEEEEEEEEEEEEDDDFFFHHHHHHHHHGGGHHHJJJGGGHHHIIIIIIJJJJJJIIIIIIKKKJJJIIIGGGFFFFFFEEEEEEDDDDDDEEEFFFFFFFFFFFFFFFAAAAAAAAAAAABBBCCCDDDEEEAAAAAAAAABBBBBBCCCCCCCCCCCCCCCCCCCCCCCCDDDEEEFFFDDDDDDDDDDDDDDDEEEEEEFFFEEEEEEEEEDDDCCCCCCBBBBBBCCCBBBBBBBBBCCCEEEGGGHHHFFFDDDBBB@@@@@@AAACCCEEEBBBBBBBBBBBBBBBBBBAAAAAA@@@???>>>>>>@@@AAAAAA@@@>>>>>>>>>>>>>>>>>>======<<<<<<<<<<<<<<<>>>???@@@@@@???>>>===<<<<<<<<<<<<::::::;;;;;;<<<;;;;;;::::::999888777777999:::;;;777777888888888999999999777999::::::888777888888999:::;;;======<<<:::999:::999999888888999999:::999:::::::::;;;:::::::::888999;;;;;;:::;;;<<<>>>::::::;;;;;;;;;;;;;;;;;;888999999::::::;;;::::::<<<;;;:::::::::;;;<<<===999999999::::::<<<======;;;;;;<<<<<<<<<;;;::::::;;;<<<<<<:::999888999:::666666555555444444555555444333333444666777555444333333222222222333444555111222333444555555555555000333666555111///111333222222222222222333444555222222222111111111111111000000////////////000000///000222333333222000//////000000111000///...---///////////////000111222000111222111000000222333222222111000///...------......////////////......---------------------------------------,,,++++++******+++,,,,,,---......,,,...///000///...///000...............---------......------------......++++++******++++++,,,---******+++++++++,,,,,,,,,((()))+++,,,------,,,,,,------+++******)))))))))++++++************++++++************************************************)))))))))))))))*********))))))*********+++++++++***))))))(((((())))))***''''''''''''((((((((()))''''''((()))))))))))))))&&&(((***+++,,,,,,+++***&&&'''((()))***+++,,,,,,+++************+++---...)))*********+++++++++,,,)))))))))***+++++++++,,,***+++,,,+++)))))),,,///************************))))))))))))((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''######$$$%%%%%%&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&''''''((('''&&&%%%&&&'''((('''%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%AAAAAABBBEEEGGGHHHGGGEEEAAACCCEEEFFFFFFFFFHHHJJJHHHHHHGGGGGGGGGGGGGGGGGGFFFFFFEEECCCBBBDDDGGGJJJFFFFFFEEEEEEDDDDDDCCCCCCDDDFFFHHHHHHGGGGGGHHHIIIGGGHHHIIIIIIJJJJJJIIIIIIKKKJJJIIIGGGFFFEEEEEEEEEDDDEEEFFFGGGGGGGGGGGGGGGDDDCCCBBBAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBCCCCCCBBBBBBBBBBBBCCCEEEFFFFFFDDDCCCCCCCCCCCCDDDEEEEEEFFFFFFEEEDDDCCCBBBAAAAAACCCBBBBBBBBBCCCFFFIIIJJJHHHFFFCCCAAA@@@@@@BBBCCC@@@AAAAAABBBBBBCCCCCCDDD@@@>>>===>>>@@@AAAAAA@@@<<<<<<<<<===============<<<;;;;;;;;;<<<===???@@@@@@@@@>>>===<<<<<<<<<<<<::::::;;;;;;<<<;;;;;;;;;:::999888777777999;;;<<<777777888888999999999999666888999:::888888888999999:::<<<======;;;:::888<<<;;;999999999999;;;<<<;;;:::::::::::::::::::::999:::<<<<<<<<<<<<===???:::::::::;;;;;;<<<<<<<<<;;;;;;;;;<<<<<<=========:::999999999:::<<<>>>???999999999:::;;;<<<===>>>;;;<<<<<<<<<;;;:::999999:::;;;;;;:::888888999;;;888777777666666666666777444333333555666777555444333333222111222333555666222222333444555555555555000333666555111///000444222222222222333333444555111111111111111111111111000000////////////000000///000222333333222000//////000111111111000...---///////////////000000111000111111111000111222444222222111000///...---------...///000000000......------------------------,,,,,,------,,,,,,+++*********+++,,,,,,---......---///111111000///000111/////////......------,,,.........------.........+++*********+++,,,,,,---******+++++++++,,,,,,,,,((()))+++,,,------,,,,,,...---,,,+++************++++++************++++++))))))))))))))))))))))))******************************)))))))))))))))))))))************+++++++++******))))))))))))******&&&'''''''''(((((())))))'''(((((()))))))))))))))&&&(((***,,,---,,,+++***&&&'''((()))***+++,,,,,,******))))))***,,,...///******+++++++++,,,,,,,,,(((((()))***+++,,,,,,---)))+++,,,+++)))))),,,000************************))))))))))))((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%&&&'''''''''&&&&&&######$$$%%%%%%&&&''''''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''(((((()))'''&&&'''((()))((('''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%EEEFFFFFFDDDCCCBBBDDDEEEEEEFFFGGGHHHHHHHHHHHHHHHHHHHHHGGGFFFEEEEEEEEEEEEFFFFFFFFFEEECCCDDDFFFHHHHHHGGGFFFEEEEEEDDDDDDEEEHHHHHHHHHHHHHHHHHHHHHHHHGGGHHHIIIIIIJJJJJJJJJIIIKKKJJJJJJIIIGGGEEECCCBBBBBBCCCDDDEEEEEEFFFEEEEEECCC@@@===???CCCEEEBBB???AAAAAABBBBBBBBBBBBBBBAAADDDBBBAAABBBEEEGGGFFFDDDDDDCCCCCCBBBBBBDDDEEEFFFGGGGGGFFFEEEDDDCCCCCCBBBAAAAAAAAAAAACCCEEEGGGIIIIIIGGGDDDBBB@@@@@@@@@AAACCCDDDEEECCCAAA???@@@AAA@@@@@@??????>>>>>>======;;;<<<<<<=====================<<<>>>??????>>><<<>>>>>>======<<<;;;999999777999;;;======;;;999777999:::;;;<<<<<<<<<;;;:::<<<>>>???>>>;;;:::999:::999999999::::::;;;;;;;;;;;;;;;::::::;;;;;;<<<===666666777777888888888999<<<<<<;;;:::;;;<<<===>>><<<;;;;;;;;;===???>>>===777888999:::;;;:::999888888:::<<<<<<<<<<<<>>>???;;;;;;:::999999999::::::>>>>>>>>>>>>>>>>>>>>>>>>===;;;:::<<>>888999:::999777666777888555555666666777777888888555555444444444555555666777555333222111222444555555555555555555555444444333333111111111111333333111222333333444444333333111111222222222222111111333222111/////////000000///111333555555333111///000000////////////000000000000//////.........---111111111111111111111111111111000000//////..............................------......------,,,+++---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,---......------------.........///111111000///////////////,,,++++++******++++++,,,******+++++++++,,,,,,,,,+++++++++***++++++,,,,,,+++++++++***++++++,,,,,,,,,,,,++++++***)))((((((++++++***************+++)))************+++++++++******)))))))))))))))***...---,,,+++******************++++++++++++******((((((((((((((((((((((((((((((((((((((((((((((((,,,+++***)))))))))***+++*********)))))))))))))))******+++,,,,,,,,,,,,+++((()))***+++++++++++++++,,,++++++***)))))))))***************************------,,,+++++++++,,,,,,,,,,,,,,,+++++++++******---,,,***)))'''&&&&&&&&&(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''&&&&&&%%%$$$######$$$%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$((('''&&&%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%""""""""""""###$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$EEEFFFGGGFFFDDDCCCDDDFFFFFFGGGHHHHHHIIIIIIHHHHHHGGGGGGFFFFFFFFFGGGGGGHHHFFFGGGFFFEEEDDDDDDEEEGGGGGGFFFEEEEEEDDDDDDDDDEEEHHHHHHHHHHHHHHHHHHHHHHHHGGGGGGHHHHHHIIIIIIIIIIIIJJJJJJIIIHHHGGGEEEDDDCCCCCCDDDDDDEEEEEEEEEEEEDDDCCC@@@>>>???CCCEEEBBB???AAABBBBBBCCCCCCCCCBBBBBBDDDBBBAAACCCEEEGGGFFFDDDDDDCCCCCCBBBCCCDDDEEEFFFFFFFFFEEEDDDDDDCCCBBBBBBCCCCCCCCCCCCCCCDDDEEEFFFEEEDDDBBBAAA@@@AAABBBCCCAAABBBCCCBBBAAA@@@AAABBB@@@@@@@@@@@@????????????======>>>???????????????@@@>>>======>>>>>>===;;;>>>>>>>>>>>>===<<<;;;;;;888999;;;<<<<<<;;;999888999:::;;;<<<<<<<<<;;;;;;;;;=========;;;999::::::999999:::::::::;;;;;;;;;999999999999999::::::;;;888888888888888888999999:::999999999999:::;;;;;;;;;;;;:::<<<===>>><<<;;;::::::;;;;;;:::999888777999:::<<<<<<;;;;;;===>>>;;;;;;;;;;;;;;;;;;<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;===;;;:::<<>>999:::;;;:::888777888999666666777777777777777888777666555444444444444444666555444333333333444555444444444444444444444444444333222222222222333444111222333333444444333333111111222222222222111111222111000/////////000111///111333555555333111///000000////////////000000000000/////////.........111111111111111111111111111111000000//////......////////////////////////------......------,,,+++---,,,,,,++++++,,,,,,---------------------......------........./////////000//////...............,,,++++++++++++++++++,,,***++++++++++++,,,,,,,,,,,,++++++***++++++,,,,,,,,,,,,++++++,,,,,,------,,,,,,++++++***))))))(((++++++***))))))******+++))))))*********+++++++++******))))))))))))******...---,,,+++******************++++++++++++******((((((((((((((((((((((((((((((((((((((((((((((((+++******))))))***+++,,,************))))))))))))******+++,,,,,,,,,,,,+++))))))***+++++++++++++++,,,,,,+++***************************************,,,,,,,,,++++++,,,------,,,,,,,,,+++++++++******,,,+++***(((''''''''''''(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%$$$$$$###$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$''''''&&&%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$FFFGGGIIIHHHFFFEEEEEEFFFGGGGGGHHHIIIIIIIIIHHHHHHFFFFFFFFFFFFGGGHHHIIIJJJGGGGGGGGGFFFDDDDDDEEEFFFFFFEEEDDDDDDDDDDDDDDDEEEGGGGGGGGGHHHHHHIIIIIIIIIFFFFFFFFFGGGGGGGGGGGGGGGIIIIIIIIIHHHGGGEEEDDDCCCDDDDDDEEEEEEEEEDDDCCCCCCCCC@@@>>>@@@CCCDDDCCC@@@BBBCCCCCCCCCCCCCCCBBBBBBCCCBBBAAABBBEEEFFFEEEDDDDDDCCCCCCCCCCCCDDDEEEEEEEEEDDDDDDCCCCCCBBBBBBBBBCCCDDDDDDDDDDDDDDDCCCCCCBBBAAA@@@@@@AAABBBDDDEEE???@@@BBBAAA@@@@@@BBBCCC@@@@@@@@@@@@@@@AAAAAAAAA??????@@@AAAAAAAAAAAA@@@BBB@@@===<<<<<<===<<<;;;>>>>>>>>>??????>>>>>>===:::::::::;;;;;;:::::::::999:::;;;;;;<<<<<<;;;;;;:::;;;<<<;;;:::999:::;;;::::::::::::;;;;;;;;;;;;888888777777888888999:::::::::::::::999999999999888999::::::;;;;;;::::::;;;;;;;;;<<<>>>===:::888<<<<<<<<<;;;:::999777777:::;;;<<<;;;::::::;;;<<<;;;;;;;;;<<<<<<===>>>>>>;;;;;;;;;;;;;;;;;;;;;;;;===<<<;;;<<<>>>??????>>>:::;;;<<<;;;999888999:::888888888888888777777777888777666444333333222222666666555555555444444444333333333333333333333333555444333333333333444555111222333333444444333333111111222222222222111111000000/////////000111111///111333555555333111///000000////////////000000000000////////////......111111111111111111111111111111000000//////......000000000000000000000000------......------,,,+++---,,,,,,++++++,,,,,,---//////......................../////////000000000//////...---------------,,,,,,++++++++++++,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,++++++***++++++,,,,,,,,,,,,,,,,,,---......,,,,,,++++++***)))))))))******)))))))))******+++)))))))))*********++++++***)))))))))))))))******---,,,+++*********************++++++++++++******((((((((((((((((((((((((((((((((((((((((((((((((***)))))))))***+++,,,,,,******************************+++,,,,,,,,,,,,+++))))))***++++++++++++***,,,,,,++++++++++++++++++************************++++++++++++,,,------...,,,,,,,,,+++++++++************)))((((((((((((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%&&&&&&%%%%%%$$$$$$$$$$$$'''&&&&&&%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$######%%%$$$$$$%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$FFFHHHJJJJJJHHHGGGFFFGGGGGGGGGHHHHHHHHHHHHGGGGGGGGGGGGFFFGGGGGGHHHIIIIIIGGGHHHHHHGGGEEEDDDEEEFFFDDDDDDDDDCCCDDDDDDEEEEEEFFFFFFGGGHHHHHHIIIJJJJJJFFFFFFEEEEEEEEEFFFFFFFFFHHHHHHHHHGGGGGGEEEDDDDDDDDDEEEEEEEEEDDDCCCBBBBBBBBBAAA@@@AAACCCDDDCCCAAACCCCCCDDDDDDDDDCCCBBBBBB@@@@@@@@@AAABBBCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDEEECCCCCCCCCCCCCCCBBBBBBBBBBBBCCCDDDEEEEEEDDDCCCBBBAAAAAA@@@@@@AAABBBCCCDDD???AAABBBAAA@@@@@@AAABBB>>>??????@@@@@@AAAAAAAAA???@@@@@@AAAAAAAAAAAAAAABBB???<<<;;;<<<=========<<<===>>>>>>?????????>>><<<;;;:::999999:::;;;<<<:::::::::;;;;;;;;;;;;;;;999:::;;;:::999999:::<<<::::::;;;;;;;;;;;;;;;;;;888888777777888888999:::<<<<<<;;;;;;::::::999999:::;;;<<<===>>>===<<<;;;;;;<<<===>>>???===:::777<<<<<<;;;;;;;;;:::999999;;;<<<<<<;;;:::999999;;;::::::;;;<<<===>>>>>>>>>========================<<<<<<<<<<<<===>>>>>>>>>;;;<<<===<<<:::999:::;;;::::::999999888888777777666555555444333333333333555555666666666555444333333333333333333444444444555555555444444555555555111222333333444444333333111222222333333222222111////////////000111111222000111333444444333111000000000////////////000000000000//////////////////111111111111111111111111111111000000//////......////////////////////////------......------,,,+++---,,,,,,++++++,,,,,,---///////////////.........////////////000000000000000///......------......+++,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,,,,------,,,,,,++++++******++++++++++++++++++,,,,,,---...+++++++++*********))))))***))))))))))))******+++))))))))))))************))))))))))))))))))***+++,,,,,,+++*********************++++++++++++******(((((((((((((((((((((((((((((((((((((((((((((((((((((()))******+++,,,---)))***************++++++******+++,,,,,,,,,,,,+++)))******+++++++++******++++++,,,,,,,,,+++++++++*********************************+++,,,---...///,,,,,,,,,+++++++++******))))))(((((((((((())))))(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%%%%$$$&&&%%%%%%%%%$$$$$$$$$$$$&&&&&&%%%%%%$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$$$$###############$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###HHHIIIJJJJJJHHHGGGGGGHHHFFFGGGGGGGGGGGGGGGFFFFFFIIIHHHGGGGGGFFFFFFFFFGGGFFFGGGHHHHHHFFFEEEEEEFFFDDDDDDDDDDDDDDDEEEFFFGGGFFFFFFGGGHHHHHHIIIJJJJJJFFFFFFEEEDDDDDDDDDEEEFFFGGGGGGGGGGGGFFFFFFEEEDDDDDDDDDDDDDDDDDDCCCBBBAAABBBAAAAAAAAACCCCCCCCCBBBCCCCCCDDDDDDCCCBBBAAAAAA>>>??????@@@@@@@@@AAABBBBBBCCCCCCDDDDDDDDDDDDDDDBBBBBBBBBCCCCCCCCCCCCCCC@@@BBBCCCEEEEEEEEEDDDDDDCCCCCCBBBBBBAAAAAABBBBBBBBBCCCCCCBBB@@@??????@@@===>>>>>>>>>??????@@@@@@>>>???@@@@@@AAAAAA@@@@@@???===;;;:::<<>>>>>>>>>>>===<<<:::999999:::<<<===::::::::::::;;;;;;<<<<<<999:::::::::888999:::<<<;;;;;;;;;;;;;;;;;;;;;;;;:::999999999999:::;;;;;;===<<<<<<<<<;;;;;;:::::::::;;;<<<===>>>===<<<;;;======>>>@@@AAA???;;;888:::::::::;;;;;;<<<<<<===<<<======<<<:::999999:::888999:::<<<====================================;;;<<<======<<<<<<======;;;<<<===<<<:::999:::;;;::::::999999888888777777333333333333333444555666555555666666555555444333333444444444555555555666555555555555555555555555111222333333444444333333222222333333333333222222//////000111111111222222000111333444444333111000000000////////////000000//////000000000000000000000000000000000000000000111111000000//////..............................------......------,,,+++---,,,,,,++++++,,,,,,---...//////000000///......////////////000000000000111000//////......//////+++,,,------------,,,+++++++++,,,,,,,,,------------,,,++++++*********+++))))))))))))***+++,,,---+++++++++***************))))))(((((()))******+++(((((()))))))))*********))))))(((((()))***++++++++++++******))))))************++++++++++++******))))))))))))))))))))))))))))))))))))))))))))))))(((((()))***+++,,,,,,,,,))))))******+++++++++,,,******+++,,,,,,,,,,,,+++******+++++++++******)))******+++,,,,,,,,,+++************************************+++,,,---...///,,,,,,,,,+++++++++******((((((((((((((())))))***(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&&&&&&&$$$$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########IIIJJJJJJIIIGGGFFFHHHJJJGGGGGGHHHHHHHHHGGGFFFFFFIIIHHHGGGFFFEEEEEEEEEEEEEEEGGGHHHHHHGGGFFFFFFGGGDDDDDDDDDDDDEEEFFFHHHHHHGGGGGGGGGHHHHHHIIIIIIIIIGGGFFFEEEDDDCCCDDDEEEFFFEEEFFFFFFFFFFFFFFFEEEEEECCCCCCDDDDDDDDDCCCBBBBBBBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCBBBAAA@@@@@@===>>>@@@@@@??????AAABBBBBBCCCCCCDDDEEEDDDDDDDDDBBBBBBBBBCCCDDDDDDDDDEEEAAABBBCCCDDDEEEEEEEEEEEEEEEEEEDDDCCCCCCBBBAAA@@@DDDEEEEEECCCAAA??????@@@>>>>>>>>>>>>>>>?????????>>>>>>???@@@@@@@@@@@@???===<<<:::;;;===@@@@@@@@@;;;<<<======>>>>>>>>>>>>===<<<;;;::::::;;;<<<===;;;::::::::::::;;;<<<===;;;<<<;;;:::888999;;;===<<<<<<<<<<<<;;;;;;;;;;;;;;;;;;::::::;;;;;;<<<===<<<<<<<<<<<<;;;;;;;;;;;;888999::::::;;;;;;::::::>>>>>>>>>@@@AAA@@@===;;;:::::::::;;;<<<===>>>???<<<===>>>===;;;:::;;;<<<888999;;;<<<======<<<;;;::::::::::::::::::::::::;;;<<<======;;;;;;<<<===;;;<<<===<<<:::999:::;;;888888888888888777777777111111222222333555666777555555444444444333333333333444444555555666666666444444555666666555444444111222333333444444333333222222333333333333222222111111222333333222222222111222333333333333222111000000////////////000000//////000000000000111111000000000000000000000000111111000000//////..............................------......------,,,+++---,,,,,,++++++,,,,,,---,,,---...///000///............/////////000000000111111000///////////////+++,,,---......---,,,+++,,,,,,,,,,,,------------------,,,+++************(((((((((((()))+++,,,---************************(((((((((((()))******+++((((((((()))))))))******(((((((((((()))***+++,,,+++******)))))))))************++++++++++++******))))))))))))))))))))))))))))))))))))))))))))))))((()))***+++++++++++++++))))))******+++,,,,,,,,,******+++,,,,,,,,,,,,+++***++++++++++++***))))))((()))***+++,,,+++***)))************************++++++++++++,,,------...,,,,,,,,,+++++++++******)))((((((((((((((()))***(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%$$$###!!!!!!!!!!!!""""""###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$############JJJJJJIIIGGGEEEEEEHHHKKKIIIJJJJJJJJJIIIIIIHHHGGGFFFFFFEEEEEEDDDEEEEEEEEECCCEEEHHHHHHHHHGGGHHHHHHDDDDDDEEEEEEFFFHHHIIIJJJHHHHHHHHHHHHHHHHHHHHHHHHHHHGGGEEEDDDCCCDDDEEEFFFEEEEEEFFFFFFFFFFFFFFFEEEBBBBBBCCCCCCDDDCCCCCCCCCAAABBBCCCCCCBBBBBBCCCDDDBBBBBBBBBBBBAAA@@@???>>>===???AAAAAA@@@@@@BBBDDDBBBBBBDDDEEEEEEEEEDDDCCCBBBBBBCCCDDDDDDEEEFFFFFFDDDDDDCCCCCCCCCCCCDDDDDDEEEEEEEEEEEEDDDCCCBBBBBBCCCDDDEEEDDDBBBAAABBBCCC@@@@@@???????????????>>>>>>>>>???@@@@@@@@@@@@@@@===<<<;;;===>>>??????>>>======>>>?????????>>>>>><<<<<<;;;;;;;;;;;;<<<<<<;;;;;;:::::::::;;;<<<============:::999999;;;======<<<<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;;;;<<<<<<===;;;;;;;;;;;;;;;;;;<<<<<<:::999999999999:::;;;;;;======<<<===??????>>><<<<<<<<<;;;;;;;;;===>>>???<<<>>>>>>>>><<<;;;<<<===:::;;;===>>>>>>===<<<;;;:::::::::::::::::::::::::::<<<>>>===;;;:::;;;===:::;;;<<<;;;999999999:::666666777777777777777888222222222222333444555555555444333222111222333333222222333444444555666666333444555555555555444333111222333333444444333333222333333444444333333222333333444444444333222111111222222333333222222111000000////////////000000//////000000000111111111000000000000000000000000111111000000//////..............................------......------,,,+++---,,,,,,++++++,,,,,,---)))+++---///000//////...------........./////////000000///............///+++,,,---//////---,,,+++,,,,,,,,,------------......---,,,+++************((((((((()))***+++---...************************'''''''''(((((()))++++++(((((((((((()))))))))***(((((((((((()))***+++,,,******))))))))))))************++++++++++++******)))))))))))))))))))))))))))))))))))))))))))))))))))***++++++++++++***)))))))))***++++++,,,------******+++,,,,,,,,,,,,++++++++++++++++++***))))))&&&''')))++++++***)))(((************************,,,,,,,,,++++++,,,------,,,,,,,,,+++++++++*********)))((((((((((((((()))(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&''''''((((((((('''$$$$$$$$$###"""!!! !!!"""###$$$%%%$$$$$$######$$$%%%%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&(((''''''&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$############KKKJJJHHHEEEDDDEEEHHHLLLKKKLLLLLLLLLKKKJJJIIIIIICCCCCCCCCCCCDDDEEEFFFGGGBBBEEEGGGIIIHHHHHHIIIIIIEEEEEEEEEFFFGGGIIIJJJKKKIIIHHHHHHHHHHHHHHHHHHHHHIIIGGGEEEDDDCCCDDDEEEFFFDDDEEEEEEFFFFFFFFFFFFEEEAAAAAABBBCCCDDDDDDDDDCCCAAABBBCCCCCCBBBBBBCCCDDDAAABBBAAAAAA@@@???>>>===>>>AAACCCCCCAAAAAACCCFFFAAABBBDDDEEEEEEEEEDDDCCCBBBCCCCCCDDDEEEFFFGGGGGGGGGFFFDDDCCCBBBBBBCCCCCCEEEEEEEEEEEEEEEEEEDDDCCCBBBCCCEEEDDDCCCCCCDDDFFFBBBAAAAAA@@@@@@???????????????@@@AAAAAAAAAAAA@@@>>>======>>>??????===;;;??????@@@@@@@@@??????>>><<<<<<<<<<<<<<<<<<<<<<<<;;;;;;:::999:::;;;<<<===??????>>>;;;999999;;;=========<<<<<<<<<;;;;;;;;;;;;;;;::::::;;;;;;<<<===999::::::;;;;;;<<<<<<<<<===<<<;;;:::;;;<<<===>>><<<;;;;;;;;;===???>>>===>>>>>><<<;;;;;;<<<===>>><<<>>>???>>>======>>>???<<<===???@@@???>>><<<;;;<<<<<<<<<<<<<<<<<<<<<<<<:::<<<>>>===;;;999;;;===:::;;;<<<;;;999888999:::555555666666777777888888444444333222222333333333555444222000000111222333111111222333333444555555222333444555555444333222222222333444444444333333222333333444444333333222444555555666555444222111222222222333333222222222000000////////////000000//////000000111111111222000000000000000000000000111111111000//////......000000000000000000000000------......------,,,+++---,,,,,,++++++,,,,,,---'''))),,,...///000///...------------........./////////...------------...+++,,,...//////...,,,+++,,,,,,,,,---------.........---,,,+++************)))))))))***+++---...///******************++++++''''''''''''((()))++++++(((((((((((())))))))))))(((((((((((()))***+++,,,***)))))))))))))))************++++++++++++******)))))))))))))))))))))))))))))))))))))))))))))))))))***+++,,,,,,+++)))((())))))***+++,,,,,,------******+++,,,,,,,,,,,,++++++++++++++++++***)))(((%%%''')))***+++***)))(((************************------,,,+++++++++,,,,,,,,,,,,,,,+++++++++************)))((((((((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&'''((())))))(((((($$$$$$$$$###!!!  !!!###$$$%%%$$$#########$$$%%%%%%&&&#########$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$############"""HHHHHHHHHHHHHHHHHHHHHHHHFFFGGGHHHGGGFFFFFFGGGIIIDDDEEEFFFGGGHHHIIIIIIIIIHHHHHHGGGGGGFFFGGGGGGGGGFFFFFFFFFFFFFFFFFFGGGGGGFFFHHHIIIIIIHHHGGGHHHIIIHHHHHHIIIIIIIIIHHHGGGFFFJJJHHHFFFFFFGGGGGGGGGFFFDDDDDDCCCBBBBBBBBBBBBCCCDDDEEEEEECCCAAA@@@AAACCCEEEDDDBBB@@@?????????@@@????????????????????????CCCDDDDDDEEEEEEEEEEEEDDDCCCDDDEEEGGGGGGGGGFFFEEEDDDDDDDDDDDDDDDDDDDDDDDDCCCDDDDDDDDDEEEEEEFFFFFFCCCCCCBBBBBBBBBAAAAAAAAABBBBBBBBBAAAAAA@@@@@@@@@AAAAAABBB@@@???>>>@@@AAA>>>===<<<<<<<<<<<<=========???AAABBBBBBAAA@@@>>>>>>======<<<<<<<<<<<<===>>>===;;;::::::;;;===>>>===<<<;;;:::::::::::::::<<<<<<======<<<;;;::::::<<<;;;:::999999;;;<<<>>>;;;::::::999:::;;;===>>>@@@>>>;;;<<<===>>>;;;999;;;:::;;;<<>>===========================;;;<<<<<<===============AAABBBDDDDDDCCCAAA>>><<<>>>===<<<===>>>>>><<<:::===============<<<<<<<<<>>>===;;;999888777666666888777666555555666777888555555444333333333333444777666444333222333333444333444555666666666555444777777666666555555444444555555555444444333333333222333333333333222111111222222333333333333333333222333444555555333111000////////////////////////000000000000000000000000---------......///000111111111000000000000111111111000...---,,,,,,------------------------------+++++++++,,,,,,---------,,,,,,---------------,,,,,,------...///000000111111111000......---------------------------------.........------,,,,,,,,,)))))))))))))))))))))))))))***+++,,,,,,+++***)))))))))))))))************+++******)))))))))))))))++++++***)))(((((())))))(((((()))***************))))))))))))(((((((((((())))))*********+++++++++)))))))))******+++++++++++++++,,,,,,,,,,,,------***)))((()))***+++***((()))************+++++++++++++++++++++++++++++++++)))+++---...---***'''%%%%%%%%%'''(((***,,,---...))))))))))))***************++++++,,,,,,++++++******************)))(((((((((((((((((('''''''''''''''((()))((('''&&&''')))''''''&&&&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&######"""  """$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###%%%$$$$$$######$$$$$$%%%&&&%%%$$$$$$############$$$$$$$$$############"""HHHHHHHHHHHHHHHHHHHHHHHHJJJKKKKKKJJJHHHHHHJJJKKKFFFGGGGGGHHHHHHHHHGGGGGGGGGFFFFFFFFFGGGHHHIIIIIIFFFFFFFFFFFFFFFGGGGGGHHHGGGHHHJJJIIIHHHGGGGGGHHHGGGHHHHHHHHHGGGGGGFFFFFFIIIGGGFFFFFFGGGGGGFFFEEEDDDDDDCCCBBBBBBBBBBBBCCCBBBBBBCCCBBBAAAAAACCCDDDDDDDDDCCCBBBAAAAAAAAAAAA????????????????????????BBBCCCCCCDDDDDDDDDDDDCCCCCCDDDEEEFFFFFFFFFEEEEEEDDDDDDDDDDDDDDDDDDDDDDDDCCCCCCCCCDDDDDDEEEEEEEEECCCCCCBBBBBBBBBAAAAAAAAABBBBBBBBBAAAAAA@@@@@@@@@@@@@@@AAA???======>>>???>>>>>>============>>>>>>???@@@AAAAAAAAA@@@??????@@@???>>>===============>>>===;;;::::::;;;===>>>???>>>===<<<<<<<<<<<<===<<<<<<===<<<<<<;;;;;;:::<<<;;;:::999999;;;<<<>>>===<<<;;;;;;;;;<<<===>>>>>><<<;;;;;;===>>>===;;;<<<;;;:::<<<>>>???>>>>>>========================<<<<<<===>>>>>>>>>>>>===AAABBBCCCCCCBBB@@@>>>===>>>===<<<===>>>>>><<<:::<<<<<<<<<<<<<<<;;;;;;;;;;;;::::::999888888999999777777666555555666777777666555444444333333444444666555444444333333333444333444555777777777666666666666666666666555555555555555555444444333333333222333333333333222111111555555555555555555444444222333444555555333111000111111111111111111111111000000000000000000000000............///000111222222222111111111111222222111000...---,,,,,,------------------------------++++++,,,,,,,,,---------,,,,,,---........................//////000000111111000///......------------------------------------------------,,,,,,,,,++++++++++++++++++++++++))))))***++++++***))))))))))))))))))************+++******)))))))))))))))++++++***)))))))))))))))(((((()))************)))*********)))))))))((((((******************++++++,,,,,,---------.........++++++,,,,,,,,,,,,------+++)))((()))***+++***((()))************+++++++++++++++++++++++++++++++++***+++,,,,,,,,,***((('''%%%%%%&&&((()))***+++,,,))))))))))))***************++++++,,,,,,++++++******************)))(((((((((((((((((('''''''''''''''((()))((('''&&&''')))(((''''''&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$###""" """$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$############"""HHHHHHHHHHHHHHHHHHIIIIIIIIIIIIIIIHHHFFFEEEFFFHHHHHHHHHHHHHHHHHHGGGFFFFFFFFFFFFFFFFFFGGGIIIJJJKKKFFFFFFFFFFFFFFFGGGHHHHHHHHHIIIJJJIIIGGGFFFFFFGGGGGGGGGGGGGGGFFFFFFFFFEEEHHHFFFEEEEEEFFFGGGFFFDDDDDDDDDCCCBBBBBBBBBBBBCCC???@@@AAAAAAAAAAAACCCEEEBBBCCCCCCDDDDDDCCCCCCBBB@@@@@@@@@@@@@@@@@@@@@@@@AAAAAABBBCCCCCCCCCCCCCCCCCCCCCDDDEEEEEEEEEDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDCCCCCCCCCCCCCCCDDDDDDDDDCCCCCCBBBBBBBBBAAAAAAAAABBBBBBAAAAAAAAAAAA@@@@@@???@@@@@@>>><<<;;;<<<===??????>>>>>>>>>??????@@@BBBAAAAAA@@@@@@?????????BBBAAA@@@???>>>=========>>>===<<<;;;;;;<<<===>>>>>>>>>======<<<<<<======<<<<<<<<<<<<<<<;;;;;;;;;;;;;;;:::999:::;;;<<<===>>>>>>===<<<<<<<<<======;;;::::::;;;===???>>>======<<<::::::<<<>>>???>>>==============================>>>???????????????BBBBBBAAAAAAAAA@@@??????>>>===<<<===>>>>>><<<:::;;;;;;;;;;;;;;;;;;;;;;;;999888888999999:::;;;<<<777666555444444555666777666555444444333444444444444555555555555444333333333444555777777888888888555555555666666666666666555555555444444444444444333333333333333222222111666666555555444444333333222333444555555333111000000000000000000000000000000000000000000000000000////////////000111222333333333222222222222333333111000///---,,,------...------------------------,,,,,,,,,,,,------------+++,,,---...///000000000000000000000000000000000111000///......---......,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------,,,,,,,,,,,,,,,,,,,,,,,,))))))************)))))))))))))))*********+++++++++******)))))))))))))))+++***))))))))))))))))))''''''((()))))))))))))))+++++++++*********))))))++++++******************---------...............++++++,,,,,,,,,,,,------+++***))))))***+++***))))))************+++++++++++++++++++++++++++++++++,,,,,,++++++***)))))))))&&&&&&'''(((((())))))***))))))))))))******************++++++++++++*********************)))(((((((((((((((((('''''''''''''''((()))((('''&&&'''))))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%###!!! ###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$&&&&&&&&&%%%%%%&&&&&&&&&'''&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$############"""HHHHHHHHHIIIIIIIIIIIIIIIHHHIIIIIIGGGEEEDDDEEEFFFGGGHHHHHHIIIHHHHHHGGGGGGGGGGGGGGGGGGGGGHHHIIIJJJFFFFFFFFFFFFGGGHHHHHHIIIJJJJJJJJJIIIFFFEEEFFFGGGHHHHHHHHHGGGGGGGGGGGGGGGFFFEEEDDDEEEFFFFFFEEEDDDDDDDDDCCCBBBBBBBBBBBBCCC???@@@AAAAAA@@@@@@BBBDDD@@@AAABBBDDDDDDDDDCCCBBB@@@@@@@@@@@@@@@@@@@@@@@@AAAAAABBBCCCDDDDDDDDDDDDCCCCCCDDDDDDDDDDDDDDDCCCDDDDDDDDDDDDDDDDDDDDDDDDBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCBBBBBBBBBAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA@@@AAAAAA???<<<;;;<<<===@@@@@@?????????@@@AAAAAACCCBBBAAA@@@????????????BBBAAA@@@???>>>===============<<<<<<<<<<<<======<<<<<<;;;;;;;;;;;;<<<<<<<<<<<<<<<;;;;;;;;;<<<<<<;;;;;;:::::::::;;;<<<===>>>>>>===<<<<<<;;;;;;;;;999999999;;;===>>>?????????<<<::::::;;;>>>??????>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>???@@@@@@@@@@@@???BBBAAA@@@??????@@@@@@AAA>>>===<<<===>>>>>><<<:::;;;;;;;;;;;;;;;<<<<<<<<<999999999999999:::;;;<<<777666555444444555666777666666555444444444444444333444555666666555444333333333444555666777777888444444555555666666777777555555555555555444444444333333444444333333222111444444333333222111000000222333444555555333111000........................000000000000000000000000000000000000111222333444222222222111111222222222111000///---------......------------............,,,,,,------------------+++,,,---///000111111111111111111111000000000000000000///...............,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,------...************************))))))))))))))))))))))))))))))*********++++++++++++******)))))))))))))))******)))))))))))))))***''''''((())))))))))))(((,,,,,,,,,+++++++++******+++++++++***************+++++++++++++++++++++++++++++++++,,,,,,,,,------+++***))))))++++++***)))))))))*********+++++++++++++++++++++++++++++++++---,,,***)))))))))******))))))))))))))))))))))))((()))))))))******************++++++++++++*********************)))(((((((((((((((((('''''''''''''''((()))((('''&&&''')))***)))((('''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$!!!  ###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&'''&&&%%%%%%$$$''''''&&&&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&&&&$$$$$$$$$#########""""""HHHHHHHHHIIIIIIJJJJJJJJJKKKLLLLLLJJJHHHGGGHHHIIIFFFFFFGGGHHHIIIJJJJJJIIIJJJJJJIIIHHHGGGGGGGGGGGGFFFFFFFFFFFFGGGHHHIIIJJJJJJJJJJJJHHHFFFEEEFFFHHHKKKJJJIIIHHHHHHHHHHHHIIIEEEDDDDDDEEEGGGGGGEEEDDDDDDDDDCCCBBBBBBBBBBBBCCCBBBBBBBBBAAA??????@@@AAA>>>???AAABBBCCCCCCBBBAAA@@@@@@@@@@@@@@@@@@@@@@@@BBBBBBCCCDDDEEEFFFFFFFFFDDDDDDDDDCCCCCCCCCCCCDDDDDDDDDDDDDDDDDDDDDDDDDDDCCCCCCCCCCCCCCCCCCBBBBBBCCCCCCBBBBBBBBBAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBAAA>>>===>>>@@@@@@@@@@@@@@@@@@AAABBBBBBCCCBBBAAA@@@????????????AAA@@@???>>>=====================<<<<<<=========<<<<<<;;;;;;;;;<<<<<<===<<<<<<;;;;;;;;;;;;<<<===::::::::::::;;;;;;<<<<<<<<<<<<<<<<<<;;;:::::::::888999:::;;;<<<===???@@@???===::::::;;;===>>>>>>????????????????????????>>>??????@@@@@@@@@@@@@@@AAA@@@???>>>>>>???AAABBB>>>===<<<===>>>>>><<<:::;;;;;;<<<<<<============;;;;;;::::::999:::::::::777666555444444555666777666666555444444444444555333444555666666666555444222222333333444555666666444444555555666666777777555555555555555555555555333444444444444333222222444444333222111111000000222333444555555333111000........................000000000000000000000000000000000111111222333444111111000000000000111111222111///...------......---------....../////////------------------------+++,,,---///000111111111111111111111000000000000000//////............///,,,,,,,,,,,,,,,,,,,,,,,,***++++++,,,,,,---------******************************))))))))))))******************+++++++++++++++******)))))))))))))))***)))))))))))))))******'''(((((())))))))))))))),,,,,,,,,,,,++++++++++++******************************))))))))))))))))))+++++++++,,,,,,,,,------+++***)))***+++,,,+++)))))))))*********+++++++++++++++++++++++++++++++++---,,,***)))((()))***++++++++++++*********))))))((()))))))))************)))******++++++******)))***************)))(((((((((((((((((('''''''''''''''((()))((('''&&&''')))***)))((('''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$!!!  ###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&'''''''''&&&%%%%%%(((''''''&&&&&&''''''(((&&&&&&&&&%%%%%%&&&&&&'''$$$$$$$$$#########""""""HHHHHHHHHIIIJJJJJJKKKKKKIIIJJJJJJIIIGGGFFFGGGIIIEEEFFFGGGIIIJJJJJJKKKKKKLLLKKKJJJHHHGGGGGGGGGGGGFFFFFFFFFFFFGGGIIIJJJKKKJJJJJJIIIHHHFFFEEEGGGIIILLLKKKIIIHHHHHHHHHIIIJJJEEEDDDEEEFFFHHHHHHFFFDDDDDDDDDCCCBBBBBBBBBBBBCCCCCCDDDDDDBBB@@@???@@@AAA???@@@@@@AAABBBBBBBBBAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBDDDEEEFFFFFFFFFFFFFFFEEEDDDCCCCCCCCCDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDCCCCCCCCCCCCCCCCCCCCCBBBBBBBBBAAAAAAAAA@@@@@@AAAAAAAAAAAABBBBBBBBBCCCCCCBBB@@@@@@AAACCC@@@@@@???@@@@@@AAABBBCCCBBBAAAAAA@@@@@@???????????????>>>============>>>========================>>>>>>======>>>>>>??????<<<<<<;;;::::::<<<===>>>:::::::::;;;;;;;;;<<<<<<;;;;;;;;;<<<;;;;;;:::999888:::;;;<<<;;;;;;===>>>???===;;;;;;<<<===>>>===????????????????????????>>>>>>???@@@@@@@@@@@@???@@@???>>>>>>???@@@AAABBB>>>===<<<===>>>>>><<<:::;;;;;;<<<<<<===>>>>>>>>>======;;;:::999999999999888777666555555666777888777666555555444444555555444444555666666666666555333333222222333333444555555555555666666666666666555555555555555666666666444444444444444333222222555555444444333333222222222333444555555333111000000000000000000000000000000000000000000000000000000000000000111222333444111000000000000000000111222111000...---......///---------...//////000000............------------+++,,,---...///000000000000000000000000000000000//////............//////------------------------++++++++++++,,,,,,,,,,,,------------------------++++++************++++++*********++++++++++++,,,+++******))))))))))))))))))))))))))))))******+++(((((()))***************,,,,,,,,,+++++++++******))))))*********+++++++++++++++++++++************++++++,,,,,,,,,,,,------,,,*********+++,,,+++***)))************+++++++++++++++++++++++++++++++++,,,+++***))))))***++++++,,,,,,,,,++++++*********))))))))))))************))))))************))))))***************)))(((((((((((((((((('''''''''''''''((()))((('''&&&'''))))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###!!! ###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''&&&%%%%%%''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%&&&&&&'''$$$$$$$$$############"""HHHHHHIIIIIIJJJKKKKKKKKKFFFGGGGGGFFFEEEDDDFFFGGGGGGGGGHHHIIIJJJJJJJJJIIIKKKJJJIIIHHHHHHHHHHHHHHHFFFFFFFFFGGGHHHIIIJJJKKKIIIIIIIIIGGGEEEFFFHHHKKKLLLJJJIIIGGGGGGHHHIIIJJJEEEEEEFFFHHHIIIIIIGGGEEEDDDDDDCCCBBBBBBBBBBBBCCCBBBCCCCCCBBBAAAAAABBBDDDBBBBBBAAAAAAAAABBBBBBCCCAAAAAAAAAAAAAAAAAAAAAAAA@@@AAACCCDDDEEEFFFFFFFFFGGGFFFEEEDDDDDDDDDEEEEEEDDDDDDDDDDDDDDDDDDDDDDDDEEEEEEEEEDDDDDDCCCCCCCCCCCCCCCBBBBBBBBBAAAAAAAAA@@@@@@@@@AAAAAABBBBBBBBBAAABBBCCCBBBAAAAAACCCEEE????????????@@@AAABBBCCC???@@@AAAAAAAAA@@@????????????>>>>>>>>>???@@@@@@======>>>>>>>>>>>>======>>>>>>>>>>>>>>>???@@@@@@===<<<:::::::::<<<===???::::::;;;;;;<<<<<<;;;;;;:::;;;<<<======<<<<<<;;;:::<<<===<<<:::999:::<<<>>>===;;;<<<===>>>===;;;@@@@@@@@@@@@@@@@@@@@@@@@===>>>>>>???@@@?????????>>>>>>>>>>>>???@@@AAABBB>>>===<<<===>>>>>><<<:::::::::;;;<<<<<<===>>>>>>======;;;::::::999999:::999888777666666777888999777666666555555555555555555555555555555666777777666555444333222333444444666666666666666555555555444555555555666666666777444444444555444444333222444444333333333333333333222333444555555333111000111111111111111111111111000000000000000000000000000000///000000111222333222111111000000111111222222111000............///---------...///000000000///.........------------,,,,,,---........................//////000000111//////............//////........................,,,,,,,,,+++++++++++++++---------------------------,,,+++******+++,,,---*********+++++++++,,,,,,+++******))))))))))))))))))))))))))))))***++++++)))******+++++++++++++++++++++++++++************(((((()))***+++,,,,,,---,,,,,,,,,+++++++++******++++++,,,,,,,,,,,,------,,,+++******,,,,,,+++***)))************++++++++++++++++++++++++++++++++++++***************+++++++++++++++***************))))))))))))************))))))************))))))***************)))(((((((((((((((((('''''''''''''''((()))((('''&&&''')))(((''''''&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###""" """$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&%%%'''&&&&&&&&&&&&&&&&&&'''$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$############"""HHHHHHIIIIIIJJJKKKLLLLLLHHHIIIJJJIIIHHHHHHJJJKKKIIIIIIJJJJJJIIIIIIHHHGGGIIIIIIHHHHHHHHHIIIJJJJJJFFFFFFFFFGGGHHHIIIKKKLLLIIIIIIHHHGGGEEEFFFIIILLLKKKJJJHHHFFFFFFGGGHHHIIIEEEEEEFFFHHHJJJJJJHHHEEEDDDDDDCCCBBBBBBBBBBBBCCCAAABBBCCCCCCBBBBBBDDDFFFDDDDDDBBBAAAAAABBBCCCDDDAAAAAAAAAAAAAAAAAAAAAAAA???@@@AAACCCDDDEEEEEEEEEHHHGGGFFFDDDDDDDDDEEEFFFDDDDDDDDDDDDDDDDDDDDDDDDFFFFFFEEEEEEDDDDDDDDDCCCCCCCCCBBBBBBBBBAAAAAAAAA@@@@@@@@@AAAAAABBBBBBBBB@@@AAABBBBBBAAAAAACCCEEE????????????@@@AAABBBCCC>>>???AAABBBBBBAAA@@@>>>????????????@@@AAABBBCCC======>>>>>>>>>>>>======<<<<<<<<<<<<<<<===>>>>>>===<<<:::::::::<<<>>>???999:::;;;;;;<<<<<<;;;;;;:::;;;<<<>>>>>>>>>======;;;===>>><<<999888999;;;===<<<<<<===>>>>>><<<:::@@@@@@@@@@@@@@@@@@@@@@@@======>>>????????????>>>======>>>???@@@AAAAAABBB>>>===<<<===>>>>>><<<:::999999::::::;;;<<<======<<<<<<;;;:::::::::;;;;;;:::999888777777888999:::777777666555555555555555666555444444444666777888888777555444333333444444777777666666555555555444444555555555666666777777444444555555444444333222111111111111111111222222222333444555555333111000000000000000000000000000000000000000000000000000////////////000111222333333222222222222222222333333222000///......//////---------...///000000111//////.........---------,,,,,,------...---------,,,------...///000000111//////.........//////000////////////////////////---,,,,,,++++++*********++++++++++++++++++++++++------,,,++++++,,,------******+++++++++,,,,,,,,,+++******)))))))))))))))))))))((())))))***++++++******+++,,,,,,,,,,,,++++++++++++*********))))))''''''(((***+++,,,---...+++++++++*********))))))++++++,,,,,,,,,---------,,,+++******,,,,,,+++***)))************+++++++++++++++++++++++++++++++++***************+++************))))))))))))))))))))))))))))))************))))))************))))))***************)))(((((()))((((((((('''''''''''''''((()))((('''&&&''')))''''''&&&&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""  """$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((''''''&&&%%%&&&&&&&&&%%%%%%&&&&&&&&&############$$$$$$%%%&&&$$$$$$$$$############"""JJJIIIHHHGGGHHHJJJLLLMMMHHHIIIHHHGGGFFFFFFHHHJJJIIIIIIJJJJJJIIIIIIHHHGGGFFFGGGHHHHHHIIIIIIIIIIIIFFFEEEEEEEEEGGGHHHGGGFFFIIIIIIJJJJJJJJJIIIHHHHHHIIIJJJKKKJJJIIIHHHIIIJJJJJJIIIHHHGGGFFFGGGHHHIIIHHHGGGEEEDDDBBBAAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBDDDAAA???@@@CCCFFFFFFDDDEEECCCAAA??????@@@CCCDDDEEEFFFGGGFFFEEEDDDEEEFFFEEEEEEEEEEEEFFFFFFFFFFFFEEEEEEEEEEEEDDDDDDDDDDDDFFFGGGGGGGGGFFFEEECCCBBB@@@AAADDDEEEEEEDDDAAA@@@CCCDDDDDDDDDCCCBBBAAAAAABBBAAA@@@??????@@@BBBCCCAAA@@@???>>>???AAADDDEEE===?????????>>>>>>@@@BBBBBBBBBBBBBBBBBBBBBBBBAAA???????????????????????????>>>===<<<;;;;;;;;;<<<999:::;;;<<<<<<;;;::::::;;;::::::999888888888999======<<<<<<<<<;;;;;;;;;>>>??????===:::999999:::;;;<<<===<<<;;;;;;<<<===<<<===???AAAAAAAAA???>>>????????????===;;;999888:::<<<>>>>>>======???AAA======>>>>>>>>>>>>>>>===;;;;;;<<<<<<<<<<<<;;;;;;>>>===<<<:::999999:::::::::;;;;;;:::888777888999999888777555555555666777333444555555666666555555444444444555555555666666555555555666555555444333666777888777666555666777555666777777666444222111000222333333222111222333222111333666444000///222///...---------///000111222222333333222111///...////////////000111222333333333222222111000000000......------------......//////.........---------......//////......---,,,,,,---...//////...---,,,................................................---,,,,,,,,,,,,---.........------,,,,,,------...,,,,,,,,,,,,,,,,,,,,,,,,---,,,,,,,,,,,,,,,,,,,,,+++++++++++++++++++++++++++***))))))((()))))))))***************************++++++,,,,,,++++++***++++++++++++++++++++++++((()))+++,,,------,,,+++))))))(((((()))***++++++***+++,,,---...---,,,,,,++++++++++++++++++++++++)))))))))))))))******+++++++++++++++++++++,,,,,,+++++++++*********))))))******))))))((((((''''''++++++***))))))***++++++))))))))))))))))))))))))++++++******************+++******)))(((''''''&&&&&&'''''''''(((((())))))((((((((()))(((((('''&&&''''''((((((((('''%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%$$$###!!!!!!###$$$%%%%%%%%%%%%$$$$$$###$$$$$$$$$$$$%%%&&&'''(((((((((((('''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%IIIIIIJJJJJJKKKKKKKKKKKKIIIJJJLLLLLLKKKJJJJJJKKKJJJJJJJJJJJJIIIHHHHHHGGGGGGHHHHHHIIIIIIIIIHHHHHHHHHGGGFFFGGGHHHIIIHHHGGGIIIIIIJJJJJJJJJJJJIIIIIIHHHJJJJJJJJJHHHHHHIIIJJJIIIIIIGGGFFFFFFFFFGGGHHHGGGFFFEEEDDDCCCBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCAAA???===>>>AAACCCCCCBBBDDDCCCAAA@@@@@@AAACCCEEEDDDEEEFFFEEEDDDCCCDDDFFFEEEEEEEEEEEEFFFFFFFFFGGGFFFEEEEEEEEEDDDDDDDDDDDDFFFFFFGGGGGGFFFEEECCCBBBAAABBBDDDEEEEEEDDDBBBAAACCCCCCDDDDDDCCCCCCBBBAAABBBCCCCCCCCCCCCCCCBBBBBBAAA@@@???>>>???AAACCCDDD@@@AAAAAA@@@>>>>>>???AAA@@@@@@@@@AAAAAABBBBBBBBB?????????@@@@@@@@@@@@@@@??????>>>=====================>>>>>>>>>>>>>>>===;;;;;;:::999999999999999============<<<<<<<<<;;;>>>??????===;;;999999:::<<<===>>>>>><<<<<<===>>><<<>>>???AAAAAAAAA???>>>????????????>>><<<:::999;;;<<<>>>>>>======???@@@<<<======>>>>>>>>>============>>>>>>>>>>>>=========<<<;;;:::999999999:::999:::;;;:::888666777888888777666555555666666777444555666666777777666666444444444555555555666666666666666666555444333333555777888777666555666777666777888888777555333222111333555555333222333444222111333666444000///222//////.........///000000111111222333222111000///////////////000111222333333333222222111000000000///..................//////.........------------......//////......---,,,,,,---...//////...---,,,........................---------------------------,,,,,,,,,,,,---.........------,,,,,,------...++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++)))))))))))))))***+++,,,***************************++++++,,,,,,++++++***,,,,,,++++++++++++++++++((()))+++,,,------,,,,,,***************+++,,,,,,***+++,,,---------,,,,,,++++++++++++++++++++++++)))))))))))))))***+++++++++++++++++++++++++++++++++++++++*********))))))(((((((((((())))))))))))************************((((((((((((((((((((((((************************+++++++++***))))))(((((('''''''''((((((((())))))((((((((((((((('''&&&&&&''''''((((((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$###"""!!!  !!!###$$$%%%%%%&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&'''''''''&&&&&&'''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%HHHJJJLLLMMMMMMLLLKKKIIIHHHKKKNNNOOOMMMKKKJJJJJJKKKKKKKKKJJJIIIHHHGGGGGGIIIIIIIIIJJJIIIIIIHHHHHHIIIHHHGGGHHHIIIJJJJJJHHHGGGHHHIIIJJJJJJKKKJJJJJJHHHIIIJJJJJJHHHHHHIIIJJJJJJIIIGGGFFFFFFFFFGGGHHHFFFFFFEEEDDDDDDDDDDDDDDDCCCCCCCCCCCCCCCCCCCCCCCC@@@???>>>>>>@@@BBBBBBBBBCCCBBBAAA@@@@@@BBBDDDFFFDDDEEEFFFEEEDDDDDDEEEFFFEEEEEEFFFFFFFFFGGGGGGGGGFFFFFFEEEEEEEEEDDDDDDDDDFFFFFFFFFFFFEEEDDDCCCCCCDDDDDDDDDDDDDDDDDDDDDDDDCCCCCCDDDDDDDDDCCCBBBBBBCCCDDDFFFGGGFFFDDDBBB@@@BBBAAA@@@??????@@@BBBBBBBBBCCCCCCAAA???>>>???AAA>>>>>>???@@@AAABBBCCCCCC??????@@@@@@AAAAAABBBBBB@@@@@@??????>>>?????????===<<<<<<;;;;;;;;;<<<<<<;;;;;;:::999999999::::::============<<<<<<<<<<<<===>>>???===;;;::::::;;;===???@@@???>>>===>>>???===>>>???AAAAAA@@@??????>>>?????????>>>===;;;:::;;;<<<>>>>>>======???@@@<<<<<<============<<<<<<======>>>>>>>>>>>>======<<<;;;:::999999888999999999::::::999777666666777777666666666666777777888666666666777777777777777444555555555555666666666777777777666555444333222555666777777555555666777666777888888777666444333333444666555444333333444222111444777555000///222//////000000000///......000000111222222222222111000000000000000111222333333333222222111000000000////////////////////////............------------......//////......---,,,------............------........................,,,,,,,,,,,,,,,,,,,,,,,,---,,,,,,,,,,,,---.........------,,,,,,------...************************++++++,,,,,,------......,,,,,,,,,,,,,,,,,,,,,,,,))))))))))))+++,,,---...++++++++++++++++++++++++***++++++,,,,,,++++++***,,,,,,,,,++++++*********))))))***,,,,,,,,,,,,,,,,,,++++++++++++,,,------***+++,,,---------,,,,,,++++++++++++++++++++++++***))))))))))))***++++++,,,,,,,,,+++*********)))+++++++++***************'''''''''((()))*********))))))***++++++***))))))''''''''''''''''''''''''************************,,,,,,++++++******))))))''''''(((((((((((())))))'''''''''(((''''''&&&%%%''''''((((((((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%"""###############""""""""""""###$$$%%%&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%###$$$$$$$$$%%%%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&JJJKKKLLLMMMMMMLLLKKKJJJHHHJJJLLLLLLKKKJJJJJJKKKLLLLLLKKKJJJIIIHHHHHHGGGJJJJJJJJJJJJJJJIIIHHHGGGIIIGGGGGGHHHIIIJJJIIIHHHFFFFFFGGGIIIJJJJJJJJJJJJHHHJJJKKKKKKJJJIIIJJJLLLKKKJJJIIIGGGGGGGGGHHHHHHEEEEEEEEEDDDDDDEEEFFFFFFAAAAAAAAAAAAAAAAAAAAAAAACCCBBBBBBCCCCCCDDDDDDDDDBBBAAAAAAAAAAAACCCEEEFFFDDDEEEGGGFFFEEEEEEFFFGGGFFFFFFFFFGGGGGGGGGHHHHHHFFFFFFFFFEEEEEEEEEDDDDDDEEEEEEEEEEEEEEEDDDDDDCCCFFFEEEDDDCCCCCCDDDEEEFFFCCCCCCDDDDDDDDDDDDCCCCCCEEEFFFFFFFFFEEEDDDBBBAAADDDCCCBBBAAAAAAAAABBBCCCBBBCCCCCCBBB@@@@@@AAACCC@@@@@@@@@AAAAAABBBBBBBBB@@@@@@@@@AAAAAABBBBBBCCCAAA@@@@@@@@@@@@@@@AAAAAA===<<<;;;999999:::;;;<<<;;;;;;::::::::::::;;;;;;<<<<<<<<<<<<;;;;;;;;;:::===>>>>>>===;;;:::;;;<<<>>>???@@@???>>>===>>>@@@>>>??????@@@@@@@@@??????>>>??????@@@???>>><<<;;;;;;===>>>>>>======>>>@@@<<<============<<<<<<;;;;;;;;;<<<<<<<<<<<<;;;;;;:::::::::999999888888888888999999888666555666777555555666666777777888888666666666666666777777777555555555555555666666666777777777777666444333222444555777666555555666777666666777777666555444333333444555555333222333333222111444777666111000222///000111111111///...,,,//////000111222222333333111000000000111111222333333333222222111000000000//////000000000000//////------------------------.........///......---,,,------------------------........................,,,,,,,,,,,,,,,,,,,,,,,,---,,,,,,,,,,,,---.........------,,,,,,------...++++++++++++++++++++++++***++++++,,,---...//////,,,,,,,,,,,,,,,,,,,,,,,,************+++,,,---...++++++++++++++++++++++++***++++++,,,,,,++++++***---,,,,,,++++++*********)))******+++,,,,,,,,,---,,,,,,++++++++++++,,,,,,++++++,,,,,,,,,---------++++++++++++++++++++++++******))))))******+++,,,---,,,,,,+++***))))))(((************************'''((((((((()))))))))***''')))***,,,,,,***)))'''(((((((((((((((((((((((())))))))))))************+++++++++******)))))))))(((((((((((((((((())))))'''''''''''''''&&&%%%%%%'''(((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$######"""###$$$$$$%%%%%%%%%%%%$$$%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&%%%$$$###""""""%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&LLLLLLKKKJJJJJJKKKMMMMMMLLLLLLKKKIIIHHHIIIKKKNNNMMMLLLKKKIIIIIIHHHIIIIIIKKKKKKKKKKKKJJJJJJIIIHHHHHHGGGFFFGGGHHHIIIIIIGGGDDDEEEFFFGGGHHHIIIIIIIIIIIIKKKLLLLLLKKKKKKLLLMMMMMMLLLJJJIIIHHHHHHHHHIIIFFFEEEEEEEEEEEEFFFGGGGGGAAAAAAAAAAAAAAAAAAAAAAAACCCDDDEEEEEEEEEDDDEEEEEEBBBAAAAAAAAABBBDDDEEEFFFEEEFFFHHHGGGFFFFFFHHHIIIGGGGGGGGGGGGHHHHHHHHHHHHFFFFFFFFFFFFEEEEEEEEEEEEEEEEEEEEEDDDDDDDDDDDDDDDFFFEEEDDDCCCCCCDDDEEEFFFCCCCCCDDDDDDDDDDDDDDDCCCGGGFFFDDDBBBAAAAAABBBBBBDDDDDDDDDCCCCCCCCCCCCCCC@@@AAABBBBBBAAABBBDDDFFFDDDDDDCCCCCCBBBBBBBBBAAA@@@@@@@@@AAAAAABBBBBBBBB@@@?????????@@@AAABBBBBBAAA@@@>>>=========>>>???<<<;;;;;;;;;;;;;;;<<<<<<;;;;;;;;;:::::::::999999<<<===>>>>>><<<;;;<<<======>>>??????======>>>?????????@@@@@@@@@?????????>>>>>>???@@@@@@???>>>===<<<===>>>>>>======>>>???======>>>>>>===<<<;;;;;;;;;;;;<<<<<<<<<<<<;;;;;;999999999999999999888888888999999888666555666777555555666666777777888888555555444444444555666777666666666666666666666666777777777777666555444333333555666666555555666888444444444444444444333333222333444444222111111222111222555888777111000222000000111111111000...---//////000000111333333444111111111111111111222333333333222222111000000000//////000111111000//////,,,,,,------------------.........///......---,,,---------,,,,,,---------........................---------------------------,,,,,,,,,,,,---.........------,,,,,,------...------------------------++++++,,,------...//////,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++,,,++++++++++++++++++++++++***++++++,,,,,,++++++***,,,,,,,,,++++++*********************+++,,,------,,,++++++*********+++++++++++++++,,,,,,,,,------++++++++++++++++++++++++***************++++++,,,,,,,,,++++++***)))((((((***************************)))))))))(((((((((''''''(((***++++++***((('''))))))))))))))))))))))))(((((()))))))))*********)))))))))))))))((((((((())))))))))))))))))((((((''''''((((((''''''&&&%%%((((((((('''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%###"""!!!######$$$$$$%%%$$$$$$###%%%$$$$$$$$$%%%&&&&&&'''&&&&&&%%%%%%$$$###!!!!!!$$$%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&KKKJJJIIIHHHIIIKKKNNNOOOOOONNNLLLJJJHHHJJJNNNQQQLLLKKKJJJIIIIIIIIIJJJKKKKKKKKKKKKLLLKKKKKKJJJJJJHHHFFFFFFGGGHHHIIIHHHGGGEEEFFFGGGHHHHHHIIIHHHHHHIIIJJJLLLLLLKKKKKKLLLNNNMMMLLLJJJIIIHHHHHHHHHHHHGGGFFFFFFFFFFFFFFFGGGGGGDDDDDDDDDDDDDDDDDDDDDDDD@@@BBBDDDDDDBBBBBBBBBCCCBBBBBBBBBBBBCCCDDDEEEEEEDDDFFFGGGGGGFFFFFFHHHIIIGGGGGGHHHHHHHHHIIIIIIIIIGGGGGGFFFFFFFFFEEEEEEEEEEEEDDDDDDCCCCCCDDDDDDEEEEEEEEECCCCCCCCCCCCEEEEEECCCCCCDDDEEEEEEEEEDDDDDDFFFDDDBBB@@@@@@@@@BBBCCCCCCDDDDDDDDDDDDDDDDDDDDD>>>???AAAAAAAAABBBEEEGGGFFFFFFEEEDDDCCCBBBAAAAAAAAAAAAAAAAAAAAA@@@@@@@@@>>>>>>>>>>>>???@@@AAABBB@@@???>>>======<<<<<<===<<<<<<;;;;;;;;;<<<======;;;;;;;;;::::::::::::999<<<===>>>>>>===<<<===???===???@@@???>>>===>>>???@@@@@@@@@???????????????>>>>>>@@@AAAAAA@@@??????<<<>>>???>>>===<<<===???>>>?????????>>>===<<<;;;======>>>>>>>>>>>>======999999::::::::::::999999999::::::999777666666777555666777777777777777666555444444333333444666777777777777666666666666555666666777777777666555555333444555666555555666888444333333333333333333333222333444444222000000111111222555999777222000222000000111111111000//////000000000000111222333444222222111111111222222333333333222222111000000000......000000000000......,,,,,,,,,,,,------------......//////......---,,,------,,,,,,,,,,,,------................................................---,,,,,,,,,,,,---.........------,,,,,,------...........................,,,,,,------......//////,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***************,,,,,,,,,,,,,,,,,,,,,,,,***++++++,,,,,,++++++***++++++++++++++++++++++++************+++,,,---...,,,++++++************+++,,,,,,+++++++++,,,---...+++++++++++++++++++++++++++************+++,,,,,,+++++++++***)))))))))(((***************+++++++++*********)))((('''''''''(((((()))******)))((((((************************'''(((((())))))*********)))(((((((((((((((((((((******))))))))))))((((((((((((((()))(((''''''&&&(((((('''''''''((()))***&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''((((((((('''&&&$$$###"""######$$$%%%%%%%%%$$$$$$%%%$$$$$$%%%%%%&&&'''(((&&&&&&&&&%%%$$$###"""!!!###$$$&&&'''(((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''''''''''''''(((((((((((('''&&&%%%%%%$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%GGGHHHHHHIIIJJJLLLMMMNNNMMMMMMLLLJJJIIIJJJMMMOOOLLLKKKIIIIIIIIIJJJLLLMMMJJJJJJKKKLLLLLLLLLKKKKKKIIIHHHGGGHHHIIIJJJIIIHHHHHHIIIIIIJJJJJJJJJIIIIIIGGGHHHJJJJJJIIIIIIKKKLLLLLLKKKIIIGGGFFFFFFFFFFFFHHHGGGGGGFFFFFFFFFGGGGGGEEEEEEEEEEEEEEEEEEEEEEEE>>>AAACCCCCCAAA???@@@AAACCCCCCCCCCCCCCCDDDDDDDDDBBBDDDEEEEEEEEEEEEGGGHHHHHHHHHHHHHHHIIIIIIIIIIIIGGGGGGGGGFFFFFFFFFEEEEEEEEEDDDCCCCCCCCCCCCDDDEEEDDDCCCCCCCCCCCCCCCCCCDDDCCCCCCDDDEEEEEEEEEEEEEEECCCCCCBBBBBBBBBBBBBBBBBB@@@AAABBBCCCCCCCCCCCCCCC???@@@AAAAAA@@@AAACCCEEEDDDDDDDDDCCCCCCBBBBBBAAAAAAAAAAAA@@@??????>>>>>>;;;;;;<<<<<<===???@@@AAA=========<<<<<<;;;:::999<<<<<<;;;<<<<<<======>>>======<<<<<<<<<;;;;;;;;;;;;===>>>>>>======>>>@@@???@@@AAA@@@???>>>???AAAAAA@@@@@@??????>>>??????===>>>@@@AAAAAAAAA@@@@@@===>>>???>>>===<<<===>>>@@@@@@@@@@@@???>>>===<<<======>>>>>>>>>>>>======999:::;;;<<<<<<;;;:::999999:::;;;:::888666777888666777777888888777666555666555444333444555777888777777777777666666666555555555666777777777777666222444555555555555666888444444444333333444444444333444555555222111111111111222666:::888222000222000000000000000000111111111111000000000222333444333222222111111222222222333333222222111000000000,,,---///000000///---,,,++++++,,,,,,,,,---------......//////......---,,,------,,,++++++,,,------........................---------------------------,,,,,,,,,,,,---.........------,,,,,,------...---------------------------------...............------------------------******)))))))))***++++++,,,,,,,,,,,,,,,,,,,,,,,,***++++++,,,,,,++++++************++++++,,,,,,---+++************,,,---...------,,,+++++++++++++++,,,,,,+++++++++,,,---...++++++++++++++++++++++++++++++******++++++,,,---************))))))))))))))))))*********+++++++++))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))''''''(((((()))******+++))))))))))))))))))))))))*********)))))))))(((((())))))******))))))((('''(((((('''''''''(((***+++''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&'''''''''''''''''''''&&&%%%%%%###$$$%%%&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%'''((((((%%%&&&&&&&&&%%%$$$######"""$$$&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''(((((('''&&&%%%%%%$$$$$$%%%%%%"""""""""#########$$$$$$CCCEEEHHHKKKLLLMMMMMMLLLIIIJJJKKKJJJIIIHHHIIIKKKKKKJJJIIIHHHIIIKKKMMMNNNJJJJJJKKKLLLLLLMMMLLLLLLJJJIIIHHHIIIKKKKKKKKKJJJKKKKKKKKKLLLKKKKKKJJJJJJEEEFFFHHHHHHHHHHHHIIIKKKJJJIIIGGGEEEDDDDDDDDDEEEIIIHHHGGGGGGFFFFFFGGGGGGDDDDDDDDDDDDDDDDDDDDDDDD>>>AAADDDDDDAAA???@@@AAADDDDDDDDDDDDDDDCCCCCCCCC@@@BBBDDDDDDCCCDDDEEEGGGHHHHHHHHHIIIIIIIIIJJJJJJGGGGGGGGGFFFFFFFFFFFFEEEEEEDDDCCCBBBBBBCCCEEEEEECCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDEEEEEEEEEEEEEEE@@@AAACCCEEEEEEDDDBBBAAA>>>???@@@AAABBBBBBCCCBBB@@@AAABBBAAA@@@@@@AAACCCAAABBBBBBBBBBBBBBBBBBBBBBBBAAAAAA@@@???>>>======:::::::::;;;<<<>>>???@@@???@@@@@@@@@@@@>>><<<;;;<<<<<<<<<<<<<<<===>>>>>>???>>>>>>>>>============;;;<<<>>>>>>======???@@@@@@AAABBBBBB@@@@@@AAABBBAAAAAA@@@???>>>>>>??????===>>>@@@AAABBBBBBAAA@@@===>>>???>>>===<<<===>>>AAAAAAAAA@@@@@@>>>======;;;;;;<<<<<<<<<<<<;;;;;;999:::;;;<<<<<<<<<;;;::::::;;;;;;:::888777888999777777888888888666555444888777555444555666888999888888777777666666666555444555666777888888888888222333555555555555666888555555444444444555555666444666777666333222222222111222666:::888222000111111000/////////111222333222111000000000111222333333333222222111222222222333333222222111000000000,,,---///000000///---,,,+++++++++,,,,,,---------......//////......---,,,------++++++++++++------........................,,,,,,,,,,,,,,,,,,,,,,,,---,,,,,,,,,,,,---.........------,,,,,,------...,,,,,,,,,,,,,,,,,,,,,,,,...............---------------------------------''''''(((((()))***,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,+++++++++))))))***+++,,,------...+++******)))***,,,---...///...------,,,,,,,,,,,,---,,,+++***+++,,,---...++++++++++++++++++++++++++++++******++++++,,,---)))))))))))))))*********))))))******++++++++++++''''''(((((())))))******))))))(((((((((((())))))((((((((((((((((((((((((&&&''''''((()))******+++******************+++++++++*********))))))((((((***************)))(((((()))(((''''''''')))***+++''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''%%%&&&&&&'''((((((''''''$$$%%%&&&'''(((((((((((($$$$$$$$$%%%&&&'''((()))%%%%%%&&&&&&&&&%%%$$$$$$"""###&&&((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%!!!""""""""""""#########KKKJJJHHHGGGGGGHHHIIIJJJJJJKKKLLLKKKIIIHHHIIIJJJIIIGGGEEEGGGJJJLLLKKKIIIIIIJJJLLLMMMNNNNNNNNNMMMLLLLLLLLLLLLKKKKKKKKKKKKJJJLLLNNNOOOOOOMMMKKKIIIEEEHHHKKKKKKHHHGGGIIIKKKKKKJJJJJJIIIHHHHHHHHHIIIEEEFFFFFFEEEDDDCCCEEEFFFDDDCCCCCCCCCDDDEEEDDDCCC@@@AAAAAABBBBBBAAAAAA@@@@@@CCCFFFGGGFFFEEEEEEEEECCCCCCAAAAAABBBDDDFFFHHHIIIHHHGGGFFFFFFGGGHHHIIIHHHGGGFFFFFFEEEFFFFFFGGGDDDDDDDDDDDDEEEEEEEEEEEECCCCCCDDDDDDDDDDDDCCCCCCFFFEEECCCBBBAAAAAABBBBBBEEECCCAAAAAADDDFFFEEECCCAAABBBDDDFFFFFFEEECCCBBBFFFDDDBBB@@@???@@@AAABBBAAA@@@@@@??????@@@@@@AAAAAAAAAAAAAAAAAAAAAAAAAAA??????>>><<<<<<;;;;;;;;;>>>>>>>>>>>>============;;;;;;;;;<<<<<<<<<<<<===???>>>===<<<<<<===>>>>>>===>>>???@@@AAAAAA@@@???>>>>>>???@@@AAAAAABBBBBBBBBBBBBBB???<<<;;;;;;<<<>>>>>>???@@@@@@@@@@@@???<<<<<<<<<<<<=========>>>BBBBBBBBBAAA???===<<<;;;;;;;;;;;;;;;;;;;;;;;;;;;======<<<<<<<<<<<<============<<<;;;::::::::::::888888888777777777777777666666666666666666666666444555555555555555555444333444666777777777666555444555666888888666555444999999888666555444222222777777666555333222111111444666888888555222000///333333222111111222333444111111111111111111111111111111222222222333333333111222444444444222000///...---,,,...111222000...,,,,,,,,,,,,,,,,,,,,,---.........------,,,,,,,,,,,,,,,++++++++++++++++++***+++,,,...///......---000000///...------,,,,,,---,,,+++***+++---///111.........------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,---------///...---,,,++++++++++++***++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------,,,,,,+++***+++++++++***)))***,,,///,,,,,,,,,,,,,,,---...///,,,,,,,,,++++++*********++++++++++++++++++++++++------,,,,,,,,,,,,++++++***+++,,,------,,,+++******************++++++++++++++++++,,,,,,+++++++++******))))))((((((''''''(((((((((((())))))))))))+++*********))))))((((((***((('''(((***+++)))&&&)))))))))))))))))))))))),,,+++)))((((((((()))***(((((((((((((((((((((((())))))((('''&&&&&&%%%%%%''''''(((((('''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((($$$%%%%%%&&&'''((())))))$$$$$$######$$$$$$%%%&&&((((((((('''&&&&&&%%%%%%&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''(((''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%$$$###"""############$$$$$$$$$JJJIIIIIIHHHHHHIIIIIIIIIIIIJJJKKKJJJIIIHHHHHHJJJIIIGGGGGGIIIKKKMMMKKKIIIHHHIIIKKKLLLMMMMMMMMMLLLLLLKKKKKKKKKJJJIIIIIIIIIIIIJJJLLLMMMNNNMMMLLLKKKHHHIIIKKKKKKJJJJJJJJJKKKHHHGGGGGGFFFEEEEEEFFFFFFGGGHHHHHHGGGFFFEEEFFFHHHDDDDDDCCCDDDDDDEEEDDDCCCBBBBBBCCCCCCCCCCCCBBBBBBBBBDDDGGGGGGFFFDDDCCCDDDEEEEEEDDDDDDDDDFFFGGGHHHGGGFFFEEEEEEEEEEEEFFFGGGFFFFFFEEEEEEDDDDDDCCCCCCCCCDDDDDDDDDDDDEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEDDDCCCBBBBBBBBBCCCEEEEEEFFFCCCBBBBBBEEEFFFFFFDDDBBBBBBDDDEEEEEEEEEDDDCCCFFFEEECCCAAA@@@AAABBBBBBAAAAAA@@@@@@@@@@@@AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA@@@???>>>============>>>>>>>>>>>>========================>>>>>>>>>>>>>>>>>>===<<<<<<===>>>?????????@@@AAA@@@@@@>>>>>>>>>??????@@@AAAAAABBBBBBCCCCCCCCC@@@===<<<<<<===>>>>>>???@@@@@@@@@@@@@@@<<<<<<<<<=========>>>>>>@@@@@@@@@?????????>>>>>><<<<<<<<<<<<<<<<<<<<<<<<======<<<<<<<<<<<<============<<<;;;::::::::::::999999888888777777777666666666666666666666666666555555666666666666555555444555555666666666666666444555777888888777555444777777666666555555444444777777666555444333333222333555888888555222000000333333111111000111222222111111111111111111111111111111222222222333333333111222333444444222111///...---,,,---000000...,,,,,,,,,,,,,,,,,,,,,,,,,,,......---------,,,,,,,,,++++++++++++++++++,,,,,,***+++,,,............---......---,,,,,,+++******,,,,,,++++++,,,---///000------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,---------...---,,,+++++++++++++++))))))))))))************,,,,,,,,,,,,,,,,,,,,,,,,---............---,,,++++++,,,+++***)))***---///---,,,,,,,,,,,,---...