BM6P6(@ ))))))((('''&&&&&&%%%%%%&&&&&&&&&''''''''''''((('''(((+++...///---)))%%%'''''''''''''''''''''''''''((()))******)))((('''***)))((('''&&&&&&'''((((((&&&%%%(((,,,...---,,,)))(((((('''''''''(((((('''((()))))))))(((&&&%%%''''''&&&&&&&&&''''''((('''(((((((((((((((''''''''''''(((((())))))******&&&(((***++++++***'''&&&''''''''''''((((((((()))(((((((((((()))))))))))))))((((((((((((***,,,---,,,,,,+++***))))))******)))************+++++++++,,,+++,,,---///...+++)))++++++******++++++,,,---000...,,,***))))))******++++++******))))))((((((//////...------------...///...---,,,+++,,,---...///...+++******,,,///000///...------,,,,,,,,,,,,///---,,,,,,...111111111333222111000////////////............////////////...///////////////....../////////000111333444555333222000...---,,,---------......///000111111222//////...------------...000000111111111111000000333333222111000000111111444333222333555777666555333444555555555444222222333333222222111000000000...000222333333111///---000000111111222222222333000000000000000///...---......//////000000111111111111///...---,,,,,,+++++++++++++++++++++++++++///...,,,***(((((((((((())))))((((((((((((((()))))),,,//////,,,))))))***))))))))))))((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%''''''''''''''''''&&&&&&'''&&&%%%%%%''''''&&&$$$&&&&&&&&&'''''''''(((((()))******)))'''%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((())))))((('''&&&&&&'''''''''&&&&&&'''''''''''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&'''(((((()))((((((&&&&&&&&&''''''''''''((((((((((((((())))))))))))((((((''''''''''''(((((((((((())))))))))))(((((((((((())))))))))))(((((())))))(((((('''''''''&&&)))))))))))))))))))))))))))(((((('''&&&&&&%%%%%%&&&&&&&&&''''''''''''((()))(((((()))******(((''''''''''''''''''''''''''''''((()))******)))((('''***)))((('''&&&''''''((('''%%%$$$%%%''')))'''&&&'''''''''((((((((((((((((((((((((((((((''''''&&&******)))((((((((('''(((%%%%%%&&&&&&&&&%%%%%%$$$((((((((((((((())))))))))))))))))((((((''''''''''''''''''((((((((())))))(((((()))))))))*********))))))(((((()))***+++,,,++++++***)))))))))))))))))))))*********+++++++++***((('''((()))+++***)))+++************+++,,,,,,---,,,***))))))***+++,,,************))))))))))))++++++,,,---...///000000///...---,,,+++,,,,,,---///...---,,,,,,,,,...///...------,,,++++++,,,,,,///...,,,,,,...000000000222222111000000///......---.........//////////////////000000000000//////.........///000111333444000000///......///111222.........///000111111111//////...------------...---......///000000//////333222111111000000000111666555555777999:::999888444444555666555444333222333333222222111000000000000111111111111111000000000000000111111222222222000000111111111000//////.../////////000000000111111000///...---,,,,,,,,,******++++++,,,,,,------,,,+++***(((((((((((()))))))))((((((((((((((()))&&&))),,,,,,***((((((((())))))))))))((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((&&&%%%%%%&&&'''&&&$$$%%%&&&&&&&&&&&&'''''''''((())))))(((&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((('''&&&&&&''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%%%%%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''''''''((()))))))))))))))&&&&&&&&&''''''''''''((('''((((((((())))))))))))((((((''''''''''''(((((('''(((((())))))(((((('''(((((())))))))))))(((((()))(((((((((''''''''''''((((((((((((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&&&&''''''''''''(((***'''%%%$$$%%%'''(((((('''''''''''''''''''''''''''(((((())))))(((((('''))))))(((''''''''''''(((***)))''''''((((((&&&%%%%%%&&&''')))))))))(((((()))((((((''''''''''''(((+++******)))((('''&&&&&&'''(((((())))))((((((((())))))((((((((((((((((((***)))'''&&&%%%&&&'''(((''''''((((((((()))))))))(((((()))))))))************)))))))))))))))*********))))))(((((((((((())))))))))))*********++++++---+++((((((***,,,---...***************++++++,,,***))))))((()))***+++---)))))))))******************+++,,,...//////////////////---,,,++++++++++++///......------,,,,,,,,,---,,,++++++***+++++++++000...------...//////...///000111111000///---,,,---------.........////////////000000000000000///---------...///000111222000000/////////000222333......//////000000111111000///......------......++++++,,,---...//////000222222111000000000000111555555666888;;;<<<:::999555555666666555555444333333333222222111000000000222111000//////000222333000000000000000111111111000000111222222222111111////////////000000000000111000///...---,,,,,,,,,)))***+++,,,------...///)))(((((('''(((((()))))))))((((((''''''((())))))&&&(((++++++***)))))))))))))))))))))((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''$$$%%%%%%&&&&&&'''''''''''''''''''''''''''''''''((('''%%%%%%&&&&&&%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&(((((('''%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((('''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''(((((()))*********))))))&&&&&&&&&''''''''''''(((''''''((((((((()))))))))((((((''''''''''''(((((('''''''''(((((('''''''''(((((())))))))))))((((((((((((((((((''''''''''''(((((((((((((((((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&''''''''''''((()))'''$$$###%%%'''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((((('''''''''((((((******)))((((((((('''&&&###%%%''')))******)))((()))((('''&&&&&&'''((()))''''''''''''&&&%%%%%%$$$((())))))************))))))))))))((((((''''''&&&&&&&&&&&&&&&&&&'''(((((('''(((((((((((()))))))))''''''((((((((()))))))))*********))))))))))))))))))(((((('''''''''(((((())))))))))))************///---******+++------,,,)))))))))))))))***++++++))))))(((((())))))***+++)))))))))******+++++++++,,,---...//////---+++***///...---,,,++++++******------...------+++)))(((++++++***************+++000...------...///...------...000111000///,,,+++,,,,,,---------...............//////000000//////............///000000111333222000............///.../////////000000000111000//////...............******+++,,,---///000111222111111000000000111111111222333666999999888666666666666555555555444444333333222222111000000000111111000000111111222222000000000000000000000000000111222222333333333333////////////000000000000000000///------,,,,,,,,,++++++,,,,,,---------...))))))))))))((()))))))))(((((('''''''''((()))))))))***+++,,,,,,,,,,,,,,,))))))))))))((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''$$$$$$%%%%%%&&&'''((((((&&&&&&&&&''''''''''''''')))'''%%%$$$%%%&&&%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&'''&&&$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((('''&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&%%%%%%&&&&&&''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''((())))))))))))((((((&&&&&&&&&''''''''''''((('''''''''((((((((())))))((((((''''''''''''((((((&&&&&&''''''''''''&&&&&&(((((())))))))))))((((((((((((((((((((('''''''''(((((((((((((((((((((((('''''''''''''''&&&&&&&&&&&&&&&&&&''''''''''''(((((('''&&&'''(((((('''&&&''''''''''''''''''''''''((((((''''''''''''((((((''''''(((((((((((((((((($$$%%%%%%%%%%%%%%%%%%&&&###%%%''')))******)))((()))((('''&&&&&&'''((()))###$$$%%%&&&''''''&&&&&&$$$%%%&&&&&&'''''''''&&&))))))((((((''''''&&&&&&!!!###%%%((()))))))))((((((((((((((()))))))))***&&&&&&&&&'''''''''((((((***************)))))))))((('''''''''''''''(((((((((((()))))))))*********+++***)))******)))&&&$$$))))))(((((())))))***+++*********)))))))))))))))))))))******++++++,,,,,,+++---...//////---+++***...------,,,,,,+++******++++++,,,,,,,,,***(((&&&*********))))))******+++///...------...///---,,,,,,---...//////...,,,***,,,,,,,,,,,,------------,,,---...///////////////000000/////////000111111111000...---,,,,,,---...////////////000000000000000000///............///+++++++++,,,...000222333222222111111111111222222111111222444666777666444666666555555444444444444333333222222111000000000...000222333444333222111111111111000000000000000000111222333333333333333000000000000////////////000///...------------------------,,,,,,+++++++++++++++++++++***)))(((((('''''''''''''''((())))))*********+++,,,---,,,,,,))))))))))))((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''$$$$$$%%%%%%&&&'''((((((&&&&&&&&&'''''''''((((((***(((%%%$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%&&&&&&$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######%%%&&&&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&''''''(((''''''&&&&&&&&&&&&&&&''''''''''''(((''''''''''''((((((((((((((((((''''''''''''((((((&&&&&&''''''''''''&&&&&&(((((())))))))))))(((((('''''''''(((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''((()))+++***'''$$$''''''''''''''''''''''''(((''''''&&&&&&''''''(((&&&'''(((((()))((((((((($$$%%%'''''''''''')))***%%%&&&''')))))))))(((((((((''''''''''''(((((()))###$$$&&&((()))))))))((($$$%%%&&&'''''''''''''''(((((('''''''''''''''''' ###&&&)))++++++)))(((((((((((()))))))))******&&&&&&'''''''''(((((((((((()))************))))))(((''''''''''''(((((()))((((((((()))))))))******+++***++++++,,,***'''$$$((((((((((((((())))))***+++++++++******))))))(((*********+++++++++++++++)))***+++---............+++,,,,,,,,,,,,++++++******++++++,,,+++***((('''*********)))******+++,,,---,,,,,,---//////---,,,+++,,,---......---,,,++++++++++++,,,,,,,,,------,,,---...//////000000///111111000000///000000000,,,,,,++++++,,,...000111////////////000000000000111000//////......//////------,,,---///111333555333222222222222333444444555444333444666777777666555555444333333333333444333333222222111000000000---///222444555444222000222222222111111111111111111111222333333333222222000000000000//////////////////...---------------...------,,,+++***)))(((,,,,,,,,,,,,+++***((((((&&&&&&&&&&&&'''((())))))***)))((((((***+++***)))))))))))))))((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''$$$%%%%%%&&&&&&'''''''''%%%%%%&&&&&&'''(((((((((+++)))%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$&&&&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&'''''''''&&&%%%%%%&&&&&&&&&''''''''''''(((&&&&&&'''''''''(((((((((((((((''''''''''''(((((('''''''''(((((('''''''''(((((())))))))))))(((((('''''''''(((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''''')))***)))'''%%%''''''''''''''''''''''''((('''&&&&&&&&&&&&'''(((%%%&&&((()))))))))((((((''')))++++++))))))+++---'''''''''(((((((((((((((&&&''''''((((((((((((((($$$%%%''')))))))))''''''%%%&&&'''((())))))))))))&&&&&&''''''''''''''''''%%%&&&((()))))))))))))))(((((()))))))))*********((((((((())))))))))))***'''((()))***++++++******((((((''''''(((((()))***(((((((((((()))))))))***,,,+++***+++------,,,***(((''''''''''''((())))))*********+++++++++++++++,,,++++++++++++++++++***)))***+++,,,---......///)))***+++,,,---,,,++++++++++++,,,,,,,,,,,,++++++***************+++,,,,,,+++++++++---///000...,,,+++++++++,,,,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,...///000111111222222222111000//////............,,,,,,,,,,,,---///111222000000000000////////////111000000///////////////...---------...000333444444333333333444444555666888666444333555666777777555444333222111222222333333333222222111000000000///000111333333333333333333333333333222222222111111222222222222222111000111000000000/////////...//////...------------...+++++++++******)))))))))))))))***++++++***)))(((&&&&&&&&&&&&'''((()))))),,,***((((((***+++)))((())))))))))))((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((((())),,,)))%%%###$$$%%%%%%%%%%%%&&&&&&&&&&&&'''''''''$$$&&&'''&&&%%%$$$%%%'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""$$$&&&&&&&&&%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&'''''''''&&&''''''&&&&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''''''''(((((('''&&&&&&%%%&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''((((((((((((''''''''''''(((((('''(((((())))))(((((('''(((((())))))))))))((((((''''''''''''((((((((()))''''''''''''''''''''''''&&&'''''''''''''''''''''&&&&&&&&&'''''''''((((((((('''&&&&&&(((((('''&&&''''''''''''''''''''''''((('''&&&%%%%%%&&&'''(((%%%&&&((()))))))))((((((%%%'''))))))&&&&&&(((***)))(((((('''''''''((((((%%%&&&((()))))))))((('''###$$$&&&''''''&&&$$$"""!!!"""###$$$%%%%%%%%%%%%%%%&&&&&&''''''(((((((((+++***)))((('''(((((()))))))))))))))************************++++++++++++&&&''')))***+++++++++***((((((((((((((()))******(((((((((((())))))))))))(((&&&%%%%%%(((***,,,,,,'''''''''''''''((())))))((()))***+++---------------,,,,,,++++++*********...---,,,+++++++++,,,,,,((()))+++,,,------,,,+++---------------------...++++++******+++,,,------******+++---///000...---,,,++++++******+++,,,,,,******+++++++++,,,,,,,,,000000111222333444444444000///...---------------111000...------...//////000000000000////////////111111000///////////////......---,,,---///222333444444444444444555666777999666333111222444555666444333222111111111222333333333222222111000000000111111000000111333444555444444444333333222222222222222222222222111000///111111000000/////////...//////...---------......)))))))))))))))*********%%%&&&(((************)))%%%%%%%%%&&&'''((()))***///,,,******,,,,,,+++)))))))))))))))((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''((())))))---)))%%%######$$$%%%%%%&&&&&&&&&'''''''''((((((%%%&&&''''''%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$ """$$$&&&'''&&&%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&'''''''''&&&(((''''''&&&&&&''''''(((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''(((((())))))((('''&&&&&&&&&&&&&&&'''''''''((((((&&&&&&&&&'''''''''((((((((((((''''''''''''(((((((((((())))))))))))(((((((((((())))))))))))((((((&&&'''''''''(((((())))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&'''((((((************************'''''''''&&&&&&%%%%%%%%% """%%%'''))))))(((''''''&&&&&&&&&'''(((***+++***)))'''&&&%%%%%%&&&&&&'''''''''''''''((()))***((((((((((((((('''''''''''''''&&&%%%%%%%%%%%%&&&&&&&&&''')))******(((%%%))))))(((((('''''''''&&&''''''''''''((((((((((((,,,***(((&&&%%%&&&''''''))))))))))))))))))))))))+++******)))))))))))))))***)))((((((((()))+++++++++++++++*********))))))+++)))'''%%%%%%&&&(((***,,,+++***)))((((((((((((++++++++++++++++++++++++++++++++++++++++++++++++------......------,,,+++,,,,,,------,,,,,,+++***,,,,,,,,,+++++++++******,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,,,,------------///............//////000...///000111111111111111000000////////////000000//////............//////...------------...//////////////////////////////,,,,,,---///000111222333555444333333444555777888777555222111222444444444555555333222111000000000444222111//////000222333222222111111111111111111555444444333333222222111555444333111000/////////000000000000000000000000++++++,,,,,,,,,+++***)))))))))))))))))))))))))))************))))))))))))((((((((((((((('''''''''))))))************))))))((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$&&&'''''''''&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$###############$$$%%%%%%%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&(((((())))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''$$$%%%&&&'''((('''&&&%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%((('''&&&%%%%%%%%%%%%%%%''''''''''''''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''(((((('''''''''&&&&&&&&&((((((((((((((((((((((((''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&''''''((('''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&%%%$$$%%%''')))******))))))'''&&&&&&&&&'''(((***+++***)))'''&&&%%%%%%&&&&&&'''''''''''''''((())))))''''''''''''(((((((((((())))))(((''''''''''''(((''''''(((***,,,+++)))''')))(((((((((''''''''''''((((((((()))***+++++++++,,,***((('''&&&&&&'''((())))))))))))))))))))))))+++***))))))(((((()))))))))(((((('''((()))***++++++++++++*********))))))((((((((((((((((((((((((***)))))))))))))))******++++++++++++++++++++++++++++++++++++++++++++++++---............---,,,,,,,,,,,,------,,,,,,+++***,,,,,,++++++************,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,------------------------------....../////////000111111111000000111111111111111111111111///..................///......---.........///000////////////////////////......///000111222222333444444333333444555666777666333111111222444555555444333222222111111111111333222111//////000222333333222111111111222333333555444444333333222111111555444222111000/////////////////////////////////------......------,,,,,,))))))))))))))))))))))))******)))))))))(((((((((((((((((((((((((((((('''(((((())))))))))))((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$############$$$%%%%%%%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$######&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&'''''''''((((((((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&&&&&&&%%%((('''&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''(((((('''''''''&&&&&&&&&''''''''''''''''''''''''''''''((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''((((((((())))))&&&&&&&&&&&&'''((()))***)))((('''&&&&&&&&&&&&&&&'''''''''''''''(((((((((&&&&&&&&&'''((((((((()))))))))(((''''''''''''((((((((()))+++,,,,,,***'''(((((((((((('''''''''''''''(((((()))***++++++,,,,,,+++)))(((''''''((()))))))))))))))))))))))))))+++***))))))(((((())))))((((((((('''((())))))***+++++++++***************&&&''')))******)))''''''(((((((((((()))***+++,,,++++++++++++++++++++++++++++++++++++++++++++++++...............---,,,,,,,,,,,,,,,,,,,,,++++++***+++************))))))))),,,,,,,,,,,,,,,,,,,,,,,,+++,,,------...---------,,,,,,,,,------.........000000000000000000///...///000111222222111000///......------------.............../////////000000////////////////////////111111111222222222333333444444333333333444555555444222000000222444555555222222111111111111222222222222111000000111222333444333111111111333555666444444444333222222111111333333111000////////////////////////////////////---------------,,,,,,,,,)))))))))))))))))))))))))))(((((((((((('''''''''''''''((((((((((((((((((''''''((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%$$$$$$######&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%$$$#########$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%%%%%%%%%%$$$$$$############$$$$$$&&&&&&&&&'''''''''(((((('''(((((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''((((((((('''''''''&&&&&&''''''&&&%%%%%%%%%&&&&&&''''''''''''''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''(((((((((''''''''''''&&&''''''''''''''''''''''''''''''(((((((((((('''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&'''''''''&&&&&&%%%%%%''''''''''''''''''''''''%%%%%%&&&&&&''''''(((((('''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''((((((((((((''''''&&&&&&&&&&&&&&&'''''''''''''''''''''%%%%%%&&&&&&'''((())))))''''''&&&%%%%%%%%%%%%&&&''''''(((***,,,,,,)))'''((((((((((((((('''''''''''''''''''''((((((((((((,,,+++***)))(((((())))))((((((((((((((((((((((((******)))(((((((((((((((((((((((()))))))))******************************'''(((((())))))))))))(((((((((((((((((()))******************************************************...............---,,,,,,+++,,,,,,,,,,,,+++*********)))))))))))))))))))))++++++,,,,,,,,,,,,------------............------,,,,,,---...////////////000000000000///......---,,,---///000000///---,,,------,,,,,,,,,,,,------//////000000000000000000////////////////////////444444444333333333333333444444333333333333333333333222000000222333333222000000000000000111222222222111111000000111222333444333222111222444777888444444333333222111111111222111000///////////////////////////////////////,,,++++++***************(((((((((((((((((((((((((((((('''''''''&&&&&&&&&''''''''''''(((((((((((('''(((((())))))(((((('''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''&&&$$$######""""""######$$$&&&&&&&&&&&&'''''''''''''''''''''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$$$$&&&&&&%%%$$$%%%&&&'''(((%%%%%%%%%&&&&&&&&&'''''')))((((((((((((''''''''''''&&&&&&%%%%%%%%%&&&&&&''''''''''''''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''((((((((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((((((((('''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&''''''(((((((((''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&'''(((''''''&&&%%%$$$%%%%%%&&&'''(((((()))''''''&&&%%%%%%%%%%%%&&&&&&&&&''')))+++***(((&&&'''''''''((((((((((((((())))))((((((''''''&&&&&&*********)))))))))))))))((((((((((((((((((((((((***))))))((('''((((((((())))))************+++***************************))))))'''''''''(((***,,,******)))(((''''''((((((************************************************---------------,,,,,,+++++++++,,,,,,++++++***))))))))))))))))))))))))***+++++++++,,,,,,---------.........//////......---,,,---///000111111111000///////////////...---,,,+++,,,...//////...,,,+++------,,,,,,,,,,,,------///000111222222222111111000000000000000000000000555555555555444444444444444444444333333222111111333222000000111111000///////////////000111222222111000000111111222222333444333222222333555777888444333333222222111000000000000//////.../////////........................,,,+++***)))))))))******((((((((((((((((((((((((''''''''''''&&&&&&&&&&&&&&&'''''''''(((((())))))((())))))******))))))(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&$$$######""""""######$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$###&&&&&&%%%$$$%%%&&&'''(((%%%%%%%%%&&&&&&&&&'''''')))(((((((((((('''''''''&&&&&&%%%%%%%%%&&&&&&'''((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''((((((((((((((((((((((((''''''''''''''''''''''''''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%###$$$%%%'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''(((((((((((((((((((((((((((''''''%%%&&&&&&'''''''''&&&&&&&&&''''''(((''''''&&&&&&&&&&&&'''((((((&&&%%%$$$%%%%%%%%%&&&'''''''''((())))))(((''''''''''''(((&&&&&&''')))******(((%%%'''''''''(((((((((((((((++++++******))))))(((((())))))))))))))))))))))))))))))))))))))))))))))))***)))((((((''''''(((((((((((()))******************************+++++++++***)))'''&&&&&&))),,,---+++***)))(((''''''''''''************************************************,,,,,,,,,,,,,,,+++******+++++++++++++++******))))))))))))************+++***++++++,,,,,,------.../////////000//////...---,,,...///111222222222111..................---,,,---...///000000///...---......------------......000111222333333333222111111111111111111111111111555555555555555555555555333444444333222111000///222000//////000111///...//////...//////000111111000000000111222222333333333333333333444555555666333333333222111111000000///............//////000...........................---,,,******++++++,,,))))))))))))))))))))))))(((''''''''''''&&&&&&&&&&&&&&&''''''((()))))))))))))))************))))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%%%%%%%%%%%%%$$$$$$#########""""""""""""%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''((((((((('''''''''&&&&&&&&&&&&%%%%%%%%%&&&''''''((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&'''''''''(((((((((((()))))))))((((((((((((((((((((((((''''''((((((((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&!!!"""$$$&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((((((((((((''''''''''''&&&'''((())))))(((((('''%%%&&&'''''''''&&&%%%%%%%%%&&&'''(((((('''&&&&&&%%%&&&'''((((((&&&$$$###&&&&&&&&&&&&&&&&&&&&&&&&))))))(((''''''''''''(((&&&'''''')))++++++(((&&&''''''''''''((((((((()))((()))))))))*********+++'''(((((())))))((((((((())))))))))))))))))))))))))))))(((''''''''''''(((&&&&&&((()))))))))((('''))))))*********+++++++++(((((((((((()))***+++,,,)))(((((('''''''''((((((***************************************************++++++++++++***))))))+++++++++++++++***))))))************++++++,,,,,,******+++,,,,,,---......000000000000000///......+++,,,///111222222111111,,,,,,---.........------........................///..................///000111333444555444333222333333333333333333333333444444555555555555555555333444444333222000///---...------...111222111000//////.........///000000//////000111222333333333222333444444444444333333333333222222111000000000...---------......///000...........................---+++***)))***+++,,,))))))))))))))))))))))))(((((((((''''''''''''&&&&&&&&&''''''((())))))***(((((())))))))))))((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%$$$%%%&&&&&&'''&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$###"""!!! $$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&'''$$$%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&'''(((((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&'''''''''((((((((())))))))))))))))))))))))))))))))))))''''''((((((((((((''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&''''''''' !!!$$$&&&(((((('''&&&(((((((((((((((((((((((())))))((((((''''''&&&&&&###$$$&&&(((((('''&&&%%%%%%&&&'''''''''&&&%%%$$$%%%&&&'''(((((((((&&&&&&%%%&&&'''((((((&&&$$$###&&&&&&&&&&&&&&&&&&%%%%%%''''''&&&%%%%%%%%%%%%&&&(((((()))+++,,,,,,***'''&&&'''''''''(((((())))))$$$$$$%%%'''(((***++++++''''''((((((((((((((('''))))))))))))))))))))))))))))))((('''''''''''''''$$$$$$&&&'''''''''&&&%%%))))))******++++++++++++&&&''')))***+++++++++***''''''&&&''''''((()))***))))))))))))))))))))))))))))))))))))))))))))))))***************)))((((((***++++++++++++***))))))******+++++++++,,,,,,,,,******+++,,,,,,---......000000000000000///......***+++...000111111000000++++++,,,---............---,,,,,,++++++,,,,,,---//////............//////000111333555555444333222444444444444444444444444444444444444555555666666333444444333222000...---******+++...111333333222//////............////////////000222222333333333111222444555555444222000333333222222111000000000---------------...///000........................,,,+++)))''''''((()))***)))))))))))))))))))))))))))(((((((((((('''''''''&&&&&&&&&'''((())))))***''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&''''''&&&$$$$$$"""###$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&#########$$$$$$%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&((('''&&&%%%$$$"""!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&'''''''''(((((($$$%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%&&&$$$%%%&&&'''((('''&&&%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((())))))))))))))))))))))))(((((((((((((((((((((((('''''''''&&&&&&''''''''''''((((((((())))))******))))))))))))))))))))))))''''''((((((((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&'''((())))))((('''&&&''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''((((((''''''''''''((((((''''''''''''''''''''''''%%%&&&&&&&&&'''(((((((((&&&&&&&&&'''''''''((((((''''''''''''((((((((((((%%%&&&((()))))))))(((''',,,,,,+++***)))(((''''''((((((((((((((('''''''''((('''&&&%%%%%%&&&((()))***((('''((()))***)))'''(((((((((((()))))))))))),,,++++++***)))(((((('''+++++++++*********))))))(((((((((((((((((((((((())))))))))))((((((((((((,,,+++++++++***)))))))))))))))))))))(((((((((((()))******))))))((('''&&&((((((((()))******++++++******+++,,,,,,---......000000000000000000000000222111000.........///000...---,,,,,,,,,---...///,,,,,,,,,,,,---...//////---...//////------...//////000222333444444333222555555555555555444444444333444555777777777666666777222---...222333///)))//////...---------......////////////////////////---...///000111222222222222222222111111111000000222000//////000000///---,,,,,,,,,---------..............................------,,,+++*********+++))))))))))))))))))))))))))))))(((((('''''''''&&&******))))))(((((((((''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%''''''%%%%%%%%%%%%''''''%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###&&&$$$"""###%%%&&&$$$"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%(((((((((''''''&&&&&&&&&'''&&&&&&&&&&&&'''((((((&&&''''''(((((((((((((((((((((((((((''''''''''''''''''''''''(((((())))))))))))(((((('''''''''&&&''''''''''''''''''''''''((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&'''((())))))((('''&&&''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&'''''''''''''''''''''''''''''''''''''''&&&&&&&&&((((((''''''''''''((((((((((((((((((((((((((((((&&&&&&&&&'''''''''''''''&&&&&&&&&'''''''''((((((''''''''''''((((((((((((&&&&&&((()))))))))((('''((())))))))))))*********''''''''''''(((((((((((('''''''''&&&&&&''''''((()))((('''((()))***)))'''''''''((((((((()))))))))(((((())))))))))))******+++++++++*********))))))(((((((((((((((((((((((()))((())))))))))))))))))++++++++++++************))))))))))))((((((((((((******++++++***)))(((((((((((())))))******++++++***++++++,,,------......////////////////////////222111///.........///000///...---,,,,,,---......,,,,,,+++,,,,,,---...///,,,...///...---,,,---...///000111333333333333333333333333333333444444444444555666777777666555555555222//////111222...+++...---------------......////////////////////////...///000111111222111111222222111111111000000000000...------......---,,,,,,,,,,,,,,,------------------------------------,,,,,,+++***************)))))))))))))))))))))))))))((((((((('''''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%$$$"""###%%%&&&%%%###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%'''''''''&&&&&&&&&%%%%%%'''&&&&&&&&&&&&'''((((((&&&&&&'''((((((((((((((())))))((((((''''''&&&&&&&&&&&&'''''''''((((((((()))(((((((((''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''''''''&&&&&&%%%%%%((((((''''''''''''(((((((((((((((((((((((((((((('''''''''''''''&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''((((((((((((&&&''''''((()))((((((((((((((())))))))))))******&&&&&&''''''(((((())))))''''''(((((((((((('''''')))(((''''''))))))((('''&&&&&&'''''''''(((((((((%%%&&&'''((()))***+++,,,+++++++++***************(((((((((((((((((((((((('''(((((())))))******************+++++++++++++++))))))))))))((((((((((((+++++++++,,,++++++******(((((())))))***++++++++++++++++++,,,------..............................111000///.........//////000///...---,,,,,,------+++++++++,,,,,,---...///,,,---......,,,,,,---...///000111222333333333333111111111222222333333333555555666777777666444444333222111000000///...---,,,,,,+++,,,,,,---...///////////////////////////000000111111222111111111111111000000000000000///...,,,++++++,,,---,,,***++++++,,,,,,,,,---------------------------------+++******)))))))))))))))((((((((((((((((((((((((((((((((((((''''''''''''%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&###$$$$$$%%%%%%$$$$$$###%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$######$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&%%%%%%%%%%%%'''&&&&&&&&&&&&'''((((((&&&&&&'''(((((((((((('''***))))))((('''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((((((''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&%%%%%%$$$(((''''''&&&&&&''''''(((((((((((((((((((((((((((((((((((('''&&&&&&&&&%%%''''''''''''''''''''''''''''''''''''((((((((((((&&&''''''(((((((((((((((++++++***)))((('''&&&&&&'''''''''((((((((((((((('''((()))******((('''&&&)))(((''''''((()))((('''&&&&&&&&&&&&'''''''''(((%%%%%%&&&((()))***+++,,,************************((((((((((((((((((((((((&&&'''((()))***+++,,,,,,*********++++++,,,,,,,,,))))))))))))((((((((((((******+++++++++++++++***((())))))******+++,,,,,,,,,,,,,,,,,,------......------------------------////////////...////////////......---,,,+++++++++++++++++++++,,,---...///,,,---...---,,,+++,,,...///000111111222333333333000000111111222333444444555555666666666444333222000222333111...,,,...///*********+++,,,---...///........................111111111222111111000000////////////////////////---+++***+++,,,---,,,***++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,))))))(((((((((((())))))''''''''''''''''''''''''((((((((((((((('''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%''''''''''''%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$###$$$%%%%%%%%%%%%%%%%%%$$$$$$######$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&'''((((((%%%&&&''''''((((((''''''******)))((('''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((('''''''''''''''''''''''''''''''''((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''&&&&&&&&&%%%'''''''''''''''''''''&&&''''''''''''((((((((((((''''''''''''((((((((()))++++++***)))((('''&&&&&&))))))((((((''''''&&&&&&((()))***+++***)))'''&&&((('''&&&'''((()))(((&&&&&&&&&&&&&&&'''''''''((('''((((((((())))))******************************))))))))))))))))))))))))&&&'''((()))***+++,,,---******++++++,,,,,,,,,---))))))))))))(((((((((((((((((()))***+++++++++***)))))))))***++++++,,,,,,,,,,,,------------......------------------------.........////////////...---------,,,+++***))))))++++++++++++,,,---......,,,---......,,,,,,---...000000000000111222333333000000111222333444444555333444555555444333222111...111333111---,,,---000*********+++,,,---...///------------------------000000111111111000//////........................---,,,+++,,,---...---,,,*********+++++++++,,,,,,++++++++++++++++++++++++)))((((((((((((((())))))&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((((((((((((((((((((((((((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&'''%%%%%%''''''''''''%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&'''((((((%%%&&&&&&'''''''''''''''***))))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''&&&&&&&&&'''''''''''''''&&&&&&&&&''''''''''''(((((((((((((((''''''''''''((())))))''''''(((((((((((()))))))))(((((((((''''''''''''***++++++******)))((('''((('''&&&&&&(((((('''&&&&&&&&&'''''''''(((((((((************))))))))))))***************+++++++++))))))))))))))))))))))))''''''((()))***,,,,,,---+++++++++,,,,,,,,,,,,,,,))))))))))))(((((((((((('''((()))***++++++++++++))))))******+++,,,,,,,,,------------------......------------------------------.../////////......,,,,,,---,,,,,,+++***)))*********++++++,,,---...---...//////------...///000000///000000111333333111111111222222333333444111111222333333222000000...000222111...,,,...000,,,,,,+++,,,,,,---...///------------------------......///000000/////////,,,------------.........---,,,+++,,,...///...---))))))*********+++++++++************************((((((((((((((())))))***'''''''''''''''''''''''''''''''''(((((((((((((((&&&&&&&&&'''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&''''''###$$$$$$%%%%%%$$$$$$######$$$$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&'''&&&%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&'''((((((%%%%%%&&&''''''''''''&&&(((((((((((('''''''''''''''''''''&&&&&&&&&&&&&&&'''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&%%%$$$######$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''(((((('''''''''&&&&&&&&&''''''''''''(((((((((((((((''''''&&&'''((()))***'''''''''(((((((((((()))&&&&&&&&&'''((())))))***,,,,,,+++***))))))))))))((('''&&&&&&(((((('''&&&''''''((((((((()))))))))+++++++++++++++*********))))))*********+++++++++))))))))))))))))))))))))(((((()))***++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++))))))))))))(((((((((((('''((()))+++,,,---------)))******++++++,,,,,,---..................------------------------------,,,---.../////////......,,,---.........---,,,,,,************+++,,,---......///000000......///000000000//////000111222333111111111111111111111111...///000111111111000//////000000///.........///...---------------......,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---.../////////...+++,,,,,,,,,---------------,,,+++,,,...///...---))))))))))))*********+++)))))))))))))))))))))))))))((((((((())))))***+++''''''''''''''''''''''''''''''''''''((((((((()))%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''(((%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''%%%%%%&&&&&&&&&&&&%%%%%%&&&'''((('''$$$###$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&'''(((((($$$%%%&&&&&&''''''&&&&&&''''''''''''((((((((((((((((((((('''''''''&&&&&&''''''''''''((((((((()))((((((((((((((((((((((((((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&%%%$$$######$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&&&&'''((('''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''%%%&&&&&&''''''((((((((((((((('''''''''&&&&&&&&&''''''''''''((((((((()))(((''''''&&&&&&((()))*********)))((('''&&&%%%%%%######%%%''')))+++,,,---...---+++)))(((((()))***((('''&&&&&&'''((('''&&&(((((((((((())))))))))))******+++++++++,,,,,,,,,))))))******++++++++++++)))))))))))))))))))))))))))))))))***++++++,,,,,,---------,,,,,,+++++++++))))))))))))((((((((((((((()))***,,,---...//////)))******++++++,,,------..................------........................+++,,,.../////////......---...///000000000///...************+++,,,---...///000111000///...///111000////////////111222333000000000000////////////,,,---...000000000////////////////////////......//////...---------......,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,---............+++++++++,,,,,,---------,,,+++***+++---...---,,,))))))))))))************)))))))))))))))))))))))))))))))))))))))***++++++((((((((((((((((((((((((&&&'''''''''(((((())))))&&&&&&&&&''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''(((((('''%%%%%%%%%%%%'''(((#########$$$$$$%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&&&&'''(((%%%&&&&&&''''''&&&&&&%%%'''(((***((($$$"""###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&''''''((((((((('''&&&&&&&&&&&&'''(((((($$$%%%&&&&&&''''''&&&&&&&&&&&&''''''((()))))))))))))))((((((((('''''''''&&&'''''''''(((((())))))))))))))))))))))))))))))((((((((((((((((((((((((((('''&&&%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$###'''''''''&&&&&&%%%%%%%%%&&&$$$###$$$''')))(((&&&$$$###"""###%%%&&&%%%$$$'''''''''''''''''''''''''''&&&%%%$$$$$$&&&''')))&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%$$$$$$%%%'''(((&&&'''((((((((('''%%%$$$''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((++++++***)))((('''&&&&&&((((((((((((((()))******,,,+++***))))))***+++,,,************************)))************+++++++++,,,,,,++++++++++++++++++++++++++++++++++++++++++(((((()))***************)))************++++++++++++,,,---.........---,,,////////////////////////000000000000////////////+++,,,------...---------.........------,,,,,,,,,+++***)))))))))***+++,,,............////////////000000111111111000000///222111000//////.........+++,,,---...////////////111000///..................,,,******+++------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++************+++,,,---...