///------,,,,,,,,,+++++++++++++++++++++++++++++++++------,,,,,,,,,,,,+++++++++++++++,,,,,,+++++++++++++++************************++++++++++++******************)))))))))((((((((((((((())))))))))))*********)))))))))(((((()))((('''(((***+++)))&&&))))))))))))))))))))))))+++***)))((((((((()))***)))))))))))))))))))))))))))(((((('''&&&&&&%%%%%%''''''(((((('''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((%%%%%%&&&&&&'''((((((((($$$$$$$$$###$$$$$$%%%&&&'''''''''''''''&&&&&&&&&'''''''''((((((((())))))&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%$$$###############$$$$$$$$$$$$HHHIIIIIIJJJJJJJJJIIIIIIIIIJJJKKKJJJHHHGGGHHHIIIIIIHHHIIIKKKMMMMMMLLLJJJIIIIIIJJJKKKLLLLLLLLLLLLKKKKKKJJJIIIIIIHHHGGGGGGHHHIIIJJJKKKLLLMMMMMMNNNKKKJJJJJJKKKMMMMMMLLLKKKJJJJJJIIIHHHHHHHHHHHHIIIIIIJJJJJJIIIHHHGGGGGGIIIDDDDDDDDDDDDDDDDDDDDDDDDDDDEEEEEEEEEEEEEEEEEEDDDDDDFFFHHHGGGEEECCCBBBCCCFFFGGGGGGHHHHHHHHHGGGGGGEEEEEEDDDDDDDDDDDDEEEEEEFFFFFFFFFFFFFFFDDDBBBAAADDDDDDEEEEEEEEEFFFFFFFFFFFFEEEDDDCCCCCCDDDEEEFFFBBBBBBBBBCCCDDDFFFGGGHHHFFFEEECCCDDDFFFGGGGGGFFFCCCCCCDDDDDDDDDEEEEEEEEEGGGEEEDDDBBBBBBBBBCCCCCCBBBBBBBBBAAAAAABBBBBBBBBAAAAAAAAA@@@@@@AAAAAABBBBBBAAA@@@???>>>>>>>>>>>>>>>>>>>>>>>>============<<<<<<=========>>>>>>>>>======<<<<<<===>>>???@@@AAAAAAAAAAAA@@@???>>>===??????@@@@@@AAAAAABBBBBBCCCCCCCCCAAA>>>===>>>???>>>??????@@@@@@@@@@@@@@@============>>>>>>>>>>>>???>>>======>>>???AAABBB========================>>>======<<<<<<======>>>>>>===<<<;;;::::::::::::::::::999888777666666555666666666666666666666666555666666666666666666555555555555555555666777777555666777888888777666555555555555666666666666666666666666555555444444444111444777777666333222111333222111000000000000000111111111111111111111111111111222222222333333333111222333444333222111000...------...//////---+++......------,,,,,,++++++...------------,,,,,,,,,******++++++,,,,,,------***+++,,,---..................------,,,+++++++++++++++,,,------......///,,,,,,------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------,,,,,,++++++***+++++++++))))))*********+++++++++,,,,,,,,,,,,,,,,,,,,,,,,......//////......------+++,,,,,,+++******---///------,,,,,,,,,---......---------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,,,,++++++,,,++++++++++++++++++,,,,,,+++++++++***)))))))))))))))************))))))++++++************))))))(((((((((((())))))))))))******))))))))))))(((((()))(((((((((******((('''))))))))))))))))))))))))+++***)))((((((((())))))))))))))))))))))))))))))((((((((('''&&&&&&%%%%%%'''''''''(((''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&'''''''''''''''(((((((((((()))))))))***&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%$$$$$$############$$$$$$$$$%%%GGGHHHJJJKKKKKKKKKIIIIIIHHHJJJJJJIIIHHHGGGHHHIIIIIIJJJKKKMMMNNNMMMLLLJJJJJJKKKKKKLLLLLLLLLLLLLLLLLLLLLKKKJJJIIIHHHGGGGGGJJJIIIIIIIIIJJJKKKMMMNNNLLLJJJHHHJJJMMMNNNLLLIIIKKKKKKJJJJJJJJJJJJJJJKKKIIIJJJKKKJJJHHHGGGGGGHHHDDDEEEFFFEEEEEEDDDEEEFFFEEEEEEEEEEEEEEEEEEEEEEEEDDDFFFGGGGGGEEEDDDDDDDDDFFFGGGIIIJJJIIIHHHFFFEEEEEEEEEEEEEEEEEEEEEEEEEEEGGGHHHIIIJJJIIIGGGDDDBBBFFFFFFFFFGGGGGGGGGHHHHHHDDDCCCAAA@@@@@@AAACCCDDDCCCCCCDDDEEEFFFGGGHHHHHHFFFFFFEEEEEEFFFGGGGGGGGGDDDDDDCCCCCCDDDDDDEEEFFFFFFFFFEEEDDDCCCCCCDDDDDDCCCCCCBBBBBBBBBBBBCCCCCCAAAAAA@@@@@@@@@AAABBBCCCAAAAAA@@@???????????????>>>>>>>>>>>>============::::::;;;;;;;;;<<<<<<<<<<<<<<<<<<===>>>??????@@@@@@@@@@@@@@@@@@@@@??????@@@@@@@@@AAAAAAAAABBBBBBBBBBBBBBB@@@>>>===>>>???>>>???@@@@@@AAAAAA@@@@@@======>>>>>>>>>????????????>>>===<<<===???AAABBB========================>>>>>>============>>>>>>>>>===<<<;;;;;;:::::::::;;;;;;:::999777666555555666666666666666666666666444555555666666555555444666555555444444555777888666666777888888777666666666666666666666666666666555555444444444444444444000333666777666444333333222222111000000/////////111111111111111111111111111111222222222333333333111222333333333222222111000////////////...---,,,//////...---,,,++++++***------------------------******++++++,,,---......++++++,,,------.........000000//////.........---***+++,,,---............,,,,,,,,,------.........------------------------,,,,,,,,,------------...++++++*********+++,,,,,,,,,,,,,,,,,,---------...,,,,,,,,,,,,,,,,,,,,,,,,------............------+++,,,,,,+++***+++---///------,,,,,,,,,------.....................------,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,+++++++++---,,,+++******+++,,,---,,,,,,,,,+++***)))(((((((((((())))))))))))((((((***)))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))((((((((((((((()))))))))((('''))))))))))))))))))))))))******))))))(((((((((((((((((((((((((((((((((((((((((('''''''''&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((('''''''''&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&%%%%%%&&&&&&'''(((((()))''''''((((((((()))))))))&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''''''''''''''''''''''''''''''''&&&'''''''''&&&&&&%%%$$$#########$$$$$$$$$%%%%%%GGGHHHJJJKKKLLLKKKJJJJJJIIIJJJKKKJJJHHHGGGHHHIIIJJJKKKLLLMMMMMMLLLLLLLLLMMMMMMMMMMMMMMMMMMNNNNNNMMMMMMMMMLLLKKKJJJJJJIIILLLKKKJJJIIIIIIJJJKKKLLLKKKIIIGGGIIILLLMMMKKKHHHHHHGGGGGGGGGGGGGGGHHHHHHHHHIIIJJJIIIGGGFFFEEEFFFDDDFFFGGGGGGEEEDDDEEEGGGEEEEEEDDDCCCCCCDDDEEEEEECCCEEEFFFFFFEEEEEEFFFGGGEEEFFFHHHIIIIIIHHHEEEDDDGGGGGGGGGGGGGGGGGGGGGGGGGGGHHHIIIJJJIIIGGGEEECCCHHHHHHIIIIIIIIIJJJJJJJJJEEEDDDBBBAAAAAABBBDDDEEEEEEFFFFFFFFFFFFFFFFFFEEEFFFFFFFFFFFFFFFFFFGGGHHHEEEDDDDDDDDDDDDEEEFFFFFFFFFEEEEEEEEEDDDDDDDDDEEEDDDCCCCCCBBBBBBCCCCCCDDDAAAAAA@@@???@@@AAACCCDDD@@@@@@???>>>>>>>>>??????>>>>>>>>>>>>============;;;;;;;;;<<<<<<<<<======;;;;;;<<<===>>>?????????>>>??????@@@@@@AAABBBCCCAAAAAAAAAAAAAAABBBBBBBBB@@@@@@@@@???===<<<>>>?????????@@@AAAAAAAAAAAA@@@>>>>>>>>>????????????@@@AAA@@@>>><<<<<<===???@@@<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>============>>>>>>>>>>>>===<<<;;;;;;;;;;;;;;;;;;:::999888777666555777777777777777777777777444444444555555444444444666555555444444555777888666666777777777777666666777777777666555555444444444444444333333333333333///222666777666444333333111111111111000000//////111111111111111111111111111111222222222333333333111222222222333222222222111111222222111///////////////...------,,,++++++------------------------******+++,,,------......++++++,,,,,,---......///000///////////////......***+++,,,---............,,,,,,,,,------.........------------------------,,,,,,---------.........+++++++++***++++++,,,,,,,,,---------............,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,---------,,,,,,+++,,,---,,,++++++---......------,,,,,,,,,------........................,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,+++++++++---,,,+++******+++,,,---,,,,,,,,,+++***)))((((((((((((((())))))((((((((('''((((((((((((((((((((((((((((((((())))))))))))(((((((((((((((((())))))'''((()))))))))((((((((((((((((((((((((((((((((())))))))))))(((((('''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((('''''''''&&&%%%%%%$$$$$$%%%%%%$$$$$$%%%%%%&&&'''$$$%%%%%%&&&'''((())))))&&&&&&'''''''''(((((((((&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&&&&&&&'''&&&&&&%%%%%%###$$$$$$$$$$$$%%%%%%%%%HHHIIIJJJKKKKKKKKKKKKKKKJJJKKKLLLKKKIIIHHHIIIJJJJJJLLLMMMLLLKKKJJJLLLMMMNNNNNNMMMMMMMMMNNNNNNOOONNNNNNNNNMMMMMMMMMLLLLLLNNNMMMKKKJJJJJJJJJKKKKKKIIIIIIIIIJJJKKKLLLKKKIIIIIIIIIHHHHHHHHHIIIJJJJJJFFFHHHJJJIIIGGGDDDDDDDDDDDDGGGIIIHHHEEEDDDFFFHHHEEEDDDCCCBBBBBBCCCDDDEEECCCEEEFFFFFFEEEFFFGGGIIIDDDEEEGGGHHHHHHGGGFFFDDDHHHHHHIIIJJJJJJIIIHHHHHHEEEFFFGGGGGGGGGFFFEEEDDDIIIIIIJJJJJJJJJKKKKKKKKKGGGFFFEEEDDDDDDEEEFFFGGGGGGGGGGGGGGGFFFEEECCCCCCEEEFFFGGGFFFEEEEEEGGGIIIDDDDDDEEEEEEEEEEEEFFFFFFEEEEEEEEEEEEEEEDDDDDDDDDCCCCCCBBBBBBBBBBBBCCCCCCBBBAAA?????????AAACCCEEE@@@@@@??????>>>??????@@@>>>>>>>>>>>>============>>>>>>?????????@@@@@@@@@;;;<<<===>>>??????>>>>>>>>>>>>>>>???AAABBBDDDEEEAAAAAAAAAAAABBBBBBBBBBBB>>>??????>>>======>>>@@@???@@@@@@AAAAAAAAAAAAAAA>>>?????????@@@@@@@@@@@@AAA@@@???===<<<<<<======<<<<<<<<<<<<<<<<<<<<<<<>>>>>======>>>>>>??????>>>===<<<;;;;;;;;;;;;;;;;;;:::999888777777666777777777777777777777777444444555555555555444444555555555555555666777777666666666555555666666666888777777666555444444444555555444444444333333333000333666777666444333333000000111222222111111000111111111111111111111111111111222222222333333333222222222222222222333333000222333333111000111111//////......------,,,,,,,,,,,,,,,------------...++++++,,,,,,------......,,,,,,,,,,,,,,,...//////------------------------++++++,,,------......///,,,,,,------------------------------------------,,,---------............------,,,++++++,,,,,,,,,+++++++++,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---,,,,,,,,,***,,,------,,,,,,---.........---,,,,,,,,,---------------...............,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,,,,++++++,,,++++++++++++++++++,,,,,,+++++++++***)))))))))(((((())))))))))))((((((&&&&&&''''''''''''(((((((((((((((((())))))))))))''''''(((((((((((())))))'''(((******((((((((()))(((((((((((((((((((((((((((((()))))))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%&&&''''''((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((('''&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%&&&&&&'''%%%%%%&&&&&&'''((())))))&&&&&&&&&&&&''''''''''''&&&&&&&&&''''''''''''(((%%%%%%&&&&&&'''(((((((((''''''''''''''''''''''''%%%&&&&&&'''&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%IIIIIIIIIIIIJJJKKKLLLMMMKKKLLLMMMLLLJJJIIIJJJKKKKKKLLLLLLJJJHHHHHHKKKNNNOOONNNMMMLLLLLLMMMNNNNNNMMMMMMMMMMMMNNNNNNNNNNNNLLLLLLKKKKKKKKKLLLMMMMMMIIIJJJLLLLLLKKKKKKKKKLLLKKKKKKKKKKKKKKKLLLMMMMMMFFFHHHJJJJJJGGGDDDCCCCCCDDDGGGJJJIIIEEEDDDFFFIIIFFFDDDCCCBBBBBBCCCDDDFFFEEEFFFGGGFFFEEEEEEFFFHHHDDDEEEFFFGGGHHHHHHGGGGGGHHHIIIJJJJJJJJJJJJIIIHHHEEEEEEFFFFFFFFFFFFGGGGGGHHHHHHIIIIIIIIIJJJJJJJJJGGGGGGGGGGGGGGGGGGGGGGGGFFFFFFFFFFFFFFFDDDCCCBBBDDDFFFGGGFFFDDDDDDFFFIIICCCDDDEEEFFFGGGFFFEEEEEECCCDDDDDDDDDDDDDDDDDDDDDCCCBBBBBBBBBBBBBBBBBBCCCBBB@@@???>>>???AAADDDEEEAAAAAA@@@@@@@@@@@@AAAAAA>>>>>>>>>>>>============@@@@@@@@@@@@AAAAAAAAAAAA<<<===>>>??????>>>======@@@?????????@@@BBBCCCDDDBBBBBBBBBBBBBBBBBBBBBBBB>>>???@@@???>>>>>>???AAA???@@@AAAAAABBBBBBAAAAAA?????????@@@@@@@@@AAAAAA?????????>>>======<<<<<<========================??????>>>>>>>>>>>>?????????>>>===<<<;;;;;;;;;;;;:::::::::999999888888888777777777777777777777777666666777777777777666666444555555666666666666666555555444444444444555555666666666666666555555555888888777666555444444333111333666777666444222222///000111333333333333222111111111111111111111111111111222222222333333333222111111111222222333444...111333333111000111333...............---------,,,,,,,,,---------......,,,,,,------------------,,,,,,++++++,,,---///000------------............,,,,,,++++++,,,---///000------------------,,,,,,........................------------............//////...---,,,,,,,,,,,,,,,,,,,,,,,,------------,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,---......------***,,,......---,,,---...///...---,,,,,,,,,,,,,,,,,,,,,---------.........------------------------------,,,,,,,,,,,,+++++++++++++++,,,,,,+++++++++++++++******************((())))))******))))))(((''''''''''''((((((((()))(((((((((((())))))))))))'''''''''((((((((())))))&&&)))+++***((('''((()))(((((((((((((((((((((((('''((()))))))))((('''&&&''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&&&&'''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''%%%&&&&&&&&&''''''((((((''''''''''''((((((((((((&&&&&&&&&''''''''''''(((%%%%%%&&&&&&'''(((((()))''''''''''''''''''''''''%%%%%%&&&&&&'''&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&JJJIIIIIIIIIJJJKKKMMMNNNKKKMMMMMMLLLKKKJJJKKKLLLLLLLLLLLLIIIFFFGGGKKKOOONNNMMMLLLKKKKKKLLLMMMMMMLLLLLLLLLMMMNNNNNNOOOOOOJJJJJJKKKLLLMMMNNNOOOOOOIIILLLOOONNNLLLKKKLLLOOOHHHHHHHHHHHHHHHIIIJJJKKKGGGIIIKKKJJJHHHEEEDDDCCCDDDHHHKKKIIIEEEDDDFFFJJJFFFEEEDDDBBBBBBDDDEEEFFFHHHHHHHHHGGGEEEDDDEEEFFFDDDEEEFFFGGGHHHIIIIIIIIIHHHHHHJJJJJJJJJJJJHHHHHHGGGGGGGGGGGGHHHIIIJJJKKKGGGGGGGGGHHHHHHHHHIIIIIIEEEEEEFFFFFFFFFFFFEEEEEEDDDEEEFFFFFFFFFDDDCCCBBBCCCEEEGGGFFFDDDCCCFFFIIIBBBDDDFFFGGGHHHGGGEEEDDDBBBCCCDDDDDDDDDDDDDDDCCCBBBBBBBBBAAAAAABBBBBBBBBBBB@@@???>>>???AAADDDFFFBBBBBBAAAAAAAAABBBBBBCCC>>>>>>>>>>>>============>>>>>>?????????@@@@@@@@@======>>>??????>>>===<<>>>>>???>>>>>>===<<<>>>>>>>>>>>>>>>>>>>>>>>>??????>>>>>>>>>>>>?????????>>>===<<<<<<;;;;;;<<<:::999999999999999999999777777777777777777777777888888999999999999888888333444666777777777666555555444444333333444444555444444555555666777777888;;;:::999888777666555444111444777777666333222111...000111333444444444333111111111111111111111111111111222222222333333333222111111111222333333444---///222222000///111333---------...............,,,,,,,,,------.........------------------,,,,,,---,,,++++++,,,---///000/////////000000000000000---,,,+++***+++---///111.........------,,,,,,,,,........................---------.........//////111000///...---,,,,,,,,,........./////////000000,,,,,,,,,,,,,,,,,,,,,,,,,,,------.../////////...***,,,......---,,,---...///...---,,,,,,,,,,,,,,,,,,,,,,,,---------......---------------------------------,,,,,,,,,++++++***+++,,,------,,,+++******************+++++++++))))))************))))))'''((((((((())))))******(((((((((((())))))))))))&&&'''''''''(((((())))))&&&)))+++***((('''(((***(((((((((((((((((((((((('''((()))))))))(((&&&%%%((((((((((((((((((((((((&&&'''''''''''''''''''''%%%%%%&&&'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&'''''''''''''''(((((((((((())))))))))))&&&&&&&&&'''''''''((((((%%%%%%&&&&&&'''((())))))((((((((((((((((((((((((%%%%%%&&&&&&'''&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&JJJJJJIIIIIIKKKMMMOOOPPPMMMMMMLLLLLLLLLLLLLLLMMMMMMJJJGGGGGGIIIKKKKKKIIIOOONNNMMMLLLKKKJJJIIIHHHMMMMMMLLLLLLKKKKKKJJJJJJKKKJJJHHHIIIKKKMMMOOOOOONNNMMMMMMLLLLLLLLLLLLLLLIIIHHHGGGGGGGGGGGGHHHIIIGGGHHHJJJJJJIIIHHHIIIIIIJJJJJJIIIHHHGGGGGGGGGGGGHHHHHHHHHFFFDDDDDDEEEGGGGGGGGGFFFFFFFFFFFFGGGGGGCCCDDDFFFHHHIIIIIIIIIHHHGGGHHHJJJLLLLLLKKKIIIHHHJJJIIIHHHGGGGGGGGGHHHIIIIIIKKKLLLJJJGGGEEEHHHJJJHHHHHHGGGGGGFFFEEEDDDDDDDDDDDDEEEEEEEEEDDDDDDCCCEEEEEEDDDCCCCCCCCCCCCCCCCCCCCCBBBBBBBBBBBBCCCCCCCCCCCCDDDEEEFFFFFFEEEEEEBBBBBBAAAAAABBBBBBCCCDDDCCCCCCBBB@@@???@@@CCCFFFDDDCCCBBBBBBAAAAAAAAAAAAAAAAAA@@@@@@???@@@@@@@@@BBBAAA@@@>>>============???>>>===============>>>===???@@@@@@@@@@@@BBBCCCAAAAAABBBBBBBBBAAA@@@@@@>>>@@@@@@@@@???>>>???@@@CCCCCCBBBAAA@@@>>>>>>===>>>>>>======>>>???@@@@@@>>>???@@@???>>>======???>>>>>>===<<<<<<===??????>>>??????>>>===<<<<<<===>>>>>>===<<<<<<<<<<<<<<<888777777777777777777777999999999999999999999999999888777666555555555666333444555666666666444444666666666666666666666666444444333333444555666777777777777777666666666666666777888777555444444444111111111000111111222333333333222222222333444555...//////000111333444555555444333222222222333333000000000000//////////////////.........---------,,,,,,------...---------------------------,,,,,,//////.........---------222111111111000000//////......////////////......////////////////////////...............///000000//////////////////////////////000000///...------......................../////////...------,,,,,,//////.........---------,,,,,,,,,------.........//////...---,,,,,,++++++------------------------,,,,,,,,,,,,,,,,,,,,,,,,+++,,,...//////...,,,***+++,,,---,,,***)))***+++************))))))))))))***************)))(((((((((((((((((())))))))))))&&&&&&&&&'''''''''((((((%%%&&&&&&&&&'''((((((((((((((((((((())))))))))))((((((((((((''''''''''''***************)))((((((''''''''''''((((((((((((''''''((((((((((((((((((&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''######$$$$$$$$$%%%%%%%%%$$$$$$%%%&&&&&&''''''((((((((('''''''''&&&&&&&&&)))((('''&&&%%%&&&&&&''''''''''''''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&KKKJJJJJJKKKKKKLLLMMMNNNLLLLLLKKKKKKKKKKKKKKKLLLMMMJJJHHHHHHJJJLLLKKKIIILLLLLLLLLLLLLLLKKKKKKKKKLLLLLLLLLKKKJJJJJJIIIIIIJJJIIIIIIJJJLLLNNNPPPPPPMMMLLLLLLKKKKKKKKKKKKKKKJJJIIIHHHHHHHHHHHHIIIJJJKKKLLLMMMKKKJJJIIIIIIJJJJJJJJJIIIHHHGGGGGGGGGGGGGGGGGGGGGEEECCCCCCEEEFFFFFFFFFEEEEEEEEEEEEFFFFFFFFFFFFGGGGGGHHHGGGGGGGGGIIIJJJKKKLLLLLLLLLKKKKKKKKKJJJIIIHHHHHHHHHIIIJJJIIIIIIIIIHHHFFFFFFGGGHHHHHHHHHGGGGGGFFFEEEEEEEEECCCDDDDDDEEEFFFFFFFFFFFFFFFEEEDDDDDDCCCCCCDDDDDDCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDEEEEEEEEEDDDDDD@@@@@@??????@@@@@@AAABBBCCCCCCAAA???>>>>>>AAADDDEEEDDDCCCBBBAAA@@@@@@@@@??????>>>>>>>>>??????@@@??????>>>>>>===>>>>>>>>>?????????>>>>>>>>>??????===???@@@@@@@@@@@@AAACCCBBBBBBBBBBBBAAAAAA@@@???>>>@@@AAA@@@???>>>???@@@?????????@@@@@@AAAAAAAAA>>>>>>>>>>>>>>>???@@@@@@>>>???@@@???>>>===>>>??????>>>===<<<<<<===>>>>>>>>>?????????===<<<===>>>======<<<;;;;;;;;;;;;;;;;;;;;;;;;::::::999999999999999999999999999999999777777777777777666666666333444555666666555444444555555555555555555555555333444444555666666777777888888888888777777777777666777888777555333333333111111111111111222333333444333222222222333444555000000000000111333444555555444333333222222333333111111000000000///////////////.........---------,,,------.........------------,,,,,,,,,,,,,,,,,,//////.........---------000000000000/////////............//////.........////////////////////////...............///000000........................///////////////...------.......................................---------//////.........---------+++++++++,,,,,,---------------------------------------------------------,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,---......------+++,,,---,,,***)))***+++************))))))))))))***************)))(((((((((((((((((())))))))))))&&&&&&&&&'''''''''(((((('''(((((((((((((((((()))''''''((((((((()))))))))((((((((((((''''''''''''))))))******)))(((((('''''''''''''''(((((((((((((((((((((((((((''''''''''''(((((((((((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''###$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%&&&&&&''''''((((((((('''''''''&&&&&&&&&)))((('''&&&&&&&&&''''''((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&KKKLLLLLLMMMLLLLLLLLLKKKKKKKKKJJJJJJJJJJJJKKKKKKLLLKKKJJJJJJLLLLLLKKKJJJIIIJJJJJJKKKLLLMMMNNNOOOLLLKKKKKKJJJJJJIIIHHHHHHIIIIIIJJJKKKLLLNNNPPPQQQLLLLLLKKKJJJJJJJJJJJJKKKKKKKKKJJJJJJJJJJJJKKKKKKMMMMMMLLLJJJHHHGGGHHHJJJJJJJJJIIIHHHGGGGGGGGGGGGEEEFFFFFFDDDCCCCCCEEEGGGFFFFFFEEEEEEEEEEEEFFFFFFIIIIIIHHHGGGFFFFFFFFFGGGLLLLLLLLLLLLLLLMMMNNNNNNLLLKKKJJJIIIIIIIIIIIIJJJIIIHHHFFFFFFGGGGGGGGGFFFHHHHHHHHHGGGFFFFFFEEEEEECCCCCCEEEFFFGGGHHHHHHHHHFFFFFFEEEDDDDDDDDDEEEEEECCCDDDEEEFFFFFFEEEDDDCCCCCCCCCDDDDDDDDDCCCBBBBBB@@@@@@@@@@@@@@@AAAAAABBBCCCCCCAAA???===>>>@@@BBBEEEDDDCCCAAA@@@@@@??????<<<=========>>>>>>??????===============>>>??????@@@@@@@@@@@@@@@@@@@@@@@@>>>???@@@@@@@@@@@@AAACCCBBBCCCBBBBBBAAA@@@???>>>???@@@AAA@@@???>>>???AAA>>>>>>???@@@AAAAAABBBBBB>>>>>>>>>>>>>>>>>>???@@@???@@@@@@@@@>>>===>>>?????????===<<<<<<<<<<<<<<<>>>?????????===<<<===>>><<<<<<;;;;;;::::::;;;;;;======<<<;;;::::::999999888888888888888888888888555666777888888888777666444555555666555555444444555555555555555555555555333444666777888888777777999999999888888888777777666777888777444222222222222222111111222222333444444333222222222333555666222111111111222222333444444444444333333333333333222222111111111000000000/////////............------...............------,,,,,,------------------/////////............---000////////////.........------------------------////////////////////////...............///000000........................///////////////......---........................---------..............................---------+++++++++++++++,,,,,,,,,++++++,,,---......//////------------------------,,,,,,,,,,,,,,,,,,,,,,,,))))))***+++,,,---......+++,,,---,,,+++***+++,,,++++++*********))))))))))))************))))))((((((((((((((())))))))))))&&&&&&'''''''''(((((((((******))))))))))))))))))&&&&&&'''''''''(((((((((((((((((((((''''''''''''(((((((((((((((((('''&&&&&&''''''''''''((((((((())))))(((((('''''''''&&&(((((())))))))))))((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%&&&&&&''''''((((((((((((''''''''''''&&&)))(((''''''&&&&&&''''''((((((((((((((()))))))))''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&LLLMMMNNNNNNMMMLLLJJJIIIKKKKKKJJJJJJJJJKKKLLLLLLLLLKKKKKKLLLLLLLLLLLLKKKIIIJJJJJJLLLMMMNNNOOOOOOLLLLLLLLLKKKJJJJJJIIIIIIKKKLLLMMMMMMMMMMMMNNNPPPMMMMMMLLLKKKKKKKKKKKKKKKLLLLLLLLLLLLLLLLLLLLLLLLKKKKKKIIIGGGEEEEEEHHHJJJJJJJJJIIIHHHGGGGGGGGGGGGEEEFFFFFFEEEDDDDDDFFFHHHHHHGGGGGGFFFFFFGGGGGGHHHKKKJJJIIIHHHGGGHHHIIIJJJMMMLLLKKKJJJKKKLLLNNNOOOKKKKKKJJJIIIIIIIIIHHHHHHJJJGGGEEEEEEHHHIIIHHHFFFHHHHHHHHHGGGGGGFFFFFFFFFDDDEEEFFFGGGGGGGGGGGGGGGFFFFFFEEEEEEEEEEEEFFFFFFCCCDDDFFFGGGGGGFFFDDDCCCCCCDDDDDDDDDCCCBBBAAAAAABBBBBBBBBBBBBBBCCCDDDDDDCCCCCCCCCAAA???>>>@@@BBBEEEDDDCCCAAA@@@??????>>><<<<<<===>>>???@@@@@@@@@>>>===============>>>>>>?????????@@@@@@@@@@@@@@@>>>???AAAAAA@@@@@@AAABBBCCCCCCCCCBBBAAA@@@???>>>???@@@AAAAAA??????@@@AAA@@@@@@@@@@@@@@@@@@@@@@@@???>>>>>>>>>>>>>>>?????????@@@AAA@@@>>>===>>>???@@@???>>>===<<<<<<;;;;;;===???@@@???======>>>???===<<<<<<;;;;;;;;;<<<<<<===<<<<<<:::999888777777777777777777777777777777333555777999:::999888777555555555555555444444444555555555555555555555555333444777888999888777666888888888777777777777666555777777666444222222222222222222222222333444444444333333222333444555666444333333222222222333333444444444444444333333222222222222222111111111000/////////..................////////////...------------...............////////////...............000000000000000/////////---------,,,,,,---------////////////////////////...............///000000------------------------...///////////////..............................,,,,,,------...//////000........................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------.../////////........................------------------------+++************+++,,,---+++,,,------+++***+++---+++++++++*********))))))))))))************)))((((((((((((((())))))))))))''''''''''''((((((((((((*********))))))(((((((((&&&&&&&&&&&&'''''''''(((((((((((((((''''''''''''&&&''''''(((''''''&&&&&&&&&&&&&&&'''''''''(((((()))))))))(((''''''&&&&&&((((((((())))))(((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&''''''(((((((((((('''''''''''''''(((((('''''''''''''''''')))))))))))))))*********''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&NNNNNNOOOOOOMMMLLLJJJHHHLLLKKKKKKKKKLLLLLLMMMNNNKKKLLLLLLLLLKKKKKKLLLLLLKKKKKKLLLLLLMMMMMMNNNNNNNNNNNNMMMMMMLLLKKKKKKKKKMMMOOOPPPOOOMMMLLLLLLNNNOOONNNMMMMMMLLLLLLMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMIIIIIIIIIGGGFFFHHHKKKMMMJJJJJJIIIHHHGGGGGGGGGGGGFFFGGGGGGFFFEEEFFFHHHKKKJJJIIIIIIHHHHHHIIIIIIJJJKKKKKKJJJIIIIIIKKKLLLMMMLLLKKKIIIHHHIIIJJJMMMNNNJJJJJJIIIIIIHHHGGGFFFFFFKKKHHHFFFFFFIIIKKKJJJGGGHHHHHHHHHGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGFFFEEEDDDFFFFFFEEEEEEEEEEEEFFFFFFDDDEEEGGGHHHHHHGGGEEEDDDCCCDDDDDDDDDCCCBBBAAAAAACCCCCCBBBBBBCCCCCCDDDEEEDDDDDDDDDCCCAAA@@@BBBDDDDDDDDDBBBAAA@@@?????????===>>>???AAAAAABBBBBBAAA@@@???>>>======<<<<<<<<<======???@@@@@@@@@??????>>>@@@AAAAAA@@@???@@@BBBBBBBBBBBBBBBAAA@@@???>>>???AAAAAAAAA@@@???@@@AAA@@@@@@@@@@@@@@@@@@@@@@@@??????>>>>>>>>>>>>>>>??????@@@AAA@@@???>>>>>>@@@@@@@@@???>>>>>>===<<<;;;===???@@@???>>>===>>>@@@>>>===============>>>>>>======<<<;;;:::888888777777777777777777777777777333555777999::::::999888666666555555444444444444555555555555555555555555333444777888999888777666777666666666666555555555555666777666444333333333333333333333333444444555444444333333333444555666555444333333333333333333444444555555555444333222222222222222111111111000///////////////////////////000000000//////...---.../////////000000000111////////////////////////111111111111111111111111...---,,,,,,,,,,,,---...////////////////////////...............///000000..............................///////////////...........................+++,,,,,,---...///000000---....................................---------................................................---------------------------,,,+++************++++++,,,------,,,+++,,,---++++++++++++************((())))))*********))))))(((((((((((())))))))))))'''''''''((((((((()))))))))))))))(((((('''''''''&&&&&&&&&&&&'''''''''(((((((((((((((''''''''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&''''''''''''))))))(((((('''''''''&&&&&&''''''((((((''''''&&&''''''''''''''''''''''''(((''''''&&&&&&''''''((($$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%&&&&&&''''''(((((((((((((((((((((((((((''''''(((((((((((((((((())))))))))))******++++++(((((((((((((((((((((((((((((((((((((((((((((((('''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''OOOOOOOOONNNMMMLLLJJJIIILLLLLLKKKLLLLLLMMMNNNOOOKKKLLLLLLJJJIIIIIIKKKNNNMMMMMMMMMMMMMMMMMMMMMMMMOOOOOONNNMMMMMMLLLLLLKKKMMMPPPRRRQQQMMMKKKLLLNNNOOOOOONNNMMMMMMMMMMMMNNNMMMMMMNNNNNNNNNNNNMMMMMMJJJKKKKKKKKKKKKLLLOOOQQQJJJJJJIIIHHHGGGGGGGGGGGGFFFGGGGGGGGGFFFGGGJJJLLLKKKKKKJJJJJJJJJJJJKKKKKKKKKKKKJJJJJJKKKLLLMMMMMMKKKJJJHHHGGGHHHIIIKKKLLLIIIJJJJJJIIIHHHGGGEEEEEEJJJIIIGGGHHHIIIJJJJJJJJJHHHHHHHHHHHHHHHHHHGGGGGGHHHHHHHHHGGGFFFEEECCCCCCEEEEEEDDDDDDDDDEEEFFFFFFDDDEEEFFFGGGGGGFFFEEEDDDCCCCCCDDDDDDDDDCCCBBBBBBAAAAAAAAAAAAAAABBBBBBCCCCCCDDDDDDDDDBBBBBBDDDEEECCCBBBAAA@@@@@@??????@@@???@@@BBBCCCCCCCCCBBBBBBBBBAAA@@@>>>======<<<<<<<<<===>>>@@@@@@@@@?????????@@@AAAAAA??????@@@AAAAAAAAABBBBBBBBBAAA@@@@@@@@@AAABBBAAA@@@???@@@BBB>>>>>>???@@@AAAAAABBBBBB@@@??????>>>>>>>>>>>>>>>@@@AAAAAAAAA???>>>???@@@@@@@@@@@@@@@???>>>=========???@@@???>>>>>>???AAA>>>>>>>>>===>>>>>>??????>>>>>>===<<<;;;;;;::::::888888888888888888888888444666777999::::::999999777666555444444444444444444444444444444444444444333444666777888888777777666666555555555444444444444666777777666555555666444444333333444444555666555444333333333444666777555555444333333444444444444555555666666444333222222222111111111000000000...////////////000000000111111111111000///...---......//////000111111111...////////////000000000111111222222222222222333///...---,,,,,,---...///////////////////////////...............///000000////////////////////////---...//////////////////........................,,,,,,------...///000000---------...............////////////............//////..........................................------------------------......---,,,+++***))))))+++,,,------,,,,,,---...,,,++++++++++++*********((())))))************)))(((((((((((())))))))))))''''''((((((((())))))))))))(((((((((((((((''''''&&&&&&'''''''''(((((((((((((((((((((''''''''''''%%%&&&''''''((('''''''''%%%&&&&&&&&&&&&'''''''''((((((((((((((((((((((((&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''((((((''''''''''''((((((%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%&&&&&&''''''((('''(((((((((((()))))))))''''''((()))))))))(((((((((((())))))******++++++((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''PPPOOONNNMMMLLLLLLKKKKKKJJJJJJJJJKKKKKKMMMNNNNNNLLLLLLKKKHHHFFFGGGKKKOOOLLLLLLMMMMMMMMMNNNNNNNNNNNNNNNMMMMMMLLLKKKKKKKKKJJJNNNRRRQQQNNNMMMNNNQQQOOONNNNNNMMMLLLMMMMMMMMMLLLMMMNNNNNNNNNNNNMMMLLLKKKMMMNNNNNNMMMMMMNNNPPPJJJJJJIIIHHHGGGGGGGGGGGGEEEFFFFFFFFFFFFGGGJJJLLLKKKKKKJJJJJJJJJJJJKKKKKKJJJJJJKKKKKKKKKJJJIIIIIIJJJIIIHHHHHHHHHIIIJJJKKKJJJKKKKKKJJJIIIHHHFFFEEEGGGHHHHHHHHHGGGGGGIIIKKKHHHHHHHHHHHHHHHHHHHHHHHHFFFFFFFFFFFFEEEDDDDDDCCCDDDDDDCCCCCCDDDDDDEEEFFFEEEEEEEEEEEEEEEEEEEEEEEECCCCCCDDDEEEEEEEEEDDDDDDAAAAAAAAAAAAAAABBBCCCCCC@@@BBBCCCCCCBBBBBBDDDFFFAAAAAA@@@@@@@@@@@@@@@AAA@@@AAACCCDDDDDDCCCBBBAAAAAAAAA@@@???????????????<<<===???AAABBBBBBAAA@@@???@@@AAAAAA??????@@@AAA@@@@@@AAAAAABBBBBBAAAAAA@@@AAABBBBBB@@@@@@AAABBB?????????@@@@@@AAAAAAAAA@@@@@@???>>>>>>>>>>>>>>>@@@AAABBBAAA???>>>???@@@???@@@AAAAAAAAAAAA@@@???===>>>@@@@@@???>>>@@@AAA===============>>>??????<<<<<<<<<<<<;;;;;;::::::999999999999999999999999777777777888888999999999888777555444333333444444444444444444444444444444333444444555666666777777666666666666555555555555333555777888777777888999444444444444444555555666555444444333333555666777555444444444444444555666444555666777666555333222111111000000000/////////.../////////000000000000111111111111000///......,,,------...//////000000.../////////000000000000000000111111222222222222000///---,,,,,,---///000////////////////////////...............///000000000000000000000000000000------...///////////////........................,,,---------......//////---------.........////////////.........---------------......//////000000................................................------......---,,,+++***+++,,,------,,,,,,---///,,,,,,+++++++++*********(((((()))***************(((((((((((())))))))))))'''((((((((())))))))))))((())))))))))))))))))***''''''((((((((()))))))))((((((((((((''''''''''''&&&&&&'''(((((((((((((((%%%%%%&&&&&&&&&'''''''''&&&&&&''''''((()))))))))''''''((((((((((((''''''''''''''''''''''''''''''((((((''''''''''''((((((%%%%%%%%%&&&&&&&&&&&&'''$$$$$$%%%&&&&&&''''''((('''((((((((())))))))))))&&&'''((()))***))))))(((''''''(((((()))******+++((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''QQQPPPNNNLLLKKKLLLLLLMMMIIIIIIIIIJJJJJJLLLMMMMMMLLLLLLJJJGGGDDDFFFKKKPPPKKKKKKLLLMMMNNNOOOOOOPPPMMMMMMLLLLLLKKKKKKJJJJJJGGGLLLQQQRRROOONNNQQQTTTNNNMMMMMMLLLLLLLLLLLLLLLLLLMMMNNNOOOOOONNNMMMLLLKKKMMMNNNNNNLLLKKKKKKLLLJJJJJJIIIHHHGGGGGGGGGGGGCCCDDDEEEEEEEEEFFFIIILLLJJJJJJIIIIIIIIIIIIJJJJJJJJJKKKKKKKKKJJJHHHFFFDDDIIIIIIIIIIIIIIIJJJKKKKKKKKKLLLLLLLLLKKKIIIGGGFFFDDDGGGIIIHHHEEEEEEHHHKKKHHHHHHHHHHHHHHHHHHHHHHHHCCCDDDDDDEEEEEEEEEEEEDDDCCCCCCCCCCCCCCCDDDEEEEEEEEEEEEDDDDDDDDDDDDEEEEEECCCCCCDDDEEEFFFFFFFFFEEEDDDCCCCCCCCCCCCDDDEEEEEE>>>@@@BBBBBBBBBBBBDDDEEE@@@@@@??????@@@@@@AAABBB@@@BBBCCCDDDDDDCCCAAA???@@@@@@@@@???@@@@@@AAABBB===>>>AAACCCCCCCCCBBBAAA???AAABBBAAA??????@@@AAA??????@@@AAABBBBBBBBBBBB@@@AAABBBBBB@@@@@@AAABBBCCCCCCBBBAAA@@@>>>>>>===@@@@@@???>>>>>>===>>>>>>@@@AAABBBAAA???>>>???@@@???@@@AAABBBCCCBBBAAA@@@===>>>@@@@@@??????@@@AAA<<<<<<<<<<<<<<<===>>>>>>999999999999999999999999999999999999999999999999888888888777888888999:::888777555444333333444444444444444444444444444444444444333333444555666777777777777777666666666666333555777888888888999;;;555444444444444555666666555555444333444555666777444444444444444555666666444555666777777555333222000000000000////////////.../////////000000111111222222222111111///......++++++,,,,,,---...//////.../////////000000111111//////000000111111111222111000...------...000111////////////////////////...............///000000000000000000000000000000------...///000000//////........................---------...............---------.........//////.........------,,,,,,,,,+++,,,---...///111222222////////////////////////........................***,,,...//////...,,,++++++,,,------,,,,,,...///,,,,,,,,,+++++++++******(((((()))***************(((((((((((())))))))))))(((((((((((())))))))))))))))))******+++++++++,,,(((((((((((()))))))))))))))(((((((((''''''''''''&&&&&&'''((()))))))))(((%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&'''((()))******(((((())))))))))))((((((((((((((((((((((((((((((((((((''''''''''''((((((%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%&&&&&&''''''((('''((((((((())))))******&&&'''(((*********)))(((&&&''''''((()))*********))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''MMMNNNOOOOOONNNMMMLLLKKKGGGHHHIIIJJJKKKKKKKKKKKKOOONNNMMMKKKKKKKKKLLLLLLLLLKKKJJJKKKNNNOOONNNKKKLLLMMMNNNNNNMMMLLLMMMOOOQQQOOOMMMMMMOOOPPPNNNKKKPPPOOONNNMMMLLLLLLLLLLLLNNNMMMMMMLLLLLLMMMMMMNNNJJJKKKLLLLLLJJJIIIJJJKKKIIIIIIIIIHHHHHHGGGGGGGGGIIIIIIIIIIIIIIIIIIIIIIIIHHHIIIIIIIIIHHHIIILLLOOONNNKKKHHHHHHJJJJJJGGGCCCJJJJJJIIIIIIIIIHHHHHHHHHKKKMMMMMMLLLJJJIIIHHHIIIJJJKKKKKKJJJHHHFFFGGGHHHHHHGGGGGGFFFEEEDDDCCCCCCEEEDDDDDDCCCCCCCCCDDDDDDEEEEEEDDDDDDCCCCCCBBBBBBBBBBBBCCCDDDDDDEEEDDDDDDBBBCCCEEEGGGGGGFFFDDDCCCAAAAAAAAAAAAAAABBBCCCDDDDDDDDDCCCCCCCCCCCCDDDDDDCCCBBB@@@@@@@@@CCCFFFGGGEEEDDDCCCBBB@@@???>>>===???@@@AAAAAAAAAAAA@@@???===>>>@@@@@@??????@@@AAA??????@@@@@@@@@AAAAAAAAA>>>???@@@AAABBBAAAAAA@@@AAAAAAAAAAAAAAAAAAAAAAAABBBAAAAAA@@@@@@AAAAAABBBBBB@@@>>>======>>>@@@BBB???>>>>>>???@@@@@@>>>===============>>>>>>>>>>>>BBBAAA@@@@@@??????@@@@@@;;;<<<===>>>>>>===<<<<<<======<<<;;;;;;;;;;;;<<<777666555777::::::777444888666555444444555666888;;;999666333222222222333666666666666666555555444444555666777777666555444444555555555555555444444666888::::::888666666666777777666555555555555555777666666555555555666666555555444333333333333444555555555555555555444444111111000000//////.........---,,,+++,,,...000222000000000000////////////...............---------////////////000000000000111222333333222111///...------......//////000000////////////////////////000000////////////000000222222222111111111000000---...............------000//////.........//////...............---------,,,,,,++++++,,,...///000///////////////......---...........................///////////////......//////000000000000//////------.........---+++***.........------,,,,,,,,,++++++,,,,,,---,,,,,,,,,***+++,,,,,,,,,***)))(((((((((''''''''''''(((((()))))))))))))))(((''''''))))))************))))))))))))))))))))))))))))))(((((((((((((((''''''''')))((('''&&&&&&&&&&&&&&&))))))((('''&&&&&&%%%%%%&&&''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))((((((((((((******))))))((((((''''''&&&'''''''''(((((())))))(((((('''''''''&&&&&&&&&LLLMMMNNNOOONNNMMMLLLKKKHHHIIIJJJJJJKKKLLLMMMMMMNNNMMMLLLKKKJJJKKKKKKLLLMMMLLLLLLMMMPPPPPPNNNLLLKKKMMMNNNNNNMMMMMMNNNPPPQQQOOONNNNNNPPPPPPNNNLLLOOOOOONNNNNNMMMMMMNNNNNNNNNNNNMMMMMMMMMMMMNNNNNNLLLMMMMMMLLLJJJJJJKKKLLLKKKJJJJJJIIIHHHHHHIIIIIIFFFFFFGGGHHHJJJKKKLLLMMMHHHIIIIIIIIIHHHIIILLLNNNMMMKKKIIIIIIIIIHHHGGGEEEIIIIIIIIIIIIHHHHHHHHHHHHHHHIIIKKKJJJIIIHHHHHHIIIJJJKKKKKKJJJHHHFFFGGGHHHGGGGGGFFFFFFEEEEEEDDDDDDDDDDDDCCCCCCCCCCCCDDDDDDDDDDDDDDDDDDDDDCCCCCCCCC@@@AAABBBDDDEEEFFFFFFFFFCCCDDDEEEFFFGGGFFFEEEEEEBBBBBBBBBBBBBBBCCCDDDDDDDDDDDDCCCCCCCCCCCCDDDDDDCCCBBBAAA@@@AAACCCEEEGGGBBBBBBAAAAAA@@@@@@??????????????????????????????===???@@@@@@??????@@@BBB???@@@@@@@@@@@@AAAAAAAAA???@@@AAABBBCCCBBBBBBAAA@@@@@@@@@@@@@@@@@@@@@@@@BBBAAAAAA@@@@@@AAAAAABBBBBBAAA???======???AAABBB???>>>======??????>>>===============>>>>>>>>>???@@@@@@???>>>>>>>>>>>>???<<<<<<===>>>>>>===<<<;;;<<<<<<;;;:::::::::::::::888777777888::::::888555999888666555555666888999999888555333222333333444555555555555555444444333555555666777777666555444444555555666666555444444666888:::999777666555555777777666444444333333333666555555444444444555555666555444444333333444444555555555555555555555555222111111000//////......------,,,+++,,,...000111000000000000////////////........................////////////000000000000000111222333333222111111/////////000000000000000////////////////////////000000////////////000000111111111000000000//////......////////////......//////............//////////////////............---,,,,,,,,,,,,---///000///////////////......---..............................////////////.........//////000000//////...------.........---,,,+++......---------,,,,,,,,,,,,,,,------------,,,,,,+++++++++++++++***)))))))))(((((('''''''''((((((***************)))(((((())))))************))))))))))))))))))))))))))))))(((((((((((((((((((((((((((''''''&&&&&&&&&'''''')))((((((''''''&&&%%%%%%&&&'''(((((())))))((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))(((((((((((()))(((((((((''''''''''''''''''''''''((((((((()))(((((('''''''''&&&&&&&&&KKKLLLMMMNNNNNNNNNMMMLLLJJJJJJJJJJJJKKKMMMNNNOOOMMMLLLKKKJJJJJJJJJKKKLLLMMMMMMNNNPPPQQQQQQNNNLLLJJJLLLNNNNNNMMMNNNOOOQQQQQQOOONNNOOOPPPPPPOOOMMMOOOOOOOOOOOOOOOPPPPPPPPPOOOOOONNNNNNNNNNNNOOOOOONNNOOONNNMMMKKKKKKMMMOOOMMMLLLJJJIIIHHHIIIKKKLLLFFFGGGHHHIIIJJJLLLLLLMMMIIIJJJJJJIIIHHHIIILLLNNNJJJKKKKKKIIIGGGFFFGGGHHHHHHHHHHHHHHHGGGGGGGGGGGGEEEFFFHHHHHHGGGGGGGGGHHHIIIJJJKKKIIIGGGFFFGGGHHHFFFFFFFFFFFFFFFFFFFFFEEECCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEE@@@AAABBBDDDFFFGGGHHHHHHDDDDDDEEEEEEEEEFFFFFFFFFDDDCCCCCCCCCCCCDDDDDDEEEDDDDDDCCCCCCCCCCCCDDDDDDCCCBBBAAA@@@AAABBBEEEFFF??????@@@@@@@@@@@@@@@@@@???>>>===<<<<<<===>>>???>>>@@@AAAAAA??????@@@BBB@@@@@@@@@@@@AAAAAAAAAAAA@@@AAACCCDDDDDDCCCBBBBBB????????????????????????AAAAAA@@@@@@@@@@@@AAAAAABBBAAA???>>>>>>???AAABBB@@@>>><<<<<<===>>>>>>>>>=========>>>>>>>>>????????????>>>============>>>===>>>>>>>>>===<<<;;;:::;;;;;;;;;::::::::::::999999888888:::;;;;;;999666888777666555555666777888777666555333333444555555444444444555444333333222666666777777777555444333444555555666666555555555666888999999777555444444777666555444333333333333555444444333333444555555666555444444333444444444555555555555555555555555222222111111000/////////...---,,,,,,---...000111000000000000////////////////////////////////////////////////000000000000///000111333333444333333111111111111000000000000////////////////////////000000////////////000000000000000/////////////////////000000000000////////////............//////000000000000/////////......------,,,------......///////////////......---..............................///////////////............//////.........------.........---,,,+++...------------,,,,,,,,,,,,------......---,,,,,,,,,+++*********************)))((((((''''''''''''***++++++++++++******)))))))))************))))))))))))))))))))))))))))))((((((((((((((((((((((((''''''&&&&&&&&&'''(((((()))((((((''''''&&&&&&&&&&&&'''(((((())))))((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))((((((''''''''''''&&&&&&''''''''''''(((((((((((('''''''''''''''&&&&&&&&&JJJKKKLLLNNNNNNNNNMMMMMMJJJIIIIIIJJJKKKLLLNNNOOOKKKKKKJJJIIIIIIJJJKKKLLLLLLMMMNNNPPPQQQOOOMMMKKKJJJLLLMMMNNNNNNNNNPPPRRROOOOOONNNNNNOOOOOONNNNNNNNNOOOPPPPPPQQQRRRRRRRRRPPPOOOOOONNNNNNOOOOOOPPPPPPPPPPPPNNNLLLLLLNNNQQQMMMLLLIIIGGGGGGIIIKKKMMMKKKKKKKKKJJJJJJJJJJJJJJJJJJKKKKKKJJJIIIIIIKKKMMMHHHJJJKKKIIIEEEDDDGGGJJJHHHHHHHHHGGGGGGGGGFFFFFFEEEGGGHHHHHHFFFEEEFFFGGGHHHIIIJJJIIIGGGFFFGGGHHHFFFFFFFFFFFFFFFFFFFFFGGGBBBBBBCCCCCCDDDDDDDDDCCCCCCCCCDDDDDDEEEEEEEEEFFFAAABBBCCCEEEFFFGGGGGGGGGDDDDDDCCCCCCCCCDDDEEEFFFEEEDDDDDDDDDDDDDDDEEEEEEDDDDDDCCCCCCCCCCCCDDDDDDCCCBBBAAA@@@AAABBBDDDEEE????????????????????????@@@>>>===;;;;;;===>>>@@@???AAABBBAAA@@@@@@AAABBB@@@@@@@@@AAAAAAAAABBBBBBAAABBBCCCDDDDDDCCCBBBAAA@@@@@@@@@@@@@@@@@@@@@@@@AAAAAA@@@@@@@@@@@@AAAAAA@@@@@@>>>======>>>@@@@@@@@@>>>;;;:::<<<>>>>>>>>>======>>>>>>>>>???????????????>>>============>>>???>>>>>>===<<<;;;;;;:::;;;<<<<<<<<<;;;;;;:::::::::::::::;;;;;;;;;999888555444333333333333444555555444444444444555666777444555555555555444333333666666777777777555444333444555555666666666666555666888999999666444333333555555555444444555555666555555444444444555666666666666555444444444444444444444444555555555555555333222222111111000///////////////...///000111222000000000000////////////////////////000000000000////////////000000000000111111222222333333333333111111111000000/////////////////////////////////000000////////////000000000000000000000000000000//////000111111111111000///............//////000222222111111000/////////.........---------------///////////////......---........................---...//////////////////------............---------------------------,,,------------------------------.........---,,,,,,,,,+++***))))))***+++,,,+++***)))(((''''''''''''*********++++++***))))))))))))************))))))((((((((((((((((((((((((((((((((((((((()))))))))&&&&&&&&&&&&&&&'''((())))))(((((((((''''''&&&&&&''''''((()))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))(((((((((((((((((((((''''''''''''(((((((((((((((''''''''''''''''''''''''JJJKKKLLLMMMNNNNNNMMMLLLIIIIIIIIIIIIJJJKKKLLLLLLJJJJJJIIIIIIIIIKKKLLLMMMKKKLLLNNNOOONNNMMMLLLKKKJJJLLLNNNNNNNNNOOOQQQRRRMMMMMMNNNNNNMMMMMMNNNNNNNNNOOOPPPRRRSSSSSSSSSSSSPPPOOOOOONNNNNNOOOOOOPPPQQQQQQQQQOOONNNMMMOOOQQQLLLJJJHHHFFFGGGHHHKKKLLLLLLLLLLLLKKKKKKJJJJJJJJJLLLLLLLLLJJJIIIIIIKKKMMMHHHIIIJJJHHHEEEDDDHHHKKKHHHHHHHHHGGGGGGGGGFFFFFFIIIJJJKKKIIIGGGEEEDDDEEEGGGIIIIIIIIIGGGFFFGGGHHHFFFFFFFFFFFFGGGGGGGGGGGGBBBCCCDDDEEEEEEEEEDDDDDDCCCDDDDDDDDDEEEEEEFFFFFFCCCDDDDDDEEEEEEEEEDDDDDDCCCCCCBBBBBBBBBCCCDDDEEEFFFEEEEEEDDDDDDDDDEEEEEEDDDDDDCCCCCCCCCCCCDDDDDDBBBBBBAAAAAAAAABBBCCCCCCAAAAAA@@@??????>>>>>>===AAA@@@>>>======>>>@@@AAAAAABBBCCCBBBAAA@@@AAABBB@@@@@@AAAAAAAAABBBBBBBBB@@@AAABBBCCCCCCBBBAAA@@@BBBBBBBBBBBBBBBBBBBBBBBBAAA@@@@@@??????@@@@@@AAA???>>>============>>>???AAA>>>;;;;;;<<<>>>??????>>>>>>>>>>>>????????????@@@@@@???>>>>>>>>>>>>?????????>>>===<<<;;;;;;;;;<<<======>>>===<<<;;;;;;:::;;;<<<<<<;;;:::999888444444333333333333444444333333444444555666666777666666666666666555444444555666777777777666444333444555555666777777666666666888999999777555444444444444555555666888999:::666666555666666777888888666666555444444444444555444444444555555555666666333333333222111111000000111111111111111222222222000000000000////////////.../////////000000111111////////////000000000000333333333222222111111111000000000//////.........000000000000000000000000000000////////////000000111111111111111111111111//////000111222222111111...............///000000333222222111000000//////..................------///////////////......---........................------...///////////////------............------------------------------------------------------------......---,,,,,,+++++++++)))))))))***+++,,,******)))((((((((((((((((((((()))))))))))))))((())))))************))))))(((((((((((((((((((((((((((((((((((())))))******&&&&&&&&&&&&&&&'''((()))(((((((((((((((''''''''''''(((((()))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((((((((((((((((((((((((''''''''''''(((((((((((())))))))))))))))))))))))'''((((((((()))))))))***))))))))))))))))))))))))((((((((((((((('''''''''&&&'''''''''''''''''''''JJJKKKLLLMMMMMMMMMLLLKKKIIIIIIJJJJJJJJJJJJIIIIIIJJJJJJIIIIIIJJJLLLNNNOOOKKKMMMNNNNNNLLLKKKKKKLLLKKKMMMOOOOOONNNOOOPPPRRRLLLNNNOOOOOOMMMMMMNNNPPPNNNOOOQQQRRRSSSSSSRRRRRROOOOOONNNNNNNNNNNNOOOOOOPPPQQQRRRQQQOOONNNOOOPPPJJJIIIHHHGGGGGGIIIKKKLLLJJJJJJKKKKKKLLLMMMMMMNNNMMMMMMMMMKKKIIIIIIJJJLLLHHHHHHGGGFFFEEEFFFIIIKKKHHHHHHHHHHHHGGGGGGGGGGGGKKKLLLLLLJJJGGGEEEDDDDDDGGGHHHIIIHHHGGGFFFGGGHHHGGGGGGGGGGGGGGGGGGFFFFFFBBBCCCEEEFFFGGGGGGFFFEEEDDDEEEEEEEEEEEEEEEEEEFFFDDDDDDDDDDDDDDDCCCCCCBBBBBBBBBCCCCCCCCCDDDDDDDDDFFFEEEEEEDDDDDDDDDDDDDDDDDDDDDCCCCCCCCCCCCDDDDDDBBBAAAAAAAAAAAAAAABBBBBBBBBBBBAAA@@@??????>>>>>>BBBAAA@@@??????@@@AAABBBBBBCCCDDDCCCAAA@@@AAABBBAAAAAAAAAAAABBBBBBBBBBBBAAAAAABBBCCCBBBAAA@@@???CCCCCCCCCCCCCCCCCCCCCCCC@@@@@@????????????@@@@@@>>>>>>>>>======>>>>>>>>>AAA???======>>>?????????>>>>>>>>>?????????@@@@@@@@@@@@???>>>>>>>>>>>>??????>>>===<<<<<<<<<<<<<<<======>>>??????===<<<;;;999;;;===<<<:::888888888666666666666666666666666333333444444555666666777666666777777666666555444444555666777777666555444444555666666777777777777666888::::::888666666666555555555666777999:::;;;666666666666777888999999777666555555444444555555333333444444555666666666444444333333222111111111222222222222222222222222000000000000////////////---......//////000000111////////////000000000000444333222111000000000000////////////............000000000000000000000000000000////////////000000111111111111222222222222...///000111111222111111......---......///000111333222222111000///......---....../////////......///////////////......---........................,,,---...///000000000000.........//////.........------,,,,,,,,,---......,,,,,,,,,------------...------------,,,+++************************+++,,,***))))))(((((())))))***''''''((())))))))))))((())))))************))))))))))))))))))))))))))))))'''(((((())))))******+++''''''&&&&&&&&&'''(((((((((((((((((((((((((((((('''((())))))******))))))((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((((((((((((((((((((((((''''''''''''(((((((((((())))))))))))))))))))))))''''''(((((())))))******))))))************++++++((((((((((((((('''''''''&&&&&&&&&'''''''''''''''KKKLLLLLLMMMMMMLLLKKKJJJJJJKKKLLLMMMLLLJJJHHHFFFJJJJJJJJJJJJKKKMMMOOOPPPNNNOOOOOOMMMKKKJJJLLLOOOMMMNNNOOOOOONNNNNNPPPQQQMMMOOOQQQQQQOOOOOOPPPSSSNNNOOOQQQRRRSSSRRRQQQPPPNNNNNNMMMMMMMMMMMMNNNNNNNNNPPPRRRSSSQQQOOONNNNNNJJJJJJIIIIIIJJJKKKKKKLLLKKKKKKKKKLLLLLLMMMMMMNNNNNNNNNMMMKKKIIIHHHJJJLLLIIIGGGEEEDDDFFFHHHIIIJJJIIIIIIIIIIIIHHHHHHHHHHHHIIIKKKKKKJJJGGGEEEEEEEEEFFFGGGHHHHHHGGGFFFGGGHHHHHHHHHHHHGGGGGGFFFFFFFFFCCCDDDFFFHHHIIIHHHGGGFFFFFFFFFFFFEEEEEEEEEEEEEEEAAABBBCCCCCCCCCCCCBBBBBBCCCCCCEEEFFFFFFFFFEEEDDDFFFEEEDDDDDDCCCCCCCCCDDDDDDDDDCCCCCCCCCCCCDDDDDDAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA@@@@@@@@@@@@AAAAAAAAAAAAAAAAAAAAAAAABBBDDDDDDCCCBBBAAAAAABBBAAAAAAAAABBBBBBBBBBBBCCCBBBCCCDDDDDDDDDBBBAAA@@@BBBBBBBBBBBBBBBBBBBBBBBB@@@@@@????????????@@@@@@@@@@@@????????????@@@@@@AAA???>>>???@@@AAA@@@???>>>>>>?????????@@@@@@@@@??????>>>============>>>>>>===<<<<<<;;;<<<======<<<===>>>???>>>===;;;:::888;;;===<<<999777777888777777777888888777777777333333444555666666666666555555666666555555444333333444555777777777666666444444666777777888888888555888::::::999888888999666666666666666777888888555555555666666777888999777666666555555555555555333333444444555666666777444444444333222222111111000111111111111111000000000000000000////////////,,,------...//////000000////////////000000000000222111000/////////000111///////////////000000000000000000000000000000000000000////////////000000000000000000111111111222---...///000111111111111---------......///000111333222111000///...------,,,---...///000000/////////////////////......---........................,,,---...///000000000000...//////000000//////...---,,,,,,,,,,,,---...///,,,,,,,,,---------......,,,,,,,,,,,,+++***)))((())))))***+++++++++++++++(((((((((((()))***++++++'''((()))***************))))))************))))))))))))))))))))))))))))))'''(((((()))******++++++(((''''''&&&&&&&&&''''''((((((((((((((((((((()))(((((()))************)))((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''(((((((((((())))))))))))))))))))))))'''''''''((()))*********((()))))))))************)))(((((((((''''''''''''&&&&&&&&&'''''''''((((((LLLLLLMMMMMMMMMKKKJJJIIIKKKMMMOOOPPPNNNKKKHHHEEEKKKJJJJJJKKKLLLNNNPPPQQQPPPQQQPPPMMMJJJJJJNNNQQQNNNOOOPPPPPPNNNNNNOOOPPPOOOQQQSSSSSSQQQPPPRRRUUUNNNOOOQQQSSSSSSRRRPPPOOONNNMMMMMMMMMMMMMMMMMMNNNMMMPPPSSSSSSRRROOONNNMMMJJJJJJKKKKKKLLLLLLLLLMMMNNNNNNNNNMMMLLLKKKKKKJJJNNNNNNNNNKKKIIIHHHJJJKKKJJJFFFCCCCCCFFFIIIJJJIIIJJJJJJIIIIIIIIIIIIHHHHHHGGGHHHIIIIIIGGGFFFFFFFFFFFFGGGHHHHHHGGGFFFGGGIIIIIIIIIHHHHHHGGGFFFEEEEEECCCEEEGGGIIIJJJIIIHHHGGGGGGGGGFFFFFFEEEEEEDDDDDD???@@@AAABBBCCCCCCCCCCCCCCCEEEGGGHHHIIIHHHFFFEEEEEEEEEDDDCCCCCCCCCCCCCCCDDDDDDCCCCCCCCCCCCDDDDDDAAAAAAAAAAAAAAAAAAAAAAAA??????@@@AAABBBBBBCCCCCC???@@@AAAAAAAAAAAA@@@???CCCDDDEEEDDDBBBAAABBBCCCAAAAAAAAABBBBBBBBBCCCCCCDDDDDDEEEEEEEEEDDDBBBAAAAAAAAAAAAAAAAAAAAAAAAAAA@@@@@@????????????@@@@@@AAAAAAAAAAAAAAAAAAAAAAAA@@@@@@???@@@BBBBBB@@@>>>>>>????????????@@@@@@@@@>>>>>>===<<<<<<<<<<<<<<<>>>===<<<;;;;;;<<<>>>???;;;<<<===>>>>>><<<:::999888;;;===<<<999666666777555555666666666666555555333444444555666666555555444444555555444444333222222333555666777888777777444444666777888888888888555888:::;;;:::::::::;;;888777666555555444444555444444444555555777888888777777666555555555555555333333444444555666777777555444444333333222222111//////000000000000///...000000000000////////////,,,,,,,,,---...//////000////////////000000000000//////.........000111222//////000000111111222222000000000000000000000000000000////////////000000.../////////000000111111------///000000111111111---------......000111111222222111000///...---,,,+++,,,...000000000000000///////////////......---........................,,,---...///000000000000//////000000000000//////---,,,,,,+++,,,---...///,,,,,,,,,------.........,,,,,,,,,+++***)))((('''((()))***,,,,,,,,,+++***''''''(((((()))+++,,,---((()))***+++++++++++++++))))))************))))))))))))))))))))))))))))))'''(((((()))***+++++++++)))((('''&&&&&&&&&&&&&&&(((((((((((())))))))))))(((((()))***************(((((((((((((((((((((((((((((((((((((((((((((((('''''''''&&&&&&'''''''''&&&''''''''''''''''''&&&))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''((((((((()))))))))))))))))))))))))))&&&''''''((()))******+++'''((((((((())))))******))))))(((((('''''''''&&&&&&&&&&&&'''''''''((((((PPPOOOMMMNNNOOOOOONNNLLLFFFIIILLLLLLKKKIIIIIIIIIGGGJJJJJJHHHIIILLLMMMKKKOOOMMMKKKIIIIIIJJJLLLNNNOOONNNNNNNNNNNNNNNNNNNNNQQQRRRQQQOOONNNNNNPPPRRRQQQQQQRRRRRRQQQPPPOOOOOORRRQQQPPPOOONNNNNNNNNNNNRRRQQQPPPPPPPPPPPPQQQQQQLLLLLLMMMMMMMMMNNNNNNNNNPPPOOOMMMLLLJJJIIIHHHHHHNNNMMMLLLJJJIIIIIIIIIIIIMMMKKKHHHFFFFFFGGGIIIKKKKKKKKKKKKKKKLLLLLLLLLLLLMMMLLLIIIGGGFFFGGGHHHIIIKKKKKKJJJHHHGGGFFFHHHJJJJJJIIIHHHGGGFFFFFFFFFFFFEEEEEEEEEEEEEEEEEEEEEEEEFFFEEEEEEEEEEEEEEEFFFGGGBBBAAAAAABBBDDDEEEDDDBBBEEEFFFFFFFFFFFFDDDBBBAAAAAAAAABBBCCCCCCBBBAAAAAAFFFEEECCCAAAAAAAAABBBCCCCCCBBB@@@>>>>>>???@@@AAA>>>???AAABBBBBBAAA???>>><<<===???@@@AAAAAA@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@===>>>???@@@AAA@@@??????BBBCCCDDDEEEEEEDDDCCCBBBBBBAAA@@@@@@@@@BBBEEEFFFAAAAAAAAAAAAAAABBBCCCDDD@@@@@@@@@@@@@@@@@@@@@@@@AAA@@@@@@??????@@@@@@AAABBBAAA@@@???>>><<<;;;;;;:::<<<======<<<;;;;;;<<<===;;;999:::===>>><<<:::======>>>>>>===<<<;;;;;;::::::888777777777888999:::888666666777777555333444444444555777777444222444444444555444444333333222333555777888777666555555666666777888999999:::999888888888888888999999;;;999777555444555666666777777888888888888777777999777555222111111222333222333555666666666555555444444444333333333222222//////............//////111111000///////////////---...///...,,,,,,...///000000000000000111111222444444333111000...------000000000000111111111111000000000000000000000000000...---...111222111///222000///111333444222000//////............//////000000000000111111111111////////////............////////////000000000000111000000///...---------////////////000000000000000000000000111111111111.........///////////////..................---------------,,,,,,+++++++++------......---+++***)))******++++++++++++******(((((())))))))))))((((((((()))***++++++++++++++++++*********))))))((((((***)))(((''''''((()))***,,,,,,,,,,,,,,,+++***)))&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&''''''''''''&&&&&&))))))))))))((((((((((((************)))))))))((('''&&&%%%&&&(((((((((''')))((('''&&&&&&'''((()))((((((((((((((((((((((((((((((((((((((((((((((((******+++++++++******)))))))))))))))))))))))))))((((((((((((((()))******))))))))))))************))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''''''''''''''LLLJJJJJJJJJLLLLLLKKKJJJHHHJJJLLLMMMKKKIIIIIIIIIIIIKKKJJJFFFGGGLLLNNNMMMNNNMMMKKKIIIIIIKKKMMMNNNNNNNNNNNNOOOOOOOOOOOOOOOQQQQQQQQQOOONNNMMMOOOQQQQQQQQQQQQQQQQQQPPPOOOOOORRRQQQPPPOOONNNNNNNNNNNNPPPPPPPPPPPPPPPPPPPPPPPPMMMNNNNNNOOOOOOPPPPPPPPPNNNNNNMMMLLLLLLLLLLLLLLLOOONNNMMMLLLKKKKKKKKKKKKLLLJJJIIIGGGGGGHHHIIIJJJIIIIIIIIIJJJJJJJJJKKKKKKLLLKKKIIIHHHGGGGGGHHHHHHJJJJJJJJJIIIGGGGGGIIIJJJJJJIIIHHHGGGFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFGGGFFFEEEEEEDDDDDDDDDDDDCCCBBBBBBCCCDDDEEECCCBBBEEEEEEFFFFFFEEECCCBBBAAAAAABBBCCCCCCCCCCCCBBBAAADDDCCCAAAAAAAAABBBDDDEEECCCBBBAAA@@@@@@@@@AAABBB>>>@@@AAABBBBBBAAA@@@>>><<<===???@@@AAAAAAAAA@@@@@@@@@@@@AAAAAA@@@@@@@@@>>>???@@@AAABBBAAA@@@@@@AAABBBCCCCCCCCCCCCBBBAAAAAAAAA@@@???@@@BBBDDDEEEAAAAAA@@@@@@@@@AAABBBBBB@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@??????@@@@@@@@@AAA@@@@@@???>>>===<<<<<<;;;<<<>>>>>><<<;;;<<<===>>><<<:::;;;===>>>===;;;;;;<<<<<<<<<<<<;;;;;;::::::999888777777777888999:::888666666777777555333444444444555666666444222444444444555555444444333222333555777888777666666444444444555666777777777999888888888888888999999:::999777555444555666777777777888888888888777777777555444222222333444555333444555666777666666555444444444333333333222222000//////......//////000111000000///////////////---......---,,,,,,---///000000000000000111111222333333222111000///......000000000000111111111111111111111111111111111111000...---...111222111///111000///111333444222000//////............//////000000000000111111111111000000000/////////......////////////000000000000111000000///......------------......//////000000//////000000000111111111000000//////......------........................---------,,,,,,,,,++++++------......---,,,***)))******++++++++++++******(((((())))))))))))(((((())))))***+++++++++++++++************)))))))))(((***)))(((''''''((()))******************)))((((((''''''&&&&&&&&&&&&'''''''''''''''(((((('''''''''))))))))))))((((((((((((++++++******)))((((((''''''&&&%%%&&&((()))(((''')))((('''&&&&&&'''((()))(((((((((((((((((((((((((((((((((((((((((((((((()))***************))))))))))))))))))))))))))))))((((((((((((((()))******))))))))))))************))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''''''''''''''JJJIIIHHHIIIJJJKKKJJJIIIIIIKKKMMMMMMKKKIIIIIIIIIIIIJJJFFFBBBBBBHHHLLLLLLNNNMMMKKKJJJJJJKKKMMMNNNNNNNNNOOOOOOPPPPPPQQQQQQPPPPPPPPPOOOMMMMMMNNNPPPPPPQQQQQQQQQQQQPPPPPPOOOQQQQQQPPPPPPOOONNNNNNNNNOOOOOOQQQQQQQQQQQQPPPOOOOOOOOOOOOPPPQQQRRRRRRRRRLLLLLLLLLLLLMMMNNNOOOPPPNNNMMMLLLKKKKKKKKKKKKKKKJJJJJJJJJIIIIIIIIIIIIIIIGGGGGGGGGHHHHHHHHHIIIIIIJJJJJJJJJIIIIIIHHHHHHGGGHHHIIIIIIIIIHHHHHHIIIKKKJJJIIIHHHGGGGGGFFFGGGGGGHHHHHHHHHHHHHHHGGGGGGGGGGGGGGGEEEDDDCCCBBBBBBBBBDDDCCCCCCCCCDDDDDDCCCAAADDDDDDDDDDDDDDDCCCBBBAAAAAABBBCCCCCCCCCCCCBBBAAAAAAAAA@@@@@@AAABBBDDDEEECCCCCCCCCBBBBBBBBBAAAAAA???@@@AAABBBBBBAAA@@@???===>>>???@@@AAAAAAAAA@@@???@@@AAABBBBBBAAA@@@??????@@@AAAAAABBBBBBAAAAAA@@@@@@AAAAAAAAAAAA@@@@@@AAA@@@@@@???@@@AAACCCDDDAAAAAA@@@?????????@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@?????????????????????????????????>>>>>>=========<<<===??????===<<<===>>>>>>===<<<<<<>>>>>>===<<<999::::::;;;;;;;;;;;;::::::999888888777777888888999888666666777777555444555444333444666666444333333444444555555555444444222444555777777777666666444444555555666666777777999999888888888888888999:::999777666555555666777666777777888888777777666555444333333333555666777444555777888888777666666444444444444333333333333000000////////////000000111000//////......//////---.........,,,,,,...///000000000000000111111222111111111111000000000000000000000111111111222222222222222222222222222222000///...///111111111000111000000111333333222000000//////......//////000000000000111111111222222111111000000000/////////////////////000000000000000000000///......------+++,,,,,,---...//////000//////000000000000111111111111000///...---,,,,,,........................------------,,,,,,,,,,,,------...------,,,+++*********++++++++++++******((())))))******))))))((())))))***++++++++++++***************))))))))))))))))))(((((((((((())))))(((((())))))((((((''''''((((((''''''''''''(((((('''(((((())))))(((((('''(((((((((((())))))))))))+++++++++***)))((((((''''''&&&%%%&&&((()))((('''((((((''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))******))))))((())))))))))))))))))))))))((((((((((((((()))******))))))))))))************))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''''''''''''''NNNMMMKKKKKKLLLLLLJJJIIIKKKLLLMMMMMMKKKIIIIIIIIIHHHGGGBBB<<<===CCCIIIJJJMMMLLLKKKJJJKKKLLLMMMNNNNNNNNNOOOPPPPPPQQQRRRRRROOOPPPPPPOOONNNMMMNNNOOOPPPPPPPPPQQQQQQPPPPPPOOOPPPPPPPPPPPPPPPOOOOOONNNNNNPPPRRRSSSSSSRRRQQQPPPOOOOOOPPPPPPQQQRRRRRRRRRLLLLLLLLLLLLMMMNNNOOOOOOJJJJJJIIIIIIIIIIIIIIIJJJIIIJJJKKKKKKKKKJJJHHHGGGGGGGGGGGGGGGHHHHHHHHHHHHIIIIIIJJJJJJIIIIIIHHHGGGGGGHHHIIIIIIHHHHHHJJJLLLIIIIIIHHHGGGGGGGGGGGGGGGIIIIIIIIIIIIHHHHHHHHHHHHFFFEEEDDDCCCCCCBBBCCCCCCEEEDDDCCCDDDEEEDDDBBB@@@CCCCCCCCCCCCCCCBBBBBBAAABBBBBBCCCCCCCCCCCCBBBBBBAAAAAAAAA@@@AAABBBCCCDDDBBBBBBBBBCCCBBBAAAAAA@@@@@@@@@AAABBBBBBAAA@@@@@@?????????@@@@@@AAAAAAAAA>>>???AAABBBBBBAAA???>>>??????@@@@@@@@@AAAAAAAAA@@@@@@@@@AAAAAA@@@@@@@@@AAA@@@@@@@@@@@@AAABBBCCCBBBBBBAAA@@@??????@@@@@@@@@@@@@@@@@@????????????>>>??????????????????>>>======>>>>>>>>>>>>>>>>>>===>>>@@@@@@>>>===>>>???>>>>>>======>>>>>>>>>===888999:::;;;;;;;;;;;;;;;999999999888888888888888888777777666777666666555555444333444555555444333333444444555555555555555333444555666777777777666666777777777888888888999:::999888888777888888888999999777666666666777777666666777777777777666666555555444444555555666777666777888999999888777666555444444444444333333333111000000//////000000111000000///............///...///000///------///111000000000000000111111222///000000000111111111111000000111111111222222222222222222222222222222222000000000000000111000000000000111111222222222111000000////////////000000000000111111111222222222111111111111000000000000////////////000000000000000000//////............,,,,,,---...//////000000////////////000000000111000000//////......---------------...............------------------,,,,,,......---------,,,,,,+++***++++++,,,,,,++++++***)))))))))******))))))))))))******+++++++++***************)))))))))))))))))))))(((((((((((())))))'''(((((((((((((((''''''))))))(((((((((((())))))(((((())))))))))))(((((((((((((((((())))))))))))))))))))))))))))))))))))(((&&&&&&'''((()))((('''(((((((((''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''(((((())))))))))))((())))))))))))))))))))))))((((((((((((((())))))***((()))))))))************(((((((((((((((((((((((())))))))))))))))))))))))''''''''''''''''''''''''QQQOOOMMMLLLLLLKKKHHHFFFJJJLLLMMMLLLJJJIIIIIIJJJHHHGGGBBB<<<===CCCIIIJJJLLLLLLKKKKKKLLLMMMNNNOOONNNNNNOOOPPPPPPQQQRRRRRROOOPPPQQQPPPNNNMMMNNNOOOOOOOOOPPPPPPPPPPPPPPPOOOPPPPPPQQQQQQQQQPPPOOONNNOOOPPPSSSTTTUUUTTTRRRQQQNNNOOOOOOOOOPPPPPPPPPPPPMMMMMMLLLKKKKKKKKKLLLLLLJJJJJJIIIIIIIIIJJJJJJKKKIIIJJJKKKLLLKKKJJJHHHGGGGGGHHHHHHHHHHHHIIIIIIIIIIIIIIIJJJJJJJJJIIIHHHGGGFFFHHHIIIJJJIIIIIIJJJKKKHHHHHHGGGFFFFFFFFFGGGGGGIIIIIIIIIHHHHHHGGGGGGGGGCCCCCCBBBCCCCCCDDDEEEEEEFFFDDDDDDDDDEEEDDDCCCAAADDDCCCCCCBBBBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCBBBBBBAAAAAAAAAAAA@@@AAAAAAAAAAAA@@@??????AAAAAAAAABBBBBBAAAAAAAAA@@@@@@@@@@@@@@@AAAAAAAAA???@@@AAAAAAAAAAAA@@@???>>>>>>>>>>>>>>>??????@@@BBBBBBAAAAAAAAAAAABBBBBBAAAAAAAAAAAAAAAAAABBBBBBDDDCCCBBBAAAAAAAAAAAAAAA@@@@@@@@@??????>>>>>>>>>===>>>>>>??????>>>>>>==================>>>>>>>>>===???@@@@@@???>>>>>>???===>>>>>>>>>======>>>>>>999:::;;;<<<<<<<<<<<<<<<999999999999888888777777777777777777666666666666555444222333444555444333333444555555666666666555333444555666666777777777777777777777888888888888:::999999888777777888888999888888777777777777777666666777777777777666666777777666666555555555555777777888999999888777666555555555444444444333333111111000000000000111111000//////...............000111111000//////000222000000000000000111111222/////////000111111222222111111111111222222222222111111111111111111111111000111111111000000000111///000111222222222222222000000////////////000000111111111111222222222222111111111111000000000000////////////000000000000////////////............---......///000000111111...////////////000000000------......//////000000---------.........//////------------------------......------------------++++++,,,,,,,,,,,,++++++))))))************))))))******+++++++++******)))))))))))))))))))))******(((((())))))))))))((((((((())))))******)))))))))))))))(((((((((((())))))(((((())))))))))))(((((('''((((((((()))))))))***''''''((()))***+++,,,,,,((('''&&&''')))))))))((('''(((((((((((((((((('''((((((((((((((((((((((((((((((((((((((((((((((((''''''((()))))))))))))))************************((((((((((((((())))))***((()))))))))************(((((((((((((((((((((((())))))))))))))))))))))))((((((((((((((((((((((((PPPNNNKKKJJJIIIHHHFFFDDDIIIJJJKKKJJJIIIHHHJJJKKKKKKKKKGGGBBBBBBGGGKKKKKKLLLLLLLLLLLLMMMNNNNNNOOONNNNNNOOOOOOPPPPPPQQQQQQOOOQQQRRRRRRPPPOOOOOOOOONNNOOOOOOPPPPPPPPPPPPOOOOOOPPPQQQRRRRRRQQQPPPOOOOOOPPPRRRSSSTTTTTTSSSRRROOOOOOOOOOOONNNNNNNNNNNNNNNNNNLLLKKKJJJJJJJJJJJJLLLLLLLLLLLLLLLMMMNNNOOOJJJJJJKKKLLLKKKJJJIIIHHHHHHHHHIIIIIIIIIJJJJJJJJJIIIIIIIIIIIIIIIIIIIIIIIIGGGHHHJJJJJJIIIHHHIIIJJJGGGFFFFFFEEEEEEEEEFFFFFFHHHHHHGGGGGGFFFFFFEEEEEEBBBBBBBBBCCCDDDEEEGGGGGGEEEDDDCCCDDDEEEEEEDDDBBBDDDDDDCCCCCCBBBCCCCCCDDDDDDDDDCCCBBBBBBCCCDDDDDDEEEDDDDDDCCCCCCBBBAAAAAAAAAAAA@@@@@@@@@?????????BBBBBBAAAAAAAAAAAABBBBBBAAAAAA@@@@@@@@@@@@AAABBB@@@@@@@@@@@@@@@@@@@@@@@@>>>============>>>??????CCCCCCBBBBBBBBBBBBCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBCCCCCCBBBBBBAAAAAABBBBBB@@@@@@@@@???