---,,,,,,******++++++++++++************))))))))))))******+++)))((()))***+++***((())))))))))))))))))))))))))))))((('''''''''''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%'''''''''&&&&&&'''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%$$$#########$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&)))((('''&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''',,,***(((%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$''''''((((((((('''%%%$$$%%%%%%%%%&&&&&&&&&''''''***)))((()))***)))'''&&&''''''&&&&&&&&&&&&''''''&&&''''''((()))******+++'''((()))***************))))))***))))))((('''&&&((('''&&&%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$###&&&&&&&&&&&&%%%%%%%%%%%%)))'''%%%%%%&&&'''%%%###%%%$$$###$$$&&&'''&&&%%%'''''''''''''''''''''''''''&&&%%%$$$$$$&&&''')))&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%&&&'''((('''''''''(((''''''&&&%%%''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((******))))))((('''''''''((((((((((((((())))))***,,,,,,+++******+++,,,,,,************************(((((()))))))))*********++++++++++++++++++++++++,,,,,,++++++++++++++++++((())))))***************************+++++++++++++++,,,---.........------000000000000000000000000........................+++,,,---.....................---------,,,,,,,,,++++++*********+++,,,---............////////////000000111111111111000000222111000///...............//////......---,,,+++//////......------------...---++++++---...---,,,++++++++++++++++++++++++,,,,,,,,,++++++************+++,,,------,,,,,,+++******++++++++++++************))))))))))))******)))((('''((()))***)))'''))))))))))))))))))))))))))))))((('''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&''''''&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&'''((('''&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''***(((&&&$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&'''((((((((('''%%%$$$%%%%%%%%%&&&&&&&&&''''''***)))((()))))))))'''&&&''''''&&&&&&&&&&&&''''''&&&''''''((())))))******(((((()))*********))))))((())))))))))))((((((''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&'''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$%%%%%%%%%%%%((('''%%%%%%&&&&&&$$$###&&&%%%$$$%%%'''((('''&&&''''''''''''''''''''''''&&&&&&%%%$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&&&&'''((()))(((((('''&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''(((((()))***---,,,+++******+++,,,---************************'''((((((((()))))))))))))))*********+++,,,,,,,,,,,,,,,,,,++++++*********))))))***++++++++++++***************+++++++++,,,+++,,,------......------........................------------------------+++,,,---...////////////...------------,,,,,,,,,,,,++++++++++++,,,---...---............/////////000000111111111111000000222111000///........................---,,,+++***------------,,,,,,,,,,,,...---,,,---...///---,,,************************+++++++++++++++*********++++++,,,,,,,,,+++************++++++++++++*********))))))(((((())))))******)))((((((******)))((())))))))))))))))))))))))))))))((('''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$%%%&&&'''(((***)))(((&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''&&&%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$###$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&&&&'''%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&''''''''''''&&&%%%%%%%%%%%%%%%&&&&&&&&&'''''')))((((((((())))))(((&&&''''''&&&&&&&&&&&&'''''''''''''''(((((())))))***))))))*********)))((((((''''''((()))))))))((((((&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''((((((%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$############$$$$$$%%%%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&%%%$$$%%%&&&''''''%%%''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&)))(((''''''''''''((())))))((('''%%%%%%&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((('''''''''((((((((())))))(((''''''''''''((()))))),,,+++***))))))***+++,,,************************((((((((()))))))))******((())))))***+++,,,,,,------,,,,,,++++++*********)))***++++++,,,,,,++++++*********+++++++++,,,,,,,,,,,,,,,---------------++++++++++++++++++++++++---------------.........+++,,,---...///000000000------------------------,,,,,,,,,,,,------......---------........./////////000000111111111111000111111///...............++++++,,,---------------++++++,,,,,,,,,+++++++++,,,++++++---......,,,***))))))))))))))))))))))))+++++++++***************++++++++++++++++++************++++++++++++******))))))(((((((((((())))))+++***)))***++++++***)))))))))))))))))))))))))))))))))((('''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&&&&'''&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%&&&''')))((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&########################$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((''''''((())))))(((&&&''''''&&&&&&&&&&&&'''''''''''''''((((((((()))))))))*********)))(((''''''&&&&&&'''((()))))))))((($$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''((((((%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$############$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%&&&%%%######$$$%%%&&&%%%$$$''''''''''''''''''''''''%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''((((((((()))((('''%%%%%%&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&''''''(((((())))))'''''''''''''''(((((()))***)))(((''''''((()))***************************)))))))))*********++++++(((((()))***++++++,,,,,,,,,,,,,,,++++++***************+++,,,,,,,,,,,,,,,***++++++++++++,,,,,,,,,,,,,,,,,,,,,------......++++++++++++++++++++++++------........./////////+++,,,---...////////////------------------------,,,,,,------............------------............//////000111111111111111111000///...------------***+++,,,,,,,,,,,,,,,,,,******+++,,,,,,+++*********)))***+++,,,,,,***((())))))))))))))))))))))))************************,,,+++++++++++++++++++++******++++++++++++******))))))(((((((((((())))))***((((((((()))***)))((((((((((((((((((((((((((())))))((('''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&'''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((())))))%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!"""###$$$&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((''''''''''''''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''((('''&&&'''))))))(((&&&''''''&&&&&&&&&&&&''''''''''''''''''(((((((((((()))))))))))))))((('''&&&%%%&&&'''(((((((((((((((###$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&'''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$%%%%%%%%%%%%'''((((((&&&###!!!!!!"""$$$###"""###%%%&&&%%%$$$''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((('''&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&''''''(((((((((''''''&&&&&&''''''((())))))((('''&&&&&&'''((()))************************************++++++++++++((()))))))))***+++++++++++++++++++++++++++++++++++++++,,,------------,,,++++++++++++,,,,,,,,,,,,---,,,,,,,,,,,,---...///,,,,,,,,,,,,,,,,,,,,,,,,---------...//////000000+++,,,------...---------,,,,,,,,,------------...+++,,,------......------,,,------------............///000111111222111111111000///...------------......---,,,+++)))((('''))))))+++,,,,,,,,,+++******)))((()))***+++)))''')))))))))))))))))))))))))))))))))***************,,,,,,++++++,,,,,,---...******++++++++++++******)))((((((''''''(((((()))'''&&&%%%%%%''''''&&&%%%(((((((((((((((((((((((())))))((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''((('''&&&%%%$$$#########$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$&&&'''((()))***%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!"""###$$$&&&'''((()))%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&'''((((((((((((((((((((((((((((((%%%%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$%%%%%%&&&'''%%%%%%%%%&&&&&&&&&'''''''''&&&&&&'''))))))(((&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''(((((()))))))))(((''''''&&&&&&'''(((((((((''''''"""###$$$%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$###&&&&&&&&&&&&%%%%%%%%%%%%&&&((((((&&&### !!!"""%%%$$$###$$$&&&'''&&&%%%''''''''''''''''''''''''%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&'''''''''(((''''''&&&%%%''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((&&&''''''''''''''''''''''''&&&&&&&&&&&&'''(((((()))((('''&&&&&&'''((()))************************))))))))))))************))))))))))))*********************++++++,,,,,,---+++,,,,,,---------------+++++++++,,,,,,,,,------------,,,,,,,,,---...///------------------------+++,,,,,,---......//////,,,,,,,,,---,,,,,,+++***,,,,,,,,,---------......***+++,,,---...------,,,,,,,,,---------............///000111111222222222000000///...---------------------,,,***)))'''&&&((()))+++------,,,+++***+++)))((((((*********)))************************((()))))))))*********+++,,,,,,++++++,,,...000111******++++++++++++******((((((''''''''''''(((((((((&&&%%%&&&'''((('''&&&(((((((((((((((((((((((())))))((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''(((((('''&&&%%%$$$$$$###$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&'''''''''&&&&&&%%%$$$$$$$$$$$$&&&&&&'''(((''''''%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%&&&''''''(((%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&'''(((''''''''''''''''''''''''%%%&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%'''((()))(((&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''(((((()))((((((((('''''''''(((''''''&&&&&&"""###$$$%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&%%%$$$$$$'''''''''&&&&&&%%%%%%%%%###%%%'''%%%###"""###&&&&&&%%%$$$%%%'''((('''&&&''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&'''((((((((('''%%%$$$''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((('''''''''''''''''''''''''''&&&&&&&&&&&&'''((((((***)))(((''''''((()))***************************(((((((((((())))))))))))*********)))))))))))))))))))))***+++,,,------...+++,,,------......------++++++,,,,,,,,,---------------,,,+++,,,---...///++++++++++++++++++++++++******+++,,,,,,---......,,,,,,,,,,,,+++***)))))),,,,,,,,,------.........***+++,,,---------,,,+++,,,,,,,,,---------............///111111222222222000000...---------------******+++++++++******)))((()))+++---...---+++***---+++(((((()))+++++++++************************(((((())))))*********+++,,,,,,+++,,,---///111333******++++++++++++******((((((''''''''''''((((((+++)))((()))***+++***)))(((((((((((((((((((((((())))))((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''''''''(((((((((''''''&&&&&&''''''((())))))((('''%%%$$$###"""###$$$$$$%%%%%%$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########"""""""""""""""&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%$$$$$$%%%&&&&&&))))))******)))'''%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$###$$$%%%'''(((%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%'''((()))(((&&&'''''''''&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&'''((()))))))))((('''((((((((('''&&&%%%%%%&&&$$$###!!!!!!"""###%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''(((((('''&&&%%%%%%&&&&&&&&&''''''''''''(((+++***)))'''&&&&&&&&&&&&'''&&&&&&&&&&&&'''((((((&&&&&&''''''((()))))))))$$$%%%''')))******)))((('''((((((((((((''''''&&&)))***++++++***)))***,,,&&&'''((())))))((('''&&&''''''((())))))))))))))))))&&&$$$$$$&&&((())))))***(((((()))***+++***)))'''((()))***+++,,,------///+++'''(((---000...,,,000///---,,,+++,,,,,,---.........------,,,,,,,,,............---,,,+++***)))))))))))))))******+++***,,,------,,,+++---...,,,---...//////...---,,,333000------///000...,,,,,,------......------,,,............000222444555000///...---,,,++++++++++++************,,,---...------,,,,,,,,,++++++++++++++++++***)))(((((('''))))))))))))))))))))))))))))))*********++++++++++++,,,---......---,,,++++++++++++************))))))((('''&&&&&&'''((()))******))))))((((((''''''''''''&&&&&&&&&&&&''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%'''((()))(((''''''''''''''''''&&&###!!! &&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$#########%%%%%%$$$###""""""######$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%%%%%%%%%%$$$$$$##################$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$)))((('''&&&%%%$$$#########$$$$$$%%%%%%$$$$$$###%%%%%%%%%$$$$$$#########&&&%%%%%%%%%%%%&&&''''''((('''%%%$$$$$$%%%'''(((&&&&&&''''''&&&&&&%%%$$$###$$$%%%%%%&&&&&&%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&'''''''''&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&'''&&&$$$###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&'''((((((''''''&&&&&&&&&&&&''''''((('''%%%$$$$$$%%%'''(((&&&''''''(((((((((((((((&&&'''((())))))***))))))))))))(((''''''''''''''''''&&&$$$"""!!!"""###$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%&&&'''((())))))%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&%%%%%%&&&&&&&&&&&&'''''''''''')))(((''''''&&&&&&&&&&&&'''&&&&&&&&&&&&'''((((((((((((((((((''''''''''''%%%%%%&&&(((((()))))))))((())))))******)))))))))'''(((******)))(((***+++&&&'''((())))))((('''&&&''''''((()))))))))))))))(((''''''((()))***((('''***(((((()))***+++***)))(((((()))***+++,,,------///,,,((()))---///...+++...---,,,++++++,,,,,,---.........------,,,,,,,,,------------,,,+++***))))))))))))))))))******+++)))+++,,,,,,+++***,,,---------...//////...------000---++++++---...---+++........................///.........///111333444111000...---++++++************))))))***+++---.../////////.........------,,,++++++***))))))((((((******************************+++++++++,,,,,,,,,,,,---...//////...---,,,+++++++++************))))))((('''&&&&&&'''((()))***)))))))))((((((((('''(((''''''&&&&&&''''''(((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''(((((())))))(((&&&$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######%%%%%%$$$###############$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%$$$$$$$$$######&&&%%%%%%%%%%%%&&&''''''(((&&&%%%$$$$$$%%%&&&(((&&&&&&&&&&&&&&&%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&'''((('''%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&'''''''''''''''&&&&&&&&&&&&''''''((('''%%%$$$$$$%%%'''(((&&&&&&'''((((((((((((((('''(((((())))))))))))(((******)))(((((((((((((((((('''%%%###""""""######$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%''')))+++,,,---%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&''''''''''''&&&&&&%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&'''(((((())))))(((((('''&&&&&&%%%&&&&&&&&&&&&&&&'''((()))((()))***++++++,,,++++++)))******)))'''&&&&&&'''''''''((((((((((((''''''''''''((()))))))))))))))(((((()))+++,,,+++(((%%%***(((((()))***+++***)))((())))))***+++,,,------000---******---...---+++,,,++++++++++++,,,,,,---.........---------------,,,,,,,,,,,,+++***)))))))))))))))))))))******+++)))***++++++******+++,,,---...////////////...------,,,***+++---......---000///............///000///////////////000111111111000...---+++******)))***)))))))))***+++,,,---000/////////............,,,,,,++++++******))))))************************************++++++++++++---...////////////...---+++++++++************)))((((((''''''''''''(((((())))))))))))(((((((((((((((''''''&&&&&&''''''(((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&&&&''''''''''''((((((''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%$$$$$$############$$$$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$######$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%&&&'''''''''&&&%%%$$$$$$%%%&&&'''&&&&&&&&&&&&%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%%%%$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%&&&&&&'''((()))(((&&&%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&'''''''''&&&%%%$$$$$$%%%&&&'''&&&&&&'''(((((((((((('''(((((()))))))))(((''''''******))))))(((((())))))&&&%%%$$$$$$###$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%'''(((***+++,,,%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&'''''''''%%%&&&&&&''''''((((((((('''&&&&&&&&&&&&'''(((((((((((((((''''''&&&&&&&&&'''&&&%%%%%%%%%&&&((()))'''((()))***+++,,,,,,,,,,,,---,,,***&&&$$$$$$$$$'''(((((((((((((((((('''''''''((())))))))))))))))))))))))***+++***(((&&&***(((((((((***+++***)))))))))***++++++,,,------000...,,,,,,------,,,***************+++,,,,,,---...............---------,,,------,,,,,,+++***))))))))))))))))))******+++)))+++,,,,,,+++***,,,------...///000000///...---------,,,---...///000000000///---,,,,,,---///000////////////////////////000///...,,,+++***))))))))))))******+++,,,,,,---.........------------,,,---,,,,,,,,,+++++++++***++++++++++++++++++++++++((()))))))))************---...///000000///...---+++++++++*********))))))(((((((((''''''((((((((())))))))))))((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&***)))'''&&&%%%%%%&&&'''$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''&&&&&&%%%$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&'''((('''&&&%%%%%%'''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&%%%%%%''''''&&&&&&&&&&&&'''''''''&&&%%%%%%%%%%%%&&&'''%%%&&&''''''((((((''''''((()))))))))((('''&&&&&&))))))((((((((((((((()))############$$$%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''&&&'''((()))******))))))'''&&&&&&&&&&&&'''((((((%%%&&&&&&&&&'''''''''(((((('''&&&%%%%%%'''((()))&&&'''((()))************+++,,,,,,***(((&&&&&&'''(((((((((''''''(((((((((''''''((()))))))))))))))+++)))&&&&&&'''))))))(((***(((((((((***+++***)))*********+++,,,,,,------///...------------,,,+++)))******+++,,,,,,,,,,,,....................................---,,,+++***)))))))))))))))******++++++,,,------,,,,,,---///---...///000000///...---,,,,,,,,,------...000111///...,,,++++++,,,...///////////////.........---///...---,,,+++*********)))******+++,,,,,,------//////.........---------------------,,,,,,,,,,,,++++++++++++++++++++++++*********+++++++++,,,,,,---...///000000///...---+++++++++*********))))))'''(((((((((((((((((('''(((((((((((())))))))))))(((((((((''''''(((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&***)))'''&&&%%%%%%&&&'''$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%'''&&&%%%$$$$$$$$$$$$%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&'''&&&$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&%%%%%%''''''&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%&&&&&&&&&%%%&&&&&&'''''''''''''''((((((((((((((('''&&&%%%''''''&&&&&&&&&''''''(((!!!""""""###$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&((()))***+++******)))'''&&&&&&&&&&&&'''(((((($$$%%%%%%&&&''''''(((((((((((('''''''''(((((()))%%%&&&'''(((((((((((((((&&&'''))))))))))))+++,,,((((((''''''''''''((((((''''''((()))))))))))))))***(((%%%%%%''')))*********(((((()))***+++***)))++++++++++++,,,,,,---------............------,,,***+++,,,,,,,,,,,,,,,+++.............../////////............---,,,++++++)))))))))))))))******+++,,,---......------...///...///000000000000///...)))***++++++***+++---///...---,,,++++++,,,---...---...............------------,,,+++++++++++++++***+++,,,---............111111111111000000000000............------------,,,,,,,,,,,,,,,,,,,,,,,,------------.........///---...////////////...---+++++++++************)))''''''((((((((((((''''''(((((((((((()))))))))))))))((((((''''''(((((()))((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&&&&''''''''''''&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$'''''''''&&&&&&%%%%%%%%%###$$$$$$%%%%%%$$$$$$######$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$'''&&&$$$#########$$$%%%###$$$%%%%%%&&&&&&%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&'''&&&$$$###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&''''''((((((((('''&&&&&&&&&&&&%%%%%%&&&&&&''''''############""""""!!!!!!$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&''')))*********(((''''''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&((()))))))))))))))((((((&&&''''''(((((((((''''''%%%'''(((((((((((()))+++)))((('''&&&&&&'''((()))''''''((()))))))))))))))((('''&&&'''***+++,,,+++***(((((()))***+++***)))+++++++++,,,,,,,,,,,,---+++---...//////...---...,,,,,,---...------++++++---........./////////000---------------+++******)))))))))))))))******++++++,,,...---,,,,,,---///...///000111111000///...)))+++,,,+++******,,,///........................,,,,,,---.........---,,,++++++******++++++,,,---+++,,,---////////////...222222222111111111000000........................------------------------,,,,,,---------.........,,,---...//////...---,,,+++++++++************)))&&&'''((())))))((('''&&&'''((((((((()))))))))***))))))(((((((((((())))))((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''(((((('''&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$%%%&&&'''$$$$$$############$$$$$$###########################$$$%%%%%%%%%%%%$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$$$$###$$$$$$%%%&&&$$$$$$$$$%%%%%%$$$$$$$$$'''&&&$$$###"""###$$$%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&'''''''''%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&'''''''''''''''&&&&&&&&&&&&''''''%%%&&&&&&&&&&&&&&&&&&%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&''''''((('''''''''&&&&&&&&&&&&&&&'''((((((%%%$$$$$$###!!! $$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''###$$$%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&''')))******((('''%%%'''&&&&&&&&&&&&'''(((((((((''''''&&&&&&%%%%%%$$$((()))***++++++***)))((('''((((((((((((((('''&&&))))))***(((&&&$$$$$$%%%)))((('''&&&&&&'''((()))'''(((((()))))))))))))))&&&&&&(((+++......---+++***(((((()))***+++***)))+++,,,,,,,,,,,,,,,,,,---***,,,/////////......///---......///...---+++***---.........//////000000,,,,,,,,,,,,+++***)))))))))))))))))))))******+++***,,,------,,,+++---......///000111111000///...+++---///---++++++---000......///000000///......++++++---.........------************+++,,,---...,,,---...000000000000///000000000000////////////.........///////////////------------------------))))))*********++++++++++++,,,---......---,,,++++++++++++************)))&&&'''((())))))((('''&&&'''((((((((())))))******))))))(((((((((((())))))((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%'''((()))((('''''''''&&&%%%$$$###$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$$$$%%%%%%&&&'''$$$$$$############$$$$$$###########################$$$%%%&&&&&&%%%$$$############$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%&&&''''''$$$$$$$$$%%%%%%$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&###$$$$$$%%%%%%$$$$$$###'''&&&$$$""""""###$$$%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&#########$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&'''((()))(((&&&%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&'''(((((('''''''''&&&&&&'''''''''%%%&&&&&&''''''&&&&&&%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%&&&'''(((((((((''''''''''''''''''((()))***%%%%%%%%%$$$$$$$$$######%%%%%%%%%$$$$$$#########''''''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%(((((('''&&&%%%######"""#########$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&''''''(((((())))))************)))(((&&&&&&'''''''''''''''((())))))(((&&&%%%&&&'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''(((((((((((((((''''''++++++++++++*********)))++++++,,,------------,,,///......---------......------,,,,,,,,,,,,++++++,,,,,,---....../////////------............------)))(((&&&%%%&&&''')))***)))))))))***+++,,,---......///000222222000///...000...,,,++++++,,,---...111000///...............------,,,+++,,,---...//////............---------...///111222333333222222000000///.............../////////000000000000000......///000000///...---***))))))+++---...,,,+++000///---,,,,,,---...///,,,,,,,,,,,,,,,,,,,,,,,,******))))))((((((''''''((((((''''''''''''(((((())))))(((((('''''''''&&&)))((('''%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%########################''''''&&&%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&'''&&&%%%%%%$$$#########$$$&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&''''''&&&%%%%%%&&&''')))***$$$%%%&&&'''((((((((((((((((((((((((((((((((((((%%%%%%%%%$$$$$$$$$######(((((('''''''''&&&&&&&&&%%%%%%$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''((((((((((((*********))))))(((&&&&&&'''''''''''''''((())))))((('''&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((''''''''''''''''''(((((((((''''''&&&(((((())))))***+++++++++******+++,,,,,,,,,,,,,,,......------------......------,,,,,,,,,,,,++++++...---------------------------............------+++***((((((((()))+++,,,************+++---...///...///000111111000///...///...,,,+++***+++------//////......------------+++******)))***+++,,,---000////////////............///111222333333222222000000//////.........///////////////////////////---...///000//////...---,,,++++++,,,......---+++......---------------...++++++++++++++++++++++++))))))))))))((((((''''''))))))(((((((((((()))))))))((((((((('''''''''&&&(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$%%%%%%&&&'''&&&%%%$$$$$$######$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''(((''''''&&&&&&&&&''''''$$$%%%&&&'''((((((((((((''''''''''''''''''''''''%%%%%%%%%$$$$$$$$$######%%%%%%%%%$$$$$$$$$$$$$$$"""#########%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&%%%%%%%%%&&&&&&'''''''''(((''''''&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&''''''((((((((('''''''''''''''))))))))))))(((''''''&&&'''''''''''''''((()))))))))(((''''''))))))((('''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&'''''''''''''''&&&%%%%%%&&&((()))+++,,,---))))))***+++++++++++++++------------------......------,,,,,,,,,,,,++++++......---,,,,,,+++******------............------******)))((()))***+++,,,******++++++,,,...///000...///000111111000///......---,,,*********+++,,,------------,,,,,,,,,,,,...------------...//////000000000////////////......///000111222222222222000000000////////////////////////......------,,,------...//////......---///---,,,---......---+++,,,,,,---------------,,,)))))))))))))))))))))))))))))))))(((((((((((('''***))))))))))))))))))***((((((((('''''''''''''''&&&''''''''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%$$$$$$######$$$$$$&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''(((((((((((('''&&&%%%$$$%%%%%%&&&'''((((((((((((''''''''''''''''''''''''%%%%%%%%%$$$$$$$$$########################""""""############$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&'''''''''(((((((((''''''&&&&&&&&&(((((())))))(((''''''&&&'''''''''''''''((())))))***((('''((()))***)))(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''(((%%%&&&&&&''''''''''''&&&$$$%%%&&&'''(((***++++++(((((()))***************,,,,,,------......------------,,,,,,,,,+++++++++,,,,,,,,,+++++++++******,,,------......------,,,(((((('''''''''((()))***+++++++++,,,---...///000///000111111111111000///------+++***************++++++,,,,,,,,,+++++++++///////////////000000111////////////............//////000000111222222222111111111111000000////////////...---,,,,,,++++++,,,---------............000...,,,,,,------+++*********,,,---------,,,+++))))))))))))))))))))))))(((((((((((((((((((((((())))))(((((((((((())))))''''''''''''''''''''''''%%%&&&'''(((''''''%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%$$$$$$###$$$$$$%%%%%%%%%$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''&&&'''((((((((('''%%%$$$%%%&&&&&&'''((((((''''''''''''''''''''''''''''''%%%%%%%%%$$$$$$$$$######%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''%%%%%%%%%%%%$$$$$$$$$$$$"""######$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&'''''''''((((((''''''&&&&&&%%%%%%'''((((((((((((''''''&&&'''''''''''''''((())))))***((('''((()))***)))(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&''''''((((((%%%&&&&&&'''((((((''''''&&&'''''''''(((((((((((((((((()))************)))++++++,,,---......------------,,,,,,,,,+++++++++*********+++++++++,,,,,,,,,,,,------------,,,,,,((((((((((((((())))))***+++++++++,,,---...///000000000111111111111000000------,,,+++*********)))******+++,,,,,,+++******++++++,,,,,,------------......---------,,,,,,,,,/////////000000111222222111111222222111111000//////......---,,,++++++***,,,,,,,,,,,,,,,---......000...+++***++++++***)))((()))+++,,,,,,,,,+++***************************'''''''''''''''((((((((('''''''''&&&&&&'''''''''&&&&&&&&&'''''''''''''''$$$%%%&&&''''''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%############""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''$$$%%%'''((((((((('''&&&%%%&&&''''''((('''''''''''''''''''''''''''''''''%%%%%%%%%$$$$$$$$$############$$$$$$$$$$$$%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&&&&&&&&&&%%%%%%$$$$$$$$$!!!!!!"""###%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$''''''&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&''''''(((((((((''''''&&&'''''''''''''''((()))))))))(((''''''))))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''((((((&&&&&&'''((())))))))))))))))))(((((('''''''''&&&(((((()))***************)))***,,,---......------------,,,,,,,,,,,,++++++))))))***++++++,,,------,,,,,,------------,,,,,,*********+++++++++,,,,,,******++++++,,,...///000111111111111111111111111......---,,,+++******)))))))))+++,,,,,,,,,+++***+++,,,---.........---------------,,,,,,,,,++++++///////////////111222222111222222333333111000///.........------,,,,,,++++++++++++++++++,,,......000---***)))*********)))(((((()))***++++++++++++))))))))))))))))))))))))&&&''''''''''''((((((((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&'''''''''$$$%%%%%%&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%#########"""""""""!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''$$$%%%&&&'''((((((((((((&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$###### !!!!!!!!!"""""""""###&&&%%%%%%%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''#########$$$%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&%%%&&&&&&&&&&&&&&&&&&'''&&&&&&'''((((((''''''&&&'''''''''''''''((())))))((('''&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$$$$%%%&&&&&&'''((((((&&&'''((()))************)))))))))(((((((((''''''((()))******++++++******(((***,,,.........---,,,------,,,,,,,,,,,,+++++++++++++++,,,,,,,,,,,,,,,+++,,,,,,------,,,,,,+++******++++++,,,,,,,,,+++************+++---...///222111111111111111111222//////...---,,,+++***)))((()))+++------,,,+++***,,,---...///000//////.........---------,,,,,,,,,//////......///000222333111222333444333222000///.........---------------+++*********+++,,,---...000---+++******+++,,,+++(((((((((((()))***++++++((((((((((((((((((((((((&&&&&&&&&'''''''''((((((''''''&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&'''''''''%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&''''''(((&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$############$$$$$$%%%%%%%%%&&&$$$$$$$$$%%%&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%&&&&&&'''((()))***++++++%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&'''''''''&&&&&&''''''(((''''''&&&'''''''''''''''((())))))(((&&&%%%&&&'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((($$$$$$%%%%%%&&&'''(((((('''''')))***++++++++++++))))))))))))))))))))))))))))))***+++++++++++++++((())),,,.........---,,,---------,,,,,,,,,++++++......---,,,,,,++++++++++++,,,,,,------,,,,,,+++(((((()))************))))))))))))***+++,,,......222222111111111111222222/////////...---,,,***)))((()))+++---...---+++***)))***+++,,,,,,,,,+++***//////.........---------//////......///000222333111222333444444222111///------..................******))))))***,,,---///111...+++***+++---------((('''''''''''')))+++,,,''''''''''''''''''''''''&&&&&&&&&'''''''''((((((((((((''''''''''''((((((%%%%%%%%%&&&&&&'''''''''%%%%%%$$$###$$$%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$$$$$$$$$$#########$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$(((((((((''''''&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''***)))'''&&&%%%%%%&&&'''&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%&&&'''((((((&&&%%%%%%&&&'''((((((&&&$$$$$$%%%''''''&&&'''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&'''''''''$$$$$$%%%%%%&&&'''((((((''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%$$$$$$&&&''')))''''''&&&&&&&&&&&&''''''(((((((((((((((((((((((())))))((('''''''''''''''%%%%%%'''((((((((('''&&&'''''''''''''''&&&&&&&&&)))(((((('''''''''(((((())))))))))))))))))))))))((((((((((((((((((((((((++++++***)))***+++---...++++++,,,,,,---.../////////---+++***++++++***))))))************++++++++++++,,,,,,------,,,,,,++++++,,,---------,,,+++***)))******++++++,,,------//////000000000000//////......---,,,,,,++++++*********+++,,,,,,,,,,,,+++++++++------------++++++++++++,,,,,,---...//////000000//////......---------...000111222222111000///...---,,,+++,,,------(((((()))***++++++,,,,,,------------------------))))))(((((((((((())))))((('''''''''&&&&&&&&&&&&''''''''''''''''''''''''&&&'''((('''&&&&&&'''(((%%%%%%&&&&&&&&&&&&%%%%%%)))((('''&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$!!!!!!"""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&&&&%%%%%%&&&$$$"""###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%''''''&&&$$$"""!!! %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%###$$$&&&'''(((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&'''&&&%%%%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&(((''''''&&&&&&''''''((((((&&&$$$$$$%%%''''''&&&'''&&&%%%%%%$$$$$$$$$%%%$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&'''''''''''''''&&&&&&&&&%%%%%%%%%'''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%$$$$$$&&&''')))''''''&&&&&&&&&&&&''''''(((((((((((((((((((((((((((((('''&&&&&&&&&&&&&&&%%%&&&'''((((((((('''&&&'''''''''''''''''''''(((''''''&&&&&&&&&&&&&&&'''))))))))))))))))))))))))((((((((((((((((((((((((*********+++,,,---......++++++,,,,,,---......//////---+++***++++++***))))))************+++++++++)))***+++,,,------...---,,,,,,---...---,,,+++************+++,,,,,,------//////000000000000//////.........---,,,,,,++++++******+++,,,,,,,,,,,,+++++++++,,,------,,,+++++++++,,,,,,---......//////000000/////////............///000111111000///......---++++++***++++++,,,((())))))***++++++,,,,,,------------------------***))))))(((((())))))*********)))))))))(((((((((''''''''''''''''''''''''&&&'''((('''&&&&&&'''(((&&&&&&''''''''''''&&&&&&''''''&&&%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$""""""######$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&(((&&&$$$$$$%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%$$$$$$$$$######""""""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%''''''((((((((((((((('''(((&&&$$$$$$&&&'''&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$%%%&&&'''(((''''''&&&&&&&&&&&&''''''((((((((((((((((((((((((''''''&&&%%%%%%%%%%%%&&&%%%&&&''''''(((((('''''''''''''''(((((()))))))))((((((''''''''''''(((((())))))))))))))))))))))))))))))))))))))))))))))))((()))+++---...//////...++++++,,,,,,------.........,,,+++***++++++***))))))************+++++++++((()))***,,,---...//////---------------,,,++++++******++++++,,,,,,------//////000000000000////////////...------,,,,,,+++***++++++,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,++++++,,,,,,------.../////////000000000////////////...000000111111000///---,,,,,,+++***)))))))))******)))))))))***++++++,,,,,,------------------------+++******************+++*********)))))))))((((((''''''''''''''''''''''''&&&'''((('''&&&&&&'''((('''''''''(((((('''''''''&&&&&&%%%$$$$$$$$$%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&'''***(((&&&&&&''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''&&&&&&&&&''''''''''''((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&'''&&&%%%%%%$$$$$$$$$$$$&&&'''((()))***)))(((''''''&&&%%%%%%&&&'''&&&%%%&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$#########%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&'''((('''&&&&&&%%%%%%&&&&&&'''((((((((((((((((((((((((''''''&&&&&&%%%&&&&&&'''&&&&&&&&&'''''''''''''''&&&''''''((()))******+++******************+++,,,))))))))))))))))))))))))************************&&&))),,,///000000///...++++++,,,,,,,,,---------...,,,******+++++++++***))))))*********+++++++++))))))+++,,,---.........---------------,,,,,,+++******++++++,,,------...//////000000000000//////......------,,,+++++++++***+++,,,,,,------,,,,,,+++++++++,,,,,,+++++++++---------....../////////////////////////////////222222222222111///---,,,+++++++++***************))))))*********+++++++++,,,,,,------------------,,,++++++******++++++,,,(((((((((''''''''''''&&&''''''''''''''''''''''''&&&'''((('''&&&&&&&&&(((''''''((((((((((((''''''&&&&&&%%%%%%%%%%%%%%%&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######%%%'''(((***(((&&&&&&&&&'''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%""""""###$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&''''''''''''((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&'''&&&%%%%%%$$$$$$$$$$$$%%%&&&((()))))))))(((''''''&&&%%%%%%''''''&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&''''''''''''(((((((((((('''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%'''&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&((((((((((((((((((((((((((('''''''''''''''((((((&&&&&&&&&&&&''''''((((((&&&''''''((()))******+++***************+++,,,,,,************************++++++++++++++++++++++++&&&(((,,,///111000///...+++++++++,,,,,,,,,,,,,,,---,,,******+++,,,+++***))))))*********+++++++++++++++,,,---------,,,,,,------,,,,,,++++++++++++***++++++,,,------......//////000000000000//////------,,,,,,+++*********++++++,,,------------,,,++++++++++++++++++++++++---------............................../////////222222333333222000...