>>>>>>======<<<===>>>??????>>>===<<<===========================>>>@@@@@@>>>===>>>???<<<===>>>>>><<<<<<===>>>:::;;;;;;<<<<<<<<<<<<;;;888999999999999888777777666777888777666555666777555333222222333444444333333444555666666666666666444444555555666777777777555555555555666666666666::::::999888777777777777888888888888888888888888555666666777777666666555888888777777666666666555777777888999999888666555555555555555444444444333222222111111111111222222000///......------......000111222111//////111222000000000000000111111222...//////000111111222222111111111222222222222333000000000000000000000000111222222222000///000111///000222222111111111333111000000//////000000111111111111222222222222333111111000000000/////////////////////000000000000//////////////////....../////////000000000000000......////////////000000,,,,,,---...///000111111,,,,,,------.../////////------------..................------------......++++++,,,,,,,,,,,,++++++)))******++++++******)))***++++++++++++***))))))))))))))))))************(((((())))))))))))(((((())))))***+++++++++******))))))(((((((((((())))))'''(((((())))))(((((('''''''''(((((())))))******&&&'''((()))***+++,,,---((('''&&&''')))***)))(((''''''((((((((((((''''''((((((((((((((((((((((((((((((((((((((((((((((((''''''((()))************************************((((((((((((((()))******))))))))))))************))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((LLLJJJIIIHHHIIIHHHFFFEEEFFFHHHIIIHHHHHHHHHJJJLLLKKKMMMKKKGGGGGGKKKLLLKKKKKKLLLLLLMMMMMMNNNOOOOOONNNNNNNNNOOOOOOOOOOOOOOOPPPRRRSSSSSSQQQPPPPPPPPPMMMNNNOOOPPPPPPPPPPPPPPPOOOPPPQQQRRRRRRQQQPPPOOOOOOOOOOOOPPPQQQRRRRRRRRRQQQQQQPPPOOONNNMMMLLLLLLOOONNNMMMLLLKKKKKKKKKKKKLLLLLLLLLMMMMMMOOOPPPPPPKKKKKKKKKKKKKKKJJJJJJIIIHHHHHHHHHIIIIIIIIIIIIJJJJJJIIIHHHHHHHHHHHHJJJJJJGGGIIIKKKKKKIIIHHHHHHHHHEEEEEEDDDDDDDDDDDDEEEEEEGGGFFFFFFEEEDDDDDDCCCCCCDDDDDDDDDDDDEEEEEEFFFGGGDDDCCCCCCDDDFFFFFFEEECCCEEEDDDCCCCCCCCCDDDEEEEEEEEEDDDCCCBBBBBBCCCDDDEEEDDDDDDDDDDDDDDDDDDCCCCCCCCCBBBAAA@@@???@@@AAAAAABBBBBBBBBAAAAAABBBBBBBBBBBBAAA@@@@@@@@@@@@AAABBBBBBAAA???>>>>>>???AAABBB???>>>=========>>>@@@@@@DDDCCCBBBAAAAAABBBCCCDDDCCCCCCCCCDDDCCCCCCCCCBBBAAAAAAAAA@@@AAAAAABBBBBB@@@@@@@@@???>>>=========;;;<<<>>>??????>>><<<;;;==================<<<<<<<<<>>>??????>>>======>>>;;;===>>>===;;;:::<<<>>>:::;;;;;;;;;;;;::::::999888999999:::999888777666555777888888555555666888555333111111333444444333333444555666777777777777444444444555555666777888666666666666555555555555;;;:::999888777777777777777888888999999888888888555555666666666666555555666666777777888888777777777777888888888777555444555555555555444444444444222222222111111222222222//////...------------...///000000///......///111000000000000000111111222//////000000111111222222111111111222222222333333111111111111111111111111111222444222000///000222...111333333111000111333111111000000000000111111111111111222222222333333000000000/////////......////////////000000000000.../////////////////////000////////////................../////////000000------......//////000000,,,,,,------...//////000------------.........//////...---,,,,,,---...///+++,,,,,,------,,,,,,+++)))******++++++******)))+++++++++++++++***))))))((()))))))))************'''((()))******)))((('''((()))******+++++++++***)))((((((''''''(((((()))'''''''''((((((''''''''''''''''''((()))*********))))))))))))************)))''''''''')))***)))(((&&&'''((())))))((('''&&&(((((((((((((((((((((((((((((((((((((((((((((((('''((()))***++++++++++++************************((((((((((((((()))******))))))))))))************))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((JJJIIIHHHHHHJJJJJJIIIHHHEEEFFFGGGGGGGGGHHHJJJLLLIIILLLKKKHHHHHHKKKKKKIIIKKKKKKLLLMMMNNNNNNOOOOOOOOONNNNNNNNNNNNNNNNNNNNNPPPRRRTTTTTTRRRQQQPPPQQQMMMNNNOOOOOOPPPPPPPPPPPPNNNPPPQQQSSSSSSRRRPPPOOONNNNNNMMMNNNNNNPPPQQQRRRSSSRRRQQQPPPNNNMMMLLLKKKOOONNNMMMMMMMMMMMMMMMMMMKKKKKKKKKKKKLLLMMMOOOOOOLLLKKKKKKKKKJJJJJJJJJJJJGGGGGGHHHHHHHHHIIIIIIIIIKKKJJJHHHGGGGGGHHHJJJKKKHHHJJJKKKKKKIIIGGGGGGGGGDDDDDDCCCCCCCCCCCCDDDEEEFFFEEEEEEDDDCCCBBBBBBAAAGGGFFFEEEEEEEEEEEEEEEFFFDDDCCCCCCDDDFFFGGGFFFDDDFFFEEEDDDCCCCCCDDDEEEFFFEEEDDDCCCBBBBBBCCCDDDEEEBBBCCCDDDEEEFFFFFFFFFFFFEEEDDDBBB@@@@@@AAABBBCCCCCCBBBBBBAAAAAABBBBBBCCCCCCBBBAAA@@@@@@@@@AAABBBCCCAAA???======???AAACCC@@@???>>>>>>>>>???AAABBBCCCCCCAAAAAAAAAAAACCCCCCCCCDDDDDDEEEDDDDDDCCCCCC????????????@@@AAABBBBBB@@@@@@@@@???>>>======<<<;;;<<<>>>??????>>><<<;;;>>>>>>======<<<<<<<<<<<<<<<===??????===<<<===>>>:::<<<>>>===::::::;;;>>>:::::::::::::::999888777888888999:::999888777666444777999888555555666999555333111111222444444333333444555666777777777777555444444555555666777888888888888888777777777777;;;:::999888777777777777777888888999999999888888555555666666666666555555444555666888999999::::::666777888888777666555444666666555555555444444444333222222111111222222333//////...------------...---...///...,,,,,,...///000000000000000111111222///000000000111111111111111111222222222333333333222222222222222222222222111333444333000...000222...111333333111000111333111111000000000000111111111111222222222333333333////////////............////////////000000000000.........////////////////////////...------,,,,,,............/////////000///////////////.........,,,,,,------...///000000---------........./////////...---,,,,,,---//////+++,,,,,,------,,,,,,+++******++++++++++++******+++++++++++++++***)))((((((((())))))*********+++'''((()))******)))((('''(((((()))***************((((((''''''''''''((((((&&&&&&''''''''''''&&&&&&&&&''''''((()))******+++++++++******)))((((((((()))((('''((()))***)))(((&&&'''((())))))((('''&&&(((((((((((((((((((((((((((((((((((((((((((((((((((((()))++++++,,,,,,,,,************************((((((((((((((()))******))))))))))))************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))JJJIIIHHHHHHIIIJJJIIIGGGKKKKKKKKKKKKLLLLLLLLLLLLKKKKKKJJJJJJJJJJJJKKKKKKJJJKKKLLLMMMOOOOOOOOOPPPOOOOOOOOOOOONNNMMMLLLLLLNNNPPPRRRRRRPPPOOONNNOOOPPPNNNLLLLLLNNNQQQRRRRRROOOQQQSSSVVVVVVUUUTTTRRRRRRQQQOOONNNNNNOOOQQQRRRQQQPPPOOOOOOOOOOOOMMMKKKOOOOOONNNNNNNNNNNNNNNNNNLLLKKKKKKJJJKKKKKKLLLMMMLLLKKKHHHGGGFFFFFFGGGHHHLLLLLLKKKJJJIIIIIIHHHHHHIIIHHHGGGFFFFFFGGGHHHIIIKKKKKKJJJIIIIIIIIIIIIJJJGGGGGGEEEDDDCCCCCCCCCCCCCCCCCCDDDEEEEEEEEEEEEEEEFFFGGGGGGGGGFFFEEECCCBBBBBBCCCCCCDDDEEEFFFFFFGGGFFFDDDBBBBBBCCCDDDDDDDDDFFFEEEEEEDDDCCCBBBBBBAAACCCDDDEEEDDDBBBBBBDDDEEEDDDDDDCCCBBBBBBBBBBBBCCC??????@@@AAA@@@???>>>======>>>@@@AAAAAA@@@???======>>>???@@@AAAAAABBBCCC???@@@@@@AAAAAA@@@@@@???AAA@@@@@@@@@AAAAAABBBCCCBBBCCCCCCCCCBBBAAAAAA@@@>>>???@@@AAABBBBBBBBBBBBAAABBBBBBBBBAAA>>>;;;999>>>@@@AAA@@@>>>;;;::::::===>>>>>>>>>===<<<;;;;;;<<<<<<<<<<<<============>>>>>>============>>>>>>???===;;;<<<======:::777777888888999999999888888666666777777777777666666333333333444333333222222222222111111222444555666444444444444444444444444777777777777777666666666888999;;;;;;999888888999;;;:::888666666777888999777777777777777777777777888777666555555666777888;;;999666333222333444555222444666888777666333111111222222333333222222111333111///---,,,,,,...///000///...------...///000222222111000000111222222000000111111111000000///000111111111111222222222444444444333333222222222000111111111111000//////333333222111000000111111222111111000000000000000000000000000000000000000////////////////////////111000...---,,,,,,---.../////////000///......---////////////////////////......//////000000111111////////////////////////---------............///------......//////000000111000...---,,,,,,---------,,,,,,++++++,,,,,,---+++++++++************)))(((((()))************))))))))))))))))))*********(((((((((((())))))))))))))))))))))))(((((((((((())))))))))))))))))))))))&&&&&&'''((((((((((((((())))))))))))))))))))))))''''''((((((((((((''''''((((((((()))******++++++))))))(((((('''''''''&&&%%%%%%%%%&&&'''((())))))'''''''''((((((((((((((((((((((((((())))))))))))+++++++++***)))(((((('''((((((((((((((()))******------+++***))))))((((((************************---,,,***(((((()))***++++++******)))(((''''''&&&JJJIIIHHHIIIJJJKKKJJJIIIIIIIIIIIIIIIJJJJJJJJJJJJLLLKKKKKKJJJIIIIIIIIIJJJIIIJJJKKKLLLMMMNNNNNNNNNOOOOOOOOOOOOOOONNNNNNMMMPPPRRRSSSSSSQQQPPPPPPPPPQQQOOONNNNNNPPPRRRRRRRRROOOQQQSSSUUUVVVUUUTTTRRRRRRQQQPPPOOOOOOPPPQQQRRRPPPPPPOOOOOOOOONNNMMMKKKMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMLLLJJJHHHGGGFFFFFFGGGHHHLLLKKKKKKJJJJJJIIIHHHHHHIIIHHHGGGFFFFFFGGGHHHIIIJJJIIIHHHHHHGGGGGGHHHHHHGGGGGGEEEDDDDDDCCCCCCCCCCCCCCCDDDEEEEEEEEEEEEEEEGGGGGGHHHHHHGGGFFFDDDCCCCCCCCCDDDDDDEEEFFFFFFGGGGGGEEEDDDCCCDDDEEEFFFFFFFFFFFFEEEEEEDDDCCCCCCBBBBBBCCCDDDCCCAAAAAACCCEEEDDDDDDCCCBBBBBBBBBBBBBBB??????@@@@@@??????>>>===:::<<<>>>AAABBBCCCBBBBBB??????@@@@@@AAAAAABBBBBB@@@@@@AAAAAAAAAAAA@@@@@@@@@@@@@@@@@@AAAAAABBBCCCBBBBBBCCCCCCBBBAAAAAA@@@>>>>>>???@@@AAAAAAAAAAAA@@@AAABBBBBBAAA???<<<;;;===???@@@@@@>>><<<<<<<<<=========>>>======<<<<<<<<<<<<<<<<<<============>>>==================>>>===;;;999:::;;;;;;888666777888888999999888888777666666666777777666666666333333444444444444333333333333222222333444555666444444444444444444444444666666666666666666666666:::;;;<<<<<<:::888999999:::999777666555666777888888888888888888888888888888777666555555666777777:::999777444333333444555444555666777666555333222111222222333333222222111222111000............///000000///......///000000111111111111111111111111000000111111111111000000000111111111111222222222333333333222222111111111111111222222111111000///333222222111111000111111222222111000//////000000111111111111111111111111000000000000000000000000000///...---------------///////////////......---////////////////////////.../////////000000000111////////////////////////---------............/////////////////////000000111000...---,,,,,,---------,,,,,,++++++,,,,,,---++++++++++++************((()))******++++++******++++++******))))))(((((((((((((((((()))))))))******)))))))))(((((((((((())))))))))))))))))))))))(((((()))************)))))))))))))))))))))))))))'''(((((())))))(((((('''((((((((()))******++++++)))(((((((((''''''''''''%%%&&&&&&''''''(((((((((''''''''''''''''''&&&&&&(((((((((((())))))))))))++++++******)))(((((('''((((((((((((((()))******,,,,,,+++***))))))))))))************************---,,,***)))((()))***+++*********)))((('''''''''KKKIIIIIIJJJLLLMMMLLLKKKIIIIIIIIIIIIJJJJJJJJJJJJLLLLLLKKKJJJIIIIIIJJJJJJJJJKKKLLLNNNOOOOOOOOOOOOOOOOOOOOOOOOPPPPPPPPPPPPQQQSSSTTTTTTRRRQQQQQQRRRQQQPPPPPPQQQRRRSSSQQQPPPOOOPPPRRRTTTUUUTTTSSSRRRSSSRRRQQQPPPPPPQQQRRRSSSPPPPPPPPPPPPOOONNNMMMMMMKKKKKKLLLLLLMMMMMMNNNNNNOOOOOOOOOOOOOOONNNMMMLLLKKKJJJHHHGGGFFFFFFGGGHHHLLLKKKKKKJJJJJJIIIIIIIIIIIIHHHHHHGGGGGGHHHHHHIIIJJJIIIIIIHHHHHHHHHHHHHHHGGGFFFEEEEEEDDDDDDDDDDDDDDDDDDEEEEEEFFFFFFEEEEEEHHHHHHHHHHHHGGGFFFEEEEEECCCDDDDDDEEEEEEFFFFFFFFFGGGFFFEEEEEEEEEEEEFFFGGGGGGGGGFFFFFFEEEDDDDDDDDDBBBCCCCCCCCCAAAAAABBBDDDDDDDDDCCCCCCBBBBBBBBBBBB@@@@@@??????>>>>>>??????<<<===???AAACCCCCCCCCBBBAAAAAAAAAAAAAAAAAABBBBBBAAAAAAAAAAAAAAAAAAAAAAAA@@@@@@AAAAAAAAAAAABBBBBBBBBBBBBBBBBBBBBAAAAAA@@@===>>>???@@@@@@AAAAAA@@@???@@@AAAAAAAAA@@@>>>===<<<>>>??????>>>======>>><<<<<<===>>>>>>>>>======<<<<<<<<<<<<==================<<<<<<<<<<<<======;;;:::999:::;;;:::888666777777888888888888777777555555666666666666555555333444444555555555444444555555444444444555555666444444444444444444444444444444444555666666666777;;;======<<<:::888888999999888666555555555666777999999999999999999999999777777666666666666777777999888777666555444444444666666555555555444444444111222222333333222222111222222111111000/////////111000000//////000000111000111222333333222111000000000111111111111111000000111111111111222222222222222111111111111111000222222222222222111111000222222222111111111111111333222111000////////////111111111111111111111111111111111111111111111111....../////////...------///////////////.........////////////////////////////////////000000000000////////////////////////---------............///000000000000000000//////000///...---------------,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++************)))******+++++++++++++++,,,,,,+++***)))(((''''''((((((((()))))))))************)))))))))((((((((()))))))))))))))))))))))))))***++++++,,,,,,++++++))))))))))))))))))))))))((())))))******))))))((('''(((((())))))******+++((((((((((((''''''''''''''''''''''''''''''''''''(((''''''&&&&&&%%%%%%%%%(((((((((((())))))))))))+++******))))))(((((('''((((((((((((((()))******++++++***************+++++++++++++++++++++++++++,,,+++***)))))))))***+++******))))))((((((''''''KKKJJJJJJKKKMMMOOONNNMMMKKKKKKKKKKKKLLLLLLLLLLLLKKKKKKKKKKKKKKKLLLMMMMMMNNNOOOPPPQQQRRRRRRRRRRRRNNNNNNOOOOOOPPPQQQRRRRRRQQQSSSTTTSSSQQQPPPQQQRRRPPPPPPPPPRRRSSSRRRPPPMMMOOOPPPRRRSSSTTTTTTSSSRRRSSSRRRQQQQQQQQQQQQRRRSSSPPPQQQRRRQQQPPPNNNNNNNNNKKKKKKLLLMMMNNNOOOOOOPPPOOOPPPPPPPPPOOOMMMLLLKKKJJJJJJIIIHHHGGGGGGHHHHHHLLLKKKKKKKKKJJJJJJIIIIIIIIIIIIHHHHHHHHHHHHIIIIIILLLKKKKKKJJJIIIJJJJJJJJJGGGFFFFFFEEEDDDDDDEEEEEEDDDEEEEEEFFFFFFFFFEEEEEEGGGGGGGGGGGGFFFFFFEEEEEEDDDDDDEEEEEEEEEFFFFFFFFFFFFFFFFFFEEEDDDDDDFFFHHHGGGGGGGGGFFFFFFFFFEEEEEECCCDDDDDDDDDBBBBBBDDDEEECCCCCCCCCCCCCCCBBBBBBAAACCCBBB@@@?????????@@@AAAAAAAAABBBBBBBBBAAA@@@@@@CCCCCCCCCBBBBBBAAAAAAAAABBBAAAAAAAAAAAAAAAAAABBB@@@AAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBAAAAAA@@@>>>???@@@AAAAAAAAAAAAAAA>>>???@@@AAAAAAAAA@@@@@@>>>???@@@???>>>======>>>;;;<<<===>>>>>>>>>>>>>>><<<<<<<<<<<<===============<<<<<<;;;;;;<<<<<<===<<<<<<<<<<<<<<<;;;:::999777777777888777777666666444555555666666555555444444444555555666555555555666666666555555555555555444444444444444444444444222333333444555666777777;;;<<<===<<<999777777777999888777666666666666777999999999999999999999999666666666666666777777777888888888777666555555444777777555444333333444444111222222333333222222111111222222222222111000///111111000000000000111111000111333444444333111000000000111222222222111111000000111111111222222222222222222222111111111111222333333333333222111111111111222222222111111111333333222000////////////111111111111111111111111111111111111111111111111------///000000///...---000000///...............////////////////////////////////////000000000000////////////////////////---------............///222222111111000000////////////......------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++***************+++,,,,,,,,,,,,++++++*********))))))(((((((((((()))))))))******************)))))))))(((((((((((((((((((((((((((((()))***++++++,,,,,,++++++(((((((((((((((((((((((())))))************))))))''''''(((((()))*********((((((((((((((('''''''''((((((((((((''''''''''''))))))((('''&&&&&&%%%%%%(((((((((((())))))))))))******))))))((((((((((((((((((((((((((())))))*********))))))***++++++,,,++++++++++++++++++++++++++++++***))))))******+++***)))))))))((((((((('''LLLKKKJJJLLLNNNOOOOOONNNKKKKKKKKKKKKLLLLLLLLLLLLJJJJJJKKKLLLMMMOOOQQQQQQOOOPPPQQQRRRRRRRRRRRRRRRNNNNNNNNNOOOPPPQQQRRRSSSPPPQQQQQQPPPOOONNNOOOPPPNNNNNNOOOQQQRRRQQQNNNKKKNNNOOOQQQRRRSSSSSSRRRRRRRRRRRRRRRQQQQQQRRRRRRRRRQQQSSSTTTRRRPPPMMMNNNNNNMMMMMMNNNNNNOOOPPPQQQQQQNNNNNNNNNNNNMMMLLLJJJJJJJJJJJJIIIIIIIIIIIIIIIIIIKKKKKKKKKKKKKKKJJJJJJJJJIIIIIIIIIIIIIIIIIIIIIIIIKKKKKKJJJIIIIIIIIIIIIIIIGGGFFFFFFEEEEEEEEEEEEFFFEEEEEEFFFFFFFFFFFFEEEEEEEEEEEEEEEDDDDDDDDDDDDDDDEEEEEEEEEEEEFFFFFFFFFFFFEEEFFFFFFEEECCCCCCEEEHHHGGGGGGGGGGGGFFFFFFFFFFFFEEEFFFFFFEEEDDDDDDEEEGGGCCCCCCDDDDDDCCCCCCBBBAAADDDCCCBBBAAA@@@AAABBBBBBBBBBBBBBBBBBAAAAAA@@@@@@DDDCCCCCCBBBBBBAAAAAA@@@BBBAAAAAA@@@@@@AAAAAABBB@@@AAABBBBBBBBBAAA@@@@@@@@@@@@AAAAAABBBAAAAAA@@@@@@AAABBBBBBCCCBBBBBBBBB>>>??????@@@AAAAAABBBBBBAAAAAAAAA@@@===<<<<<<===<<<<<<===>>>?????????>>><<<<<<<<<<<<============<<<<<<;;;;;;;;;;;;<<<<<<:::;;;<<<<<<;;;:::::::::777777777777777666555444444444555555555555444444333444444555666666666555666666666666666666555555444444444444444444444444222333333444555666777777:::;;;<<<:::888666555666999999888888777777777777999999999999999999999999555555666777777777777777888888888777777666555555888777555333333333444555111222222333333222222111111222222222222222111000000000111111111111000000000111333444444333111000000000111222222222222222000000111111111222222222222333333333333333333333222333333333333222111111000111111222222222111111333222111000////////////111111111111111111111111111111111111111111111111,,,---///000111000//////000000///............///////////////////////////000000000000////////////////////////////////////---------............///222222111111000000//////...............---------+++,,,,,,------,,,,,,+++,,,,,,,,,++++++++++++*********+++,,,,,,,,,,,,+++(((((())))))*********+++))))))))))))************************))))))))))))((((((((((((((((((((((((((()))******++++++******(((((((((((((((((((((((())))))************))))))'''''''''((())))))******'''''''''(((((((((((((((((((((((((((((((((''''''+++******)))((('''&&&&&&(((((((((((()))))))))))))))))))))(((((((((((((((((((((((((((((())))))***))))))))))))***+++,,,,,,++++++++++++++++++++++++******************++++++))))))))))))((((((((((((LLLKKKKKKLLLNNNOOONNNMMMIIIIIIIIIIIIJJJJJJJJJJJJJJJJJJKKKLLLNNNOOOQQQRRRNNNNNNOOOPPPPPPPPPPPPPPPOOONNNNNNNNNNNNPPPRRRSSSOOOPPPPPPNNNMMMLLLNNNOOONNNNNNNNNPPPRRRQQQNNNLLLNNNOOOPPPQQQRRRRRRRRRRRRQQQQQQQQQQQQQQQQQQQQQQQQQQQSSSTTTRRRMMMJJJKKKLLLNNNNNNOOOOOOPPPPPPQQQQQQMMMMMMLLLKKKJJJJJJJJJKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKIIIJJJJJJKKKKKKJJJJJJIIIHHHGGGGGGFFFFFFFFFFFFFFFGGGFFFFFFEEEEEEFFFFFFFFFFFFFFFGGGGGGFFFFFFEEEEEEEEEDDDDDDCCCCCCCCCDDDDDDFFFFFFFFFFFFFFFFFFFFFFFFDDDFFFGGGEEEBBBBBBEEEHHHFFFFFFFFFFFFFFFFFFFFFFFFFFFGGGGGGGGGEEEEEEGGGHHHBBBCCCDDDDDDDDDCCCAAA@@@DDDCCCBBBBBBAAAAAABBBBBB?????????@@@AAABBBBBBCCCCCCBBBBBBBBBAAAAAA@@@@@@AAAAAA????????????AAAAAA@@@AAABBBCCCBBBAAA@@@??????@@@@@@AAAAAAAAAAAAAAABBBBBBCCCCCCCCCCCCBBBBBB?????????@@@AAABBBBBBCCCBBBCCCBBB@@@===;;;<<<=========>>>?????????>>>>>><<<<<<<<<<<<============;;;;;;::::::::::::;;;;;;777999::::::888777888999666777777666666555444333333333444444444444333333222333444555555555555555555555666666666666666555444444444444444444444444444444444555666666666777888::::::999777555555666999999999999888888888777999999999999999999999999444555666777888888888777999888777777666666666777999777666444333333333444111222222333333222222111222111111111111111111111///000000111111000000///111222333444444333222111000000111222333333333333000111111111111222222222333333333333333444444444222222222222222111111000///000111333333222111111222111111000000000000000222222222222222222222222111111111111111111111111,,,---...///000111111111111000///------......///////////////////////////000000000000////////////////////////////////////---------............///000000000000000000//////---......///......------++++++------------++++++,,,,,,,,,,,,++++++++++++)))******+++++++++++++++''''''((()))***+++,,,,,,)))))))))*********++++++++++++*********)))))))))))))))))))))))))))))))))'''((())))))***)))))))))))))))))))))))))))))))))((())))))******))))))(((&&&''''''(((((())))))***'''''''''(((((((((((((((((((((((((((((((((((((((+++******))))))((((((((((((((((((((())))))))))))((((((((((((((((((((((((((((((((((((((()))*********)))))))))***+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,)))*********++++++++++++))))))))))))((((((((((((MMMLLLKKKLLLMMMNNNMMMLLLIIIIIIIIIIIIJJJJJJJJJJJJKKKKKKKKKKKKLLLMMMNNNNNNNNNNNNOOOPPPPPPPPPOOOOOOOOONNNMMMMMMMMMOOOPPPRRROOOOOOOOOMMMLLLLLLMMMOOONNNNNNNNNPPPRRRRRRQQQOOONNNOOOOOOPPPQQQQQQRRRRRRPPPPPPQQQQQQQQQQQQPPPPPPOOORRRSSSPPPJJJFFFFFFHHHOOOOOOOOOOOOOOOOOOOOOOOONNNLLLJJJIIIIIIJJJLLLMMMLLLLLLLLLMMMMMMMMMLLLLLLKKKKKKKKKKKKKKKKKKKKKLLLIIIJJJKKKLLLLLLKKKJJJIIIGGGFFFEEEEEEDDDDDDEEEEEEGGGFFFFFFEEEEEEFFFGGGGGGFFFGGGGGGGGGGGGFFFEEEDDDEEEEEEDDDCCCCCCDDDEEEFFFFFFFFFFFFFFFFFFFFFFFFFFFEEEGGGHHHFFFCCCBBBFFFJJJFFFFFFFFFFFFFFFFFFFFFFFFFFFGGGGGGFFFEEEEEEFFFHHHBBBCCCDDDEEEDDDCCCAAA@@@AAAAAAAAAAAAAAA@@@@@@???????????????@@@@@@AAABBBAAAAAAAAAAAAAAA@@@@@@@@@AAA@@@>>>======>>>@@@AAA@@@AAABBBCCCCCCAAA???>>>??????@@@AAAAAAAAAAAAAAAAAABBBBBBCCCCCCBBBBBBAAA@@@@@@@@@@@@AAAAAABBBCCCAAABBBAAA???===<<<>>>???>>>>>>?????????>>>======<<<<<<<<<<<<============;;;;;;::::::::::::;;;;;;666888::::::888777888999666666666666555444333222333333444444444444333333111222333444444555555555222333555666777666666555444444444444444444444444666666666666666666666666888999::::::888777777777888888888888888777777666888888888888888888888888333444666777888888888777:::999777555555666777888888777666555444333333333111222222333333222222111222111000//////000111222...///000000000000///...333333333333333333333333///000111222333333333333000111111111111222222222111111222222333333333333111111222222111111000///...000111333333333111000000000000000000111111222222222222222222222222222000000000000000000000000---------...///111222333111000...---------///000////////////////////////111000000000/////////...////////////////////////---------............/////////////////////000000,,,---...//////...------***+++---......---+++***------,,,,,,,,,+++++++++((()))******++++++******(((((())))))******++++++))))))*********++++++++++++++++++*********))))))))))))))))))))))))))))))'''((())))))******))))))))))))))))))))))))))))))'''(((((())))))(((((('''&&&&&&''''''((()))))))))''''''''''''((((((((()))''''''(((((())))))******))))))))))))(((((((((((((((((((((((())))))))))))((((((((((((((((((((((((((((((((((((((()))************************++++++,,,,,,,,,,,,,,,,,,,,,,,,))))))***+++++++++++++++(((((((((((())))))))))))NNNLLLKKKLLLMMMMMMLLLKKKKKKKKKKKKKKKLLLLLLLLLMMMLLLLLLKKKJJJJJJJJJJJJJJJPPPPPPQQQQQQRRRQQQQQQQQQOOONNNMMMLLLLLLNNNOOOQQQOOOPPPOOONNNLLLLLLNNNPPPOOONNNOOOPPPRRRSSSSSSQQQNNNNNNOOOPPPPPPQQQQQQRRROOOPPPPPPQQQQQQPPPPPPOOOMMMPPPQQQNNNGGGBBBCCCEEEOOOOOONNNNNNNNNNNNNNNNNNNNNLLLJJJHHHHHHJJJMMMOOOLLLMMMMMMNNNNNNNNNMMMMMMKKKKKKKKKKKKLLLLLLLLLLLLIIIJJJKKKLLLLLLKKKJJJIIIHHHGGGGGGFFFEEEFFFFFFFFFGGGFFFFFFFFFFFFFFFGGGGGGGGGGGGGGGGGGGGGFFFEEEDDDFFFFFFEEEDDDDDDEEEFFFGGGGGGGGGFFFFFFFFFFFFFFFFFFFFFHHHJJJHHHDDDCCCGGGKKKEEEEEEEEEEEEEEEEEEFFFFFFEEEFFFFFFEEEDDDDDDEEEGGGBBBCCCDDDEEEEEECCCAAA@@@??????@@@AAA@@@???>>>===BBBAAA@@@???>>>>>>>>>>>>@@@@@@@@@@@@@@@@@@@@@@@@@@@???===<<<<<<===???@@@@@@AAACCCCCCCCCAAA???>>>>>>???@@@AAAAAAAAAAAAAAAAAAAAAAAABBBBBBAAA@@@@@@AAA@@@@@@@@@AAAAAABBBCCC@@@@@@@@@???======@@@BBB???????????????>>>===<<<<<<<<<<<<<<<=========>>>;;;::::::999999::::::;;;777:::<<<<<<:::888:::<<<666666666666555444333222222333333444444333333222000111222333444444444444111222444666666666666666444444444444444444444444777777777777777666666666888999;;;;;;999888888999777777777777777666666555777777777777777777777777333444666777888888888777;;;999777555444666888:::888777666555444333222222222222222333333222222222222111///......000111333---...///000000///...---444333333222222333333444///000111222333444444444000111111111111222222222000000111111222222222222111111111111111000//////...///111333444333111000////////////000111222333222222222222222222222222////////////////////////...---------///111333444222000...---,,,---///000////////////////////////111111000000/////////...////////////////////////---------.........//////------......//////000000,,,---.../////////------***+++---......---+++***---------,,,,,,,,,++++++(((((()))***************************)))))))))))))))************++++++++++++++++++************)))))))))))))))))))))))))))(((((()))***************))))))))))))))))))))))))''''''((((((((((((''''''&&&&&&''''''((()))))))))&&&'''''''''(((((())))))&&&''''''((()))******+++'''''''''((((((((((((((((((((((((((())))))))))))'''''''''(((((((((((((((((((((((((((((()))******++++++***************+++,,,,,,,,,,,,,,,,,,,,,,,,((()))***+++++++++++++++(((((((((((())))))))))))LLLLLLLLLLLLMMMNNNOOOPPPKKKLLLNNNOOOOOONNNLLLKKKNNNMMMLLLLLLLLLMMMOOOOOOPPPPPPNNNNNNNNNNNNPPPPPPUUURRRLLLIIIKKKPPPOOOJJJLLLLLLMMMNNNNNNNNNNNNNNNIIIKKKMMMOOOPPPPPPPPPPPPQQQOOOMMMKKKLLLNNNQQQTTTSSSSSSSSSSSSRRRRRRRRRRRRRRRTTTTTTPPPIIIFFFGGGJJJPPPPPPQQQQQQQQQPPPNNNMMMLLLKKKJJJJJJJJJLLLMMMNNNMMMOOOPPPOOOMMMLLLLLLLLLNNNMMMLLLJJJIIIIIIIIIIIIIIIJJJKKKLLLLLLKKKJJJIIIHHHGGGEEEDDDDDDFFFGGGIIIDDDBBBAAACCCFFFHHHGGGEEEHHHHHHHHHGGGFFFEEEDDDCCCEEEEEEDDDDDDEEEEEEFFFGGGEEEFFFFFFFFFFFFEEEDDDDDDDDDDDDDDDDDDEEEEEEEEEEEEJJJIIIHHHGGGFFFDDDCCCCCCFFFFFFFFFFFFEEEEEEEEEEEEGGGGGGFFFFFFEEEDDDDDDDDDBBBBBBBBBBBBAAAAAA@@@???BBBBBBBBBBBBBBBBBBBBBBBB@@@@@@AAABBBBBBBBBBBBAAACCCAAA???=========???@@@@@@AAABBBBBB@@@@@@AAABBB????????????@@@AAABBBCCCBBBAAA@@@AAABBBBBB@@@??????>>>>>>>>>???AAACCCEEECCCCCCCCCCCCBBBAAAAAA@@@<<<===>>>??????>>>===<<<>>>===<<<<<<<<<===???@@@======<<<;;;;;;;;;;;;<<<888888999999999888888777777777666555555555555555333333444444333333222111444444555666555444222111333333333444444444555555666666777777666555444333666555444444444555777888;;;:::888777666777888999888888888888888888999:::555666888999999888777555666666666666777888999:::::::::999999777666444333888777555444333333333444444333222222333333111000111111000000000000000111000000////////////000000111111222222222333333333111111222333333333333222444444444333333222222222111///...///111444555555333333333333222111000///000000000000111111111111000000//////000111222222333222222222111111000000//////000000000000/////////000111222333444555555222111000.........///000......------------......//////000000000000//////---------------------------------.........//////111000---,,,,,,---000111........................////////////...---,,,+++++++++++++++++++++++++++------,,,++++++******)))((((((((((((''''''''''''++++++++++++++++++++++++***+++,,,------+++***((('''(((***+++++++++***)))******))))))((((((''''''((((((((((((((()))******)))))))))))))))(((''''''%%%''')))***+++***)))((())))))))))))))))))))))))'''''''''''''''((())))))(((((((((((((((((((((((((((((())))))((('''&&&&&&(((((((((((())))))))))))((((((((((((((((((((((((---+++***(((((()))+++,,,+++++++++++++++***)))(((***+++,,,------,,,+++***((((((((((((((((((((((((NNNNNNNNNNNNNNNOOOOOOPPPLLLMMMNNNOOOOOONNNMMMLLLNNNMMMLLLLLLLLLMMMOOOOOOPPPOOOOOONNNNNNOOOOOOPPPRRRQQQNNNLLLMMMPPPLLLEEEEEEGGGIIIKKKMMMNNNNNNNNNLLLMMMNNNPPPQQQRRRRRRRRRQQQPPPMMMLLLLLLNNNQQQSSSSSSSSSSSSRRRRRRRRRQQQQQQQQQSSSTTTQQQKKKHHHIIIKKKPPPPPPQQQQQQQQQPPPNNNNNNLLLKKKKKKJJJKKKLLLMMMNNNLLLNNNOOONNNKKKJJJIIIJJJLLLLLLKKKKKKJJJIIIHHHHHHIIIJJJKKKLLLLLLKKKJJJIIIHHHGGGEEEDDDDDDEEEGGGHHHFFFDDDCCCDDDGGGHHHGGGEEEHHHIIIIIIHHHHHHGGGFFFEEEGGGFFFFFFFFFFFFGGGHHHHHHGGGGGGGGGGGGGGGFFFEEEEEEDDDDDDDDDDDDDDDEEEFFFFFFDDDDDDEEEEEEFFFFFFFFFFFFEEEEEEEEEEEEEEEEEEEEEEEEFFFFFFFFFEEEDDDDDDCCCCCCBBBCCCCCCCCCCCCBBBAAA@@@AAAAAAAAAAAAAAAAAAAAAAAA??????@@@AAAAAAAAAAAAAAABBBAAA???>>>>>>??????@@@@@@BBBBBBAAA@@@???@@@BBB>>>??????@@@AAAAAABBBBBBCCCBBBAAAAAABBBBBB@@@>>>>>>>>>>>>???@@@AAACCCCCC@@@@@@@@@@@@@@@@@@??????<<<===>>>??????>>>===<<<===<<<;;;;;;;;;<<<>>>>>>======<<<;;;;;;;;;;;;;;;999999888888888888888888888777666666555555666666444444444444444333333222444444444444444333222222444333333333444444555555777777777666666555555555777666555555555666888888<<<;;;999777666666777888888777777777777888999999666777888999999888777777777777777777888999:::;;;:::::::::999888666555444777666555444333333444444444333111222333333222000111111000000000000111111000000////////////000000111111111111222222222222222222333444444444444333444333333333222222222222111///...///111444444444444444444333333222111000000000000000111111111111000000000000000111222222222222111111111000000000//////000000000000////////////000111222333444444222111///.........///000///................../////////000000000000//////---------------------------------.........//////000///...------...///000........................////////////...---,,,+++++++++++++++++++++++++++,,,,,,++++++++++++******((((((((((((((((((((((((++++++++++++++++++++++++***+++,,,------+++***((('''((()))*********)))))))))))))))))))))(((((((((((((((((((((((()))******)))))))))))))))(((''''''&&&'''(((*********)))((((((((((((((((((((((((((('''''''''''''''((())))))((((((((((((((((((((((((((((((((((((((('''&&&&&&(((((((((((())))))))))))((((((((((((((((((((((((,,,+++***(((((()))+++,,,,,,,,,,,,,,,,,,+++******)))***+++,,,,,,+++***)))((((((((((((((((((((((((QQQPPPPPPOOOOOOOOOOOOOOOLLLMMMNNNOOOOOONNNMMMLLLNNNMMMLLLLLLLLLMMMOOOOOOPPPOOOOOONNNNNNOOOOOOPPPOOOQQQPPPOOOPPPOOOIIIAAA???AAAEEEIIIMMMNNNOOOOOOPPPPPPPPPQQQRRRSSSTTTUUUQQQPPPNNNMMMMMMOOOQQQRRRSSSRRRRRRRRRRRRQQQQQQQQQOOORRRTTTRRRNNNKKKKKKMMMOOOPPPQQQQQQQQQPPPOOONNNLLLLLLKKKKKKKKKLLLMMMMMMLLLMMMNNNLLLJJJHHHGGGHHHIIIJJJKKKKKKJJJIIIHHHGGGIIIIIIJJJKKKKKKJJJIIIIIIGGGGGGEEEDDDDDDEEEFFFGGGGGGFFFEEEEEEGGGGGGGGGEEEHHHIIIIIIIIIIIIIIIHHHHHHHHHHHHHHHHHHHHHIIIJJJJJJHHHHHHIIIIIIHHHHHHGGGFFFEEEEEEDDDCCCDDDEEEFFFGGGBBBCCCCCCDDDEEEFFFGGGGGGEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEDDDCCCCCCBBBBBBCCCCCCDDDDDDCCCCCCBBBBBB@@@@@@@@@@@@@@@@@@@@@@@@>>>>>>???@@@@@@@@@@@@@@@???@@@@@@@@@@@@AAAAAAAAAAAABBBBBBAAA???>>>@@@AAA>>>???AAABBBBBBBBBBBBAAACCCBBBAAAAAABBBAAA???======>>>???@@@AAABBBBBBBBB???????????????@@@@@@@@@======>>>>>>>>>>>>======;;;;;;;;;;;;;;;<<<============<<<<<<;;;;;;;;;;;;:::999888777777888999:::999888888777666777777777555555555555444444333333444333333222222222222333555444333333333444666777888888666555555666666777888777777777777888999999===<<<999777666666666777777666666666777777888999999999999999999999888888888888888888999:::;;;;;;::::::::::::999888666666666555555444444444555555444222111222333333222000111000000000000000111111000000////////////000000000000000000111111111111222333333444444444444444222222222222222111111111111///...///222444444333444444444444333222111111000000000111111111222222111000000000000111222222111111000000000000////////////000000000000//////......///000111111222222111000///.........///000000//////......//////000...//////000000//////...---------------------------............//////////////////....../////////........................////////////...---,,,,,,++++++++++++++++++++++++*********+++++++++++++++))))))))))))))))))))))))++++++++++++++++++++++++++++++,,,---,,,+++***)))''''''((()))))))))))))))(((((())))))))))))))))))((((((((((((((())))))***)))))))))))))))(((''''''(((((((((((())))))))))))(((((((((((((((((((((((('''''''''''''''((())))))(((((((((((((((((((((((((((((((((((((((''''''&&&(((((((((((())))))))))))((((((((((((((((((((((((++++++***))))))***+++,,,,,,,,,,,,---,,,,,,+++***))))))************))))))))))))))))))))))))))))))RRRQQQPPPOOONNNNNNNNNNNNMMMNNNNNNOOOOOONNNNNNMMMNNNMMMLLLLLLLLLMMMOOOOOOOOOOOOOOOOOOOOOOOOOOOOOONNNPPPQQQPPPPPPQQQLLLEEE???BBBFFFKKKNNNPPPPPPPPPRRRRRRQQQPPPQQQRRRTTTUUUQQQPPPOOONNNOOOOOOPPPQQQRRRRRRRRRQQQQQQQQQPPPPPPMMMPPPSSSSSSQQQNNNNNNNNNOOOPPPQQQQQQQQQPPPOOONNNLLLLLLLLLLLLLLLLLLMMMMMMLLLMMMNNNMMMJJJHHHGGGHHHGGGHHHJJJKKKKKKIIIGGGFFFHHHIIIJJJKKKKKKJJJIIIHHHGGGFFFFFFEEEDDDEEEEEEFFFFFFFFFEEEEEEEEEEEEEEEDDDFFFGGGHHHIIIIIIIIIIIIIIIHHHHHHHHHHHHHHHIIIJJJJJJIIIJJJJJJJJJJJJIIIHHHHHHFFFEEEDDDCCCDDDEEEGGGHHHEEEEEEEEEEEEFFFFFFFFFFFFDDDDDDEEEEEEEEEEEEEEEFFFEEEDDDDDDCCCBBBBBBAAAAAABBBBBBCCCCCCCCCCCCBBBBBB????????????????????????======>>>???????????????>>>>>>@@@AAABBBBBBBBBBBBBBBBBBBBB@@@>>>>>>???AAA>>>@@@BBBCCCDDDCCCBBB@@@DDDCCCAAAAAABBBAAA???======>>>@@@AAABBBBBBAAAAAA@@@@@@@@@@@@@@@AAABBBBBB>>>>>>>>>>>>>>>=========;;;;;;;;;<<<<<<<<<======<<<<<<<<<<<<<<<;;;;;;::::::999888777777888:::<<<:::999888888777777888888666666555555444444444444444333222111000111222333555555333333333444666777999888666555555666777999888888888888999999::::::>>><<<:::777555555666666666555555555666777888999;;;:::999999888999999999777777777777888999:::;;;:::::::::::::::999888777555444444444555555555666333222111111333333222111000000000000000000111222000000////////////000000////////////000000000000111222333333444444333333111111111111111111111111111//////000222333333222444444444444444333222222000000111111111222222222111111111000000111222222000000000/////////////////////000000000000//////------......///000111111000000......---...///000000000////////////000000...//////////////////........................................../////////---...///000000///...---..............................//////...------,,,++++++++++++++++++++++++((())))))***+++,,,,,,,,,***************+++++++++++++++++++++++++++++++++++++++,,,,,,,,,+++***)))''''''(((((())))))))))))((((((((())))))******+++))))))(((((((((((()))))))))))))))))))))(((''''''))))))(((((((((((()))***(((((((((((((((((((((((('''''''''''''''((())))))(((((((((((((((((((((((('''(((((((((((((((''''''(((((((((((())))))))))))((((((((((((((((((((((((+++******))))))***+++,,,+++++++++,,,,,,++++++***(((((())))))))))))(((((())))))))))))))))))))))))RRRQQQPPPNNNMMMMMMMMMMMMNNNNNNNNNOOOOOONNNNNNNNNNNNMMMLLLLLLLLLMMMOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOQQQQQQOOOPPPRRRQQQMMMEEEGGGJJJNNNPPPQQQQQQQQQRRRRRRPPPPPPPPPQQQRRRSSSPPPPPPPPPPPPPPPPPPPPPPPPQQQQQQQQQQQQPPPPPPPPPPPPMMMOOORRRSSSRRRPPPOOOOOONNNOOOPPPQQQQQQQQQPPPOOOMMMMMMMMMMMMMMMMMMLLLLLLMMMOOOOOONNNLLLJJJIIIJJJFFFGGGIIIKKKKKKJJJHHHGGGGGGHHHIIIJJJJJJIIIHHHGGGGGGFFFFFFEEEEEEDDDDDDDDDDDDDDDDDDDDDCCCCCCCCCDDDDDDEEEFFFGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGHHHIIIIIIIIIJJJJJJJJJJJJIIIHHHHHHFFFEEEEEEDDDDDDFFFGGGHHHFFFFFFGGGGGGGGGGGGHHHHHHDDDEEEEEEEEEFFFFFFGGGGGGDDDDDDCCCCCCBBBAAAAAAAAA@@@AAAAAABBBBBBBBBAAAAAA????????????????????????======>>>????????????>>>===>>>???@@@AAABBBBBBBBBBBBBBBAAA???======???AAA???AAACCCDDDDDDCCCBBBAAACCCBBBAAAAAABBBAAA???======>>>@@@AAABBBBBBAAA@@@???????????????@@@AAABBB??????>>>===============<<<<<<======>>>>>>>>>>>><<<<<<======<<<<<<;;;::::::999888777777999;;;===::::::999888888888888888777666555444444444444555333222111000111222333444555555444444444555666777888777555444444666888999888999999:::::::::::::::>>><<<:::777555555666666555555555555666777888999;;;;;;999999888888999999666555555666666777888999999999:::::::::999999888444444555555555555555555333222111111333333333111000000//////000111222222000000////////////000000....../////////000000000000000111222222222222222111111111111111111111111000000///111222333333111333333444444333333222222111111111111222222222222222222111111111111111222///////////////000000000//////000000000000//////---------......//////000//////...------...///000000000////////////000000......////////////..............................////////////////////////---...///000000///...---.................................///......---,,,++++++++++++++++++++++++(((((()))***++++++,,,---)))*********+++++++++,,,++++++++++++++++++++++++,,,,,,,,,,,,++++++******((((((((((((((())))))***(((((())))))******++++++))))))(((((((((((()))))))))))))))))))))(((''''''***)))(((((((((((())))))'''''''''''''''''''''''''''''''''''''''((())))))((((((((((((((((((((((((''''''((((((((((((((('''(((((((((((())))))))))))))))))))))))))))))))))))***))))))******++++++,,,))))))************))))))(((((((((((((((((((((((())))))))))))))))))))))))QQQQQQOOONNNMMMMMMMMMMMMOOOOOOOOOOOOOOOOOOOOOOOONNNMMMLLLLLLLLLMMMOOOOOONNNOOOOOOPPPPPPOOOOOONNNOOORRRQQQNNNOOOSSSTTTRRRLLLLLLNNNOOOPPPQQQQQQQQQRRRQQQQQQPPPPPPPPPPPPQQQPPPQQQQQQQQQQQQPPPOOOOOOQQQQQQPPPPPPPPPOOOOOOOOONNNOOOPPPQQQQQQQQQPPPPPPNNNOOOPPPQQQQQQQQQPPPOOOMMMMMMNNNNNNNNNMMMLLLKKKMMMOOOPPPOOOMMMLLLLLLLLLGGGHHHIIIJJJKKKKKKJJJIIIGGGGGGHHHIIIIIIHHHGGGGGGFFFFFFFFFEEEEEEDDDDDDCCCBBBCCCDDDDDDBBBBBBCCCDDDCCCCCCDDDEEEFFFFFFEEEEEEFFFFFFFFFFFFFFFGGGGGGHHHHHHHHHIIIIIIHHHHHHGGGFFFEEEEEEEEEFFFFFFFFFGGGGGGDDDEEEFFFGGGIIIJJJKKKLLLEEEFFFFFFGGGGGGHHHHHHHHHDDDDDDDDDCCCBBBBBBAAAAAA@@@@@@AAAAAABBBAAAAAAAAA????????????????????????======>>>???????????????======>>>???@@@@@@AAAAAAAAAAAA@@@>>>===>>>@@@CCCAAABBBCCCDDDDDDCCCBBBBBBBBBAAA@@@AAABBBBBB@@@???>>>???@@@AAAAAAAAAAAAAAA>>>===<<<<<<<<<===>>>???@@@???>>>===<<<<<<======<<<======>>>???>>>>>>>>>;;;<<<=========<<<:::999999999888888999:::;;;<<<:::999888888777888888888777666444333333333444555333222222222222333333444444444555555666666666666666666555444444555777777888999999:::;;;:::::::::===<<<999777666666666777555555555666777888999::::::::::::999888888777777555555555555666777888888888888999999999999999999444555555666555555444444222111111111333444333222////////////000111222333000000////////////000000////////////000000000000///000000111111111111111111111111222222222222222000000000111333333222111222222222333333222222111111111111222222222222333333333222111111111111222//////000000000000111111//////000000000000//////------.........////////////...---------...///000000//////......//////000---......//////......---........................000000000////////////...---...///000000///...---........................---...............------++++++++++++++++++++++++(((((())))))***+++,,,,,,)))))))))***++++++,,,,,,++++++++++++++++++++++++,,,,,,,,,+++++++++******)))))))))))))))***++++++))))))*********************))))))((((((((((((((()))))))))))))))(((''''''))))))))))))(((((((((((('''''''''''''''''''''''''''''''''''''''((())))))((((((((((((((((((((((((&&&'''(((((((((((((((((((((((((((((()))))))))))))))))))))))))))))))))))))))))))))***++++++,,,,,,'''((())))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))QQQQQQPPPOOOOOOOOOOOOOOOOOOOOOOOONNNNNNOOOOOOOOONNNMMMLLLLLLLLLMMMOOOOOONNNOOOOOOPPPPPPOOOOOONNNNNNRRRRRROOOOOORRRSSSQQQNNNNNNMMMMMMNNNOOOQQQRRRQQQRRRRRRRRRQQQPPPPPPOOOPPPQQQRRRRRRRRRQQQOOONNNPPPPPPPPPOOOOOOOOOOOONNNOOOOOONNNOOOPPPPPPPPPPPPNNNNNNPPPQQQQQQQQQPPPPPPMMMNNNNNNNNNNNNMMMLLLKKKLLLNNNOOOOOONNNMMMMMMNNNHHHHHHIIIJJJKKKKKKLLLLLLFFFGGGHHHIIIIIIHHHGGGFFFFFFFFFFFFFFFEEEDDDCCCBBBAAACCCEEEDDDCCCCCCDDDGGGCCCDDDDDDEEEEEEEEEDDDDDDFFFFFFFFFFFFFFFGGGHHHHHHGGGGGGGGGGGGGGGFFFEEEEEECCCEEEFFFHHHHHHGGGFFFEEEDDDEEEEEEGGGHHHIIIJJJJJJFFFGGGGGGHHHIIIIIIJJJJJJEEEEEEDDDDDDCCCBBBBBBBBB@@@AAAAAABBBCCCCCCBBBBBB@@@@@@@@@@@@@@@@@@@@@@@@===>>>??????@@@@@@??????>>>>>>=========>>>@@@AAA?????????======>>>BBBDDDCCCCCCCCCCCCCCCCCCCCCCCCAAA@@@@@@AAABBBCCCBBB@@@@@@@@@??????@@@@@@AAAAAA???>>><<<;;;;;;<<<===>>>AAA@@@>>>===<<<<<<<<<===;;;<<<===>>>>>>>>>======;;;<<<===>>>===<<<:::999888888999999:::;;;;;;<<<999999888777777777777777666555333222111222333444222222333444444444444444333444666777777777555555333444444444555555555666777888999:::;;;::::::999<<<;;;999777666666777888666666666777888999:::;;;888999999999999777666555555555555555666777888999666777777888999999999888555555666666666444333222222111000111333444333222////////////000111222333000000////////////000000//////000000000111111111000000111222222222222111222222222222333333333444000000000222333333222000000111111222222111111000111111111222222222333333444333222222111111111222000000000111111111222222//////000000000000//////............////////////......---,,,---...///000///..................///---......//////......---........................000000000000/////////.........////////////..............................------...............---++++++++++++++++++++++++(((((())))))******++++++(((((())))))***++++++,,,++++++++++++++++++++++++,,,,,,++++++******+++++++++******)))***+++,,,---++++++************************)))((((((((((((((()))))))))))))))(((''''''((()))*********((('''&&&'''''''''''''''''''''''''''''''''''''''((())))))((((((((((((((((((((((((&&&&&&'''((((((((((((((((((((((((((())))))))))))))))))))))))))))))))))))(((((()))***+++,,,,,,,,,(((((()))*********************)))(((((()))******((((((((((((((((((((((((RRRRRRQQQPPPPPPPPPPPPQQQPPPOOOOOONNNNNNOOOOOOPPPNNNMMMLLLLLLLLLMMMOOOOOONNNNNNPPPPPPPPPPPPNNNNNNNNNRRRSSSPPPOOOPPPPPPMMMNNNMMMKKKKKKLLLNNNPPPRRRRRRRRRSSSSSSSSSQQQPPPOOOPPPQQQRRRSSSSSSQQQOOOMMMPPPPPPPPPOOOOOOOOONNNNNNPPPOOOMMMMMMOOOPPPPPPOOOMMMNNNPPPQQQQQQQQQPPPPPPMMMNNNOOOOOONNNMMMLLLKKKKKKMMMNNNOOONNNMMMNNNOOOIIIIIIIIIIIIJJJLLLMMMNNNFFFGGGHHHHHHHHHHHHGGGFFFFFFFFFFFFFFFEEEDDDBBBBBB@@@CCCEEEEEEDDDDDDFFFIIIDDDDDDEEEEEEEEEEEEDDDDDDGGGGGGFFFFFFGGGGGGHHHIIIEEEFFFFFFFFFFFFEEEDDDDDDCCCDDDGGGIIIIIIHHHFFFDDDGGGGGGGGGFFFFFFFFFEEEEEEGGGGGGHHHIIIIIIJJJKKKKKKEEEEEEEEEDDDCCCCCCBBBBBBAAABBBBBBCCCDDDDDDDDDCCC@@@@@@@@@@@@@@@@@@@@@@@@>>>>>>???@@@@@@@@@@@@@@@???>>><<<;;;;;;===???@@@>>>>>>>>>===<<<>>>BBBFFFEEEDDDCCCCCCCCCCCCDDDDDD@@@??????AAACCCCCCBBBAAAAAA@@@?????????@@@AAABBBBBBAAA>>>===<<<===>>>???AAA@@@>>>===<<<<<<<<<===::::::<<<=========<<<;;;;;;<<<===>>>>>><<<:::999777888999:::;;;<<<;;;;;;999888888777666777777777666444333111111222333444111222444555666555444444222444666888999777555444222222333444555555444444777888999:::;;;:::999999;;;:::888777666777888999666666666777888:::;;;<<<777888999:::999777555333666666666666777888999:::555666777888888888888888666666777777666444222111222111000111333444333222////////////000111222333000000////////////000000000000000000111111111111111111222333333333333222222222222333333444444444000000000222333333111//////000000111111111000000111111222222222333333333444333333222111111111222000000111111222222222333//////000000000000//////.........///////////////...------,,,---...///000......------------......---..................---////////////////////////111111000000/////////...////////////////////////........................------...............---++++++++++++++++++++++++))))))))))))************'''(((((()))******++++++++++++++++++++++++++++++---,,,++++++******++++++,,,+++*********+++------,,,+++++++++***)))))))))******)))((((((((((((((()))))))))))))))(((((('''((()))***+++***)))'''%%%'''''''''''''''''''''''''''''''''''''''((())))))((((((((((((((((((((((((&&&&&&'''((())))))(((((((((((((((((())))))))))))))))))))))))))))))))))))(((((()))++++++,,,,,,,,,((()))***++++++++++++++++++***)))(((((()))***+++((((((((((((((((((((((((QQQQQQQQQQQQQQQQQQQQQQQQNNNOOOOOOPPPOOONNNMMMLLLJJJKKKLLLMMMMMMLLLKKKKKKJJJKKKLLLNNNNNNMMMLLLLLLMMMNNNNNNOOOOOOPPPPPPQQQNNNNNNOOOOOOPPPQQQRRRRRRSSSRRRRRRRRRRRRQQQQQQQQQOOOPPPQQQRRRRRRPPPNNNMMMNNNNNNOOOOOOPPPQQQQQQRRRRRRQQQPPPOOONNNOOOPPPQQQRRRQQQOOOMMMLLLKKKJJJJJJLLLKKKKKKKKKLLLMMMNNNNNNNNNOOOPPPPPPOOOMMMJJJHHHHHHIIIIIIJJJJJJIIIIIIHHHMMMLLLJJJHHHGGGGGGGGGGGGFFFEEECCCBBBAAABBBDDDEEEFFFFFFFFFEEEEEEEEEEEEDDDCCCDDDEEEDDDCCCBBBCCCEEEEEEEEEFFFFFFFFFFFFEEEEEEEEEEEEFFFFFFGGGGGGGGGGGGGGGFFFFFFDDDCCCBBBAAA@@@DDDEEEGGGHHHHHHGGGFFFEEEIIIHHHHHHGGGFFFFFFFFFGGGCCCCCCDDDDDDDDDDDDCCCCCCBBBBBBAAA@@@?????????@@@CCCBBBAAAAAA@@@@@@@@@@@@@@@AAABBBCCCBBBAAA@@@???AAABBBBBB@@@>>>======>>>===<<<<<<<<<===???BBBDDDEEECCC@@@>>>===???BBBDDDBBBAAAAAACCCDDDCCCAAA???@@@@@@@@@?????????>>>>>>@@@@@@@@@????????????>>>???????????????>>>===<<<@@@@@@???>>>===<<<;;;;;;???>>>===<<<<<<===>>>???<<<<<<;;;;;;;;;:::::::::===;;;888666555666888999666666555444333333222222333333444444555666777777333444666777777777666555555333333555888999777555666777888777666666888:::>>>===<<<;;;999888777666888888888888999:::;;;<<<::::::999888777777888888777777666666666666777777777777777777777777777777888888777777666666555555555555444333222222222222444333222000//////......222111111000///......---///000111222222111000///000111333444444333222111000111333555555444333222333333333333333333333333111111000000111222333333222222222111111111000000222222111111111111222222111//////000111222111000000000000000000000000000//////000000///...------,,,------...............///////////////...------......////////////......---...///000000111000000//////.........------------------............///...---,,,---......---+++............---,,,+++++++++++++++************)))))))))***++++++++++++*********))))))))))))******))))))************))))))---,,,,,,,,,+++*********++++++******************---,,,+++***))))))))))))++++++)))(((''''''''''''(((((()))***++++++,,,,,,***************)))(((((((((((('''''''''&&&&&&&&&(((((('''''''''&&&&&&&&&'''((()))))))))(((&&&%%%)))((('''%%%%%%%%%&&&'''))))))(((((((((((())))))******))))))((((((''''''))))))))))))((((((((((((***************)))(((((())))))))))))***************'''$$$###%%%'''((()))OOOOOOOOOOOOOOOOOOOOOOOONNNOOOOOOOOOOOONNNMMMLLLKKKKKKMMMNNNNNNNNNMMMMMMLLLMMMMMMNNNNNNNNNNNNNNNNNNOOOOOOPPPPPPQQQRRRRRRPPPPPPQQQQQQRRRRRRSSSSSSSSSSSSSSSRRRRRRRRRQQQQQQPPPQQQRRRSSSSSSQQQOOONNNQQQQQQQQQQQQRRRRRRRRRRRRSSSRRRQQQQQQPPPPPPPPPPPPQQQPPPOOOMMMLLLKKKKKKKKKMMMMMMLLLLLLMMMMMMNNNNNNNNNOOOOOOOOONNNLLLJJJHHHIIIIIIIIIJJJJJJIIIIIIIIILLLKKKIIIHHHGGGFFFFFFGGGHHHFFFEEECCCCCCDDDEEEFFFGGGGGGGGGFFFFFFFFFEEEEEECCCDDDEEEEEEDDDCCCDDDEEEEEEFFFFFFFFFFFFEEEEEEEEEDDDDDDDDDEEEEEEEEEFFFFFFFFFEEEDDDCCCBBBAAA@@@@@@EEEEEEFFFGGGHHHGGGGGGFFFIIIHHHGGGGGGFFFFFFGGGGGGCCCDDDDDDDDDDDDDDDDDDCCCAAAAAA@@@@@@@@@AAABBBBBBBBBBBBAAA@@@@@@@@@AAAAAA???@@@@@@@@@@@@???======@@@AAAAAA@@@>>>===>>>??????>>>>>>>>>???AAACCCEEEBBBAAA???>>>===???AAABBBAAAAAAAAABBBDDDDDDBBB@@@@@@@@@@@@?????????>>>>>>@@@@@@@@@????????????>>>????????????>>>>>>>>>============<<<;;;;;;::::::>>>>>>===<<<<<<===>>>>>><<<<<<;;;;;;;;;:::::::::<<<:::888777666666777888666666555444444333222222333333444444555666666777555555777888888888777666666444333444777999888666777888888888777777999:::>>>>>>===;;;:::888777777888888777888888999:::;;;999999999888888888777777777777666666666666777777777777777777777777777777888777777777666666666555555444333222222111111111333222111000////////////111111111000///.........///000111111111111000//////000222333333333111000000111333444555444333222333333333333333333333333111111000000111222222333222222222111111111000000222111111000000111111222111//////000111222111000000000000000000000000000///////////////...------------...///////////////000000000000///...------......////////////.........//////000000000000/////////.........------------------............///...---,,,---......---+++---------...------,,,,,,++++++++++++************))))))***+++++++++++++++******))))))))))))******))))))************))))))+++++++++++++++*********************************---,,,+++***))))))))))))+++***)))(((''''''''''''(((((()))******+++,,,,,,***************)))((((((''''''''''''''''''''''''(((((('''''''''&&&&&&&&&'''((()))))))))(((&&&%%%(((((('''&&&&&&&&&&&&&&&(((((())))))))))))((((((***)))))))))(((((((((''')))))))))***************+++++++++++++++***))))))))))))))))))***************'''$$$###%%%'''((((((NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNOOOOOOOOONNNMMMMMMKKKLLLMMMNNNOOOPPPPPPPPPOOONNNMMMMMMMMMNNNPPPPPPOOOOOOPPPQQQQQQRRRRRRSSSQQQQQQQQQQQQQQQQQQRRRRRRSSSSSSSSSRRRRRRRRRRRRQQQQQQRRRSSSTTTSSSRRRQQQPPPSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSRRRQQQPPPOOOPPPOOONNNMMMMMMLLLLLLLLLOOOOOONNNNNNNNNNNNNNNNNNMMMNNNNNNNNNMMMLLLJJJIIIIIIIIIJJJJJJJJJJJJIIIIIIKKKJJJIIIHHHGGGFFFFFFFFFGGGFFFEEEDDDDDDDDDEEEFFFFFFFFFFFFFFFEEEEEEEEEDDDDDDFFFGGGFFFEEEDDDEEEFFFGGGGGGGGGFFFFFFEEEEEEDDDEEEEEEEEEFFFFFFFFFFFFFFFFFFFFFEEEEEEDDDCCCBBBBBBEEEEEEFFFGGGHHHHHHGGGGGGHHHHHHGGGGGGFFFFFFGGGGGGDDDDDDDDDDDDDDDDDDDDDDDD@@@@@@@@@AAAAAABBBCCCDDDAAAAAA@@@@@@@@@AAABBBBBB@@@@@@@@@@@@???>>>===<<<>>>@@@AAA@@@???>>>???@@@AAA@@@@@@@@@AAABBBDDDEEE@@@??????>>>>>>???@@@@@@@@@@@@@@@BBBDDDDDDCCCAAA@@@@@@@@@???????????????@@@@@@@@@????????????>>>@@@???>>>=========>>>???<<<<<<<<<<<<<<<<<<<<<<<<======<<<<<<<<<<<<======<<<<<<;;;;;;;;;:::::::::999999888888777666666666666666555555444333333333333333444444555666666666666666777888888888888777777555333444666888888888777888999999777888999;;;???>>>===<<<;;;999888888888777777777777777888888888888999:::999888777666777777666666666666777777777777777777777777777777777777777777666666666666444333222111111000111111111111000000000000111111111111000000//////......///000000111111000000///...///000222222222111000000111333444444444333222222222222222222222222222111111111000111111222333222222222111111111111111222111111000000111111222111//////000111222111000000000000000000000000000///////////////......---......///000000000000000000000000000///...---,,,...//////000000//////...///000000000000//////.../////////.........---------------............///------,,,---//////---,,,,,,,,,------...---------,,,+++++++++************)))******+++++++++++++++******))))))))))))******))))))************))))))))))))******************************************,,,,,,+++***))))))))))))+++***)))((((((''''''(((((())))))******+++++++++))))))******))))))((((((''''''''''''''''''(((((((((((((((''''''''''''&&&((((((((()))(((((('''&&&'''''''''(((''''''&&&%%%'''((()))******)))((('''))))))))))))(((((((((((())))))******++++++,,,,,,+++,,,,,,,,,,,,+++******)))))))))*********++++++)))'''$$$###$$$&&&''''''PPPPPPPPPPPPPPPPPPPPPPPPNNNNNNNNNNNNNNNNNNNNNNNNKKKLLLMMMNNNOOOPPPQQQQQQPPPNNNLLLKKKKKKMMMPPPQQQOOOOOOOOOPPPQQQQQQRRRRRRPPPPPPPPPOOOOOOOOOOOOOOORRRRRRRRRQQQQQQQQQPPPPPPQQQRRRSSSSSSSSSRRRQQQQQQQQQQQQRRRSSSTTTTTTUUUUUURRRSSSSSSSSSRRRQQQOOOMMMOOOOOONNNMMMMMMMMMNNNNNNPPPPPPPPPPPPOOONNNNNNMMMMMMMMMNNNMMMMMMKKKJJJIIIJJJJJJKKKKKKKKKKKKJJJJJJLLLKKKKKKJJJIIIHHHHHHHHHGGGFFFEEEDDDDDDDDDDDDEEEEEEEEEDDDDDDDDDCCCCCCCCCEEEFFFGGGGGGEEEEEEFFFGGGHHHHHHGGGFFFEEEEEEEEEEEEHHHHHHHHHHHHHHHHHHHHHHHHIIIIIIHHHHHHGGGGGGGGGFFFEEEFFFFFFGGGHHHHHHHHHHHHHHHHHHGGGGGGFFFGGGGGGHHHEEEDDDDDDDDDDDDDDDDDDEEEAAAAAAAAA@@@AAAAAABBBBBB@@@@@@@@@@@@AAAAAABBBCCCCCCBBBBBBAAA@@@???>>>>>>===???@@@@@@??????@@@AAAAAAAAAAAAAAAAAABBBCCCDDD>>>??????@@@@@@@@@@@@@@@??????@@@BBBDDDEEECCCBBB????????????????????????@@@@@@@@@?????????>>>>>>AAA???>>><<<<<<===???@@@============>>>>>>??????===<<<<<<<<<<<<<<<<<<===<<<<<<;;;;;;;;;:::::::::777888888999888777666555666666555555444444444333444444444555555555666666555666666666777777777777777666444444555777999:::888999:::999888888:::<<>>===<<<;;;:::999999888777777666666666666777666888999::::::999777666777777666666666666777777777777777777777777777777777777777777666666666666444333222111000000000000000000//////000111222222111000000000/////////...///000000000000000000///---...///000111111000000000111222333333333333222111111111111111111111111222111111111111111222222111111111111111111111111111111000000000000111111111/////////111222111000////////////////////////...///////////////......//////000111111111111111111111111000000///------//////000000000000//////000000111000000///...---////////////............---------............///------,,,---//////...---++++++,,,---............,,,,,,+++++++++*********)))***++++++,,,,,,+++++++++******))))))******+++)))******++++++******)))((((((((()))*********+++***************+++++++++,,,++++++***))))))************)))(((((((((((((((((()))))))))*********+++((()))))))))))))))(((((()))(((((((((''''''&&&&&&((((((((('''''''''''''''((((((((((((((((((''''''&&&&&&((((((((('''&&&%%%&&&((()))++++++)))(((&&&))))))))))))(((((((((((((((((()))******+++,,,,,,***++++++,,,++++++******))))))*********+++++++++)))'''$$$###%%%&&&&&&&&&PPPPPPPPPPPPPPPPPPPPPPPPNNNNNNNNNNNNNNNNNNNNNOOOKKKKKKLLLMMMNNNPPPQQQQQQOOOMMMKKKIIIJJJLLLOOOQQQNNNNNNNNNOOOPPPPPPQQQQQQPPPPPPPPPPPPPPPPPPPPPOOOQQQQQQQQQPPPPPPPPPOOOOOOQQQQQQQQQRRRRRRQQQQQQQQQNNNNNNPPPQQQSSSTTTVVVVVVQQQQQQRRRRRRQQQPPPNNNMMMOOOOOONNNNNNNNNNNNNNNOOOPPPPPPPPPPPPPPPOOONNNMMMNNNNNNMMMMMMMMMLLLKKKKKKJJJKKKKKKLLLLLLKKKKKKJJJMMMMMMMMMLLLLLLKKKJJJJJJIIIHHHHHHGGGGGGGGGGGGGGGFFFFFFEEEEEEEEEDDDDDDDDDEEEGGGHHHGGGFFFEEEFFFHHHHHHHHHGGGFFFEEEEEEFFFFFFHHHHHHHHHHHHHHHHHHHHHHHHIIIIIIIIIIIIIIIIIIHHHHHHFFFFFFFFFGGGGGGHHHIIIJJJHHHGGGGGGFFFGGGGGGHHHHHHFFFEEEDDDDDDDDDDDDEEEFFFDDDCCCBBB@@@@@@?????????@@@@@@@@@@@@AAAAAABBBCCCBBBBBBAAA@@@??????>>>>>>===>>>@@@@@@??????@@@BBB@@@@@@@@@@@@@@@AAAAAAAAA>>>???AAABBBBBBBBBAAAAAA??????@@@BBBDDDEEECCCBBB????????????????????????@@@@@@@@@?????????>>>>>>@@@???===<<<<<<>>>???AAA<<<<<<======>>>?????????<<<==================<<<<<<<<<;;;;;;;;;:::::::::666777999999999888666555666555555555555555444444444444444555555555555555444444444444555555666666777666555444555666999;;;888999:::999888888:::<<<>>>>>>===<<<;;;::::::999777777666666555666666666666777999::::::999888666777777666666666666777777888888888888888888888888666666666666777777777777444333222111000000000000////////////000111222333000000000000////////////000//////////////////000------...///000000111111111111222222222333333222111111111111111111111111222222111111111111111222111111111111111111111111111000000000000000000111111/////////111222111000////////////////////////......///////////////...///000000111111111111111000000000000000//////...//////000000000000//////000000111000000///...---000000/////////.........---------............///---,,,,,,...///000///---++++++,,,---............,,,,,,,,,++++++++++++*********+++,,,,,,,,,,,,+++++++++************++++++******++++++++++++******((((((((()))*********+++))))))*********+++++++++,,,+++******)))************))))))(((((((((((())))))))))))))))))*********'''(((((()))))))))((((((++++++***((('''&&&%%%$$$(((((((((((((((((((((((((((((('''''''''(((((((((%%%&&&'''(((((('''&&&%%%&&&((()))++++++)))(((&&&(((((((((((())))))))))))''''''(((((()))***++++++))))))***************)))************++++++++++++)))'''%%%$$$%%%&&&&&&%%%OOOOOOOOOOOOOOOOOOOOOOOONNNNNNMMMMMMNNNNNNOOOPPPMMMLLLLLLMMMNNNOOOPPPQQQNNNMMMKKKIIIJJJLLLNNNPPPMMMMMMNNNNNNOOOPPPPPPQQQSSSSSSSSSSSSSSSSSSSSSTTTQQQQQQQQQPPPPPPPPPOOOOOOQQQQQQQQQQQQQQQQQQRRRRRRMMMMMMOOOPPPRRRSSSUUUUUUPPPPPPPPPPPPPPPPPPOOONNNPPPOOOOOONNNNNNNNNNNNOOONNNOOOPPPQQQPPPOOONNNMMMOOONNNNNNMMMMMMMMMLLLLLLKKKKKKLLLLLLLLLLLLKKKKKKMMMNNNNNNNNNNNNMMMLLLKKKLLLLLLLLLKKKKKKKKKJJJJJJHHHHHHHHHHHHGGGGGGGGGGGGEEEGGGGGGGGGFFFEEEFFFGGGHHHGGGFFFEEEEEEFFFGGGHHHFFFFFFFFFFFFFFFEEEEEEEEEGGGGGGGGGGGGGGGGGGHHHHHHFFFFFFFFFFFFGGGIIIJJJKKKGGGGGGFFFFFFGGGGGGHHHHHHFFFFFFDDDDDDDDDDDDFFFFFFFFFEEECCCAAA@@@?????????AAAAAA@@@@@@@@@AAABBBBBB??????>>>============>>>===>>>@@@@@@??????@@@BBB@@@@@@@@@@@@@@@????????????@@@AAABBBBBBBBBBBBBBB@@@@@@@@@BBBDDDDDDCCCAAA???????????????@@@@@@@@@@@@@@@@@@????????????>>>???>>>=========>>>???@@@:::;;;;;;;;;<<<<<<============>>>>>>>>>>>>======<<<<<<;;;;;;;;;:::::::::777888999::::::999888777555555555555555555555555555555555555555555555555444444333333333444555666666666777666555666999;;;777888999999777888999;;;======<<<<<<;;;::::::999777666666666666666777777666777888999:::999888888777777666666666666777777888888888888888888888888666666666666777777777777444333222111111000111111000000//////000111222222000000000000////////////000//////......//////000------...///000111222222111111111111222222222333222222222222222222222222333222111111000111111111111111111111111222222222111000000//////000000111111//////000111222111000000000000000000000000000---...////////////////////////000111111111111111//////000000111111000000///000000111111000000//////000000000000//////...000000000/////////......---------............///---,,,,,,...000111000...,,,,,,------...---------,,,,,,,,,,,,++++++++++++***++++++,,,,,,,,,,,,,,,++++++************++++++******++++++++++++******))))))******************)))))))))***++++++,,,,,,++++++***************+++))))))(((((((((((())))))))))))))))))))))))))))))''''''((()))))))))((((((++++++***)))'''&&&%%%%%%'''(((((((((((()))))))))(((''''''''''''((())))))%%%&&&''''''(((''''''''''''((()))******)))((('''(((((((((((())))))))))))''''''(((((())))))******(((((()))************)))*********++++++++++++,,,***(((&&&&&&''''''&&&%%%PPPPPPPPPPPPPPPPPPPPPPPPNNNNNNMMMMMMMMMNNNOOOPPPOOOOOONNNNNNNNNPPPQQQRRRNNNMMMLLLKKKKKKMMMOOOPPPNNNNNNOOOOOOPPPQQQQQQQQQSSSSSSTTTTTTUUUUUUVVVVVVSSSSSSRRRRRRRRRQQQQQQQQQRRRQQQQQQQQQRRRSSSSSSTTTOOOPPPPPPQQQQQQRRRRRRSSSPPPPPPPPPPPPPPPQQQQQQRRRQQQPPPOOONNNNNNNNNNNNNNNLLLMMMOOOPPPPPPPPPNNNMMMPPPOOOOOONNNNNNNNNNNNNNNKKKLLLLLLMMMMMMLLLLLLKKKMMMMMMNNNNNNNNNMMMLLLKKKLLLLLLLLLLLLLLLKKKJJJJJJGGGGGGGGGGGGFFFFFFFFFFFFEEEFFFGGGFFFEEEDDDEEEGGGGGGFFFEEEEEEFFFGGGIIIJJJFFFFFFEEEEEEEEEDDDDDDDDDFFFFFFFFFGGGGGGHHHHHHHHHFFFFFFFFFFFFGGGIIIKKKLLLGGGGGGFFFFFFGGGGGGHHHIIIGGGFFFDDDCCCCCCDDDFFFGGGFFFFFFEEECCCBBBBBBBBBBBBBBBBBBAAA@@@@@@@@@AAAAAA>>>======<<<<<<===??????>>>???@@@@@@???>>>???AAA@@@@@@@@@@@@@@@???>>>>>>?????????@@@AAAAAABBBBBBAAAAAAAAABBBDDDDDDBBB@@@>>>>>>?????????@@@@@@@@@@@@@@@@@@????????????>>>===>>>>>>>>>????????????;;;;;;;;;<<<<<<<<<<<<<<<===>>>???@@@@@@???>>>===<<<<<<;;;;;;;;;:::::::::999999::::::::::::999999555555555555666666666666555555555555555555555555555444444333444555666777444666888888666666888;;;777888888888777777999:::<<<<<<;;;;;;::::::999999666666666666777888999999777777888888888999999999777777666666666666777777888888888888888888888888555666666666777777777888555444333222222111111111111000000000000000111111////////////000000000000000///............///000.........///000111333333111111111111111222222333333333333333333333333333333222222111000000111111000000111111111222222222000000////////////000000111//////000111222111000000000000000000000000000------...///////////////...///000000111111000000---...///000111222222222000000111111111111000000...//////000000000000///000000000000/////////...---------............///---,,,,,,...000111000///---------...------,,,,,,------,,,,,,,,,+++++++++***+++,,,,,,------,,,,,,,,,++++++******++++++,,,***++++++,,,,,,++++++***+++++++++++++++*********((())))))***++++++,,,,,,+++***************++++++))))))(((((((((((()))))))))))))))))))))))))))(((&&&''''''((())))))(((((()))))))))((((((((((((((('''((((((((())))))))))))(((''''''&&&'''((()))***&&&&&&&&&&&&&&&'''(((((((((((())))))))))))(((((('''((((((((()))))))))***))))))))))))))))))))))))((()))******+++++++++************+++++++++,,,,,,+++)))((('''(((((('''%%%SSSSSSSSSSSSSSSSSSSSSSSSNNNNNNMMMMMMMMMNNNPPPQQQRRRQQQPPPOOOOOOPPPRRRSSSNNNNNNMMMMMMMMMNNNOOOPPPOOOOOOPPPPPPQQQRRRRRRSSSQQQQQQRRRSSSTTTUUUUUUVVVTTTTTTTTTTTTSSSSSSSSSSSSSSSSSSRRRRRRSSSTTTUUUUUUSSSSSSRRRRRRQQQQQQPPPPPPQQQQQQPPPPPPPPPRRRTTTUUURRRQQQPPPOOONNNNNNNNNNNNKKKLLLNNNPPPPPPPPPNNNMMMPPPPPPOOOOOONNNOOOOOOOOOLLLLLLMMMMMMMMMMMMLLLLLLLLLLLLMMMNNNNNNMMMKKKJJJIIIIIIJJJJJJIIIIIIHHHGGGDDDDDDDDDDDDCCCCCCCCCCCCDDDFFFFFFFFFEEEDDDEEEFFFGGGFFFEEEEEEFFFHHHJJJLLLHHHGGGGGGGGGFFFFFFEEEEEEGGGHHHHHHIIIIIIJJJJJJJJJFFFFFFFFFFFFGGGIIIKKKLLLGGGFFFFFFFFFGGGHHHHHHIIIGGGFFFEEECCCCCCEEEFFFGGGGGGFFFEEEEEEEEEEEEEEEFFFCCCBBBBBBAAA@@@@@@@@@@@@??????>>>>>>>>>@@@AAABBB>>>@@@AAA@@@???>>>???@@@AAAAAAAAAAAA@@@???>>>>>>>>>>>>>>>>>>???@@@AAABBBBBBBBBBBBCCCDDDCCCAAA???>>>>>>??????@@@@@@@@@@@@@@@@@@@@@????????????>>><<<===>>>???????????????>>>>>>>>>>>>>>>>>>>>>>>>>>>???@@@AAAAAA@@@???>>><<<<<<;;;;;;;;;::::::::::::::::::::::::::::::;;;555555555666666666666666555555555555555555555444666555555444444666777888333666999999777777888:::666777888777666666888:::;;;;;;;;;::::::999999999666666666666777999::::::888888777777888999::::::777777666666666666777777888888888888888888888888555666666666777777888888666555444333222222222222111111000000000000111111////////////000000000000000///...------...///000......//////000222333444111111000000111111222333333333333333333333333333333333222111000000111111000000111111222222222222000000////////////000000111//////000111222111000000000000000000000000000------...///000000//////......///000000000000000,,,---///000222333333444000000111111111111000000......///000000111000000000000000000////////////---------.........