---,,,,,,,,,,,,,,,+++++++++***************+++++++++,,,,,,,,,---------......,,,,,,++++++++++++,,,,,,)))(((((((((''''''''''''''''''''''''''''''''''''&&&'''((('''&&&&&&&&&(((''''''((((((((((((''''''''''''&&&&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######%%%'''((((((&&&$$$$$$%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((&&&&&&&&&''''''''''''((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%&&&'''((((((((((((&&&%%%%%%&&&''''''&&&$$$%%%%%%$$$$$$$$$%%%&&&&&&&&&'''''''''((((((((((((&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&(((((((((((((((((((((((((((''''''''''''((())))))'''&&&&&&&&&&&&'''(((((('''''''''(((((()))))))))((('''''''''((()))***+++************************************************'''))),,,...000///...---++++++++++++,,,,,,,,,,,,---+++******+++,,,++++++)))************+++++++++,,,,,,,,,------,,,,,,+++,,,,,,+++***************++++++,,,,,,------......//////000000000000//////...------,,,,,,+++******++++++,,,---------------++++++************++++++---------------------------------------.........000000111222222111000///---............---,,,+++************************+++,,,,,,------.........,,,++++++******++++++,,,++++++*********)))))))))''''''''''''''''''''''''&&&'''((('''&&&&&&'''((('''''''''(((((('''''''''''''''&&&&&&&&&'''(((((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&'''%%%$$$"""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%############$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%&&&&&&'''''''''%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&'''''''''(((((((((&&&&&&&&&''''''''''''(((########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&$$$$$$$$$%%%%%%&&&'''(((&&&%%%%%%&&&((((((&&&$$$%%%$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%&&&&&&&&&'''%%%%%%&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&'''''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''(((((()))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&(((((((((((((((((((((((('''&&&&&&&&&''''''((()))'''&&&&&&%%%&&&'''((()))'''''''''''''''''''''(((''''''&&&'''((()))******************************************************((()))+++---......---,,,++++++++++++++++++++++++---+++******+++,,,,,,+++)))************+++++++++***+++,,,,,,------------+++***)))((((((((()))***++++++,,,,,,---.........//////000000000000//////000//////...------,,,,,,+++,,,------...---------,,,+++***))))))***+++,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,,,,------+++,,,...///000000000///---......///...---,,,+++************************++++++,,,,,,---......///++++++************+++++++++++++++*********))))))''''''''''''''''''''''''&&&'''((('''&&&&&&'''(((&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&'''((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$"""!!!"""$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$%%%%%%%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%&&&&&&&&&&&&'''&&&$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&''''''(((%%%%%%&&&&&&&&&'''''''''''''''''''''((((((((((((&&&&&&&&&''''''''''''(((########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$%%%&&&&&&'''$$$$$$######$$$%%%'''(((&&&%%%%%%'''((((((&&&$$$$$$$$$$$$$$$%%%%%%&&&'''######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&'''''''''$$$$$$%%%%%%&&&'''((((((''''''&&&&&&&&&%%%%%%%%%!!!"""###$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&((((((((((((((((((((((((%%%%%%%%%%%%%%%&&&'''(((''''''&&&%%%&&&'''((()))'''''''''''''''&&&&&&&&&(((((((((((()))***+++,,,************************)))))))))))))))))))))))))))***+++,,,,,,,,,,,,+++++++++++++++++++++++++++---+++)))***+++,,,,,,+++)))************+++++++++((()))***,,,---...//////+++***((('''''''''((()))++++++,,,------....../////////000000000000//////111111111000//////......+++,,,------......------,,,+++***))))))***+++,,,++++++++++++++++++++++++*********++++++,,,,,,,,,((()))+++---///000000///,,,---...///...---,,,+++++++++******************++++++,,,,,,---...//////+++******************+++))))))))))))((((((((((((''''''''''''''''''''''''&&&'''((('''&&&&&&'''(((%%%&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%&&&''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$#####################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&&&&%%%%%%###"""!!!"""%%%&&&'''&&&$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%!!!""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$%%%&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''***(((&&&$$$"""!!!!!!!!!%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%'''&&&$$$$$$$$$$$$&&&'''%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&'''((((((&&&&&&&&&''''''(((((((((''''''''''''((((((((()))&&&&&&&&&'''''''''(((((($$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$%%%&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""###%%%%%%$$$$$$%%%&&&%%%%%%%%%&&&'''((()))***)))'''%%%$$$%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%***)))((('''''''''''''''%%%&&&((()))***)))(((&&&&&&&&&&&&''''''''''''(((((((((((((((((('''''''''((((((''''''''''''(((((((((((()))***************+++++++++*********)))))))))+++------+++***++++++---,,,,,,,,,,,,---......+++,,,,,,+++******+++---******))))))))))))******---------,,,,,,+++++++++++++++************++++++++++++++++++,,,,,,------+++,,,...000000000000///++++++,,,---///...,,,)))+++,,,,,,------,,,,,,+++++++++,,,,,,,,,---------///......------,,,++++++...---+++))))))***+++,,,'''(((***+++------------000000///...------,,,,,,,,,++++++***))))))******///...---,,,***)))((('''+++++++++***)))(((((('''))))))((('''&&&%%%%%%%%%'''((((((((((((((('''''''''''''''(((((((((((((((&&&&&&''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%!!!!!!""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!###$$$%%%&&&'''######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######&&&&&&%%%$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$###$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$###""""""$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''''''''''''''((((((((((((***)))(((''''''((()))***$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&&&&&&&$$$$$$&&&(((%%%%%%%%%%%%&&&'''((())))))'''%%%$$$%%%&&&&&&%%%$$$%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&))))))((('''''''''''''''%%%&&&((()))))))))''''''&&&&&&&&&''''''''''''((((((((((((((((((((((((''')))((((((''''''(((((()))(((((()))***************+++++++++*********)))))))))+++,,,,,,+++***+++,,,---,,,,,,,,,,,,---......------------,,,,,,---...******))))))))))))******---------,,,,,,++++++++++++******))))))******+++,,,,,,---...............+++,,,...///000000//////---,,,---...//////,,,***,,,,,,------------,,,,,,******+++++++++,,,,,,,,,......------,,,+++++++++++++++))))))***+++---...***++++++,,,---...////////////...------,,,++++++,,,++++++************+++---,,,,,,,,,+++++++++***++++++******)))(((((('''))))))(((&&&&&&%%%%%%&&&&&&''''''(((((((((((((((&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%############$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%&&&&&&'''######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&&&&%%%%%%$$$###$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$######"""$$$%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''((('''&&&%%%%%%&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&$$$######%%%'''$$$$$$$$$$$$%%%&&&''''''(((&&&$$$$$$%%%&&&%%%%%%"""###%%%&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''''''''''''''''''''''''''((((((((('''''''''''''''%%%&&&'''((()))(((''''''&&&&&&&&&''''''''''''(((''''''((((((((((((((((((***))))))(((((())))))***(((((()))***************+++++++++******************+++,,,,,,*********,,,,,,,,,,,,,,,,,,---......---,,,,,,++++++,,,,,,---******))))))))))))******------,,,,,,,,,,,,++++++******))))))))))))******---...000111111000///...,,,,,,---...////////////......---...//////,,,***,,,,,,------------,,,,,,*********+++++++++,,,,,,---------,,,++++++******((((((((()))+++---///111......------...//////000......------,,,,,,+++++++++++++++******+++,,,,,,***++++++,,,,,,------...++++++******)))((((((((()))((('''&&&&&&&&&&&&&&&&&&&&&'''((()))))))))(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%########################!!!"""###$$$%%%&&&&&&'''"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$#########&&&%%%%%%%%%%%%%%%%%%$$$&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%%%%&&&&&&&&&&&&''''''&&&%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###!!!!!!$$$$$$$$$######$$$%%%%%%&&&'''%%%$$$$$$&&&&&&%%%$$$###$$$%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''&&&%%%&&&'''(((((((((''''''&&&&&&&&&''''''''''''(((''''''''''''((((((((((((******))))))))))))******(((((()))******************************************+++++++++))))))***,,,,,,,,,++++++,,,,,,---...)))(((''''''((()))((((((******))))))))))))******,,,,,,,,,,,,,,,,,,,,,,,,***))))))(((((())))))***,,,...000222222111...---,,,,,,------............///...---.........,,,)))------............------+++++++++,,,,,,,,,---------,,,,,,++++++******)))((((((((()))+++---///000//////............///000//////......------------,,,++++++++++++,,,------+++++++++,,,------......************))))))(((((()))((('''&&&&&&&&&&&&&&&'''((((((((((((((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#################################%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%&&&&&&&&&&&&(((((((((((((((((((((((($$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$""" !!!###$$$$$$#########$$$%%%%%%%%%$$$$$$$$$&&&&&&%%%$$$%%%&&&&&&'''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((('''&&&&&&%%%&&&&&&'''''''''''''''&&&&&&&&&''''''''''''(((&&&'''''''''(((((())))))******))))))))))))******(((((()))******************************************++++++***((((((***,,,,,,++++++++++++,,,------)))&&&%%%%%%'''((('''&&&******))))))))))))******,,,,,,,,,,,,,,,,,,,,,,,,******))))))))))))******,,,---///111111///---+++,,,,,,,,,,,,,,,---------...---,,,,,,------,,,***---......//////......------------.........//////---,,,,,,++++++******))))))*********+++,,,------///............/////////000000000000////////////---,,,,,,,,,,,,,,,---------,,,,,,,,,,,,,,,++++++*********)))))))))))))))(((((('''&&&&&&&&&&&&'''))))))))))))((('''%%%%%%((((((((((((''''''&&&&&&((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%$$$$$$##############################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$###&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&&&&'''''''''''''''((((((((((((''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$&&&''''''(((######$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$###$$$%%%%%%$$$$$$######$$$%%%%%%$$$######$$$&&&&&&%%%###&&&&&&''''''&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&(((((('''&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&''''''''''''(((&&&&&&''''''((()))))))))***))))))(((((())))))***(((((()))******************************+++++++++***+++***)))((((((***,,,+++++++++++++++,,,------,,,)))&&&'''***+++***'''******))))))))))))******++++++,,,,,,,,,,,,------++++++************++++++,,,---...//////...,,,+++,,,,,,+++++++++,,,,,,---...---,,,,,,...///...,,,......////////////.............../////////000000---------,,,++++++******++++++++++++++++++++++++---...///000000000000///111111111111111111000000///...------,,,,,,,,,---------,,,++++++***))))))******))))))))))))))))))(((''''''&&&&&&&&&''''''))))))))))))((('''%%%$$$)))))))))(((''''''&&&&&&(((((((((''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######&&&&&&%%%%%%$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%$$$&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$$$$$$$######$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""%%%'''((('''%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%#########%%%&&&'''%%%###%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&(((((('''&&&%%%&&&%%%%%%%%%&&&&&&''''''&&&&&&&&&''''''''''''(((&&&&&&''''''((())))))***)))((((((''''''(((((()))(((((()))***************))))))*********+++++++++*********((('''(((***,,,+++++++++***++++++,,,---...+++((())),,,...,,,)))******))))))))))))******+++++++++,,,,,,---------,,,,,,++++++++++++,,,,,,---............---,,,+++---,,,+++******+++,,,,,,///...---...000111111000/////////000000/////////............////////////......------,,,+++++++++******++++++,,,,,,,,,+++,,,...000333333333222000000000000000000000000000111000///---,,,,,,,,,,,,,,,,,,+++******)))(((((()))))))))))))))))))))***''''''&&&&&&&&&''''''(((''''''((((((((((((''''''))))))(((''''''&&&%%%%%%(((((('''&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""######$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$"""""""""#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&&&&%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%%%%&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$######$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""&&&''''''%%%$$$$$$&&&&&&%%%%%%$$$%%%%%%%%%###"""###%%%&&&'''%%%######$$$%%%&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&"""######$$$&&&(((***+++''''''''''''''''''''''''###$$$&&&(((((('''&&&%%%&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&'''''''''((((((&&&&&&&&&'''((())))))***((((((''''''''''''(((((((((((()))***************))))))******++++++++++++*********(((''''''***,,,++++++******++++++,,,---///+++((()))---...,,,)))******))))))))))))******+++++++++,,,,,,------------,,,,,,++++++,,,,,,---//////......---------------,,,+++*********+++,,,111///...///222444444444//////000000000000//////---------........./////////......------,,,,,,+++((()))***+++,,,------,,,,,,...222555666555333222////////////000000000000222111///...,,,,,,++++++*********))))))))))))))))))))))))))))))*********''''''&&&&&&&&&''''''((($$$%%%&&&((()))*********(((((('''&&&%%%%%%$$$$$$''''''&&&%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%'''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%""""""""""""""""""""""""""""""###$$$%%%&&&&&&'''#########$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!!!!"""######$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%###$$$$$$%%%%%%$$$$$$###!!!""""""""""""#########%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&###$$$%%%%%%&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''######$$$$$$$$$%%%%%%%%%&&&&&&'''(((((('''&&&&&&#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$#########$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%+++***(((&&&%%%%%%%%%&&&######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''((((((%%%$$$%%%(((***(((&&&%%%%%%%%%&&&'''((())))))'''&&&&&&%%%&&&'''((()))''''''(((***++++++++++++)))))))))))))))******++++++******)))))))))))))))))))))))))))(((((((((((((((((()))***++++++,,,,,,)))************+++++++++******))))))******+++,,,***)))***+++...000000///000---(((%%%$$$&&&))),,,,,,------...............//////...------------...---.../////////...,,,,,,,,,---///111111000...---///////////////////////////---,,,,,,,,,,,,***))))))***,,,------,,,***)))------///444999999444///000000111000000///...---000000///...,,,+++***)))+++***))))))******(((&&&&&&&&&'''''''''''''''&&&&&&''''''(((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###111...***%%%######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""###$$$$$$%%%$$$#########$$$%%%&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%###"""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&''''''&&&$$$$$$ !!!###$$$%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$''''''&&&%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''(((((('''''''''&&&&&&&&&(((((())))))))))))(((((($$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$$$$######$$$$$$%%%$$$$$$######$$$$$$%%%#################################$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%)))((('''%%%%%%%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''(((%%%$$$"""$$$&&&'''&&&$$$%%%%%%&&&&&&''''''(((((('''&&&&&&%%%&&&'''((()))%%%&&&'''((((((((((((((())))))(((((())))))***+++******)))(((((((((((()))***)))))))))(((((((((((((((((()))******+++,,,,,,))))))*********+++++++++******))))))******+++,,,,,,++++++,,,///000000///111///---+++++++++,,,---------...////////////...//////...------------........./////////...---,,,---...000222222111000///000000000000000000000000111///...---......,,,+++***+++,,,......,,,+++***...---...222777777333...///000000000000//////.........------,,,,,,++++++***)))((()))******(((&&&&&&&&&'''((((((''''''&&&(((((())))))******))))))'''(((((((((((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###...,,,(((%%%$$$###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$#########$$$%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$''''''&&&%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&(((((())))))))))))((((((%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%$$$$$$######$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''(((%%%$$$###$$$&&&&&&&&&%%%&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&'''((((((&&&''''''(((((((((''''''))))))(((((())))))***+++***)))((((((''''''((((((******)))))))))(((((((((((())))))******+++++++++)))))))))*********++++++******))))))******+++,,,---,,,,,,---000111111000000000000//////...------......///000000000//////000///......------.........////////////...---,,,...///111222333222111111111111111111111111111111222111//////000000///---+++,,,---......---,,,+++///...---000333333000---......///000000000//////,,,,,,,,,,,,,,,,,,,,,,,,)))(((((((((***)))(((&&&'''''''''((((((''''''&&&'''''''''((((((((())))))''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###)))((('''%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$######$$$$$$%%%&&&$$$$$$############$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$&&&&&&&&&%%%$$$###"""!!!######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&'''&&&&&&%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%'''''''''''''''&&&&&&&&&'''(((((())))))(((((('''%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$%%%$$$%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$#################################$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%#########$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''(((''''''&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&'''''''''''')))))))))***))))))((((((((((((((((((((()))******))))))((('''''''''''''''*********)))))))))((((((((()))))))))*********+++))))))))))))******************))))))******+++,,,///...---...000222111000///......---------,,,,,,...//////000000000000000000//////...............///////////////......---...///000111222222222111111111111111111111111111222111///000000111///...------...//////...------000...------///000...,,,------...///000000000///,,,,,,,,,,,,++++++++++++***)))((()))******)))''''''((((((((((((''''''&&&$$$$$$$$$$$$%%%%%%&&&&&&''''''((())))))(((''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$$$$$$$###"""$$$###$$$$$$$$$$$$%%%%%%$$$$$$############$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%&&&&&&&&&%%%$$$###"""!!!