//////---,,,---...000111000///............---,,,++++++---------,,,,,,,,,++++++***+++,,,,,,------,,,,,,,,,++++++******++++++,,,***++++++,,,,,,++++++***---,,,,,,,,,+++*********((())))))***++++++,,,,,,+++***************++++++))))))(((((((((((()))***))))))))))))((((((((((((&&&&&&'''((())))))((((((&&&''''''((()))******+++'''((((((((())))))******((('''&&&&&&'''((()))***'''&&&%%%%%%&&&'''((()))))))))(((((((((((())))))'''((((((((())))))******+++++++++***************)))***+++,,,,,,,,,,,,,,,******+++++++++,,,,,,,,,,,,***)))((())))))'''%%%QQQQQQQQQQQQQQQQQQQQQQQQRRRPPPNNNLLLLLLNNNQQQRRRRRRQQQPPPPPPQQQRRRQQQPPPMMMNNNNNNNNNNNNMMMLLLLLLNNNOOOPPPPPPQQQQQQPPPPPPQQQSSSTTTTTTSSSSSSTTTUUUUUUUUUUUUTTTSSSRRRQQQPPPSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSRRRRRRQQQQQQPPPPPPOOOOOOOOOPPPPPPPPPQQQQQQOOOOOONNNNNNNNNNNNNNNNNNNNNLLLJJJJJJMMMNNNMMMKKKIIIJJJJJJKKKKKKKKKKKKKKKPPPNNNLLLKKKMMMNNNNNNNNNKKKJJJJJJIIIIIIJJJJJJKKKKKKKKKJJJIIIHHHHHHGGGGGGDDDEEEEEEEEEEEEEEEEEEEEEBBBDDDFFFGGGGGGGGGHHHIIIHHHGGGGGGFFFFFFGGGGGGHHHFFFFFFFFFFFFFFFFFFFFFFFFGGGHHHHHHHHHGGGEEECCCBBBFFFFFFGGGGGGHHHIIIJJJJJJFFFKKKLLLHHHGGGJJJHHHCCCHHHGGGFFFFFFEEEEEEFFFFFFDDDDDDDDDDDDDDDCCCBBBBBB????????????????????????============>>>>>>>>>>>>>>>>>>============>>>>>>BBBBBBAAAAAA@@@???>>>>>>@@@@@@??????>>>?????????CCCCCCCCCBBBBBBAAAAAAAAA============>>>???@@@AAA??????>>>>>>>>>>>>>>>???>>><<<<<<===>>>???>>>===;;;;;;;;;<<<<<<<<<<<<<<<>>>???@@@@@@@@@>>>===<<<:::::::::::::::;;;<<<===<<<<<<;;;:::999999888888666555444333222333444444888888777777666666555555444555555666666666666666555555666777777777777777777777777888888999999999<<<;;;:::999888888888888888999999:::999888666555777777777888999999::::::999999999999999999999999;;;:::888777666555666666777777777777666666666666555444444333222111000000222333333222000///000222111000///......///000111////////////////////////...///111222333333222222444444444333333222222222222333333444444333333222111000/////////111222333222333333444444333333222000000000000000/////////000000000000000000000000111111111000000000000000000000000///////////////000000000000000000000000---...///000111222333333///000111111111111000///000111111111111222222222111111000///...------,,,................................................//////...---,,,,,,++++++.........------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***)))++++++***************+++)))******++++++***************************************+++++++++,,,,,,,,,++++++************++++++))))))))))))))))))))))))******))))))((((((''''''))))))))))))))))))))))))((((((''''''''''''(((((((((((('''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''((((((((((((((('''''''''(((((((((((())))))))))))************************++++++******++++++,,,---************************+++******)))))))))))))))PPPPPPPPPPPPPPPPPPPPPPPPSSSQQQNNNLLLKKKLLLNNNPPPQQQPPPOOOOOOPPPQQQPPPOOOMMMMMMMMMMMMMMMLLLLLLKKKNNNNNNOOOPPPPPPPPPPPPOOOQQQRRRSSSSSSRRRRRRSSSTTTWWWWWWWWWWWWVVVUUUTTTSSSSSSSSSSSSTTTTTTTTTUUUUUURRRRRRRRRRRRRRRRRRRRRRRRQQQQQQQQQPPPPPPOOOOOOOOONNNNNNNNNNNNOOOOOOOOOOOOOOOMMMKKKKKKMMMOOONNNLLLKKKKKKLLLMMMMMMMMMMMMMMMNNNLLLJJJJJJKKKMMMMMMLLLIIIIIIHHHHHHHHHHHHIIIIIIJJJJJJIIIHHHHHHGGGFFFFFFFFFEEEEEEDDDDDDCCCCCCCCCCCCEEEGGGHHHGGGHHHIIIJJJHHHGGGGGGFFFFFFGGGGGGHHHHHHGGGGGGGGGFFFFFFEEEEEEFFFGGGHHHHHHHHHGGGFFFEEEFFFFFFFFFGGGHHHHHHIIIIIIFFFJJJKKKGGGGGGJJJIIIEEEHHHGGGFFFFFFEEEEEEFFFFFFDDDDDDEEEEEEDDDDDDCCCCCC@@@@@@@@@@@@@@@@@@@@@@@@>>>>>>?????????@@@@@@@@@>>>>>>============>>>>>>AAAAAAAAA@@@@@@?????????AAA@@@@@@?????????@@@@@@@@@@@@@@@?????????>>>>>>??????>>>>>>>>>>>>????????????>>>>>>>>>>>>??????>>>===<<<<<<>>>??????>>>??????>>>>>>======<<<<<>>======;;;;;;;;;;;;;;;<<<<<<===;;;;;;::::::999888888888888777666444444555555666777777777777666666555555444555666666777777666666666777888888999888888888888888888999999999::::::<<<;;;:::999888888888888888999:::::::::999888777666666777888999999::::::999999999999999999999999999888777666666777888888777777777777666666666666555444444333222111000000111222222111//////000111111000///......///000111000000000000000000000000...///111222333333222222444444444333333222222222111111111222222111111111111000//////000111222333222222333333333333222222////////////////////////////////////////////////000000000000000111111111000000000000000000000000000000000000000000000000...//////000111222333444111111111111111111111111111111111111222222222222/////////......------,,,................................................000000///......---,,,,,,......---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++************)))))))))))))))******+++++++++++++++***)))******************************+++++++++,,,,,,,,,++++++************++++++******************************))))))(((((((((((())))))))))))))))))))))))((((((''''''''''''(((((((((((('''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''(((((((((((((((((((((((((((((()))))))))*********************************++++++******++++++,,,,,,************************+++******)))))))))))))))RRRRRRRRRRRRRRRRRRRRRRRRRRRQQQNNNLLLKKKLLLMMMNNNPPPOOONNNOOOPPPPPPOOONNNMMMMMMMMMMMMMMMLLLKKKKKKMMMNNNNNNOOOPPPOOOOOOOOOPPPQQQSSSRRRQQQQQQRRRTTTSSSSSSTTTTTTTTTTTTSSSSSSSSSTTTTTTTTTUUUUUUVVVVVVQQQQQQQQQRRRRRRRRRRRRRRRSSSSSSRRRQQQPPPOOONNNMMMNNNNNNNNNOOOPPPPPPQQQQQQPPPNNNMMMMMMNNNOOONNNMMMMMMNNNNNNOOOOOOOOOOOOOOOLLLKKKIIIIIIJJJKKKKKKJJJHHHHHHGGGGGGGGGGGGHHHHHHIIIIIIHHHHHHGGGFFFFFFFFFGGGGGGFFFDDDCCCAAA@@@@@@CCCEEEGGGHHHHHHHHHIIIJJJHHHGGGGGGFFFFFFGGGGGGHHHHHHHHHGGGGGGFFFFFFFFFEEEFFFGGGHHHHHHIIIIIIHHHHHHFFFFFFFFFGGGHHHHHHIIIIIIHHHJJJJJJGGGGGGIIIJJJHHHHHHGGGFFFFFFEEEEEEFFFFFFEEEEEEEEEEEEDDDDDDDDDDDDAAAAAAAAAAAAAAAAAAAAAAAA@@@@@@AAAAAAAAABBBBBBBBB???>>>>>>======>>>>>>???@@@@@@@@@@@@@@@@@@??????AAAAAA@@@@@@@@@@@@AAAAAABBBBBBBBBBBBAAAAAAAAAAAABBBAAA@@@???>>>=========???>>>>>>>>>>>>>>>?????????===;;;;;;===?????????BBBAAA@@@???>>>======<<>>>>>======>>>>>><<<<<<<<<<<<<<<<<<======;;;;;;::::::999888888888:::999777666666666777888777777777666666666666555444555666666777777666666777888999999::::::999999999999:::::::::::::::;;;<<<;;;:::999999888888999888999:::;;;;;;;;;:::999555666777888999:::;;;;;;888888888888888888888888777777777777777888999:::777777777777666666666666555555444333222111000000000111111000......///111111000////////////000111222222222222222222222222//////111222222333222222444444333333333333222222111111111111111111111111111111000000000111222222222222333333333333222222................................................//////000000111111222222111111111111111111111111000000000000000000000000///000000111222333444444333222111000000111222333111111111111222222222333............------------................................................000000000///......------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++***))))))((((((((())))))***,,,,,,,,,,,,,,,+++***)))******************************+++++++++,,,,,,,,,++++++************++++++***************************))))))))))))((((((((())))))))))))))))))))))))((((((''''''''''''((((((((((((((('''''''''&&&&&&$$$%%%%%%%%%&&&&&&&&&&&&(((((((((((((((((((((((())))))*********+++++++++******************************+++++++++,,,,,,,,,+++++++++++++++++++++++++++******)))))))))))))))TTTTTTTTTTTTTTTTTTTTTTTTQQQPPPOOONNNNNNNNNOOOOOOQQQPPPOOOOOOQQQQQQPPPOOONNNNNNOOOOOONNNNNNMMMLLLNNNOOOPPPPPPQQQQQQPPPPPPQQQRRRSSSSSSRRRRRRSSSTTTRRRRRRSSSTTTUUUUUUTTTTTTVVVVVVVVVUUUUUUUUUTTTTTTRRRRRRRRRRRRRRRQQQQQQQQQSSSRRRRRRQQQPPPOOOOOOOOONNNNNNOOOPPPQQQQQQRRRRRRQQQPPPOOONNNNNNOOOOOOOOONNNNNNOOOPPPPPPPPPPPPPPPLLLKKKIIIJJJKKKLLLKKKJJJHHHHHHHHHGGGGGGHHHHHHHHHIIIIIIIIIHHHHHHGGGGGGGGGIIIHHHFFFDDDBBB@@@???>>>BBBDDDGGGGGGGGGGGGHHHJJJHHHGGGGGGFFFFFFGGGGGGHHHFFFFFFFFFGGGGGGGGGHHHHHHHHHIIIIIIIIIIIIIIIIIIIIIGGGGGGHHHHHHIIIIIIIIIIIIKKKKKKIIIGGGFFFGGGHHHHHHHHHGGGFFFFFFEEEEEEFFFFFFFFFFFFEEEEEEDDDDDDDDDDDDCCCCCCCCCCCCCCCCCCCCCCCCAAAAAAAAAAAABBBBBBBBBBBB???>>>>>>>>>>>>>>>>>>???????????????@@@@@@@@@@@@AAAAAA@@@@@@AAAAAABBBBBBCCCCCCCCCCCCCCCBBBBBBBBBAAAAAA@@@???>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>???@@@???===;;;;;;===>>>??????@@@@@@@@@??????>>>>>>>>>???>>>===<<<<<<===>>>???<<<<<<==================;;;;;;;;;;;;::::::999999:::999888777666777888888666666666666666666666666555555666777777777777777777888888999999999999999;;;;;;;;;;;;;;;;;;;;;;;;<<<;;;:::999999999999999888999;;;<<<<<<<<<;;;;;;555555666888999:::;;;<<<777777777777777777777777888888888888888888888999777777777777666666666666555555444333222111111000///000000///......///111111111000//////000111111222222222222222222222222///000000111222222333333333333333333333333333333333333333333333333333333111111111111111111111222111111222222222222111111---------.............................................///000111222222333111111111111111222222222000000000000000000000000000111111222333333444444444333111000000111333444111111111222222222333333............////////////................................................////////////......------,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,------+++,,,,,,---,,,,,,++++++***))))))))))))******+++,,,,,,---,,,,,,+++***)))******************************+++++++++,,,,,,,,,++++++************++++++************************))))))))))))))))))))))))((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((''''''''''''%%%%%%%%%%%%&&&&&&&&&&&&((((((((((((((()))))))))******+++++++++,,,,,,,,,******************************++++++,,,,,,,,,,,,+++++++++++++++++++++++++++******)))))))))))))))SSSSSSSSSSSSSSSSSSSSSSSSNNNOOOOOOPPPQQQRRRSSSSSSSSSQQQPPPQQQRRRSSSRRRPPPPPPQQQQQQQQQQQQPPPOOOOOOPPPQQQQQQRRRRRRRRRRRRRRRRRRTTTUUUUUUTTTSSSUUUVVVVVVWWWXXXYYYYYYZZZZZZYYYYYYXXXWWWVVVUUUSSSRRRRRRTTTSSSSSSRRRQQQPPPPPPOOOQQQQQQQQQQQQQQQQQQQQQQQQOOOOOOPPPQQQRRRSSSSSSSSSQQQQQQPPPOOONNNNNNOOOOOOMMMNNNOOOOOOPPPPPPOOOOOOMMMLLLKKKLLLMMMMMMLLLKKKJJJJJJIIIIIIIIIIIIJJJJJJJJJJJJJJJJJJIIIIIIIIIIIIIIIHHHGGGEEECCCAAA???>>>AAACCCFFFGGGFFFFFFGGGIIIHHHGGGGGGFFFFFFGGGGGGHHHDDDDDDEEEGGGHHHIIIJJJKKKKKKKKKJJJIIIHHHHHHHHHGGGIIIIIIIIIIIIJJJJJJJJJJJJLLLJJJHHHGGGFFFEEEFFFGGGHHHGGGFFFFFFEEEEEEFFFFFFFFFFFFEEEDDDCCCDDDDDDDDDCCCCCCCCCCCCCCCCCCCCCCCC@@@@@@@@@@@@AAAAAAAAABBB??????>>>>>>>>>>>>???????????????????????????@@@AAA@@@@@@@@@AAAAAABBBCCC??????????????????@@@@@@@@@@@@????????????@@@@@@>>>>>>======>>>???@@@@@@???===;;;;;;===?????????=========>>>>>>????????????>>>===<<<<<<===>>>???<<<======>>>>>>===<<<<<<<<<<<<<<<<<<;;;;;;;;;;;;999888777666666666777777555555555555555666666666555666666777777777777777666777888888999999888888;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;::::::999:::::::::888999;;;<<<===<<<<<<;;;555666777888999:::;;;;;;777777777777777777777777:::::::::999888777777666777777777777666666666666666555555444333222111111///000000///......000111222111000//////000111222111111111111111111111111000000000111111222333333333333333333333333333333444333333222222333333444111222222222222111111111000111111222222111111000------------......//////..............................///000111222222333000000111111222222222222111111111111111111111111111111111222333333333444444333111000000111333444111222222222222333333333000000000000111111111111////////////////////////////////////////////////......------------------,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,---------+++,,,,,,---------,,,,,,+++*********++++++,,,---,,,,,,,,,,,,++++++***)))******************************+++++++++,,,,,,,,,++++++************++++++************************))))))))))))************((((((((((((((((((((((((((((((''''''''''''(((((())))))((((((((('''''''''%%%%%%&&&&&&&&&'''''''''(((((((((((())))))******++++++++++++,,,,,,,,,,,,************************)))***+++,,,,,,,,,+++++++++++++++++++++++++++++++++******)))))))))))))))PPPPPPPPPPPPPPPPPPPPPPPPMMMNNNPPPRRRTTTUUUUUUUUUSSSRRRQQQRRRSSSSSSSSSQQQRRRRRRRRRRRRRRRQQQQQQPPPQQQRRRSSSSSSTTTTTTSSSSSSSSSTTTVVVUUUTTTTTTUUUWWWVVVVVVWWWXXXXXXXXXXXXXXXYYYXXXWWWUUUTTTRRRQQQQQQSSSSSSSSSRRRQQQQQQPPPPPPPPPPPPQQQQQQQQQRRRRRRRRRQQQQQQQQQRRRSSSSSSSSSTTTPPPQQQQQQOOOMMMMMMNNNOOOMMMMMMNNNOOOOOOOOOOOOOOONNNMMMMMMNNNOOOOOOMMMLLLLLLLLLKKKKKKKKKKKKLLLLLLKKKKKKKKKJJJJJJJJJJJJJJJHHHHHHGGGEEEDDDBBBAAAAAABBBDDDFFFGGGGGGGGGHHHIIIHHHGGGGGGFFFFFFGGGGGGHHHDDDDDDEEEGGGHHHJJJKKKLLLLLLLLLJJJIIIHHHGGGGGGGGGIIIIIIIIIIIIIIIJJJJJJJJJHHHFFFEEEGGGGGGEEEFFFHHHHHHGGGFFFFFFEEEEEEFFFFFFFFFEEECCCBBBBBBBBBCCCDDDCCCCCCCCCCCCCCCCCCCCCCCC?????????@@@@@@@@@AAAAAA@@@??????>>>>>>??????@@@??????????????????>>>>>>@@@??????@@@@@@AAABBBCCC@@@@@@@@@AAAAAAAAAAAAAAA@@@@@@?????????@@@@@@AAA============>>>???@@@AAA>>><<<<<<===??????>>>===:::;;;;;;<<<===>>>??????======<<<<<<======>>>>>>;;;<<<===>>>===<<<;;;:::<<<<<<<<<;;;;;;;;;;;;;;;999888666555555555666777444555555555555666666666555666777777888888777777666777777888999888888888<<<;;;;;;;;;;;;;;;::::::;;;;;;::::::::::::;;;;;;999:::;;;<<<<<<<<<;;;:::777777777888999999::::::888888888888888888888888;;;;;;;;;:::999777666555777777777777666666666666666666555444333222111111///000111000//////111222222111000000000000111222000000000000000000000000000000000000111222333444222222333333333333444444333222111000000111222333222222222333222222111000000000111111111111000000---------...//////000000........................//////000000111111222222//////000000111222222222111111111111111111111111111111111111222222333333333222111000000111222333222222222222333333333333222222222222111111111111////////////////////////////////////////////////------------------------++++++++++++,,,,,,,,,,,,***++++++,,,,,,------...+++,,,,,,---------------+++++++++++++++,,,---...)))******+++++++++************************************+++++++++,,,,,,,,,++++++************++++++++++++++++++++++++++++++)))))))))************+++))))))))))))))))))))))))((((((''''''''''''(((((()))))))))(((((((((''''''&&&'''''''''(((((((((((('''(((((())))))******+++******+++++++++,,,,,,,,,************************)))***+++,,,---,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,+++******)))))))))))))))PPPPPPPPPPPPPPPPPPPPPPPPMMMNNNPPPSSSTTTTTTTTTSSSSSSQQQPPPQQQRRRSSSRRRQQQRRRRRRRRRRRRRRRQQQPPPPPPQQQQQQRRRSSSSSSSSSSSSSSSRRRTTTUUUUUUTTTTTTUUUVVVSSSSSSTTTTTTUUUTTTTTTTTTVVVUUUUUUTTTTTTSSSRRRRRRPPPQQQQQQQQQRRRRRRSSSSSSRRRRRRRRRRRRQQQQQQQQQQQQSSSSSSSSSSSSSSSSSSSSSSSSOOOQQQQQQOOOLLLKKKMMMOOOMMMNNNOOOOOOPPPPPPOOOOOONNNMMMMMMNNNPPPOOOMMMLLLLLLLLLLLLKKKKKKLLLLLLLLLJJJJJJJJJJJJJJJJJJJJJJJJGGGGGGFFFFFFEEEEEEDDDDDDDDDFFFHHHIIIIIIIIIJJJKKKHHHGGGGGGFFFFFFGGGGGGHHHFFFFFFGGGHHHHHHIIIIIIJJJKKKJJJIIIGGGGGGGGGHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHBBB???AAAGGGIIIFFFGGGKKKHHHGGGFFFFFFEEEEEEFFFFFFEEEDDDBBBAAAAAAAAABBBCCCCCCCCCCCCCCCCCCCCCCCCCCC??????@@@@@@@@@AAAAAAAAA@@@??????>>>>>>??????@@@@@@@@@??????>>>>>>======>>>>>>>>>??????AAABBBBBBBBBBBBBBBCCCCCCDDDDDDDDDBBBBBBAAA@@@????????????============>>>???@@@AAA<<<<<<===>>>@@@@@@>>><<<;;;<<<<<<======>>>>>>>>>;;;<<<<<<===>>>>>>======;;;;;;=========<<<:::999::::::::::::::::::::::::999888777555555666666777444444444555555555666666666666777888888888888777777888999999::::::999999;;;;;;;;;;;;::::::999999;;;;;;:::::::::;;;;;;<<<::::::;;;<<<<<<;;;999888888888888888888888888888999999999999999999999999999::::::::::::999777777777777777777666666666666666666555444333222222111///000111111000000222333222222111000000111222222000000000000000000000000111000000000000222333444222222222333333444444444333222000//////000222333222222333333333222111000///000000000000000000///------...//////000111111////////////////////////000000000000000111111111......///000000111222222111111111111111111111111000000000111111111111222111111111111111111111111222222222333333333444444333222222111111000000000////////////////////////////////////////////////---------...............******+++++++++,,,,,,,,,******+++,,,,,,---......+++,,,,,,---......------************+++,,,---...''''''((()))******************************************+++++++++,,,,,,,,,++++++************++++++++++++++++++++++++++++++))))))*********+++++++++))))))))))))))))))))))))((((((''''''''''''(((((())))))))))))((((((((('''(((((((((((())))))))))))'''(((((()))******++++++************++++++++++++************************(((***+++------,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,+++******)))))))))))))))SSSSSSSSSSSSSSSSSSSSSSSSMMMOOOQQQSSSSSSSSSQQQPPPRRRQQQPPPPPPQQQRRRQQQPPPQQQQQQRRRRRRQQQQQQPPPOOOPPPQQQQQQRRRRRRRRRRRRRRRQQQSSSTTTTTTSSSSSSTTTUUUUUUUUUVVVVVVVVVUUUUUUTTTRRRSSSSSSSSSSSSTTTTTTTTTMMMNNNOOOQQQRRRTTTUUUVVVTTTTTTSSSRRRQQQPPPPPPOOOTTTTTTTTTSSSSSSSSSSSSSSSOOOPPPQQQOOOLLLJJJLLLNNNNNNOOOPPPPPPQQQQQQPPPPPPMMMMMMMMMNNNOOOOOOMMMKKKLLLLLLKKKKKKKKKKKKLLLLLLIIIIIIIIIIIIIIIIIIIIIIIIFFFFFFFFFFFFFFFFFFFFFFFFFFFHHHJJJKKKJJJJJJLLLMMMHHHGGGGGGGGGGGGGGGGGGHHHIIIIIIIIIHHHHHHGGGGGGGGGIIIHHHGGGFFFGGGHHHIIIJJJGGGFFFFFFFFFFFFFFFFFFFFF<<<:::>>>FFFJJJHHHIIINNNHHHGGGGGGFFFEEEFFFFFFFFFEEECCCAAA@@@@@@@@@BBBCCCCCCCCCCCCCCCCCCCCCCCCCCC@@@@@@@@@AAAAAAAAABBBBBB@@@@@@????????????@@@@@@AAA@@@@@@???>>>======<<<>>>>>>>>>>>>???@@@AAABBB?????????@@@@@@AAAAAAAAAEEEDDDBBB@@@???>>>==================>>>???@@@AAA;;;;;;===@@@AAA@@@===;;;>>>>>>>>>>>>============:::;;;===>>>>>>>>>===<<<:::;;;<<<======;;;999888888888888888888888888999999999777666666666777888444444444555555555666666666666777888888888888888999999:::;;;;;;;;;::::::;;;;;;;;;::::::999999999;;;;;;:::::::::;;;;;;<<<:::;;;;;;;;;;;;:::888777999999999888888888888777999999999999999999999999777888999:::;;;:::999999777777777777666666666666666666555444333222222111000111222111000111222444333222111000000111222333000000000000000000000000111000000000000222333444222222222333333444444444555444222111111222444555222333333444333222111000//////000000000000//////.........///000111111222000000000000000000000000111111111000000000000000---......///000111111111111111111111111111111111000000000000000111111111///000111111111111000///222222333333333444444444333222222111000///......000000000000000000000000000000000000000000000000.........///////////////*********++++++,,,,,,,,,******+++,,,,,,---......+++,,,,,,---.........---))))))))))))***+++,,,---%%%&&&''')))******************************************+++++++++,,,,,,,,,++++++************++++++++++++++++++++++++++++++))))))******++++++++++++))))))))))))))))))))))))((((((''''''''''''(((((())))))))))))(((((((((((())))))))))))************'''(((((()))***+++++++++))))))*********+++++++++************************(((***+++------,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,+++******)))))))))))))))UUUTTTSSSRRRQQQQQQQQQRRRRRRRRRQQQQQQRRRSSSTTTTTTQQQQQQQQQQQQQQQQQQPPPPPPTTTTTTSSSQQQQQQPPPPPPPPPRRRRRRRRRRRRQQQPPPOOOOOORRRRRRRRRRRRSSSTTTVVVVVVTTTTTTTTTTTTTTTUUUUUUUUUQQQRRRRRRSSSSSSSSSSSSRRRQQQPPPOOORRRVVVXXXWWWUUUTTTTTTUUUTTTTTTSSSRRRQQQWWWTTTQQQQQQSSSSSSQQQOOOPPPOOONNNMMMNNNOOOPPPQQQOOOOOOOOOOOOOOOOOOOOOOOOKKKKKKLLLMMMOOOPPPQQQRRRNNNMMMLLLKKKKKKJJJJJJJJJLLLLLLKKKKKKJJJJJJJJJIIIGGGHHHIIIIIIJJJJJJIIIIIIIIIHHHGGGHHHJJJKKKJJJIIIKKKKKKKKKIIIGGGFFFGGGHHHJJJIIIIIIIIIIIIJJJKKKKKKIIIIIIIIIIIIIIIJJJKKKLLLJJJIIIHHHIIIJJJHHHDDD@@@<<>>>>>@@@CCCEEEAAADDDKKKHHH>>>;;;AAABBBBBBBBBBBBAAAAAA@@@???=========???AAABBBAAA@@@DDDCCCAAA???===<<<==================>>>>>>>>>>>>???===;;;<<<>>>>>><<<:::>>>???@@@???>>>===>>>???======<<<<<<<<<<<<======<<<=========<<<;;;;;;:::999999888888999:::<<<===:::999888666666666777888555555555555666666666777666666777888888888888888444444555777888:::;;;;;;999::::::999888888999;;;;;;::::::999999::::::;;;=========<<<;;;999888777666666777888999999::::::>>><<<999999;;;===>>>>>>777888999999::::::999999888888777777666555555555555666888999999777555444111111111111111111111111111111111111111111111111111111000000000000111111222000......000222222222333222222111222444555666555444333333222222333333111111111111000...---,,,111111222222222222111111111000///------......///..................------000000000000000000000000//////000000000000//////......//////000000111111000000111222222222222111333222000......///111222444444444333333222222222000000000000000000000000//////000000000000//////000000000000000111111111//////000000000000/////////...---,,,+++,,,------------------------------++++++,,,,,,---...//////***++++++***((('''(((***(((((()))***+++,,,,,,,,,******+++,,,,,,,,,++++++++++++,,,,,,,,,++++++***---,,,***((('''''''''(((***************************************************)))(((&&&&&&((()))******)))))))))((((((''''''*********)))((('''''''''''''''((((((((((((''''''))))))))))))************,,,,,,,,,+++++++++******))))))))))))))))))))))))************************++++++******++++++,,,---******))))))))))))******SSSSSSRRRRRRRRRRRRRRRRRRQQQQQQQQQRRRRRRSSSSSSSSSQQQQQQQQQQQQQQQQQQQQQQQQSSSRRRRRRQQQQQQQQQRRRRRRRRRRRRRRRRRRQQQQQQPPPOOOSSSSSSSSSSSSSSSTTTUUUVVVUUUUUUTTTTTTTTTTTTTTTTTTRRRRRRSSSSSSSSSSSSRRRRRRRRRPPPPPPQQQTTTUUUTTTQQQQQQQQQRRRRRRRRRQQQQQQPPPVVVSSSQQQPPPRRRRRRQQQOOONNNNNNNNNNNNNNNOOOPPPPPPOOOOOOOOOOOOOOOOOOOOOOOOLLLLLLMMMNNNOOOPPPPPPQQQNNNMMMLLLKKKKKKJJJJJJJJJLLLKKKKKKKKKJJJJJJJJJJJJHHHHHHIIIIIIJJJJJJIIIIIIIIIHHHGGGHHHJJJKKKJJJIIIKKKKKKKKKJJJGGGFFFGGGIIIHHHHHHHHHHHHHHHIIIJJJJJJIIIIIIIIIIIIIIIJJJKKKLLLKKKIIIHHHHHHIIIIIIFFFCCC???AAADDDGGGHHHIIIHHHGGGFFFFFFFFFFFFFFFFFFFFFFFFDDDCCCCCCCCCBBBBBBBBBAAABBBBBBBBBBBBBBBCCCCCCCCC@@@AAAAAAAAAAAA@@@??????@@@AAAAAA@@@>>>>>>@@@BBBDDDAAADDDKKKHHH>>>;;;@@@@@@@@@@@@@@@@@@???>>>>>>@@@???>>>???@@@AAA@@@???AAA@@@???>>>======>>>>>>============>>>>>>>>>>>>???===;;;<<<>>>>>><<<:::>>>???@@@???>>>===>>>???======<<<<<<<<<<<<======<<<<<<<<<<<<<<<;;;::::::===<<<;;;:::999::::::;;;999888777666555666666777555555555666666666777777666777777888888888888888888888888888999999999:::888999::::::999:::<<<>>>;;;::::::999999::::::;;;>>>>>>>>>===<<<;;;999999777777888888999::::::;;;;;;888666666777999:::999888999999:::::::::::::::::::::999888888777777666444555666777777555333222000000000000000000000000111111111111111111111111111111000000000000111111222000...///000222222222333333222222333444666777555444333333222222333333111111111000000///......111111222222222222111111111000///...---...//////........................000000000000000000000000//////000000000000//////////////////000000111111000000111222222222222111222111000//////000111222444333333333222222222222000000000000000000000000///000000000000000//////000000000000000000000000//////000000000000/////////...---,,,+++,,,------------------------------******++++++,,,------...***++++++***(((((()))+++))))))******++++++,,,,,,++++++,,,,,,,,,++++++************++++++******))),,,+++***)))))))))******************************************************+++***(((''''''(((***+++*********))))))((((((((((((((())))))))))))))))))''''''((((((((((((''''''))))))))))))*********************++++++,,,,,,,,,************************+++++++++++++++++++++++++++++++++++++++,,,,,,---******))))))))))))******SSSSSSSSSTTTTTTTTTUUUUUUPPPQQQRRRSSSTTTSSSRRRRRRQQQQQQQQQQQQRRRRRRRRRRRRRRRRRRQQQQQQRRRRRRSSSTTTQQQRRRRRRRRRRRRQQQQQQPPPTTTTTTSSSSSSSSSTTTTTTUUUVVVUUUUUUUUUTTTSSSSSSSSSSSSSSSTTTSSSSSSRRRQQQPPPRRRQQQPPPQQQRRRRRRQQQOOOPPPPPPPPPQQQQQQQQQQQQQQQUUUSSSQQQPPPQQQRRRQQQPPPMMMNNNOOOOOOPPPPPPOOOOOOPPPPPPPPPPPPPPPPPPPPPPPPMMMMMMNNNNNNNNNOOOOOOOOONNNMMMLLLKKKKKKJJJJJJJJJKKKKKKKKKKKKJJJJJJJJJJJJHHHHHHHHHIIIIIIIIIJJJJJJIIIHHHGGGHHHJJJKKKJJJIIIJJJKKKKKKJJJHHHGGGHHHIIIGGGGGGGGGGGGGGGHHHHHHIIIHHHHHHHHHIIIIIIKKKLLLLLLKKKJJJHHHHHHIIIIIIHHHGGGBBBDDDFFFHHHIIIIIIHHHHHHGGGGGGGGGGGGGGGGGGGGGGGGDDDDDDDDDDDDCCCCCCCCCCCCBBBBBBBBBBBBAAAAAAAAAAAA@@@AAAAAAAAAAAA@@@??????@@@AAAAAA@@@??????@@@BBBBBB@@@DDDJJJHHH???<<<@@@@@@@@@AAAAAAAAA@@@??????BBB@@@>>>>>>???@@@???>>>??????>>>>>>>>>??????@@@============>>>>>>>>>>>>???===<<<<<<>>>>>>===;;;>>>???@@@???>>>>>>???@@@>>>======<<<<<<======>>>;;;;;;<<<<<<;;;;;;::::::@@@???===<<<::::::999999888777666666555666666666555555666666666777777777666777888888999999888888;;;;;;;;;:::999999888888777999:::;;;;;;<<>>===???@@@@@@???@@@@@@@@@??????@@@@@@@@@============>>>>>>>>>>>>???>>>===============<<<===???@@@@@@???>>>???AAA>>>>>>============>>>>>>:::;;;;;;;;;;;;;;;::::::@@@???>>>===<<<;;;::::::888888777777777777777777555666666666666777777777777777888999999999999888;;;;;;::::::999999888888888999;;;;;;;;;;;;>>>@@@;;;;;;::::::::::::;;;;;;888888888888777666555444999999999::::::;;;;;;;;;;;;999777666777888888777999:::;;;;;;<<<<<<;;;;;;<<<;;;;;;:::999999888888555555555555333222000///000000000000000000000000111111111111111111111111222111111000000111111222222000///000222333222111222222222333333444555555555444333333222222333333/////////000000111111222111111222222222222111111000000000///////////////............////////////000000000000000000000000000000000111111000000000000000000000000000000000000000111222222222222111111111000000000111222333111111111111111111111111000000000000000000000000111111111111111000///...000000000000000///////////////000000000000/////////...---,,,+++,,,------------------------------******++++++,,,,,,,,,---+++,,,,,,+++******+++---+++++++++++++++++++++***---------,,,+++***)))(((((()))******************+++++++++++++++,,,,,,,,,************************************************++++++***))))))***++++++++++++******************'''(((((()))******++++++(((((())))))))))))((((((((()))))))))************((())))))***+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,,,,,,,,,,******))))))))))))******QQQRRRTTTUUUVVVWWWVVVVVVSSSTTTVVVWWWWWWVVVTTTSSSRRRRRRRRRSSSSSSSSSTTTTTTVVVVVVTTTSSSQQQQQQPPPPPPQQQQQQRRRSSSTTTTTTTTTTTTRRRQQQQQQPPPPPPPPPQQQQQQVVVVVVVVVUUUTTTSSSRRRRRRTTTTTTTTTTTTSSSQQQPPPPPPOOOPPPRRRSSSSSSSSSSSSSSSQQQQQQPPPPPPQQQRRRSSSTTTTTTTTTTTTSSSRRRRRRSSSSSSOOOPPPRRRSSSSSSSSSRRRQQQQQQQQQQQQQQQQQQQQQQQQQQQOOOOOOOOONNNNNNNNNNNNMMMNNNMMMLLLKKKJJJJJJJJJJJJJJJJJJJJJKKKKKKKKKKKKKKKIIIIIIHHHHHHHHHIIIJJJKKKIIIHHHGGGHHHJJJKKKJJJIIIGGGIIIKKKKKKJJJIIIJJJJJJHHHHHHHHHHHHHHHIIIIIIJJJHHHHHHHHHIIIJJJKKKLLLMMMKKKJJJIIIHHHHHHIIILLLNNNIIIIIIHHHHHHHHHHHHIIIIIIGGGGGGGGGGGGGGGGGGGGGGGGEEEEEEEEEEEEEEEEEEEEEEEECCCCCCBBBAAA@@@??????>>>@@@AAAAAAAAAAAA@@@?????????@@@AAAAAA@@@???@@@AAA???@@@CCCFFFEEE@@@???@@@AAAAAABBBCCCCCCBBBBBBBBB???>>>===>>>@@@AAAAAAAAABBBBBBBBBAAAAAA@@@??????============>>>>>>>>>>>>>>>>>>???>>>===============???@@@@@@??????@@@BBB>>>>>>============>>>>>>::::::;;;<<<<<<;;;;;;;;;========================999999999999999999999999666666666666777777777888777777888999999999999999888888888999999999999999999:::;;;:::999999;;;===<<<;;;;;;::::::;;;;;;<<<<<<<<<<<<<<<<<<;;;:::999999:::::::::::::::;;;;;;:::999777888999:::999888999:::;;;;;;<<<<<<;;;;;;:::::::::999888888777777777777666555444333222111222222222222222222222222111111111111111111111111222222111111111111222222111000000111333333222111000111222222333444444444555444333333222222333333000000//////000111222333111111222222222222111111000000000000000/////////........./////////000000000000000000000000000000000000111111111111000000111111111111000000000000000000111222222222222111111111111111111222333333111111111111111111111111000000000000000000000000111111111111111000//////000000000000//////......//////000000000000/////////...---,,,+++,,,------------------------------,,,,,,,,,,,,------------+++,,,,,,+++******+++---,,,,,,,,,+++++++++++++++---------,,,+++***)))((()))******+++,,,,,,++++++,,,,,,,,,,,,++++++******************************************************++++++************++++++******************++++++************************(((((())))))))))))((((((((()))))))))************************************,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++***+++,,,---------,,,,,,******))))))))))))******NNNOOOQQQSSSTTTTTTSSSRRRUUUUUUVVVWWWVVVUUUTTTSSSRRRRRRSSSSSSTTTTTTUUUUUUXXXWWWUUUSSSQQQPPPPPPOOOQQQQQQRRRTTTUUUUUUUUUUUUQQQQQQPPPPPPPPPPPPQQQRRRVVVUUUUUUUUUTTTSSSSSSSSSSSSSSSTTTSSSSSSRRRQQQPPPNNNPPPRRRSSSSSSRRRSSSUUUPPPOOONNNMMMMMMOOOPPPQQQRRRSSSTTTSSSQQQQQQRRRTTTPPPQQQRRRRRRSSSSSSRRRRRRPPPPPPPPPPPPPPPPPPPPPPPPOOONNNNNNNNNNNNNNNNNNNNNNNNMMMLLLKKKKKKJJJJJJJJJJJJJJJJJJKKKKKKKKKKKKKKKIIIIIIHHHGGGHHHIIIJJJKKKIIIHHHGGGHHHJJJKKKJJJIIIFFFIIIKKKLLLKKKJJJKKKKKKHHHHHHHHHHHHHHHIIIJJJJJJGGGGGGHHHHHHJJJKKKMMMNNNJJJKKKJJJHHHGGGHHHKKKMMMJJJIIIHHHGGGGGGHHHIIIJJJHHHHHHHHHHHHHHHHHHHHHHHHDDDDDDDDDDDDEEEEEEEEEEEEDDDCCCCCCBBBAAA@@@@@@???@@@AAAAAAAAAAAA@@@??????>>>@@@BBBBBB@@@???@@@@@@???AAACCCCCCBBBAAAAAABBB>>>>>>???@@@@@@@@@??????===<<<===???AAABBBBBB@@@BBBBBBBBBBBBAAA@@@???>>>============>>>>>>>>>>>>>>>???@@@???===<<<===>>>===???@@@@@@??????AAABBB???>>>>>>======>>>>>>???;;;;;;<<<<<<======<<<<<<:::;;;<<<===>>>>>>>>>>>>999999:::;;;;;;;;;;;;:::666666666777777777888888777888999999:::999999999666777777888999::::::;;;:::;;;;;;:::999999:::<<<<<<<<<;;;;;;;;;;;;<<<<<<;;;<<<<<<<<<;;;;;;:::999999999999999::::::::::::777666666777888999888777999999:::;;;;;;;;;;;;;;;999999999888777777666666888777777666555444333333333333333333333333333333111111111111111111111111222222111111111111222222111000000222333444222111000111222333444444444444555444333333222222333333111000000///000111333444111111222222222222111111000000111111111000///............//////000000111000000000000000000000000000111111222222111111000222111111111111000000000000000111222222222222111000000111222222333333333111111111222222222222222000000000000000000000000000111111222222111111000111000000//////......---//////000000000000/////////...---,,,+++,,,------------------------------------------------------***+++++++++)))***+++---+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++***))))))***+++,,,,,,,,,,,,,,,++++++,,,,,,+++***))))))************************************************************************)))))))))************************************)))((())))))******))))))((())))))))))))************++++++*********))))))))),,,,,,,,,,,,,,,,,,,,,,,,***************************+++---.........---,,,******))))))))))))******OOOPPPRRRSSSTTTSSSRRRQQQUUUUUUTTTTTTTTTSSSSSSSSSRRRRRRSSSTTTTTTUUUVVVVVVWWWVVVUUUSSSRRRQQQQQQQQQPPPQQQSSSTTTUUUVVVVVVVVVQQQQQQQQQQQQRRRRRRSSSTTTUUUUUUTTTTTTTTTTTTTTTTTTRRRRRRSSSSSSSSSSSSRRRRRROOOQQQSSSSSSQQQPPPQQQRRRQQQPPPNNNMMMLLLMMMOOOPPPPPPQQQRRRQQQOOOOOOQQQSSSPPPPPPPPPPPPPPPQQQQQQRRROOOOOOOOOOOOOOOOOOOOOOOONNNNNNNNNNNNNNNNNNNNNOOONNNMMMLLLKKKKKKJJJJJJJJJJJJJJJJJJJJJKKKKKKKKKLLLJJJIIIHHHGGGGGGIIIJJJLLLIIIHHHGGGHHHJJJKKKJJJIIIFFFHHHKKKMMMLLLKKKKKKLLLGGGGGGGGGGGGGGGHHHHHHIIIGGGGGGGGGHHHJJJLLLMMMNNNIIIJJJKKKIIIGGGGGGIIILLLJJJIIIGGGFFFFFFGGGIIIKKKHHHHHHHHHHHHHHHHHHHHHHHHCCCCCCCCCDDDDDDEEEEEEEEEDDDCCCCCCCCCBBBBBBAAAAAA@@@AAAAAAAAAAAA@@@??????>>>@@@BBBBBBAAA??????@@@@@@AAABBB@@@???AAACCCDDD<<<===>>>>>>?????????>>>======>>>AAACCCBBB@@@===>>>???@@@@@@@@@???>>>>>>============>>>>>>>>>>>>>>>???AAA???===<<<===???===???@@@@@@@@@@@@AAACCC??????>>>>>>>>>>>>??????;;;<<<======>>>>>>======999:::;;;===>>>>>>======888999:::;;;;;;;;;::::::666666777777777888888888777888999999::::::999999888888999999:::;;;;;;;;;:::;;;<<<;;;:::;;;===>>><<<<<<;;;;;;;;;;;;<<<<<<999999999:::999999888777999999999999999999999999555555555666999:::999888888999999:::::::::::::::999999999888777777666666777777666555555444555555222222222222222222222222111111111111111111111111333222222111111222222333111111111222444444222111222333444666666666666555555444333333222222333333222111000//////111222333111111222222222222111111000000111222111000///...---......///000000111111000000000000000000000000000111111222222111111000222222222111111111000000000000111222222222222111000000111222333333333333222222222222333333333444000000000000000000000000//////000111222222222222111000000///......------//////000000000000/////////...---,,,+++,,,------------------------------,,,,,,,,,,,,,,,,,,,,,,,,((()))******))))))+++---***++++++,,,,,,---------++++++,,,,,,,,,++++++***((()))***++++++,,,,,,,,,((()))***+++++++++***)))************************************************((())))))))))))))))))(((((((((((())))))*********)))))))))******++++++,,,))))))************))))))))))))))))))************))))))))))))************++++++++++++++++++++++++++++++++++++++++++++++++***+++---...///...---,,,******))))))))))))******RRRSSSUUUVVVVVVVVVTTTSSSTTTTTTSSSRRRQQQQQQRRRRRRRRRSSSSSSTTTUUUUUUVVVVVVUUUUUUTTTSSSRRRRRRSSSSSSPPPQQQSSSTTTVVVVVVWWWWWWRRRRRRRRRRRRSSSUUUVVVVVVTTTTTTTTTTTTTTTUUUUUUUUUQQQRRRSSSSSSSSSSSSSSSRRROOORRRSSSRRROOOMMMNNNOOOSSSRRRPPPNNNNNNNNNPPPQQQMMMOOOQQQOOOMMMMMMOOORRRPPPOOONNNMMMNNNOOOPPPQQQOOOOOOOOOOOOOOOOOOOOOOOOMMMMMMNNNNNNNNNOOOOOOOOONNNMMMLLLKKKKKKJJJJJJJJJIIIJJJJJJJJJKKKKKKLLLLLLJJJIIIHHHGGGGGGIIIJJJLLLIIIHHHGGGHHHJJJKKKJJJIIIEEEHHHKKKMMMLLLLLLLLLLLLFFFFFFFFFEEEFFFGGGGGGHHHGGGGGGGGGHHHJJJLLLMMMNNNHHHJJJKKKJJJGGGFFFHHHJJJJJJHHHFFFEEEEEEGGGJJJKKKHHHHHHHHHHHHHHHHHHHHHHHHBBBCCCCCCCCCDDDDDDEEEEEEDDDCCCCCCCCCCCCBBBBBBBBB@@@AAAAAAAAAAAA@@@??????>>>@@@BBBBBBAAA@@@???@@@@@@BBBAAA>>>>>>@@@DDDEEE===>>>???@@@@@@@@@@@@@@@>>>>>>@@@BBBCCCBBB===::::::;;;===>>>?????????>>>============>>>>>>>>>>>>===@@@AAA@@@===<<<===???===???@@@@@@@@@@@@BBBCCC??????>>>>>>>>>>>>??????<<<<<<===>>>??????>>>>>>999:::<<<=========<<<;;;777888999:::;;;::::::999777777777777888888888888888888999::::::::::::999::::::;;;;;;;;;;;;;;;;;;999:::<<<<<<<<<===@@@BBB<<<<<<;;;;;;;;;;;;<<<<<<;;;;;;<<<<<<<<<;;;::::::999888888888888888888888555555666888;;;<<<;;;:::888888999::::::::::::999::::::999999888777777666666555555444444444555555111111111111111111111111111111111111111111111111333222222111111222222333111111111333444444333111444555666888888888888777555444333333222222333333333222111//////000222333111111222222222222111111000111111222222000///...---......///000111111222000000000000000000000000111111222222222222111111222222222222111111000000000000111222222222222111///000111222333444444444222222222333333444444444000000000000000000000000...///000111222333333333111000000///...---------//////000000000000/////////...---,,,+++,,,------------------------------++++++++++++++++++++++++((()))***)))((()))***,,,******+++,,,,,,---......******+++,,,,,,,,,++++++''''''(((******+++++++++%%%&&&(((***++++++++++++************************************************(((((())))))))))))((((((''''''(((((()))))))))***''''''(((***+++,,,---...))))))************))))))))))))))))))************''''''((()))***+++,,,,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,***+++---//////...---,,,******))))))))))))******TTTSSSRRRPPPPPPRRRSSSTTTRRRQQQQQQRRRRRRSSSTTTUUUPPPQQQQQQRRRSSSTTTTTTUUUYYYUUUTTTVVVUUUQQQOOOOOOPPPPPPPPPSSSUUUWWWVVVUUUSSSRRRQQQSSSWWWXXXVVVTTTYYYVVVSSSTTTUUUVVVUUUSSSWWWVVVUUUUUUVVVVVVUUUSSSQQQQQQRRRRRRQQQPPPOOOOOOPPPQQQRRRQQQOOOOOOQQQRRRQQQQQQPPPOOOOOOOOOOOOPPPRRRQQQQQQQQQQQQPPPPPPPPPQQQQQQQQQPPPPPPOOOOOOOOOLLLKKKKKKKKKKKKMMMNNNOOOPPPMMMKKKKKKMMMNNNLLLJJJJJJJJJIIIHHHGGGHHHLLLOOOMMMLLLKKKIIIIIIIIIJJJKKKKKKIIIHHHHHHJJJKKKKKKJJJHHHIIIIIIJJJIIIGGGFFFEEEHHHHHHGGGGGGGGGGGGGGGGGGGGGGGGGGGHHHIIIJJJKKKLLLMMMLLLKKKIIIIIIKKKLLLMMMJJJJJJIIIIIIIIIHHHHHHHHHLLLKKKIIIHHHHHHIIIJJJKKKFFFEEEEEEEEEEEEEEEFFFGGGBBBAAAAAA@@@@@@AAAAAABBBDDDCCCBBBAAA@@@AAABBBBBBCCCCCCBBBAAAAAA@@@??????AAAAAAAAABBBBBBBBBCCCCCCBBBAAA???>>>===>>>???@@@AAA???===???CCCEEEDDDAAA;;;;;;===>>>>>>?????????>>>=========<<<<<<<<<<<>>;;;:::>>>@@@AAA@@@???>>>???@@@======>>>>>>>>>>>>======::::::<<<===>>>>>>>>>>>>===<<<<<<===>>>>>>===;;;999777666777:::;;;:::777888888888888777777777777777888999;;;<<<<<<;;;;;;;;;:::999:::;;;;;;:::888:::<<<>>>>>>>>>===>>>???888888777666666777888999<<<:::888999;;;<<<:::888===;;;999:::<<<===;;;999888888777777888888999:::999:::;;;;;;::::::<<<===999999888777666666777777555555666666555555444333333333333222111000//////111111000000111222333333333111///000222333222///222222111111111111222222444555777888777666444333555555444444444444555555555444333222111111111111222222222222111111000000000000000000000000000000000000000000////////////000000000000111111111111111111000000/////////...000000000000////////////000000000000111111111111111111111111111111111111000111333444444333222000111222222333333222222111000000000000111111111111000000000000////////////------......//////000000000///...---------------......---------,,,,,,,,,******+++,,,,,,,,,,,,+++((())))))))))))*********---,,,+++******+++,,,---++++++++++++++++++++++++************************))))))***++++++++++++***++++++++++++++++++++++++,,,,,,,,,+++++++++******+++)))((()))******)))((('''(((((()))***+++++++++)))))))))***+++++++++,,,(((((())))))*********+++)))************+++++++++++++++++++++++++++++++++******+++++++++,,,,,,,,,++++++,,,,,,,,,------------------------------------,,,++++++******++++++UUUTTTRRRQQQQQQRRRTTTUUUSSSRRRRRRQQQQQQQQQRRRRRRQQQQQQRRRRRRSSSTTTTTTUUUWWWTTTSSSVVVVVVRRRQQQRRRPPPPPPQQQSSSVVVWWWVVVUUUUUUSSSSSSUUUWWWXXXWWWUUUXXXVVVSSSTTTUUUVVVUUUTTTWWWUUUTTTTTTUUUVVVTTTSSSRRRSSSSSSSSSRRRRRRQQQPPPQQQQQQRRRQQQPPPOOOQQQSSSQQQQQQPPPOOOOOOOOOOOOPPPRRRQQQQQQQQQQQQPPPPPPPPPQQQQQQQQQQQQPPPPPPOOOOOOOOONNNNNNMMMMMMNNNOOOPPPQQQOOOLLLLLLMMMNNNNNNLLLJJJJJJJJJHHHGGGHHHLLLNNNMMMMMMKKKJJJJJJJJJKKKKKKKKKIIIHHHHHHJJJKKKJJJIIIGGGHHHIIIJJJJJJIIIHHHGGGGGGGGGGGGGGGGGGHHHHHHHHHHHHHHHHHHHHHIIIJJJKKKKKKMMMLLLJJJIIIIIIJJJLLLMMMJJJJJJIIIIIIHHHHHHHHHHHHIIIIIIHHHGGGGGGHHHIIIJJJEEEEEEDDDDDDDDDDDDDDDEEECCCBBBBBBAAAAAABBBBBBCCCDDDCCCBBBAAA@@@AAAAAABBBCCCCCCBBBAAA@@@@@@??????AAAAAAAAABBBBBBBBBCCCCCCAAAAAA@@@@@@??????@@@@@@???>>>===>>>@@@AAAAAA@@@======>>>???@@@@@@@@@@@@>>>>>>=========<<<<<<<<<>>>???@@@@@@@@@>>><<<;;;<<<>>>???>>>===<<<===>>>>>>>>>????????????>>>>>>;;;;;;<<<===>>>>>>>>>======<<<;;;<<<===>>><<<:::999777666777999:::999777777777777777777777777777777888999;;;<<<<<<;;;;;;<<<;;;:::;;;<<<<<<;;;999:::<<<>>>???>>>>>>???AAA::::::999888888999:::;;;===;;;999999;;;<<<:::888<<<:::888999;;;<<<;;;999999999999999999::::::;;;999:::;;;;;;::::::;;;===::::::999888888888888888555555666666555555444333333333222222111111000000111111111111111222333333333111000111333444222000222222111111111111222222444555666777777666555444555555444444444444555555555444333222111111111111222222222222111111111000111111111111111111111111111111111000000//////...000000000000111111111111111111000000000/////////111000000000//////////////////000000000111111111222222222222222222222222111111333333333333222111111222222333333222222111000000000000111111111111111111000000000/////////........./////////////////////...---------------.........---------,,,,,,******+++,,,,,,,,,,,,,,,))))))*********+++++++++,,,,,,+++******+++,,,,,,++++++++++++++++++++++++******************************+++,,,,,,,,,,,,,,,++++++++++++++++++++++++,,,,,,,,,++++++++++++***+++)))((()))***+++***(((((((((((()))***+++++++++***************+++++++++((()))))))))************)))************+++++++++++++++++++++++++++++++++******+++++++++,,,,,,,,,++++++,,,,,,,,,------------------------------------,,,++++++******++++++UUUTTTSSSRRRRRRSSSTTTUUUTTTSSSRRRQQQPPPPPPPPPPPPQQQRRRRRRSSSSSSTTTTTTTTTUUUSSSSSSVVVUUURRRQQQSSSQQQPPPQQQSSSVVVWWWWWWVVVVVVUUUUUUVVVXXXXXXVVVUUUVVVUUUSSSTTTUUUVVVVVVUUUVVVUUUTTTTTTUUUUUUTTTRRRSSSSSSTTTTTTTTTSSSRRRRRRQQQRRRRRRQQQPPPPPPQQQSSSQQQQQQPPPOOOOOOOOOOOOPPPRRRQQQQQQQQQQQQPPPPPPPPPQQQQQQQQQPPPPPPPPPPPPOOOQQQQQQPPPOOOOOOOOOOOOPPPPPPNNNKKKJJJKKKMMMMMMMMMJJJKKKJJJIIIHHHHHHKKKNNNNNNMMMLLLLLLKKKLLLLLLLLLKKKIIIHHHIIIJJJJJJIIIHHHGGGHHHIIIJJJJJJJJJIIIHHHFFFGGGGGGHHHHHHIIIIIIIIIHHHHHHHHHHHHIIIIIIJJJKKKLLLKKKJJJIIIIIIJJJKKKLLLJJJIIIIIIHHHHHHHHHHHHHHHFFFFFFFFFFFFGGGHHHIIIIIIFFFEEEDDDCCCCCCBBBCCCCCCDDDCCCCCCBBBBBBCCCCCCDDDCCCCCCBBBAAAAAAAAAAAAAAABBBBBBAAAAAA@@@@@@??????AAAAAAAAABBBBBBBBBCCCCCCBBBBBBBBBBBBBBBAAA@@@@@@>>>???@@@@@@???>>>???@@@??????@@@AAAAAABBBBBBBBB>>>>>>>>>=========<<<<<<===>>>???@@@@@@???>>>===<<<>>>???>>>===<<<===>>>>>>??????@@@@@@??????>>><<<<<<===============<<<<<<;;;:::;;;======;;;:::888666666666888999888777777777777777777777777777888888999:::;;;;;;;;;;;;<<<;;;;;;<<<===>>><<<::::::<<<>>>???>>>???AAABBB===<<<;;;::::::;;;<<<<<<===<<<::::::;;;<<<:::999:::999888999::::::999888::::::999999::::::;;;<<<999:::;;;;;;::::::;;;<<<::::::::::::999999999999555666666666666555444444222222222222222222222222222111111111111222222333444222111222333444333111222222111111111111222222333444555777777777666666555555444444444444555555444444333222111111111111222222222222111111111111111111111111111111111111222222111111000///......000000000111111111222222111111111000000000000000111111000000000//////////////////000000000111111444444444444444444444444222222222222222222222222111222222333333222222111000000000000111111111111222222111111111000000000///////////////.........//////...------------............------------,,,***+++,,,,,,------,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,------------,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++)))((()))***+++***)))(((((())))))***++++++++++++++++++***************))))))))))))************)))************+++++++++++++++++++++++++++++++++******+++++++++,,,,,,,,,,,,,,,,,,,,,---------------------------------------,,,++++++******++++++UUUUUUTTTSSSSSSTTTUUUUUUTTTTTTSSSRRRRRRRRRRRRRRRRRRRRRSSSSSSSSSTTTTTTTTTTTTSSSSSSUUUSSSOOOOOORRRQQQQQQQQQSSSVVVXXXWWWVVVVVVVVVVVVVVVWWWVVVUUUTTTUUUTTTTTTTTTUUUVVVWWWWWWVVVTTTSSSSSSTTTUUUSSSRRRSSSSSSSSSTTTTTTSSSRRRRRRQQQRRRRRRQQQPPPPPPQQQSSSQQQQQQPPPOOOOOOOOOOOOPPPRRRQQQQQQQQQQQQPPPPPPPPPOOOOOOOOOOOOOOOOOOOOOOOOQQQPPPPPPOOONNNMMMMMMMMMMMMKKKHHHGGGGGGIIIKKKKKKKKKKKKKKKJJJHHHIIIKKKMMMNNNMMMMMMMMMMMMMMMMMMMMMKKKJJJIIIIIIJJJJJJHHHFFFHHHIIIJJJJJJJJJJJJIIIHHHFFFGGGGGGHHHIIIJJJJJJKKKHHHHHHHHHHHHHHHIIIJJJKKKKKKJJJJJJIIIIIIJJJJJJKKKJJJIIIHHHGGGGGGGGGHHHHHHEEEEEEEEEFFFGGGHHHIIIIIIGGGFFFEEEDDDCCCBBBBBBBBBCCCCCCBBBBBBBBBBBBCCCCCCBBBBBBBBBAAAAAAAAAAAAAAAAAAAAAAAA@@@@@@@@@@@@@@@AAAAAAAAABBBBBBBBBCCCCCCBBBCCCDDDDDDDDDCCCAAA@@@???BBBDDDCCC@@@>>>@@@CCC@@@@@@@@@@@@AAAAAABBBBBB>>>>>>>>>============<<<<<<===>>>???@@@?????????>>>@@@AAA@@@???>>>???@@@>>>>>>????????????>>>>>><<<===============<<<;;;;;;::::::;;;<<<<<<;;;999777666666777888888888888666666777777777777777888999999999::::::;;;;;;;;;;;;::::::;;;======<<<:::;;;<<<>>>>>>>>>???AAACCC>>>===<<<;;;;;;;;;<<<======<<<<<<;;;;;;;;;:::999999888888888999999888888999999999999999:::;;;;;;999:::;;;;;;:::999:::;;;999:::::::::::::::999999666666666666666555444444222222222333333333333333222222222111111222222333333333333333333444333333222222111111111111222222222333444666777888888888555555444444444444555555444333222222111111111222222222222222222222222222111111111111111111111111333333222111000000///...000000111111111222222222111111111111111111111111111111111000000000///////////////000000000111111333333333333333333333333444333222111111111222222111222222333333222222111///000000000111111111111222222222222111111111000000000//////......------///......---------..................------------+++,,,,,,---------------,,,,,,,,,,,,------------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++***++++++,,,---,,,,,,,,,+++++++++,,,,,,,,,,,,,,,------,,,,,,,,,+++++++++***)))((()))+++,,,+++***)))))))))******+++++++++,,,+++++++++***))))))))))))))))))))))))*********))))))*********+++++++++++++++++++++++++++++++++******+++++++++,,,,,,,,,,,,,,,,,,------------...---------------------------,,,++++++******++++++UUUUUUTTTTTTTTTTTTUUUUUUTTTTTTSSSSSSTTTUUUUUUVVVSSSSSSSSSSSSTTTTTTTTTTTTUUUTTTTTTUUUQQQKKKKKKNNNQQQQQQQQQTTTVVVXXXWWWVVVTTTUUUUUUVVVUUUTTTTTTTTTTTTTTTTTTTTTTTTUUUVVVWWWVVVUUUTTTTTTUUUUUUTTTRRRQQQRRRRRRSSSSSSRRRRRRRRRQQQRRRSSSRRRPPPPPPRRRSSSQQQQQQPPPOOOOOOOOOOOOPPPRRRQQQQQQQQQQQQPPPPPPPPPMMMMMMMMMMMMMMMMMMMMMMMMNNNNNNMMMMMMLLLKKKJJJIIIKKKJJJIIIHHHGGGHHHJJJLLLKKKLLLLLLJJJIIIIIIKKKMMMMMMMMMMMMNNNNNNNNNNNNMMMKKKJJJIIIIIIJJJIIIGGGEEEIIIIIIJJJJJJJJJIIIGGGFFFGGGGGGHHHIIIJJJJJJKKKKKKIIIIIIHHHHHHHHHIIIJJJJJJJJJJJJIIIIIIIIIIIIJJJJJJJJJIIIHHHFFFFFFGGGHHHIIIEEEEEEFFFGGGHHHIIIIIIIIIHHHGGGFFFEEEDDDDDDCCCDDDBBBBBBAAAAAAAAAAAABBBBBBAAAAAAAAAAAAAAA@@@@@@@@@???@@@@@@@@@@@@@@@@@@@@@AAAAAAAAABBBBBBBBBCCCCCCCCCCCCDDDEEEEEECCCBBBAAA???BBBDDDCCC@@@>>>@@@CCC@@@????????????@@@AAAAAA???>>>>>>>>>============<<<===>>>>>>??????@@@@@@>>>@@@AAA@@@???>>>???@@@<<<<<<============<<<<<<<<<===============<<<;;;;;;::::::;;;<<<<<<;;;999666777777777777777888999666777777777888888999999::::::::::::::::::;;;;;;:::999999:::<<<<<<;;;:::;;;<<<>>>======>>>AAACCC>>>===<<<;;;::::::;;;<<<<<<===<<<;;;:::999999999888888888888888888888888888888888888888999::::::999:::;;;;;;999888999;;;888888999::::::999999888666666777777666666555444333333333333333444444444333333222222222222222333333333444333333333333333222222111111111111222222222333444555777888888999555555444444444444555555333333222222111111222222222222222222222222222333111111111111111111111111444333333222111000000000111111111111222222222222111111111222222222222222111111111111000000000000000000000000111111111111333333333333333333333333444333222111111111222222111222222333333222222111///000000000111111111111222222222222111111111000000000//////......------......---------....../////////.........---------,,,,,,---............---,,,------------.........,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++)))******+++++++++++++++++++++,,,,,,,,,------------------,,,,,,,,,++++++***)))))))))+++,,,,,,***************++++++++++++,,,+++++++++***)))))))))******))))))))))))))))))))))))*********+++++++++++++++++++++++++++++++++******+++++++++,,,,,,,,,,,,,,,---------.........---------------------------,,,++++++******++++++TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTUUUVVVWWWXXXTTTTTTTTTTTTTTTTTTTTTTTTUUUUUUUUUUUUPPPJJJIIIMMMRRRQQQRRRTTTWWWXXXXXXWWWRRRTTTUUUUUUTTTSSSTTTUUUTTTUUUVVVUUUTTTTTTVVVWWWWWWVVVTTTUUUVVVVVVUUUSSSQQQQQQRRRRRRSSSSSSRRRRRRRRRSSSSSSRRRQQQQQQRRRTTTQQQQQQPPPOOOOOOOOOOOOPPPRRRQQQQQQQQQQQQPPPPPPPPPLLLLLLMMMMMMMMMMMMNNNNNNLLLLLLLLLLLLKKKJJJIIIHHHJJJKKKLLLLLLKKKKKKLLLNNNKKKLLLMMMKKKJJJIIIKKKLLLLLLLLLMMMNNNNNNNNNNNNMMMKKKJJJJJJJJJJJJHHHEEECCCGGGHHHIIIIIIIIIHHHGGGFFFHHHIIIIIIJJJJJJKKKKKKKKKIIIIIIIIIHHHHHHIIIIIIJJJIIIIIIIIIIIIIIIIIIIIIIIIJJJIIIGGGFFFEEEFFFHHHIIIEEEFFFGGGHHHHHHHHHHHHHHHHHHGGGFFFEEEEEEDDDEEEEEEAAAAAAAAA@@@@@@AAAAAAAAAAAAAAAAAAAAAAAA@@@??????>>>>>>??????@@@@@@AAAAAAAAAAAAAAABBBBBBBBBCCCCCCDDDDDDDDDDDDDDDCCCBBBBBB>>>???@@@@@@???>>>???@@@@@@???>>>======>>>???@@@??????>>>>>>>>>===============>>>>>>?????????@@@<<<>>>???>>>===<<<===>>>;;;<<<<<<======<<<<<<;;;<<<<<<===============<<<<<<;;;:::;;;======;;;:::666888999999888888999:::777888888999999:::::::::;;;::::::999999::::::;;;999888888999;;;<<<;;;:::<<<======<<<<<<===???AAA>>>===<<<::::::::::::;;;;;;<<<===;;;999777888999777888999999888777888999888888777777888888999:::999:::;;;:::999888999:::666777999:::::::::999888666777777777777666555555444444444444444444444444444333333222222222222333222333444333222111222444222222111111111111222222333333444555666777888999555555444444444444555555333333222222111222222333222222222222333333333333222222222222222222222222333333333222222222222111111111111222222222222333222222222222222333333333222222111111111000000000111111111222222222333333222222222222222222222222444333333222222111111111111222222333333222222111000000000000111111111111222222111111111000000000///////////////............------------...///////////////.........------,,,---......//////......------------............,,,,,,------------,,,,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,))))))***++++++++++++***++++++,,,,,,------......------------,,,,,,,,,,,,***))))))***,,,---,,,++++++++++++++++++++++++++++++++++++***************************)))))))))))))))************+++++++++++++++++++++++++++++++++******+++++++++,,,,,,,,,,,,---------............---------------------------,,,++++++******++++++RRRSSSSSSSSSSSSSSSSSSRRRUUUUUUUUUTTTTTTUUUVVVVVVTTTTTTTTTTTTTTTTTTTTTTTTUUUUUUWWWWWWQQQKKKLLLPPPRRRRRRRRRTTTWWWXXXXXXWWWQQQTTTVVVVVVUUUTTTUUUWWWUUUVVVWWWVVVSSSSSSUUUWWWXXXWWWVVVVVVWWWWWWVVVTTTQQQRRRSSSSSSTTTTTTTTTSSSRRRSSSSSSRRRQQQQQQRRRTTTQQQQQQPPPOOOOOOOOOOOOPPPRRRQQQQQQQQQQQQPPPPPPPPPMMMNNNNNNNNNOOOOOOOOOOOOLLLMMMMMMNNNMMMLLLJJJJJJHHHKKKNNNNNNLLLKKKLLLNNNKKKMMMMMMLLLJJJJJJJJJLLLKKKKKKMMMNNNNNNNNNMMMMMMKKKJJJJJJJJJJJJHHHDDDBBBBBBDDDFFFHHHIIIIIIIIIIIIJJJJJJJJJJJJJJJKKKKKKKKKJJJIIIIIIHHHHHHIIIIIIIIIHHHHHHHHHIIIIIIHHHHHHHHHKKKIIIGGGEEEEEEFFFHHHIIIDDDEEEFFFGGGGGGFFFFFFEEEFFFEEEEEEDDDDDDDDDEEEEEEBBBBBBAAAAAAAAAAAABBBBBB@@@AAAAAABBBAAA@@@???>>>===>>>>>>???@@@AAAAAAAAAAAAAAAAAABBBBBBBBBCCCCCCDDDDDDCCCBBBBBBBBBBBBCCC???>>>===>>>@@@AAAAAA@@@AAA@@@>>>======>>>???@@@?????????>>>>>>>>>======>>>>>>>>>>>>>>>>>>??????<<<>>>???>>>===<<<===>>><<<<<<============<<<<<<;;;;;;<<<===>>>>>>>>>======<<<;;;<<<===>>><<<:::777999;;;:::999888:::<<<888999999:::;;;;;;<<<<<<;;;;;;:::999999999:::;;;999999999:::<<<===<<<;;;=========;;;::::::===??????>>><<<;;;::::::;;;;;;:::<<<<<<:::777555666888777999;;;:::888777888:::999888888888888999::::::999:::;;;:::888777888999777888:::;;;<<<;;;:::999777777777777777666555555666666555555444444333333555444333222222222222222000222444333111000111333222222111111111111222222444444444555666777888888555555444444444444555555333222222111222222333333222222222333333333444444222222222222222222222222222222222333333333333333111111111222222222333333222222222333333333444444222222222111111111000000222222333333333444444444444444444444444444444444333333444444333222000///111222222333333222222111000000000000111111111111111111000000000/////////.........///////////////---------------...//////////////////............------...///////////////,,,,,,---------.........,,,,,,---......---,,,,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,)))***++++++,,,,,,++++++++++++,,,,,,---......///...------------,,,,,,,,,***))))))***,,,------,,,++++++++++++++++++++++++***************+++++++++************)))))))))((()))************+++++++++++++++++++++++++++++++++******+++++++++,,,,,,,,,------------............---------------------------,,,++++++******++++++RRRRRRSSSSSSSSSSSSRRRRRRWWWVVVUUUTTTSSSSSSSSSSSSUUUUUUTTTTTTTTTTTTTTTTTTTTTUUUXXXXXXSSSMMMOOOTTTRRRRRRRRRTTTWWWYYYXXXWWWQQQTTTWWWWWWVVVUUUWWWYYYUUUWWWXXXVVVSSSRRRTTTVVVYYYWWWVVVVVVWWWXXXVVVUUURRRSSSTTTUUUUUUUUUUUUUUURRRSSSSSSSSSQQQQQQSSSTTTQQQQQQPPPOOOOOOOOOOOOPPPRRRRRRQQQQQQQQQPPPPPPPPPOOOOOOOOOPPPPPPQQQQQQQQQNNNNNNOOOPPPOOONNNMMMLLLEEEIIIMMMNNNLLLJJJJJJKKKLLLMMMMMMMMMKKKJJJJJJKKKJJJKKKLLLMMMNNNNNNMMMLLLKKKJJJJJJJJJJJJHHHDDDAAA???@@@CCCFFFIIIJJJKKKKKKKKKKKKKKKKKKKKKJJJJJJJJJJJJIIIIIIHHHHHHHHHIIIIIIGGGHHHHHHIIIIIIHHHHHHGGGKKKIIIGGGEEEDDDFFFHHHIIIDDDDDDEEEFFFFFFEEEDDDCCCDDDDDDCCCCCCCCCDDDDDDEEECCCCCCCCCBBBBBBCCCCCCCCC@@@@@@AAABBBAAA@@@???>>>======>>>???@@@AAAAAABBBAAAAAAAAABBBBBBBBBCCCCCCEEEDDDCCCAAAAAABBBCCCCCCAAA???===???CCCEEEDDDAAABBB@@@???======>>>@@@AAA????????????>>>>>>>>>>>>??????>>>>>>>>>>>>??????>>>@@@AAA@@@???>>>???@@@======>>>>>>>>>>>>======::::::<<<===>>>>>>>>>>>>===<<<<<<===>>>>>>===;;;777:::<<<;;;999888:::===999999:::;;;;;;<<<======<<<;;;:::999999999:::;;;:::::::::;;;>>>>>>>>><<<=========;;;999999<<<>>>@@@???===<<<;;;;;;;;;<<<999;;;<<<:::666444555777777:::;;;:::888777999;;;::::::999999::::::;;;<<<999:::;;;:::888777888999888999;;;======<<<;;;:::777777777777777666666555777777666555444333333333555444333333222222222222///222333222000///111333222222111111111111222222555555444555555666777888555555555444444555555555222222222111222222333333222222222333333444444444222222222222222222222222111222222333333444444555111111222222222333333333222222222333333444444444222222222111111111111000333333333444444444555555555555555555555555555555222333444555444222000...222222222333333222222222000000000000111111111111000000000000////////////---.........//////000000---------------...///000000/////////............---......///////////////,,,,,,,,,---------......,,,,,,---......---,,,,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,------------,,,++++++,,,,,,---...//////......---------,,,,,,,,,***))))))***,,,...---,,,++++++++++++++++++++++++))))))******+++++++++,,,+++*********))))))(((((()))************+++++++++++++++++++++++++++++++++******+++++++++,,,,,,,,,---------.........//////---------------------------,,,++++++******++++++SSSSSSSSSSSSTTTUUUVVVWWWWWWVVVVVVUUUTTTSSSRRRRRRQQQQQQSSSTTTVVVXXXYYYZZZRRRTTTUUUUUUTTTRRRRRRRRRWWWVVVTTTSSSSSSSSSTTTTTTWWWWWWUUUUUUUUUWWWYYYZZZXXXXXXXXXVVVTTTSSSTTTVVVXXXXXXWWWWWWWWWWWWXXXXXXUUUTTTTTTSSSSSSTTTTTTUUUWWWUUURRRPPPOOOPPPRRRSSSTTTSSSSSSRRRQQQPPPPPPOOOPPPPPPPPPQQQSSSSSSQQQOOOPPPPPPPPPPPPPPPPPPPPPPPPOOOPPPQQQQQQPPPOOOLLLKKKNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNMMMLLLKKKJJJIIIIIIOOOOOONNNMMMLLLKKKJJJJJJMMMJJJGGGIIILLLKKKGGGBBB???@@@AAACCCEEEHHHIIIJJJLLLLLLNNNNNNMMMKKKIIIGGGIIIJJJLLLMMMMMMJJJGGGDDDHHHGGGGGGFFFFFFGGGGGGHHHIIIIIIIIIHHHHHHGGGGGGGGGGGGFFFEEECCCCCCCCCDDDDDDEEEEEEEEEEEEFFFGGGHHHIIIBBBBBBBBBCCCCCCEEEFFFFFFFFFEEEBBB@@@???@@@AAABBBAAA@@@??????@@@AAACCCDDDAAABBBBBBCCCCCCBBBBBBAAABBBCCCCCCCCCBBBBBBDDDEEEBBBAAAAAA@@@AAABBBCCCDDDCCCBBB@@@>>>===>>>>>>???>>>???@@@AAAAAAAAAAAAAAACCCAAA===:::999;;;===?????????>>>>>>======<<<<<<<<<===>>>??????>>>===<<<@@@?????????>>>>>>======<<<<<<<<<<<<<<<===>>>???999999999::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;<<<;;;;;;;;;;;;<<<======::::::::::::::::::::::::@@@>>><<<::::::;;;===???>>>>>>===<<<<<<<<<<<<<<<;;;;;;;;;:::999888777666::::::::::::999888777777999999:::::::::;;;;;;;;;:::::::::999999888888888:::::::::999999999888888999999999888888666555555777777666555444444333333222222222222222222222222111333333222000///000111444444333222111111111111555555555333222333666999666666666666555555555555333333333222222222111111222333333444444333333222333333222111000000111111222222222222222222222222111111111111111111111111222222333333444555666666222222111000000111222333222222333444444555555666555555444444444333333333444444444333333222222222333333333333333333333333111111000000000000111111......////////////......///////////////000111111000000////////////000000000000//////.........---///...------------...///111111000///...---,,,,,,......---------,,,,,,,,,+++,,,,,,---.........---++++++,,,,,,,,,---------...---,,,+++************++++++,,,,,,,,,---------......---,,,,,,+++************+++++++++,,,,,,,,,+++,,,,,,------,,,,,,+++******+++++++++,,,,,,,,,)))************+++++++++++++++++++++++++++++++++******+++++++++,,,,,,,,,,,,,,,++++++,,,,,,---...//////...---,,,++++++***.........------,,,,,,,,,,,,,,,,,,++++++*********SSSRRRRRRSSSSSSTTTUUUVVVXXXWWWWWWVVVVVVUUUUUUTTTSSSTTTTTTTTTUUUUUUVVVVVVUUUWWWYYYYYYXXXWWWWWWWWWWWWVVVUUUTTTTTTTTTUUUVVVWWWXXXXXXXXXXXXYYYYYYZZZUUUVVVWWWWWWVVVVVVWWWXXXWWWWWWVVVVVVVVVVVVWWWWWWUUUUUUTTTTTTTTTTTTUUUUUUUUUTTTRRRQQQRRRTTTVVVXXXUUUTTTTTTTTTSSSRRRRRRRRRQQQPPPPPPRRRSSSSSSQQQOOOPPPPPPOOOOOOOOOOOOOOOOOOQQQRRRSSSSSSRRRPPPNNNMMMOOOOOOOOOOOOPPPPPPPPPPPPPPPOOONNNMMMLLLKKKJJJJJJNNNNNNMMMLLLLLLKKKJJJJJJNNNKKKIIIJJJMMMLLLIIIDDDBBBCCCDDDFFFGGGIIIJJJKKKMMMMMMNNNNNNMMMKKKJJJIIIKKKKKKKKKKKKJJJIIIHHHGGGIIIHHHHHHGGGGGGHHHHHHIIIHHHHHHHHHHHHHHHHHHGGGGGGGGGFFFEEEDDDDDDDDDEEEEEEHHHGGGFFFFFFEEEEEEFFFFFFBBBBBBBBBBBBCCCDDDEEEFFFEEEDDDBBBAAA@@@@@@BBBBBBAAA@@@@@@@@@AAABBBCCCDDDAAABBBBBBCCCCCCBBBBBBAAABBBCCCCCCCCCBBBBBBDDDEEEBBBBBBAAAAAAAAABBBDDDEEEBBBAAA@@@???>>>>>>>>>???>>>???@@@@@@AAAAAAAAAAAADDDBBB???=========???@@@???>>>>>>>>>=========<<<<<<===>>>??????>>>===<<>>>>>>>>=========<<<<<<<<<<<<<<<===>>>>>>999999999::::::;;;;;;;;;;;;;;;;;;;;;::::::::::::<<<;;;;;;;;;;;;<<<======;;;;;;;;;;;;;;;;;;;;;;;;???>>><<<;;;;;;<<<>>>@@@>>>======<<<<<<<<<<<<<<<<<<<<<<<<;;;;;;:::888888888999999:::::::::999999::::::::::::;;;;;;;;;;;;:::::::::999999999888888999999999999888888888888:::::::::999999888666666777666666555444444333333333333333333333333333333222333333222111000000222333333222222111222222222555555555444333444666999666666666555555555444444333333222222222111111111222333333444444333333222333222222111000000111111222222222222222222222222111111111111111111111111111111222222333444444555333333222111000111222222222222333333444555555555444333333333222222222222444444444333333222222222333333333333333333333333111111111000000111111111//////000000000000/////////////////////000111111111000000/////////000000000/////////............///...---,,,,,,---...///000000000///......------.........---------,,,,,,+++,,,------.........---++++++,,,,,,,,,---------...---,,,+++************++++++,,,,,,,,,---------......------,,,++++++******++++++++++++,,,,,,,,,+++,,,,,,------,,,,,,+++***++++++++++++,,,,,,,,,************++++++++++++++++++++++++++++++++++++******+++++++++,,,,,,,,,,,,++++++++++++,,,------.........---,,,,,,++++++...---------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++RRRQQQQQQRRRRRRSSSTTTUUUVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVUUUTTTSSSSSSRRRRRRRRRTTTWWWWWWWWWVVVVVVWWWWWWVVVUUUUUUUUUVVVWWWXXXVVVWWWWWWXXXXXXXXXXXXXXXRRRUUUXXXYYYYYYYYYZZZ[[[VVVVVVUUUUUUUUUUUUVVVVVVUUUUUUTTTTTTTTTTTTUUUUUUUUUUUUSSSSSSTTTVVVXXXYYYSSSSSSSSSSSSSSSSSSRRRRRRRRRQQQQQQRRRTTTSSSQQQOOONNNNNNNNNOOOOOOOOOOOOOOOQQQQQQRRRRRRRRRPPPOOONNNPPPPPPPPPQQQQQQRRRRRRRRRQQQQQQPPPNNNMMMKKKJJJJJJLLLLLLLLLKKKKKKJJJJJJJJJNNNLLLJJJKKKMMMMMMJJJGGGFFFGGGGGGHHHIIIJJJKKKKKKMMMMMMMMMLLLKKKKKKJJJJJJLLLKKKJJJIIIHHHHHHHHHIIIIIIIIIHHHHHHHHHHHHIIIIIIGGGGGGGGGHHHHHHHHHHHHHHHFFFEEEEEEEEEEEEFFFGGGGGGJJJIIIGGGFFFEEEDDDCCCCCCAAAAAAAAAAAABBBCCCDDDEEEDDDCCCBBBAAAAAABBBCCCCCCAAAAAAAAAAAABBBCCCDDDEEEBBBBBBCCCCCCCCCCCCBBBBBBBBBCCCCCCCCCBBBBBBDDDEEECCCCCCBBBBBBCCCCCCDDDEEEBBBAAA@@@??????>>>???????????????@@@@@@@@@@@@@@@BBBAAA@@@???>>>>>>>>>???>>>>>>>>>>>>==================>>>>>>>>>>>>======>>>>>>===============<<<<<<<<<<<<<<<============999999::::::::::::;;;;;;;;;;;;::::::999999999888<<<;;;;;;;;;;;;<<<======<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>===<<<===>>>@@@AAA>>>===<<<<<<;;;;;;<<<<<<<<<<<<===<<<<<<;;;:::999777888999:::;;;;;;;;;;;;999::::::::::::;;;;;;;;;:::::::::999999999999888888888888888777777777777::::::::::::999888777777666666666555444444333333444444444444444444444444222333444333111000111222333222222222222333333444666666666555444555777999666666555555555444444444222222222111111111111111222333333444444333333222333222111111000111111111222222222222222222222222222222222222222222222222000111111222222333333333555444333222222222222222222222333333444444555555222222222222111111111111444444333333333333222222333333333333333333333333222222111111111111222222000000111111111111000000000////////////000111111222111000///////////////////////////..................---,,,,,,---......////////////////////////.........------------,,,,,,,,,---............---,,,,,,,,,,,,------------...---,,,++++++******+++,,,,,,,,,,,,------------......------,,,+++++++++++++++++++++,,,,,,,,,,,,,,,,,,------------,,,,,,++++++++++++,,,,,,,,,,,,************+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,******+++++++++,,,,,,,,,+++++++++++++++,,,------------------,,,,,,,,,,,,------,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,,,,------QQQPPPPPPQQQQQQRRRSSSTTTRRRRRRSSSSSSTTTTTTTTTUUUVVVVVVUUUTTTSSSRRRQQQPPPOOOQQQTTTVVVUUUUUUVVVWWWWWWWWWVVVVVVVVVXXXYYYZZZVVVUUUTTTSSSSSSTTTVVVWWWRRRUUUYYY[[[[[[ZZZZZZ[[[VVVVVVUUUUUUUUUUUUVVVVVVUUUUUUTTTTTTTTTTTTUUUUUUXXXWWWUUUTTTSSSTTTUUUVVVPPPPPPPPPPPPPPPPPPPPPQQQRRRRRRRRRSSSTTTSSSQQQOOOMMMMMMNNNNNNNNNNNNOOOOOONNNOOOOOOOOOOOONNNMMMLLLOOOOOOPPPPPPQQQRRRRRRRRRQQQQQQOOONNNLLLKKKIIIIIIKKKKKKKKKKKKJJJJJJJJJJJJMMMKKKJJJJJJLLLMMMKKKIIIIIIIIIIIIJJJJJJJJJKKKKKKLLLLLLKKKJJJIIIIIIJJJJJJJJJJJJJJJIIIIIIHHHHHHHHHIIIHHHHHHGGGGGGHHHHHHIIIFFFFFFGGGGGGHHHHHHHHHIIIEEEEEEEEEFFFFFFGGGHHHIIIIIIHHHGGGEEEDDDDDDDDDCCCAAAAAAAAAAAAAAABBBCCCDDDCCCCCCBBBBBBBBBBBBCCCDDDAAAAAABBBBBBCCCDDDDDDEEEBBBBBBCCCCCCCCCCCCBBBBBBAAACCCCCCCCCBBBBBBCCCEEEDDDDDDCCCCCCDDDDDDDDDDDDAAAAAA@@@@@@????????????@@@???????????????@@@@@@>>>>>>>>>>>>>>>===<<<<<<>>>>>>>>>>>>==================>>>>>>>>>>>>==================<<<<<<<<<<<<<<<<<<===============<<<::::::::::::::::::::::::;;;::::::999999888888777<<<;;;;;;;;;;;;<<<=================================>>>>>>>>>???@@@AAABBB======<<<;;;;;;;;;;;;<<<<<<<<<<<<<<<<<<;;;::::::888999999:::;;;;;;::::::888888888999999999::::::999999999999999999999999777777777777666666666666999999999999999888777666666666555555555444444444333333333333444444444444222333444333222111222333222222222222222333444555666666777666555555777999777777666666666666555555111111111111111111111111222333333444444333333222222222111111111111111222222222222222222222222222222222222222222222222222111111222222333333333444555555444333333222222222111222222333444444555555333222222222222111111111333333333333333333333333222222222222222222222222333222222222222222222333111111111222222111111111000000//////000000111222222222111000///////////////////////////............------------------...............//////000000............------------------............------,,,,,,,,,------------......---,,,+++++++++++++++,,,,,,,,,------------.........------,,,,,,,,,,,,+++++++++,,,,,,,,,------,,,,,,------------,,,,,,+++++++++,,,,,,,,,------*********+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,******+++++++++,,,,,,,,,+++++++++***+++,,,,,,---++++++,,,,,,,,,---------,,,,,,,,,,,,++++++++++++++++++,,,,,,---------...PPPPPPPPPPPPQQQRRRSSSTTTQQQRRRRRRSSSSSSTTTTTTUUUUUUUUUTTTTTTSSSRRRRRRRRRPPPSSSVVVWWWWWWWWWXXXYYYXXXXXXWWWWWWWWWXXXZZZ[[[YYYWWWSSSQQQQQQSSSVVVYYYUUUWWWZZZ[[[[[[YYYYYYYYYWWWWWWVVVVVVVVVVVVWWWWWWUUUTTTTTTSSSSSSTTTTTTUUUUUUUUUSSSSSSRRRSSSSSSTTTOOOOOOOOOOOOOOOPPPPPPPPPRRRRRRQQQRRRSSSSSSPPPNNNMMMMMMMMMNNNNNNOOOOOOOOONNNNNNNNNNNNNNNNNNMMMMMMNNNNNNOOOOOOOOOPPPPPPPPPOOOOOONNNMMMKKKJJJIIIHHHJJJJJJJJJJJJKKKKKKKKKKKKKKKJJJIIIIIIJJJKKKKKKJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJIIIHHHHHHHHHIIIIIIGGGHHHJJJKKKKKKIIIGGGEEEGGGGGGFFFFFFFFFFFFGGGGGGFFFFFFFFFGGGGGGHHHHHHHHHDDDDDDEEEFFFGGGHHHHHHIIIFFFEEEEEEEEEEEEEEEEEEFFFBBBBBBAAAAAAAAABBBCCCCCCCCCCCCBBBBBBCCCCCCCCCDDDAAAAAABBBCCCCCCDDDDDDDDDBBBCCCCCCDDDDDDCCCCCCBBBAAACCCCCCCCCBBBBBBCCCEEEDDDDDDDDDDDDDDDDDDCCCCCCAAAAAAAAAAAA@@@@@@@@@???@@@@@@???>>>>>>??????@@@======>>>???>>>===<<<<<<============>>>>>>>>>>>>>>>>>>============>>>>>><<<<<<<<<<<<============<<<<<<===>>>======<<<;;;:::::::::::::::::::::::::::::::::999999888888888<<<;;;;;;;;;;;;<<<======>>>>>>>>>>>>>>>>>>>>>>>>======>>>@@@@@@AAAAAAAAA======<<<;;;;;;;;;;;;;;;:::;;;;;;;;;;;;::::::999;;;;;;;;;;;;;;;:::999888777777777777888888888888999999999999999999999999777777777666666666555555777777777777777666666555555555555555555444444444111111222222333333333333222333444444333222333555222222222222333444555555555666777777666666777999888888888777777777666666111111111111111111222222222333333444444333333222222111111111111111222222222222222222222222222222222222222222222222222222333333333333444444444444444444444444333333222222111111222222333444444555333333333333222222222222333333333333333333333333222222222222222222222222333222222222222222222333111111222222222222111111000000000000000111222222222222111000000000000000.........///////////////........................------......///000000000//////.........------------......//////...------,,,,,,---------.........------,,,,,,+++,,,,,,,,,,,,,,,---------...............------------,,,,,,++++++,,,,,,,,,---------,,,------......------,,,++++++,,,,,,,,,---------***++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,******+++++++++,,,,,,,,,+++************+++,,,,,,******+++,,,,,,---------+++++++++++++++++++++++++++++++++,,,,,,---------QQQPPPPPPQQQQQQRRRSSSTTTTTTTTTTTTUUUUUUUUUVVVVVVUUUUUUTTTTTTTTTSSSSSSSSSOOORRRUUUVVVVVVUUUVVVWWWYYYXXXWWWWWWWWWXXXYYYZZZ\\\ZZZVVVSSSSSSUUUYYY[[[WWWYYY[[[[[[YYYXXXWWWXXXWWWWWWVVVVVVVVVVVVWWWWWWSSSSSSSSSRRRRRRSSSSSSSSSPPPPPPPPPQQQRRRTTTUUUVVVQQQQQQQQQQQQQQQQQQQQQPPPRRRQQQQQQRRRRRRRRROOOMMMMMMMMMNNNNNNOOOOOOPPPPPPPPPPPPPPPOOOOOOOOOOOOOOONNNNNNNNNNNNNNNNNNNNNNNNNNNMMMMMMLLLKKKJJJIIIIIIJJJJJJJJJKKKKKKLLLLLLLLLIIIIIIIIIIIIJJJKKKLLLLLLJJJJJJJJJJJJJJJJJJJJJJJJIIIIIIIIIIIIIIIIIIIIIHHHEEEGGGJJJLLLLLLJJJGGGEEEFFFFFFEEEEEEEEEEEEFFFFFFFFFFFFFFFGGGGGGGGGGGGGGGCCCDDDEEEFFFGGGGGGGGGGGGCCCCCCCCCDDDEEEFFFGGGHHHCCCBBBBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC@@@@@@BBBCCCCCCDDDCCCCCCCCCCCCDDDDDDDDDDDDCCCCCCBBBCCCCCCCCCBBBBBBDDDEEECCCCCCDDDDDDDDDCCCBBBBBB@@@@@@AAAAAAAAAAAA@@@@@@AAA@@@???======>>>????????????@@@@@@@@@@@@???>>>============>>>>>>>>>>>>>>>>>>============>>>>>><<<============>>>>>>>>><<<===>>>>>>>>>===;;;;;;;;;;;;::::::::::::999999999:::::::::::::::::::::<<<;;;;;;;;;;;;<<<======>>>>>>>>>>>>>>>>>>>>>>>><<<===???AAAAAAAAA@@@???===<<<;;;;;;::::::;;;;;;::::::;;;;;;;;;::::::999<<<<<<<<<<<<;;;:::999888666666777777777888888888888999999999999:::::::::777777777777666666666666555666666777666666555555555555555555555555555555000111111222222333333444222444555555333333444666444333333333333444444555444555777777666555666888888888888777777777666666222222222222222333333333222333333444444333333222111111111000111111222333222222222222222222222222333333333333333333333333444444444444444444444444222222333333333333222222111111222222333333444444444333333333222222222222222222333333333333444444222222222222222222222222222222111111111111222222111111222222222222111111111000000000000111222222111111111000000111111222.........///////////////...///000000000000///...---.........//////000000/////////.........------...////////////...------,,,---------............------,,,,,,,,,,,,------,,,---------..................------------------,,,,,,,,,,,,------------------............------,,,,,,,,,,,,------------++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,******+++++++++,,,,,,,,,***************+++,,,,,,******++++++,,,,,,------)))************+++++++++***+++++++++++++++,,,,,,QQQQQQQQQQQQRRRSSSTTTUUUTTTTTTTTTTTTUUUUUUUUUUUUWWWVVVVVVUUUTTTTTTSSSSSSNNNQQQTTTUUUTTTTTTTTTUUUZZZYYYXXXWWWWWWWWWXXXYYYZZZZZZXXXWWWWWWWWWXXXXXXWWWXXXYYYYYYWWWWWWXXXYYYVVVVVVUUUUUUUUUUUUVVVVVVRRRRRRQQQQQQQQQQQQRRRRRROOOOOOPPPQQQSSSTTTUUUVVVRRRQQQQQQQQQPPPOOOOOOOOOQQQPPPPPPQQQQQQPPPNNNKKKNNNNNNNNNOOOPPPPPPQQQQQQPPPOOOOOOOOOOOOOOOPPPPPPOOOOOOOOONNNMMMMMMLLLLLLMMMMMMMMMLLLLLLLLLKKKKKKJJJJJJKKKLLLLLLMMMNNNNNNJJJJJJJJJJJJJJJKKKMMMOOOJJJJJJJJJJJJKKKKKKKKKKKKIIIIIIKKKKKKKKKKKKJJJIIIFFFGGGIIIJJJJJJIIIHHHGGGGGGFFFFFFFFFFFFFFFFFFGGGGGGGGGGGGGGGFFFFFFFFFFFFBBBCCCEEEFFFFFFFFFFFFEEECCCCCCCCCDDDDDDEEEGGGGGGDDDDDDCCCCCCBBBCCCCCCDDDDDDDDDDDDDDDDDDCCCBBBBBB???@@@AAABBBCCCCCCBBBBBBCCCCCCDDDDDDDDDDDDCCCCCCBBBCCCCCCCCCBBBBBBDDDEEEBBBCCCCCCDDDCCCBBBAAA@@@@@@@@@AAABBBBBBAAAAAA@@@AAA@@@>>>=========>>>?????????????????????@@@@@@<<<=========>>>>>>>>>??????>>>===<<<<<<===>>>???=========>>>>>>>>>??????<<<===>>>???>>>===;;;:::;;;;;;;;;::::::999999999999999::::::;;;;;;<<<<<<<<<;;;;;;;;;;;;<<<======>>>>>>>>>>>>>>>>>>>>>>>><<<===???AAAAAA@@@>>>======<<<;;;;;;::::::;;;;;;;;;;;;<<<<<<<<<<<<;;;;;;:::;;;;;;;;;;;;;;;::::::888888888888999999999999888888999999999:::::::::888888888777777777666666666666777777777777666666555555555555555555555555111111222222333444444555222444555555444444555777555444444333333333444444333555666666555555666777666666666666555555555555222222333333333444444444222333333444444333333222111111000000111222222333222222222222222222222222333333333333333333333333333333333333333333333333///000111333333333333222111111111222333333444444222222222222111111111111222222222333333444444444111111111111111111111111111111111000000111111111000000111111111111000000111111000000111111222333000000000000111222333333............/////////000///000111222222111000///.........///////////////////////////............///////////////...------------------............------,,,,,,,,,------...------------............------..................,,,,,,,,,------------...------............------,,,,,,,,,------------...+++++++++,,,,,,,,,------------------------------******+++++++++,,,,,,,,,***************++++++,,,+++++++++++++++,,,,,,,,,))))))))))))******+++++++++******************)))RRRQQQQQQRRRRRRSSSTTTUUUSSSSSSSSSRRRRRRRRRRRRRRRYYYXXXWWWVVVUUUSSSRRRRRRSSSUUUXXXYYYXXXWWWXXXXXXZZZYYYXXXWWWVVVVVVWWWXXXVVVWWWXXXYYYYYYWWWUUUTTTVVVWWWXXXWWWVVVWWWYYY[[[UUUUUUTTTTTTTTTTTTUUUUUUQQQQQQPPPPPPPPPPPPQQQQQQRRRRRRRRRRRRSSSSSSSSSSSSPPPPPPOOONNNNNNMMMLLLLLLQQQPPPOOOPPPQQQPPPMMMKKKNNNNNNOOOPPPPPPQQQRRRRRRNNNMMMMMMLLLMMMMMMNNNNNNQQQPPPPPPOOONNNMMMLLLLLLMMMMMMMMMMMMMMMMMMMMMMMMJJJJJJKKKLLLMMMNNNOOOOOOKKKKKKKKKKKKKKKLLLOOOQQQKKKKKKKKKKKKLLLLLLLLLLLLIIIJJJLLLNNNNNNMMMKKKJJJHHHHHHHHHGGGGGGHHHIIIIIIHHHGGGGGGGGGGGGGGGGGGHHHHHHGGGGGGGGGFFFFFFEEEEEEBBBCCCEEEFFFFFFEEEDDDDDDDDDDDDDDDDDDDDDEEEFFFFFFEEEDDDDDDCCCCCCCCCDDDDDDEEEEEEEEEEEEDDDCCCAAAAAA>>>???AAABBBCCCBBBBBBAAACCCCCCDDDDDDDDDDDDCCCCCCBBBCCCCCCCCCBBBBBBDDDEEEBBBBBBCCCCCCCCCBBB@@@??????@@@AAABBBBBBBBBAAA@@@BBB@@@>>>===<<<===>>>???>>>===============>>>???<<<=========>>>>>>?????????>>>===<<<<<<===>>>???======>>>>>>??????@@@@@@<<<===>>>???>>>===;;;999;;;;;;;;;::::::999999999888999:::;;;<<<<<<===>>><<<;;;;;;;;;;;;<<<==============================<<<>>>@@@AAAAAA???===;;;<<<<<<;;;::::::::::::;;;<<<<<<===============<<<999999:::;;;<<<<<<<<<<<<999999:::::::::;;;;;;;;;888888888999999:::::::::888888888888777777777777666777888888888888777777444555555555555555555555222222333444444555666666333444555555444444666777666555444444333333333333222444666666555444555666555555444444444333333333333333333444444555555555222333333444444333333222111111000000111222333333222222222222222222222222333333333333333333333333222222222222222222222222---...000222333333333222000111111222333333444444111111111111000000000000222222222333333444444444111111111111111111111111111111000000000000111111000000111111111111000000111111111000111111222333//////000000111222444444---.........//////000000000111222333333222111000////////////////////////000/////////............//////000000///...---------------.........//////------,,,,,,,,,------...---------.........//////------..................,,,,,,,,,---------......------............------,,,,,,,,,---------......++++++,,,,,,,,,---------------------------------******+++++++++,,,,,,,,,*********)))***++++++,,,++++++++++++++++++++++++(((((())))))*********++++++*********))))))((((((UUURRROOOPPPSSSVVVVVVVVVQQQRRRRRRSSSTTTUUUUUUUUUYYYXXXWWWVVVUUUTTTTTTTTTVVVWWWWWWWWWWWWWWWWWWWWWXXXWWWWWWVVVVVVWWWWWWXXXYYYYYYXXXVVVUUUUUUXXXZZZWWWWWWXXXXXXWWWUUUTTTSSSUUUUUURRROOOOOOSSSTTTQQQRRRPPPNNNOOORRRSSSRRRPPPRRRSSSTTTSSSRRRQQQRRRSSSTTTSSSQQQNNNMMMLLLLLLMMMNNNOOONNNMMMLLLLLLOOOQQQPPPPPPPPPQQQQQQRRRRRRRRRPPPPPPOOONNNMMMKKKJJJIIIMMMNNNOOOOOOOOOOOOMMMMMMLLLLLLLLLKKKKKKKKKKKKKKKLLLLLLMMMNNNNNNNNNNNNMMMNNNOOOOOONNNMMMMMMNNNPPPNNNLLLKKKKKKMMMNNNOOOOOONNNNNNNNNNNNNNNMMMLLLKKKMMMJJJGGGGGGJJJLLLKKKJJJHHHHHHGGGFFFGGGHHHIIIJJJEEEFFFGGGGGGHHHIIIJJJJJJFFFFFFEEEFFFGGGFFFDDDBBBDDDCCCCCCCCCCCCDDDEEEEEEDDDDDDCCCCCCCCCBBBBBBBBBDDDCCCAAABBBBBBCCCAAA@@@BBB@@@???AAADDDEEECCCAAACCCDDDEEEDDDBBBBBBDDDEEEDDDDDDDDDCCCBBBBBBAAAAAADDDCCCAAA@@@???@@@AAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBBAAA???>>>===<<<======@@@@@@@@@@@@@@@@@@@@@@@@>>>??????@@@@@@@@@???????????????>>><<<===???AAA===============<<<;;;;;;;;;<<<===??????===<<<;;;>>>>>>===;;;;;;:::::::::;;;;;;;;;<<<<<<<<<======>>><<<;;;::::::;;;===>>><<<===>>>???????????????>>>>>>>>>>>>>>>>>>>>>>>><<<<<<;;;;;;<<<===???@@@=========<<<;;;;;;;;;:::;;;;;;;;;::::::999999999999888888888999::::::;;;:::999888888888999:::;;;888888888888888999999:::555666888999888777555444666666666666555555555555555444444333333333444444222333333444555666777777666555444333222111111111222333444666666666666555555555444444444333333333444444444444444333333333444444333333333222222222000000000111222222222333444444333222222111111000555444444333222111000000444333333222222333333444111111111111111111111111222222333333333444444444333222000/////////000111444444444444333333222111222222222222111111000000000111111111111222222222000000000000000111111222333222111111222222111///000000000000111111111111//////000000000000////////////000000000000//////000000000000000000000000111111000......---------////////////...,,,+++***+++++++++,,,---...///000......------------......,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,+++***........................,,,,,,,,,,,,,,,,,,,,,,,,------------------------,,,,,,------,,,,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,------...------,,,,,,,,,---------,,,,,,++++++,,,,,,---************))))))((((((,,,++++++******++++++,,,WWWTTTRRRRRRUUUWWWXXXWWWRRRRRRRRRSSSSSSTTTUUUVVVWWWWWWVVVVVVVVVVVVVVVWWWVVVVVVVVVVVVWWWWWWWWWWWWWWWWWWVVVVVVVVVVVVWWWWWWXXXXXXXXXXXXWWWYYY\\\___XXXXXXYYYYYYXXXWWWUUUTTTTTTUUURRROOOQQQUUUVVVSSSRRRPPPOOOPPPRRRSSSRRRPPPQQQRRRSSSRRRQQQPPPPPPRRRSSSRRRPPPOOOMMMMMMMMMNNNOOOOOOOOONNNMMMMMMOOOQQQNNNOOOOOOOOOOOOPPPPPPPPPPPPPPPOOOOOONNNMMMKKKKKKLLLMMMNNNOOOPPPOOONNNMMMLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLMMMNNNNNNNNNNNNNNNLLLMMMNNNNNNMMMMMMOOOQQQNNNMMMLLLLLLMMMNNNOOOOOOMMMMMMNNNNNNNNNMMMLLLLLLLLLJJJGGGGGGJJJKKKKKKIIIHHHHHHGGGGGGGGGHHHIIIJJJGGGGGGHHHHHHHHHHHHHHHHHHFFFFFFEEEFFFGGGGGGDDDBBBBBBCCCCCCCCCCCCDDDDDDDDDCCCCCCCCCCCCBBBBBBBBBBBBDDDBBBAAAAAABBBBBBAAA@@@AAA@@@???AAACCCDDDCCC@@@BBBCCCCCCCCCAAAAAACCCDDDBBBBBBCCCCCCCCCCCCCCCCCCCCCBBBAAAAAA@@@@@@AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA@@@???>>>======>>>>>>@@@@@@@@@@@@@@@@@@@@@@@@??????@@@@@@@@@??????>>>?????????>>>======???AAA>>>>>>>>>>>>>>>===<<<<<<;;;<<<>>>??????>>><<<;;;???>>>===<<<;;;;;;;;;;;;;;;;;;;;;<<<<<<<<<======<<<;;;;;;:::;;;===???@@@===>>>>>>????????????>>>>>>>>>>>>>>>>>>>>>>>>>>>???>>>===<<<;;;<<<<<<===<<<<<<<<<<<<<<<;;;;;;;;;;;;;;;;;;::::::999999999999888888888999999:::;;;999999888888888999:::;;;888777777777777888999999666777888999999777555444666666666666555555555555555444444333333444444444444444444555666666666777555555444333222222222222222333444666666666666555555555555444444444333333444444444444444555555555444444444444333333333222111111111111222222222222333333333222222222222111444333333222222111111111444333333222222333333444111111111111111111111111222222222222333333333333333222111000///000000111333333444444333333222111111111111111000000//////000111111111111222222222000000000000000111111222333111000000111111000////////////000000000111111//////000000000000//////......////////////......////////////////////////111000///......---------....../////////......---,,,,,,,,,,,,------.../////////............//////---------------------------------------,,,,,,+++........................------------------,,,,,,------------------------,,,,,,------,,,,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,------...------,,,,,,------------,,,,,,++++++,,,,,,---+++++++++******))))))))),,,++++++******++++++,,,WWWUUUSSSSSSUUUVVVVVVVVVTTTSSSRRRRRRSSSTTTVVVWWWWWWVVVVVVVVVVVVWWWXXXYYYUUUUUUUUUUUUVVVVVVVVVWWWWWWWWWVVVVVVVVVVVVWWWWWWUUUVVVVVVWWWWWWZZZ^^^aaaYYYYYYYYYYYYXXXWWWVVVVVVTTTTTTSSSPPPRRRWWWXXXUUUQQQPPPOOOPPPRRRSSSRRRQQQPPPRRRRRRQQQPPPOOOPPPQQQQQQPPPPPPOOONNNOOOOOOOOOOOOPPPPPPOOONNNNNNOOOQQQNNNNNNNNNNNNNNNMMMMMMLLLOOOOOOOOOOOOOOONNNMMMMMMLLLMMMNNNOOOPPPOOOOOONNNKKKLLLLLLLLLMMMNNNNNNNNNLLLLLLMMMMMMNNNNNNNNNNNNKKKLLLMMMMMMMMMNNNPPPRRRNNNNNNMMMLLLMMMNNNOOOPPPLLLLLLMMMMMMNNNMMMMMMMMMKKKJJJHHHHHHIIIJJJJJJIIIHHHHHHGGGGGGGGGHHHIIIJJJIIIIIIHHHHHHGGGGGGGGGGGGFFFFFFEEEGGGHHHGGGEEECCCAAAAAACCCDDDDDDDDDCCCBBBCCCCCCBBBBBBBBBAAAAAAAAACCCAAA@@@@@@BBBBBBAAA???AAA@@@@@@AAABBBCCCBBB@@@AAABBBCCCBBB@@@@@@BBBCCCAAAAAABBBBBBCCCDDDDDDEEEAAABBBBBBBBBBBBAAAAAA@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@???>>>>>>??????@@@@@@@@@@@@@@@@@@@@@@@@@@@AAA@@@@@@@@@???>>>>>>>>>???@@@???>>>======???AAA??????????????????>>>======>>>???@@@@@@???>>>===??????>>>>>>===<<<<<<<<<;;;;;;<<<<<<<<<=========<<<;;;;;;<<<===???AAACCC>>>????????????>>>>>>===>>>>>>>>>>>>>>>>>>>>>>>>AAA@@@>>>===;;;;;;::::::;;;;;;;;;<<<<<<<<<<<<<<<;;;;;;::::::::::::999999999888888888888999::::::999888888888888999::::::777777666666666777888888777888999999999888666555666666666555555555555444444444444444444444444444666666666666666666666666444444333333333333444444333333444666666666666666555555555444444444444333444444444555555666666777555555444444444333333333222222222222222111111111111111222222222333333333222222222222222222222222333333222222222222333333111111111111111111111111000111111111222222222222222222111000000000000111333333333333333222222111000000000000000/////////000111111111111222222222000000000000000111111222111000//////000000///............////////////000//////000000000000//////------............------////////////////////////111000///......---......---...//////000000000///------,,,,,,,,,------...000000////////////000000.......................................------,,,........................------..................------------------------,,,,,,------,,,,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,---------------,,,,,,------...---,,,,,,++++++,,,,,,---,,,,,,++++++++++++******,,,++++++******++++++,,,UUUTTTSSSRRRRRRSSSSSSSSSUUUTTTSSSRRRSSSTTTVVVWWWXXXWWWWWWVVVWWWWWWXXXXXXTTTTTTTTTUUUUUUVVVVVVWWWWWWVVVVVVVVVVVVVVVVVVWWWRRRSSSTTTTTTUUUWWW[[[^^^XXXXXXXXXXXXXXXWWWVVVVVVUUUVVVUUURRRTTTXXXWWWTTTQQQQQQQQQQQQRRRRRRRRRRRRQQQRRRSSSRRRPPPOOOPPPQQQOOOOOOOOOOOOPPPPPPQQQQQQPPPQQQQQQQQQOOONNNOOOQQQNNNNNNOOOOOONNNMMMLLLKKKNNNOOOOOOPPPPPPPPPOOOOOOKKKLLLNNNOOOPPPPPPOOONNNKKKKKKLLLMMMNNNOOOOOOPPPMMMMMMMMMMMMMMMNNNNNNNNNLLLMMMNNNMMMLLLLLLNNNPPPNNNNNNNNNMMMLLLMMMNNNPPPKKKKKKLLLMMMMMMNNNMMMMMMJJJJJJIIIIIIIIIIIIIIIHHHGGGGGGGGGHHHHHHHHHIIIIIIHHHGGGGGGGGGGGGGGGGGGGGGFFFEEEFFFGGGHHHHHHFFFCCC???AAACCCDDDEEEDDDBBBAAABBBBBBBBBBBBAAAAAAAAAAAABBBAAA@@@@@@AAABBBAAA???@@@@@@@@@AAABBBBBBAAA@@@BBBCCCCCCBBBAAAAAABBBDDDBBBBBBBBBCCCCCCCCCDDDDDD@@@AAABBBCCCCCCBBBAAA@@@@@@@@@@@@@@@@@@@@@@@@@@@????????????@@@@@@AAAAAA@@@@@@@@@@@@@@@@@@@@@@@@BBBAAA@@@???>>>>>>>>>===???@@@@@@>>>======???AAA???@@@@@@AAA@@@@@@??????>>>???@@@@@@@@@@@@???>>>????????????>>>>>>======<<<<<<<<<<<<=====================>>>???@@@BBBCCC???????????????>>>===<<<>>>>>>>>>>>>>>>>>>>>>>>>@@@???>>>===<<<;;;:::::::::;;;;;;;;;<<<=========::::::::::::::::::::::::999888888888888888999999888888888888888999999:::666666666666666777777888888999999999999888777777666666555555555444444444333333444444444444444444777777777777777666666666333333333333333444555555333444555555666777777777555555555555444444444444333444444555666777888888555555555444444444333333333333333222222111111111000000111222333333444444111111111222222333333333333333222222222222333333111111111111111111111111000000000000111111111111222222111111111000000000222222333333333222222111111111111111000000000000000000111111111222222222000000000000000111111222111///......//////...------------.........////////////000000000000//////---......//////......---////////////////////////000000///...............//////000000000000000///......---,,,,,,,,,------//////............//////------------............///////////////......---....................................////////////------------------------,,,,,,------,,,,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,,,,------------,,,,,,,,,---......---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++******++++++,,,TTTTTTTTTSSSSSSRRRSSSSSSUUUTTTTTTSSSSSSTTTUUUVVVYYYYYYXXXWWWVVVUUUUUUUUUSSSSSSTTTUUUUUUVVVWWWWWWVVVVVVVVVUUUUUUVVVVVVVVVTTTTTTTTTTTTSSSUUUYYY[[[WWWWWWWWWVVVVVVVVVVVVVVVXXXYYYWWWSSSTTTWWWUUUQQQQQQQQQRRRRRRRRRRRRRRRSSSRRRSSSTTTSSSQQQPPPQQQRRRNNNNNNOOOPPPQQQQQQQQQRRRPPPQQQRRRQQQOOONNNOOOPPPNNNOOOPPPPPPPPPNNNMMMLLLNNNNNNOOOPPPPPPPPPOOOOOOLLLMMMNNNOOOPPPOOOOOONNNKKKKKKLLLMMMNNNOOOOOOPPPMMMMMMLLLLLLLLLMMMNNNOOOOOOPPPOOONNNKKKJJJKKKLLLMMMNNNNNNMMMKKKKKKMMMOOOJJJKKKLLLMMMMMMMMMMMMMMMIIIJJJJJJIIIHHHHHHHHHHHHGGGGGGHHHHHHHHHIIIIIIIIIEEEEEEFFFGGGGGGHHHIIIIIIFFFEEEFFFGGGHHHHHHFFFDDD@@@AAACCCEEEEEEDDDCCCBBBCCCCCCBBBBBBBBBAAAAAAAAABBBAAA@@@@@@BBBBBBBBB@@@@@@AAABBBBBBAAAAAA@@@AAACCCDDDDDDCCCBBBBBBCCCEEEDDDDDDCCCCCCCCCBBBBBBBBB@@@AAACCCCCCDDDCCCBBBAAABBBBBBBBBBBBBBBBBBBBBBBB??????@@@@@@AAAAAABBBBBB@@@@@@@@@@@@@@@@@@@@@@@@BBBBBB@@@???>>>>>>>>>>>>@@@@@@@@@???===>>>@@@BBB@@@@@@AAAAAAAAAAAA@@@@@@??????@@@@@@@@@@@@??????>>>??????@@@??????>>>===<<<<<<<<<=========>>>>>>???????????????@@@@@@AAA???????????????>>>===<<<>>>>>>>>>>>>>>>>>>>>>>>><<<===============<<<<<<:::;;;;;;;;;<<<=========::::::::::::::::::::::::999999888777777888888888777777888888999999999999666666666666666777777888999999999999999888777777555555555555444444444444222333444555555555444444777777777777777666666666333333333333444555666666444444555555666777777888666666555555555444444444333444444555666777888888555555444444444333333333444333333333222222111111000000111222333444444555111111111222222333333444333222222111111222222333111111111111111111111111//////000000000111111111222222222222111111111000111111222333333222222222222222222222222222222222000000111111111222222222000000000000000111111222000///......//////...,,,------------............//////000000000000///////////////000000/////////........................000//////............///111111111111000///...---......---,,,,,,,,,------...------,,,,,,------...++++++,,,,,,,,,---------//////000000//////...---////////////////////////.........//////000000000------------------------,,,,,,------,,,,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,,,,------,,,,,,,,,,,,,,,---...///---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,---,,,++++++******++++++,,,TTTUUUVVVVVVUUUTTTUUUVVVTTTUUUUUUUUUUUUUUUUUUUUUYYYYYYWWWVVVUUUTTTTTTTTTSSSTTTTTTUUUVVVWWWXXXXXXVVVVVVUUUUUUUUUUUUVVVVVVWWWWWWWWWUUUUUUVVVYYY[[[WWWVVVVVVUUUUUUUUUVVVVVVXXXYYYWWWTTTTTTVVVTTTOOOPPPRRRSSSSSSRRRQQQSSSTTTSSSTTTTTTTTTRRRQQQRRRSSSNNNNNNPPPQQQRRRRRRRRRRRROOOQQQRRRQQQOOONNNNNNNNNNNNOOOQQQRRRRRRPPPNNNMMMNNNNNNOOOOOOOOOOOOOOONNNMMMNNNOOOOOOOOOOOOMMMMMMKKKLLLLLLLLLMMMNNNNNNNNNNNNMMMLLLLLLLLLMMMOOOPPPQQQQQQPPPNNNKKKIIIIIIJJJLLLMMMNNNLLLIIIHHHKKKNNNKKKKKKLLLLLLMMMLLLLLLLLLHHHJJJKKKJJJHHHGGGGGGGGGFFFGGGHHHIIIIIIIIIHHHHHHDDDDDDEEEFFFGGGHHHIIIIIIFFFEEEFFFGGGIIIIIIGGGEEEBBBBBBDDDEEEEEEEEEDDDCCCDDDDDDCCCCCCCCCBBBBBBBBBBBBAAA@@@AAACCCDDDCCCBBBAAACCCDDDCCCBBBAAAAAABBBCCCDDDEEEDDDBBBBBBDDDEEEEEEDDDDDDCCCBBBBBBAAAAAAAAABBBBBBCCCCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBBBB???@@@AAABBBBBBBBBBBBBBB@@@@@@@@@@@@@@@@@@@@@@@@BBBAAA???>>>>>>>>>??????@@@AAA@@@???>>>>>>@@@BBB???@@@AAAAAAAAAAAAAAAAAA????????????????????????===>>>???@@@@@@???>>>===<<<<<<=========>>>>>>>>>@@@@@@@@@@@@@@@@@@@@@???>>>????????????>>>>>>===>>>>>>>>>>>>>>>>>>>>>>>>:::;;;<<<===>>>>>>>>>>>>;;;;;;;;;<<<<<<<<<<<<<<<999999::::::::::::;;;;;;999999888777777777777888666777888888999999888888777777666666666777888888999999888888777777777777555555555444444444444333111222444555666555555444666666666666666666666666444444333333444555666666555555555555666777888999666666666555555555444444444444444555555666666777444444333333333222222222333333333333333222222222000000111222333333444444111111111222222333333333222222111111111111222222111111111111111111111111///000000000111111111111222222333333222222111000000111222222222222222222222222222333333333333333000111111111111222222222000000000000000111111222000///......//////...------------............/////////000000000000////////////000000000000//////........................//////............//////111111111000///...,,,,,,------,,,,,,,,,------...---,,,,,,,,,,,,,,,,,,---***++++++,,,,,,---------///////////////......---////////////////////////------......///000000000------------------------,,,,,,------,,,,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,------,,,,,,,,,,,,---......///---,,,,,,++++++,,,,,,---++++++,,,,,,,,,,,,------,,,++++++******++++++,,,RRRTTTVVVVVVUUUTTTVVVXXXSSSTTTVVVWWWWWWVVVTTTSSSWWWVVVUUUTTTTTTTTTTTTTTTTTTTTTUUUVVVWWWXXXYYYYYYVVVVVVUUUUUUUUUUUUVVVVVVVVVVVVVVVUUUTTTUUUXXX[[[XXXWWWVVVUUUVVVVVVWWWXXXVVVWWWVVVSSSTTTVVVTTTOOOPPPRRRTTTSSSQQQQQQSSSUUURRRSSSTTTSSSQQQPPPQQQRRRNNNOOOPPPQQQRRRRRRQQQQQQNNNPPPQQQQQQOOOMMMLLLMMMMMMNNNPPPRRRRRRQQQOOONNNMMMNNNNNNNNNNNNNNNMMMMMMNNNOOOPPPPPPOOONNNLLLKKKLLLLLLLLLLLLLLLLLLLLLLLLNNNMMMLLLKKKLLLMMMOOOPPPOOOPPPOOOMMMKKKIIIJJJKKKJJJMMMNNNKKKGGGFFFJJJMMMLLLLLLLLLLLLLLLLLLKKKJJJGGGJJJLLLKKKHHHFFFFFFGGGFFFGGGHHHIIIIIIIIIHHHHHHEEEEEEFFFFFFGGGGGGGGGHHHFFFEEEFFFGGGIIIIIIHHHFFFDDDDDDDDDEEEEEEEEEEEEFFFEEEEEEDDDDDDDDDCCCCCCCCCCCCBBBAAABBBDDDEEEDDDCCCBBBDDDFFFEEEBBBAAABBBCCCCCCCCCDDDCCCBBBAAACCCEEECCCCCCCCCCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBCCCDDDDDDAAAAAAAAAAAAAAAAAAAAAAAA@@@AAABBBCCCCCCBBBBBBAAA@@@@@@@@@@@@@@@@@@@@@@@@AAA@@@???======>>>@@@AAA@@@AAAAAA???>>>>>>@@@BBB??????@@@AAAAAAAAAAAAAAA??????>>>>>>>>>>>>??????<<<===>>>@@@@@@???===<<<<<<=========>>>>>>>>>>>>>>>>>>???@@@@@@@@@@@@@@@===>>>>>>????????????>>>>>>>>>>>>>>>>>>>>>>>>>>>::::::<<<===>>>>>>>>>===<<<<<<<<<<<<<<<;;;;;;;;;999999999::::::;;;;;;;;;999999888777777777777777555666777888999888888777888777777777777888999999888888777777666666666777555555555444444444333333000222444555666666555444444444444555666666666777555444444444444555555666666555555555666777888999666666666666555555555555444444444444444555555555333333222222222111111111222222333333333333333333111111111222222333333333222222222222222222333333222222111111111111222222111111111111111111111111000000000111111111222222222222333333333222111000000000111222222222222222111111222222222333333333000111111111111222222222000000000000000111111222111000...///000000///------............///////////////000000000000//////...//////////////////...........................//////............/////////////////////...---,,,,,,,,,,,,,,,------...///---------,,,,,,---------++++++,,,,,,---......///...////////////...------////////////////////////,,,,,,---......///000000------------------------,,,,,,------,,,,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,------,,,,,,,,,,,,---...//////---,,,,,,++++++,,,,,,---***+++++++++,,,,,,,,,,,,,,,++++++******++++++,,,OOORRRTTTUUUSSSSSSTTTWWWSSSTTTWWWXXXXXXVVVTTTRRRTTTTTTSSSSSSTTTTTTUUUVVVTTTUUUUUUVVVXXXYYYYYYZZZVVVUUUUUUUUUUUUUUUUUUVVVRRRSSSSSSRRRRRRTTTWWWZZZYYYXXXWWWVVVVVVWWWYYYYYYTTTUUUUUUSSSTTTWWWUUUQQQPPPRRRTTTTTTQQQQQQSSSUUUQQQRRRRRRRRRPPPOOOPPPQQQNNNOOOQQQRRRRRRRRRQQQPPPNNNOOOQQQQQQNNNLLLKKKLLLKKKMMMOOORRRRRRQQQOOONNNNNNNNNNNNNNNNNNMMMLLLKKKOOOPPPPPPPPPOOOMMMKKKJJJLLLLLLLLLLLLKKKKKKKKKKKKNNNMMMLLLKKKKKKMMMOOOPPPNNNNNNNNNMMMKKKJJJKKKLLLIIILLLMMMKKKFFFEEEIIIMMMLLLLLLMMMLLLLLLKKKJJJJJJGGGJJJLLLKKKHHHEEEEEEFFFFFFGGGHHHIIIJJJIIIHHHHHHGGGGGGGGGFFFFFFFFFFFFFFFFFFEEEFFFHHHIIIJJJHHHFFFEEEEEEEEEDDDEEEFFFGGGGGGEEEEEEEEEEEEDDDDDDDDDDDDDDDBBBBBBCCCEEEFFFEEEDDDBBBEEEGGGFFFCCCAAABBBDDDBBBBBBCCCBBBAAA@@@BBBDDDAAAAAABBBBBBCCCDDDDDDDDDCCCBBBAAAAAABBBCCCDDDEEE@@@@@@@@@@@@@@@@@@@@@@@@AAAAAACCCCCCCCCBBBAAA@@@@@@@@@@@@@@@@@@@@@@@@@@@AAA@@@>>>======???AAABBB@@@AAAAAA@@@>>>>>>@@@BBB>>>???@@@@@@AAAAAAAAAAAA??????>>>>>>>>>>>>??????;;;<<<>>>??????>>>===<<<============>>>>>>>>>>>>;;;<<<>>>???AAAAAABBBBBB<<<===>>>???????????????>>>>>>>>>>>>>>>>>>>>>>>>:::;;;===>>>>>>>>>===<<<=========<<<<<<;;;;;;:::999999999::::::;;;;;;;;;999999888777777666777777555666777999999888888777888888888888888999999:::888777777666666666666666555555444444444333333333000111444666666666555444222333333444555666777777666555555444444444555555666666555555666777999:::777666666666555555555555444444444444444444333333222222222111111111000000222222222333333444444444111222222222222333333333222222222222222222222222222222111111111111222222111111111111111111111111111111111111222222222222222222333444333222111000///000111222222222222222000000111111222222222222000111111111111222222222000000000000000111111222222000//////000000///............////////////000//////000000000000//////---..................---........................//////.........//////000,,,---..................+++++++++,,,---...///000.........------.........,,,,,,------...///000000...............------,,,000000000000000000000000,,,,,,,,,---...//////000------------------------,,,,,,---------,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,---------+++++++++,,,---...///000---,,,,,,++++++,,,,,,---*********++++++,,,,,,,,,,,,++++++++++++++++++,,,QQQRRRRRRSSSTTTUUUUUUUUUUUUUUUUUUUUUUUUTTTSSSRRRVVVWWWXXXWWWTTTQQQPPPQQQSSSSSSTTTUUUUUUVVVWWWWWWVVVUUUTTTUUUWWWXXXWWWVVVSSSSSSTTTTTTUUUUUUUUUVVVUUUVVVWWWXXXXXXWWWVVVVVVTTTVVVYYYYYYWWWUUUTTTTTTXXXVVVTTTRRRQQQQQQRRRSSSTTTRRROOONNNOOOOOOOOOOOOMMMNNNNNNOOOOOONNNNNNMMMQQQPPPOOONNNMMMMMMMMMMMMNNNOOOPPPPPPQQQQQQQQQQQQPPPOOONNNLLLLLLLLLMMMMMMMMMOOOPPPPPPOOOMMMMMMMMMLLLMMMNNNNNNNNNLLLKKKJJJKKKKKKLLLMMMNNNNNNOOOOOOKKKKKKLLLLLLLLLLLLKKKKKKLLLJJJIIIIIIJJJMMMNNNOOONNNMMMMMMLLLKKKJJJJJJIIIIIIKKKMMMLLLJJJHHHGGGGGGHHHHHHHHHHHHHHHHHHHHHHHHIIIFFFDDDDDDGGGHHHGGGEEEGGGFFFFFFEEEEEEEEEEEEEEEGGGFFFEEECCCCCCBBBBBBBBBGGGGGGFFFEEEDDDCCCBBBBBBBBBCCCEEEFFFFFFFFFEEEDDDDDDDDDCCCBBBBBBBBBBBBCCCDDDDDDEEEEEEEEECCCBBBAAABBBCCCCCCDDDEEEFFFFFFFFFFFFFFFEEEDDDCCCBBBAAAAAACCCCCCBBBAAA@@@@@@???>>>???@@@AAABBBBBBBBBAAA@@@DDDBBB@@@>>>======>>>??????????????????@@@@@@@@@CCC@@@>>>???BBBEEEEEEDDDBBBAAAAAA@@@?????????@@@@@@@@@??????>>>======<<>>>>>======>>>@@@@@@@@@????????????>>>@@@>>>======>>>??????>>>@@@???>>>>>>===>>>>>>???>>>>>>>>>>>>>>>======<<<;;;;;;<<<<<<===>>>>>>>>>===<<<;;;:::::::::::::::;;;:::999999;;;<<<<<<<<<<<<;;;:::999888888888888888888888888777777777777888888888777777777777777888777666444444555555666666555444333222333444444333333333444444444555555444444444444444444444444222222333333444555666666666555555444444666777888666666555555555555666666555444444333333444444555444333333222111111111222222222111111111222444555333333444444444333333222000111111111111000000///333333333222111000//////111111111222222111111111333333333333333333333333111111222222222333333333111111222222222333333333111111111111111111111111000111222333333222111000////////////000000000000///000111222222111000///......//////000000111111.........///////////////,,,---...///000000000000---.........,,,,,,...000...//////000//////...---........................------,,,------...///000......------------......---------............///000///...------------------///111222000///...///---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,------------------------------,,,,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,+++,,,---...////////////------,,,,,,,,,+++++++++++++++++++++++++++++++++*********++++++,,,,,,,,,QQQRRRRRRSSSTTTTTTUUUUUURRRSSSSSSTTTTTTTTTSSSSSSVVVWWWWWWUUUSSSQQQRRRSSSVVVUUUSSSSSSSSSUUUWWWYYYVVVUUUTTTUUUWWWWWWVVVUUURRRRRRRRRSSSSSSSSSTTTTTTUUUVVVWWWXXXXXXWWWWWWVVVSSSUUUXXXXXXVVVTTTSSSSSSXXXWWWVVVTTTSSSSSSTTTTTTRRRQQQPPPPPPQQQRRRRRRQQQNNNNNNOOOOOOOOOOOONNNNNNQQQPPPOOONNNMMMMMMMMMMMMLLLMMMNNNNNNOOOOOOOOONNNNNNMMMLLLKKKKKKKKKKKKLLLMMMOOOPPPPPPNNNMMMMMMMMMKKKLLLMMMMMMMMMLLLKKKJJJKKKLLLLLLMMMNNNNNNOOOOOOLLLLLLMMMMMMMMMMMMLLLLLLLLLKKKIIIIIIJJJMMMNNNOOOMMMMMMLLLLLLKKKKKKJJJJJJIIIKKKLLLLLLJJJHHHGGGHHHHHHHHHHHHHHHHHHHHHHHHHHHIIIGGGEEEFFFHHHIIIHHHFFFEEEDDDDDDDDDEEEFFFGGGGGGFFFEEEDDDCCCCCCCCCCCCCCCEEEEEEDDDDDDCCCBBBBBBBBBBBBCCCDDDEEEFFFEEEEEEDDDCCCCCCBBBBBBCCCDDDEEEEEEDDDEEEFFFFFFFFFEEECCCBBBCCCCCCDDDDDDEEEFFFFFFGGGGGGFFFFFFEEEDDDCCCBBBAAAAAAAAAAAAAAAAAAAAAAAAAAA@@@@@@AAABBBBBBAAAAAA@@@CCCBBB@@@>>>======>>>???@@@@@@@@@???????????????BBB@@@???@@@CCCEEEDDDCCCBBBAAAAAA@@@??????@@@@@@AAAAAA@@@??????>>>>>>===;;;;;;;;;;;;<<<===>>>????????????>>>>>>>>>>>>===AAA@@@>>>???@@@AAA@@@??????????????????>>>>>>>>>>>>>>>??????>>>>>>===<<<::::::;;;;;;<<<<<<<<<======<<<;;;;;;:::::::::;;;;;;:::999999;;;<<<<<<;;;;;;;;;:::999888888888888888888888777777777666666888888888888888888888888888777666555444555666666666555444333333333444444222222222333333333444444444444444444444444444444222333333444444555555555666666555444555666777888666666555555555555666666444333333222222333333444444333333222111111222222222222111111111222444444222222333333333333222222000000111111111111111000444444444333333222000000111222222333333222222111333333333333333333333333111111222222222333333333111111111222222222333333111111111111111111111111000111222222222222111000............///////////////000111111111111000///000000000000///////////////////////////.........,,,---...///000000000000.../////////......000222000000//////.........---------------------------------,,,------...///000......------------......---------............/////////...------------------///111111000/////////------,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,------------------------,,,,,,+++++++++*********,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,---............------------,,,,,,,,,+++++++++++++++++++++++++++******+++++++++,,,,,,,,,RRRRRRRRRSSSTTTTTTUUUUUUPPPQQQRRRTTTTTTTTTTTTSSSUUUUUUUUUSSSRRRRRRSSSUUUYYYVVVSSSQQQQQQTTTWWWYYYWWWVVVUUUUUUVVVWWWVVVTTTQQQQQQQQQQQQRRRRRRRRRRRRTTTUUUVVVWWWXXXWWWVVVVVVRRRUUUWWWWWWVVVTTTSSSSSSUUUUUUUUUUUUUUUTTTSSSSSSOOOPPPQQQRRRSSSSSSSSSSSSOOOOOOPPPPPPPPPPPPOOOOOOPPPPPPOOONNNMMMMMMMMMMMMMMMMMMNNNOOOOOOOOONNNNNNNNNNNNMMMLLLLLLLLLMMMMMMMMMOOOPPPPPPNNNMMMMMMNNNJJJKKKKKKLLLLLLLLLLLLKKKLLLLLLLLLMMMNNNNNNOOOOOOLLLLLLMMMMMMMMMMMMLLLLLLLLLKKKJJJJJJJJJLLLNNNOOOLLLLLLLLLLLLKKKKKKKKKKKKIIIKKKLLLKKKIIIHHHGGGHHHHHHHHHHHHHHHHHHHHHHHHHHHIIIHHHFFFFFFHHHIIIHHHGGGCCCCCCCCCDDDEEEFFFHHHHHHEEEDDDDDDCCCCCCCCCDDDDDDCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDEEEEEEEEEEEEEEEBBBBBBCCCCCCDDDFFFGGGHHHEEEFFFFFFGGGGGGFFFDDDDDDDDDDDDEEEEEEFFFFFFGGGGGGGGGGGGFFFEEEDDDDDDCCCBBB@@@@@@@@@AAAAAABBBBBBBBB@@@@@@AAAAAAAAAAAA@@@@@@BBBAAA@@@>>>>>>>>>???@@@AAAAAA@@@@@@??????>>>>>>AAA@@@@@@AAADDDDDDCCCBBBBBBAAAAAA@@@@@@@@@@@@@@@BBBBBBAAAAAA@@@@@@??????;;;;;;;;;;;;<<<===>>>>>>???>>>>>>>>>>>>=========@@@???>>>>>>@@@@@@???>>>===>>>???@@@@@@???>>>>>>>>>????????????>>>======<<<<<<<<<<<<===============<<<;;;;;;:::;;;;;;;;;;;;:::999999;;;<<<<<<;;;::::::999999888999999999888888777777777777666666777777888888999999::::::888777666555555555666666666555444333333333333444111111111222222222333333444444444444444444444444444444444444444444444444666666555555555666777888777666666555555666666777333333222222222222333333444333333222222222222222333222111111111222333444111111222222222222222111///000111222222222222222444444444444444333222111222333333444444333333222222222222222222222222222111111222222222333333333111111111222222222222333000000000000000000000000000111222222222222111000---------........./////////000000111111000000///111111111000///.........000000//////......------,,,---...///000000000000...///000000000000333555222111///...---------...,,,,,,,,,,,,,,,,,,,,,,,,------,,,------...///000......------------......---------............///.........------------------///111111///...///000......------------......------------------------,,,,,,,,,,,,,,,,,,,,,,,,+++++++++*********))))))++++++,,,,,,,,,,,,,,,,,,******+++,,,------------......---------,,,,,,,,,++++++++++++++++++++++++***++++++++++++,,,,,,,,,RRRRRRSSSSSSTTTTTTTTTTTTQQQRRRTTTUUUUUUTTTSSSRRRTTTTTTSSSRRRQQQRRRUUUXXXXXXVVVTTTSSSSSSTTTVVVWWWWWWVVVTTTUUUVVVVVVUUUTTTQQQQQQRRRRRRRRRRRRRRRRRRSSSTTTUUUWWWWWWWWWVVVUUURRRUUUWWWXXXVVVTTTTTTTTTPPPQQQSSSTTTTTTRRRQQQOOONNNPPPRRRSSSSSSRRRQQQRRROOOPPPPPPQQQQQQPPPPPPOOOPPPOOONNNNNNMMMMMMMMMNNNOOOPPPPPPQQQQQQPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPQQQNNNOOOPPPOOONNNMMMMMMNNNJJJJJJKKKKKKLLLLLLLLLLLLLLLLLLMMMMMMMMMNNNNNNNNNKKKLLLLLLLLLLLLLLLLLLKKKLLLLLLLLLJJJJJJKKKNNNPPPKKKKKKKKKKKKLLLLLLLLLLLLIIIJJJKKKJJJHHHGGGHHHIIIGGGGGGGGGGGGGGGGGGGGGGGGHHHGGGFFFFFFGGGGGGGGGGGGCCCCCCCCCDDDDDDEEEGGGGGGDDDCCCCCCCCCCCCDDDDDDEEEAAABBBBBBCCCCCCDDDEEEEEECCCDDDDDDEEEEEEEEEEEEEEEDDDDDDDDDDDDEEEFFFGGGHHHDDDEEEFFFFFFFFFEEEDDDDDDEEEEEEEEEEEEFFFFFFGGGGGGGGGGGGGGGFFFEEEDDDDDDDDDAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA@@@@@@@@@???AAAAAA@@@?????????@@@@@@BBBBBBAAA@@@??????>>>>>>@@@@@@AAACCCDDDDDDBBBAAABBBAAAAAA@@@@@@@@@AAAAAACCCCCCBBBBBBAAAAAAAAAAAA@@@@@@???>>>============????????????>>>>>>>>>>>>===<<<;;;<<<===>>><<<;;;<<<>>>@@@AAAAAA@@@???>>>??????@@@@@@??????>>>===@@@@@@@@@???????????????<<<<<<;;;;;;;;;;;;<<<<<<<<<:::999999:::;;;;;;:::999999999888999999::::::888777777777666666666666777777888999::::::;;;;;;777777777666666666666666555555444444333333333333222222222222333333333333444444444444444444444444444444444444444444333333666666666666666777777777777777666666666666777777444333333222222333333444444333333222222222333333333222111111111222333444000000111222222222111111///000111222333333333333333333444444333222111111333444444444444444444333111111111111111111111111111111222222222333333333111111111111222222222222000000000000000000000000111111111222222111111111.........////////////000/////////000000000000000111000000000/////////...111111000///...------,,,------...//////000//////---...000000000111333555333222///---,,,,,,---...------------------------------,,,------...///000......------------......---------............///------.........------------...000000///...///000//////............//////........................,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++************+++++++++++++++,,,,,,,,,)))***+++,,,,,,,,,,,,,,,.........---------,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++SSSSSSSSSSSSSSSTTTTTTTTTUUUVVVWWWXXXWWWUUURRRQQQRRRSSSRRRQQQQQQRRRUUUXXXUUUUUUVVVVVVVVVUUUTTTTTTVVVUUUTTTTTTVVVVVVUUUTTTSSSSSSSSSSSSSSSSSSSSSSSSSSSTTTUUUVVVVVVUUUTTTSSSRRRUUUWWWXXXWWWUUUUUUUUUNNNPPPRRRSSSTTTRRRQQQOOONNNQQQSSSSSSPPPOOONNNOOOOOOPPPPPPQQQQQQPPPPPPOOOOOOOOONNNNNNMMMMMMNNNNNNPPPPPPPPPQQQQQQPPPPPPOOOOOOOOOPPPPPPQQQQQQQQQQQQNNNOOOPPPOOOMMMLLLMMMOOOJJJKKKKKKKKKLLLLLLMMMMMMMMMMMMMMMMMMMMMNNNNNNNNNJJJKKKKKKLLLLLLKKKKKKJJJLLLMMMMMMKKKJJJJJJNNNQQQKKKKKKKKKKKKLLLLLLLLLLLLIIIJJJJJJIIIHHHGGGHHHIIIGGGGGGGGGGGGGGGGGGGGGGGGFFFFFFFFFEEEEEEEEEFFFFFFEEEEEEDDDDDDDDDDDDDDDEEEDDDCCCCCCCCCCCCDDDDDDEEEAAABBBCCCDDDEEEFFFGGGGGGDDDDDDDDDDDDDDDEEEEEEFFFGGGFFFFFFEEEEEEEEEFFFFFFBBBCCCDDDEEEEEEEEEDDDCCCEEEEEEEEEEEEEEEFFFFFFFFFGGGGGGFFFFFFEEEEEEDDDDDDCCCCCCBBBAAAAAA@@@??????AAAAAA@@@@@@????????????@@@@@@@@@@@@@@@@@@AAAAAACCCBBBBBBAAA@@@???>>>>>>???AAACCCCCCCCCBBBBBBAAABBBAAAAAA@@@AAAAAABBBBBBCCCCCCCCCBBBBBBBBBBBBBBBAAA@@@???>>>>>>===>>>>>>AAAAAA@@@@@@@@@@@@??????<<<<<<<<<===>>>>>><<<:::<<<>>>@@@AAABBBAAA???>>>@@@@@@@@@@@@@@@??????>>>AAAAAA@@@@@@??????>>>>>><<<<<<;;;;;;;;;<<<<<<===<<<:::888999:::;;;:::999999999999888999999::::::777777777666666666666555777777888999::::::;;;;;;777777777777777666666666444444444444444333333333333333333333444444444444444444444444444444444444444444444444444444333333666666666777777777777777777777666666666666777777555555444444444444555555444333333222333333444444444333222111111111222333///000111222222222222222000000111333444444444444111222222222222111111000333444444555555444444333111111111111111111111111111111222222222333333333000000111111111222222222000000000000000000000000222111111111111111111222///000000000000111111111....../////////000000111.../////////000000000111111111000///...------,,,---...//////////////////+++---.........///111444333111///---,,,---...///////////////////////////------,,,------...///000......------------......---------............///------.../////////...------...//////......///111000//////......//////000........................,,,,,,,,,,,,,,,,,,,,,,,,---,,,,,,,,,,,,+++++++++*********++++++,,,,,,,,,******++++++,,,+++++++++......---------,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++SSSSSSSSSSSSSSSSSSTTTTTTWWWXXXYYYYYYXXXUUURRRPPPQQQRRRSSSRRRQQQRRRUUUWWWRRRTTTVVVWWWXXXVVVTTTSSSUUUTTTSSSTTTVVVVVVVVVUUUUUUUUUUUUUUUTTTTTTTTTTTTUUUUUUVVVVVVUUUTTTRRRQQQQQQTTTVVVWWWVVVUUUTTTTTTOOOQQQSSSTTTUUUTTTSSSRRROOORRRTTTRRROOOLLLMMMOOOOOOOOOPPPPPPPPPPPPOOOOOOOOOOOONNNNNNMMMNNNNNNOOONNNNNNOOOOOOOOONNNMMMMMMKKKLLLMMMNNNOOOPPPPPPOOOOOOOOOPPPNNNLLLLLLMMMOOOMMMLLLLLLLLLLLLLLLMMMNNNMMMMMMMMMMMMMMMMMMMMMMMMKKKKKKLLLLLLLLLLLLKKKKKKMMMNNNNNNLLLJJJJJJMMMQQQLLLLLLLLLLLLKKKKKKKKKKKKHHHIIIIIIHHHGGGGGGHHHJJJGGGGGGGGGGGGGGGGGGGGGGGGDDDEEEFFFEEECCCCCCEEEFFFFFFEEEDDDDDDCCCCCCCCCDDDEEEDDDDDDCCCCCCCCCDDDDDDBBBBBBCCCDDDEEEFFFGGGGGGDDDDDDDDDDDDDDDEEEFFFFFFGGGGGGFFFEEEEEEEEEEEEEEEAAABBBDDDEEEEEEDDDCCCCCCDDDDDDDDDDDDDDDEEEEEEEEEFFFFFFEEEEEEEEEDDDDDDDDDDDDCCCCCCBBB@@@??????>>>BBBAAA@@@??????>>>????????????@@@@@@AAAAAABBBBBBBBBBBBAAAAAA@@@@@@??????@@@BBBCCCCCCBBBAAABBBBBBAAAAAAAAAAAAAAABBBBBBCCCCCCCCCBBBBBBBBBBBBBBBBBB============>>>???@@@@@@BBBBBBAAAAAAAAA@@@@@@@@@???>>>>>>@@@AAAAAA???======>>>???AAAAAAAAAAAA@@@@@@AAAAAAAAAAAA@@@??????@@@??????>>>===<<<<<<;;;<<<<<<<<<;;;<<<<<<===>>><<<:::888888999:::999888::::::999999888999999999777777666666666666555555777777888888999999::::::777777888888888777666555444444555555444444333222333333444444444555555555444444444444444444444444444444444444444444444444555666777888888888777777888777777666666777777888666666555555555555666666333333333333333444444555444333222111111111222333000000111222333333333333111222333333444444444444111111111222222111111000333444444555555444444333222222222222222222222222111111222222222333333333000000000111111111111222111111111111111111111111222222111000000111222222000000111111111222222222............///000111111.........///000111111111000000//////......------......///////////////...+++,,,------------///111111000///...---...//////////////////////////////------,,,------...///000......------------......---------............///---...///000111000///...,,,---......------000111//////............//////---------------------------------------------------------,,,,,,,,,++++++))))))******+++,,,,,,,,,***++++++,,,,,,+++++++++------,,,,,,,,,+++++++++++++++++++++++++++++++++,,,,,,,,,++++++++++++***TTTSSSSSSSSSSSSSSSSSSSSSTTTVVVXXXYYYXXXUUURRRPPPPPPRRRSSSSSSRRRRRRTTTUUUSSSTTTUUUVVVVVVVVVVVVVVVSSSRRRRRRSSSVVVWWWWWWVVVVVVVVVUUUUUUUUUTTTTTTTTTVVVVVVVVVVVVTTTRRRPPPOOOOOOQQQTTTUUUTTTSSSRRRSSSOOOPPPQQQSSSTTTTTTSSSSSSOOORRRTTTRRRNNNMMMPPPSSSNNNNNNOOOOOOOOOOOONNNNNNOOONNNNNNMMMNNNNNNOOOOOONNNOOOOOOOOONNNNNNMMMLLLIIIKKKLLLNNNOOOPPPOOOOOOOOOPPPOOONNNLLLLLLNNNOOOOOONNNMMMLLLLLLMMMNNNNNNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNNNNNNNNNNNMMMMMMMMMOOOOOOMMMIIIIIIMMMRRRMMMMMMLLLLLLKKKKKKJJJJJJHHHIIIIIIHHHFFFGGGIIIJJJFFFFFFFFFFFFFFFFFFFFFFFFDDDFFFGGGFFFDDDCCCEEEHHHDDDDDDCCCCCCCCCDDDDDDEEEFFFEEEDDDCCCCCCCCCCCCCCCAAABBBBBBCCCDDDEEEFFFFFFEEEDDDDDDCCCDDDEEEFFFGGGEEEEEEDDDDDDDDDEEEFFFFFFBBBCCCDDDEEEFFFEEEEEEDDDDDDCCCCCCCCCCCCCCCCCCCCCEEEEEEDDDDDDDDDDDDCCCCCCBBBBBBBBBAAAAAA@@@@@@@@@BBBAAA@@@???>>>>>>>>>???>>>???@@@AAABBBBBBBBBBBBAAAAAAAAAAAAAAAAAAAAAAAAAAACCCDDDBBB@@@@@@BBBDDDAAAAAAAAAAAAAAABBBCCCCCCBBBBBBBBBBBBBBBBBBBBBBBB>>>>>>>>>>>>???@@@AAABBBAAAAAAAAA@@@@@@@@@???????????????AAABBBBBB???===>>>>>>???@@@@@@AAABBBBBBAAAAAAAAABBBAAA@@@@@@???@@@???>>>===<<<;;;::::::<<<<<<<<<<<<<<<===>>>>>><<<:::888888999:::999888;;;;;;:::999888888888888777777666666666555555555888888888888888888888888777777888999888777666555444444555555555444333222222222333333333444444444444444444444444444444444222333333444444555555555555666777888999888777777888888777777777777888888555555555444444555555555333333333333333444555555444444222111111111222222000111222333444444444444333333444444444444444333111222222333333222222111333333444444444444333333333333333333333333333333111111222222222333333333000000000000111111111111222222222222222222222222222222111000000111222222000000000000111111111111......------...///111222////////////000000000000///////////////...............////////////......,,,---...---,,,,,,...000............////////////////////////////////////------,,,------...///000......------------......---------............///...///111222333222111000,,,---...---,,,---000222///......------......///,,,,,,,,,,,,,,,,,,,,,,,,........................,,,,,,,,,,,,+++++++++***((())))))***++++++,,,,,,+++,,,,,,,,,,,,,,,++++++,,,,,,+++++++++*********++++++++++++++++++++++++,,,,,,,,,+++++++++******TTTTTTTTTSSSSSSSSSSSSSSSQQQSSSVVVXXXXXXUUUSSSQQQPPPRRRSSSTTTSSSRRRSSSTTTTTTTTTSSSSSSTTTVVVXXXYYYRRRQQQQQQSSSVVVWWWWWWWWWVVVUUUUUUUUUTTTTTTSSSSSSWWWWWWWWWVVVTTTQQQOOOMMMLLLOOORRRSSSRRRQQQQQQQQQMMMNNNOOOPPPQQQQQQRRRRRROOORRRSSSRRROOOOOOSSSXXXMMMNNNNNNOOOOOONNNNNNMMMNNNNNNNNNMMMNNNNNNOOOOOOQQQQQQQQQQQQPPPPPPOOONNNJJJLLLNNNPPPQQQQQQQQQQQQOOOPPPOOONNNLLLLLLNNNPPPQQQPPPNNNMMMMMMMMMNNNNNNNNNNNNMMMMMMMMMMMMMMMMMMNNNOOOOOOPPPPPPOOOOOONNNMMMOOOPPPMMMIIIIIIMMMRRRNNNMMMMMMLLLKKKJJJJJJIIIHHHIIIIIIGGGFFFFFFIIIKKKFFFFFFFFFFFFFFFFFFFFFFFFEEEGGGHHHGGGDDDDDDFFFIIIBBBBBBBBBCCCDDDEEEFFFGGGGGGFFFEEECCCCCCBBBBBBBBBAAAAAABBBBBBCCCDDDDDDEEEEEEDDDCCCCCCCCCDDDFFFGGGCCCCCCCCCCCCDDDFFFGGGHHHCCCDDDEEEFFFGGGGGGFFFEEECCCCCCCCCCCCCCCBBBBBBBBBDDDDDDDDDDDDCCCCCCCCCCCC@@@@@@AAAAAAAAAAAABBBBBBCCCBBB@@@>>>>>>>>>>>>???>>>???@@@AAABBBCCCCCCCCCAAAAAAAAAAAAAAAAAAAAABBBBBBCCCDDDBBB??????BBBEEEAAAAAAAAAAAAAAABBBCCCDDDAAABBBBBBBBBBBBBBBBBBBBBDDDDDDCCCBBBAAAAAAAAAAAA@@@@@@@@@????????????>>>======>>>@@@AAA@@@>>>;;;????????????@@@AAABBBCCCAAAAAABBBBBBAAAAAA@@@???BBBAAA@@@???>>>===<<<;;;<<<<<<<<<<<<<<<===>>>>>><<<:::888888999999999888<<<;;;:::999888888888888777666666666555555555555888888888777777777777777777888888999999777666555333444555555555444333222111111222222222333333333444444444444444444444444222222333333444555666666555666777999999888888777888888777777777777888888555444444333333444444555333333333333333444555666555444222111111111222222000111222333444555555555444444444555444444333333222222333444444444333333222333333444444333333222333333333333333333333333111111222222222333333333000000000000111111111111333333333333333333333333333222111000000111222333////////////000000000000...---------...///111222111111000000//////...............///////////////...///////////////......---.........,,,,,,...000,,,---...///000000000000........................---------------...000000.........------.........---------.........//////...000222333444333222111,,,---------,,,---000222......------------......,,,,,,,,,,,,,,,,,,,,,,,,////////////////////////+++++++++************)))((())))))***++++++,,,,,,,,,,,,---------,,,,,,++++++++++++*********))))))++++++++++++++++++++++++,,,,,,,,,++++++*********UUUTTTSSSQQQQQQQQQRRRSSSXXXUUUSSSSSSUUUWWWVVVTTTWWWVVVSSSQQQPPPRRRSSSUUUQQQRRRTTTUUUVVVVVVUUUUUUTTTTTTTTTVVVXXXXXXVVVTTTVVVVVVVVVTTTRRRRRRTTTVVVYYYWWWVVVTTTSSSSSSTTTTTTVVVVVVUUUUUUTTTSSSSSSRRRQQQPPPPPPQQQRRRRRRPPPOOORRRSSSTTTSSSQQQPPPPPPPPPNNNPPPPPPPPPNNNNNNNNNPPPRRRQQQQQQPPPOOOOOONNNNNNSSSSSSRRRRRRQQQPPPNNNNNNOOOOOOOOONNNNNNOOOPPPPPPOOONNNMMMMMMMMMNNNOOOPPPOOONNNMMMLLLLLLMMMNNNNNNMMMMMMMMMKKKKKKLLLOOORRROOONNNMMMLLLLLLLLLMMMMMMOOOOOONNNMMMLLLLLLMMMMMMNNNMMMKKKJJJJJJJJJKKKLLLIIIJJJKKKKKKJJJHHHFFFEEEEEEEEEFFFGGGGGGGGGGGGFFFIIIHHHFFFEEEEEEEEEFFFFFFDDDDDDDDDDDDDDDDDDDDDDDDDDDEEEFFFGGGFFFEEECCCAAADDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDAAA@@@AAACCCGGGHHHFFFCCC@@@AAABBBDDDEEEFFFFFFFFFAAAAAABBBCCCDDDEEEFFFGGGEEEDDDBBBBBBDDDEEEDDDCCCDDDCCCAAA?????????AAABBBDDDBBBAAA???>>>>>>????????????@@@AAAAAABBBCCCCCCAAABBBBBBCCCCCCBBBBBBAAABBBBBBBBBCCCCCCCCCCCCCCC>>>>>>???@@@AAACCCCCCDDDBBBBBBCCCCCCCCCCCCBBBBBBCCCBBBAAAAAAAAAAAABBBCCC@@@AAAAAAAAAAAA@@@????????????@@@AAAAAA???>>>===============>>>???@@@AAAAAAAAAAAAAAA@@@>>>===<<>>===;;;:::999;;;===>>>>>>===<<<;;;999777777777999:::;;;;;;::::::999888888888:::999999888777666555555777777888888888888777777888888888888777777777666444444444333333333222222111222333333333333222111000111222222444444555666222111111000222444666888888888777666666666666666555555555666666666666666555555666666555444333333444444333333333333222222222111000......000111222333222000//////111333555444444444333333222222222000000111111111111000000000000000000000000000000111111222222222333333333555555444444444444333333111222222111///...///111000000000111111222222222111111222222222333333333111111000000111111222333............------------111111000000//////......111000///......---..................////////////,,,,,,,,,------.........000///...---------------///////////////000111111...------,,,,,,,,,------000000//////.........---///...---,,,,,,---...///000000000000000000000000------------------------........................------------------------.........////////////////////////...---------,,,++++++++++++++++++++++++,,,++++++******++++++,,,...---,,,***)))******+++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,VVVUUUTTTSSSRRRSSSSSSTTTWWWUUUSSSTTTVVVWWWUUUSSSVVVTTTSSSRRRSSSUUUWWWYYYTTTUUUUUUVVVVVVUUUTTTSSSTTTSSSSSSTTTVVVVVVUUUTTTUUUUUUVVVTTTSSSRRRSSSUUUWWWVVVTTTSSSRRRRRRSSSSSSTTTTTTTTTTTTTTTTTTTTTTTTSSSRRRQQQRRRSSSSSSRRRPPPRRRSSSTTTTTTRRRPPPPPPQQQOOOPPPQQQQQQOOOOOOPPPQQQLLLMMMNNNPPPQQQSSSTTTTTTQQQQQQQQQQQQPPPOOONNNMMMOOONNNNNNNNNNNNNNNOOOOOONNNNNNMMMMMMMMMNNNOOOPPPOOONNNMMMLLLKKKLLLLLLMMMMMMNNNNNNNNNMMMNNNPPPRRROOONNNNNNNNNNNNMMMMMMMMMOOONNNNNNMMMMMMLLLMMMMMMNNNMMMLLLLLLKKKKKKKKKLLLIIIIIIIIIIIIHHHGGGFFFEEEDDDDDDEEEFFFFFFFFFFFFEEEHHHGGGFFFEEEEEEEEEFFFGGGDDDDDDDDDDDDDDDDDDDDDDDDCCCDDDEEEEEEEEEDDDBBBAAADDDDDDDDDDDDDDDDDDDDDDDDCCCDDDDDDDDDDDDDDDDDDCCCCCCBBBAAACCCEEEFFFEEECCCAAABBBCCCEEEFFFGGGGGGGGGEEEEEEEEEEEEEEEEEEEEEEEEEEEDDDBBBBBBDDDEEEDDDCCCDDDCCCAAA@@@???@@@AAABBBCCCBBBAAA@@@?????????@@@???@@@@@@AAABBBBBBCCCCCCAAABBBBBBCCCCCCBBBBBBAAABBBBBBBBBCCCCCCCCCCCCDDD??????@@@AAABBBCCCDDDEEEBBBBBBCCCDDDDDDDDDDDDDDDCCCBBBAAAAAAAAAAAABBBCCCBBBBBBBBBAAA@@@???>>>===???@@@@@@@@@@@@???>>>>>>=========>>>>>>???@@@AAA@@@@@@??????>>>======<<<>>>??????@@@???>>>===<<<;;;::::::;;;===>>>>>>===>>><<<;;;999999999;;;<<<;;;::::::999888888777777999999999888777666666555777777888888888888777777888888888777777777666666444444444333333333222222111222333333333333222111111222222333333444444555222222111111222444666888888888777666666666666666555666666666666666666666555555666666555444444333444444333333333333222222222111000//////000111222222111///......000333444444444333333333222222222000000111111111111000000111111111111111111111111111111222222222333333333333333222222222111111111111222222111//////000222111111111111222222222333222222222222222222222222111111000000111111222333000000000////////////...000000000000///////////////...---,,,,,,+++,,,,,,............////////////,,,,,,---------.........//////......------------//////......///000000111......---------------...000/////////............000///...------...//////////////////////////////------------------------........................------------------------//////.................................---------,,,,,,,,,,,,,,,,,,,,,,,,---,,,,,,,,,,,,,,,,,,------,,,+++*********+++,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,VVVUUUTTTTTTTTTTTTTTTUUUUUUTTTTTTUUUWWWVVVTTTRRRRRRQQQQQQQQQSSSVVVXXXZZZVVVVVVVVVVVVUUUTTTSSSRRRTTTRRRQQQRRRSSSUUUTTTTTTSSSTTTVVVUUUTTTSSSSSSTTTUUUTTTSSSRRRQQQQQQQQQRRRQQQRRRRRRSSSTTTUUUUUUVVVTTTSSSRRRSSSTTTUUUTTTSSSSSSTTTUUUTTTRRRQQQQQQQQQPPPQQQRRRRRRPPPPPPQQQRRRRRRRRRRRRRRRQQQQQQPPPPPPPPPPPPPPPPPPOOONNNMMMMMMNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNMMMMMMNNNNNNOOOPPPOOONNNMMMLLLKKKJJJJJJJJJLLLNNNPPPPPPPPPPPPQQQRRRNNNOOOPPPPPPPPPOOOMMMLLLNNNNNNNNNMMMMMMMMMMMMMMMMMMMMMMMMNNNMMMMMMLLLKKKIIIIIIHHHGGGFFFFFFFFFFFFCCCCCCDDDEEEEEEEEEEEEEEEFFFFFFFFFEEEFFFFFFGGGHHHEEEEEEEEEEEEEEEEEEEEEEEEBBBCCCDDDDDDDDDCCCAAA@@@DDDDDDDDDDDDDDDDDDDDDDDDCCCCCCDDDDDDDDDDDDCCCCCCEEECCCBBBBBBCCCDDDDDDCCCBBBCCCDDDFFFGGGGGGGGGGGGHHHHHHGGGFFFEEEDDDCCCCCCEEEDDDBBBBBBDDDEEEDDDCCCCCCCCCAAA@@@@@@@@@AAABBBCCCCCCAAA@@@@@@@@@@@@@@@@@@@@@@@@AAABBBBBBCCCCCCBBBBBBCCCCCCCCCCCCBBBBBBBBBBBBCCCCCCCCCDDDDDDDDDAAAAAABBBCCCDDDDDDEEEEEECCCCCCDDDEEEEEEEEEEEEEEECCCBBBBBBAAAAAABBBBBBCCCAAAAAAAAAAAAAAA@@@@@@???AAA@@@??????>>>?????????>>>>>>>>>>>>>>>???AAAAAA@@@???>>>===<<<<<<===>>>>>>>>>??????>>>>>>===<<<<<<;;;:::<<<>>>???>>>===???>>><<<;;;;;;<<<======::::::999999888777777777999999888888777777666666777777888888888888777777777777777777666666666666444444444444333333333333111222222333333222222111333333333333333333333333222222111111222444666777888777777666666666666666666666666666666666555555555555555666555555444333444444333333333333222222222111000//////000111222111000///......000222333333333333333222222222222000000111111111111000000111111111111111111111111111111222222222333333333222222222222111111111111222333333222000000111333111222222222222333333333222222222222222222111111111000000000000111222222222222111111111000000000////////////000000000000///...---,,,,,,+++,,,,,,............////////////---------...............//////..................///............///000000///......---......//////////////////............000000////////////000000........................------------------------........................------------------------/////////...---------,,,---------...............,,,,,,,,,,,,,,,,,,,,,,,,...------,,,,,,------...++++++******++++++,,,---++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,TTTTTTTTTTTTTTTTTTTTTTTTSSSSSSUUUVVVWWWVVVTTTRRROOONNNNNNOOOQQQSSSVVVWWWTTTTTTTTTTTTSSSSSSRRRRRRTTTQQQPPPOOOQQQSSSSSSSSSQQQSSSVVVVVVTTTSSSRRRSSSTTTSSSSSSRRRRRRQQQQQQQQQQQQQQQRRRRRRSSSTTTTTTUUUTTTSSSRRRRRRTTTUUUTTTSSSSSSTTTUUUTTTRRRQQQQQQQQQOOOPPPQQQQQQPPPPPPQQQRRRUUUUUUTTTTTTRRRPPPNNNMMMOOOOOOPPPPPPPPPOOOOOONNNOOOOOOOOOOOOOOOOOONNNNNNNNNMMMNNNNNNNNNNNNOOOOOOOOONNNMMMLLLJJJJJJIIIIIIKKKMMMPPPRRRQQQPPPPPPPPPNNNOOOPPPQQQQQQOOOMMMLLLMMMMMMNNNNNNNNNMMMMMMMMMLLLMMMNNNOOOOOONNNMMMLLLJJJIIIGGGFFFFFFFFFGGGHHHCCCDDDEEEEEEFFFFFFEEEEEEEEEEEEEEEFFFFFFGGGHHHHHHEEEEEEEEEEEEEEEEEEEEEEEEBBBCCCDDDDDDDDDCCCBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDEEEEEEDDDCCCCCCFFFDDDCCCAAAAAABBBCCCCCCBBBCCCDDDEEEFFFFFFFFFFFFHHHGGGFFFFFFEEEDDDCCCCCCEEEDDDBBBBBBDDDEEEDDDCCCCCCBBBAAAAAAAAAAAABBBBBBCCCCCCBBBAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBCCCCCCBBBBBBCCCCCCCCCCCCBBBBBBBBBBBBCCCCCCDDDDDDEEEEEEBBBCCCCCCDDDEEEEEEFFFFFFFFFFFFFFFFFFFFFEEEDDDDDDBBBBBBBBBBBBBBBBBBBBBBBB>>>???@@@AAABBBBBBBBBBBBBBBAAA???>>>>>>>>>???@@@>>>>>>>>>>>>???@@@AAAAAAAAA@@@>>><<<<<<===???@@@???????????????>>>>>>======<<<;;;<<<>>>???>>>===>>>>>>===<<<<<<======>>>:::999999888888777666666888888888777777777777777777888888999999888888777777777666666666555555555555444444444444333333333222222222222222222222222444444444333333222222222333222222222333444666777777777666666666666777777666666666666555555555555444555555555555555444444444444333333333222222222222111111000000111111222000///.........///111222333222222222222222222222000111111222222111111000111111111111111111111111111111222222222333333333444444444333333333333222222333333222111111222444222222222222222333333333222222222222111111111111000000000000000111222222222222222111111111000000.........///000111111111111000///......---..................////////////.....................///....../////////..................------.../////////............///000000///////////////.........000000000000000111111111////////////////////////................................................------------............000//////...---,,,,,,+++,,,---------.../////////------------------------------,,,,,,,,,,,,------)))*********+++,,,------++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,RRRRRRSSSSSSSSSSSSSSSSSSRRRSSSUUUVVVVVVUUUSSSRRRPPPPPPPPPPPPQQQRRRTTTTTTQQQQQQQQQQQQRRRRRRSSSSSSSSSQQQOOOOOOQQQRRRSSSRRRPPPSSSUUUUUUTTTSSSSSSSSSSSSSSSSSSSSSSSSRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRSSSQQQPPPPPPRRRSSSSSSSSSRRRTTTUUUTTTRRRPPPPPPQQQMMMOOOPPPPPPOOOOOOPPPQQQNNNOOOQQQSSSTTTTTTSSSRRROOOPPPPPPQQQQQQQQQQQQPPPQQQQQQRRRRRRQQQQQQOOOOOOMMMMMMNNNNNNOOOOOOOOOOOONNNNNNMMMLLLKKKJJJIIIHHHIIILLLPPPQQQQQQOOOOOOOOONNNOOOPPPQQQQQQOOOMMMLLLLLLMMMMMMNNNNNNNNNMMMMMMLLLMMMNNNOOOOOONNNMMMLLLKKKJJJHHHGGGGGGHHHIIIIIIDDDEEEFFFFFFGGGGGGFFFFFFEEEEEEFFFFFFGGGGGGGGGGGGEEEEEEEEEEEEEEEEEEEEEEEEDDDDDDDDDEEEEEEDDDDDDDDDBBBBBBBBBBBBBBBBBBBBBBBBBBBCCCDDDEEEEEEDDDCCCBBBEEEEEECCCBBBAAAAAABBBCCCBBBBBBCCCDDDEEEEEEEEEEEEDDDDDDDDDDDDDDDDDDDDDDDDEEEDDDBBBBBBDDDEEEDDDCCCBBBBBBBBBBBBBBBBBBBBBCCCCCCCCCCCCCCCBBBBBBBBBAAAAAAAAABBBBBBBBBBBBCCCCCCBBBCCCCCCDDDDDDCCCCCCBBBBBBBBBCCCCCCDDDEEEEEEFFFCCCDDDDDDEEEEEEFFFFFFFFFIIIHHHHHHGGGFFFDDDBBBAAABBBBBBBBBBBBBBBBBBBBBBBBAAAAAABBBBBBBBBAAAAAA@@@BBBAAA???>>>>>>>>>???@@@>>>>>>>>>>>>???@@@AAABBBBBB@@@???>>>>>>???AAACCCAAAAAA@@@@@@@@@?????????>>>===<<<===?????????===<<<<<<<<<<<<<<<<<<======::::::999999888777777777777777777777777888888888888888999999999999888888666666666555555555555444555555555444444444333333222222222222222222222222555444444333333222222111333333333333444555555666777777666666666666777777777777666666555555555444444444555555555555555444444444333333333222222222222222111111111111222222000///......//////111111222222222222222222222222111111222222222222111111111111111111111111111111111111222222222333333333444444333333333222222222222333333222111111222444222222222222222222222222111111111111111111111111000000//////000000111222111111000000000/////////------...///000111222222111000///......---..................////////////////////////////////////......///000000//////.........---------------..................///000000.........//////////////////000000111111111111111000000000000000000000000........................////////////////////////---------....../////////000000///...------,,,,,,,,,---------.../////////------------------------,,,,,,++++++++++++,,,,,,((()))***+++,,,---------++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,QQQQQQRRRSSSSSSSSSSSSRRRQQQSSSVVVVVVTTTSSSSSSTTTTTTTTTTTTSSSTTTTTTUUUUUUPPPPPPPPPPPPQQQRRRSSSTTTRRRPPPOOOPPPQQQSSSRRRRRRQQQRRRTTTTTTSSSRRRSSSTTTRRRRRRSSSSSSSSSSSSRRRRRRRRRRRRRRRRRRQQQQQQQQQQQQQQQPPPNNNNNNPPPRRRSSSRRRRRRSSSTTTSSSQQQPPPPPPPPPLLLNNNOOOOOONNNNNNPPPQQQPPPQQQRRRSSSSSSRRRPPPNNNOOOOOOPPPQQQRRRRRRRRRRRRRRRSSSSSSTTTSSSRRRPPPOOOLLLMMMNNNOOOOOOOOOOOONNNMMMNNNNNNMMMLLLKKKJJJIIIJJJLLLPPPQQQPPPOOOOOOOOONNNOOOPPPPPPPPPOOOMMMLLLKKKLLLMMMOOOOOONNNMMMMMMLLLLLLMMMMMMNNNMMMMMMMMMJJJIIIIIIHHHHHHIIIIIIIIIEEEEEEFFFGGGGGGGGGGGGGGGEEEEEEFFFGGGGGGGGGFFFFFFEEEEEEEEEEEEEEEEEEEEEEEEDDDDDDDDDDDDEEEEEEEEEEEEBBBBBBBBBBBBBBBBBBBBBBBBBBBCCCDDDFFFFFFDDDCCCBBBCCCDDDDDDCCCAAA@@@AAACCCBBBBBBCCCDDDDDDDDDDDDDDDBBBBBBCCCCCCDDDDDDEEEEEEEEEDDDBBBBBBDDDEEEDDDCCCBBBBBBBBBBBBCCCCCCCCCCCCBBBCCCCCCDDDDDDCCCBBBBBBBBBBBBBBBBBBBBBBBBCCCCCCCCCCCCDDDDDDDDDDDDCCCCCCBBBBBBCCCDDDEEEEEEFFFGGGDDDDDDDDDEEEEEEFFFFFFFFFIIIIIIHHHGGGEEECCCBBBAAAAAABBBBBBCCCCCCBBBBBBAAAEEEEEEDDDCCCAAA???===<<>>???????????????>>>??????@@@AAABBBAAA@@@??????@@@AAABBBCCCBBBBBBAAA@@@@@@@@@@@@AAA???>>>===>>>???@@@???>>>;;;;;;;;;<<<<<<<<<<<<<<<;;;;;;::::::999888888777666666777777888888999999888888999999999999888888666555555555444444444444555555555555444444444333333222222111111222222333444444444333333222222222333333444444555555555555666666666666666777777888777777777666555555444444333444555555666555555555444444333333333333222222222222222222222222222222000/////////000000111111111111111222222222222222111111222222222222111111222222222222222222222222111111222222222333333333111111111111000000000000111222222222000111222444222222222111111111111000000000000111111111222222000////////////000111111000000/////////.........