######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$%%%%%%""""""###$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%'''''''''''''''''''''''''''(((((((((((((((((('''%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$#################################$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%$$$""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''((('''''''''''''''&&&''''''&&&&&&&&&&&&&&&%%%%%%%%%''''''''''''''''''&&&&&&((())))))))))))(((((('''((((((((('''((())))))***))))))((('''''''''''''''************)))))))))))))))))))))))))))*********(((((()))))))))***************))))))******+++,,,......---///111222222111///...,,,******+++---......//////000000000000000000000///............///000000//////..................///000111111111222111111111111111111111111111///...///000000///...........................///...---,,,---------,,,,,,---...///////////////...---,,,+++***)))((((((***))))))***++++++***((((((((())))))(((''''''&&&%%%$$$$$$###$$$%%%&&&&&&&&&'''((())))))((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###!!!"""###%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$###############$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%""""""###$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&'''''''''''''''''''''''''''((((((((((((''''''%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%"""""""""######$$$$$$%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''(((%%%&&&&&&&&&$$$###$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''(((''''''&&&%%%%%%&&&&&&'''''''''&&&&&&((((((''''''(((((()))******)))((((((''''''((((((++++++*********)))))))))))))))))))))))))))))))))((((((((()))))))))************))))))******+++,,,---,,,,,,...111333333222111///---++++++,,,///000......///000000000//////111000//////......//////111000//////......//////.........///000111222222111111111111111111111111000...---...///000///---........................---------------,,,,,,,,,------.../////////.........---,,,+++)))((('''&&&)))(((((()))++++++***((())))))))))))(((((('''&&&''''''&&&%%%&&&'''((()))&&&'''(((******((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###!!!"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""###$$$$$$"""###$$$%%%%%%%%%%%%$$$%%%%%%$$$$$$$$$$$$%%%%%%#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$"""###$$$%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''''''''&&&''''''((((((''''''&&&$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%$$$$$$######$$$$$$%%%!!!""""""###$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$###$$$%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''((($$$&&&'''&&&$$$"""$$$%%%$$$$$$$$$%%%%%%&&&&&&'''''''''((((((((('''%%%%%%$$$$$$%%%&&&''''''''''''(((''''''''''''((())))))******)))(((((((((((()))+++++++++*********)))))))))))))))))))))))))))((((((((((((((()))))))))*********))))))******+++,,,+++***+++---111333333333.........------......///------...////////////...111000000///////////////111111///.........///000/////////000111222333444000000000000000000000000000...---...///000///......------------------...+++,,,......------------.........///......------,,,++++++***)))((((((((('''&&&&&&''')))***((('''*********))))))(((&&&&&&((('''&&&%%%&&&''')))***%%%''')))******)))'''%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###"""#########$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$"""!!!!!!"""$$$&&&"""###$$$%%%%%%%%%$$$$$$$$$$$$############$$$$$$"""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$#########$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$%%%%%%%%%%%%$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((&&&''''''((((((''''''&&&#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%%%%&&&%%%$$$$$$$$$$$$$$$$$$%%%######$$$%%%&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%&&&'''&&&&&&$$$$$$######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((&&&(((***(((%%%$$$%%%(((######$$$%%%%%%&&&''''''''''''((((((((('''%%%$$$%%%&&&'''((())))))))))))'''''''''''''''((())))))++++++***)))))))))))))))+++++++++************)))))))))))))))(((((((((((((((((((((((())))))))))))*********)))***++++++,,,***)))***---000333444444***,,,---//////...,,,+++,,,------...............111111000///////////////222111///.........///000000000000111222444555666////////////////////////000///...///000111000///------,,,,,,,,,,,,------***,,,...///...---------.../////////...---,,,,,,******))))))))))))))))))%%%$$$$$$&&&'''((('''%%%************)))(((&&&&&&'''&&&%%%$$$$$$&&&''')))%%%''')))******)))'''%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$#########$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''%%%""" """%%%'''"""###$$$%%%&&&%%%$$$$$$######""""""""""""######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$#########$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###%%%&&&'''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&''''''&&&%%%$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&'''((((((%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&'''''''''((((((&&&''''''''''''''''''&&&$$$%%%&&&%%%###"""###$$$!!!"""###$$$$$$%%%$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$#########"""""""""!!!!!!######$$$$$$$$$%%%%%%%%%'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%'''((())))))*********)))'''%%%%%%''')))***&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%&&&'''(((((((((((((((((()))******))))))************))))))''')))***)))((('''(((***))))))(((((((((((())))))(((((((((((())))))))))))''''''(((((())))))*********+++---//////...---,,,++++++,,,,,,,,,++++++***---...///000111111111111000000///............///...------,,,,,,------...//////000000111111111222444333111////////////000------,,,,,,,,,---......222///------000222000...////////////...---,,,+++000///...---,,,,,,+++,,,,,,++++++***))))))******)))************))))))(((&&&''''''((()))******+++&&&''''''((()))******+++$$$&&&(((***+++)))'''&&&$$$$$$$$$############"""%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$#########$$$$$$%%%%%%%%%%%%$$$###""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$##################""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$""""""$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###"""######%%%&&&'''((((((%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######'''&&&%%%%%%$$$###"""!!!%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$'''&&&&&&%%%%%%$$$$$$###%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&'''''''''%%%$$$$$$&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''''''''''''''&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&"""###%%%%%%$$$$$$%%%&&&$$$%%%%%%$$$$$$###"""!!!%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''((((((((((((((('''&&&%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((&&&&&&%%%%%%&&&''''''(((((((((((((((((())))))***(((((((((((((((((((((((((((***+++***)))((()))***))))))(((((((((((())))))((((((((()))))))))******(((((((((((()))))))))))))))+++,,,......---,,,++++++++++++,,,,,,++++++***,,,---...///000000000000000///......------.........------,,,,,,------...//////000000000111111111222111000...............------,,,,,,------......000///------///111111111222222222222111000///...///...---,,,++++++++++++******************++++++((())))))*********))))))''''''(((((())))))******,,,+++***)))((('''&&&%%%%%%&&&((()))***)))((('''%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$""""""$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$&&&&&&%%%%%%$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&%%%###$$$&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''''''''''')))((('''&&&&&&&&&&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& """$$$$$$$$$$$$&&&(((%%%%%%%%%%%%$$$###"""!!!%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&'''((((((''''''&&&&&&''''''((((((((((((''''''(((((()))***)))((('''&&&&&&'''((())))))***++++++))))))***+++)))((((((''''''(((((())))))))))))*********++++++))))))))))))(((((((((((())))))+++,,,,,,,,,+++******++++++,,,,,,+++++++++,,,,,,---...///////////////......---------------......------------......//////000000000000111111000000///...------------------,,,,,,---......///000000000///...///222444222333333222222111000///...---,,,++++++***++++++,,,++++++***))))))******'''(((((()))************((((((((((((((((((((((((,,,,,,+++)))'''&&&$$$$$$&&&''''''(((((((((((((((&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###&&&&&&%%%$$$###""""""!!!%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$%%%%%%&&&''''''(((%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%$$$######%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&!!!###$$$$$$$$$$$$&&&'''""""""###$$$%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$###%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((('''''''''(((((()))(((''''''''''''((())))))***)))'''&&&&&&''')))***((()))******)))((()))***(((((((((''''''((((((((()))*********++++++++++++******))))))((((((''''''((((((******+++***************+++,,,,,,,,,++++++,,,---...///000000000000......---,,,,,,,,,,,,---......------------......//////000000000000000000000//////......---------------,,,------...///000444555555222//////222666000000000000000///...------,,,++++++*********+++///...,,,***)))(((''''''&&&'''((()))************((((((((((((((((((''''''''''''((((((((((((((((((''''''''''''((((((((()))&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%$$$$$$&&&''''''&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%$$$######%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###&&&%%%%%%$$$###"""!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&"""""""""######$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%###"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###%%%%%%%%%######$$$%%%"""###$$$%%%%%%&&&%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$###"""%%%&&&''''''''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&''')))(((((('''''''''(((((('''''''''''''''(((((()))+++***(((''''''(((***+++'''((()))(((''''''''')))((((((''''''''''''(((((()))*********++++++++++++******))))))((((((''''''(((((()))))))))***)))))))))***+++,,,,,,,,,,,,,,,...///000111111222111111......---,,,,,,,,,,,,---///......------......///000000////////////////////////////////////......------------...///000111999:::999555111000333666......//////......------,,,,,,+++*********++++++,,,,,,+++***))))))))))))%%%&&&'''))))))*********((((((((((((''''''''''''$$$%%%&&&'''((()))***+++''''''''''''((((((((()))%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%$$$$$$&&&''''''&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###%%%%%%$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&'''''''''&&&$$$%%%%%%&&&&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$######"""""""""%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%###"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&%%%###"""###$$$&&&&&&&&&&&&%%%$$$###"""%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&((((((''''''&&&&&&''''''''''''&&&&&&''''''((()))+++***)))(((((()))***+++&&&'''((((((&&&&&&'''((((((''''''&&&&&&''''''((()))))))))*********++++++))))))))))))((((((((((((((((((((()))))))))******)))***++++++,,,,,,,,,,,,//////000111222222222222///......---------------//////............//////000000////////////......//////000000000//////...,,,,,,------...///111111:::::::::777555333333444//////000000000000//////,,,,,,++++++++++++,,,,,,((((((((()))***,,,---...&&&''''''((())))))))))))''''''''''''''''''''''''&&&&&&'''''''''(((((((((&&&''''''(((((((((((((((%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%&&&&&&&&&$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!###%%%%%%%%%$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###"""#########$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&'''&&&&&&$$$$$$%%%%%%&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&(((''''''&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%$$$######%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&'''((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%$$$###$$$&&&&&&&&&&&&&&&%%%$$$###"""%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""#########$$$$$$$$$%%%$$$$$$$$$$$$%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&%%%$$$'''&&&%%%$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&''''''(((''''''&&&%%%%%%&&&&&&'''&&&&&&&&&&&&'''(((((())))))))))))))))))))))))'''((()))((('''&&&''')))(((''''''&&&&&&''''''(((((((((((()))))))))******(((((((((((())))))))))))))))))((()))))))))***+++))))))***+++,,,,,,,,,,,,...///000111111222222222000///......------......//////............//////000000/////////.........------.../////////...---,,,,,,------...000111222777777666777777666444222///000000111111111000000------,,,,,,,,,,,,------***)))))))))***+++,,,,,,''''''((((((((((((((('''%%%&&&&&&''''''(((((((((''''''''''''''''''''''''%%%&&&((()))***)))((('''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$############$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&&&&'''$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ """%%%&&&%%%$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$%%%&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$'''''''''&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&%%%###$$$&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&'''((()))%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&!!!"""$$$$$$$$$$$$&&&(((######$$$%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&&&&&&&%%%###""""""###%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&'''((((((((('''&&&%%%%%%%%%%%%%%%'''&&&&&&&&&&&&'''((((((''''''((((((((((((''''''((()))***)))((('''(((***'''''''''&&&&&&'''''''''(((((((((((())))))))))))''''''(((((())))))******)))))))))))))))***++++++((()))***+++,,,------------...///000111111111111000000///............/////////............//////000000//////.........---+++,,,---.........---,,,,,,,,,------///000111222444222333555888999555111...//////000000000//////---------,,,,,,---......///...,,,***)))((('''''''''(((((((((((((((''''''%%%%%%&&&&&&'''((())))))%%%&&&&&&''''''((((((((($$$&&&(((***+++)))'''&&&(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&#########$$$$$$%%%%%%%%%%%%$$$###""""""###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$%%%%%%&&&''''''$$$$$$$$$$$$######""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ """%%%&&&%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&!!!"""###$$$%%%%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''%%%$$$$$$&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%$$$$$$#########$$$$$$###"""###$$$&&&'''&&&&&&&&&&&&%%%$$$######&&&&&&%%%%%%%%%&&&''''''#########$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%$$$$$$#########$$$#########$$$$$$%%%%%%%%%((('''%%%""" !!!$$$&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&'''((()))$$$$$$%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%&&&&&&&&&%%%%%%'''(((,,,+++)))((((((((()))***)))))))))(((''''''&&&&&&''''''''''''''''''''''''(((((((((((()))))))))))))))))))))))))))((((((((()))((('''(((******)))(((((((((***,,,---.../////////...---------///000111111000///...------...///,,,,,,,,,++++++,,,------........................+++---//////...---.../////////////////////////////////000000000111111111/////////......---------,,,+++******,,,---,,,******)))(((''''''((()))***''''''''''''''''''''''''&&&&&&&&&''''''''''''((((((((('''''''''&&&&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$%%%&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&&&&'''((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$!!!###%%%&&&'''(((&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''''''''&&&&&&###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%$$$$$$$$$######%%%$$$#########$$$%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$'''&&&&&&%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%&&&&&&%%%###""""""$$$&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&%%%%%%'''(((++++++)))((((((((())))))))))))((((((''''''&&&&&&'''''''''''''''''''''''''''''''''((((((((())))))%%%&&&&&&&&&''''''(((((((((&&&&&&&&&((()))(((''''''''')))+++,,,---......111000///------------...111000///...------...///,,,,,,,,,++++++,,,,,,---------------------------+++---...///...---...///........................------...///000111222333.........------,,,,,,,,,,,,+++******,,,,,,+++******)))(((''''''((()))***'''''''''''''''''''''''''''''''''(((((((((((()))((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%'''&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((&&&%%%&&&'''((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''''''''&&&&&&$$$$$$%%%&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###%%%%%%$$$#########$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%((('''&&&%%%%%%$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&$$$$$$$$$$$$%%%%%%%%%%%%"""$$$%%%%%%######%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%'''(((******)))((((((((())))))))))))(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((''''''((()))***+++,,,,,,'''&&&%%%&&&((()))((('''&&&'''(((***+++,,,,,,,,,///...------------......000///......---.........,,,,,,++++++++++++,,,,,,------------------------***,,,......---------...------------------------,,,,,,------...//////000,,,,,,,,,,,,,,,+++++++++,,,+++******+++,,,+++***))))))(((((((((((())))))'''''''''''''''''''''''''''(((((((((((()))))))))''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$########################$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%&&&'''((('''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&'''''''''''''''&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$#########!!!"""###$$$%%%%%%%%%%%%((('''&&&%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%$$$######"""!!!!!!!!!"""%%%%%%%%%%%%%%%%%%%%%%%% """%%%&&&%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$###$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%'''((()))))))))((((((((()))))))))((((((''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((((()))******+++,,,,,,((('''&&&''')))******)))&&&'''(((***+++,,,,,,,,,))))))***+++---///000111........................---,,,++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,***,,,------,,,,,,---...---------------------------,,,,,,,,,++++++++++++++++++++++++************,,,+++******++++++***)))))))))(((((((((((())))))''''''''''''''''''''''''''''''''''''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''&&&&&&%%%%%%$$$$$$$$$$$$$$$#########""""""######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$(((''''''&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$###%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&''''''((('''''''''$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$######""" !!!###$$$$$$$$$$$$((('''&&&%%%$$$#########%%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%&&&%%%$$$"""!!! %%%%%%%%%%%%%%%%%%%%%%%%"""%%%&&&&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$######$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&%%%%%%'''(((((((((((()))))))))((((((((((((((('''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%&&&((())))))(((((((((***+++,,,,,,,,,,,,'''((()))+++---...//////------..................---,,,++++++************,,,,,,,,,,,,,,,,,,,,,,,,)))+++------,,,+++,,,---++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,------************************,,,+++)))***++++++)))((((((((())))))))))))((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''&&&&&&&&&%%%%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$###%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''%%%$$$%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&'''((((((''''''%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$$$$#########$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$###### !!!"""###$$$$$$$$$'''&&&%%%$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%)))(((&&&%%%######""""""&&&&&&&&&&&&%%%%%%%%%%%% """%%%&&&%%%%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&''''''&&&$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$%%%%%%&&&&&&'''''''''''''''''''''''''''''''''%%%&&&&&&&&&%%%%%%'''(((''''''((()))))))))((((((((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%$$$######$$$&&&(((''''''((()))***+++,,,,,,,,,,,,******++++++++++++***))),,,,,,---............------,,,+++******)))******++++++++++++++++++++++++(((***,,,,,,+++++++++,,,++++++++++++++++++++++++***++++++,,,...//////000)))))))))***************,,,+++))))))******)))'''(((((())))))))))))((((((''''''''''''''''''''''''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$%%%&&&'''&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$###"""!!! $$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((((((((%%%%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$%%%%%%$$$###"""######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%"""###$$$%%%%%%%%%$$$$$$""""""###$$$%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%'''&&&&&&%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%!!!###%%%%%%$$$$$$%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%'''(((((('''&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&%%%%%%'''(((&&&&&&((()))))))))(((((((((''''''&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''(((((((((((())))))))))))%%%$$$$$$&&&(((***))))))'''((()))***++++++++++++***++++++++++++)))((('''+++,,,---.........---------,,,+++***))))))))))))++++++++++++++++++++++++(((***,,,,,,+++***+++,,,*********************************))))))))))))))))))))))))******+++++++++,,,+++))))))******(((''''''((()))******)))((('''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''(((((()))((((((''''''&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$######$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$######"""$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''((((((((((((%%%&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$%%%%%%$$$###"""#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%!!!"""$$$%%%&&&%%%%%%$$$$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$###$$$$$$%%%%%%#########$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%############$$$%%%&&&''''''''''''&&&&&&%%%%%%%%%###$$$%%%%%%######%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%'''))))))((('''&&&$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%%%%&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%'''(((%%%&&&((()))))))))(((((((((''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''(((((($$$$$$%%%&&&'''((()))))))))(((((())),,,------,,,&&&'''((())))))***))))))'''((()))+++++++++***)))***+++---...///...---------,,,+++***))))))))))))************************(((***++++++******+++,,,))))))))))))))))))))))))+++***(((%%%### ))))))******+++++++++,,,---+++))))))***)))(((&&&'''((()))******)))((('''''''''''''''''''''''''''&&&&&&&&&'''''''''(((((($$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&'''((((((***))))))(((''''''&&&&&&%%%$$$$$$$$$######""""""%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$#########$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%%%%&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""$$$%%%&&&'''''''''$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''$$$%%%&&&'''((((((((((((%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&'''&&&$$$"""$$$&&&$$$$$$########################$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&'''((((((((('''%%%$$$$$$$$$###""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&'''''''''%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&''''''''''''(((%%%&&&&&&''''''&&&&&&%%%(((((('''''''''&&&&&&&&&$$$$$$%%%&&&&&&''''''(((%%%%%%%%%&&&&&&''''''''''''''''''''''''''''''&&&''''''''''''(((((((((((((((((('''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&%%%%%%$$$$$$&&&''')))******((('''%%%&&&&&&&&&'''((())))))***,,,,,,,,,+++++++++******))))))))))))))))))))))))(((((()))***++++++,,,,,,...------,,,+++***))))))))))))))))))(((((((((((())))))))))))******************))))))))))))******))))))))))))))))))))))))((()))***++++++++++++++++++******)))))))))))))))***)))(((&&&&&&''''''((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%'''(((((((((''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$######$$$$$$%%%&&&########################$$$$$$######$$$$$$%%%&&&######$$$$$$$$$%%%%%%%%%######""""""""""""############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$###"""$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$""" !!!###%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&"""###%%%&&&'''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$###############$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&%%%%%%%%%((('''&&&%%%$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%"""$$$&&&%%%######%%%'''%%%%%%%%%%%%%%%%%%%%%%%%)))(((''''''%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&%%%$$$$$$%%%%%%$$$###"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''%%%%%%&&&&&&&&&&&&%%%%%%((('''''''''&&&&&&&&&&&&$$$$$$%%%&&&&&&''''''(((&&&&&&'''''''''''''''(((((('''''''''''''''''''''''''''''''''(((((((((((((((((('''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&'''''''''''''''&&&&&&'''((())))))((('''&&&&&&&&&''''''((())))))***,,,+++++++++************))))))))))))))))))))))))((())))))***++++++,,,,,,++++++******)))((((((((('''(((((())))))*********))))))))))))*********++++++******))))))))))))***************************)))***++++++,,,,,,+++++++++******)))))))))))))))***)))((('''&&&''''''((((((''''''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%'''((((((((('''&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###$$$$$$%%%&&&$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&###$$$$$$$$$$$$%%%%%%%%%$$$######""""""######$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$###"""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((&&&&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$"""!!!!!!###%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&'''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%((('''&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%!!!###$$$$$$$$$$$$%%%'''$$$$$$$$$%%%%%%&&&&&&''')))(((''''''%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$'''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$#########$$$&&&&&&%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&''''''''''''%%%%%%&&&&&&&&&&&&%%%%%%''''''''''''&&&&&&&&&&&&$$$$$$%%%&&&&&&''''''(((((((((((((((((('''''''''''''''''''''''''''((((((&&&''''''''''''((((((((('''''''''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&'''((()))))))))))))))&&&'''((())))))((('''&&&&&&&&&''''''((()))))))))************)))))))))))))))))))))))))))))))))))))))))))))***++++++,,,,,,************************''''''((()))***++++++,,,))))))*********++++++++++++++++++******)))))))))************************++++++,,,,,,------,,,,,,+++******)))))))))))))))))))))(((''''''''''''((((((''''''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''')))((('''&&&%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&''''''''''''&&&'''''''''''''''&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$%%%&&&&&&$$$%%%%%%%%%&&&&&&''''''$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$######""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''((()))((('''&&&''')))%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$###############$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###!!!!!!###%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###$$$$$$%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%$$$%%%%%%!!!!!!"""###$$$$$$%%%%%%#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%###""""""###$$$%%%''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$###"""!!!"""###%%%&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&''''''((()))(((((((((''''''&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&'''''''''(((((('''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''%%%&&&'''))))))*********&&&'''(((((()))(((((('''''''''''''''(((((()))))))))))))))))))))((((((((())))))))))))))))))))))))))))))*********++++++++++++++++++,,,,,,---------)))))))))******+++++++++*********+++++++++,,,,,,,,,,,,,,,++++++***))))))************************,,,,,,---------------,,,+++******))))))))))))))))))(((((((((''''''''''''(((''''''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''')))((('''&&&%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&%%%%%%%%%%%%%%%%%%$$$%%%$$$$$$$$$$$$%%%&&&&&&$$$$$$%%%%%%&&&&&&''''''$$$$$$######$$$$$$%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$###############$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&%%%$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$############$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%$$$""""""$$$&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%############$$$%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&%%%%%%$$$$$$!!!!!!"""###$$$$$$%%%%%%#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######"""""""""###$$$%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&''''''((((((''''''&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''$$$%%%&&&'''((()))))))))&&&''''''(((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))***************++++++++++++++++++,,,------......,,,,,,++++++******))))))++++++++++++,,,,,,,,,,,,,,,,,,,,,---,,,+++***)))************************------.........------,,,+++******)))))))))))))))(((((((((((((((''''''&&&(((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((('''&&&%%%$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&''''''''''''''''''''''''&&&%%%%%%$$$######%%%%%%$$$$$$%%%%%%&&&'''###$$$$$$$$$%%%%%%&&&&&&$$$$$$######$$$$$$%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$$$$###"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%######$$$&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&'''''''''((((((%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%############$$$%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$%%%%%%&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&$$$%%%&&&&&&%%%###$$$$$$$$$%%%%%%&&&&&&''')))(((''''''%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%""""""######$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%&&&&&&''''''(((&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%&&&&&&''''''%%%&&&&&&&&&&&&'''''''''&&&&&&&&&''''''''''''''''''&&&&&&%%%%%%&&&&&&'''$$$%%%&&&&&&''''''''''''&&&&&&''''''(((((())))))''''''(((((((((((((((((((((((((((((())))))))))))))))))))))))))))))))))))************************)))*********++++++,,,,,,...------,,,+++***))))))++++++,,,,,,,,,---------++++++---......---,,,+++++++++++++++++++++++++++------......------,,,,,,+++******)))))))))))))))((((((((()))(((''''''&&&(((''''''''''''&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''&&&%%%%%%$$$######%%%%%%%%%%%%%%%&&&&&&'''%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&%%%$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&%%%$$$$$$%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&'''''''''%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&&&&'''''''''%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###$$$$$$%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###!!! """%%%&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%)))(((''''''%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""######$$$$$$######!!!"""###%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%!!!"""$$$%%%&&&%%%$$$###%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%&&&&&&''''''(((&&&&&&&&&&&&''''''''''''%%%%%%&&&''''''((())))))%%%%%%&&&&&&&&&'''''''''&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%&&&&&&'''%%%&&&&&&'''''''''&&&&&&&&&&&&&&&''''''((()))***((((((((((((((((((((('''((((((((())))))*********))))))))))))))))))))))))******************************++++++++++++++++++---------,,,+++++++++***,,,,,,,,,,,,------------)))+++,,,...///...---,,,++++++++++++++++++++++++---------------,,,+++++++++******)))))))))))))))'''((()))))))))(((&&&&&&(((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''''''''&&&&&&%%%%%%$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%$$$$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%$$$###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""$$$&&&&&&%%%$$$%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&''''''(((%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&&&&%%%$$$$$$########################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!#########"""!!! """$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%!!!"""%%%''''''&&&$$$"""%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%&&&&&&''''''(((&&&'''''''''(((((())))))'''''''''((()))******+++%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''&&&&&&&&&&&&&&&'''''')))******((((((((((((((('''''''''(((((())))))******++++++))))))))))))))))))))))))++++++******************------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------......(((***,,,...//////...---++++++++++++++++++++++++,,,---------,,,,,,+++***+++******)))))))))))))))'''((()))))))))(((&&&%%%(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&'''((((((&&&%%%%%%$$$$$$%%%%%%&&&((('''%%%$$$###$$$%%%%%%#########$$$$$$%%%%%%%%%!!!!!!###$$$&&&'''))))))&&&%%%%%%%%%%%%&&&''''''))))))((('''&&&%%%%%%$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%&&&&&&&&&''''''%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%%%%"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%&&&&&&'''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""$$$&&&&&&%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''((((((%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%$$$###!!!!!!%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$############$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$############$$$&&&'''((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$ ###%%%&&&%%%$$$######$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$""""""######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""###$$$&&&''' !!!"""###$$$%%%%%%%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$((('''&&&&&&$$$$$$###"""######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&''''''''''''''''''&&&''''''&&&%%%&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''(((((((((************))))))))))))((((((((('''&&&&&&%%%%%%***)))(((''''''((()))***+++***)))(((((('''((((((---,,,++++++******++++++..................------(((***,,,...//////...---..................------...///000000000000000///,,,)))((())),,,...---,,,+++++++++*********))))))))))))))))))))))))))))))(((((((((((())))))))))))''''''''''''''''''''''''***((('''%%%%%%&&&'''((('''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%&&&&&&''''''(((((())))))((('''&&&&&&)))(((&&&###"""!!!!!!"""&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&'''&&&$$$######$$$&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$'''%%%###%%%''')))'''%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$!!!"""###%%%%%%%%%%%%$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%#########$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$$$$"""######$$$$$$$$$$$$###%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%'''&&&&&&%%%&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%&&&''''''(((((()))******)))))))))(((((((((&&&&&&''''''((())))))******)))(((((('''((()))******))))))(((((((((((()))---,,,++++++******++++++---------------,,,,,,,,,***+++---/////////...---/////////////////////////////////000000///......---+++)))***,,,---,,,+++---,,,,,,,,,++++++++++++))))))))))))))))))))))))'''((((((((())))))))))))''''''''''''''''''''''''(((&&&%%%######$$$%%%&&&''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%&&&&&&&&&'''((((((((((((''''''&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&'''&&&$$$######$$$&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&$$$###$$$'''((('''%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$######$$$$$$%%%%%%&&&&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%""""""!!!!!!"""###%%%&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""#########"""!!!!!!$$$$$$$$$$$$$$$###""""""%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&&&&''''''((()))))))))))))))(((((((((''''''''''''(((((()))*********))))))((((((((())))))***))))))((((((((()))******,,,,,,+++************++++++++++++++++++,,,,,,,,,------///000000///...---///000000000000000000000///////////////...---,,,...---++++++,,,---,,,***.........---------,,,,,,((((((((((((((((((((((((''''''((((((((()))))))))'''''''''''''''''''''''''''&&&%%%$$$###$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$%%%%%%%%%&&&&&&''''''((('''''''''%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$&&&%%%$$$$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%$$$###$$$%%%&&&%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###############$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&'''###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###"""!!! """$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$###!!! $$$$$$$$$%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''&&&&&&&&&'''(((((())))))((((((((((((''''''''''''******))))))(((''''''&&&))))))))))))))))))******(((((((((((()))***++++++,,,++++++***************++++++++++++,,,,,,,,,,,,//////000000///...------///////////////000000000////////////...---++++++,,,,,,,,,,,,------,,,+++......---------,,,,,,,,,(((((((((((((((((((((((('''''''''((((((((())))))'''''''''''''''''''''''')))((('''&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$%%%&&&'''''''''''''''(((((())))))(((&&&$$$"""%%%%%%$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&'''###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$""" !!!"""#########$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&%%%$$$"""!!!""""""###%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&&&&'''!!!!!!###$$$&&&'''))))))%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$###%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&''''''((())))))***(((((((((((('''''''''''')))((((((''''''&&&&&&%%%(((((()))***************))))))((())))))***+++,,,,,,+++******))))))******++++++,,,,,,---------...000000000//////...