---......///000111111222///...---,,,,,,+++,,,,,,............////////////000000000000////////////---...///000111000///.........---,,,,,,,,,,,,---------------...///000000.........///////////////...///000111111222111111111111111111111111111111........................////////////////////////---------...//////000000000000000///......---------------...............,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++******++++++,,,((()))***+++,,,------,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,QQQRRRSSSTTTUUUTTTTTTSSSRRRTTTUUUUUURRRRRRSSSUUUTTTTTTTTTTTTUUUUUUVVVVVVTTTSSSRRRRRRRRRSSSTTTTTTQQQPPPPPPQQQSSSSSSRRRQQQQQQRRRSSSRRRRRRRRRTTTUUUPPPQQQRRRRRRRRRRRRQQQPPPPPPPPPPPPQQQQQQRRRRRRSSSQQQOOOMMMMMMPPPRRRSSSSSSQQQRRRSSSRRRPPPOOOOOOOOOMMMNNNPPPPPPOOOPPPQQQSSSTTTTTTUUUTTTRRRNNNJJJHHHMMMNNNOOOPPPQQQQQQRRRQQQRRRRRRSSSTTTSSSQQQOOONNNLLLMMMNNNOOOOOOOOONNNNNNMMMMMMNNNNNNNNNMMMKKKJJJLLLNNNPPPQQQPPPPPPPPPQQQOOONNNNNNNNNNNNMMMMMMMMMJJJLLLMMMOOOOOOOOOMMMLLLLLLKKKKKKKKKLLLLLLMMMNNNGGGHHHHHHIIIIIIIIIHHHHHHDDDEEEEEEFFFFFFFFFFFFFFFFFFFFFGGGHHHGGGFFFEEEEEEDDDDDDDDDDDDDDDDDDDDDDDDCCCCCCCCCCCCDDDDDDEEEEEEAAAAAAAAAAAAAAAAAAAAAAAAAAACCCEEEFFFFFFEEECCCAAA@@@CCCDDDDDDBBB@@@AAABBBCCCCCCDDDEEEEEEEEEEEEDDDCCCCCCDDDDDDDDDEEEEEEEEEEEEDDDBBBBBBDDDEEEDDDCCCAAABBBBBBCCCCCCCCCCCCCCCBBBCCCDDDDDDEEEDDDCCCBBBCCCCCCCCCCCCCCCCCCBBBBBBCCCCCCDDDDDDDDDDDDCCCCCCBBBBBBCCCDDDEEEFFFGGGGGGDDDDDDDDDEEEEEEEEEEEEEEEFFFFFFFFFFFFEEEDDDCCCBBBAAAAAABBBCCCCCCBBBAAAAAADDDDDDDDDCCCBBB@@@???>>>???@@@@@@@@@@@@???>>>>>>????????????@@@AAABBBBBB>>>>>>???@@@AAAAAABBBBBBBBBAAA@@@?????????@@@@@@@@@???>>>>>>@@@@@@???>>>:::;;;;;;<<<=========<<<<<<<<<;;;;;;:::999999999555666666777888999999999888999999::::::999999888555555555444444444333333555555555555444444444444333333222111111222333333333333333333333333333333333444444555555555555555666666666666666777888888888777777666555555444444333444444555666666555555444444333333333333222222111222222222222222222111000000000000111111222222000111111111222222222222111222222333333222222111222222222222222222222222111111222222222333333333111111111111000000000000///000111111000000222444111111111000000000//////......///000111222333333///////////////000111111000000/////////...............//////000000111111///...---,,,,,,+++,,,,,,............////////////111111111000000000//////---...000111111111//////...------,,,++++++,,,,,,,,,,,,,,,,,,---...///000............/////////000---...///111111111111111000000000000000000000000........................////////////////////////---------...///000000000000000000000000000//////...............---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,)))***+++,,,---,,,,,,+++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,RRRSSSTTTUUUVVVVVVUUUTTTRRRTTTUUUTTTQQQQQQSSSVVVQQQRRRRRRSSSTTTUUUUUUUUUWWWVVVUUUSSSSSSSSSTTTTTTPPPPPPQQQRRRTTTTTTRRRPPPRRRRRRRRRQQQQQQQQQTTTVVVNNNOOOPPPQQQQQQQQQPPPOOOMMMNNNOOOPPPRRRSSSTTTUUURRRPPPMMMNNNPPPRRRTTTTTTPPPQQQRRRQQQOOONNNNNNNNNNNNOOOQQQQQQQQQQQQRRRTTTMMMOOOQQQRRRRRRQQQOOOMMMLLLMMMNNNOOOPPPQQQQQQQQQQQQRRRSSSSSSRRRPPPNNNMMMLLLMMMNNNOOOPPPOOONNNNNNLLLMMMNNNOOOOOONNNLLLLLLMMMOOOQQQRRRQQQQQQRRRSSSOOONNNMMMLLLLLLLLLMMMMMMJJJKKKMMMOOOPPPOOOMMMLLLLLLKKKJJJJJJJJJKKKMMMNNNEEEFFFHHHIIIIIIHHHGGGFFFCCCDDDDDDEEEEEEEEEEEEEEEFFFGGGHHHHHHGGGFFFEEEDDDDDDDDDDDDDDDDDDDDDDDDDDDBBBBBBBBBBBBBBBCCCDDDEEEAAAAAAAAAAAAAAAAAAAAAAAAAAACCCEEEFFFFFFEEECCCAAA>>>BBBEEEEEEBBB@@@AAABBBDDDEEEEEEFFFFFFFFFFFFEEEFFFFFFFFFEEEEEEEEEEEEEEEEEEDDDBBBBBBDDDEEEDDDCCCAAAAAABBBCCCDDDDDDDDDCCCBBBCCCDDDEEEEEEDDDCCCCCCCCCCCCCCCCCCCCCCCCBBBBBBCCCCCCDDDDDDDDDDDDCCCCCCBBBBBBCCCDDDEEEFFFGGGGGGDDDDDDDDDDDDEEEEEEEEEEEECCCCCCDDDEEEEEEEEEEEEEEEAAAAAABBBCCCCCCBBBAAAAAA???@@@AAABBBCCCDDDDDDDDD??????@@@AAAAAA???>>>===????????????@@@AAABBBCCC<<<===>>>@@@AAAAAAAAAAAAAAAAAA???>>>>>>>>>???@@@AAA???>>>???@@@@@@???>>>;;;;;;<<<===>>>>>>=========<<<<<<;;;;;;::::::999555555666777888999999:::888999999::::::999999888555555444444444333333333666666555555555444444444444333222111111222333444333333333333333333333333444444555555666555555555666666666666666777888888888777777666555444444444333333444555666666666555444444444333333333222222111222222333333222222111000111111111222222222222000000111111222222222222111222222333333222222111222222222222222222222222111111222222222333333333333333333222222222222111///000111000///000111333111000000000//////......------...000111222333444///////////////000111111000000000000////////////////////////000000000000111111///.........................../////////000222111111111000000//////,,,...000111222111000///...---,,,,,,+++++++++++++++++++++,,,---...///000---.........//////000000,,,---///000111111111000////////////////////////////////////////////////000000000000000000000000---------...///000000111000000000000111111111111/////////......------,,,++++++++++++++++++++++++...------,,,,,,------...)))***+++,,,---,,,++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,XXXWWWUUUSSSRRRRRRSSSSSSUUUVVVVVVUUUTTTSSSUUUVVVUUUTTTRRRQQQQQQSSSUUUVVVTTTTTTSSSTTTTTTTTTSSSQQQSSSSSSSSSSSSSSSRRRRRRRRRTTTRRRPPPRRRUUUVVVUUUSSSTTTSSSQQQOOONNNOOOQQQRRRPPPQQQRRRSSSSSSRRRQQQPPPPPPOOOOOONNNOOOPPPQQQRRRQQQQQQRRRRRRQQQOOOMMMLLLMMMMMMNNNOOOPPPRRRSSSTTTSSSRRRQQQPPPOOOOOONNNOOOPPPPPPPPPPPPPPPPPPPPPPPPNNNPPPQQQRRRQQQPPPOOOOOOQQQQQQPPPNNNLLLKKKMMMNNNPPPPPPPPPOOOOOONNNNNNNNNPPPPPPPPPPPPPPPQQQRRRSSSOOOOOONNNNNNMMMNNNNNNNNNMMMMMMMMMMMMMMMNNNNNNNNNQQQOOOLLLMMMNNNNNNLLLIIIMMMMMMLLLJJJIIIHHHGGGFFFKKKJJJHHHGGGFFFEEEEEEEEEFFFGGGGGGGGGFFFEEECCCAAAFFFDDDCCCDDDEEEFFFEEECCCDDDBBB???@@@BBBDDDBBBAAACCCCCCBBBBBBBBBBBBCCCCCCCCCCCCDDDDDDDDDDDDDDDDDDCCCBBBAAA@@@@@@BBBCCCEEEEEECCCCCCEEEHHHIIIFFFCCCCCCCCCCCCCCCCCCDDDEEEFFFEEEEEEDDDCCCBBBAAAAAAAAADDDCCCCCCCCCDDDEEEGGGHHH???AAABBBAAA@@@@@@AAABBBBBBBBBBBBCCCCCCCCCCCCDDDBBBBBBCCCCCCCCCCCCCCCCCCFFFCCCBBBCCCFFFGGGFFFCCCEEEFFFFFFEEECCCAAABBBCCCAAABBBDDDFFFHHHIIIJJJJJJDDDEEEEEEFFFFFFDDDCCCBBBAAAAAAAAAAAABBBCCCDDDDDDAAAAAABBBBBBAAA@@@>>>===?????????@@@AAAAAAAAABBB@@@@@@@@@@@@AAAAAA@@@???===>>>???@@@@@@@@@@@@@@@??????@@@@@@@@@??????>>>;;;;;;;;;<<<<<<<<<<<<<<<;;;;;;<<<===>>>>>>======888777777777888999::::::999999:::::::::;;;;;;;;;777777666555444333333333444444444444444444444444444444444444444444444444444333333222222333333444666666666666777777777777777777777777666666666666555666999::::::888666444444444555555555555444444333333333333333333333333111111222222222333333333111111111222222333333333000111111111111222222222111111000000111111222333333333333222222222111111111111111222222333333333111111111111111111111111000333666555222000000111111111111111111111111111000000111111111111000000000000000000000///......000000//////.........---///...---,,,,,,---...///000000//////.........---............////////////000000////////////000000000000000000000000000000,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,,,,---------...///...,,,,,,...//////......---------......000000///............///---------.........//////......///000000000000000...///000///...---...000111///...///000111000...///............---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------...------,,,,,,..................---------,,,++++++******++++++UUUTTTSSSRRRRRRSSSSSSTTTTTTUUUVVVUUUSSSSSSTTTVVVUUUTTTSSSRRRRRRSSSTTTUUUTTTSSSSSSTTTTTTSSSRRRQQQSSSSSSSSSSSSSSSSSSTTTTTTRRRPPPPPPRRRUUUWWWWWWUUUTTTSSSRRRQQQPPPQQQQQQRRRQQQQQQRRRRRRRRRRRRQQQQQQPPPPPPOOOOOOOOOPPPQQQRRRQQQQQQRRRRRRQQQOOONNNMMMNNNNNNNNNOOOPPPQQQRRRSSSRRRQQQPPPOOONNNNNNNNNNNNPPPPPPPPPPPPPPPPPPPPPPPPOOOPPPQQQRRRQQQPPPPPPPPPPPPPPPPPPNNNLLLLLLMMMOOOPPPOOOOOOOOOOOOOOOOOONNNQQQPPPPPPPPPPPPQQQQQQRRRQQQPPPOOONNNMMMLLLLLLLLLMMMMMMMMMMMMMMMMMMMMMMMMOOOMMMKKKKKKLLLLLLJJJHHHJJJJJJJJJIIIHHHHHHGGGGGGHHHHHHGGGFFFFFFFFFGGGGGGFFFFFFGGGFFFFFFEEEDDDCCCDDDCCCBBBCCCDDDEEEDDDBBBFFFDDDBBBBBBDDDEEEDDDCCCDDDDDDDDDCCCCCCDDDDDDDDDCCCCCCCCCCCCBBBBBBBBBBBBCCCBBBAAA@@@@@@BBBDDDEEEDDDCCCCCCEEEGGGHHHEEECCCBBBBBBBBBBBBBBBCCCDDDDDDEEEEEEDDDBBBBBBAAAAAABBBCCCBBBBBBBBBCCCDDDEEEFFFAAABBBCCCBBBAAA@@@AAABBBBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDEEECCCBBBCCCFFFGGGFFFDDDDDDEEEEEEDDDBBB@@@AAABBBBBBCCCDDDFFFGGGHHHIIIIIIEEEEEEFFFFFFFFFEEEDDDCCCBBBBBBAAAAAAAAABBBCCCCCCAAABBBBBBBBBBBB@@@???>>>?????????@@@@@@@@@@@@@@@???>>>>>>???@@@@@@???>>>>>>>>>???@@@@@@@@@@@@@@@>>>>>>?????????>>>>>>===<<<<<<<<<<<<<<<<<<;;;;;;:::;;;<<<<<<=========<<<888888888888888999999999::::::::::::;;;;;;;;;;;;777777777666666555555555444444444444444444444444444444444444444444444444444333333222222333333444555666666666777777777777777777777777666666666666555777999::::::999777555444555555555555555555444333333333333333333333333111111222222222333333333111111222222222333333333111111111111222222222222111111000000111111222333333333222222222111111111111111222222222333333333111111111111111111111111000333555444222000000111111111111111111111111111000000111111111111000000000000000000000///......000/////////............///...------------...///000/////////........................////////////000//////......//////000////////////////////////------------------------,,,,,,---------.........---...///...,,,,,,...//////......------.........000//////...---.........---------.........//////......///000000000000000...///000///...---...000111///...///000111000...///............---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------...---------........................------,,,+++++++++++++++RRRRRRRRRRRRRRRSSSTTTUUUTTTUUUVVVUUUTTTTTTUUUVVVUUUUUUSSSRRRRRRSSSTTTUUUSSSSSSSSSSSSSSSRRRQQQQQQRRRRRRSSSSSSTTTTTTUUUUUUPPPPPPPPPRRRUUUWWWWWWVVVSSSSSSSSSSSSSSSRRRRRRRRRRRRRRRQQQQQQQQQQQQQQQRRRPPPPPPOOOOOOOOOPPPQQQQQQQQQQQQQQQQQQQQQPPPOOONNNOOOOOOOOOOOOOOOPPPQQQQQQPPPOOONNNMMMMMMMMMMMMMMMOOOOOOOOOOOOPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPOOOPPPPPPOOOMMMMMMOOOPPPNNNOOOOOOOOOOOOOOOOOOPPPRRRQQQQQQPPPPPPPPPPPPPPPRRRQQQOOONNNLLLKKKKKKKKKNNNNNNNNNMMMMMMLLLLLLKKKMMMKKKJJJJJJJJJJJJIIIGGGGGGHHHHHHHHHHHHHHHHHHHHHFFFFFFFFFFFFFFFGGGHHHIIIFFFFFFEEEEEEEEEEEEFFFFFFDDDBBBAAABBBCCCDDDCCCBBBEEEDDDBBBBBBDDDEEEDDDCCCEEEEEEDDDDDDDDDDDDEEEEEECCCCCCBBBBBBAAAAAAAAA@@@CCCBBBAAAAAAAAABBBDDDEEECCCBBBBBBCCCEEEEEEDDDBBBBBBBBBBBBBBBBBBBBBCCCCCCEEEDDDCCCBBBBBBBBBBBBBBBAAAAAAAAAAAABBBCCCDDDEEECCCDDDDDDCCCAAA@@@AAABBBBBBBBBBBBBBBCCCCCCCCCCCCBBBBBBCCCCCCDDDDDDDDDDDDCCCBBBBBBCCCFFFGGGGGGFFFCCCDDDDDDCCCAAA@@@AAABBBCCCDDDDDDEEEFFFFFFGGGGGGFFFFFFGGGGGGFFFFFFEEEDDDCCCCCCBBBAAAAAAAAABBBBBBBBBBBBBBBBBBAAA@@@???>>>??????????????????>>>>>>======>>>>>>>>>>>>======>>>???@@@@@@@@@@@@@@@@@@<<<======>>>>>>>>>===============<<<;;;;;;;;;:::::::::;;;;;;<<<<<<;;;;;;999999999999888888888888999::::::::::::;;;;;;;;;777777777777777777777777444444444444444444444444333333333333333333333333444444333333333333444444555555666666666777777777666666666666777777777777666777999::::::999888666555555555555555555555555333333333333333333333333111111222222222333333333111222222222222333333333111111111111222222222333111111000000111111222333222222222111111111111111111222222222222333333333222222222222222222222222111222444333222000111111111111111111111111111111000000111111111111000000000000000000000//////...////////////............///...------------...///////////////........................///////////////..................///////////////////////////........................---------.........//////---...///...,,,,,,...//////......---......////////////...------------...------........./////////......///000000000000000...///000///...---...000111///...///000111000...///............---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,---.......................................------,,,,,,,,,,,,,,,TTTSSSSSSSSSSSSSSSTTTTTTTTTVVVWWWWWWVVVVVVVVVWWWVVVUUUTTTSSSSSSSSSTTTTTTRRRSSSTTTSSSRRRQQQQQQQQQQQQQQQRRRRRRSSSTTTUUUUUUQQQQQQRRRSSSTTTUUUVVVUUURRRRRRSSSSSSSSSRRRRRRQQQSSSRRRQQQPPPOOOPPPQQQRRRPPPPPPPPPPPPPPPPPPPPPPPPQQQQQQQQQQQQQQQPPPPPPPPPPPPPPPOOOOOONNNOOOOOOPPPNNNNNNMMMLLLLLLLLLLLLLLLOOOOOOOOOOOOOOOPPPPPPPPPPPPNNNMMMMMMNNNOOOOOONNNNNNOOOPPPPPPOOONNNPPPQQQNNNNNNNNNOOOOOOPPPPPPPPPSSSRRRQQQPPPOOOOOOOOOOOOPPPPPPNNNMMMLLLLLLLLLLLLOOONNNNNNMMMLLLKKKKKKJJJKKKKKKJJJJJJJJJJJJIIIHHHHHHHHHHHHHHHHHHHHHHHHHHHFFFFFFFFFFFFFFFGGGGGGHHHFFFEEEDDDDDDDDDEEEGGGHHHDDDCCCBBBBBBDDDDDDCCCBBBCCCBBBAAAAAAAAABBBBBBBBBEEEDDDDDDDDDDDDDDDDDDEEEDDDDDDCCCBBBBBBAAAAAAAAACCCBBBBBBAAABBBCCCDDDDDDBBBBBBBBBBBBCCCCCCBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCEEEDDDCCCBBBBBBBBBBBBBBBAAAAAABBBBBBBBBCCCCCCDDDDDDEEEEEEDDDBBB@@@AAABBBAAAAAABBBBBBBBBCCCCCCCCCAAAAAABBBBBBCCCCCCDDDDDDBBBBBBCCCDDDEEEFFFGGGGGGCCCDDDEEEDDDBBBAAABBBCCCEEEEEEEEEEEEEEEEEEFFFFFFGGGGGGGGGGGGFFFFFFEEEEEEEEEDDDCCCBBBAAA@@@@@@AAAAAAAAA@@@@@@@@@??????>>>@@@?????????>>>=========<<<===??????>>>======>>>??????@@@AAAAAA@@@@@@@@@<<<===>>>>>>???>>>>>>>>>>>>>>>===<<<;;;:::::::::999::::::;;;;;;:::::::::::::::::::::999888888777888888888999999999::::::666777777777777777777777444444444444444444444444333333333333333333333333444444333333333333444444555555555666666666777777666666666666777777777777666777999:::::::::888888555555555444444555555555444444444444444444444444111111222222222333333333222222222222222222222222111111111222222222333333111111000000111111222333111111111111111111111111222222222222222222222222222222222222222222222222111222222222111111111111111111111111111111111111000000111111111111000000//////000000000000/////////////////////..................------.........///////////////.....................////////////......------------......////////////////////////........................------------............---...///...,,,,,,...///...............//////000///......---------------............////////////......///000000000000000...///000///...---...000111///...///000111000...///............---------------------------------,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,---............---------.....................---,,,,,,,,,------WWWWWWVVVVVVUUUTTTSSSSSSUUUWWWYYYYYYXXXXXXXXXYYYVVVVVVUUUTTTTTTTTTTTTTTTQQQSSSUUUTTTRRRQQQQQQRRRPPPPPPQQQRRRRRRSSSTTTTTTTTTTTTTTTTTTSSSSSSSSSSSSPPPPPPQQQRRRRRRQQQQQQPPPSSSRRRQQQOOOOOOOOOPPPQQQPPPPPPPPPPPPPPPPPPPPPOOOOOOOOOOOOOOOOOOPPPPPPPPPPPPPPPOOONNNNNNNNNNNNOOOMMMMMMLLLKKKKKKKKKLLLLLLNNNNNNNNNOOOOOOOOOPPPPPPOOOMMMJJJIIIKKKMMMMMMMMMNNNPPPQQQQQQPPPOOOPPPQQQNNNNNNNNNOOOOOOPPPPPPPPPSSSRRRQQQPPPOOONNNNNNNNNMMMMMMMMMLLLMMMMMMNNNNNNNNNNNNMMMMMMLLLKKKJJJJJJKKKLLLLLLKKKKKKJJJJJJKKKKKKKKKJJJJJJIIIHHHHHHHHHHHHGGGFFFFFFEEEEEEFFFFFFEEEEEEDDDDDDDDDFFFGGGHHHEEEDDDCCCDDDEEEEEEDDDCCCBBBBBBBBBAAAAAAAAABBBCCCDDDCCCCCCBBBBBBCCCCCCDDDDDDDDDDDDDDDCCCCCCBBBBBBBBBBBBBBBBBBCCCCCCDDDDDDBBBBBBBBBAAAAAAAAAAAABBBDDDDDDEEEEEEEEEEEEDDDCCCDDDDDDCCCBBBBBBBBBBBBCCCBBBCCCCCCCCCDDDDDDDDDDDDDDDEEEEEEDDDBBB@@@AAABBBAAAAAAAAABBBBBBBBBBBBCCC??????@@@AAABBBBBBCCCCCCBBBCCCDDDDDDEEEEEEFFFGGGDDDEEEFFFEEEDDDCCCDDDEEEFFFFFFEEEDDDEEEEEEFFFFFFGGGGGGGGGFFFFFFFFFFFFFFFEEEDDDCCCBBBAAA@@@@@@@@@?????????>>>>>>>>>>>>>>>@@@?????????>>>============???AAAAAA???>>>>>>@@@@@@@@@AAAAAAAAA@@@@@@???===>>>??????@@@@@@@@@???>>>>>>===<<<;;;:::::::::999:::::::::::::::999999:::::::::::::::999888777777777777777888888888888666666666666666666666777444444444444444444444444333333333333333333333333555444444333333444444555555555555555666666666666555666666666777777777888666777888999999999999888666555444444444444555666444444444444444444444444111111222222222333333333222222222222222222222222111222222222222333333333111111000000111111222333111111111111111111222222222222222222222222222222222222222222222222222222111111000111111222111111111111111111111111111111000000111111111111000000//////000000000000//////.........///////////////---..................---.........///////////////............////////////......------------..............................------------------------+++,,,,,,,,,,,,------------...///...,,,,,,...///...............///000111//////...------------............/////////000000......///000000000000000...///000///...---...000111///...///000111000...///............---------------------------------,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,---............---------.........//////......---,,,,,,,,,------XXXXXXXXXWWWVVVUUUSSSRRRTTTVVVYYYZZZYYYXXXXXXYYYVVVVVVVVVUUUUUUTTTSSSSSSRRRTTTWWWVVVSSSQQQRRRTTTQQQQQQRRRRRRSSSSSSTTTTTTUUUVVVVVVUUURRRQQQQQQRRRPPPPPPPPPPPPQQQQQQQQQQQQRRRRRRQQQPPPOOOOOOOOOOOOPPPPPPQQQQQQQQQPPPOOONNNNNNNNNMMMMMMNNNOOOPPPQQQPPPOOONNNNNNNNNNNNNNNOOOMMMLLLLLLKKKKKKLLLLLLLLLMMMMMMNNNNNNOOOOOOPPPPPPQQQLLLHHHGGGJJJMMMMMMLLLOOOQQQSSSRRRQQQPPPPPPQQQNNNOOOOOOOOOOOOOOOOOOPPPRRRQQQPPPOOONNNNNNNNNNNNLLLLLLLLLLLLLLLMMMOOOOOOMMMMMMMMMLLLLLLKKKKKKJJJKKKMMMMMMMMMKKKKKKLLLMMMLLLLLLKKKJJJIIIIIIHHHHHHHHHGGGFFFEEEEEEEEEEEEEEEEEEEEEDDDEEEEEEFFFGGGGGGFFFDDDCCCDDDEEEFFFEEEDDDCCCDDDEEEDDDBBBBBBDDDEEECCCCCCBBBBBBBBBBBBCCCCCCDDDDDDDDDDDDDDDDDDDDDDDDBBBBBBCCCCCCDDDDDDDDDDDDBBBCCCCCCAAA@@@???AAABBBDDDEEEFFFGGGFFFEEEDDDCCCDDDCCCCCCBBBBBBBBBCCCCCCBBBCCCDDDDDDDDDDDDCCCCCCCCCDDDDDDCCCAAA@@@AAABBBAAAAAAAAAAAABBBBBBBBBBBB??????@@@AAABBBCCCCCCDDDCCCDDDEEEEEEDDDDDDEEEFFFDDDFFFFFFFFFDDDDDDEEEFFFGGGGGGEEEEEEEEEFFFGGGHHHGGGGGGFFFEEEEEEEEEEEEFFFEEEDDDCCCBBBAAA@@@@@@@@@@@@???>>>>>>>>>>>>????????????????????????>>>>>>>>>AAACCCBBB@@@>>>@@@BBBAAAAAAAAAAAAAAAAAA@@@???===>>>???@@@@@@AAA@@@@@@=========<<<;;;;;;;;;:::::::::;;;;;;::::::999999999:::;;;;;;;;;:::999888666666777777777888888888666666666666666666666666444444444444444444444444444444444444444444444444555555444444444444555555444444555555555666666666555555666666777777888888555666777888888888888888666555444333333444555666444444444444444444444444111111222222222333333333333333333222222222222111222222222222333333333333111111000000111111222333222222222222222333333333333333333222222222222111333333333333333333333333222000//////111222222111111111111111111111111111000000111111111111000000...//////000000000000000.........///////////////------...//////...------.........///////////////............///////////////..................///........................------------------------+++++++++,,,,,,,,,---------...///...,,,,,,...///............///000111111000000///...................../////////000000000......///000000000000000...///000///...---...000111///...///000111000...///............---------------------------------,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,---............,,,,,,------.../////////...------,,,,,,,,,,,,,,,UUUVVVVVVWWWVVVUUUTTTSSSRRRTTTWWWYYYXXXWWWWWWXXXVVVVVVVVVVVVUUUTTTSSSSSSRRRVVVXXXWWWSSSQQQSSSVVVTTTTTTTTTTTTTTTTTTUUUUUUSSSUUUVVVUUURRRQQQRRRSSSRRRQQQPPPPPPPPPQQQSSSTTTQQQQQQQQQQQQPPPOOONNNMMMPPPPPPQQQQQQQQQPPPOOONNNLLLLLLLLLLLLLLLNNNOOOPPPOOONNNNNNNNNNNNNNNOOOOOOMMMLLLLLLLLLLLLLLLMMMMMMLLLMMMMMMNNNOOOOOOPPPPPPSSSNNNHHHHHHKKKNNNOOONNNQQQRRRTTTSSSRRRPPPOOOPPPPPPOOOOOOOOOOOOOOOOOONNNQQQQQQPPPOOONNNNNNNNNNNNMMMLLLLLLLLLLLLMMMMMMNNNLLLLLLLLLLLLLLLKKKKKKKKKJJJLLLNNNMMMKKKJJJLLLNNNIIIIIIIIIIIIIIIIIIIIIIIIFFFEEEEEEEEEEEEFFFFFFGGGDDDEEEEEEFFFFFFFFFFFFEEEEEEDDDCCCCCCEEEEEEDDDCCCCCCDDDEEEDDDBBBBBBDDDFFFDDDDDDCCCCCCCCCCCCDDDDDDAAABBBBBBCCCCCCDDDDDDEEEBBBCCCCCCDDDDDDDDDDDDDDDBBBCCCDDDBBB??????AAACCCDDDEEEFFFGGGFFFEEECCCBBBCCCCCCBBBBBBBBBCCCCCCDDDAAABBBCCCCCCCCCCCCBBBAAAAAABBBCCCBBBAAA@@@AAABBB@@@@@@AAAAAAAAABBBBBBBBB@@@AAAAAABBBDDDEEEEEEFFFDDDEEEGGGFFFCCCBBBDDDEEECCCEEEFFFEEEDDDCCCDDDFFFHHHGGGFFFEEEFFFGGGIIIJJJGGGFFFEEEDDDDDDDDDEEEEEEDDDCCCBBBAAAAAAAAAAAAAAAAAAAAA@@@??????@@@AAABBB?????????@@@@@@@@@@@@@@@===AAADDDCCC@@@>>>@@@CCCAAAAAABBBBBBAAAAAA@@@???<<<===>>>???@@@@@@@@@@@@<<<<<<<<<<<<<<<<<<;;;;;;;;;;;;;;;;;;;;;:::999999777999:::<<<<<<;;;:::999888888888888999999999999888888888777777666666666444444444444444444444444555555555555555555555555555555444444444444555555444444444555555555666666555555555666777888888888444555555666777777888888777666444333333444666777555555555555555555555555111111222222222333333333333333333222222222111111222222222333333333444444111111000000111111222333222222333333333444444444333333333222222222111111333333333333333333333333222000......111222222111111111111111111111111111000000111111111111000000......///000000000000000............/////////000------...//////...------............/////////000............////////////000//////......//////000................................................,,,,,,,,,,,,---------...---...///...,,,,,,...///............///000111222111111000////////////000.../////////000000000000......///000000000000000...///000///...---...000111///...///000111000...///............---------........................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------...---------,,,,,,------...//////000------,,,+++++++++++++++RRRSSSTTTUUUVVVUUUTTTTTTPPPSSSVVVWWWWWWVVVVVVVVVWWWWWWWWWVVVUUUTTTSSSRRRSSSVVVYYYXXXTTTRRRTTTWWWWWWWWWVVVVVVVVVVVVVVVVVVQQQTTTVVVUUURRRQQQSSSUUUSSSRRRQQQPPPQQQRRRTTTVVVPPPQQQRRRRRRQQQOOONNNLLLPPPPPPQQQRRRQQQPPPNNNMMMKKKKKKJJJJJJKKKMMMOOOPPPNNNNNNMMMMMMNNNNNNOOOPPPMMMMMMLLLLLLLLLLLLMMMNNNLLLLLLMMMNNNOOOOOOPPPPPPUUUOOOIIIHHHLLLPPPQQQOOOQQQSSSUUUTTTRRRPPPOOOOOOPPPPPPPPPOOOOOONNNNNNNNNPPPPPPOOOOOONNNNNNOOOOOONNNNNNMMMLLLLLLKKKLLLLLLKKKKKKKKKKKKLLLLLLLLLLLLIIILLLNNNMMMJJJJJJKKKNNNFFFFFFGGGHHHHHHIIIJJJJJJCCCCCCDDDDDDEEEGGGHHHIIIDDDEEEFFFGGGGGGFFFEEEDDDDDDCCCBBBBBBCCCDDDCCCBBBAAABBBDDDBBB@@@???BBBDDDEEEEEEDDDDDDDDDDDDEEEEEE???@@@@@@AAABBBCCCDDDDDDBBBCCCCCCDDDEEEDDDDDDDDDCCCDDDDDDBBB??????AAADDDCCCDDDEEEFFFEEEDDDBBB@@@CCCCCCBBBBBBBBBCCCCCCDDD@@@AAABBBBBBBBBAAA@@@??????AAABBBBBB@@@@@@AAABBB@@@@@@AAAAAAAAABBBBBBBBBBBBBBBCCCDDDEEEFFFGGGHHHDDDFFFHHHFFFCCCAAACCCEEEBBBDDDEEEDDDCCCCCCDDDEEEHHHGGGFFFFFFFFFHHHKKKLLLGGGFFFDDDCCCCCCCCCDDDEEECCCCCCBBBAAAAAAAAABBBBBBCCCBBBAAAAAAAAABBBCCCDDD?????????@@@AAAAAAAAABBB===AAADDDCCC???===???BBBBBBBBBBBBBBBAAAAAA@@@???;;;<<<===>>>????????????;;;;;;;;;<<<<<<<<<<<<<<<<<<<<<<<<<<<;;;;;;:::999777888:::<<<<<<<<<:::999999999:::::::::;;;;;;;;;;;;::::::999888777666666444444444444444444444444666666666666666666666666555555444444444444555555444444444555555555666666444555555666777888888999444444444555666777777888777666444333333444666777555555555555555555555555111111222222222333333333333333333222222111111111222222333333333444444444111111111000111222222333333333333444444555555555333333333222222111111111333333333333333333333333222000---...111333222111111111111111111111111111000000111111111111000000......///000000000000000---.........//////000000,,,---...//////...---,,,---.........//////000000............/////////000000000////////////000000........................000000000000000000000000---------.........//////---...///...,,,,,,...///............///000222222222111111000000000000000////////////000000000000...//////000000000000000...///000///...---...000111///...///000111000/////////.........---------........................,,,,,,,,,,,,,,,,,,,,,,,,---------...------,,,,,,,,,,,,------...///000000---,,,++++++******++++++QQQQQQQQQRRRRRRRRRRRRSSSUUUVVVWWWWWWWWWWWWVVVUUUWWWVVVUUUTTTTTTTTTVVVVVVXXXXXXYYYYYYXXXWWWVVVUUUVVVVVVUUUUUUTTTUUUUUUUUUXXXXXXXXXWWWWWWVVVVVVVVVWWWWWWWWWSSSOOOOOOQQQTTTSSSSSSRRRQQQQQQQQQQQQQQQPPPQQQSSSTTTSSSQQQNNNLLLLLLMMMOOOQQQQQQPPPOOONNNMMMNNNOOOPPPQQQPPPOOONNNNNNNNNMMMLLLLLLKKKKKKKKKPPPPPPOOOOOOOOONNNNNNNNNOOOPPPPPPOOOMMMMMMOOOPPPRRRSSSTTTUUUTTTQQQNNNLLLQQQPPPOOOOOONNNMMMLLLKKKNNNNNNNNNNNNNNNNNNNNNNNNRRRQQQPPPOOONNNLLLKKKKKKNNNMMMLLLKKKKKKJJJJJJJJJMMMKKKJJJHHHHHHJJJLLLMMMJJJJJJIIIHHHGGGGGGGGGGGGFFFEEEEEEEEEGGGHHHGGGFFFEEEEEEFFFFFFGGGGGGHHHHHHDDDDDDDDDCCCBBBBBBAAAAAACCCCCCBBBBBBBBBBBBCCCCCCDDDCCCCCCCCCCCCDDDEEEEEEDDDDDDDDDDDDDDDEEEFFFFFFCCCCCCBBBAAAAAAAAAAAABBBDDDDDDDDDCCCBBBBBBBBBAAABBBBBBCCCCCCCCCCCCBBBBBB@@@AAACCCDDDDDDDDDCCCBBBDDDDDDCCCBBBBBBBBBBBBCCC@@@AAABBBCCCDDDDDDDDDDDDBBBBBBCCCCCCDDDEEEEEEEEEBBBCCCCCCCCCDDDDDDEEEEEEBBBDDDEEEDDDBBBAAADDDFFFDDDDDDDDDDDDDDDDDDDDDDDDGGGGGGGGGGGGGGGGGGGGGGGGIIIHHHHHHGGGFFFEEEDDDDDDFFFBBB??????@@@BBBAAA???@@@@@@?????????@@@BBBCCC??????@@@@@@@@@@@@??????@@@@@@AAAAAAAAABBBBBBBBB???@@@@@@@@@@@@???>>>>>>>>>===<<<===???AAAAAA@@@??????>>>===<<<;;;::::::??????>>>===<<<;;;;;;:::;;;<<<=========<<<;;;:::<<<;;;::::::999999::::::999888777666555444333222555555444444444333333333222222333444555555555555444444444555555555555555444555555666666666666666444555777888999999888888888888888888888888888888666666666666666666666666555555555666666666777777666555333222111111222333222222222222222333444555222333333444444333333222111111000000111111222333555444333222222222333333444444444444444444444444666555444333333333333333///000111222333444444444222222222111111111111000...//////000000000000000111111111111000000000000000000000000000///......---------------------...***+++,,,...///000000000,,,,,,,,,------.....................////////////111111000000//////......111000///......///000111//////............//////////////////////////////////////////////////////......///000000000000000111111111000000000000000000000000///......---------------......000111111111111000/////////////////////.........---------,,,,,,,,,---------......---.../////////...---,,,............---,,,+++***+++,,,---.........---,,,------+++***))))))((((((PPPQQQQQQQQQQQQRRRRRRRRRTTTUUUVVVWWWWWWVVVUUUTTTUUUTTTSSSRRRRRRSSSTTTTTTXXXXXXXXXXXXXXXXXXWWWWWWVVVUUUTTTSSSSSSSSSSSSSSSVVVWWWWWWWWWWWWVVVUUUTTTVVVWWWVVVSSSPPPOOOQQQSSSSSSSSSRRRQQQQQQQQQQQQQQQPPPQQQSSSTTTSSSQQQNNNMMMLLLNNNOOOQQQQQQPPPOOONNNMMMMMMNNNOOOPPPPPPOOOOOONNNNNNNNNNNNOOOOOOOOOOOOPPPPPPPPPPPPOOOOOOOOOOOOQQQRRRRRRQQQOOOOOOPPPRRRRRRSSSTTTTTTSSSQQQNNNMMMOOOOOOOOONNNMMMMMMLLLLLLNNNNNNNNNNNNNNNNNNNNNNNNPPPPPPOOONNNMMMLLLLLLKKKNNNMMMLLLKKKKKKJJJJJJJJJLLLLLLKKKJJJJJJJJJKKKKKKKKKJJJIIIHHHHHHGGGGGGHHHFFFEEEEEEEEEGGGHHHGGGFFFEEEEEEEEEFFFFFFFFFFFFFFFDDDDDDCCCCCCCCCCCCBBBBBBCCCCCCCCCBBBBBBCCCCCCCCCCCCCCCBBBBBBCCCCCCDDDEEEDDDDDDDDDDDDDDDEEEFFFFFFDDDDDDCCCCCCBBBBBBCCCCCCCCCCCCCCCCCCCCCBBBBBBBBBBBBBBBCCCCCCCCCCCCBBBBBBAAABBBBBBCCCDDDDDDCCCCCCBBBBBBAAAAAA@@@@@@@@@AAA@@@AAABBBCCCDDDDDDDDDDDDBBBBBBCCCCCCDDDDDDEEEEEECCCCCCCCCDDDDDDDDDEEEEEEDDDFFFHHHFFFCCCAAAAAAAAAEEEEEEEEEEEEEEEEEEEEEEEEFFFGGGGGGHHHHHHGGGGGGFFFHHHGGGGGGFFFEEEDDDDDDDDDDDDBBB???@@@AAABBBAAA@@@@@@@@@?????????@@@AAABBB??????@@@@@@@@@@@@??????@@@@@@@@@@@@AAAAAAAAAAAA???@@@@@@@@@@@@???>>>>>>===<<<;;;<<<>>>??????>>>>>>>>>>>>===<<<<<<;;;;;;???>>>>>>===<<<;;;;;;;;;:::;;;<<<=========<<<;;;<<<;;;::::::999999::::::999888888777666555444444555555555444444444333333111111333444555555555555555555555555555555444444444555555666666666666666444555777888999999888888888888888888888888888888666666666666666666666666333333333444444444555555555444333222222222333444333333333333333444555555333333444444444444333333222222222222222333333444555444333222222222333333444444444444444444444444666555444333333333333444000111222333333333333333222222222111111111111000...//////000000000000000000000000////////////...///////////////...------,,,------...------,,,,,,***+++,,,.../////////000,,,,,,,,,------.....................////////////111111000000////////////111000///......///000111//////............//////000000000000000000000000////////////////////////......///000000000000000111000000000000000000000000000000///......---------------......///000111111111000/////////////////////.........---------,,,,,,---------.........------...............---............---,,,+++***+++,,,---.........---,,,---,,,+++***))))))))))))PPPPPPPPPQQQQQQQQQQQQRRRSSSTTTUUUVVVVVVUUUTTTSSSTTTSSSSSSRRRSSSSSSTTTTTTXXXXXXXXXWWWXXXXXXYYYZZZUUUUUUSSSRRRQQQQQQQQQQQQTTTUUUVVVWWWWWWUUUSSSRRRUUUUUUTTTRRRPPPOOOQQQRRRSSSRRRQQQQQQPPPQQQQQQQQQPPPQQQSSSSSSRRRQQQNNNMMMMMMNNNOOOPPPQQQPPPOOONNNOOOOOOOOOOOOPPPQQQSSSSSSOOOPPPPPPQQQRRRRRRSSSSSSQQQQQQQQQPPPPPPPPPPPPOOOSSSTTTTTTRRRQQQPPPQQQSSSTTTSSSSSSRRRQQQPPPOOOOOONNNNNNNNNNNNNNNNNNNNNNNNOOOOOOOOOOOOOOOOOOOOOOOONNNNNNMMMMMMMMMLLLLLLLLLNNNMMMLLLKKKKKKJJJJJJJJJLLLLLLLLLLLLKKKKKKJJJIIIKKKJJJIIIHHHHHHGGGGGGHHHFFFEEEEEEEEEGGGHHHGGGFFFFFFEEEEEEEEEEEEEEEEEEDDDCCCCCCCCCCCCDDDDDDDDDDDDCCCCCCCCCCCCCCCCCCCCCCCCBBBBBBBBBBBBBBBCCCCCCDDDDDDDDDDDDDDDDDDEEEEEEFFFEEEEEEEEEDDDDDDDDDCCCCCCBBBBBBBBBCCCCCCCCCCCCCCCBBBBBBCCCCCCCCCCCCBBBBBBCCCBBBBBBBBBBBBCCCDDDDDDBBBBBBAAAAAAAAA@@@@@@@@@@@@AAABBBCCCCCCDDDDDDCCCBBBBBBBBBCCCDDDDDDEEEEEECCCCCCDDDDDDDDDDDDEEEEEEDDDEEEGGGGGGEEEBBBAAAAAAFFFFFFFFFEEEEEEFFFFFFFFFEEEFFFHHHIIIIIIHHHFFFEEEFFFFFFEEEEEEDDDDDDCCCCCCAAA@@@@@@AAACCCCCCBBB@@@@@@@@@?????????@@@AAABBB??????@@@@@@@@@@@@??????>>>?????????@@@@@@@@@@@@??????@@@@@@??????>>>======<<<;;;<<<===>>>===<<<========================>>>>>>======<<<<<<;;;;;;:::;;;<<<===============<<<;;;::::::999999::::::888888888888777777666666555555555444444444444333///000222333444555555555666666666555444444444333444555555666666666666666444555666777888888888888888888888888888888888888666666666666666666666666333333333444444444444444444333222222222333555555444555555555555555666666444444555555555555444444333333222222333333444555555444333222222222333333444444444444444444444444555555444333333333444444222222333333333333222222222222222111111111111000...///000000111111000000////////////...........................------,,,,,,---...//////---+++******+++,,,---......//////---------------.....................////////////111000000000000/////////111000///......///000111//////............//////000000000000000000000000////////////////////////......///000000000000000000000000000000000111111000000000///......------......---......///000111000000000000////////////...............---------,,,------------.........---------------...///000...............---,,,+++++++++,,,---------------,,,,,,+++***)))))))))***PPPPPPPPPPPPQQQQQQQQQQQQRRRSSSTTTUUUUUUTTTSSSRRRUUUUUUUUUUUUUUUUUUVVVVVVXXXXXXWWWWWWWWWYYYZZZ[[[VVVUUUTTTRRRQQQPPPPPPPPPQQQSSSUUUVVVVVVUUURRRQQQSSSSSSRRRQQQPPPPPPPPPQQQRRRQQQQQQPPPPPPQQQQQQQQQQQQRRRRRRSSSRRRPPPOOOMMMMMMNNNOOOPPPPPPPPPOOOOOOQQQPPPPPPPPPRRRTTTVVVWWWQQQQQQRRRRRRRRRSSSSSSSSSRRRRRRQQQQQQQQQPPPPPPPPPSSSTTTTTTSSSQQQPPPRRRSSSTTTSSSRRRPPPOOOOOOPPPPPPNNNNNNOOOOOOOOOPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPLLLLLLLLLLLLLLLLLLLLLMMMNNNMMMLLLKKKJJJJJJJJJJJJKKKLLLMMMNNNMMMKKKIIIHHHJJJIIIHHHGGGGGGFFFFFFGGGFFFEEEEEEEEEGGGHHHGGGFFFFFFFFFEEEEEEDDDDDDCCCCCCBBBBBBCCCDDDEEEEEEFFFFFFCCCCCCDDDDDDDDDDDDCCCCCCBBBAAAAAAAAAAAABBBCCCCCCEEEEEEDDDDDDDDDDDDEEEEEEEEEEEEEEEEEEDDDDDDCCCCCCAAABBBBBBBBBCCCDDDDDDDDDBBBBBBCCCCCCCCCCCCBBBBBBDDDCCCBBBAAAAAABBBDDDDDDCCCCCCDDDCCCCCCCCCBBBBBB@@@@@@AAABBBCCCCCCCCCCCCAAAAAABBBCCCCCCDDDDDDEEEDDDDDDDDDDDDDDDDDDEEEEEEBBBCCCCCCDDDDDDEEEFFFGGGGGGFFFEEEEEEEEEEEEFFFGGGDDDFFFHHHJJJJJJHHHFFFDDDDDDDDDDDDDDDDDDCCCCCCCCC???@@@AAACCCDDDDDDBBBAAA@@@@@@@@@@@@@@@@@@@@@AAA??????@@@@@@@@@@@@??????>>>>>>>>>>>>???????????????????????????>>>>>>===>>>===<<<===>>>>>>===;;;<<<<<<<<<<<<======>>>>>>===============<<<<<<<<<::::::;;;<<<===>>>>>>>>><<<;;;::::::999999::::::999888888888888888888888555555555555444444444444///000111333444555555555777777666555444333333333444555555666666666666666555555666777777888888888888888888888888888888888666666666666666666666666666666666666666666666666333333222222333444666777666666666777777777666666555555666666666666555555222222222222222333444444555444333222222222333333333333333333333333333333555444444333333333444444333333444444333222222111222222222111111111000000//////000111111111111000000000/////////...............//////......---,,,,,,...///000///---***(((***+++,,,---............---------...........................////////////000000000000000000000000111000///......///000111//////............//////111111111111111111111111////////////////////////......///000000000000000000000000000000111111111000000000///......------...............///000000///000000000000000//////........................------------............---,,,,,,,,,---...000111...............---,,,,,,++++++,,,,,,------------++++++******)))*********PPPPPPPPPQQQQQQQQQRRRRRRRRRSSSTTTTTTTTTTTTSSSRRRTTTTTTUUUUUUVVVVVVVVVVVVWWWWWWVVVWWWWWWXXXYYYYYYVVVVVVTTTSSSQQQQQQPPPPPPPPPRRRTTTVVVVVVTTTRRRPPPQQQQQQPPPPPPPPPPPPPPPPPPQQQQQQPPPPPPPPPPPPQQQQQQQQQRRRRRRRRRQQQPPPOOONNNNNNNNNOOOOOOPPPPPPPPPOOOPPPOOOOOOOOOPPPRRRTTTVVVSSSRRRRRRRRRQQQQQQQQQPPPRRRRRRQQQQQQQQQPPPPPPPPPQQQRRRRRRQQQPPPPPPQQQSSSTTTSSSQQQOOONNNOOOPPPQQQOOOOOOPPPPPPQQQRRRRRRRRRPPPPPPPPPPPPPPPPPPPPPPPPLLLLLLLLLLLLLLLMMMMMMMMMNNNMMMLLLKKKJJJJJJJJJJJJJJJLLLMMMNNNNNNLLLJJJHHHIIIHHHGGGFFFEEEEEEEEEEEEFFFEEEEEEEEEGGGHHHGGGFFFFFFFFFEEEEEEDDDDDDCCCCCCBBBCCCCCCDDDEEEFFFGGGGGGCCCCCCDDDEEEEEEDDDCCCCCCBBBAAAAAAAAAAAABBBCCCCCCEEEEEEDDDDDDDDDDDDEEEEEECCCDDDDDDDDDDDDCCCBBBAAAAAABBBBBBBBBCCCDDDDDDDDDBBBBBBCCCCCCCCCCCCBBBBBBDDDDDDBBBAAAAAABBBCCCDDDCCCCCCDDDDDDDDDCCCBBBAAA???@@@AAABBBCCCCCCCCCCCCAAAAAABBBBBBCCCDDDDDDDDDEEEEEEEEEEEEEEEEEEDDDDDDEEECCCAAAAAACCCFFFIIIJJJGGGFFFDDDCCCCCCDDDFFFGGGDDDFFFHHHJJJJJJHHHFFFDDDCCCCCCCCCCCCCCCDDDDDDDDD???@@@BBBDDDDDDCCCBBBBBB@@@@@@@@@@@@@@@@@@@@@@@@??????@@@@@@@@@@@@??????======>>>>>>>>>?????????>>>????????????>>>======???>>>>>>>>>@@@???>>><<<;;;;;;<<<<<<===>>>>>>>>><<<<<<<<<===============;;;;;;;;;<<<===>>>??????<<<;;;::::::999999::::::999999999999888888888888666666555555555444444444000000222333444555555555777777666555444333333333444555555666666666666666555555555666666777888888777777777777777777777777666666666666666666666666666666666666666666666555333222222222333555777888666777777888888777666666555666666777777666666555111111111111111222333333555444333222222222333333333333333333333333333333444444333333333444444555444444444444333333222111222222222111111111000000///000000111111111111111111111111000000000/////////000000000000///......,,,...///000///---***(((++++++,,,---................................................////////////000000000000111111111111111000///......///000111//////............//////000000000000000000000000////////////////////////......///000000000000000//////000000111111111111000000000///......------///............//////000...///000000000000//////---.....................---------.........//////---,,,,,,,,,---...000111......//////......------++++++++++++,,,,,,------*********)))******++++++QQQQQQQQQRRRRRRRRRRRRSSSRRRSSSTTTUUUUUUTTTSSSRRRQQQRRRSSSTTTTTTTTTTTTTTTUUUUUUVVVWWWWWWWWWVVVVVVVVVUUUTTTRRRQQQQQQQQQQQQPPPRRRSSSUUUUUUTTTSSSRRRPPPOOONNNOOOPPPQQQPPPOOOPPPPPPPPPOOOPPPPPPQQQRRRRRRRRRRRRRRRQQQPPPOOONNNNNNNNNNNNOOOOOOOOOPPPPPPMMMMMMMMMMMMNNNOOOPPPQQQRRRRRRQQQQQQPPPOOOOOONNNQQQQQQQQQPPPPPPPPPPPPOOONNNOOOPPPPPPOOOPPPRRRSSSSSSRRRPPPOOOOOOOOOPPPQQQPPPPPPPPPQQQQQQRRRRRRRRRQQQQQQQQQQQQQQQQQQQQQQQQLLLMMMMMMMMMMMMMMMMMMMMMNNNMMMLLLKKKKKKJJJJJJJJJJJJKKKMMMNNNNNNMMMKKKJJJIIIHHHGGGFFFFFFEEEEEEEEEFFFEEEEEEEEEGGGHHHGGGFFFFFFEEEEEEEEEEEEEEEEEEDDDCCCDDDDDDEEEFFFGGGGGGHHHCCCDDDEEEFFFFFFEEEDDDCCCBBBBBBBBBBBBBBBCCCCCCDDDFFFEEEEEEDDDDDDDDDDDDDDDCCCCCCDDDEEEDDDCCCBBBAAABBBBBBBBBCCCCCCCCCCCCCCCBBBBBBCCCCCCCCCCCCBBBBBBDDDDDDCCCBBBBBBBBBBBBCCC@@@AAABBBBBBBBBAAA@@@??????@@@AAABBBBBBCCCCCCBBBAAAAAAAAABBBCCCCCCDDDDDDFFFFFFEEEEEEEEEEEEDDDDDDHHHFFFBBBAAACCCEEEGGGGGGGGGFFFDDDCCCCCCDDDFFFGGGEEEFFFHHHIIIIIIHHHFFFEEEBBBBBBCCCCCCDDDDDDEEEEEE@@@BBBDDDDDDBBBBBBBBBCCC@@@@@@AAAAAAAAA@@@????????????@@@@@@@@@@@@??????===>>>>>>>>>????????????>>>>>>??????>>>>>>===<<<>>>===>>>???AAAAAA>>><<<;;;<<<<<<<<<======>>>>>>;;;;;;<<<<<<======>>>>>><<<<<<<<<<<<===>>>??????<<<;;;::::::999999::::::999999999999888888777777666666666555555555444444222222333444555555555555666666666555444444444333444555555666666666666666555555555555666777888999777777777777777777777777666666666666666666666666444444444444444333333333444333333333444555777888666777888999888777666555555555666666666666555555111111000000111111222333555444333222222222333333333333333333333333333333444444333333333444555555444444444444444333222222222222222111111111111000///000111111222222111111111111111111000000000000000000000000000//////...,,,---...//////---+++***,,,---......//////....../////////...........................////////////000000000111111111111222111000///......///000111//////............//////////////////////////////////////////////////////......///000000000000000/////////000111111222222000000000///......------//////............//////---...000111111000//////---------...............------........./////////---------------...///000....../////////......---+++++++++++++++,,,------***)))))))))***+++,,,,,,RRRRRRRRRSSSSSSSSSTTTTTTSSSSSSTTTUUUUUUTTTSSSSSSPPPQQQSSSTTTUUUUUUTTTTTTSSSTTTVVVXXXWWWVVVTTTRRRSSSRRRRRRQQQPPPPPPQQQQQQQQQRRRSSSTTTTTTTTTTTTTTTNNNMMMLLLNNNPPPQQQPPPNNNPPPOOOOOOOOOPPPPPPQQQRRRRRRRRRRRRQQQQQQPPPOOOOOOOOONNNNNNNNNOOOOOOPPPPPPLLLMMMNNNOOOOOOOOOOOOOOOPPPPPPPPPPPPPPPOOOOOOOOOPPPPPPPPPPPPOOOOOOOOOOOOLLLNNNOOOOOOOOOQQQSSSUUUQQQQQQPPPPPPOOOOOOPPPPPPOOOOOOOOOOOOPPPPPPPPPPPPQQQQQQQQQQQQQQQQQQQQQQQQNNNNNNNNNNNNNNNMMMMMMMMMNNNMMMLLLKKKKKKJJJJJJJJJIIIJJJLLLMMMNNNNNNMMMMMMKKKJJJIIIHHHGGGGGGGGGGGGFFFEEEEEEEEEGGGHHHGGGFFFEEEEEEEEEFFFFFFFFFFFFFFFEEEEEEEEEFFFFFFGGGGGGGGGCCCDDDEEEFFFFFFEEEDDDCCCCCCCCCBBBBBBCCCCCCDDDEEEFFFFFFEEEDDDDDDDDDDDDDDDCCCDDDEEEFFFFFFDDDCCCAAACCCCCCCCCCCCCCCBBBBBBBBBBBBBBBCCCCCCCCCCCCBBBBBBCCCCCCDDDDDDCCCBBBBBBAAA@@@AAABBBCCCCCCAAA???>>>??????@@@AAABBBBBBBBBBBB@@@AAAAAABBBBBBCCCCCCDDDFFFFFFFFFEEEEEEEEEDDDDDDEEEDDDCCCDDDGGGHHHGGGEEEHHHGGGEEECCCCCCEEEGGGHHHFFFGGGGGGHHHHHHGGGGGGFFFBBBBBBCCCDDDEEEEEEFFFFFFBBBDDDEEECCCAAA@@@BBBDDD@@@AAAAAAAAAAAA@@@???>>>??????@@@@@@@@@@@@??????>>>>>>>>>?????????@@@@@@>>>>>>>>>>>>>>>======<<<;;;<<<<<>><<<<<<<<<<<<===============;;;;;;;;;<<<===>>>>>>???>>>>>>===<<<<<<===>>>???<<<;;;::::::999999::::::::::::999888777666666555666666666666555555555555444555555666666555555555555555555555555555444444444555555666666666666666555555444444555666888999777777777777777777777777666666666666666666666666555555444444444333333333555444333333444555666777666777888999888777555444444555555666666555555444222111111111111222333333555444333222222222333333222222222222222222222222333333333333333444555666444444444444444444333333222222222111111111111000000000111222222222222111111000000000000///////////////000000//////...---,,,------...------,,,,,,......//////000000//////000/////////.........---............////////////000000111111111222222222111000///......///000111//////............//////........................////////////////////////......///000000000000000...//////000111111222222000000000///......------//////............//////---...000111111111000///---------.........//////............////////////------...............---......////////////......,,,+++*********+++,,,---))))))))))))***+++,,,---SSSSSSSSSSSSTTTTTTTTTTTTSSSTTTUUUVVVVVVUUUTTTSSSRRRSSSUUUVVVWWWWWWVVVVVVRRRTTTVVVXXXWWWUUURRROOOQQQQQQPPPOOOOOOOOOPPPPPPSSSSSSSSSSSSTTTTTTUUUUUUNNNLLLKKKMMMPPPRRRPPPMMMOOOOOOOOOOOOPPPPPPQQQRRRSSSRRRRRRQQQPPPPPPOOOOOOOOOOOONNNNNNNNNOOOPPPQQQOOOPPPQQQRRRRRRRRRQQQPPPNNNNNNOOOOOOPPPQQQQQQQQQPPPPPPOOOOOOOOONNNNNNNNNLLLMMMOOOPPPPPPRRRUUUWWWPPPPPPPPPPPPPPPPPPOOOOOONNNNNNNNNNNNNNNNNNNNNNNNRRRRRRRRRRRRRRRRRRRRRRRROOOOOOOOONNNNNNNNNMMMMMMNNNMMMLLLKKKKKKJJJJJJJJJIIIJJJKKKLLLMMMNNNNNNNNNLLLLLLKKKJJJIIIIIIIIIIIIFFFEEEEEEEEEGGGHHHGGGFFFEEEEEEFFFFFFGGGGGGHHHHHHFFFFFFFFFFFFFFFGGGGGGGGGCCCDDDEEEGGGGGGEEEDDDCCCDDDCCCCCCCCCCCCDDDEEEEEEFFFFFFEEEDDDDDDDDDDDDDDDDDDEEEGGGHHHGGGFFFDDDCCCDDDDDDDDDCCCCCCBBBBBBAAABBBCCCCCCCCCCCCCCCCCCBBBBBBCCCDDDEEEDDDCCCAAA@@@BBBCCCDDDEEEEEECCCAAA@@@??????@@@AAABBBBBBBBBBBB@@@@@@AAABBBBBBCCCCCCDDDGGGFFFFFFFFFEEEEEEDDDDDD??????BBBGGGKKKLLLIIIEEEJJJHHHFFFDDDDDDFFFHHHJJJGGGGGGGGGGGGGGGGGGGGGGGGBBBCCCCCCDDDEEEFFFGGGGGGDDDEEEEEECCC@@@???BBBEEE@@@AAAAAABBBAAA@@@???>>>??????@@@@@@@@@@@@??????????????????@@@@@@@@@@@@>>>>>>>>>>>>>>>======<<<999:::;;;>>>@@@@@@>>><<<========================:::;;;;;;<<<===>>>?????????>>>===<<<<<<===>>>>>><<<;;;::::::999999::::::::::::999888777666555444777666666666555555555555666666666777666666555444444444444555555555555555444555555666666666666666555555444444555666888999777777777777777777777777666666666666666666666666777777666666666555555555555555444333444555666777666777888999888777555333444444555555555555444444333333222222333333444555555444333222222222333333222222222222222222222222333333333333333444555666333333444555555444444333222222222111111111111000000000111222222222222111000/////////..................//////......---,,,---------------------......///000000000000000///000000//////.........---............/////////000000000111111222222222222111000///......///000111//////............//////........................////////////////////////...//////000000000000000...//////000111222222222000000000///......------000//////.........//////,,,...000111222111000///---------.........//////............/////////000---.../////////...---,,,......///////////////...,,,+++*********+++,,,---))))))))))))***+++------OOOPPPQQQSSSSSSRRRRRRQQQUUUUUUUUUTTTSSSRRRQQQPPPUUUUUUSSSSSSSSSUUUWWWYYYVVVUUUUUUUUUUUUUUUUUUUUUQQQOOONNNOOORRRTTTSSSQQQQQQRRRTTTUUUTTTSSSQQQPPPPPPOOONNNNNNOOOPPPRRRSSSRRRRRRQQQPPPOOOOOONNNNNNPPPQQQRRRRRRPPPNNNNNNOOONNNOOOPPPOOONNNOOORRRTTTOOOOOOQQQQQQQQQPPPOOONNNPPPPPPRRRRRRRRRQQQPPPOOOSSSRRRQQQQQQRRRQQQOOOMMMMMMMMMMMMNNNOOOPPPRRRSSSQQQQQQPPPOOOOOOOOOOOOPPPPPPPPPPPPPPPOOOOOONNNMMMRRRRRRRRRRRRRRRRRRRRRRRRRRRQQQOOONNNMMMMMMNNNOOOOOOMMMLLLJJJJJJJJJKKKKKKJJJJJJKKKNNNOOOOOOMMMKKKKKKKKKJJJJJJJJJIIIIIIIIIEEEFFFFFFGGGGGGFFFFFFEEEFFFFFFGGGGGGGGGGGGFFFFFFFFFFFFGGGGGGGGGHHHHHHHHHEEEFFFFFFFFFFFFEEEDDDDDDGGGFFFEEEEEEFFFFFFEEECCCEEEEEEDDDAAA???>>>@@@BBBCCCEEEHHHIIIGGGDDDCCCBBBCCCCCCAAA>>>===>>>BBBEEEEEEDDDCCCBBBAAABBBCCCCCCBBBBBBCCCDDDEEEEEEDDDDDDCCCCCCCCCCCCCCCDDDEEEEEEBBBCCCCCCCCCDDDDDDEEEEEEFFFDDDBBB@@@@@@BBBDDDFFFFFFFFFEEEDDDCCCBBBAAAAAACCCBBBAAACCCFFFHHHGGGFFFHHHGGGEEEDDDDDDEEEGGGHHHIIIHHHFFFFFFFFFFFFHHHIIIFFFFFFDDDCCCCCCDDDEEEEEECCCCCCCCCBBBBBBAAAAAAAAA@@@@@@@@@@@@@@@@@@@@@@@@AAA@@@@@@@@@???>>>>>>>>>>>>>>>>>>>>>???@@@AAABBB@@@??????>>>===<<<;;;;;;:::===@@@AAA???>>>>>>@@@AAA???===<<<;;;<<<>>>???<<<<<<;;;;;;;;;;;;<<<<<<>>>>>>======<<<<<<<<<;;;;;;;;;;;;<<<;;;;;;::::::999999999999999888777777777777666666666666777777999777666666777777666444555555555555555444444444555555666666777777777888888888777777777777777777666666777777777777666666999999999888888777777777666666555555555555666666444444444555555777888888888777777666555444444444444555666777777666555444555555555444444333333333222222222333333444444444444444444444333222111111222222222333444555666777555555555555444333222111000000111222333444444555000000000111222222222333333000...///111333111000//////.........//////000000///...---------------......///000000000000000111222222111///...///000///////////////.........111222222333333222222111333222111000000111222333---...///000000///...---////////////////////////000000000000000000000000000000000111222222333333000000//////000222444555111111111111111000//////222222111000000000000000---...000111111111000///........................////////////////////////////////////..................////////////......***++++++,,,,,,++++++************+++,,,---...///SSSTTTVVVWWWWWWWWWVVVUUUUUUUUUUUUUUUTTTSSSRRRRRRUUUUUUTTTSSSTTTVVVWWWYYYXXXXXXXXXWWWVVVUUUTTTTTTRRRQQQOOOPPPSSSTTTRRRQQQQQQRRRSSSTTTTTTRRRQQQPPPNNNNNNMMMMMMNNNPPPQQQRRRRRRQQQQQQPPPOOOOOONNNNNNOOOPPPQQQQQQOOONNNOOOPPPPPPPPPPPPOOONNNOOOQQQSSSPPPQQQRRRSSSSSSSSSRRRQQQPPPQQQQQQQQQQQQQQQPPPPPPPPPOOOOOOPPPQQQQQQPPPNNNMMMMMMMMMMMMOOOPPPQQQRRRRRRQQQQQQPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPOOONNNNNNQQQQQQQQQQQQQQQQQQQQQQQQQQQPPPNNNMMMLLLLLLMMMMMMLLLLLLJJJJJJIIIJJJJJJKKKKKKJJJKKKMMMOOONNNLLLJJJIIIIIIIIIHHHHHHHHHGGGGGGGGGHHHHHHIIIIIIHHHHHHGGGEEEFFFFFFGGGGGGFFFFFFEEEFFFFFFFFFFFFGGGGGGGGGHHHEEEEEEEEEEEEFFFFFFFFFFFFHHHFFFEEEEEEFFFGGGEEEDDDEEEEEEEEEDDDBBBAAABBBDDDGGGIIIKKKJJJGGGEEECCCCCCDDDCCCBBB???>>>???CCCFFFEEEDDDCCCBBBBBBBBBCCCCCCCCCCCCDDDDDDDDDDDDDDDDDDDDDCCCCCCCCCCCCDDDEEEEEEBBBBBBBBBBBBCCCCCCDDDDDDEEEDDDBBBAAAAAABBBDDDEEEEEEEEEEEEDDDCCCCCCBBBBBBDDDCCCBBBDDDGGGIIIHHHGGGIIIHHHGGGFFFFFFGGGHHHIIIHHHHHHGGGGGGGGGGGGHHHHHHGGGGGGEEEEEEDDDEEEEEEFFFCCCCCCBBBBBBBBBAAAAAAAAA@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@????????????>>>>>>>>>>>>???@@@AAABBB@@@@@@??????>>>===<<<<<<<<>>@@@???===<<<<<<<<<===>>>===<<<<<<;;;;;;<<<<<<===>>>=========<<<<<<<<<<<<:::;;;;;;;;;:::999999888888999999999888888777666777666666666666666666777888777666666777777666444333333333444444444444444666666666666666777888888999999999999999999999999777888888999999888888777:::999999999888888888888666666555555555555666666444444444555555666777888666666666555444333333333555555555666666555555555555555444444444333333333333333333333333333444444333333444444444333222222333222222333333444555666555555555555444333222111111111111222333333444444111111111111222222222222222000......000222111/////////..................111111000///////////////...///000000111111000000000111222111/////////000////////////////////////111111111222222111111111222222111111111111222222......///000000///......////////////////////////000000000000000000000000000000000111222222333333111000000000000222333444000111111111111000//////222111000////////////000---...///000111000000///........................////////////////////////////////////..................////////////......***++++++,,,,,,++++++*********++++++,,,...///000RRRSSSTTTVVVVVVUUUUUUTTTTTTTTTUUUUUUUUUUUUTTTTTTUUUUUUTTTTTTTTTVVVXXXYYYZZZZZZYYYXXXVVVUUUTTTTTTUUUSSSRRRRRRSSSTTTRRRQQQQQQRRRRRRSSSRRRQQQPPPOOOLLLLLLLLLMMMNNNPPPQQQRRRQQQQQQQQQPPPPPPOOOOOONNNMMMOOOPPPPPPOOONNNOOOPPPQQQRRRQQQPPPNNNNNNPPPRRRQQQRRRSSSTTTTTTTTTTTTTTTQQQQQQPPPPPPPPPQQQQQQRRRMMMMMMMMMOOOQQQRRRQQQPPPLLLLLLLLLMMMNNNOOOPPPQQQSSSRRRQQQQQQPPPPPPQQQQQQPPPPPPPPPQQQPPPPPPOOONNNQQQQQQQQQQQQQQQQQQQQQQQQOOONNNMMMLLLLLLKKKLLLLLLJJJJJJIIIIIIIIIJJJKKKKKKKKKKKKKKKLLLMMMMMMJJJHHHGGGGGGGGGGGGFFFFFFFFFFFFGGGHHHHHHIIIIIIHHHHHHGGGEEEEEEFFFFFFFFFFFFEEEEEEEEEEEEEEEFFFFFFFFFGGGGGGEEEEEEDDDDDDEEEFFFHHHIIIIIIGGGFFFFFFGGGGGGFFFEEEDDDFFFGGGGGGEEEDDDEEEFFFLLLLLLLLLJJJGGGEEEEEEEEEDDDDDDCCCAAA???@@@DDDFFFEEEDDDCCCCCCBBBBBBCCCCCCDDDDDDDDDDDDDDDCCCCCCCCCDDDDDDCCCCCCDDDDDDEEEFFFAAABBBBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDDDDDDDDDDEEEDDDDDDEEEHHHIIIIIIHHHJJJIIIHHHGGGGGGHHHIIIJJJHHHHHHIIIIIIIIIIIIHHHHHHHHHHHHGGGFFFEEEFFFFFFFFFCCCBBBBBBBBBBBBAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA?????????@@@@@@@@@@@@@@@>>>>>>>>>>>>???@@@AAAAAAAAA@@@@@@??????>>>>>>>>>???@@@AAAAAA>>>=========>>>>>>>>>>>>===============<<<<<<;;;;;;<<<<<<===============<<<<<<<<<<<<;;;;;;;;;:::999888777666777888888888888777666666666666555555555555666666888666555666777777666444111222222333333444444444777777666555555666888999999999999999999999999999999999::::::::::::999999:::::::::999999999999888777666666555555666666777555555444555555666777888555555555444333333222222555555444444444444555555555444444444444333333333444444444444333333333333222222333444444444444333444333333222222333333444555555444444333333222222222222222222333333333333222222222222222111111111111000......///000000///000///...---------------111111000000000000/////////000111111222222111111000111222111000///000111//////////////////000000000111111111111111111000111111222222222222111111...//////000000//////...////////////////////////000000000000000000000000000000000111222222333333222111111000111111222222000000000000000///......000000//////......//////......///000000000000000......................../////////////////////////////////............---......////////////......***++++++,,,,,,++++++***+++++++++,,,---...///000QQQRRRSSSTTTUUUTTTSSSSSSSSSTTTUUUVVVVVVVVVVVVVVVUUUUUUTTTUUUUUUVVVXXXXXXYYYXXXXXXWWWVVVUUUUUUTTTVVVVVVUUUTTTTTTSSSRRRRRRQQQRRRRRRRRRQQQPPPOOONNNLLLLLLMMMNNNPPPQQQRRRSSSQQQQQQPPPPPPPPPOOOOOOOOOMMMNNNOOOOOONNNNNNPPPQQQSSSSSSRRRPPPNNNNNNOOOQQQPPPQQQQQQRRRSSSSSSSSSSSSRRRQQQPPPOOOOOOPPPRRRSSSOOONNNNNNPPPRRRRRRQQQPPPMMMLLLLLLMMMNNNOOOPPPPPPSSSSSSRRRQQQQQQQQQQQQRRRPPPPPPQQQQQQQQQQQQPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPOOONNNNNNMMMLLLLLLKKKKKKIIIIIIIIIJJJKKKLLLMMMMMMLLLKKKJJJKKKLLLKKKIIIGGGGGGGGGGGGGGGFFFFFFFFFFFFEEEFFFFFFGGGGGGFFFFFFEEEDDDEEEEEEFFFFFFEEEEEEDDDDDDEEEEEEEEEEEEFFFFFFFFFEEEEEEDDDCCCDDDGGGIIIKKKIIIHHHFFFGGGHHHHHHGGGEEEBBBEEEGGGHHHGGGFFFFFFGGGLLLLLLKKKIIIFFFEEEFFFHHHEEEEEEDDDBBBAAAAAADDDGGGEEEDDDDDDCCCCCCCCCCCCCCCEEEDDDDDDCCCCCCCCCCCCCCCDDDDDDDDDCCCDDDEEEEEEFFFCCCCCCCCCCCCCCCCCCCCCCCCBBBCCCDDDEEEEEEDDDCCCBBBCCCCCCCCCCCCDDDDDDEEEEEEDDDDDDDDDEEEGGGHHHHHHHHHIIIIIIHHHGGGGGGHHHIIIIIIGGGHHHJJJJJJJJJJJJHHHGGGHHHGGGGGGFFFEEEEEEEEEEEEBBBBBBBBBBBBBBBBBBBBBBBBAAAAAAAAAAAAAAAAAAAAAAAA?????????@@@@@@AAAAAAAAA??????>>>>>>???@@@@@@AAAAAA@@@@@@@@@@@@@@@@@@@@@??????@@@@@@???>>>>>>???>>>>>>>>>???>>>===<<<<<<======<<<<<<<<<<<<=====================<<<<<<<<<<<<<<<;;;;;;999888777666777777888888888777777666666666555555555555666666777666555555666777666555111111222333444555555555888777666555555666777999666666666666777777777777999::::::::::::::::::999:::::::::999999999999999777777666666666666777777555555555555555666777777555555555444444444333333555444333222222333444555444444444444444444444444555555444444333333333222111222333444555555555555444444333222222222222222555444444333333222222222444444333333333222222222333333333222222111111111111000///...////////////000///...---,,,,,,,,,---....../////////.........000000111222222222222222000111222111000///000111//////000000000000111111222222111111111111222222000111222333333222111000/////////000000/////////////////////////////////000000000000000000000000000000000111222222333333333222222111111111000000///000000000000///......//////............//////...//////000000000000000........................//////////////////////////////.........------------......//////......---***++++++,,,,,,++++++***+++++++++,,,---...000000SSSTTTUUUWWWWWWVVVVVVUUUSSSTTTUUUVVVVVVVVVVVVVVVUUUUUUUUUUUUVVVWWWXXXXXXUUUUUUUUUUUUUUUVVVVVVVVVWWWWWWWWWUUUTTTSSSRRRSSSRRRRRRRRRQQQQQQPPPOOONNNNNNNNNOOOPPPQQQRRRSSSSSSPPPPPPPPPPPPPPPOOOOOOOOONNNOOOOOOOOONNNNNNPPPRRRTTTTTTSSSQQQNNNNNNOOOQQQOOOOOOOOOOOOOOOPPPPPPQQQQQQPPPOOOOOOOOOQQQRRRSSSRRRQQQQQQQQQSSSSSSQQQPPPMMMMMMMMMMMMNNNOOOPPPPPPSSSSSSRRRQQQQQQQQQQQQRRRPPPQQQQQQRRRRRRQQQQQQQQQPPPPPPPPPPPPPPPPPPPPPPPPOOOOOOOOONNNNNNMMMLLLLLLJJJJJJKKKLLLMMMNNNNNNNNNMMMKKKJJJJJJKKKKKKIIIHHHHHHHHHHHHHHHGGGGGGGGGGGGEEEFFFFFFGGGGGGFFFFFFEEEEEEEEEFFFFFFFFFFFFEEEEEEDDDEEEEEEEEEEEEFFFFFFFFFEEEDDDDDDDDDEEEGGGJJJLLLIIIHHHFFFGGGHHHHHHGGGEEEAAACCCFFFGGGFFFEEEFFFFFFIIIIIIHHHGGGEEEEEEHHHJJJEEEEEEDDDCCCBBBBBBDDDGGGDDDDDDDDDDDDDDDCCCCCCCCCEEEDDDCCCCCCCCCCCCDDDDDDDDDDDDDDDDDDDDDEEEFFFFFFEEEEEEEEEDDDDDDDDDDDDDDDBBBCCCEEEFFFFFFEEECCCBBBBBBBBBCCCCCCDDDEEEEEEEEECCCDDDDDDEEEEEEEEEFFFGGGHHHHHHGGGGGGGGGGGGHHHHHHGGGHHHJJJJJJJJJJJJHHHGGGFFFFFFFFFEEEEEEDDDCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBAAAAAAAAAAAAAAAAAAAAAAAA??????@@@@@@AAAAAAAAABBB?????????>>>??????@@@AAA@@@@@@@@@@@@@@@AAAAAAAAA>>>>>>>>>>>>@@@AAAAAABBB>>>>>>>>>???>>>===<<<<<<=========<<<<<<=========<<<<<<<<<========================<<<;;;999888777777777888888888888777777666666555555555555666666666555444555666777666555222333333444555666666777888777666555555666777777555555666666666777777777888888999999999999888888999999999999999999999999777777666666666666777777666555555555555666666777666666666555555555555555555444333222222333444555444444444444444444444444555555555444444333333333111222333444555666666666555555444333222222222222444444333222222222333333555555444333333222222222444333333333222222111111111111000///......//////000///...------------------...///000000///......000000111222222222222222///000111111000///000222000000000000111111222222444333222222222222333444000111222333333222111000000000000//////000000000000000000000000000000000000000000000000000000000000000000111222222333333333222222222111000000///000000000000000//////...//////............/////////////////////000000111////////////////////////////////////////////////............------------------............------***++++++,,,,,,++++++***+++++++++,,,---...///000RRRSSSTTTUUUVVVUUUTTTTTTSSSSSSTTTUUUVVVVVVUUUUUUUUUUUUVVVVVVWWWXXXXXXXXXSSSTTTTTTUUUUUUVVVVVVWWWVVVWWWWWWVVVTTTRRRSSSTTTTTTSSSSSSRRRQQQPPPOOOOOOOOOPPPQQQRRRSSSSSSRRRRRRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPOOONNNOOOQQQSSSTTTTTTSSSQQQOOONNNPPPQQQOOOOOONNNMMMMMMNNNNNNOOOPPPPPPPPPPPPPPPQQQRRRSSSSSSRRRRRRRRRTTTTTTRRRPPPOOONNNNNNNNNOOOOOOPPPQQQSSSRRRQQQQQQPPPPPPQQQQQQPPPQQQRRRRRRSSSRRRRRRRRROOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOONNNMMMLLLKKKJJJKKKLLLMMMNNNOOOOOONNNMMMKKKJJJJJJLLLLLLKKKJJJJJJIIIIIIIIIHHHHHHHHHHHHGGGHHHHHHIIIIIIHHHHHHGGGFFFFFFGGGGGGGGGGGGFFFFFFEEEEEEEEEFFFFFFFFFGGGGGGEEEEEEEEEEEEFFFHHHJJJKKKIIIGGGFFFFFFGGGGGGFFFEEEAAACCCEEEEEEEEEDDDEEEFFFFFFGGGGGGFFFEEEEEEHHHJJJDDDDDDDDDCCCBBBBBBDDDFFFDDDEEEEEEEEEEEEDDDCCCBBBDDDCCCBBBBBBBBBDDDEEEFFFEEEEEEDDDDDDEEEEEEFFFGGGFFFFFFFFFEEEEEEEEEEEEDDDCCCDDDEEEFFFFFFEEEDDDCCCBBBCCCCCCCCCDDDDDDEEEEEEBBBDDDEEEEEEDDDDDDEEEFFFGGGGGGGGGHHHHHHGGGGGGGGGHHHHHHIIIIIIIIIIIIHHHHHHFFFFFFFFFFFFEEECCCBBBAAAAAAAAAAAABBBBBBBBBBBBCCCAAAAAAAAAAAAAAAAAAAAAAAA@@@@@@@@@AAAAAAAAAAAAAAA@@@???????????????@@@@@@?????????@@@@@@AAAAAABBB>>>===<<<>>>@@@CCCCCCCCC>>>>>>>>>>>>============>>>======<<<<<<======>>><<<<<<<<<========================<<<;;;:::999888777777888999999999999888777777666666666666777777555444444444666777666555333444444555555666666666777777777777777666666666666777777888888999999999777777888888888888777777777888888888888999999999888777777666666777777888666666555555555555666666666666666666666666666666555555444444444444555555333333333444444444444555555555555444444444444444222222333555555666666666666555444444333333333333444333222111111222333444555555444444333333222222333333333333333222222222222222222111///...///111//////.........////////////000111222333222111000///000111111222222111111///000111111000000111222000000000111222222333333555444333222222333444555111111222222222222111111111000000//////000000111000000000000000000000000000000000000000000000000000000000111222222333333222222222222222111000///111111111111111000////////////......//////000000///////////////000111111////////////////////////////////////////////////.........------------,,,------............------***++++++,,,,,,++++++************+++,,,---...///QQQRRRSSSTTTTTTTTTSSSRRRSSSSSSTTTTTTUUUTTTTTTTTTTTTUUUVVVWWWXXXXXXXXXXXXUUUUUUUUUVVVVVVVVVVVVVVVTTTVVVWWWVVVSSSRRRSSSUUUUUUUUUSSSRRRQQQPPPPPPPPPPPPPPPQQQRRRRRRQQQPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPRRRRRRRRRPPPNNNOOOQQQSSSSSSSSSSSSQQQOOOOOOQQQRRRRRRQQQPPPOOONNNNNNOOOOOONNNOOOPPPQQQRRRRRRRRRRRRQQQPPPPPPQQQSSSTTTSSSRRRPPPPPPOOOOOOPPPPPPQQQQQQRRRQQQQQQPPPPPPPPPPPPPPPQQQQQQRRRSSSSSSSSSSSSSSSNNNNNNNNNNNNNNNNNNNNNNNNMMMNNNNNNNNNNNNLLLKKKJJJJJJKKKLLLMMMNNNNNNMMMMMMMMMKKKJJJKKKLLLMMMMMMLLLIIIIIIIIIIIIHHHHHHHHHHHHGGGHHHHHHIIIIIIHHHHHHGGGGGGGGGHHHHHHHHHHHHGGGGGGFFFFFFFFFFFFGGGGGGGGGHHHEEEEEEFFFGGGGGGHHHIIIIIIHHHFFFEEEEEEFFFGGGEEEDDDDDDEEEEEEEEECCCCCCEEEGGGFFFGGGHHHGGGEEEEEEFFFHHHCCCDDDDDDCCCBBBBBBCCCEEEDDDEEEEEEFFFEEEDDDCCCBBBCCCBBBAAAAAABBBDDDFFFHHHEEEEEEDDDDDDEEEEEEFFFGGGFFFEEEEEEEEEDDDDDDDDDDDDDDDDDDEEEEEEEEEEEEDDDDDDCCCCCCCCCDDDDDDDDDDDDDDDCCCEEEGGGFFFDDDDDDEEEGGGHHHHHHIIIIIIIIIIIIHHHHHHHHHHHHGGGGGGGGGGGGHHHHHHGGGGGGGGGGGGFFFDDDBBBAAAAAAAAAAAABBBBBBBBBCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBAAAAAAAAAAAAAAAAAA@@@@@@@@@@@@???????????????@@@>>>>>>>>>???@@@AAAAAABBB@@@>>><<<===@@@CCCCCCBBB@@@???===<<<<<<<<<===>>>>>>>>>============>>>>>><<<<<<<<<<<<=========>>>;;;;;;;;;;;;;;;:::999888888888999:::::::::::::::888888777777777777888888555444333444666777666555444444444444444444444444666777888888888777555444666666777777888999999:::777777888888888888777777666666777777777888888888888888777777777777888888666666555555555555666666555555555555555555555555555555555666666555555555333333333444444444555555444444444444555555555555333333444555666666555555666666555444444444555555444333111000000222333444444444444444444333333333222222333333333333333333333444444222///...000222///////////////000111222...000111333333333111000...///000000111111000000...000111111000000111222000000111111222333333444555444222111111222444555222222111111111111222222111111000//////000111111000000000000000000000000000000000000000000000000000000000111222222333333111111222222222111000000222222222222222111111000000////////////000111222000//////...///000111222////////////////////////////////////////////////.........---------,,,,,,,,,------......------,,,***++++++,,,,,,++++++***)))))))))***+++,,,---...UUUVVVWWWXXXYYYXXXWWWWWWSSSSSSTTTTTTTTTSSSSSSRRRTTTUUUVVVWWWXXXXXXXXXXXXXXXXXXXXXWWWWWWVVVVVVVVVSSSUUUWWWVVVSSSRRRSSSUUUVVVUUUTTTRRRQQQQQQPPPPPPOOOPPPQQQQQQQQQPPPOOONNNPPPPPPPPPPPPPPPPPPPPPPPPTTTTTTSSSQQQOOOOOOQQQSSSSSSSSSSSSQQQPPPOOOQQQSSSVVVTTTSSSQQQPPPPPPPPPPPPMMMNNNPPPRRRSSSSSSRRRQQQMMMMMMNNNPPPSSSTTTTTTSSSQQQQQQPPPPPPPPPQQQRRRRRRQQQQQQPPPOOOOOOOOOOOOPPPQQQQQQRRRSSSSSSSSSSSSSSSNNNNNNNNNNNNNNNNNNNNNNNNLLLLLLMMMMMMMMMKKKIIIHHHIIIJJJLLLMMMMMMLLLLLLKKKMMMKKKJJJKKKMMMNNNNNNNNNIIIIIIIIIHHHHHHHHHGGGGGGFFFFFFFFFGGGGGGFFFFFFFFFGGGHHHHHHIIIIIIHHHHHHGGGFFFGGGGGGGGGGGGHHHHHHHHHEEEEEEGGGHHHHHHHHHHHHHHHGGGFFFEEEEEEFFFFFFEEECCCFFFFFFFFFEEECCCCCCFFFHHHHHHIIIJJJHHHFFFEEEEEEFFFBBBCCCDDDCCCAAAAAACCCDDDDDDEEEFFFFFFFFFEEECCCBBBBBBBBBAAAAAABBBEEEGGGIIIEEEEEEEEEEEEEEEFFFFFFGGGEEEEEEDDDDDDCCCCCCCCCBBBEEEEEEDDDDDDDDDDDDEEEEEEDDDDDDDDDDDDDDDDDDDDDDDDDDDFFFHHHGGGEEEDDDFFFIIIIIIIIIJJJJJJJJJJJJIIIIIIIIIHHHFFFFFFFFFFFFHHHIIIHHHHHHIIIHHHGGGEEECCCBBBAAAAAAAAABBBBBBCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBAAAAAA@@@@@@@@@@@@@@@???????????????@@@======>>>???@@@AAAAAABBBCCC@@@======@@@BBBBBB@@@AAA???===<<<;;;<<<>>>???>>>>>>============>>>>>>;;;<<<<<<<<<======>>>>>>999999:::::::::999999888888999:::;;;;;;;;;;;;;;;999999888888888888999999555444333444666777666555444333333333333333333333555666888:::999777444222333444444555666777777888888888888999999888888888555555666666777777777888888888777777777777888888777666666555555555666666444444444444444444444444444555666777777666555444333333333444444555555555333444444444555666666666333444555555666555555555666666555555555666666777444333111000000222333555444444444444444444444444222222222333333444444444333555555333000///000333////////////000222333444,,,...000111222111000///......///000000000000000...000111111000000111333000000111222333333444444444333111000000111333444333222111000000111222333222111000//////000111222000000000000000000000000000000000000000000000000000000000111222222333333000111222333333222111000222333333333333222111111000000000000000111222222000///.........///111222000000000000000000000000////////////////////////......---------,,,,,,,,,,,,------......------,,,+++++++++,,,,,,+++++++++((((((((()))***+++------QQQQQQRRRTTTUUUVVVWWWXXXWWWUUURRRRRRRRRSSSSSSRRRVVVUUUTTTTTTTTTVVVXXXZZZRRRRRRRRRSSSTTTUUUWWWWWWTTTTTTSSSRRRRRRRRRRRRRRRVVVUUUSSSRRRQQQPPPQQQQQQOOOPPPSSSTTTSSSQQQNNNMMMOOOPPPPPPQQQQQQPPPPPPOOOTTTTTTSSSSSSRRRQQQQQQQQQRRRRRRSSSSSSSSSSSSRRRRRRQQQRRRRRRSSSTTTUUUUUUUUUQQQQQQQQQSSSUUUUUUSSSPPPRRRRRRRRRRRRSSSSSSSSSSSSNNNOOOPPPPPPQQQPPPPPPPPPQQQPPPOOOOOONNNNNNNNNNNNOOOQQQRRRQQQPPPOOOOOOOOOQQQQQQPPPOOONNNNNNNNNNNNOOOMMMLLLLLLMMMMMMLLLJJJJJJJJJKKKKKKLLLLLLLLLMMMNNNNNNMMMLLLKKKJJJIIIIIIHHHHHHHHHHHHHHHHHHHHHHHHLLLKKKHHHGGGFFFFFFGGGHHHHHHFFFEEEFFFHHHJJJJJJIIIJJJJJJJJJIIIIIIHHHHHHHHHCCCDDDDDDEEEFFFFFFGGGGGGFFFFFFGGGGGGGGGGGGFFFFFFDDDDDDDDDEEEFFFHHHIIIJJJKKKIIIFFFDDDCCCDDDCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCFFFFFFFFFDDDBBBBBBDDDFFFCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCBBBDDDDDDCCCBBBBBBBBBBBBCCCCCCCCCDDDDDDDDDDDDCCCBBBHHHIIIIIIIIIHHHHHHIIIKKKHHHHHHIIIIIIJJJKKKKKKKKKGGGGGGFFFFFFGGGIIIJJJKKKEEEFFFGGGGGGHHHHHHGGGGGGDDDDDDDDDCCCBBBBBBAAAAAAAAA@@@?????????@@@AAABBBBBBCCCCCCCCCBBBAAAAAA@@@@@@@@@????????????@@@@@@===>>>???@@@AAABBBBBBBBBCCCAAA>>>???@@@@@@>>>;;;>>>>>>>>>>>>>>>>>>>>>>>>;;;;;;;;;<<<<<<<<<=========<<<<<<===>>>??????>>><<<<<<<<<;;;;;;:::::::::999999::::::::::::;;;;;;999999888777666555444444333333333444555666666777555555555555555555444444555666666666666444333222444555666777888999::::::888888999:::;;;;;;<<<<<<777777666666666666777777666666666666777777777777888777666555444444555666555444444555666666555333444555666777777666555444333333333444444444555555111222333333444444444333444555555666777666666666666666555444444444444555555444444333333333444444444444444444333333222111000111111111111222222222333333333222222111111111222111000000111111///...---///111222333222000///111111111000000000000000000000000000111111111111000000000111222222222333333333222000///000444777111222222333333222222111000000111111222222222222111222222333333222222111000000000000111111111111000111111111111222222222111111222222222333333333222222222222222111000/////////000111111111111111////////////////////////000///////////////000000////////////////////////........................///............------------------,,,+++***)))(((***))))))((()))+++---...QQQRRRSSSTTTUUUWWWWWWXXXVVVUUUUUUVVVWWWVVVTTTRRRVVVVVVUUUTTTUUUWWWYYYZZZTTTSSSSSSTTTTTTUUUVVVWWWUUUUUUTTTSSSSSSSSSSSSSSSUUUTTTSSSRRRQQQQQQRRRRRRPPPQQQSSSSSSSSSQQQPPPNNNOOOPPPPPPPPPPPPPPPPPPOOOSSSSSSRRRRRRRRRRRRQQQQQQRRRRRRRRRSSSSSSRRRRRRRRRQQQRRRRRRSSSTTTTTTUUUUUUQQQQQQRRRTTTVVVUUUSSSQQQQQQRRRRRRRRRSSSSSSSSSSSSSSSTTTTTTTTTSSSRRRRRRQQQQQQQQQPPPOOOOOOOOOOOOOOOOOOPPPRRRQQQOOONNNNNNOOORRRQQQPPPOOONNNNNNNNNNNNMMMLLLKKKKKKLLLLLLKKKIIIKKKKKKKKKKKKLLLLLLMMMMMMMMMMMMMMMLLLKKKJJJJJJIIIIIIIIIIIIIIIIIIIIIIIIIIIKKKJJJHHHFFFEEEFFFGGGHHHHHHGGGFFFGGGIIIJJJJJJJJJHHHHHHHHHHHHHHHGGGGGGGGGDDDDDDEEEFFFFFFGGGHHHHHHGGGGGGHHHHHHHHHHHHGGGGGGDDDDDDEEEEEEFFFHHHIIIJJJMMMKKKGGGEEEDDDDDDEEEEEECCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDCCCAAAAAABBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBEEEDDDCCCBBBBBBBBBBBBBBBFFFFFFGGGGGGGGGGGGFFFFFFEEEFFFGGGGGGGGGGGGIIIKKKJJJJJJJJJJJJIIIIIIIIIIIIIIIIIIHHHHHHHHHJJJKKKLLLKKKKKKJJJJJJIIIHHHFFFEEEEEEEEEDDDDDDCCCBBBAAAAAABBBAAA@@@??????@@@AAABBBBBBBBBBBBBBBBBBAAA@@@@@@@@@??????????????????@@@===>>>???@@@AAAAAAAAAAAAAAA???======>>>>>><<<:::<<<<<<<<<<<<<<<<<<<<<<<<;;;;;;;;;<<<<<<<<<=========<<<<<<<<<>>>???>>>===<<<<<<;;;;;;;;;:::::::::999999::::::::::::;;;;;;999999888777666555444444333444444555666666777777555555555555555555555555333444555666666666555444555666666777888999:::;;;888888888999:::;;;;;;;;;777777777666666777777777666666666777777777888888777777555444444444555555555444444555666666555333444555666777777666555444333333333444444444555555111222333333444444444444444555555666666666666666666666555444444444444444555444444333333444444444333444444444333333222111000111111111111222222222333333333333222222222111333111000000111111000///...///111222222222000///111111111111000000000000000000000000111111111222111111111111222222222222222333222111000111333666222222333333333333222222//////000000111111111111111222222333333222222111000000000000111111111111000000111111111222222222111111111222222222333333222222222222222111000000//////000111111111111111111111111111111111111111222111000000////////////////////////////////////........................///............------------------,,,,,,***))))))***)))))))))***+++,,,---QQQRRRSSSUUUVVVWWWXXXXXXVVVVVVWWWYYYZZZYYYVVVSSSWWWVVVUUUUUUVVVWWWYYYZZZVVVUUUUUUTTTUUUUUUVVVVVVVVVUUUUUUTTTTTTTTTTTTTTTTTTSSSRRRQQQQQQRRRSSSTTTSSSSSSRRRRRRRRRRRRQQQQQQPPPPPPPPPPPPPPPPPPPPPPPPQQQRRRRRRRRRRRRSSSSSSSSSQQQQQQRRRRRRRRRRRRQQQQQQQQQRRRRRRSSSSSSTTTTTTUUURRRRRRSSSUUUWWWVVVTTTRRRQQQQQQRRRRRRRRRSSSSSSSSSVVVVVVVVVUUUTTTRRRQQQPPPQQQQQQPPPPPPOOOOOOPPPPPPNNNPPPQQQPPPOOONNNNNNNNNSSSRRRQQQPPPOOOOOOOOOOOOMMMKKKJJJJJJKKKLLLKKKIIIKKKKKKLLLLLLLLLLLLMMMMMMLLLLLLLLLKKKKKKJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJIIIGGGFFFEEEFFFFFFGGGIIIHHHGGGHHHJJJKKKKKKKKKFFFFFFGGGGGGGGGGGGGGGHHHEEEFFFFFFGGGGGGHHHHHHIIIHHHHHHHHHIIIIIIHHHHHHHHHEEEEEEEEEEEEFFFHHHIIIJJJOOOLLLIIIEEEDDDEEEGGGHHHCCCCCCCCCCCCCCCCCCCCCCCCBBBCCCDDDDDDBBBAAABBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC??????@@@@@@AAAAAABBBBBBFFFEEEDDDCCCBBBAAAAAAAAACCCDDDDDDEEEEEEDDDDDDDDDDDDEEEFFFFFFEEEFFFHHHJJJKKKKKKJJJIIIIIIHHHGGGGGGKKKJJJJJJJJJJJJJJJKKKLLLLLLLLLLLLLLLKKKIIIHHHGGGGGGGGGFFFEEECCCBBBBBBAAABBBBBBAAAAAAAAAAAABBBBBBAAAAAABBBBBBBBBAAA@@@@@@????????????????????????>>>>>>???@@@AAAAAAAAA@@@???===<<<<<<<<<<<<;;;999<<<<<<<<<<<<<<<<<<<<<<<<;;;;;;<<<<<<<<<============<<<<<<<<<>>>???>>>===<<<;;;;;;;;;;;;:::::::::999999::::::::::::;;;;;;999999888777666555555444555555666666777777888888555555555555555555555555222333444666666777666666666777777888999:::;;;;;;777777888888999:::::::::888888777777777777888888777777777888888888999999666666555444444444444555666555444555666777555333444555666666666666555444333333333444444444555555222222333333333333444444444444555555666666666666666555555444444444444444444444444444444444444444333333444444444333222222000111111111111222222222444444333333333333222222333222111111222222111000...///000222222111111000111111111111111111111111000000111111111222222222222222222222222111111111111222333333222222333555222222333333333333222222/////////000000000000000111222222333333222222111000000000000111111111111000000000111111111222222111111111222222222222333111222222222222111000000///000111111222111111111111111111111111111111111444333222111000////////////////////////////////////////////////////////////............---------,,,------,,,,,,+++***)))******)))******+++,,,---QQQRRRTTTVVVWWWXXXXXXXXXXXXWWWWWWXXXYYYYYYWWWUUUVVVVVVVVVVVVWWWXXXYYYZZZWWWWWWVVVUUUUUUTTTUUUUUUUUUTTTTTTSSSSSSTTTTTTTTTSSSRRRQQQQQQQQQSSSTTTUUUTTTSSSRRRQQQQQQRRRSSSTTTPPPPPPPPPOOOOOOPPPPPPPPPRRRRRRRRRSSSTTTUUUUUUVVVQQQQQQRRRRRRRRRRRRQQQQQQRRRRRRRRRRRRSSSSSSTTTTTTSSSSSSSSSUUUWWWWWWUUURRRQQQQQQQQQRRRRRRRRRSSSSSSRRRSSSSSSRRRQQQPPPOOOOOORRRRRRQQQPPPPPPQQQQQQRRRNNNOOOQQQPPPOOOMMMMMMNNNSSSSSSRRRQQQPPPPPPPPPPPPMMMLLLKKKKKKLLLMMMLLLJJJLLLLLLLLLLLLLLLLLLLLLLLLKKKKKKKKKKKKKKKKKKJJJJJJKKKKKKKKKKKKKKKKKKKKKKKKIIIHHHGGGFFFFFFFFFFFFGGGJJJHHHGGGHHHJJJLLLLLLKKKFFFFFFGGGGGGHHHHHHIIIIIIGGGGGGGGGHHHHHHIIIIIIIIIGGGGGGHHHHHHHHHHHHGGGGGGFFFFFFFFFFFFGGGHHHIIIJJJOOOMMMIIIFFFCCCDDDGGGIIICCCCCCCCCCCCCCCCCCCCCCCCBBBDDDGGGGGGEEEDDDDDDDDDCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC>>>>>>>>>???@@@AAABBBBBBFFFEEEDDDCCCBBBAAAAAAAAABBBBBBCCCCCCDDDDDDCCCCCCEEEFFFGGGFFFEEEEEEGGGHHHIIIIIIIIIIIIHHHHHHGGGGGGKKKJJJJJJJJJJJJJJJJJJJJJIIIIIIJJJKKKKKKKKKKKKJJJHHHGGGFFFEEEDDDCCCBBBAAACCCCCCBBBBBBBBBBBBBBBBBB@@@@@@AAAAAAAAAAAA@@@@@@?????????@@@@@@?????????>>>??????@@@@@@@@@@@@???======<<<<<<<<<<<<;;;:::<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<============>>><<<;;;<<<>>>>>>===<<<;;;;;;;;;;;;;;;;;;;;;;;;999999999:::::::::;;;;;;:::999999888777666555555666666777777888888888888555555555555666666666666444444555666666666666666777888888999::::::;;;;;;777777888888888999999999888888777777777777888888777888888888999999999999555555555444444444444555666555444555777777555444555555555555555555555555333333333444444444555555333333333333333333333444444444444444555555666666666555444444333333444444333333444444444444444444333333333444444333333222000000111111111222222222444333333333333333333333333222111222333333222111//////000111111111111000000111111111111111222222111111111222222222333333333333333222222111111111000222444555444333333444222333333333333333333222000000000000111111111111111222222333333222222111///000000000111111111111000000000000111111111111111111111111222222222222111111222222222111111000000111111222222111111111111111111111111111111111333333222111000000000111////////////////////////000000000000000000000000///............---------,,,,,,------,,,++++++***************++++++,,,,,,QQQSSSUUUWWWYYYYYYYYYXXXZZZWWWTTTTTTUUUWWWXXXXXXUUUUUUVVVVVVWWWXXXXXXYYYWWWWWWVVVUUUTTTTTTTTTTTTSSSSSSRRRRRRRRRSSSSSSTTTRRRRRRQQQQQQRRRSSSTTTUUUTTTSSSRRRQQQQQQRRRTTTUUUQQQPPPOOOOOOOOOOOOPPPQQQSSSSSSTTTUUUVVVVVVWWWXXXQQQQQQRRRRRRRRRRRRQQQQQQRRRRRRRRRRRRRRRSSSSSSSSSSSSSSSSSSUUUWWWWWWUUURRRQQQQQQQQQQQQRRRRRRRRRRRROOOPPPPPPQQQQQQPPPPPPPPPSSSRRRRRRQQQRRRRRRSSSSSSNNNPPPQQQQQQOOONNNNNNOOOSSSSSSRRRQQQPPPPPPPPPPPPNNNMMMLLLLLLNNNNNNNNNLLLKKKKKKKKKKKKKKKKKKKKKKKKJJJJJJJJJJJJKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKHHHHHHGGGGGGGGGGGGGGGGGGJJJHHHGGGHHHJJJLLLLLLKKKGGGGGGHHHHHHIIIIIIJJJJJJHHHHHHHHHHHHHHHIIIIIIIIIFFFFFFGGGGGGGGGGGGFFFFFFFFFFFFFFFFFFGGGHHHIIIIIIMMMLLLJJJFFFCCCCCCFFFIIIDDDDDDDDDDDDDDDDDDDDDDDDBBBDDDFFFGGGEEEDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD>>>>>>???@@@AAAAAABBBBBBEEEEEEDDDBBBBBBAAAAAAAAADDDEEEFFFGGGGGGGGGGGGGGGHHHHHHHHHGGGEEEDDDEEEGGGGGGGGGGGGGGGHHHHHHIIIIIIHHHHHHHHHHHHHHHHHHGGGGGGFFFGGGHHHHHHIIIIIIHHHHHHGGGGGGFFFEEEDDDCCCBBBBBBCCCCCCCCCBBBBBBAAAAAAAAA??????@@@@@@@@@@@@@@@???>>>???@@@@@@@@@@@@???>>>??????@@@@@@@@@???>>>>>>===>>>>>>======<<<<<<===========================<<<<<<<<<=========>>>>>>>>><<<;;;<<<===>>><<<;;;;;;;;;;;;;;;;;;;;;;;;;;;999999999:::::::::;;;;;;::::::999888777666555555777777777888888888888888555555555666666666777777777777666666555555555555888888888999:::::::::;;;888888888888888888999999888888777777777777888888777888888888999999999999444555555555555555555555666555555666777777666444555555444444444444555555333333333444444444555555444444333222222222333444555444444333444555666666555555444333333333333333222333444555555555444444222333333444444333333333000000111111111222222222333333333333333333333333333222111111333444333111//////000111111111111111000000111111222222222333222222222222333333333333444333333333222222111111///222555555444333333333333333333444444333333333222222222222222222222222111222222333333222222111///000000000111111111111//////000000000111111111000000111111111222222222000111111222222222111111111111222222222222111111000000000000000000000000111000000000111222333333000000000000000000000000000000000000000000000000///............---------,,,,,,---------,,,++++++***+++++++++,,,,,,,,,,,,QQQSSSVVVXXXZZZZZZYYYXXXZZZWWWSSSQQQSSSVVVXXXYYYTTTTTTUUUVVVVVVWWWWWWXXXVVVVVVUUUTTTSSSSSSSSSTTTRRRRRRRRRRRRRRRRRRSSSTTTSSSRRRQQQQQQQQQSSSTTTUUUSSSRRRQQQQQQQQQRRRSSSTTTQQQPPPOOONNNNNNOOOPPPQQQSSSTTTTTTUUUVVVWWWWWWWWWRRRRRRSSSSSSSSSSSSRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRSSSUUUWWWVVVTTTRRRPPPPPPQQQQQQQQQRRRRRRRRRPPPPPPQQQRRRRRRRRRRRRRRRSSSSSSRRRRRRSSSSSSTTTTTTOOOQQQRRRQQQPPPOOOOOOOOOSSSRRRQQQPPPOOOOOOOOOOOONNNMMMLLLMMMOOOPPPOOONNNKKKKKKJJJJJJJJJJJJIIIIIIIIIIIIIIIJJJJJJKKKKKKLLLKKKKKKKKKKKKKKKKKKKKKKKKHHHHHHHHHHHHHHHHHHHHHHHHIIIHHHGGGHHHJJJKKKKKKKKKHHHIIIIIIIIIIIIIIIJJJJJJHHHHHHHHHHHHHHHHHHHHHHHHEEEFFFFFFGGGGGGFFFFFFEEEGGGGGGGGGGGGGGGHHHIIIIIIKKKLLLLLLHHHDDDCCCEEEHHHDDDDDDDDDDDDDDDDDDDDDDDD@@@BBBDDDDDDCCCBBBCCCDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD@@@@@@AAAAAABBBBBBCCCCCCDDDDDDCCCBBBBBBBBBBBBCCCCCCCCCDDDEEEFFFFFFFFFFFFHHHHHHHHHGGGEEEDDDEEEFFFEEEEEEFFFGGGGGGHHHIIIIIIEEEFFFGGGGGGGGGGGGFFFFFFGGGGGGGGGGGGFFFDDDCCCBBBFFFEEEEEEDDDDDDCCCCCCBBBBBBBBBCCCBBBBBBAAA@@@???>>>>>>???@@@@@@@@@??????>>>???@@@AAAAAA@@@???>>>???@@@@@@@@@???>>>=========?????????======>>>???>>>>>>>>>>>>>>>>>>>>>>>><<<<<<=========>>>>>>>>>>>><<<;;;<<<======<<<::::::::::::;;;;;;;;;;;;<<<999999::::::::::::;;;;;;::::::999888777666666555777777777777777888888888555555555666666777777888999888777666555555555555888888888888999999::::::999999999999999999999999777777666666666666777777777777777888888888999999444555666666777666666666666666555666777888666444555555444444444444555555333333333444444444555555555444333222111222333444555444333333333444666777555444444333333333333333111222444555666555555444222222333444444444333333000111111111111222222222111111222222222222333333222111000111222333222111000000000000000111111111000000111111222333333333222222333333333444444444333333333333333222222222000222555555444333333444333333444444444444333333333333333333333222222222111222222333333222222111000000000000111111111111/////////000000000111111000000000111111111111222000000111222222222222111222222222333222222111000/////////////////////////////////000111222333444000000000000000000000000///////////////////////////............---------,,,,,,------------,,,,,,++++++,,,,,,,,,,,,++++++RRRTTTWWWYYY[[[ZZZYYYXXXXXXVVVSSSSSSUUUWWWXXXXXXSSSSSSTTTUUUVVVVVVVVVVVVTTTTTTSSSSSSRRRSSSSSSSSSSSSSSSRRRRRRSSSSSSTTTUUUSSSSSSRRRQQQQQQRRRSSSTTTQQQQQQPPPPPPQQQRRRRRRSSSRRRQQQOOONNNNNNOOOQQQRRRSSSSSSSSSTTTTTTUUUUUUUUUSSSSSSTTTTTTTTTTTTSSSSSSRRRRRRRRRRRRRRRRRRRRRRRRQQQQQQRRRTTTVVVUUUSSSQQQPPPPPPPPPQQQQQQQQQRRRRRRRRRSSSSSSSSSSSSRRRRRRQQQSSSSSSSSSSSSSSSTTTUUUUUUPPPRRRSSSSSSQQQPPPPPPQQQRRRQQQPPPOOONNNNNNNNNNNNMMMLLLLLLLLLNNNOOONNNMMMJJJJJJIIIIIIIIIHHHHHHHHHHHHHHHIIIIIIJJJKKKLLLLLLJJJJJJJJJJJJJJJJJJJJJJJJHHHIIIIIIJJJJJJIIIIIIIIIHHHGGGFFFGGGIIIJJJJJJJJJIIIIIIIIIHHHHHHHHHHHHHHHHHHHHHHHHGGGGGGGGGGGGGGGFFFGGGGGGHHHHHHGGGGGGFFFHHHHHHGGGGGGGGGHHHIIIIIIJJJMMMNNNKKKGGGDDDFFFIIIDDDDDDDDDDDDDDDDDDDDDDDDAAABBBCCCBBBBBBBBBCCCEEEDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDCCCCCCCCCCCCCCCDDDDDDDDDCCCBBBBBBBBBBBBCCCDDDDDD@@@AAABBBCCCDDDDDDDDDDDDDDDEEEEEEEEEDDDDDDFFFHHHFFFFFFFFFFFFGGGGGGGGGGGGCCCDDDFFFGGGGGGGGGGGGFFFFFFFFFFFFEEEDDDCCCAAAAAACCCCCCCCCCCCCCCCCCCCCCCCAAABBBBBBBBBAAA@@@???>>>===>>>>>>???@@@@@@??????===???@@@AAAAAA@@@???===@@@@@@@@@@@@???>>>===<<<<<<>>>@@@???===<<<>>>@@@========================<<<=========>>>>>>>>>>>>>>>===;;;;;;<<<===;;;::::::::::::;;;;;;;;;<<<<<<999999::::::::::::;;;;;;;;;::::::999888777666666777777777777777777777777444555555666777777888888888777666555555666777777777777777888888888888999:::::::::::::::999999999666666555555555555666666666666666777777777888888555555777888888888777777777666555666888888666555555444444333333444444555333333333444444444555555666555333111111222333444555444333222222444555777555444333333222222333333000222444555666666555444111222333333444444444333000111111111111222222222000000000111111222222222111000///000222333222111000000000000000111111222000000111222222333444444333333333333444444444444222222333333333333333333111333555555444333444555333333444444444444333333333333333222222222111111111222222333333222222111000000000000111111111111////////////000000000111000000000000111111111111000000111222222222222222222333333333222222111000000000000000000000000000////////////000000111222000000000000000000000000........................///............---------,,,,,,---------------,,,+++,,,,,,------,,,++++++RRRTTTWWWZZZ[[[[[[ZZZYYYWWWVVVUUUVVVXXXYYYXXXWWWRRRRRRSSSUUUUUUUUUUUUUUUSSSSSSRRRRRRRRRRRRSSSSSSTTTTTTSSSSSSTTTUUUVVVVVVTTTSSSRRRQQQQQQRRRSSSTTTOOOPPPPPPQQQQQQQQQRRRRRRRRRQQQOOONNNNNNOOOQQQRRRRRRRRRRRRRRRSSSSSSSSSSSSTTTTTTUUUUUUUUUUUUTTTTTTRRRRRRRRRRRRRRRQQQQQQQQQQQQQQQRRRTTTUUUUUUSSSPPPPPPPPPPPPQQQQQQQQQRRRRRRSSSSSSSSSSSSRRRPPPOOONNNTTTTTTSSSSSSTTTUUUVVVVVVQQQRRRTTTSSSRRRPPPPPPQQQQQQQQQPPPOOONNNNNNNNNNNNLLLKKKKKKKKKMMMNNNNNNMMMIIIIIIIIIHHHHHHGGGGGGGGGGGGHHHHHHIIIJJJKKKLLLLLLJJJJJJJJJJJJJJJJJJJJJJJJIIIIIIJJJKKKKKKJJJJJJIIIHHHFFFEEEFFFHHHJJJJJJIIIIIIHHHHHHGGGGGGFFFFFFFFFGGGGGGGGGGGGGGGGGGGGGGGGGGGHHHHHHIIIIIIHHHHHHGGGHHHHHHGGGGGGGGGHHHIIIIIIJJJNNNPPPNNNIIIFFFGGGIIIEEEEEEEEEEEEEEEEEEEEEEEEDDDDDDEEEDDDCCCDDDFFFHHHEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEDDDDDDDDDBBBBBBBBBBBBBBBCCCDDDEEECCCDDDEEEFFFGGGGGGGGGGGG???AAABBBCCCCCCDDDGGGIIIHHHHHHGGGGGGFFFEEEEEEEEECCCDDDFFFGGGHHHHHHHHHGGGBBBBBBCCCDDDDDDDDDDDDDDDBBBBBBBBBCCCCCCCCCCCCDDDAAAAAABBBBBBAAA???>>>=========>>>???????????????===>>>@@@AAAAAA@@@>>>===@@@@@@@@@@@@???===<<<;;;;;;>>>@@@???<<<<<<===@@@<<<<<<<<<<<<<<<<<<<<<<<<============>>>>>>>>>>>>>>>===;;;;;;<<<<<<;;;::::::::::::;;;;;;<<<<<<<<<999999:::::::::;;;;;;;;;;;;::::::999888777666666777777777666666666666666444555555666777888888999666666555555555777888:::777777777777777888888888::::::::::::::::::::::::555555444444444444555555666666666666777777777777555666777999999999888777777666666666888888666555555444333333333333444555333333333444444444555555666555333111111222333444555444333222222444555777555444333333222222333333000111444666666666555444111222333333444444444444000111111111111222222222//////000000111111111222000///...///111222222000000000000000000111111222000000111222333333444444333333333444444444555555222222222333333444444444222333555444333333444666333444444555555444444333222222222222111111000000222222222333333222222222000000000000111111111111////////////000000000000000000000000111111111111///000111222222222222222333333333333333222111000111111111111111111111111111000///////////////000000000000000000000000000........................//////.........---------,,,,,,------...---------+++,,,---------,,,+++***UUUTTTTTTWWWZZZ[[[XXXVVVXXXWWWVVVVVVUUUUUUUUUVVVXXXWWWVVVUUUVVVWWWXXXYYYWWWWWWWWWWWWWWWWWWWWWVVVXXXWWWVVVUUUUUUUUUVVVVVVUUUVVVUUUTTTQQQQQQRRRSSSQQQQQQQQQQQQPPPOOONNNMMMPPPRRRSSSRRROOONNNPPPRRRPPPRRRSSSSSSRRRRRRSSSUUUUUUUUUUUUUUUUUUUUUUUUUUURRRTTTUUUVVVVVVUUUTTTRRRPPPQQQQQQQQQRRRRRRSSSSSSQQQRRRTTTUUUUUUTTTSSSSSSSSSSSSRRRQQQPPPOOOOOOOOOPPPQQQTTTVVVWWWWWWVVVUUUUUUUUUUUUSSSQQQOOOPPPQQQRRRPPPMMMMMMOOOPPPOOOMMMJJJIIIHHHIIIJJJJJJHHHFFFHHHIIIGGGEEEDDDFFFGGGFFFGGGHHHIIIHHHGGGGGGHHHJJJJJJIIIHHHGGGGGGHHHJJJLLLJJJIIIHHHGGGFFFGGGGGGHHHIIIIIIIIIIIIIIIIIIIIIIIIJJJJJJJJJIIIHHHGGGFFFEEEJJJJJJJJJKKKKKKJJJIIIIIIHHHHHHHHHHHHHHHIIIJJJKKKLLLKKKJJJIIIHHHGGGGGGGGGJJJJJJIIIIIIIIIHHHHHHHHHHHHHHHHHHGGGFFFEEEDDDDDDCCCCCCCCCCCCCCCDDDEEEFFFCCCCCCDDDEEEEEEEEEEEEEEEGGGFFFDDDCCCBBBBBBBBBCCCCCCDDDEEEFFFFFFEEEDDDCCCCCCCCCBBBAAABBBCCCDDDEEEBBBCCCCCCDDDDDDDDDDDDDDDCCCCCCCCCCCCCCCDDDDDDEEEGGGFFFFFFFFFFFFFFFFFFGGGFFFHHHIIIIIIFFFDDDDDDDDDBBBCCCCCCCCCCCCCCCBBBBBBEEEEEEDDDCCCBBBBBBAAAAAAAAAAAAAAA@@@???>>>===<<<======>>>??????????????????@@@AAAAAAAAA@@@???>>>???@@@@@@AAA@@@???>>>===>>>>>>>>>>>>============>>>>>>>>>>>>============>>>>>>>>>>>>????????????===<<<;;;::::::;;;<<<===<<<:::888999<<<======;;;;;;;;;<<<===<<<;;;999888999;;;===;;;777777<<>>======>>>>>>??????????????????@@@AAAAAABBBAAA@@@?????????@@@AAA@@@???>>>==================<<<<<<<<<>>>>>>>>>=========<<<<<<>>>>>>>>>>>>>>>============<<<;;;;;;;;;;;;<<<===<<<:::888999<<<===<<<;;;:::;;;<<<<<<<<<;;;:::999:::<<<===;;;888888<<>>??????@@@@@@??????>>>???@@@AAABBBBBBBBBAAA>>>???@@@@@@@@@???>>>===<<<<<<<<<<<<<<<<<<<<<<<<============<<<<<<<<<<<<>>>>>>======<<<<<<;;;;;;===<<<;;;;;;;;;;;;<<<===<<<:::::::::<<<===<<<;;;::::::;;;<<<<<<<<<;;;;;;:::<<<===;;;888999<<>>@@@@@@???AAADDDFFFHHHIIIIIIHHHGGGHHHIIIHHHHHHHHHHHHIIIKKKLLLMMMLLLKKKJJJIIIIIIJJJKKKLLLJJJJJJJJJJJJJJJJJJJJJJJJFFFFFFGGGHHHHHHHHHHHHHHHEEEEEEFFFFFFGGGGGGFFFFFFKKKJJJJJJJJJJJJJJJKKKKKKJJJIIIHHHHHHGGGGGGGGGHHHHHHHHHHHHGGGGGGGGGFFFFFFGGGHHHHHHHHHGGGGGGFFFEEEDDDEEEFFFGGGFFFDDDBBBAAAEEEFFFFFFFFFFFFEEEDDDDDDEEEFFFGGGHHHGGGFFFDDDCCCDDDCCCBBBAAAAAABBBCCCDDDCCCCCCCCCCCCCCCDDDDDDEEEBBBCCCCCCDDDDDDDDDDDDDDDCCCCCCCCCCCCCCCDDDEEEEEEGGGGGGFFFFFFFFFFFFGGGGGGGGGHHHIIIHHHFFFEEEFFFGGGEEEEEEFFFGGGGGGGGGFFFFFFEEEDDDDDDDDDCCCCCCBBBBBB???@@@AAAAAAAAAAAAAAA@@@>>>>>>???@@@@@@@@@@@@???>>>??????@@@AAABBBBBBCCC===>>>???@@@@@@???>>>===<<<<<<<<<===========================<<<<<<<<<;;;======<<<<<<;;;:::999999<<<<<<<<<;;;;;;<<<<<<<<<;;;;;;;;;<<<<<<<<<<<<;;;999::::::;;;;;;<<<<<<<<<999:::;;;:::888888:::<<<888777666777888999888777666777888999999888777666666777777777777777666666777777777777777888888888999999999999999999999999;;;:::999999888888888888999999888777777888888888;;;:::999888777777777777::::::999888777666555444555555555555555555555555555555555555555555666666777777555444333222222222333333222222333444555666666666555555444444444333222333444444333333444666444444333333222222222111333333444444333333222111111222333444444333222111333333222222222222333333222222333444333222000//////000111222333222111111000111222222333333222222111222333444555555555555555444444444444555666666777666555444444444555555000111222222333333333333333333333222222222111111333333333333333333333333111111111111111111111111111111111000111111222333222222333333333444444444111111222222222222111111111111111000000000000000000000000000////////////222111111000000//////...000000000000000000000000............//////000000,,,,,,,,,,,,,,,,,,,,,,,,************************UUUUUUVVVVVVUUUVVVVVVWWWVVVVVVVVVUUUUUUVVVVVVWWWSSSTTTUUUUUUVVVWWWWWWWWWSSSSSSRRRRRRSSSUUUVVVWWWUUUUUUVVVVVVUUUUUUTTTSSSQQQSSSUUUUUUSSSQQQPPPOOORRRSSSSSSTTTUUUUUUUUUTTTPPPPPPQQQSSSTTTTTTSSSRRRSSSTTTUUUTTTSSSRRRSSSTTTXXXWWWVVVUUUUUUUUUVVVVVVSSSTTTTTTTTTTTTTTTTTTSSSTTTTTTTTTTTTTTTTTTTTTSSSSSSSSSSSSTTTUUUUUUVVVWWWSSSSSSRRRRRRQQQQQQRRRRRRTTTSSSPPPNNNNNNNNNPPPQQQQQQRRRRRRQQQOOONNNOOOQQQOOOOOOOOONNNMMMMMMNNNNNNMMMMMMLLLLLLKKKIIIDDDAAA???999777888888666999>>>DDDFFFHHHIIIIIIHHHIIIJJJJJJJJJJJJKKKLLLMMMNNNNNNLLLKKKJJJJJJJJJJJJLLLLLLIIIIIIIIIIIIIIIIIIIIIIIIFFFGGGHHHIIIIIIIIIIIIIIIFFFGGGGGGHHHIIIIIIIIIHHHJJJJJJIIIIIIHHHIIIIIIJJJKKKJJJJJJIIIIIIIIIIIIJJJHHHHHHHHHGGGGGGGGGFFFFFFGGGHHHHHHHHHHHHGGGFFFFFFDDDEEEFFFGGGGGGEEECCCAAAEEEEEEFFFFFFFFFFFFEEEEEEDDDEEEFFFGGGFFFEEEDDDCCCDDDCCCBBBAAAAAABBBCCCDDDCCCCCCCCCDDDDDDDDDDDDDDDBBBCCCCCCDDDDDDDDDDDDDDDAAAAAAAAAAAAAAABBBCCCCCCEEEEEEDDDDDDDDDDDDEEEEEEEEEFFFGGGFFFDDDDDDEEEFFFEEEEEEFFFGGGHHHHHHGGGGGGDDDDDDDDDDDDDDDCCCCCCCCC@@@AAAAAABBBBBBBBBAAAAAA>>>>>>???@@@@@@@@@@@@@@@>>>>>>>>>???@@@AAABBBBBB======??????@@@???>>>=========>>>>>>>>>?????????>>>============<<<<<<<<<===<<<<<<;;;:::999999888;;;<<<<<<<<<<<<<<<<<<;;;;;;<<<=========<<<;;;;;;::::::::::::;;;<<<<<<<<<888999999888777777888999888777666777888999888777666777888999999888777666555666666777777777666666666666777777888888888888999999999999999999999999;;;:::999999999999999999999888888888888888999999999888888888888888999999;;;:::999888666666555555555555555555555555555555444444444444444444444444666666555444333222222222222333333333444555666666666555555555555555444444222444555555444333555666444444444333333222222222333444444444444333222222000111222333333222111000111222222222222222222111222222333444444333111000///000111222333222111111000111222222333333222222444444444444444444444333555444444444444555666666666555555444444444444444000111222222333333333333333333333222222222111111222222222222222222222222111111111111111111111111111111000000111222222333222222333333333444444444111111222222222222111111000000000000000000111111000000000000////////////000000000//////.........000000000000000000000000------...//////000000000,,,,,,,,,,,,,,,,,,,,,,,,************************UUUVVVVVVUUUTTTTTTVVVXXXXXXWWWVVVVVVUUUUUUUUUVVVTTTUUUVVVVVVWWWVVVVVVVVVSSSSSSSSSTTTUUUUUUUUUVVVTTTUUUVVVVVVVVVUUUSSSSSSPPPRRRTTTTTTSSSQQQQQQRRRTTTTTTTTTUUUTTTTTTSSSSSSPPPOOOOOOPPPSSSUUUUUUTTTUUUWWWWWWWWWUUUTTTUUUVVVUUUUUUVVVVVVWWWXXXXXXXXXTTTTTTTTTTTTTTTTTTTTTTTTUUUUUUUUUUUUTTTTTTTTTTTTUUUTTTTTTTTTTTTUUUVVVVVVSSSRRRRRRQQQQQQRRRRRRRRRTTTRRRPPPNNNNNNOOOPPPQQQPPPQQQQQQPPPNNNNNNOOOPPPNNNOOOOOONNNLLLKKKMMMNNNNNNMMMLLLKKKIIIEEE@@@<<<888000,,,......,,,111:::AAADDDGGGIIIJJJJJJKKKLLLLLLLLLMMMMMMMMMNNNNNNNNNKKKKKKJJJIIIIIIKKKLLLMMMIIIIIIIIIIIIIIIIIIIIIIIIHHHHHHIIIJJJJJJJJJJJJJJJHHHIIIIIIJJJKKKKKKKKKKKKJJJJJJIIIHHHHHHHHHHHHIIIKKKKKKJJJJJJJJJJJJKKKKKKHHHHHHHHHHHHGGGGGGGGGGGGGGGHHHHHHHHHHHHHHHGGGGGGDDDEEEFFFFFFFFFEEEDDDCCCDDDEEEFFFFFFGGGGGGFFFFFFDDDEEEEEEEEEEEEEEEDDDDDDDDDCCCCCCCCCCCCCCCCCCDDDBBBCCCDDDEEEEEEEEEEEEDDDBBBCCCCCCDDDDDDDDDDDDDDDBBBBBBBBBBBBBBBCCCDDDDDDDDDDDDCCCCCCCCCCCCDDDDDDEEEEEEFFFEEECCCCCCEEEFFFEEEEEEFFFGGGHHHHHHHHHHHHDDDDDDDDDDDDDDDDDDDDDDDDBBBBBBBBBCCCCCCBBBAAAAAA>>>???@@@@@@AAA@@@@@@@@@>>>>>>>>>>>>>>>???@@@AAA<<<===>>>?????????>>>======>>>>>>??????@@@@@@AAA>>>>>>>>>>>>============<<<<<<;;;;;;::::::999999;;;;;;<<<======<<<;;;;;;:::<<<>>>>>>===;;;;;;;;;;;;;;;:::::::::;;;<<<<<<999999888888888888777777999777666777888888777666666777888999999888777666555555666777777777666666666666666777888888999999888999999999999:::::::::::::::999999999999::::::999888888888888999::::::888888777777888999999:::::::::888777666666666666444444444444444444444444444444444555444444333222444444444444333333333333222222333444555666666777555555555555555555555555222444555555444444555666555444444444444444333333444444444444444333222222111222222333333222222111111111222222222222111111222222333333333222222111000111111222333222222222111222222333333333333333555555444444444333333333555444444444444555666666555555555555444444333333111111222333333333222222333222222222111111111111111111111111111111111111111111111111111111111111000000000000111222333333222222222222333333333333111111222222222222111111000000000000111111111111000000000000////////////.............../////////////////////////////////------.../////////......,,,,,,,,,,,,,,,,,,,,,,,,************************UUUVVVWWWUUUSSSSSSUUUXXXYYYXXXWWWVVVUUUTTTTTTTTTTTTUUUUUUVVVVVVUUUSSSSSSSSSTTTUUUVVVWWWVVVTTTSSSSSSTTTUUUVVVUUUTTTRRRQQQOOOQQQRRRRRRQQQRRRSSSTTTSSSSSSTTTTTTTTTTTTSSSSSSTTTQQQOOOPPPSSSUUUVVVVVVVVVWWWXXXWWWUUUTTTUUUVVVRRRTTTVVVWWWXXXXXXWWWVVVWWWVVVVVVVVVVVVVVVVVVWWWVVVVVVUUUUUUUUUTTTTTTTTTWWWVVVUUUTTTTTTTTTUUUUUUTTTSSSSSSRRRRRRSSSSSSTTTRRRQQQPPPOOOOOOPPPQQQQQQPPPPPPQQQOOONNNMMMOOOPPPNNNOOOPPPOOOLLLKKKMMMOOONNNMMMKKKJJJGGGAAA;;;666000&&& ###%%%%%%,,,888???BBBFFFIIIJJJKKKLLLMMMMMMMMMNNNNNNMMMMMMLLLLLLJJJJJJIIIIIIIIIJJJKKKLLLJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJKKKKKKKKKKKKKKKKKKIIIIIIKKKLLLLLLMMMMMMMMMKKKKKKJJJIIIIIIIIIIIIIIIJJJJJJIIIIIIIIIJJJJJJKKKIIIIIIIIIIIIHHHHHHHHHHHHGGGGGGHHHHHHIIIHHHHHHGGGEEEEEEEEEEEEEEEFFFFFFFFFCCCDDDEEEFFFGGGHHHHHHHHHFFFFFFFFFEEEEEEFFFFFFGGGCCCDDDDDDEEEEEEDDDDDDCCCBBBCCCDDDEEEFFFEEEEEEDDDBBBCCCCCCDDDDDDDDDDDDDDDCCCBBBBBBBBBBBBCCCDDDDDDDDDDDDCCCCCCCCCCCCDDDDDDEEEFFFFFFEEECCCDDDFFFHHHDDDEEEFFFGGGGGGHHHHHHHHHDDDDDDDDDDDDDDDDDDDDDEEECCCCCCDDDCCCCCCBBBAAA@@@>>>???@@@@@@AAAAAA@@@@@@>>>>>>===<<<<<<===>>>???;;;<<<>>>?????????>>>============>>>??????@@@@@@@@@?????????>>>>>>>>>>>>;;;;;;;;;;;;;;;;;;::::::;;;;;;<<<======<<<;;;;;;:::===@@@@@@===;;;;;;;;;===<<<;;;:::::::::;;;;;;;;;:::::::::::::::999777:::888777777888888666555666777888999999888777666444555555666777777666666555666666777888888999999888888999999999::::::::::::::::::999999::::::;;;999888888888999999:::;;;999999888888777888888888:::999888666666666777777555555555555555555555555444555666666666444333222222222333333444444444333111222333555666666777777555555555555666666666666333444555555444444555777444555555555555555555666444444444555444444333222444444333333333333444444111222333444444333222111222222111111111111222222222222222222222333444444222222333444444444444444444444333333333444444555555444444444444555666666444555555555444444333333222222333333333222111111222222111111111000000000111111111111111111111111000000000000000000000000000000000000111222333444111111111222222222222333111111222222222222111111///000000000111111111111000000000000////////////.........///000000111111........................------...///......,,,,,,++++++++++++++++++++++++************************UUUVVVWWWUUUSSSRRRUUUXXXZZZYYYXXXVVVUUUTTTSSSSSSTTTTTTUUUUUUTTTSSSQQQPPPSSSTTTWWWXXXXXXVVVTTTRRRQQQRRRTTTUUUTTTSSSQQQPPPOOOPPPQQQQQQQQQRRRTTTVVVQQQRRRSSSTTTTTTTTTTTTTTTXXXTTTQQQPPPSSSVVVWWWVVVTTTUUUVVVUUUSSSRRRSSSTTTQQQSSSVVVXXXXXXWWWUUUTTTYYYXXXXXXWWWWWWXXXXXXYYYVVVVVVVVVUUUUUUTTTTTTTTTXXXWWWVVVTTTSSSTTTTTTUUUUUUTTTTTTTTTTTTTTTUUUUUUQQQQQQQQQPPPPPPQQQQQQRRROOOPPPPPPOOONNNMMMOOOPPPOOOPPPQQQPPPMMMLLLNNNQQQNNNMMMKKKIIIEEE???888333***!!!***888===AAAFFFIIIKKKLLLMMMOOOMMMNNNNNNMMMMMMLLLKKKJJJJJJIIIHHHHHHIIIJJJKKKLLLKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKLLLLLLLLLLLLKKKKKKIIIJJJKKKLLLMMMMMMMMMMMMMMMLLLKKKJJJJJJJJJJJJJJJIIIIIIHHHHHHHHHIIIIIIJJJJJJJJJIIIIIIIIIIIIHHHHHHGGGGGGHHHIIIIIIHHHHHHHHHEEEEEEDDDDDDEEEFFFGGGHHHBBBCCCEEEFFFHHHHHHIIIIIIHHHGGGFFFFFFFFFGGGHHHIIICCCDDDEEEFFFFFFEEEDDDCCCBBBCCCEEEFFFFFFFFFEEEDDDBBBCCCCCCDDDDDDDDDDDDDDDBBBAAAAAAAAAAAABBBCCCCCCEEEEEEDDDDDDDDDDDDEEEEEEFFFGGGGGGFFFDDDEEEGGGIIICCCDDDEEEFFFGGGHHHHHHHHHDDDDDDDDDDDDEEEEEEEEEEEEDDDDDDDDDDDDCCCBBBAAA@@@??????@@@AAAAAAAAAAAA@@@>>>>>><<<;;;;;;<<<======;;;<<<===?????????>>>===;;;<<<<<<===>>>??????@@@@@@@@@@@@@@@?????????>>>;;;;;;;;;;;;;;;;;;;;;<<<:::;;;<<<======<<<;;;::::::===@@@@@@===;;;:::;;;>>>===;;;:::999::::::;;;<<<<<<;;;;;;<<<<<<:::888;;;999777777888777666444666777888999999888777666444444555666777777666666555666666777888999999999888888888999999::::::::::::::::::999999:::;;;;;;999888888888999::::::;;;;;;;;;999888777777666666999888777666666777888888888888888888888888888888666666777777777666444333111111222333444444444444111222333555666777777777555555555666666666666666333444555555444444555777444555555555666777777777444444555555444444333222666555444333333444555666333333444555555444333333222111000000000111222333444333222111222333444555222333444444555555444444222222222333444555666777555444444444444555666666444444555555444444333222333333333333333222111000111111111000000000000///111111111111111111111111////////////////////////000000000000111222333444000000111111111222222222111111222222222222111111//////000000111111111222000000000000////////////......///000111222333333........................------.........---+++***++++++++++++++++++++++++))))))))))))))))))))))))SSSSSSTTTUUUVVVVVVVVVVVVXXXXXXXXXXXXWWWVVVTTTTTTVVVVVVUUUUUUTTTSSSRRRRRRXXXXXXWWWVVVUUUSSSSSSRRRSSSRRRRRRTTTVVVWWWVVVTTTSSSRRRQQQPPPQQQRRRTTTVVVSSSTTTUUUVVVVVVVVVVVVVVVSSSSSSTTTUUUVVVVVVVVVVVVUUUTTTSSSUUUWWWXXXXXXWWWTTTUUUUUUVVVVVVUUUUUUTTTUUUVVVXXX[[[\\\YYYUUUQQQWWWWWWWWWVVVUUUTTTSSSSSSUUUUUUTTTSSSRRRRRRUUUXXXVVVUUUTTTSSSRRRRRRRRRRRRRRRPPPPPPQQQSSSSSSPPPMMMQQQPPPOOOPPPRRRRRRRRRQQQRRRRRRQQQPPPNNNMMMLLLKKKIIIIIIIIIHHHEEE???777111""" !!!)))222777<<>>???@@@AAAAAA@@@???>>>=========??????===<<<888999;;;===>>>???>>>>>>>>>======<<<<<<>>>???@@@BBBAAAAAA@@@???>>>======<<<<<<;;;;;;;;;:::::::::::::::;;;;;;;;;;;;::::::@@@@@@???>>>===<<<;;;;;;:::;;;;;;;;;:::999999888;;;::::::::::::;;;<<<<<<<<<:::888666555555666777888888888888777555444333888888777777666666555555555555666888888999999999999888777666666777888888::::::999999999999999:::999999888888888888999999777777777777777777777777888888888888888888888888666666666666555555555555777666555444333222222222333333333333333333333333222333444555666666666666444444333333333444555555555555555444333222111000666666777777777777666666444444444444555666777777666666555555555444444444333333444444333333222111...///111333444333111000000111111111111222222222333333222222333333444555666666555444444444444555111222444555555555444444777777666555444333333222333333222222222222333333333333333222222111111111222111111111000000//////////////////////////////222111000000000111222333///000111222333222111111000000000111222222333333333111000000111222222111222111000000000000000111////////////000000000000111111000......---------++++++---...//////000000******))))))******+++,,,,,,,,,,,,,,,,,,,,,,,,,,,SSSTTTUUUVVVVVVWWWWWWWWWYYYYYYYYYXXXWWWVVVVVVUUUWWWWWWWWWVVVUUUTTTTTTTTTUUUUUUUUUUUUUUUUUUUUUUUUWWWUUUTTTUUUVVVVVVUUUTTTUUUTTTRRRRRRRRRTTTUUUWWWRRRSSSTTTUUUUUUVVVVVVVVVTTTUUUUUUVVVWWWWWWWWWWWWWWWVVVUUUWWWYYYZZZZZZYYYUUUUUUVVVVVVVVVVVVUUUUUUVVVVVVXXXZZZ[[[YYYUUURRRXXXXXXVVVUUUTTTSSSSSSRRRUUUUUUUUUSSSRRRRRRUUUWWWUUUUUUTTTSSSRRRRRRRRRRRRQQQPPPOOOPPPRRRRRROOOMMMQQQPPPOOOPPPRRRRRRRRRQQQQQQQQQPPPOOONNNMMMLLLLLLKKKJJJIIIHHHFFF@@@:::555%%%$$$"""###(((///777<<>>???@@@AAA@@@@@@???>>>===<<<>>>??????>>><<<:::;;;===???@@@@@@@@@@@@======<<<<<<<<<===>>>???AAAAAA@@@???>>>>>>=========<<<<<<<<<;;;;;;;;;;;;;;;;;;<<<<<<<<<<<<;;;;;;>>>>>>==================<<<<<<======<<<;;;;;;:::;;;;;;;;;;;;;;;<<<<<<===;;;999888666555666777888888888888888777666555555888888777777666666666666555666777888888999888888999888777777666777888999999999888888888999999:::999999888888888888999999999999999999999999999999888888888888888888888888999888888888777777777777777666555444333333333333444444444444444444444444222333444555666666666666555444333333333333444444555555555555444333222222666666777777777777666666444444333333333444444555666666555555555444444444333444444444444333222222///000222333333333222111111111111111222222222222333333222222333333444555666666555444444444444555222333444555555555444333666666666666555444333222222222222111111222222222333333333222222222111111222111111111000000000000000000000000000000000000333222111000000111111222///000111222333222111111000000000111222222333333333111000000111222222111111111000////////////000.........////////////000111000///......---------,,,,,,---...////////////******))))))******+++,,,,,,,,,,,,,,,,,,,,,,,,,,,TTTTTTUUUVVVWWWWWWWWWWWW[[[ZZZYYYXXXXXXWWWXXXXXXXXXXXXWWWWWWVVVVVVUUUUUUSSSSSSTTTUUUVVVWWWWWWXXXZZZXXXVVVUUUUUUVVVUUUTTTVVVUUUTTTSSSTTTUUUVVVWWWQQQRRRRRRSSSTTTUUUUUUUUUUUUVVVVVVWWWXXXXXXXXXYYYYYYXXXWWWYYY[[[\\\[[[ZZZVVVVVVVVVWWWWWWVVVVVVVVVXXXWWWWWWXXXYYYYYYVVVTTTYYYXXXVVVTTTSSSRRRSSSSSSUUUUUUUUUTTTRRRRRRTTTWWWTTTTTTSSSRRRQQQQQQQQQQQQQQQPPPPPPPPPQQQQQQOOOMMMQQQPPPOOOPPPRRRRRRRRRQQQPPPPPPOOOOOOOOONNNNNNNNNNNNLLLKKKIIIGGGCCC>>>:::,,,,,,,,,---111777===AAACCCFFFIIIJJJJJJJJJKKKLLLIIIJJJJJJKKKKKKJJJJJJIIIMMMKKKIIIIIIJJJKKKKKKJJJKKKLLLLLLMMMNNNNNNMMMMMMNNNNNNNNNMMMMMMMMMLLLLLLMMMMMMLLLLLLKKKKKKLLLLLLIIIIIIIIIJJJJJJKKKKKKLLLMMMLLLLLLKKKKKKLLLLLLMMMIIIIIIHHHGGGGGGGGGGGGGGGHHHGGGFFFEEEEEEEEEEEEEEEEEEEEEEEEFFFGGGHHHJJJKKKIIIIIIIIIIIIIIIHHHHHHHHHHHHHHHGGGGGGGGGGGGHHHHHHDDDDDDFFFFFFFFFFFFDDDDDDCCCDDDDDDDDDEEEEEEEEEFFFEEEEEEEEEEEEDDDDDDDDDDDDDDDCCCCCCCCCCCCCCCCCCDDDEEEEEEDDDDDDEEEEEEFFFGGGFFFEEEDDDEEEGGGGGGEEEDDDBBBCCCCCCDDDEEEDDDDDDDDDBBBBBBCCCDDDDDDEEEEEEFFFCCCCCCBBBBBBAAAAAA@@@@@@>>>>>>???@@@@@@@@@@@@???===<<<<<<>>>???@@@???===<<<===???AAABBBBBBAAAAAA<<<<<<<<<<<<<<<===>>>>>>?????????>>>>>>===============<<<<<<<<<;;;;;;;;;<<<<<<<<<======<<<<<<<<<;;;;;;<<<===>>>??????@@@>>>>>>>>>>>>>>>======<<<;;;;;;;;;;;;;;;<<<======999999777666666777888999888888888888888888888888888777777777777666666666777777888888888888888777999888888777777888999999888777777777888999::::::999999888888888888999999;;;;;;;;;;;;;;;;;;;;;;;;999999999999999999999999999999888888888777777777666666555444333333333333555555555555555555555555333333444555555666666666555444444333222222222222444555555666666555555444555666666777777666666555555555444444333333444444666666666555555555444444444444555555444444333222000000222333333333222111111111111111222222222333333333333333333444444555666666555444444444444555444444555666555444333222333444666777777555444333222222111111111111222222333333333333222222222222111111111111111000000000111111111111111111111111333333222111000000000111///000111222333222111111000000000111222222333333333111000000111222222111000000//////............---------.........//////111000///......---......------...............---***))))))))))))***++++++,,,,,,,,,,,,,,,,,,,,,,,,TTTUUUVVVWWWWWWXXXWWWWWW[[[ZZZYYYXXXXXXYYYYYYZZZXXXWWWWWWWWWVVVVVVUUUUUUSSSSSSTTTUUUVVVWWWWWWXXXZZZWWWTTTSSSTTTUUUVVVVVVUUUUUUTTTTTTTTTTTTUUUVVVQQQQQQQQQRRRSSSTTTUUUUUUUUUUUUUUUVVVWWWWWWXXXYYYZZZYYYXXXYYY[[[\\\[[[ZZZWWWWWWWWWWWWWWWWWWWWWWWWYYYXXXWWWWWWXXXXXXWWWVVVWWWVVVTTTSSSSSSTTTUUUVVVUUUUUUUUUTTTSSSRRRTTTVVVSSSSSSRRRQQQQQQQQQQQQQQQRRRRRRQQQQQQQQQQQQPPPPPPQQQPPPOOOPPPRRRRRRRRRQQQPPPPPPPPPPPPPPPPPPPPPPPPQQQOOOLLLJJJIIIFFFBBB???555555666777:::===AAACCCGGGHHHJJJJJJIIIIIIKKKLLLMMMMMMMMMMMMMMMMMMMMMMMMNNNLLLKKKKKKJJJKKKJJJJJJMMMNNNNNNOOONNNNNNMMMMMMNNNMMMLLLLLLKKKKKKLLLLLLOOONNNMMMLLLLLLMMMNNNOOOIIIIIIJJJJJJKKKKKKKKKLLLMMMMMMLLLLLLLLLLLLMMMMMMHHHHHHGGGGGGGGGFFFFFFFFFGGGGGGGGGGGGFFFEEEDDDDDDFFFFFFFFFFFFGGGHHHIIIJJJKKKKKKJJJJJJIIIIIIIIIHHHHHHHHHGGGGGGGGGGGGHHHHHHCCCDDDEEEFFFFFFEEEDDDCCCCCCCCCDDDDDDEEEEEEFFFFFFEEEEEEEEEEEEDDDDDDDDDDDDDDDDDDCCCCCCCCCCCCDDDDDDDDDDDDDDDDDDDDDEEEEEEFFFFFFEEEDDDEEEGGGGGGEEEDDDAAABBBCCCCCCDDDDDDCCCCCCDDDDDDDDDCCCBBBBBBAAAAAABBBBBBBBBAAAAAAAAA@@@@@@????????????@@@?????????===<<<<<<>>>@@@AAA@@@>>>===>>>???AAABBBBBBAAAAAA<<<<<<<<<<<<<<<=========>>>>>>>>>===============<<<<<<<<<;;;;;;;;;::::::<<<<<<============<<<<<<:::;;;;;;<<<===>>>??????>>>>>>>>>??????>>>>>>===:::::::::::::::;;;;;;<<<999888777777777888999999888888888888888999999:::777777777777777777777777888888999999999888777777888888888888999999999:::777777777777888999:::::::::999999888888999999:::;;;;;;;;;;;;;;;;;;;;;;;;999999999999999999999999777777777666666666555555666666555444444444444444555555555555555555555555444444444444555555666666666555444333222111111111333333444555555555555555555666666666666666666555555444444444444555666777666666666666555555555555555555555555555444333333111111222333333222222111111111111222222222333333333333333333333444555555666666555444444444444555555555666666666444333222111333555777888777555333222111111000000111111222333333333333333333333333111111111111111111111111111111111111111111111111444333222111111000/////////000111222333222111111000000000111222222333333333111000000111222222111/////////......---,,,,,,+++,,,,,,------.........000000///.....................//////...------,,,)))))))))))))))***++++++++++++,,,,,,,,,,,,------TTTTTTUUUVVVWWWWWWWWWWWWZZZZZZYYYYYYYYYZZZZZZ[[[VVVVVVVVVVVVUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUWWWTTTRRRQQQSSSUUUWWWWWWTTTTTTTTTSSSSSSTTTTTTTTTPPPPPPPPPQQQRRRSSSUUUVVVUUUTTTTTTTTTUUUVVVWWWXXXZZZXXXXXXXXXZZZ[[[ZZZYYYXXXWWWWWWVVVVVVWWWWWWXXXZZZYYYWWWWWWXXXXXXXXXVVVTTTSSSSSSTTTUUUWWWXXXZZZUUUVVVVVVUUUSSSRRRSSSUUUSSSRRRRRRQQQQQQQQQQQQRRRSSSSSSSSSRRRRRRQQQRRRRRRQQQPPPOOOPPPRRRRRRRRRQQQQQQQQQQQQQQQRRRRRRRRRRRRRRRPPPMMMLLLKKKIIIFFFDDD>>>>>>>>>>>>@@@AAABBBCCCIIIJJJKKKJJJIIIIIIKKKLLLNNNNNNNNNNNNNNNNNNNNNNNNMMMMMMMMMLLLKKKJJJKKKKKKOOOOOOOOOOOOOOONNNNNNMMMLLLLLLKKKJJJJJJJJJJJJKKKMMMLLLKKKJJJJJJKKKMMMMMMJJJJJJJJJKKKKKKKKKKKKKKKLLLLLLMMMMMMMMMMMMLLLLLLHHHHHHHHHGGGGGGGGGFFFFFFFFFGGGGGGHHHGGGFFFEEEDDDHHHGGGGGGFFFFFFFFFGGGGGGKKKKKKKKKJJJJJJIIIIIIIIIGGGGGGFFFFFFFFFFFFGGGGGGCCCDDDEEEFFFFFFEEEDDDCCCCCCCCCCCCDDDEEEFFFFFFFFFDDDDDDDDDDDDEEEEEEEEEEEEDDDDDDCCCCCCCCCCCCDDDDDDCCCBBBBBBBBBBBBCCCDDDDDDFFFEEEDDDEEEGGGGGGEEEDDDAAAAAABBBCCCCCCCCCCCCCCCCCCBBBBBBAAAAAA@@@@@@???AAAAAAAAAAAAAAA@@@@@@@@@@@@@@@??????????????????>>>======>>>@@@AAA???>>><<<===>>>@@@@@@@@@??????<<<<<<<<<==============================>>>>>>>>>;;;;;;;;;;;;:::::::::999<<<<<<============<<<<<<<<<<<<<<<<<<============<<<======>>>>>>>>>======999999999888999::::::;;;888888888888888999999999888777777777888999:::;;;777777777777888888888888888999999999999888888777888888999999::::::::::::888888777777888999::::::::::::999999999999::::::;;;;;;;;;;;;;;;;;;;;;;;;999999999999999999999999777777777777666666666666666666555444444444555555444444444444444444444444555555444444444555666666666555444333222222111111111222333444444444444444555555666666666666555555000000000222333555777888777777666666666555555555555666666666666555444444222222333333333222222222111222222222222333333333444444333333444444555666666666555444444444444555555666666666666555333222000222555777888777555444222222111111111111222222333333333333333333333333111111111111111222222222000000000000000000000000333333333222111000/////////000111222333222111111000000000111222222333333333111000000111222222111////////////...---+++++++++++++++,,,---......///000//////............///////////////...---,,,+++))))))(((((())))))***++++++++++++,,,,,,---------SSSSSSTTTUUUVVVVVVVVVVVVWWWXXXYYYZZZ[[[[[[ZZZZZZVVVVVVVVVUUUUUUUUUUUUUUUVVVVVVVVVUUUUUUTTTTTTTTTTTTSSSQQQRRRTTTVVVVVVVVVTTTTTTTTTTTTTTTSSSSSSSSSQQQPPPPPPPPPRRRTTTVVVWWWUUUTTTSSSSSSTTTUUUWWWXXXYYYXXXWWWXXXYYYZZZYYYXXXXXXWWWVVVUUUUUUVVVWWWXXXZZZYYYXXXXXXYYYYYYXXXVVVSSSSSSTTTVVVXXXYYYZZZZZZUUUVVVVVVUUUSSSRRRSSSTTTSSSSSSRRRQQQQQQRRRRRRSSSSSSTTTTTTRRRQQQPPPRRRSSSQQQPPPOOOPPPRRRRRRRRRQQQQQQRRRRRRRRRRRRRRRRRRRRRRRRPPPOOONNNMMMKKKIIIFFFCCCCCCCCCCCCCCCDDDDDDEEEIIIJJJLLLKKKJJJJJJKKKMMMMMMLLLLLLKKKKKKLLLLLLMMMMMMMMMNNNMMMKKKKKKLLLNNNNNNOOOOOOOOOOOOOOONNNNNNKKKKKKJJJJJJJJJIIIIIIIIIIIIIIIHHHHHHHHHIIIJJJJJJKKKKKKKKKKKKKKKKKKKKKKKKKKKLLLLLLMMMMMMLLLLLLKKKHHHHHHHHHIIIHHHGGGGGGFFFFFFFFFGGGGGGHHHGGGGGGFFFIIIHHHGGGGGGFFFFFFFFFGGGJJJJJJJJJJJJJJJIIIIIIIIIGGGGGGFFFFFFFFFFFFGGGGGGDDDDDDFFFFFFFFFFFFDDDDDDBBBBBBCCCDDDEEEFFFGGGGGGDDDDDDDDDDDDEEEEEEEEEEEEDDDCCCCCCCCCCCCCCCCCCDDDBBBBBBAAAAAABBBBBBCCCDDDFFFEEEDDDEEEGGGGGGEEEDDDAAABBBBBBCCCDDDCCCCCCCCC??????@@@@@@AAABBBBBBCCCAAAAAAAAAAAA@@@@@@@@@@@@AAA@@@??????>>>????????????>>>>>>???@@@@@@???===;;;<<<>>>?????????>>>===<<<======>>>???>>>>>>>>>=========>>>>>>?????????<<<<<<;;;;;;;;;:::::::::<<<<<<<<<======<<<<<<<<<=========<<<<<<;;;;;;;;;;;;<<<<<<===============999999999999999::::::;;;999999999999999999888888888777666666777888999:::777777777888888888888999888888999999999999999888888888:::;;;;;;;;;;;;;;;::::::999999999999999:::::::::999999999999::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::999999999888888888666666555555555555555666444444444444444444444444666555444333333444666666666555555444333333333333111222222333444444444333444555555666666555555444++++++,,,...111333555777777777777666666666555555666666666777666666555444333333333333222222222222222222222222333333333333444444444444444555555666666666555444444444444555444555666777666555444333222333555666777666555444333222222222222222222333333333333333444444444444111111111222222222222222000000000000000000000000222222222222222111000//////000111222333222111111000000000111222222333333333111000000111222222111//////000000///---+++******++++++,,,---...////////////............//////.../////////...---,,,,,,)))(((((((((((()))*********++++++,,,,,,------...RRRRRRSSSTTTUUUUUUUUUUUUTTTVVVYYY[[[\\\[[[ZZZYYYVVVVVVVVVWWWWWWWWWWWWWWWVVVVVVVVVUUUUUUUUUTTTTTTVVVTTTSSSTTTVVVVVVUUUTTTUUUUUUVVVUUUUUUTTTTTTSSSQQQQQQPPPQQQRRRTTTWWWXXXVVVUUUTTTTTTTTTVVVXXXYYYZZZYYYXXXXXXYYYZZZYYYXXXWWWVVVUUUTTTTTTUUUVVVWWWZZZYYYXXXYYYZZZZZZXXXVVVTTTVVVXXXYYYZZZZZZYYYXXXUUUVVVWWWVVVTTTRRRRRRSSSSSSSSSSSSRRRRRRSSSSSSTTTQQQRRRRRRQQQNNNNNNPPPRRRQQQPPPOOOPPPRRRRRRRRRQQQQQQQQQQQQPPPPPPPPPPPPPPPQQQPPPOOOOOOOOOMMMJJJGGGEEEEEEEEEEEEFFFGGGIIIJJJHHHJJJLLLLLLLLLKKKLLLMMMKKKKKKJJJIIIIIIJJJKKKKKKKKKMMMNNNMMMKKKKKKMMMPPPMMMNNNNNNOOOOOOOOONNNNNNJJJKKKLLLLLLLLLKKKIIIHHHHHHHHHIIIJJJJJJJJJJJJJJJLLLKKKKKKKKKKKKKKKKKKKKKJJJKKKLLLLLLLLLLLLKKKJJJHHHIIIIIIJJJIIIHHHGGGFFFFFFFFFFFFGGGGGGHHHHHHIIIIIIHHHHHHHHHHHHHHHIIIJJJIIIIIIIIIIIIIIIJJJJJJJJJHHHHHHGGGGGGGGGGGGHHHHHHDDDEEEFFFGGGGGGFFFEEEDDDBBBBBBCCCDDDEEEFFFGGGGGGCCCDDDDDDDDDEEEEEEEEEFFFCCCCCCBBBBBBBBBBBBCCCCCCBBBBBBBBBBBBBBBCCCDDDDDDFFFEEEDDDEEEGGGGGGEEEDDDBBBBBBCCCDDDDDDDDDDDDDDD@@@AAAAAABBBCCCCCCDDDDDD@@@@@@@@@@@@@@@@@@@@@@@@AAAAAA???>>>>>>>>>??????AAA@@@??????@@@@@@>>><<<<<<===>>>?????????>>>=========???@@@@@@@@@???>>>======>>>>>>???@@@AAAAAA>>>=========<<<<<<<<<<<<;;;;;;<<<<<<<<<<<<;;;;;;======<<<<<<<<<;;;;;;;;;;;;<<<<<<===>>>>>>======;;;;;;::::::;;;;;;<<<===::::::::::::999888888777888777666555555666888999777777888888888999999999777777888999::::::::::::888999:::;;;<<<<<<<<<;;;<<<<<<;;;:::999999999999;;;::::::999999::::::;;;:::::::::::::::::::::::::::::::::::::::::::::::::::::::::999999999888888666666555555555555666666555555555555555555555555777666444333333444555666666666555444444555555555333333444444444444444333444555555666666555555444,,,,,,---///111333555666777777777777666666666555666777777777777666555555444444333333222222222222222222222333333333444444444444444444444555666666666666555444444444444555444444666777777666555555444444555555666555555555444444333333333333444444333333333444444444555555111111111222222333333333111111111111111111111111000111222222222222111000///000111222333222111111000000000111222222333333333111000000111222222111///000111111000---+++***++++++,,,---...///000000//////............//////..................------((((((((((((((()))************+++,,,,,,---......QQQRRRSSSTTTTTTUUUTTTTTTSSSUUUYYY\\\]]][[[YYYWWWWWWXXXXXXXXXXXXXXXXXXXXXUUUUUUUUUUUUUUUUUUUUUUUUXXXWWWVVVWWWWWWWWWUUUSSSWWWWWWWWWWWWWWWVVVUUUTTTRRRQQQQQQQQQRRRUUUXXXYYYWWWVVVUUUUUUUUUWWWYYY[[[[[[YYYXXXYYYZZZZZZYYYXXXWWWVVVTTTSSSSSSTTTVVVWWWYYYYYYYYYZZZ[[[ZZZXXXUUUVVVXXXZZZ\\\[[[ZZZWWWUUUUUUVVVWWWVVVTTTRRRRRRSSSTTTSSSSSSSSSSSSSSSTTTTTTOOOQQQQQQOOOLLLLLLNNNQQQQQQPPPOOOPPPRRRRRRRRRQQQPPPPPPOOOOOOOOONNNNNNNNNPPPPPPPPPPPPPPPNNNKKKHHHFFFEEEEEEFFFHHHJJJMMMNNNGGGJJJLLLMMMMMMLLLLLLMMMLLLKKKJJJIIIIIIJJJKKKLLLKKKMMMNNNNNNLLLLLLNNNQQQLLLMMMNNNNNNOOOOOOOOONNNJJJKKKMMMNNNNNNLLLJJJIIIJJJKKKLLLNNNNNNNNNMMMLLLLLLLLLLLLLLLKKKKKKKKKKKKIIIJJJKKKLLLLLLKKKJJJIIIIIIIIIJJJKKKJJJIIIHHHGGGEEEEEEEEEFFFGGGHHHJJJJJJHHHHHHHHHIIIJJJKKKLLLMMMGGGHHHHHHIIIIIIJJJJJJJJJJJJIIIIIIHHHHHHIIIIIIJJJEEEFFFGGGHHHHHHGGGFFFEEEBBBBBBCCCDDDEEEFFFGGGGGGCCCDDDDDDDDDEEEEEEFFFFFFBBBBBBBBBAAAAAABBBBBBBBBCCCCCCCCCCCCCCCDDDEEEEEEFFFEEEDDDEEEGGGGGGEEEDDDBBBCCCDDDDDDEEEEEEDDDDDDFFFEEEEEEDDDCCCCCCBBBBBB@@@@@@@@@@@@@@@@@@@@@@@@BBBAAA???>>>>>>>>>??????BBBAAA@@@@@@@@@???===;;;<<<===???@@@@@@???>>>>>>===>>>???AAAAAA@@@@@@???======>>>???@@@AAAAAABBB????????????>>>>>>>>>>>>:::;;;;;;;;;;;;;;;;;;:::<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<===>>>>>>>>>>>>>>>===<<<<<<<<<<<<===>>>>>>;;;;;;;;;:::999888777666999777666444444555777888777777888888999999999999666777888999:::;;;;;;;;;777999:::<<<======<<<<<<>>>===<<<;;;:::999999999;;;::::::999999::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;::::::::::::::::::::::::888888888777777777777666666666555555555666666777777777777777777777777777777666444333333444555666666666555555555666666777444555555555555555444444444555555555555555555444000111111222333555666777777777777777666666666666777777777777777666666555555444333333222222222333222222333333333444444444555444444444444555666666666666555444444444444555333444555777777777666666555555555555555555555555555444444333333444444555333333333444444555555555111111111222222333333333222222222222222222222222///000222333333222111000///000111222333222111111000000000111222222333333333111000000111222222111000000111111000...+++***++++++,,,---...000000111//////.........//////000------...............---((((((((((((((()))************+++,,,,,,---......UUURRRSSSYYY[[[XXXUUUVVVXXXVVVTTTVVVYYYZZZYYYVVVXXXVVVSSSSSSUUUWWWXXXXXXWWWWWWWWWWWWVVVUUUTTTTTTVVVUUUTTTSSSTTTUUUVVVWWWSSSTTTUUUVVVUUUTTTSSSRRRXXXVVVTTTTTTUUUUUUUUUSSSRRRTTTUUUUUUTTTUUUWWWYYYWWWXXXYYYZZZYYYXXXVVVTTTWWWVVVVVVUUUVVVWWWYYYZZZXXXXXXXXXYYYYYYYYYYYYYYY]]]]]]\\\ZZZXXXVVVTTTSSSTTTUUUVVVWWWVVVTTTRRRPPPTTTSSSRRRPPPOOOOOOOOOOOONNNNNNOOOPPPOOONNNMMMLLLNNNMMMLLLLLLLLLMMMNNNOOOQQQPPPOOONNNMMMNNNNNNOOOOOOOOOOOOMMMKKKKKKLLLNNNIIIHHHGGGFFFGGGIIIKKKLLLJJJKKKKKKLLLMMMNNNNNNNNNOOOMMMKKKLLLNNNOOOMMMKKKKKKKKKKKKKKKLLLNNNOOOPPPMMMMMMMMMMMMLLLLLLLLLLLLOOOOOONNNLLLIIIIIIKKKNNNKKKKKKKKKKKKLLLLLLLLLLLLJJJJJJKKKKKKKKKKKKJJJJJJHHHHHHHHHHHHHHHIIIJJJKKKHHHHHHHHHHHHHHHHHHHHHHHHGGGGGGHHHHHHHHHHHHIIIIIIHHHHHHIIIIIIIIIIIIHHHHHHHHHIIIJJJJJJJJJHHHFFFDDDEEEFFFHHHIIIIIIHHHGGGEEEHHHGGGFFFDDDDDDEEEGGGHHHHHHFFFEEEDDDDDDEEEFFFHHHGGGFFFDDDCCCBBBBBBBBBBBBGGGFFFEEEDDDDDDCCCDDDDDDCCCCCCBBBBBBCCCEEEHHHJJJHHHHHHGGGGGGFFFGGGGGGGGGEEEEEEDDDBBBBBBAAAAAAAAADDDDDDDDDDDDCCCCCCCCCCCCDDDDDDCCCBBBBBBAAA@@@@@@BBBAAA???>>>>>>>>>??????@@@@@@@@@@@@@@@???>>>======@@@BBBBBB@@@>>>======>>>@@@BBBBBB???===;;;;;;>>>===;;;<<<>>>@@@AAAAAABBB@@@>>>>>>??????===;;;999:::;;;;;;<<<<<<;;;;;;=========<<<<<<=========888999:::::::::;;;===???<<<<<<;;;;;;;;;<<<<<<===::::::::::::999888777666777777777777777777777777888888999999999:::::::::888888777777777888:::;;;<<<<<<;;;::::::;;;;;;;;;<<<=========<<<;;;;;;:::;;;;;;<<<<<<<<<<<<;;;;;;999999999::::::;;;;;;;;;<<<<<<<<<;;;;;;:::::::::888888777777777777888888555444333222333444666888555555666666555444333333444444444444444444444444444555555666666666666666555444444333333444444555555555444444444333333333333333444444555666777777555666666666555444333333444666777999999777666444444444444333333222222222333333222111111222222333444444555555555555444444333555888888777555555555444555666777777666555444666666666666666666666666555444444555666666555333222222222111111111111000000000000111111222222222444333111000000000111111333222222222111000000000111000000000222333222111111111111111111111111111111111000000000000111111222111111111000000//////111000///------......///......---,,,---...///000000...,,,---......,,,)))''''''((()))))))))))))))((((((((()))******++++++TTTRRRSSSWWWWWWTTTSSSUUUTTTRRRQQQRRRTTTUUUTTTRRRXXXUUUSSSSSSUUUWWWXXXXXXWWWWWWXXXXXXWWWWWWVVVVVVXXXWWWVVVUUUUUUUUUUUUUUUSSSTTTUUUVVVVVVVVVUUUTTTXXXVVVTTTTTTUUUVVVUUUTTTTTTUUUVVVUUUUUUUUUWWWYYYXXXXXXZZZZZZZZZYYYWWWVVVWWWWWWVVVVVVWWWWWWXXXYYYYYYYYYYYYYYYXXXXXXXXXXXX[[[[[[ZZZYYYWWWUUUSSSRRRVVVVVVXXXXXXWWWUUUSSSRRRUUUTTTSSSSSSQQQQQQPPPOOOPPPQQQQQQRRRQQQPPPOOONNNLLLLLLLLLLLLLLLMMMNNNOOORRRQQQOOONNNNNNNNNOOOOOOOOOOOOOOONNNLLLLLLNNNOOOLLLKKKJJJIIIIIIKKKLLLMMMLLLLLLMMMNNNNNNOOOPPPPPPPPPNNNMMMMMMOOOPPPOOOMMMKKKKKKKKKKKKLLLMMMNNNNNNLLLLLLLLLLLLLLLLLLLLLLLLNNNNNNMMMJJJHHHHHHIIIKKKJJJJJJKKKKKKKKKLLLLLLLLLIIIIIIJJJJJJJJJJJJIIIIIIHHHHHHIIIIIIJJJJJJJJJJJJHHHHHHHHHHHHHHHHHHHHHHHHGGGGGGHHHHHHHHHHHHIIIIIIJJJJJJKKKKKKKKKKKKJJJJJJIIIIIIJJJKKKJJJIIIHHHGGGHHHIIIJJJKKKJJJIIIGGGFFFHHHGGGEEEDDDEEEFFFHHHIIIFFFEEECCCBBBBBBCCCEEEFFFEEEEEEDDDCCCCCCCCCDDDDDDFFFEEEDDDDDDDDDDDDDDDDDDDDDCCCCCCBBBCCCEEEGGGIIIFFFFFFEEEEEEEEEEEEFFFGGGFFFFFFEEEDDDCCCBBBCCCCCCDDDDDDDDDDDDCCCCCCCCCCCCCCCCCCBBBBBBAAA@@@@@@???AAAAAA???>>>>>>>>>??????@@@@@@@@@?????????>>>>>>>>>@@@BBBBBB@@@>>>>>>>>>???AAABBBBBB@@@>>>===>>>@@@???======???@@@AAABBBAAA???>>>>>>>>>>>>===;;;::::::;;;<<<<<<<<<<<<;;;<<<======>>>>>>======<<<:::;;;<<<;;;::::::<<<===<<<<<<;;;;;;;;;<<<<<<===;;;;;;;;;;;;:::999888777777777777777777777777777888888888888999999999999999888888777777888999:::;;;;;;::::::::::::;;;;;;<<<<<<<<<<<<<<<;;;::::::<<<<<<============<<<<<<;;;;;;;;;;;;;;;;;;<<<<<<;;;;;;;;;;;;;;;;;;::::::888888777777777777888888666555444333444555777888444444555555555555555444444444444444444444444444444555555666666666666666555444444444444444444555666555555555444444444444333333444555555666666777555555666666555555444333555666777888888777666555444444444333333333222222333333333222333333444444444444555555555555444444333555888888777555555555555666777777777777666555666666666666666666666666555444444555666666555333222222222222111111111111111111111111222222222333333333111000000000111111222222222222111111111111111000///000222333222111111111111111111111111111111111111000000111111111222111111111000000000000111000///...---......///...------,,,---...///000///---,,,---......+++)))''''''((()))))))))))))))((((((((()))******++++++UUUTTTVVVWWWUUUQQQRRRWWWUUUTTTSSSTTTUUUVVVUUUTTTWWWUUUSSSSSSUUUWWWWWWWWWVVVWWWWWWXXXXXXXXXXXXXXXYYYYYYYYYXXXWWWVVVTTTTTTTTTUUUVVVWWWXXXXXXWWWVVVVVVUUUTTTUUUWWWWWWWWWVVVVVVWWWXXXWWWVVVUUUWWWYYYYYYYYYZZZ[[[[[[ZZZXXXWWWVVVWWWXXXXXXXXXXXXXXXXXXZZZYYYYYYYYYXXXWWWWWWWWWZZZYYYXXXWWWUUUTTTSSSRRRTTTUUUWWWWWWVVVUUUSSSQQQTTTUUUUUUUUUTTTRRRPPPOOOQQQQQQRRRRRRQQQQQQPPPOOOJJJJJJLLLMMMNNNNNNNNNNNNQQQQQQPPPOOOOOOOOOPPPPPPNNNOOOOOOOOONNNNNNOOOQQQOOONNNMMMLLLLLLLLLMMMNNNLLLLLLLLLMMMNNNNNNOOOOOOPPPOOONNNOOOPPPQQQPPPOOOKKKKKKKKKKKKKKKKKKLLLLLLKKKKKKKKKKKKKKKKKKKKKKKKMMMMMMLLLIIIGGGFFFHHHIIIIIIIIIJJJJJJJJJKKKKKKKKKIIIIIIIIIIIIIIIIIIIIIIIIHHHIIIJJJKKKLLLKKKJJJJJJHHHHHHHHHHHHHHHHHHHHHHHHGGGGGGHHHHHHHHHHHHIIIIIILLLLLLLLLLLLLLLLLLLLLLLLJJJJJJJJJJJJJJJKKKKKKKKKLLLLLLMMMMMMLLLJJJHHHGGGGGGFFFEEEEEEEEEGGGHHHIIIFFFEEEDDDCCCCCCDDDEEEFFFDDDCCCCCCCCCCCCDDDEEEFFFDDDDDDDDDCCCDDDDDDEEEEEEEEEDDDDDDCCCDDDEEEFFFGGGCCCCCCCCCCCCDDDDDDEEEFFFGGGFFFEEEDDDDDDDDDDDDDDDDDDDDDDDDCCCCCCCCCCCCBBBBBBBBBAAAAAA@@@?????????AAA@@@??????>>>?????????AAA@@@???>>>>>>>>>???@@@???@@@AAA@@@???>>>???@@@@@@AAABBBAAA@@@???@@@BBBAAAAAA@@@??????@@@AAABBB@@@???======>>>>>><<<;;;:::;;;;;;<<<<<<<<<<<<<<<<<<<<<===>>>>>>===<<<<<<<<<======<<<::::::;;;<<<===<<<<<<;;;;;;;;;<<<<<<;;;;;;<<<;;;;;;:::999888777777777777777777777777777777777777888888888888:::999999888888888888999::::::999999999999::::::;;;;;;<<<<<<;;;;;;::::::========================<<<<<<<<<<<<<<<<<<;;;;;;::::::;;;;;;;;;;;;;;;;;;888888777777777777888888777666555444555666777888444444555555666555555555444444444444444444444444444555555666666666666666555555444444444444555555777777666666666666555555444444444555555666666777555555666666666555444444555666777888888777666555444444444444333333333333333333333333444444555666444444555555555555444444333555777888666555555555666666777888888777666666666666666666666666666666555444444555666666555333333222222222111111111111111222222222222333333333333222111111000111111111111111111222222222222222111000///000222333222111111111111111111111111111222222111111111111222222111111111111111000000000000000///............///...------------...//////...---,,,,,,------+++)))''''''((()))))))))))))))((((((((()))******++++++WWWWWWYYYYYYUUUPPPTTT[[[VVVVVVVVVVVVVVVWWWVVVVVVWWWUUUTTTTTTUUUVVVVVVUUUTTTUUUVVVWWWXXXXXXXXXXXXXXXXXXYYYYYYYYYXXXVVVUUUTTTUUUWWWXXXYYYYYYYYYXXXVVVUUUUUUVVVXXXYYYXXXVVVXXXYYYYYYXXXVVVVVVWWWYYYZZZZZZ[[[[[[[[[[[[ZZZYYYWWWWWWYYYZZZZZZYYYXXXWWWZZZZZZYYYXXXWWWWWWVVVVVVYYYYYYWWWVVVUUUTTTSSSSSSQQQRRRTTTTTTTTTRRRQQQOOOSSSTTTUUUVVVUUURRRPPPNNNPPPPPPPPPPPPOOOOOOOOONNNJJJKKKMMMOOOPPPPPPOOOOOOQQQPPPPPPPPPPPPPPPPPPPPPNNNOOOPPPPPPOOOOOOQQQRRRQQQPPPOOONNNMMMMMMMMMMMMJJJJJJJJJKKKKKKLLLLLLLLLOOOOOOOOOOOOPPPPPPPPPPPPLLLLLLLLLLLLKKKKKKJJJJJJIIIIIIIIIJJJJJJJJJJJJJJJLLLMMMLLLJJJHHHGGGHHHIIIIIIIIIIIIIIIJJJJJJJJJKKKJJJJJJJJJIIIIIIJJJJJJJJJHHHJJJKKKMMMMMMLLLJJJIIIHHHHHHHHHHHHHHHHHHHHHHHHGGGGGGGGGHHHHHHHHHIIIIIIMMMLLLLLLLLLLLLLLLLLLMMMIIIIIIIIIIIIJJJKKKLLLMMMLLLLLLLLLLLLLLLKKKJJJIIIFFFFFFFFFFFFFFFGGGIIIIIIHHHGGGGGGFFFFFFGGGGGGHHHDDDDDDDDDDDDDDDDDDEEEEEECCCCCCCCCCCCCCCDDDEEEFFFFFFEEEEEEDDDDDDEEEFFFFFFBBBBBBBBBCCCDDDEEEFFFGGGFFFEEEEEEDDDCCCCCCDDDDDDDDDDDDCCCCCCCCCBBBBBBBBB@@@@@@@@@@@@??????>>>>>>@@@@@@??????????????????BBB@@@>>>======>>>@@@AAA@@@AAAAAA@@@>>>>>>@@@BBB???@@@AAA@@@???@@@BBBDDDBBBAAAAAA???>>>>>>???AAA???>>>======>>>>>>===;;;;;;;;;<<<============<<<===<<<;;;::::::;;;<<<===<<<======<<<;;;;;;<<<>>>======<<<;;;;;;;;;;;;<<<;;;<<<<<<<<<;;;;;;:::999777777777777777777777777666666666666777777777777;;;::::::999888888888888999999888888888999:::::::::;;;;;;;;;;;;;;;::::::======<<<<<<<<<<<<============<<<<<<;;;;;;:::::::::::::::;;;;;;<<<<<<<<<888888777777777777888888777777666666666666777888555555666666555444444333555555555555555555555555444555555666666666666666666666555555555555666666777777777777777777777777444444555555666666666777555555666666666666555555666666777777777777666666444444444444444444333333333333222333333444555666333444444555555444444333444555777777666555555666666777888999999888777666666666666666666666666666555444444555666666555333333333222222222111111111222222222222222333333333222222111111111111111111111111111222222333333333111000///000111222222000111111111111111111111111333222222222222222222333111111111111111111111111000/////////............------------......//////------,,,,,,,,,+++***)))''''''((()))))))))))))))((((((((()))******++++++VVVWWWYYYYYYTTTPPPSSSZZZTTTTTTUUUTTTTTTTTTTTTTTTWWWUUUTTTTTTUUUVVVUUUTTTRRRSSSTTTUUUVVVWWWWWWWWWUUUVVVXXXYYYZZZYYYYYYXXXUUUVVVWWWYYYZZZZZZZZZYYYVVVUUUVVVWWWYYYZZZXXXWWWXXXYYYYYYXXXWWWVVVXXXYYYZZZZZZ[[[[[[[[[[[[[[[ZZZXXXYYYZZZ[[[ZZZYYYXXXWWWZZZYYYYYYXXXWWWVVVVVVUUUYYYXXXWWWVVVUUUUUUUUUUUUQQQRRRSSSTTTTTTSSSQQQPPPSSSSSSTTTUUUTTTQQQOOOMMMQQQQQQPPPPPPPPPOOOOOOOOOMMMNNNPPPQQQRRRRRRQQQQQQOOOOOOPPPPPPPPPPPPPPPPPPMMMOOOQQQQQQPPPPPPQQQRRRQQQPPPOOONNNMMMMMMLLLLLLKKKKKKKKKKKKLLLLLLLLLLLLMMMNNNNNNOOOOOOOOOOOOPPPLLLMMMMMMMMMLLLKKKJJJIIIHHHIIIIIIIIIJJJJJJJJJKKKLLLMMMMMMLLLJJJIIIJJJKKKIIIIIIIIIIIIJJJJJJJJJKKKLLLLLLKKKJJJJJJKKKLLLLLLIIIJJJLLLMMMMMMKKKJJJHHHHHHHHHHHHHHHHHHHHHHHHHHHGGGGGGGGGHHHHHHHHHIIIIIILLLKKKKKKJJJJJJKKKKKKLLLHHHHHHHHHHHHIIIJJJLLLMMMIIIIIIJJJJJJKKKKKKKKKKKKGGGGGGFFFGGGGGGHHHHHHIIIHHHHHHGGGGGGGGGGGGHHHHHHFFFFFFFFFEEEEEEDDDCCCBBBCCCCCCBBBCCCCCCDDDEEEEEEFFFEEEEEEEEEEEEFFFFFFFFFCCCCCCCCCDDDEEEFFFGGGHHHDDDDDDCCCBBBBBBBBBCCCCCCCCCCCCCCCCCCBBBBBBBBBBBB@@@@@@????????????>>>>>>????????????@@@?????????AAA@@@>>>======>>>@@@BBB@@@AAAAAA@@@??????AAABBB>>>???@@@???>>>???AAACCC@@@AAAAAA???<<<<<<>>>@@@???>>>======>>>>>>===<<<;;;<<<======>>>>>>======>>><<<888666666888<<<>>>;;;<<<======<<<===???AAA======<<<;;;;;;;;;;;;;;;;;;;;;<<<<<<;;;;;;::::::777777777777777777777777555555666666666777777777::::::::::::999999888888999888888888999999:::;;;::::::;;;<<<<<<;;;;;;;;;<<<;;;;;;::::::;;;;;;<<<<<<;;;;;;;;;::::::999999:::::::::;;;;;;<<<<<<<<<888888777777777777888888777777777666666666777777777777777666555333222111555555555555555555555555444555555666666666666666777666666555555666666777888888888888888888888888555555555666666666666666555555666666666666666555666666777777777777666666444444444444444444444444222222111222222333444444333333444444444444333333444666777777555555555666666777888999999888777666666666666666666666666666555444444555666666555333333333333222222222222111222222222222222222222222111111111111222111111111111111222222333333333444000///...///111222111000000000000000000000000000333222222222222222222333111111111111111222222222///////////////......------------...............+++,,,,,,,,,+++***))))))''''''((()))))))))))))))((((((((()))******++++++SSSRRRTTTUUUSSSOOOPPPUUUUUUWWWWWWWWWUUUTTTUUUVVVVVVUUUTTTTTTUUUVVVTTTSSSRRRRRRTTTUUUVVVVVVVVVVVVUUUUUUWWWXXXYYYZZZZZZZZZVVVWWWXXXYYYZZZZZZYYYXXXWWWWWWWWWXXXZZZZZZXXXVVVWWWXXXYYYXXXVVVVVVXXXZZZZZZZZZZZZZZZZZZ[[[[[[[[[ZZZZZZZZZZZZZZZYYYYYYXXXYYYXXXXXXXXXWWWVVVVVVVVVYYYXXXVVVUUUTTTUUUVVVVVVSSSTTTVVVWWWWWWVVVTTTSSSSSSTTTTTTTTTSSSQQQOOONNNTTTTTTSSSRRRRRRRRRRRRSSSPPPQQQQQQRRRRRRRRRRRRRRRMMMNNNOOOPPPPPPPPPOOOOOONNNOOOQQQQQQPPPOOOPPPQQQPPPPPPOOOOOONNNMMMLLLLLLNNNNNNNNNNNNNNNNNNOOOOOOLLLMMMOOOOOONNNNNNPPPQQQLLLMMMNNNNNNNNNLLLKKKJJJHHHHHHIIIIIIJJJKKKKKKKKKLLLMMMNNNMMMLLLKKKLLLMMMIIIIIIJJJJJJJJJKKKKKKKKKNNNMMMLLLKKKKKKLLLMMMNNNJJJJJJKKKLLLKKKJJJIIIHHHHHHHHHHHHHHHHHHHHHHHHHHHGGGGGGHHHHHHHHHHHHIIIIIIKKKKKKIIIIIIIIIIIIKKKKKKGGGGGGHHHIIIJJJJJJKKKKKKGGGGGGHHHIIIJJJKKKLLLLLLHHHHHHHHHHHHHHHHHHGGGGGGFFFFFFFFFFFFFFFFFFFFFFFFGGGGGGGGGFFFEEEDDDBBBAAACCCCCCCCCBBBCCCCCCDDDDDDEEEEEEEEEFFFFFFGGGGGGGGGEEEEEEEEEEEEFFFGGGHHHHHHCCCCCCBBBBBBBBBBBBCCCCCCCCCCCCCCCBBBBBBBBBBBBAAA????????????????????????>>>>>>???@@@@@@@@@@@@???@@@???>>>>>>>>>???@@@AAA???@@@AAAAAA@@@@@@AAABBB===???@@@@@@??????@@@BBB???@@@AAA???;;;;;;===@@@@@@>>>===>>>???@@@???===<<<======>>>>>>>>>>>>>>>???<<<888555555888<<>>@@@BBB>>>===<<<;;;;;;;;;;;;;;;::::::;;;;;;;;;;;;::::::777777777777777777777777666666666666777777777777999::::::;;;::::::999888999999888999999:::;;;<<<;;;;;;<<<<<<======<<<<<<<<<;;;:::999999:::;;;<<<::::::::::::::::::999999::::::;;;;;;;;;;;;;;;;;;888888777777777777888888777777666666666666555555777777777666555333222111555555555555555555555555444555555666666666666666777777666666666666777777777777888888888888888999666666666666666666666666555555666777777777666666777777666666666666777777444444444444555555555555333222222111111222222222333333444444444444333333555666777666555444555777666666777888888777666666666666666666666666666666555444444555666666555333333333333333222222222222222222222111111111111000000000111222222222222111222222222333333333333333000///...///111222111000000000000000000000000000222222111111111111222222111111111222222222222222/////////000///......---,,,---......//////......***,,,---,,,***(((((()))''''''((()))))))))))))))((((((((()))******++++++QQQOOOPPPTTTTTTQQQPPPRRRWWWXXXZZZXXXVVVUUUVVVXXXVVVUUUTTTTTTUUUUUUTTTRRRSSSTTTUUUUUUVVVVVVVVVVVVVVVVVVVVVVVVWWWXXXYYYYYYVVVWWWXXXYYYYYYYYYXXXWWWXXXXXXXXXZZZ[[[ZZZWWWUUUUUUVVVWWWWWWVVVWWWXXXZZZYYYYYYYYYYYYZZZZZZ[[[[[[\\\[[[ZZZZZZYYYYYYYYYZZZWWWWWWWWWWWWWWWWWWWWWWWWWWWVVVTTTSSSSSSTTTUUUVVVTTTUUUVVVXXXXXXWWWUUUTTTVVVUUUTTTTTTSSSRRRQQQPPPUUUTTTSSSRRRRRRRRRSSSTTTSSSRRRRRRQQQQQQQQQQQQQQQLLLMMMNNNOOOOOOOOONNNNNNNNNPPPQQQQQQPPPNNNNNNOOOPPPPPPPPPPPPOOONNNNNNMMMPPPPPPOOOOOOOOOOOOOOOOOOLLLNNNPPPPPPOOOOOOQQQSSSLLLMMMOOOOOOOOONNNLLLKKKHHHIIIIIIJJJKKKKKKLLLLLLJJJKKKMMMNNNMMMMMMNNNOOOJJJJJJKKKKKKKKKLLLLLLLLLMMMLLLKKKJJJJJJKKKLLLMMMJJJJJJJJJJJJIIIIIIHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHGGGGGGHHHHHHHHHHHHIIIIIILLLKKKIIIHHHHHHIIIKKKLLLHHHIIIJJJKKKLLLLLLKKKJJJIIIIIIIIIIIIJJJJJJKKKLLLIIIIIIIIIIIIHHHGGGFFFFFFFFFGGGGGGGGGGGGGGGGGGFFFEEEFFFFFFGGGFFFEEEDDDCCCDDDDDDCCCBBBBBBBBBCCCCCCCCCDDDEEEFFFGGGHHHHHHHHHFFFFFFFFFEEEEEEFFFGGGGGGDDDDDDCCCCCCCCCCCCDDDDDDCCCCCCCCCBBBBBBBBBAAAAAA@@@@@@@@@@@@@@@@@@@@@@@@===>>>???@@@AAA@@@@@@???>>>>>>?????????@@@@@@@@@>>>@@@BBBCCCBBBAAAAAABBB>>>@@@BBBCCCAAA@@@@@@AAA>>>AAABBB@@@<<<;;;???BBB@@@???>>>???@@@AAA@@@???======>>>????????????>>>===<<<:::999999:::<<<===<<<>>>>>>>>>======???AAA>>>>>>===;;;;;;::::::;;;999999::::::::::::999999777777777777777777777777666666777777777888888888888999:::;;;;;;;;;:::999999999999999:::;;;<<<===;;;<<<======>>>>>>=========<<<:::999999:::<<<===:::::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;::::::888888777777777777888888666666666666666555444444555555555666555555444333555555555555555555555555444555555666666666666666888777777666666777777888777777777777888888888999777666666666666666666666555555666777777777777777777777666666666666777777444444444444555555555666555444333222222222222222222333333444444333333222555666777666444444666777555666777777777777666555666666666666666666666666555444444555666666555333444444333333333222222222111111111000000000/////////000111222333222222111333333333333333333222222000///...///111111111///000000000000000000000000111111111000000111111111111111111222222333333333...///000000000///------,,,---.../////////...---)))+++---,,,)))'''((()))''''''((()))))))))))))))((((((((()))******++++++RRROOOPPPUUUWWWTTTRRRRRRSSSUUUVVVUUURRRPPPRRRTTTVVVUUUTTTUUUUUUUUUSSSQQQUUUUUUVVVWWWWWWWWWVVVVVVYYYXXXVVVUUUUUUVVVWWWXXXWWWXXXXXXYYYYYYXXXWWWVVVYYYYYYYYYZZZ[[[ZZZWWWTTTTTTUUUVVVVVVVVVWWWYYY[[[YYYYYYXXXXXXYYYZZZ[[[[[[]]]\\\ZZZYYYYYYYYYZZZ[[[VVVVVVWWWWWWWWWWWWWWWWWWVVVTTTSSSQQQQQQRRRTTTUUURRRSSSUUUVVVVVVUUUTTTSSSXXXWWWUUUTTTSSSRRRRRRSSSTTTSSSQQQPPPPPPPPPQQQRRRTTTSSSQQQPPPOOOOOOPPPQQQKKKLLLMMMNNNOOONNNNNNMMMNNNPPPQQQQQQOOOMMMMMMMMMPPPPPPPPPQQQPPPPPPOOONNNNNNNNNNNNNNNNNNNNNNNNNNNMMMOOORRRRRRPPPPPPRRRUUULLLMMMOOOPPPPPPOOONNNLLLIIIIIIJJJJJJKKKLLLMMMMMMHHHJJJLLLMMMMMMMMMNNNPPPKKKKKKKKKKKKLLLLLLLLLLLLMMMKKKJJJIIIIIIJJJKKKMMMKKKJJJIIIHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHGGGGGGHHHHHHHHHIIIIIIIIIMMMKKKJJJIIIIIIJJJKKKMMMIIIJJJLLLNNNNNNMMMKKKJJJLLLKKKKKKJJJJJJJJJJJJKKKJJJJJJJJJIIIHHHGGGFFFEEEHHHIIIIIIJJJJJJIIIIIIHHHCCCDDDFFFGGGGGGFFFEEEEEEEEEDDDCCCBBBBBBBBBBBBBBBBBBCCCEEEFFFHHHHHHIIIIIIGGGFFFFFFEEEEEEEEEEEEFFFEEEEEEDDDDDDDDDDDDEEEFFFCCCCCCBBBBBBBBBAAAAAAAAA@@@@@@@@@@@@@@@@@@AAAAAA===>>>???@@@AAAAAA@@@???===>>>???@@@@@@@@@@@@@@@===???BBBDDDCCCAAAAAAAAA???AAADDDEEECCCAAAAAAAAA>>>AAACCCAAA===<<<@@@DDDAAA@@@??????AAABBBAAA@@@======>>>???????????????<<<<<<===>>>>>>===<<<<<>>??????>>>===<<<;;;:::::::::888888999:::::::::999999777777777777777777777777777777777777888888888888777888:::;;;<<<;;;;;;:::::::::::::::;;;<<<===>>><<<<<<===>>>??????>>>>>>>>>===;;;::::::;;;===>>>:::;;;;;;<<<<<<=========<<<<<<<<<;;;;;;:::::::::888888777777777777888888555555666666555444333333222333444555666666666666666666666666666666666666444555555666666666666666888888777777777777888888666666777777888888888888777777777777666666666666555555666777777777777777777777666666666666777777444444444555555555666666777666555444333222222222222333333444444333333222555666777666444444666777444555666777777666555444666666666666666666666666555444444555666666555333444444444333333333222222111000000000//////......///000111222333333222111444444444333333222222222000///...///000111111///000000000000000000000000111111000000000000111111111111111222222333333333...///000000000///---,,,,,,,,,.../////////...---)))+++---,,,((('''''')))'''(((((()))))))))))))))((((((((()))******++++++PPPPPPPPPSSSUUUUUUTTTRRRVVVWWWXXXXXXXXXVVVTTTRRRTTTUUUWWWXXXXXXWWWUUUTTTWWWWWWWWWWWWWWWWWWVVVVVVTTTTTTTTTUUUUUUVVVVVVVVVVVVWWWXXXYYYYYYXXXWWWVVVWWWWWWWWWXXXXXXXXXYYYYYYWWWWWWWWWWWWXXXZZZ[[[\\\\\\\\\\\\[[[YYYXXXYYYZZZ[[[[[[\\\\\\\\\\\\[[[[[[XXXYYYYYYVVVSSSSSSWWW[[[TTTTTTTTTTTTTTTSSSRRRQQQSSSTTTVVVWWWWWWVVVTTTSSSQQQSSSUUUVVVVVVVVVTTTSSSTTTSSSRRRQQQQQQRRRSSSTTTRRRRRRQQQOOONNNNNNQQQSSSOOOOOOPPPPPPPPPOOONNNMMMMMMNNNOOOPPPPPPPPPOOONNNRRRQQQPPPOOOOOOOOOOOOOOORRRTTTVVVUUUSSSQQQPPPPPPQQQQQQQQQQQQQQQQQQQQQQQQOOOLLLJJJMMMQQQQQQMMMIIIMMMMMMNNNNNNNNNMMMMMMLLLNNNOOOOOOOOOOOONNNMMMLLLMMMLLLKKKJJJJJJKKKLLLLLLMMMKKKIIIIIIJJJKKKLLLKKKHHHIIIJJJLLLLLLLLLLLLKKKMMMLLLJJJHHHGGGGGGGGGGGGEEEGGGHHHHHHHHHHHHIIIKKKLLLKKKIIIHHHHHHIIIKKKLLLOOOMMMLLLMMMNNNNNNKKKHHHHHHHHHIIIIIIJJJKKKKKKLLLHHHGGGGGGFFFEEEEEEEEEFFFFFFGGGHHHIIIIIIGGGFFFDDDFFFFFFGGGGGGGGGGGGFFFFFFEEEEEEEEEEEEEEEEEEEEEEEECCCDDDDDDEEEEEEEEEEEEEEEFFFFFFGGGFFFDDDDDDEEEGGGFFFFFFFFFEEEEEEEEEEEEEEEFFFFFFDDDCCCBBBAAAAAA@@@CCCBBBAAA@@@????????????===???@@@AAAAAA@@@>>>===BBB@@@>>>???AAABBBAAA>>>???@@@AAAAAA??????@@@AAAAAAAAAAAAAAA@@@???>>>>>>>>>@@@AAA@@@???>>>???@@@<<<>>>???@@@@@@???>>><<>>>>>??????@@@AAAAAA???======>>>>>><<<::::::;;;===>>>>>>>>>===<<<>>>======<<<;;;:::::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;::::::::::::;;;<<<<<<;;;::::::999888888888999::::::999999888999999999;;;::::::::::::;;;<<<<<<======>>>???????????????========================;;;::::::999999::::::;;;;;;<<<<<<:::888666666777999999999888888888888888777666666555555555666666555555555666666666666666555666666666666666555555777777777666555555444444666666666666666555555555777888999::::::::::::999999999999888888888888888999999999999888888888777666555555444444666777888666555444333333444555666666666555555555444444444777666444444333444555666444555666555333333555666888888777777777777888888888888888777777777777777888666555666777888777666666444222333444444111...111111111111111111111111000111333333333222000...000000111111111111000000444333111000000000111111000000000000000000000000111111111111111111111111000000000000000000000000///............---------+++******+++---......---+++*********))))))((((((''''''((())))))))))))))))))******++++++,,,------PPPPPPQQQTTTVVVXXXWWWUUUYYYXXXVVVUUUTTTSSSRRRRRRRRRSSSUUUWWWXXXXXXWWWVVVWWWWWWWWWWWWXXXXXXXXXXXXUUUUUUUUUVVVVVVVVVVVVVVVVVVWWWWWWWWWWWWWWWWWWVVVWWWWWWWWWXXXXXXXXXYYYYYYYYYYYYYYYXXXYYYYYYZZZZZZ[[[\\\\\\ZZZXXXWWWXXXZZZ\\\\\\\\\\\\[[[ZZZYYYXXXWWWXXXXXXWWWVVVUUUVVVWWWTTTTTTUUUUUUUUUTTTSSSSSSTTTUUUVVVWWWWWWVVVTTTSSSPPPQQQSSSTTTUUUTTTSSSRRRRRRQQQPPPOOOOOOPPPQQQRRRSSSSSSSSSQQQOOOOOOQQQSSSQQQPPPPPPPPPOOOOOOOOOOOOOOOOOOQQQRRRRRRRRRQQQPPPRRRQQQPPPOOOOOOOOOOOOPPPQQQRRRTTTSSSQQQOOOOOOOOOQQQQQQQQQQQQQQQRRRRRRRRROOOMMMKKKLLLPPPQQQNNNJJJMMMMMMNNNNNNNNNNNNMMMMMMMMMMMMMMMMMMMMMLLLLLLLLLKKKJJJJJJJJJJJJKKKMMMNNNMMMKKKIIIIIIJJJKKKKKKKKKFFFGGGIIIJJJKKKKKKJJJJJJLLLKKKIIIGGGFFFFFFFFFFFFEEEGGGHHHHHHHHHHHHIIIKKKJJJHHHGGGFFFFFFGGGHHHJJJMMMLLLLLLMMMOOONNNKKKHHHHHHHHHIIIIIIJJJKKKKKKLLLJJJIIIHHHGGGGGGGGGGGGHHHFFFGGGHHHIIIIIIGGGFFFDDDFFFFFFGGGGGGGGGGGGFFFFFFDDDDDDDDDDDDDDDDDDDDDDDDCCCDDDDDDEEEEEEEEEEEEEEEEEEFFFFFFEEEDDDDDDFFFHHHFFFEEEEEEEEEEEEEEEEEEEEEFFFEEEDDDCCCBBBAAAAAAAAACCCBBBAAA@@@????????????>>>???@@@AAAAAA@@@???>>>AAA@@@???@@@BBBBBB@@@>>>???AAABBBAAA@@@???@@@AAAAAAAAABBBAAAAAA@@@???>>>>>>???@@@???>>>>>>???@@@===>>>@@@AAAAAA@@@>>>===@@@@@@??????@@@@@@AAABBB@@@???======>>>>>><<<;;;;;;<<<===>>>>>>>>>===<<<>>>>>>======<<<;;;;;;:::;;;;;;;;;;;;;;;;;;;;;;;;;;;::::::::::::;;;<<<<<<;;;::::::999999888999999999999999888999999::::::;;;:::::::::;;;;;;<<<<<<======>>>????????????>>>========================;;;;;;::::::::::::;;;;;;;;;<<<<<<;;;888666777888:::999999999888777777777777666666555555555666666555666666666666666666666555555666666666666555555555555666666666666666666777777777777777777777777888888999:::::::::999999:::999999999888777777777999888888888777777777777666555555444555666777888666666555444444555666666666555555555444444444444666555444333333444555555444555666555333333555666888888777777777777888888888777777777777777777777777666555555777777666555666444333333444444222///111111111111111111111111000111222333333111000///111111222222222222111111333333111000000000111111111111111111111111111111111111111111111111111111111111111111111111111111///............------------+++***+++,,,,,,+++************)))))))))((((((''''''((())))))))))))))))))******++++++,,,------RRRQQQRRRUUUXXXYYYYYYWWWZZZXXXUUURRRQQQPPPQQQRRRQQQRRRTTTVVVXXXXXXXXXXXXWWWWWWXXXXXXYYYYYYZZZZZZWWWWWWWWWWWWWWWVVVVVVVVVXXXXXXWWWWWWWWWWWWXXXXXXWWWWWWWWWXXXXXXXXXXXXXXX\\\[[[ZZZYYYYYYYYYYYYZZZZZZ[[[[[[YYYWWWWWWXXXYYY]]]]]]\\\[[[ZZZXXXWWWVVVXXXXXXYYYZZZ[[[ZZZWWWTTTTTTTTTUUUVVVVVVVVVUUUUUUUUUVVVWWWWWWWWWVVVTTTSSSQQQRRRSSSUUUUUUTTTSSSSSSQQQPPPPPPOOOOOOPPPPPPQQQUUUUUUTTTRRRPPPOOOQQQSSSSSSRRRQQQPPPOOOPPPPPPQQQQQQQQQRRRSSSSSSSSSSSSRRRQQQQQQPPPOOOOOOOOOPPPPPPOOOQQQRRRQQQOOONNNMMMNNNPPPPPPQQQQQQRRRRRRRRRSSSPPPMMMKKKLLLNNNPPPNNNLLLMMMNNNNNNOOOOOONNNNNNNNNLLLLLLKKKJJJJJJKKKLLLMMMIIIIIIIIIJJJKKKLLLNNNOOOMMMKKKIIIIIIJJJKKKKKKJJJHHHHHHIIIJJJKKKKKKKKKKKKKKKJJJHHHGGGFFFEEEFFFFFFEEEGGGHHHHHHHHHHHHIIIKKKIIIHHHGGGFFFFFFGGGHHHIIIKKKKKKLLLNNNOOONNNKKKHHHIIIIIIIIIIIIJJJJJJKKKLLLKKKKKKJJJIIIIIIIIIJJJJJJGGGGGGHHHIIIHHHGGGFFFEEEFFFFFFGGGGGGGGGGGGFFFFFFDDDDDDDDDDDDDDDDDDDDDDDDCCCDDDEEEEEEFFFFFFEEEEEEDDDEEEFFFFFFEEEEEEGGGIIIEEEEEEEEEEEEEEEEEEFFFFFFFFFEEEDDDCCCBBBAAAAAAAAABBBBBBAAAAAA@@@@@@??????@@@@@@@@@@@@@@@@@@@@@@@@@@@???@@@BBBCCCCCC@@@>>>@@@AAABBBBBB@@@@@@AAABBBBBBBBBBBBBBBAAA@@@???>>>===>>>??????======>>>???>>>>>>@@@@@@@@@@@@>>>>>>@@@@@@@@@@@@@@@AAAAAABBB@@@???======>>>>>><<<;;;;;;<<<===>>>>>>>>>======??????>>>>>>======<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;:::::::::::::::;;;<<<<<<::::::::::::999999999999888888888888999:::;;;;;;:::;;;;;;;;;;;;<<<<<<<<<<<<======>>>>>>>>>>>>>>>========================;;;;;;::::::::::::;;;;;;;;;<<<<<<;;;888777777888::::::999999888777666666666666666555555666666777666666666666666666555555555555666666666666666555444444555666666777888888777777777777888888888888999999:::::::::999999888::::::999999888777666666777777777777666666666666666555555555555666777777666666555555555555666666555555555555444444444444444444333333333444444555444555666555333333555666888777777666666777777888777777777777777777888888666555444444666666555444555444333444444444222000222222222222222222222222111111222333222111000///222222333333333333222222333222111111000111111111222222222222222222222222111111111111111111111111111111111111111111111111///............------------,,,******+++***)))'''))))))))))))((((((((((((''''''((())))))))))))))))))******++++++,,,------TTTSSSSSSTTTWWWXXXWWWVVVXXXVVVUUUSSSRRRRRRRRRSSSRRRSSSTTTVVVWWWWWWWWWWWWWWWXXXXXXYYYZZZ[[[[[[\\\YYYYYYXXXXXXWWWWWWWWWVVVZZZYYYXXXWWWWWWXXXYYYZZZXXXXXXXXXXXXXXXXXXXXXXXX[[[[[[ZZZZZZZZZZZZ[[[[[[ZZZZZZZZZYYYWWWVVVWWWXXX\\\\\\[[[[[[YYYXXXWWWVVV\\\ZZZYYY[[[]]]]]]YYYVVVTTTTTTUUUVVVWWWWWWWWWWWWVVVWWWWWWWWWVVVUUUTTTSSSTTTTTTUUUVVVWWWVVVVVVUUURRRRRRRRRRRRRRRRRRRRRRRRVVVVVVVVVTTTQQQPPPQQQSSSUUUSSSQQQPPPOOOPPPRRRSSSQQQQQQRRRRRRSSSSSSSSSSSSQQQPPPPPPOOOOOOOOOPPPPPPOOOPPPQQQPPPOOOMMMNNNOOOOOOOOOOOOPPPQQQQQQRRRRRRQQQNNNLLLLLLMMMOOOOOONNNMMMNNNOOOOOOOOOOOOOOOOOOMMMLLLJJJIIIIIIKKKMMMNNNLLLLLLLLLLLLMMMMMMNNNNNNMMMKKKJJJJJJKKKKKKJJJIIIKKKKKKLLLMMMMMMNNNNNNNNNKKKJJJIIIGGGFFFFFFGGGGGGEEEGGGHHHHHHHHHHHHIIIKKKJJJJJJIIIHHHHHHIIIJJJJJJIIIJJJLLLNNNOOONNNKKKIIIJJJIIIIIIHHHIIIJJJKKKLLLKKKKKKJJJJJJJJJJJJJJJKKKGGGGGGHHHHHHHHHGGGFFFEEEFFFFFFGGGGGGGGGGGGFFFFFFCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDEEEFFFFFFFFFFFFEEECCCEEEFFFFFFEEEFFFHHHJJJEEEEEEEEEEEEEEEFFFFFFFFFEEEEEEDDDBBBBBBAAAAAAAAABBBBBBBBBAAAAAA@@@@@@???AAA@@@@@@@@@@@@AAABBBBBB>>>@@@BBBCCCDDDBBB@@@>>>@@@BBBCCCBBBAAA@@@AAACCCBBBBBBBBBBBBAAA@@@???>>><<<>>>???>>>===<<<===>>>===>>>>>>??????>>>>>>===?????????>>>???@@@@@@AAA@@@>>>======>>>>>>===;;;<<<<<<======>>>>>>>>>>>>????????????>>>>>>======<<<<<<<<<<<<<<<<<<<<<<<<::::::999999::::::;;;<<<::::::::::::::::::999999888888888888999:::;;;<<<:::;;;;;;<<<<<<<<<<<<<<<;;;<<<======>>>>>>==============================<<<<<<;;;;;;;;;;;;<<<<<<;;;<<<<<<;;;999777888999;;;::::::999888777666666666666666666666666777888666666666666555555555555444555666666666666666666555555666666777777777777666777777777777777888888999999:::::::::999888888;;;::::::999888777666666777666666666666555555555555555555555666666666777666666666666666666666666444444444444444444444444333333333333333444444444444555666555333333555666777777666666666666777777777777777777777888888888555444333333555555444333555444444444444444333222222222222222222222222222111222222222222111000///111222222222222222222111222222111111111111111111222222222222222222222222111111111111111111111111111111111111111111111111///............---------,,,***))))))******)))'''((((((((((((((((((((((((''''''((())))))))))))))))))******++++++,,,------UUUSSSRRRSSSTTTUUUTTTSSSSSSTTTUUUVVVVVVVVVUUUTTTTTTTTTUUUUUUUUUUUUUUUUUUXXXXXXYYYYYYZZZ[[[\\\\\\YYYYYYYYYXXXXXXWWWWWWWWWYYYXXXVVVVVVVVVVVVXXXYYYXXXXXXXXXXXXXXXXXXXXXWWWYYYYYYYYYYYYZZZ[[[\\\]]]ZZZZZZZZZYYYWWWVVVWWWXXXYYYZZZZZZZZZZZZYYYYYYXXX\\\ZZZWWWXXXZZZ[[[YYYWWWTTTUUUVVVWWWWWWWWWWWWWWWVVVVVVVVVUUUUUUTTTTTTSSSTTTTTTUUUUUUVVVVVVVVVVVVSSSSSSSSSSSSSSSSSSSSSSSSUUUVVVVVVTTTRRRQQQRRRSSSUUUTTTRRRPPPPPPQQQRRRSSSQQQPPPQQQQQQQQQRRRRRRRRRPPPPPPOOOOOOOOOPPPPPPQQQPPPQQQRRRQQQOOOOOOPPPQQQNNNNNNOOOOOOOOOPPPPPPPPPPPPOOOMMMLLLMMMNNNOOOOOONNNNNNOOOPPPPPPPPPPPPPPPOOONNNLLLKKKKKKLLLNNNOOOOOOOOOOOOOOONNNMMMMMMMMMLLLKKKJJJJJJKKKKKKJJJHHHKKKKKKLLLLLLMMMMMMNNNOOOLLLKKKJJJIIIHHHHHHIIIIIIEEEGGGHHHHHHHHHHHHIIIKKKIIIIIIIIIHHHHHHIIIIIIIIIGGGIIILLLNNNNNNMMMKKKJJJKKKJJJIIIHHHHHHIIIKKKLLLJJJIIIIIIIIIIIIIIIJJJJJJHHHHHHHHHHHHGGGGGGFFFFFFFFFFFFGGGGGGGGGGGGFFFFFFDDDDDDDDDDDDDDDDDDDDDDDDDDDEEEEEEFFFFFFFFFFFFFFFDDDEEEFFFFFFFFFFFFHHHJJJDDDDDDEEEEEEFFFFFFFFFFFFEEEDDDCCCBBBBBBBBBBBBBBBAAAAAABBBBBBBBBAAA@@@@@@AAAAAA@@@@@@AAABBBCCCCCC>>>@@@CCCDDDDDDBBB@@@???AAABBBCCCCCCBBBAAABBBCCCBBBBBBBBBBBBAAA@@@??????<<<>>>???>>>===<<<===>>><<<==================<<<===============>>>>>>??????>>>======>>>>>>===<<<============>>>>>>?????????????????????>>>>>>>>><<<<<<<<<<<<<<<<<<<<<<<<:::999999999999:::;;;;;;999::::::;;;;;;;;;:::999888888888888999:::;;;<<<:::;;;<<<=========<<<<<<;;;;;;<<<============<<<>>>>>>>>>>>>>>>>>>>>>>>>===<<<<<<;;;;;;<<<<<<===;;;<<<<<<;;;999888999:::::::::999999888777777666666666666666666777888888777777666666555555555444444444555666666666666666888888777777666666666666555555555666666777777777999999:::::::::999999888::::::999999888777777666666666666666555555555444444555555666666666666666555555666666666666555555333333444444444444444444333333333444444555555555444555666555333333555666777777666666666666777777666666777777888888888888555333222333444555444333444444555555444444333333222222222222222222222222222222222222111111000000000000111111111111000000111111111111222111111111111111111111111111111111111111111111111111111111111111111111111111111111///............---------)))((('''(((***+++***)))'''''''''''''''''''''(((''''''((())))))))))))))))))******++++++,,,------TTTRRRQQQQQQRRRSSSSSSRRRPPPRRRTTTWWWXXXWWWVVVUUUUUUUUUUUUUUUTTTTTTUUUUUUXXXXXXYYYYYYZZZZZZ[[[[[[XXXXXXXXXXXXXXXWWWWWWWWWUUUUUUTTTTTTTTTTTTUUUUUUXXXXXXXXXXXXXXXWWWWWWWWWXXXXXXXXXYYYZZZ[[[]]]]]]ZZZ[[[[[[YYYWWWWWWXXXYYYYYYZZZZZZ[[[[[[ZZZZZZZZZYYYWWWUUUUUUVVVVVVVVVUUUUUUUUUVVVWWWWWWWWWVVVVVVTTTTTTTTTTTTTTTTTTTTTTTTRRRRRRRRRRRRRRRSSSSSSSSSQQQRRRRRRSSSSSSRRRRRRQQQSSSTTTUUUTTTSSSRRRRRRTTTTTTSSSRRRQQQPPPQQQQQQRRRPPPPPPOOOOOOPPPPPPQQQRRRPPPPPPOOOOOOOOOPPPQQQQQQQQQRRRRRRQQQPPPPPPQQQSSSOOOOOOOOOOOOOOOOOOOOOOOOOOOOOONNNNNNNNNNNNOOOOOONNNNNNOOOPPPQQQQQQQQQQQQQQQPPPNNNMMMMMMMMMNNNOOOPPPPPPPPPPPPOOOMMMLLLKKKLLLKKKKKKKKKLLLKKKIIIGGGIIIIIIIIIIIIJJJKKKLLLMMMMMMLLLJJJIIIIIIIIIJJJKKKEEEGGGHHHHHHHHHHHHIIIKKKFFFFFFGGGGGGGGGGGGFFFFFFGGGIIIKKKLLLLLLLLLLLLMMMLLLJJJIIIHHHHHHIIIKKKLLLIIIHHHHHHHHHHHHIIIJJJJJJHHHHHHHHHGGGGGGGGGFFFFFFFFFFFFGGGGGGGGGGGGFFFFFFEEEEEEEEEEEEEEEEEEEEEEEEDDDEEEFFFFFFGGGGGGFFFFFFEEEFFFGGGFFFFFFFFFHHHJJJDDDDDDDDDEEEFFFFFFGGGGGGDDDDDDCCCBBBBBBBBBBBBBBB@@@AAABBBCCCCCCBBBAAA@@@@@@AAAAAABBBBBBCCCCCCDDD???AAADDDDDDCCCAAA@@@AAABBBCCCDDDDDDBBBBBBCCCDDDCCCCCCCCCBBBBBBAAA@@@???===>>>??????======>>>???========================<<<<<<<<<<<<<<<======>>>???===<<<===>>>???>>><<<>>>>>>=========>>>???@@@?????????>>>>>>>>>>>>>>><<<<<<<<<<<<<<<<<<<<<<<<999999999999999:::;;;;;;888999;;;<<<<<<;;;::::::888888888888999:::;;;;;;:::;;;<<<===>>>===<<<<<<:::;;;;;;<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>======<<<<<<<<<<<<======;;;<<<<<<;;;:::999999:::999999999888888888888888666666666666777888999999777777777666555555444444333444555666777777777777999999888777777666555555444444555555666666777777777888999::::::::::::999999999999888888888888888666666666666555555555555444555555666777666666666444444555555555555444444333333333333444444444444333333444555666666666666444555666555333333555666777666666555555666666777666666666777888888999999555444333333555555444333333555666666444333444555333333333333333333333333222222222111111111111111000000000111111000000000000000111222222222222111000000000000000000000000111111111111111111111111222222222222222222222222///............---------(((''''''(((***,,,+++***&&&&&&&&&'''''''''''''''''''''((())))))))))))))))))******++++++,,,------QQQPPPOOOPPPRRRTTTUUUUUURRRRRRSSSTTTTTTUUUUUUUUUTTTSSSSSSTTTTTTUUUVVVVVVYYYYYYYYYYYYYYYYYYYYYYYYWWWWWWWWWWWWWWWXXXXXXXXXTTTUUUUUUVVVVVVUUUUUUTTTYYYYYYXXXXXXXXXWWWWWWWWWXXXXXXXXXXXXYYYZZZZZZ[[[[[[\\\\\\ZZZXXXWWWXXXZZZ[[[\\\\\\\\\[[[ZZZYYYYYYUUUWWWXXXXXXWWWUUUUUUUUUUUUVVVVVVVVVVVVUUUUUUTTTQQQQQQQQQRRRRRRSSSTTTTTTQQQQQQQQQQQQQQQRRRRRRSSSRRRSSSTTTUUUUUUTTTSSSRRRQQQRRRTTTTTTSSSRRRSSSTTTRRRRRRRRRQQQQQQQQQPPPPPPPPPPPPOOOOOOOOOPPPQQQRRROOOOOOOOOOOOOOOPPPQQQRRRQQQRRRRRRQQQPPPPPPRRRTTTSSSRRRRRRQQQQQQPPPPPPOOONNNOOOPPPPPPOOONNNNNNOOONNNOOOPPPQQQQQQRRRRRRRRRQQQQQQPPPOOONNNMMMMMMLLLMMMNNNNNNNNNNNNMMMKKKJJJLLLKKKKKKKKKLLLKKKIIIGGGIIIHHHHHHHHHHHHJJJKKKLLLLLLKKKJJJIIIHHHIIIJJJJJJEEEGGGHHHHHHHHHHHHIIIKKKFFFFFFFFFGGGGGGFFFFFFFFFGGGIIIKKKKKKJJJJJJMMMPPPLLLKKKIIIGGGGGGIIIKKKLLLIIIHHHHHHHHHIIIIIIJJJKKKHHHHHHGGGGGGFFFFFFGGGGGGFFFFFFGGGGGGGGGGGGFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEEEEEEFFFGGGGGGGGGGGGFFFFFFGGGHHHGGGFFFFFFGGGIIICCCDDDDDDEEEFFFFFFGGGGGGDDDDDDCCCBBBBBBBBBBBBCCC@@@AAABBBDDDDDDCCCAAA@@@???@@@BBBCCCDDDDDDDDDCCC???BBBDDDCCCAAA@@@AAACCCBBBDDDEEEDDDCCCBBBCCCDDDCCCCCCCCCCCCBBBAAA@@@???>>>???@@@???>>>>>>???@@@??????>>>>>>>>>>>>??????<<<<<<<<<<<<<<<===>>>>>>>>>===<<<===>>>???>>>===???>>>=========>>>???@@@>>>>>>>>>>>>>>>>>>>>>>>><<<<<<<<<<<<<<<<<<<<<<<<999999999888999999:::;;;888999;;;<<<===<<<;;;:::999999999888999999:::::::::;;;===>>>>>>>>><<<<<<::::::;;;<<<<<<<<<<<<;;;>>>>>>>>>>>>>>>>>>>>>>>>>>>==================>>>:::<<<<<<<<<:::999:::;;;888888888888888999999999666666666666777888999:::888777777666555555444444333444555666777777777777888888777777777777777777444555555666777777888888666777888999:::;;;;;;;;;888888888888888999999999777777777666666666555555444444666777777777666555222333444555555444333222222222333333333444444444333444555777777777777777444555666555333333555666666666555555555555666666555666666777888888999999555444333444555666555333222555777666444333444666333333333333333333333333333222222111111111111111000111111222222111111000///000111222333222222111111111111111111111111111111111111111111111111111222222222222222222222222///............---------+++)))((()))++++++***)))%%%%%%&&&&&&&&&'''''''''''''''((())))))))))))))))))******++++++,,,------OOONNNNNNOOOSSSVVVXXXXXXUUUSSSRRRQQQQQQRRRSSSTTTRRRRRRRRRSSSTTTVVVWWWXXXYYYYYYYYYYYYXXXXXXXXXXXXUUUVVVVVVWWWWWWXXXXXXXXXVVVWWWYYYYYYYYYYYYWWWVVVYYYYYYXXXXXXXXXWWWWWWWWWZZZYYYYYYXXXXXXXXXXXXXXX\\\\\\\\\[[[YYYXXXYYYZZZ^^^^^^^^^]]][[[ZZZXXXWWWTTTXXX]]]^^^[[[WWWVVVVVVVVVVVVVVVVVVUUUUUUTTTSSSPPPPPPPPPPPPQQQSSSTTTUUURRRRRRRRRRRRRRRSSSTTTTTTUUUVVVWWWXXXXXXWWWVVVUUUOOOQQQSSSSSSSSSRRRSSSTTTQQQQQQQQQRRRQQQQQQPPPOOOQQQQQQPPPOOOPPPQQQRRRSSSOOOOOOOOOOOOOOOPPPQQQRRRQQQQQQQQQPPPOOOOOOQQQTTTUUUUUUTTTSSSRRRQQQPPPPPPMMMOOOQQQQQQPPPOOONNNNNNNNNOOOPPPQQQRRRRRRRRRRRRQQQQQQQQQPPPNNNMMMKKKJJJJJJJJJLLLMMMMMMLLLKKKJJJLLLLLLKKKLLLLLLKKKIIIFFFJJJJJJIIIIIIJJJKKKMMMNNNKKKJJJIIIHHHGGGHHHIIIJJJEEEGGGHHHHHHHHHHHHIIIKKKGGGHHHHHHIIIIIIHHHHHHGGGGGGIIIJJJJJJIIIJJJNNNQQQMMMKKKIIIGGGGGGHHHKKKLLLIIIIIIIIIIIIIIIJJJKKKLLLIIIHHHGGGGGGFFFFFFGGGGGGFFFFFFGGGGGGGGGGGGFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEEEEEEFFFGGGGGGGGGGGGFFFGGGHHHHHHGGGFFFEEEGGGHHHCCCDDDDDDEEEFFFGGGGGGGGGDDDDDDCCCBBBBBBBBBCCCCCC@@@AAACCCDDDDDDCCCAAA@@@???@@@BBBDDDEEEEEEDDDCCC@@@BBBDDDCCC@@@@@@BBBDDDCCCDDDEEEDDDCCCBBBCCCEEECCCCCCCCCCCCBBBAAA@@@@@@>>>@@@AAA@@@???>>>???@@@AAAAAA@@@@@@@@@@@@AAAAAA===============>>>??????>>>===<<<===>>>???>>>===???>>>=========>>>@@@AAA===============>>>>>>>>>========================999999888888999999:::;;;888999;;;======<<<;;;:::::::::999999888999999999:::;;;===>>>???>>>===;;;999:::;;;;;;<<<<<<;;;;;;>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>============>>>>>>:::<<<<<<<<<:::999:::;;;777777777888999999::::::666666666666777888999:::888777777666555444444444333444555666777777777777666666666777888888999999555666666777888999999999555666777999:::;;;<<<<<<777777777888999999::::::777777777777666666666666333444666777777777666555222222333444444333222222222222222333333444444444333444666888888888888777444555666555333333555666666666555555555555666666555666666777888999999999666555444444666666555444222555777777444333444666333333333333333333333333333222111111000000111111222222222333333222222222///000111222333333222111222222222222222222222222111111111111111111111111222222222222222222222222//////.........------------,,,******++++++)))(((%%%%%%%%%&&&&&&''''''''''''(((((())))))))))))))))))******+++,,,,,,------PPPQQQSSSUUUVVVUUUTTTSSSQQQRRRSSSTTTTTTTTTTTTTTTRRRSSSUUUWWWXXXWWWUUUTTTXXXXXXYYYYYYYYYXXXVVVUUUWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWVVVVVVYYYYYYYYYYYYXXXVVVUUUTTT[[[[[[\\\\\\[[[ZZZYYYYYYWWWXXXZZZ[[[ZZZYYYZZZ[[[ZZZ[[[\\\]]]]]]\\\[[[ZZZYYYYYYYYYYYYZZZZZZZZZZZZXXXXXXWWWUUUSSSRRRTTTUUUTTTTTTTTTTTTUUUVVVWWWWWWZZZYYYWWWUUUTTTSSSRRRRRRRRRRRRSSSTTTUUUVVVVVVWWWRRRPPPMMMNNNPPPRRRPPPOOOQQQPPPPPPOOOOOOOOOPPPPPPPPPPPPQQQQQQQQQQQQQQQQQQNNNOOOQQQQQQQQQQQQRRRTTTTTTTTTSSSSSSRRRRRRQQQQQQWWWWWWVVVSSSQQQPPPQQQSSSPPPOOOOOOPPPQQQQQQPPPNNNRRRRRRRRRQQQOOONNNPPPQQQOOOOOONNNNNNMMMLLLLLLKKKMMMJJJHHHIIIKKKMMMLLLJJJNNNMMMKKKKKKLLLKKKJJJHHHGGGGGGGGGHHHJJJLLLMMMNNNLLLJJJIIIJJJLLLKKKHHHDDDFFFFFFFFFFFFFFFFFFFFFFFFIIIIIIHHHGGGHHHIIIJJJKKKIIIIIIIIIIIIIIIIIIIIIIIIJJJKKKKKKHHHFFFFFFKKKOOOMMMLLLLLLKKKKKKKKKLLLLLLHHHHHHIIIIIIHHHHHHGGGGGGEEEFFFGGGGGGGGGHHHKKKMMMEEEEEEEEEEEEEEEDDDCCCCCCFFFEEEDDDDDDDDDEEEGGGHHHFFFFFFGGGGGGGGGGGGFFFFFFGGGGGGFFFEEEEEEFFFGGGHHHEEEBBB??????BBBDDDCCCAAAAAAAAABBBBBBBBBBBBBBBBBBDDDEEEEEEDDDBBBBBBCCCEEEDDDAAA???@@@CCCDDDCCCBBBBBBBBBBBBCCCCCCEEEFFFFFFFFFEEEDDDCCCBBBAAA@@@???AAA@@@???>>>>>>???@@@AAA@@@@@@???>>>>>>???@@@AAA>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>======<<<<<<<<<;;;<<<===>>>@@@AAAAAAAAAAAA>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>===<<<;;;;;;::::::999999999::::::;;;;;;;;;888888999999999:::::::::999999888888888888888999<<<===>>>??????@@@@@@???<<<<<<<<<<<<<<<<<<;;;;;;???>>>===<<<<<<<<<<<<<<<<<<<<<======<<<<<<;;;:::888888888999:::;;;<<<===;;;:::999999888888888888999999888888888888999999999999777666555555555555666666666666777777777777777888999::::::999888777888888999999999:::::::::;;;;;;:::999999999:::::::::::::::;;;;;;<<<<<<<<<888888888888777666555444555555555555555555555555444444222222222222444444111222222333444555666666333444444555555444444333444444555555666777777777666666666666666555555555444444555555666888999:::555555444444444555555666444444444444444444444444333444444555555444444333333444444222111111333555111222333333333333222111111111000000000000000111444333222222111111222222333222111000000000111222444444444444333222111111//////000000000000//////...---+++***))))))(((((('''&&&&&&%%%%%%%%%&&&&&&(((((((((((())))))))))))******+++++++++,,,,,,,,,PPPQQQSSSUUUUUUUUUTTTSSSSSSSSSTTTTTTTTTTTTSSSSSSPPPPPPRRRSSSSSSSSSRRRRRRYYYYYYZZZZZZZZZYYYWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWVVVVVVVVVVVVVVVVVVVVVVVVXXXXXXYYYYYYYYYXXXXXXWWW[[[[[[[[[[[[[[[ZZZYYYYYYUUUWWWYYYYYYXXXXXXXXXZZZZZZ[[[\\\\\\\\\[[[ZZZYYYYYYYYYYYYYYYYYYYYYYYYYYYXXXWWWUUUTTTTTTTTTTTTUUUTTTTTTTTTTTTUUUUUUVVVWWWXXXWWWUUUTTTRRRQQQQQQPPPRRRRRRSSSTTTTTTUUUVVVVVVSSSPPPNNNOOOQQQRRRQQQOOORRRQQQQQQQQQQQQQQQRRRSSSQQQQQQQQQQQQQQQQQQQQQQQQNNNPPPQQQQQQPPPPPPRRRTTTSSSSSSSSSSSSRRRRRRRRRRRRVVVVVVVVVSSSQQQPPPQQQSSSPPPOOOOOOPPPQQQQQQPPPNNNQQQRRRRRRRRRPPPOOOOOOQQQOOOOOOOOONNNMMMLLLLLLLLLLLLJJJHHHIIILLLMMMMMMKKKMMMLLLJJJKKKLLLLLLKKKIIIIIIIIIIIIIIIJJJJJJKKKLLLMMMKKKIIIJJJKKKKKKHHHFFFGGGGGGGGGGGGGGGGGGGGGGGGIIIIIIHHHHHHHHHIIIJJJKKKIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIHHHHHHIIIKKKNNNLLLKKKKKKJJJJJJKKKKKKKKKJJJJJJJJJJJJIIIHHHGGGFFFDDDFFFGGGGGGEEEEEEEEEFFFEEEEEEEEEEEEEEEDDDCCCCCCEEEEEEEEEEEEEEEFFFGGGGGGFFFFFFFFFGGGGGGFFFFFFFFFHHHGGGFFFEEEEEEFFFFFFGGGEEEBBB@@@@@@BBBCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBCCCDDDCCCBBBAAAAAACCCDDDBBB@@@AAACCCEEEDDDCCCBBBBBBBBBBBBCCCDDDEEEFFFFFFEEEEEEDDDBBBAAA@@@@@@@@@@@@???>>>>>>???@@@@@@AAA@@@???>>>>>>??????@@@>>>>>>>>>>>>>>>>>>>>>>>>=========<<<<<<<<<;;;;;;:::;;;<<<===>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>===<<<<<<;;;::::::999999999999999::::::;;;;;;;;;888888999999999:::::::::999999888888888888999999;;;;;;<<<===>>>>>>>>>>>><<<<<<<<<<<<<<<<<<<<<<<<>>>======<<<<<<<<<<<<===<<<<<<======<<<<<<;;;:::999999999999:::;;;<<<===;;;;;;:::999999999999999999999888888888888999999:::999888777777666666666666666666777777777888888888888999::::::999888888888888999999999::::::::::::::::::;;;;;;;;;;;;;;;:::::::::;;;;;;;;;;;;;;;777777888777666555444444333333333333333333333333444444333222222333444444222333333333333333333333333444444555555444444333333444444555666666777777666666666666666666666555555555555555777888999:::555555444444444555555666444444444444444444444444333444444555555444444333333444444333111111333555111222333333333333222111333222222111111222222222444333222222111111222222333222111000111111222333444444444444333222111000//////000000000000//////...---+++***))))))(((((('''&&&&&&%%%%%%&&&&&&'''''''''((((((((()))))))))*********+++++++++,,,,,,PPPQQQSSSTTTUUUUUUTTTSSSTTTTTTTTTUUUTTTTTTSSSRRRTTTTTTTTTTTTUUUUUUUUUUUUYYYZZZ[[[[[[[[[ZZZYYYXXXWWWWWWWWWWWWWWWWWWWWWWWWTTTTTTUUUUUUVVVVVVWWWWWWWWWXXXYYYYYYZZZZZZZZZYYYZZZZZZZZZZZZYYYYYYYYYYYYWWWXXXZZZZZZYYYXXXYYYZZZZZZZZZ[[[\\\[[[ZZZXXXWWWYYYYYYXXXXXXXXXXXXXXXXXXXXXUUUSSSTTTVVVWWWUUUSSSSSSSSSSSSSSSTTTUUUVVVWWWXXXWWWUUUTTTRRRRRRQQQQQQRRRRRRSSSSSSTTTTTTUUUUUUSSSQQQPPPQQQRRRSSSRRRQQQRRRRRRRRRRRRSSSTTTTTTUUUQQQQQQQQQQQQQQQQQQQQQQQQPPPPPPQQQPPPOOOPPPRRRUUURRRRRRRRRRRRSSSSSSSSSSSSUUUVVVUUUSSSQQQPPPQQQRRRPPPOOOOOOPPPQQQQQQPPPNNNOOOQQQRRRRRRQQQOOOOOOOOOPPPOOOOOONNNNNNMMMMMMLLLLLLJJJIIIJJJMMMOOOOOONNNMMMLLLKKKKKKLLLMMMLLLJJJKKKKKKJJJJJJIIIJJJJJJJJJMMMKKKIIIIIIJJJJJJIIIHHHHHHHHHHHHHHHHHHHHHHHHHHHIIIHHHHHHHHHHHHIIIJJJKKKIIIIIIIIIIIIIIIIIIIIIIIIHHHGGGGGGHHHJJJLLLKKKKKKJJJJJJIIIIIIIIIJJJJJJKKKKKKKKKKKKKKKJJJIIIHHHGGGEEEGGGHHHGGGEEECCCBBBBBBEEEEEEFFFFFFEEEEEEDDDDDDDDDEEEFFFFFFGGGGGGFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFHHHHHHGGGFFFEEEEEEFFFFFFEEECCC@@@@@@BBBCCCCCCCCCDDDCCCCCCCCCBBBAAAAAAAAA@@@BBBDDDCCCBBB@@@@@@@@@DDDBBBAAAAAACCCDDDDDDCCCBBBBBBBBBBBBCCCDDDEEEEEEEEEEEEEEEDDDCCCBBBAAAAAA@@@??????>>>>>>??????@@@AAAAAA@@@???>>>>>>??????>>>>>>>>>>>>>>>>>>>>>>>>============<<<<<<<<<<<<:::;;;<<<======>>>======>>>>>>>>>>>>>>>>>>>>>>>><<<<<<;;;;;;:::999999999999999::::::::::::;;;;;;888888999999999:::::::::999999888888888888999999::::::;;;<<<============<<<<<<<<<<<<<<<<<<<<<<<<==================>>>>>><<<<<<======<<<<<<;;;:::::::::::::::;;;<<<<<<===<<<;;;;;;:::::::::::::::999999888888888888999999;;;:::999888777777777888666777777777777888888888888999999::::::999999888888888999999999:::::::::999:::;;;=========<<<<<<;;;;;;;;;;;;::::::::::::666777777777666555444333444444444444444444333333444444333333333333444444333333333333222222111111444444555555555555444444333333333444555555666666555555666666666666666666555555555666777888999:::666555555444444444555555444444444444444444444444333444444555555444444333333444444333222111333555111222222333333222222111444444333333333333444444444333222222111111222222222222111111222333444555333333333333333222000000//////000000000000//////...---+++***))))))(((((('''&&&&&&&&&&&&&&&''''''''''''''''''((((((((((((*********++++++++++++,,,PPPQQQRRRSSSTTTTTTTTTSSSSSSSSSTTTUUUUUUUUUTTTTTTXXXWWWVVVVVVVVVWWWXXXXXXXXXYYYZZZ[[[ZZZZZZXXXXXXWWWWWWWWWWWWWWWWWWWWWWWWTTTTTTUUUVVVWWWWWWXXXXXXYYYYYYZZZZZZZZZZZZZZZYYYXXXXXXWWWWWWWWWWWWWWWXXXZZZ[[[]]]]]][[[[[[[[[\\\ZZZZZZ[[[[[[ZZZYYYWWWVVVXXXXXXXXXXXXWWWWWWWWWWWWWWWTTTQQQTTTXXXYYYVVVRRRRRRRRRRRRSSSTTTUUUVVVWWWYYYXXXWWWUUUUUUTTTTTTTTTRRRRRRSSSSSSSSSSSSSSSSSSRRRRRRRRRSSSSSSSSSRRRRRRRRRRRRRRRRRRSSSTTTUUUUUUQQQQQQQQQQQQQQQPPPPPPPPPPPPQQQQQQOOOOOOOOORRRUUUSSSSSSSSSSSSRRRRRRRRRRRRTTTUUUUUUSSSQQQPPPQQQRRRPPPOOOOOOPPPQQQQQQPPPNNNMMMPPPRRRSSSQQQPPPOOOOOOPPPPPPOOOOOONNNNNNNNNNNNKKKKKKKKKLLLMMMOOOPPPQQQPPPOOOMMMMMMNNNMMMLLLJJJKKKKKKJJJJJJJJJJJJKKKKKKMMMKKKIIIHHHHHHIIIJJJJJJJJJJJJJJJJJJIIIIIIIIIIIIHHHHHHHHHHHHIIIIIIJJJJJJIIIIIIIIIIIIIIIIIIIIIIIIGGGFFFFFFHHHLLLMMMKKKHHHIIIIIIHHHHHHHHHIIIJJJJJJJJJKKKKKKKKKKKKJJJJJJIIIIIIIIIHHHGGGDDDCCCDDDFFFEEEEEEFFFFFFFFFEEEEEEDDDDDDEEEFFFGGGHHHGGGFFFEEEGGGFFFFFFFFFFFFFFFFFFGGGHHHHHHGGGFFFFFFEEEEEEEEEDDDCCCBBBAAABBBBBBCCCDDDEEEDDDDDDCCCBBBAAAAAA@@@???BBBDDDDDDCCCAAA@@@???BBBBBBAAAAAABBBCCCCCCCCCBBBBBBBBBBBBBBBCCCDDDEEEEEEDDDDDDCCCCCCBBBBBBBBB??????>>>>>>>>>>>>??????AAAAAA@@@??????>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>======>>>>>>?????????>>>>>>>>>>>>>>>>>>>>>>>>>>>>>><<<<<<<<<;;;;;;:::::::::::::::::::::::::::::::::888888999999999:::::::::999999888888888999::::::::::::;;;<<<============<<<<<<<<<<<<============<<<<<<======>>>>>>>>>>>><<<<<<<<<===<<<<<<;;;:::;;;:::::::::;;;<<<<<<===<<<;;;;;;::::::;;;;;;;;;999999888888888888999999:::999888888777777777888777777777888888888999999888888888888888888888888888888999999999:::::::::888:::<<<>>>??????>>>===<<<;;;;;;::::::999999999666666666666666555444444777777777666666666666666444444444333333444444444333333333333333333333333444444555555555555444444222222333333444555555555555555555555666666666666666666666666777888999:::666666555444444444444555444444444444444444444444333444444555555444444333222333444333222222333444222222222222222222222222444333333333333444444555444333222222111111222222111111222222333444555666333333333333222111000/////////000000000000//////------+++***)))((((((((('''&&&&&&&&&&&&''''''(((&&&'''''''''((((((((((((************++++++++++++PPPQQQQQQRRRSSSSSSTTTTTTRRRRRRSSSUUUVVVVVVVVVVVVVVVVVVUUUTTTTTTUUUUUUVVVVVVWWWXXXYYYYYYYYYXXXWWWWWWWWWWWWWWWWWWWWWWWWWWWUUUVVVVVVWWWXXXYYYZZZZZZ[[[[[[[[[[[[ZZZYYYXXXWWWWWWVVVUUUUUUUUUVVVVVVWWWZZZ\\\]]]]]][[[ZZZ[[[\\\YYYZZZ[[[[[[ZZZYYYXXXWWWWWWWWWWWWWWWVVVVVVUUUUUUVVVSSSRRRUUUYYYZZZUUUQQQQQQQQQQQQRRRSSSTTTVVVWWWWWWVVVUUUUUUTTTTTTTTTTTTSSSSSSRRRRRRRRRRRRRRRRRRQQQRRRTTTTTTSSSSSSRRRRRRRRRQQQQQQQQQRRRRRRSSSTTTRRRRRRQQQQQQQQQPPPPPPPPPPPPQQQQQQPPPOOOOOORRRTTTUUUTTTTTTSSSRRRQQQQQQPPPSSSTTTTTTTTTRRRPPPQQQRRRPPPOOOOOOPPPQQQQQQPPPNNNLLLOOORRRRRRQQQOOOOOOOOOPPPPPPPPPOOOOOOOOOOOOOOOKKKKKKLLLLLLMMMOOOPPPRRRTTTRRRPPPOOOOOONNNLLLJJJJJJJJJJJJJJJJJJKKKMMMMMMKKKKKKJJJIIIHHHHHHJJJKKKKKKKKKKKKJJJJJJJJJIIIIIIHHHHHHHHHIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIGGGFFFFFFIIILLLMMMJJJGGGHHHHHHHHHHHHHHHIIIJJJJJJIIIIIIJJJKKKLLLLLLLLLLLLIIIHHHFFFDDDBBBCCCGGGJJJEEEEEEFFFFFFFFFFFFEEEEEEDDDEEEGGGHHHHHHHHHGGGFFFGGGGGGFFFEEEEEEFFFGGGGGGGGGGGGGGGGGGFFFFFFEEEEEEDDDDDDCCCBBBAAABBBCCCEEEEEEEEEDDDCCCBBBBBBAAAAAA@@@BBBEEEEEEDDDAAA@@@@@@AAAAAAAAAAAAAAAAAABBBCCCCCCBBBBBBBBBBBBCCCCCCDDDCCCCCCCCCCCCBBBBBBBBBBBB>>>>>>>>>>>>>>>>>>>>>>>>@@@@@@@@@@@@??????>>>>>>????????????????????????????????????????????????>>>???????????????>>>===>>>>>>>>>>>>>>>>>>>>>>>>============<<<<<<<<<<<<::::::::::::::::::::::::888888999999999:::::::::999999888888999::::::;;;;;;;;;<<<===>>>>>>>>>>>><<<<<<<<<=========>>>>>>;;;<<<===>>>??????>>>>>><<<<<<<<<===<<<<<<;;;:::;;;;;;:::::::::;;;<<<<<<;;;;;;;;;::::::;;;;;;<<<999999888888888888999999888888777666666666777777888888888888999999999999777777777666666777777777888888999999999:::::::::999:::===?????????>>>===;;;;;;;;;::::::999999888666666666666666666555444888888888777777666666666444444444444444444444444333333444444555666666777444555555666666555555444222222333333444555555555444555555555666666777777777777666777777888999:::666666555444444444444444444444444444444444444444333444444555555444444333222333444444333222333444222222222222222222222222222222222222222333444444444333222222111111222222111111222333444444555555222222222222111000////////////000000000000//////------+++***)))(((((((((&&&&&&&&&&&&&&&'''((()))'''''''''(((((((((((()))))))))*********+++++++++PPPQQQQQQRRRRRRSSSTTTTTTRRRSSSTTTUUUVVVVVVVVVVVVWWWWWWWWWWWWWWWVVVVVVVVVVVVVVVXXXYYYYYYYYYXXXWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWXXXXXXYYYYYYZZZZZZ[[[[[[[[[ZZZYYYXXXVVVVVVWWWVVVUUUUUUUUUVVVWWWXXXXXXYYY[[[ZZZYYYXXXXXXYYYYYYYYYZZZ[[[[[[[[[ZZZYYYWWWWWWVVVVVVUUUUUUTTTTTTTTTTTTTTTWWWYYYXXXTTTPPPPPPPPPPPPQQQRRRTTTUUUVVVSSSRRRRRRQQQQQQQQQRRRRRRSSSSSSRRRRRRQQQQQQPPPPPPPPPRRRTTTUUUSSSRRRRRRRRRRRRQQQQQQPPPPPPQQQQQQRRRRRRRRRRRRQQQPPPPPPOOOOOOOOOQQQRRRRRRPPPPPPQQQRRRTTTTTTTTTSSSRRRRRRQQQQQQQQQSSSTTTTTTRRRQQQQQQQQQPPPOOOOOOPPPQQQQQQPPPNNNLLLOOOQQQQQQPPPOOOOOOPPPPPPPPPPPPPPPPPPPPPPPPPPPKKKLLLMMMMMMLLLMMMOOOQQQUUUSSSQQQPPPPPPOOOLLLJJJJJJJJJJJJJJJKKKLLLMMMNNNJJJJJJKKKJJJHHHHHHJJJKKKLLLLLLKKKKKKJJJIIIIIIIIIGGGHHHIIIIIIJJJJJJIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIGGGGGGHHHIIIKKKJJJIIIGGGHHHHHHHHHHHHIIIIIIJJJKKKHHHIIIJJJKKKLLLLLLLLLLLLFFFEEEDDDBBBAAACCCGGGKKKEEEEEEFFFFFFGGGGGGFFFFFFEEEFFFGGGGGGHHHGGGGGGGGGHHHGGGFFFEEEEEEFFFGGGHHHEEEFFFGGGGGGGGGGGGFFFFFFDDDDDDDDDCCCAAAAAADDDFFFEEEDDDDDDDDDCCCBBBBBBBBBAAACCCEEEEEECCCAAAAAAAAAAAABBBBBBBBBAAAAAACCCDDDCCCBBBBBBBBBBBBBBBCCCCCCAAAAAAAAAAAAAAABBBBBBBBB===>>>>>>??????>>>>>>===>>>???@@@@@@@@@@@@??????????????????????????????????????????@@@@@@@@@@@@>>>>>>???>>>>>>===<<<;;;>>>>>>>>>>>>>>>>>>>>>>>>========================;;;;;;::::::::::::999999888888999999999:::::::::999999888999999:::;;;<<<;;;;;;<<<===>>>>>>>>>>>><<<<<<<<<======>>>>>>???<<<===>>>???@@@???>>>===<<<<<<======<<<<<<;;;::::::::::::999999::::::;;;:::::::::::::::;;;;;;<<<999999888888888888999999777777666666666666666777888888999999999:::::::::888777666666666666777888888888999999999::::::::::::;;;<<<>>>>>>>>>======::::::::::::999999999999666666777777777777666666777777666666555555444444444444555555555555444444333333444555666777888888555555666666666666555555333333333444555555666666444444555555666777777777777777777777777888999:::777666555444444444444444444444444444444444444444333444444555555444444333111333555444333222222333333222222111111222222333111000000111111222333444444333222222111111222222000111222333444444333333111111222111111000///...//////000000000000//////...---+++***))))))((((((&&&&&&&&&&&&'''((())))))(((((((((((()))))))))))))))))))))************+++QQQPPPQQQQQQRRRSSSSSSTTTVVVVVVVVVVVVUUUUUUTTTSSSWWWXXXYYYYYYYYYXXXVVVUUUVVVWWWXXXZZZZZZZZZYYYXXXWWWWWWWWWWWWWWWWWWWWWWWWXXXXXXXXXXXXXXXXXXXXXXXXYYYYYYYYYYYYYYYXXXWWWVVVYYYXXXWWWVVVWWWXXXZZZ[[[WWWYYYZZZZZZXXXWWWWWWWWWXXXYYYZZZ\\\\\\\\\\\\[[[WWWVVVVVVUUUTTTTTTSSSSSSSSSUUUWWWYYYYYYVVVRRRPPPOOOOOOPPPQQQRRRTTTUUUVVVQQQQQQPPPPPPPPPPPPQQQQQQSSSSSSRRRQQQQQQPPPOOOOOOOOORRRUUUUUUSSSQQQQQQRRRSSSSSSRRRQQQPPPPPPPPPPPPSSSRRRRRRQQQPPPPPPOOOOOONNNPPPSSSSSSRRRPPPPPPPPPQQQQQQRRRRRRSSSSSSTTTTTTPPPRRRTTTTTTRRRQQQPPPQQQPPPOOOOOOPPPQQQQQQPPPNNNMMMOOOPPPPPPOOOOOOPPPQQQPPPPPPPPPPPPPPPQQQQQQQQQKKKLLLNNNMMMKKKKKKNNNPPPQQQPPPNNNNNNOOOOOOMMMLLLLLLKKKKKKKKKKKKKKKLLLLLLGGGJJJLLLKKKIIIHHHIIIKKKLLLLLLKKKJJJJJJIIIHHHHHHGGGHHHIIIJJJJJJJJJIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIGGGIIIJJJIIIHHHGGGGGGHHHHHHHHHHHHHHHIIIJJJKKKLLLJJJKKKKKKKKKKKKJJJIIIHHHDDDEEEFFFFFFEEEEEEFFFHHHDDDEEEFFFGGGGGGGGGGGGFFFGGGFFFFFFFFFGGGGGGHHHHHHHHHGGGFFFDDDDDDFFFGGGHHHDDDDDDFFFGGGHHHHHHGGGGGGCCCDDDEEECCCAAAAAADDDFFFDDDDDDDDDDDDCCCCCCCCCCCCAAABBBCCCBBBAAA@@@@@@AAABBBDDDEEEDDDBBBBBBDDDGGGCCCBBBBBBAAAAAABBBBBBCCC?????????@@@@@@AAAAAAAAA<<<===>>>??????>>>===<<<======???@@@AAAAAA@@@@@@????????????????????????=========>>>>>>?????????@@@@@@@@@@@@???>>>===<<<>>>>>>>>>>>>>>>>>>>>>>>>========================;;;;;;;;;::::::999999999888888999999999:::::::::999999999999:::;;;<<<<<<::::::;;;<<<============;;;<<<<<<===>>>>>>??????===>>>???@@@@@@???===<<<<<<<<<======<<<<<<;;;::::::999999888888999999999999999999999999:::;;;;;;999999888888888888999999888777777666777777888888999999999::::::::::::;;;:::999888777777888999:::888888999999999:::::::::<<<<<<<<<<<<<<<<<<<<<<<<999999999999999:::::::::777777888888888888888777888888777666666555444444333444555666666555444333444444444555555666666666555555666666666666555555333444444555666666777777444444555555666777777888888888777777888888999999777777666444444333333444444444444444444444444444333444444555555444444333111333555555333222222333333333222111111222333333000000000000111222333444444333222222111111222222000111222333333222222111111111111111000///...---//////000000000000//////...---+++***))))))((((((&&&&&&&&&&&&'''((()))***))))))))))))*********+++))))))))))))************QQQPPPPPPQQQQQQRRRSSSTTTYYYXXXXXXWWWUUUSSSQQQPPPRRRSSSUUUUUUUUUSSSQQQPPPWWWXXXYYY[[[[[[[[[ZZZYYYWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWVVVVVVVVVWWWXXXXXXXXXXXXXXXXXX[[[ZZZYYYXXXYYYZZZ\\\^^^YYY[[[\\\[[[YYYXXXXXXYYYXXXYYYZZZ\\\]]]]]]]]]]]]VVVVVVUUUUUUTTTSSSSSSRRRRRRVVVYYYZZZXXXTTTQQQPPPOOOOOOOOOPPPRRRTTTUUUVVVRRRQQQQQQQQQQQQRRRSSSSSSSSSSSSRRRQQQPPPOOOOOONNNNNNQQQUUUUUURRRPPPPPPQQQUUUTTTSSSQQQPPPPPPPPPPPPSSSSSSRRRQQQPPPPPPOOOOOOMMMPPPSSSTTTSSSQQQOOOOOONNNOOOPPPRRRSSSUUUVVVWWWPPPRRRTTTTTTRRRQQQPPPQQQPPPOOOOOOPPPQQQQQQPPPNNNNNNOOOOOOOOONNNNNNPPPRRRPPPPPPQQQQQQQQQQQQQQQQQQKKKMMMNNNMMMJJJJJJLLLOOOMMMLLLKKKLLLNNNOOONNNMMMNNNMMMLLLKKKJJJJJJJJJJJJFFFIIILLLLLLJJJHHHIIIJJJLLLKKKKKKJJJIIIHHHHHHHHHGGGHHHIIIJJJJJJJJJIIIHHHIIIIIIIIIIIIIIIIIIIIIIIIHHHJJJKKKJJJFFFEEEFFFIIIHHHHHHHHHIIIJJJKKKLLLMMMMMMMMMLLLKKKJJJHHHFFFEEEEEEHHHKKKLLLJJJHHHGGGFFFDDDEEEFFFGGGGGGGGGGGGGGGHHHGGGFFFEEEFFFGGGHHHIIIHHHGGGEEEDDDDDDEEEGGGHHHBBBDDDEEEGGGHHHHHHHHHGGGCCCEEEEEEDDDAAAAAADDDGGGCCCCCCCCCDDDDDDDDDDDDDDDAAAAAABBB@@@>>>>>>@@@AAACCCEEEGGGFFFDDDDDDFFFIIICCCBBBBBBAAAAAAAAABBBBBB>>>>>>>>>??????@@@@@@AAA<<<===>>>??????>>>===<<<;;;===>>>@@@AAAAAAAAA@@@????????????????????????;;;<<<<<<<<<======>>>>>>CCCCCCCCCBBBAAA@@@???>>>>>>>>>>>>>>>>>>>>>>>>>>>;;;;;;<<<<<<<<<<<<<<<<<<;;;;;;;;;::::::999999999888888999999999:::::::::999999999999:::;;;<<<===999999:::;;;<<<<<<<<<<<<;;;<<<<<<===>>>??????@@@>>>???@@@AAA@@@>>><<<;;;<<<<<<======<<<<<<;;;:::999999888888777888888888888888888888999999:::;;;999999888888888888999999999888888888888888999999999999:::::::::;;;;;;;;;<<<;;;:::999999:::;;;<<<888888999999999:::::::::===<<<<<<;;;;;;;;;<<<<<<888888888999999::::::;;;777888888999999999888888:::::::::999888777777666333444555666666555444333555555444444444333333333555555666666666666555555444444555555666777777777444444444555666777777888888888888888888888999999888777666555444333333333444444444444444444444444333444444555555444444333111333555555444222222333444333222111111222333444111111111111222333444555444333222222111111222222000111222333222111000///111111111111000///...---//////000000000000//////...---+++***))))))((((((&&&&&&&&&'''''')))******)))*********++++++++++++))))))))))))************UUUVVVUUURRRPPPQQQVVVZZZVVVUUUTTTTTTSSSSSSSSSTTTWWWVVVUUUTTTUUUWWWYYY[[[]]]YYYWWWWWWYYY[[[[[[YYYYYYYYYYYYYYYYYYYYYXXXXXXXXXWWWVVVUUUUUUUUUUUUUUUXXXYYYYYYYYYYYYYYYXXXXXXZZZ[[[[[[ZZZXXXXXXYYY[[[\\\ZZZYYYWWWVVVWWWXXXYYYXXXYYY[[[\\\\\\[[[ZZZYYY[[[XXXTTTSSSTTTUUUSSSRRRTTTTTTUUUVVVUUUSSSQQQOOORRRQQQQQQPPPPPPPPPQQQQQQQQQPPPOOONNNNNNOOOPPPQQQTTTSSSPPPNNNNNNOOOQQQRRRUUUTTTSSSRRRQQQQQQRRRRRRUUUUUUTTTTTTSSSSSSRRRRRRPPPPPPPPPOOOOOONNNNNNNNNMMMOOORRRTTTTTTRRRPPPNNNOOOOOOOOOOOOPPPRRRTTTUUUSSSRRRQQQRRRTTTTTTPPPMMMRRRQQQPPPQQQRRRQQQOOONNNMMMNNNNNNOOOPPPQQQRRRRRRUUUSSSPPPNNNMMMOOOQQQSSSLLLKKKKKKKKKLLLMMMNNNNNNLLLLLLLLLLLLMMMMMMMMMMMMMMMLLLJJJHHHIIIKKKMMMOOOLLLMMMNNNNNNMMMLLLKKKJJJGGGGGGHHHHHHHHHHHHHHHHHHGGGGGGFFFFFFGGGGGGHHHIIIKKKHHHEEEEEEHHHKKKLLLKKKIIIIIIHHHGGGFFFFFFFFFFFFKKKKKKKKKKKKKKKKKKJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJLLLKKKJJJIIIHHHGGGHHHHHHJJJHHHGGGFFFFFFGGGIIIKKKKKKHHHFFFFFFHHHJJJHHHFFFGGGFFFEEEDDDDDDEEEFFFGGGIIIGGGEEEDDDCCCDDDEEEFFFDDDCCCCCCCCCCCCDDDDDDEEEAAAAAA@@@BBBCCCDDDCCCAAA@@@AAABBBBBBBBBAAA@@@???AAABBBCCCDDDDDDCCCBBBAAAAAAAAAAAABBBBBBBBBCCCCCCBBBAAA@@@@@@??????@@@@@@@@@@@@@@@>>><<<<<<>>>@@@>>>>>>>>>>>>>>>===<<<<<<======>>>>>>>>>>>>======?????????>>>>>>>>>>>>>>>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@????????????>>>>>>>>>>>>>>>============888999999::::::;;;;;;<<<;;;;;;;;;999777666777999;;;::::::999999888888888;;;;;;;;;<<<<<<<<<======<<<<<<===??????@@@@@@@@@<<<<<<<<<<<<<<<;;;;;;;;;>>><<<::::::;;;;;;:::999<<<<<<;;;:::999999999999<<<;;;::::::999999999999999999999999999999999999666777888999:::;;;;;;;;;<<<;;;;;;:::999999999:::777888999999888777888:::::::::999888777777888888;;;<<<===>>>>>>===<<<;;;999999999999999999999999888888999::::::::::::999999999999888888888888888444444444444444444444444666555444333333444555666777777777777777666555555555555555555555444444444444555555666777888888999777777777777888888888888999888777666555444333333333444555666666555444333555555555555444333222111222333333333333222111111333222111000000000222222222222111111000111111111555444333333222222222222222222222111111111000000333222000///.........///222111000///------,,,,,,************))))))(((((('''&&&&&&''''''((()))*********+++,,,,,,,,,,,,+++************+++,,,,,,---SSSTTTSSSQQQOOOQQQUUUYYYYYYXXXWWWWWWVVVVVVVVVWWWUUUUUUTTTTTTUUUVVVXXXYYY]]]ZZZWWWWWWYYYZZZZZZYYYVVVVVVWWWXXXXXXYYYZZZZZZYYYXXXWWWVVVVVVVVVVVVWWWXXXXXXYYYYYYYYYYYYXXXXXXXXXYYYZZZYYYXXXXXXYYY[[[\\\ZZZYYYWWWWWWWWWYYYZZZYYYZZZ[[[\\\\\\[[[YYYXXXZZZWWWTTTSSSUUUUUUTTTSSSTTTUUUVVVWWWVVVUUUSSSQQQRRRQQQQQQQQQRRRRRRSSSTTTTTTSSSRRRQQQQQQQQQRRRSSSRRRRRRQQQQQQQQQPPPPPPPPPTTTTTTSSSSSSSSSRRRRRRRRRTTTTTTTTTTTTTTTSSSSSSSSSRRRRRRQQQQQQPPPPPPPPPPPPPPPRRRTTTUUUUUUSSSQQQPPPPPPOOOOOOOOOPPPRRRTTTUUUTTTSSSRRRTTTUUUUUUSSSPPPRRRQQQQQQRRRSSSSSSQQQOOOPPPPPPPPPQQQQQQRRRRRRSSSTTTRRROOOMMMMMMNNNQQQRRROOONNNMMMMMMLLLLLLLLLLLLKKKKKKKKKLLLLLLMMMMMMMMMMMMLLLJJJJJJJJJKKKMMMNNNLLLLLLMMMMMMMMMLLLKKKJJJJJJJJJJJJIIIIIIIIIIIIIIIHHHGGGGGGGGGGGGHHHIIIIIIKKKHHHEEEFFFHHHKKKKKKKKKJJJJJJIIIHHHHHHHHHHHHIIIJJJJJJJJJJJJJJJJJJJJJJJJIIIIIIIIIIIIIIIIIIIIIIIIKKKJJJIIIHHHHHHGGGGGGGGGHHHHHHGGGFFFGGGHHHIIIJJJJJJHHHFFFFFFHHHJJJIIIGGGGGGGGGFFFEEEEEEFFFHHHHHHHHHGGGEEEDDDCCCDDDEEEFFFFFFEEEEEEDDDDDDDDDEEEEEEBBBAAAAAABBBDDDDDDCCCAAA@@@@@@AAABBBBBBBBBAAA@@@BBBBBBCCCDDDDDDCCCBBBBBBBBBBBBBBBBBBCCCCCCCCCCCCBBBBBBAAA@@@@@@@@@@@@@@@@@@@@@@@@>>>===<<<>>>@@@>>>>>>>>>>>>>>>===<<<<<<======>>>>>>>>>>>>======????????????>>>>>>>>>>>>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@????????????>>>>>>>>>>>>============;;;;;;;;;;;;::::::::::::;;;<<<<<<:::888777888999:::::::::999999999888888;;;;;;;;;;;;<<<<<<<<<<<<<<<<<<===??????@@@@@@???===========================<<<::::::<<<======<<<<<<<<<;;;:::999999999999;;;;;;:::999999999999999999999999999999999999999777777888999::::::::::::;;;;;;:::999999999999999888999:::999888777888999::::::999888888888888888;;;;;;<<<======<<<;;;;;;999999999999999999999999777888888999999999999999:::999999999888777777777444444444444444444444444666555444444444444555666666777777888777666555444555555555555555555555555555555555666777888888888777777777777888888888888999888777666555444333333444444555666666555444444555555555555444333222111222333333333333222111111333222111000000111222222222222111111111222222333555444333222222222222222222222222111111111000000333222000///.........///222111000...------,,,,,,++++++*********)))))))))''''''''''''((()))************+++,,,,,,,,,,,,+++++++++++++++,,,------...QQQRRRQQQPPPPPPRRRUUUXXXVVVVVVUUUTTTTTTTTTTTTUUUUUUVVVVVVWWWXXXXXXXXXXXX\\\ZZZXXXXXXYYYYYYYYYXXXVVVVVVVVVWWWWWWXXXXXXXXXXXXWWWVVVVVVVVVVVVVVVVVVWWWXXXXXXYYYYYYXXXXXXXXXWWWXXXYYYXXXXXXXXXZZZ\\\\\\ZZZYYYWWWWWWXXXYYYZZZZZZZZZ[[[[[[[[[YYYXXXWWWYYYWWWTTTTTTUUUVVVUUUUUUUUUUUUVVVWWWWWWVVVUUUTTTRRRRRRRRRRRRSSSTTTTTTUUUUUUTTTSSSQQQQQQQQQRRRSSSPPPQQQRRRSSSSSSQQQPPPOOOSSSSSSTTTUUUTTTSSSRRRQQQTTTTTTTTTTTTTTTTTTUUUUUUSSSSSSSSSSSSRRRRRRRRRRRRSSSSSSSSSSSSSSSRRRQQQPPPPPPPPPPPPPPPQQQRRRTTTUUUSSSRRRRRRSSSUUUUUUSSSRRRSSSRRRRRRSSSTTTUUUSSSRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRQQQNNNLLLLLLNNNPPPQQQSSSRRRPPPNNNLLLKKKJJJJJJIIIJJJJJJKKKLLLMMMMMMNNNKKKKKKKKKLLLLLLLLLMMMMMMLLLLLLLLLMMMLLLLLLKKKJJJLLLLLLLLLKKKKKKJJJJJJIIIHHHGGGGGGGGGGGGHHHIIIIIIJJJHHHFFFFFFHHHJJJKKKKKKJJJJJJJJJJJJJJJJJJKKKLLLJJJJJJJJJJJJJJJJJJJJJJJJIIIIIIIIIIIIHHHHHHHHHHHHIIIIIIHHHHHHGGGGGGFFFFFFGGGGGGGGGGGGHHHHHHIIIIIIHHHGGGFFFFFFHHHJJJJJJIIIHHHGGGFFFFFFGGGHHHIIIJJJGGGGGGEEEDDDDDDDDDEEEFFFHHHGGGFFFEEEEEEDDDEEEEEEBBBAAAAAABBBDDDEEECCCBBB???@@@AAABBBBBBCCCBBBBBBBBBBBBCCCDDDDDDCCCBBBBBBCCCCCCCCCCCCDDDDDDDDDDDDCCCBBBBBBAAAAAAAAAAAAAAA???@@@@@@???======>>>@@@>>>>>>??????>>>>>>============>>>>>>>>>>>>======????????????????????????AAAAAAAAAAAAAAAAAAAAAAAAAAA@@@@@@@@@????????????>>>>>>>>>>>>==================<<<<<<;;;::::::999<<<<<<<<<;;;999888999;;;::::::::::::999999999999:::::::::;;;;;;;;;<<<<<<<<<<<<===>>>????????????======>>>>>>??????@@@@@@<<<;;;:::;;;===>>>???>>><<<;;;:::999999888888999;;;:::999999888999999999999999999999999999999999777888888999::::::::::::::::::999888888888888999999:::;;;:::888777777888:::999999888888888888999::::::;;;;;;;;;;;;::::::999999999999999999999999666777888888999999888888::::::999999888777666666555555555555555555555555666555555444444555555666555666777888888777555333444444444555555666666777555555666666777777888888777777777777888888888888888888777666666555444444444444555666666555444444555555555555444333222222333333333333333222222111222111111000111111222222222222111222222333444555444333333222222222222333222222222111111111111111222111000///.........///111000///...---,,,,,,,,,+++++++++++++++*********''''''''''''((()))***+++***++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,---...///000QQQQQQQQQQQQRRRTTTVVVWWWTTTTTTSSSSSSSSSSSSTTTTTTWWWXXXZZZ\\\\\\[[[ZZZYYY[[[ZZZYYYYYYXXXXXXXXXWWWYYYYYYXXXWWWUUUTTTSSSSSSVVVVVVUUUTTTTTTUUUUUUVVVWWWWWWXXXYYYYYYYYYXXXXXXVVVWWWXXXXXXWWWXXXZZZ\\\\\\ZZZYYYWWWWWWXXXZZZ[[[ZZZZZZ[[[ZZZYYYXXXWWWVVVXXXWWWUUUTTTUUUVVVVVVVVVTTTUUUVVVVVVWWWVVVVVVUUUTTTSSSSSSRRRRRRRRRSSSSSSTTTSSSRRRPPPPPPPPPPPPQQQRRRRRRRRRRRRRRRQQQPPPPPPRRRSSSUUUVVVVVVUUUSSSRRRSSSTTTTTTUUUUUUVVVVVVVVVTTTSSSSSSSSSSSSSSSSSSSSSSSSRRRQQQPPPOOOOOOOOOOOOQQQQQQPPPPPPQQQSSSTTTUUUPPPPPPPPPQQQRRRRRRRRRRRRSSSRRRRRRTTTVVVVVVUUUTTTSSSSSSSSSRRRRRRQQQQQQQQQQQQOOOMMMLLLLLLMMMOOOPPPSSSRRRPPPNNNMMMLLLKKKKKKIIIIIIJJJKKKLLLMMMMMMNNNJJJKKKLLLMMMNNNMMMLLLLLLKKKKKKKKKKKKKKKKKKKKKJJJMMMMMMLLLKKKJJJIIIIIIHHHGGGFFFFFFFFFFFFGGGHHHHHHHHHHHHGGGGGGIIIJJJKKKKKKIIIIIIIIIIIIJJJKKKLLLMMMIIIIIIIIIIIIJJJJJJJJJJJJIIIHHHHHHHHHHHHHHHGGGGGGHHHHHHHHHHHHGGGGGGFFFFFFEEEFFFGGGHHHHHHHHHHHHHHHGGGFFFFFFGGGHHHIIIJJJKKKGGGGGGFFFFFFGGGHHHIIIJJJGGGFFFEEEDDDDDDEEEFFFFFFHHHGGGFFFEEEDDDDDDCCCDDDCCCBBBBBBCCCEEEEEEDDDBBB???@@@AAABBBBBBCCCCCCDDDBBBCCCCCCCCCCCCCCCCCCBBBDDDDDDDDDDDDEEEEEEEEEEEECCCCCCBBBAAAAAAAAABBBBBB???@@@AAA@@@>>>===>>>@@@>>>>>>?????????>>>>>>=========>>>>>>>>>>>>======>>>???????????????@@@@@@AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA@@@@@@@@@?????????>>>>>>>>>>>>==================<<<<<<<<<;;;;;;;;;<<<<<<===;;;999999:::<<<999999::::::::::::::::::::::::::::::;;;;;;;;;;;;<<<<<<===>>>??????>>>>>><<<<<<===>>>???@@@@@@AAA<<<;;;::::::<<<======<<<<<<;;;:::999888888888888999999888888888888999999888888888888999999999999777888999:::::::::::::::999999888888777888888999:::;;;;;;:::888666777888:::999999888888999999999999999999::::::999999999999999999999999999999999666666777888888888888777;;;::::::999888777666666555555555555555555555555666666555555555555666666444555777888888777555333333444444555666777777888555666666666777777777888666777777777888888888888888888777777666555555444444555555555555555555444444555555555444444333222333333444444333333222111111111111111111111222222222111222222333444555666333333222222222222222333111111111111111111111111111111000///////////////000///...---,,,,,,,,,,,,++++++++++++++++++++++++(((((((((((()))***++++++***+++,,,,,,------,,,,,,------------...///111111QQQQQQRRRSSSUUUVVVWWWWWWWWWWWWVVVVVVVVVWWWWWWXXXWWWXXXZZZ\\\\\\[[[YYYXXXYYYYYYZZZYYYXXXWWWWWWWWWYYYXXXWWWVVVUUUTTTSSSSSSWWWWWWVVVVVVVVVVVVWWWXXXWWWXXXXXXYYYZZZZZZZZZYYYVVVWWWXXXXXXXXXXXX[[[]]][[[ZZZYYYXXXXXXYYY[[[\\\ZZZZZZZZZYYYXXXWWWVVVVVVWWWWWWVVVUUUUUUUUUVVVWWWTTTTTTUUUUUUUUUUUUUUUUUUUUUTTTSSSRRRQQQPPPPPPPPPTTTSSSRRRQQQPPPQQQQQQRRRUUUSSSQQQPPPPPPPPPRRRSSSRRRSSSUUUWWWWWWVVVTTTSSSTTTTTTUUUUUUVVVVVVWWWWWWSSSSSSSSSSSSTTTTTTTTTTTTTTTSSSRRRPPPOOOOOOOOOPPPSSSRRRQQQQQQRRRSSSUUUVVVPPPQQQQQQQQQQQQRRRSSSTTTTTTSSSSSSTTTVVVWWWVVVTTTSSSSSSRRRRRRQQQPPPPPPPPPOOONNNMMMLLLLLLMMMOOOPPPQQQPPPOOONNNMMMMMMMMMMMMJJJJJJJJJKKKLLLMMMMMMNNNJJJKKKMMMNNNNNNNNNMMMLLLJJJJJJJJJJJJJJJJJJKKKKKKKKKKKKJJJJJJIIIHHHGGGGGGEEEEEEEEEEEEEEEFFFGGGGGGGGGHHHHHHHHHIIIIIIJJJKKKGGGGGGHHHHHHIIIJJJLLLLLLIIIIIIIIIJJJJJJJJJKKKKKKIIIIIIIIIHHHHHHGGGGGGGGGGGGGGGHHHHHHHHHGGGFFFEEEDDDEEEFFFGGGHHHHHHHHHHHHFFFFFFGGGGGGHHHIIIJJJKKKGGGFFFFFFEEEFFFGGGHHHIIIEEEEEEEEEEEEEEEEEEFFFFFFGGGFFFEEEDDDCCCBBBBBBBBBCCCCCCCCCDDDEEEFFFEEECCC@@@@@@AAAAAABBBCCCDDDEEECCCCCCCCCBBBBBBCCCCCCCCCDDDDDDDDDEEEEEEEEEFFFFFFCCCCCCBBBAAAAAAAAABBBBBB???@@@AAAAAA???>>>>>>???>>>>>>????????????>>>>>>======>>>>>>>>>>>>======>>>>>>??????@@@@@@@@@AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA@@@@@@@@@@@@???>>>>>>>>>>>>============;;;;;;;;;<<<<<<<<<======;;;<<<<<<;;;:::999:::<<<999999999::::::;;;;;;;;;:::::::::;;;;;;;;;<<<<<<<<<======>>>>>>>>>>>>===;;;;;;<<<<<<===>>>??????===;;;999999:::::::::999;;;;;;:::999888888888888888888777777777888888999777777777888888999999999888888999:::::::::999999999888888777888888999999:::;;;<<<:::888777777888:::999999999999999::::::999999999888888999999999999999999999999999999999666666777888888888888777::::::999999888777777666666666666666666666666666666666666666666666666666333444666777777666555444444444555555666777888888666666666666777777777777666777777777888888888888888888777777666666555555555555555444444555555555444444444555444444333333333444444444444333222222000000111111222222222222222111222222333444555666222222222111111222222333111111111111111111111111000000000000000////////////...---,,,,,,+++,,,,,,++++++++++++++++++++++++))))))((())))))***+++,,,++++++,,,------------,,,---------...///000222333RRRRRRRRRTTTVVVWWWVVVUUUUUUUUUUUUUUUUUUVVVVVVWWWTTTUUUWWWXXXXXXWWWVVVTTTVVVXXXZZZZZZXXXWWWXXXYYYUUUUUUUUUVVVVVVWWWWWWWWWYYYYYYYYYYYYYYYZZZZZZ[[[XXXXXXYYYZZZ[[[[[[[[[[[[XXXYYYZZZYYYYYYYYY[[[]]][[[ZZZYYYXXXXXXZZZ[[[]]]YYYYYYXXXXXXWWWWWWVVVVVVXXXXXXXXXVVVTTTTTTVVVXXXUUUUUUUUUUUUTTTTTTTTTTTTUUUTTTSSSRRRQQQPPPPPPPPPVVVUUUTTTSSSSSSTTTUUUVVVVVVTTTQQQOOOOOOPPPSSSTTTSSSTTTUUUVVVWWWVVVUUUUUUVVVVVVVVVVVVVVVVVVWWWWWWTTTTTTTTTTTTTTTUUUUUUUUUVVVVVVUUUTTTSSSSSSSSSSSSTTTSSSRRRRRRRRRTTTUUUVVVTTTUUUVVVUUUTTTTTTVVVWWWUUUTTTTTTUUUVVVWWWUUUTTTRRRRRRRRRQQQQQQPPPPPPPPPOOONNNMMMMMMMMMNNNOOOPPPOOONNNNNNMMMMMMMMMNNNNNNLLLLLLLLLLLLMMMMMMMMMMMMKKKLLLMMMNNNNNNNNNMMMLLLJJJIIIIIIIIIIIIJJJKKKKKKIIIIIIIIIHHHGGGGGGGGGFFFEEEEEEEEEEEEEEEFFFGGGGGGFFFHHHIIIIIIIIIIIIJJJLLLGGGGGGGGGGGGHHHIIIJJJKKKIIIIIIJJJJJJKKKLLLLLLLLLJJJJJJIIIIIIHHHHHHGGGGGGFFFGGGHHHIIIIIIHHHGGGFFFDDDEEEEEEFFFGGGHHHIIIIIIFFFGGGHHHHHHGGGGGGIIIKKKHHHGGGFFFEEEEEEFFFGGGHHHEEEEEEEEEEEEFFFFFFFFFFFFFFFEEEDDDCCCCCCBBBCCCCCCDDDCCCCCCDDDFFFGGGEEEDDDBBBAAAAAAAAABBBCCCDDDEEEDDDCCCBBBBBBBBBBBBCCCDDDDDDDDDDDDDDDEEEEEEEEEEEECCCBBBBBBAAAAAAAAAAAAAAA???@@@BBBAAA@@@>>>>>>???>>>>>>??????@@@@@@??????======>>>>>>>>>>>>======>>>>>>??????@@@AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA@@@@@@@@@@@@>>>>>>>>>>>>============999::::::;;;<<<<<<======:::;;;;;;:::999999:::<<<888999999:::;;;<<<<<<===;;;;;;;;;<<<<<<<<<======<<<======>>>>>>=========::::::;;;;;;<<<<<<=========;;;999888999999888777;;;:::999888888777777888777777777666777777888999666666777777888999999999888999999::::::999999999999888888888888999:::::::::;;;<<<;;;999888888999:::999999999999::::::;;;999999888888888888999999999999999999999999999999666777888888999999888888999999999888888888888888777777777777777777777777555666666777777666666555444444555666666666666555555555555666666777777888666666666666777777777777777777777777888888888888888888888777777666666666666555444444444444555666333444444555444444333333444444444444444333222222///000111222222222222222222222111222222333444555222111111111111222222333111111111111111222222222//////000000000000//////...---,,,+++++++++++++++*********+++++++++++++++))))))))))))***+++,,,---++++++,,,------------------------...///111222333RRRRRRRRRTTTVVVWWWTTTRRRSSSSSSRRRRRRSSSTTTTTTUUUSSSTTTUUUVVVUUUUUUTTTSSSTTTVVVYYYZZZXXXWWWXXXZZZTTTUUUUUUVVVWWWXXXXXXYYYXXXXXXXXXXXXXXXYYYZZZZZZYYYZZZ[[[\\\\\\]]]]]]]]]ZZZ[[[[[[[[[YYYYYY[[[]]][[[ZZZYYYXXXXXXZZZ\\\]]]XXXXXXWWWWWWWWWWWWWWWWWWYYYZZZYYYWWWTTTSSSUUUWWWXXXWWWVVVUUUUUUUUUUUUUUUSSSSSSSSSRRRRRRSSSSSSTTTUUUTTTTTTSSSTTTUUUWWWXXXTTTTTTRRRQQQQQQQQQRRRSSSUUUUUUUUUVVVVVVVVVWWWWWWWWWWWWWWWWWWVVVVVVVVVVVVUUUUUUVVVVVVVVVWWWWWWWWWVVVVVVVVVVVVUUUUUUUUUUUUUUUTTTSSSSSSSSSTTTUUUVVVVVVXXXXXXVVVTTTTTTVVVXXXUUUTTTTTTUUUVVVVVVTTTRRRSSSSSSRRRRRRRRRRRRRRRRRRNNNNNNNNNNNNNNNOOOPPPPPPNNNNNNMMMLLLLLLLLLLLLMMMNNNNNNNNNNNNMMMMMMMMMMMMLLLLLLMMMMMMNNNNNNNNNMMMIIIIIIHHHHHHHHHIIIKKKKKKHHHHHHHHHHHHGGGGGGGGGGGGGGGGGGGGGGGGGGGHHHHHHIIIEEEHHHJJJJJJIIIHHHJJJLLLHHHGGGGGGGGGHHHIIIJJJJJJJJJJJJKKKKKKLLLMMMMMMNNNKKKKKKJJJJJJIIIHHHHHHGGGFFFHHHIIIJJJJJJIIIHHHGGGEEEEEEDDDEEEFFFGGGIIIJJJGGGHHHIIIHHHFFFFFFHHHKKKKKKJJJHHHGGGFFFFFFGGGGGGDDDDDDEEEFFFFFFFFFFFFFFFEEEEEEDDDDDDDDDDDDDDDEEEEEEDDDDDDEEEGGGGGGFFFDDDCCCCCCBBBAAABBBBBBCCCDDDDDDCCCBBBBBBBBBBBBCCCDDDCCCCCCCCCDDDDDDDDDEEEEEEBBBBBBAAA@@@@@@@@@@@@@@@???@@@BBBBBB@@@?????????===>>>???@@@@@@@@@@@@???======>>>>>>>>>>>>======>>>>>>???@@@@@@AAABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBAAAAAAAAA@@@@@@@@@>>>>>>>>>>>>============::::::::::::;;;;;;;;;;;;999:::::::::888888:::;;;888888999:::;;;<<<===>>><<<<<<<<<=========>>>>>><<<===============<<<<<<;;;;;;;;;;;;;;;;;;<<<<<<<<<:::999999:::;;;:::999;;;:::999888777777777777666666666666666777888888666666666777888999999999999999999::::::999999888999999999999999:::;;;;;;999:::;;;;;;999888999;;;999999999999999:::;;;<<<:::999888888888888999:::999999999999999999999999777888888999999999999999888888888888888999999999777777777777777777777777555666777888888777666555555444444444444555666777666666666666666777777777777777777777666666666666777777777777888888888888888888888777777777777777666555444444444444555666333333444444555444444333444444444555444444333222...///111222333333222222222222111111111222222333111111111111111222333333000000111111111222222222...///000111111000//////---,,,,,,+++++++++++++++)))))))))*********++++++************+++,,,------+++,,,------...---------,,,,,,,,,---///111222333RRRQQQQQQSSSVVVVVVRRROOOVVVUUUUUUUUUVVVWWWXXXXXXUUUUUUUUUVVVVVVUUUUUUTTTRRRUUUYYYZZZXXXXXXYYY[[[WWWWWWWWWWWWWWWWWWWWWWWWUUUUUUUUUUUUUUUVVVWWWXXXZZZZZZ[[[\\\]]]^^^^^^^^^[[[\\\]]]\\\ZZZZZZ[[[]]][[[ZZZYYYXXXYYYZZZ\\\^^^WWWWWWVVVVVVVVVWWWXXXXXXYYYZZZZZZWWWTTTRRRTTTWWWZZZYYYXXXWWWVVVUUUUUUUUURRRRRRRRRSSSTTTVVVWWWXXXRRRRRRQQQQQQRRRTTTVVVWWWRRRSSSTTTTTTTTTSSSQQQPPPVVVUUUUUUUUUUUUVVVWWWXXXXXXXXXXXXWWWWWWVVVVVVVVVWWWWWWWWWXXXXXXXXXYYYYYYSSSSSSTTTUUUUUUUUUTTTTTTUUUTTTSSSSSSSSSTTTUUUVVVVVVWWWWWWUUURRRRRRTTTWWWVVVUUUTTTTTTUUUUUUSSSQQQSSSSSSSSSSSSSSSTTTTTTTTTOOONNNNNNNNNOOOPPPPPPQQQOOONNNMMMLLLKKKKKKKKKKKKPPPPPPOOOOOONNNMMMMMMMMMMMMMMMMMMMMMMMMNNNNNNNNNIIIHHHHHHGGGHHHIIIKKKKKKGGGHHHHHHHHHHHHHHHHHHHHHIIIIIIHHHHHHIIIIIIJJJKKKEEEHHHJJJJJJIIIHHHJJJLLLIIIHHHHHHHHHHHHIIIJJJJJJJJJKKKKKKLLLMMMNNNNNNOOOLLLLLLKKKJJJIIIIIIHHHHHHGGGHHHJJJKKKKKKJJJHHHGGGEEEEEEDDDDDDEEEGGGJJJKKKGGGIIIJJJIIIFFFEEEGGGJJJMMMLLLJJJHHHGGGGGGGGGHHHCCCDDDEEEFFFFFFFFFFFFFFFFFFEEEEEEEEEEEEEEEFFFGGGEEEDDDDDDEEEGGGGGGFFFEEEEEEDDDBBBAAAAAABBBCCCDDDDDDCCCBBBAAAAAABBBCCCDDDCCCCCCCCCCCCDDDDDDDDDDDDBBBAAA@@@@@@??????@@@@@@???AAABBBBBBAAA?????????===>>>???@@@@@@@@@@@@@@@======>>>>>>>>>>>>======>>>>>>???@@@AAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBAAAAAAAAA@@@@@@>>>>>>>>>>>>============<<<;;;;;;::::::999999888888999:::999888888999;;;888888999:::<<<===>>>>>>============>>>>>>>>>>>><<<===============<<<<<<<<<<<<<<<<<<<<<;;;;;;;;;;;;:::999999;;;======<<<;;;:::999888777777777777666666666666666777888888555666666777888999999999999999:::::::::999999888:::999999999:::;;;;;;<<<888:::;;;;;;999999:::<<<999999999999::::::;;;<<<;;;:::999888888999:::;;;999999999999999999999999888888999::::::::::::999777777777888999999::::::777777777777777777777777555666777888888777666555666555333222333555777888777777777777666666666666777777777777666666666666777777777777888888888888888888888888777777777777666555444333333444555666333333444444555444444444444444555555444444333222...///111222333333222222222222111111000111111111111111000000111222333333000000111111222222222222...///000111111000//////,,,,,,++++++***+++++++++(((((())))))*********+++************+++,,,---...+++,,,------......------+++,,,,,,---///000222333