---------------....../////////////////////...---++++++***+++,,,------,,,,,,,,,,,,,,,,,,,,,+++++++++***((((((((((((((((((((((((''''''''''''((((((((((((''''''''''''''''''''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##################$$$$$$$$$$$$%%%&&&&&&'''&&&&&&(((((())))))(((&&&$$$###%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%$$$$$$###$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###############"""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&%%%###"""!!!!!!""""""######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$###!!!"""###%%%&&&&&&''''''###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&!!!!!!###$$$&&&'''))))))%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$%%%&&&&&&&&&&&&%%%$$$%%%%%%&&&&&&'''''''''###$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''%%%%%%&&&&&&'''(((((((((&&&''''''(((((()))******)))))))))(((((((((''''''%%%%%%&&&&&&'''((((((((((((((()))***++++++++++++******)))))))))***++++++++++++***))))))))))))***++++++,,,,,,------......000//////......---------,,,,,,------....../////////////////////...---,,,(((***------,,,+++***+++++++++*********)))))))))((((((((((((((((((((((((&&&&&&'''''''''(((((((((''''''''''''''''''''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%&&&'''((((((((((((&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###""""""###$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$###$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%&&&%%%$$$###$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$#########"""""""""!!!"""#########$$$$$$$$$$$$######$$$%%%%%%$$$###"""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%###$$$$$$%%%&&&&&&&&&%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$###$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''((($$$$$$%%%%%%&&&''''''(((''''''''''''''''''''''''%%%%%%&&&&&&'''(((((()))'''''''''((())))))************)))))))))(((((((((&&&&&&&&&'''(((((())))))'''(((***+++,,,,,,++++++++++++******)))*********++++++***)))))))))))))))*********+++,,,---------......---------------------------...//////000000/////////000000///......***,,,...---***'''&&&'''++++++*********)))))))))))))))))))))))))))))))))&&&&&&&&&'''''''''((((((''''''''''''''''''''''''%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$###%%%%%%%%%%%%&&&'''((()))'''''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&######$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%'''((('''$$$###$$$&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$#########""""""!!!!!!""""""######$$$$$$$$$$$$!!!###$$$%%%%%%$$$"""!!!$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%"""###$$$%%%%%%&&&%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!!!!!!!###$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%&&&'''&&&%%%%%%$$$$$$%%%%%%&&&'''((((((%%%%%%&&&&&&'''((())))))''''''''''''''''''''''''%%%%%%&&&&&&'''((())))))''''''(((((())))))******************))))))))))))*********)))(((((('''''''''(((***+++,,,,,,++++++,,,,,,+++***)))))))))***+++******)))))))))))))))((())))))***++++++,,,,,,------,,,,,,,,,------...---......///000111111222...///000000000000000///,,,...000...)))$$$######+++++++++*********))))))************************&&&&&&&&&'''''''''((((((''''''''''''''''''''''''''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###""")))(((&&&%%%$$$$$$%%%&&&(((((('''''''''&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$"""!!!!!!"""$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&'''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&"""###$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%''')))'''%%%###%%%'''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$#########""""""!!!!!!"""$$$%%%'''$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!!!!""""""%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$""""""#########$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$#########$$$%%%%%%&&&'''''''''&&&&&&%%%%%%%%%!!!###%%%%%%$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&'''''''''&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&'''''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&+++*********))))))((((((******))))))((((((''''''))))))))))))((((((((((((******+++++++++,,,,,,,,,***,,,---......---+++************))))))))))))(((,,,,,,+++***))))))******)))***+++,,,,,,+++***)))---...///000000111111111000///...---+++***((((((---------,,,,,,+++++++++(((((())))))************&&&&&&'''((())))))(((((((((''''''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&'''(((%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''&&&%%%###"""$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%################################################%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$"""!!!!!!"""$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$"""###%%%&&&%%%"""###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%$$$$$$%%%&&&'''$$$$$$$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$#########$$$%%%&&&''''''&&&&&&##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###"""""""""""""""%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$######$$$$$$%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$###$$$&&&&&&$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&*********)))))))))((((((***)))))))))((((((((('''))))))))))))((((((((((((*********+++++++++,,,,,,((()))***++++++***)))(((+++************)))))))))++++++***))))))))))))))))))***+++,,,,,,+++***)))------///000000000000000///.........------,,,,,,---------,,,,,,++++++***)))))))))))))))*********'''((())))))))))))))))))(((''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$############$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$"""###%%%&&&%%%###$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))(((&&&%%%$$$%%%&&&'''%%%%%%$$$$$$$$$%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$######%%%'''))))))'''%%%###"""""""""###$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$############$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$######$$$&&&'''&&&$$$""""""###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&######$$$%%%&&&&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&&&&'''(((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&******))))))))))))(((((())))))))))))(((((((((((((((((((((((()))))))))))))))*********+++++++++++++++,,,---......---,,,++++++++++++************)))***))))))(((((((((((())))))***+++,,,,,,+++***))),,,---...///000000000000------......///000000111...------,,,++++++***************))))))))))))))))))***************)))((((((''''''''''''&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%''''''&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$############%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%))))))((('''&&&%%%%%%$$$&&&&&&%%%%%%$$$$$$######'''&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$###$$$%%%&&&%%%###$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$######$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&***)))'''&&&%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%###"""!!!!!!"""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########"""######$$$%%%$$$$$$$$$%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&&&&$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&!!!"""###$$$%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((('''''''''''''''''''''''''''))))))))))))))))))(((((())))))))))))(((((((((((((((((((((((()))))))))))))))))))))************+++,,,---.../////////......++++++++++++************)))(((((('''''''''(((((()))***+++,,,,,,+++***))),,,,,,---...////////////,,,------...///000000111...------,,,+++***))))))************))))))))))))************))))))((('''(((''''''''''''&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%''''''&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$(((((((((''''''&&&&&&&&&&&&&&&&&&%%%%%%$$$######$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%###""""""###%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&******((('''&&&%%%%%%%%%'''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$#########$$$$$$!!!!!!"""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""###$$$$$$%%%############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&!!!###%%%%%%$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&!!!"""###$$$%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((((((((((((''''''''''''''''''''''''(((((((((((((((((())))))(((((((((((())))))))))))'''((((((((()))))))))***(((((()))))))))*********))))))******+++++++++++++++++++++*********))))))((('''''''''''''''(((((()))***+++,,,,,,+++***)))+++,,,---......//////...------------------.........------,,,***))))))(((*********)))))))))))))))))))))))))))((('''&&&&&&(((''''''''''''&&&&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&''''''((((((&&&&&&&&&%%%%%%%%%$$$$$$!!!""""""###$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%###""""""###%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&))))))((('''&&&%%%%%%%%%'''&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$$$$$$$%%%%%%%%%&&&%%%$$$######%%%&&&'''"""""""""###$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""###$$$%%%%%%""""""#########$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$######$$$$$$%%%%%%&&&&&&&&&&&&''''''!!!"""%%%%%%$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&######$$$%%%&&&&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&%%%%%%%%%&&&''''''''''''(((((((((''''''''''''''''''''''''''''''(((((((((((())))))(((((((((((())))))))))))''''''(((((())))))******(((((((((((())))))))))))))))))******++++++,,,,,,*********))))))))))))((((((''''''''''''(((((())))))***+++,,,,,,+++***)))***+++,,,---............,,,,,,,,,,,,,,,+++++++++...------+++***)))((('''((()))))))))************'''((((((((((((''''''&&&(((''''''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&'''(((&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%&&&'''((((((%%%%%%%%%%%%&&&&&&&&&&&&""""""###$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&'''&&&%%%$$$%%%'''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%$$$######$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$#########$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%"""######$$$$$$%%%%%%%%%##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""""""""###$$$%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""###$$$%%%&&&#########$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%$$$$$$######$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&"""$$$%%%%%%$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''''''''''''''((((((((())))))'''((((((((()))))))))***'''''''''((()))*********'''''''''((((((((())))))++++++++++++,,,---......)))))))))(((((((((''''''((((((''''''(((((()))***)))***+++,,,,,,+++***)))***+++,,,------...------+++++++++,,,,,,,,,,,,,,,...---,,,+++***(((''''''''''''((()))***++++++,,,'''(((((()))))))))(((((((((''''''''''''&&&&&&&&&%%%%%%%%%&&&'''((()))***&&&&&&%%%%%%%%%%%%&&&&&&#########$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$%%%&&&&&&&&&$$$$$$%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$$$$%%%&&&'''$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&((('''%%%$$$%%%'''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&"""#########$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%%%%!!!###$$$$$$"""!!!$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$""""""!!!!!!"""###$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""###$$$%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$#########$$$#########$$$$$$%%%%%%%%%$$$&&&'''&&&$$$""""""###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&'''''''''&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''((((((((((((((((((((((((&&&'''''''''(((((())))))'''((((((((())))))******&&&''''''((()))******+++''''''''''''((((((((()))''''''''''''((()))***+++((((((((((((''''''''''''((((((((((((((()))******)))***+++,,,,,,+++***)))******+++,,,------------***++++++,,,,,,---------......,,,+++***((('''&&&&&&&&&''')))***+++,,,---'''((()))***************(((((('''''''''&&&&&&&&&%%%%%%&&&&&&((()))+++,,,'''&&&&&&%%%%%%&&&&&&'''""""""###$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!"""###$$$$$$%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%&&&'''((((((+++***)))((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$'''&&&$$$######$$$&&&'''$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&((('''%%%$$$%%%(((%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''######$$$$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&""""""######$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&""""""###$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&'''&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&'''%%%""""""$$$$$$###!!!&&&&&&&&&%%%%%%$$$$$$$$$"""############$$$$$$$$$"""###$$$%%%&&&%%%$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$########################$$$%%%&&&''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$'''&&&$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$#########$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''((((((((((((((((((((((((%%%%%%%%%%%%%%%&&&'''(((+++***)))(((((()))***+++&&&'''((())))))((('''&&&''''''''''''((((((((((((*********************************)))))))))))))))))))))))))))))))))))))))(((***+++***)))((()))***(((((()))***++++++,,,,,,)))***+++,,,,,,+++)))(((------,,,,,,+++***))))))''''''((()))))))))))))))))))))))))))(((((((((((((((((('''''''''&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&''')))(((&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%###""""""###%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%&&&''''''((((((''''''&&&&&&&&&&&&%%%%%%$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''((())))))))))))'''%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&'''&&&$$$$$$''')))(((''''''&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&###""""""$$$&&&%%%###%%%%%%%%%$$$$$$#########"""############$$$$$$$$$"""###$$$%%%%%%%%%$$$$$$######$$$$$$$$$$$$##############################$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$&&&%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$#########$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''((((((((((((((((((((((((''''''&&&&&&&&&'''((((((''''''(((((((((((('''''''''''''''(((((('''''''''''''''''''''((((((((((((***************************)))))))))))))))))))))************************(((***+++***)))((()))***(((((()))******+++,,,,,,((()))+++,,,,,,+++)))(((------,,,++++++***))))))''''''((()))))))))))))))))))))((((((((('''''''''((('''''''''&&&&&&&&&&&&%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&''')))(((&&&%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$""""""$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%&&&&&&'''''''''''''''%%%&&&&&&&&&%%%%%%$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&'''((((((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""!!!!!! %%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&'''&&&$$$$$$&&&(((%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''$$$"""!!!"""$$$&&&&&&%%%$$$$$$###############""""""############$$$$$$$$$"""###$$$%%%%%%%%%%%%$$$"""##################"""########################$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$&&&%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&%%%%%%$$$$$$$$$$$$%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%&&&&&&'''(((((((((((((((((((((((())))))((('''''''''((((((%%%'''(((******((('''%%%''''''&&&&&&&&&&&&''''''''''''''''''((((((((((((************************))))))))))))))))))******************************(((***+++***)))((()))***((())))))******+++++++++((()))***+++++++++)))))),,,,,,,,,+++******))))))'''(((((()))))))))))))))(((((('''''''''&&&&&&&&&''''''''''''&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''((('''&&&%%%$$$$$$$$$%%%########################%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%&&&'''''''''''''''%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&###$$$%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########"""""""""%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''&&&$$$$$$%%%'''######$$$$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''###"""""""""###$$$$$$$$$$$$$$$$$$$$$############""""""#########$$$$$$$$$######$$$$$$%%%%%%%%%%%%""""""############""""""########################%%%$$$###""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########"""""""""######$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''(((((((((((((((((((((((())))))((('''&&&&&&&&&'''((()))***++++++***)))((('''&&&%%%$$$$$$%%%&&&'''''''''''''''((((((((((((************************)))))))))))))))*********************************(((***+++***)))((()))***((()))))))))*********+++((()))******+++******))),,,+++++++++******))))))(((((())))))))))))((((((''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%&&&'''''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&######$$$%%%&&&&&&&&&'''''''''''''''''''''''''''%%%%%%%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%'''((()))***%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''######"""!!!!!! !!!"""$$$%%%%%%%%%%%%%%%%%%%%%""""""#########$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%""""""############""""""########################&&&%%%$$$######$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########"""""""""######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%&&&&&&'''((((((((((((((((((((((((((((((((('''&&&%%%%%%%%%%%%+++***)))(((((()))***+++'''&&&%%%$$$$$$%%%&&&'''''''''''''''(((((((((((())))))))))))))))))))))))(((((())))))************************************(((***+++***)))((()))***)))))))))))))))*********(((((())))))************++++++***************)))(((((())))))))))))((((((&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''&&&%%%$$$$$$###"""'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$%%%%%%&&&'''&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%''')))***+++,,,%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''###$$$$$$"""  """%%%%%%%%%%%%%%%&&&&&&&&&"""############$$$$$$$$$$$$$$$######$$$$$$%%%&&&"""##################"""########################%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%''''''''''''&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&''''''((((((((((((((((((((((((((('''&&&&&&%%%%%%%%%&&&&&&***((('''%%%%%%'''(((***''''''&&&&&&&&&&&&''''''''''''''''''(((((((((((())))))))))))))))))))))))((((((((()))******++++++++++++++++++++++++++++++(((***+++***)))((()))***))))))))))))))))))))))))'''((((((((()))******+++************************)))))))))))))))(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&(((((('''&&&%%%$$$######'''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$%%%&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$"""###%%%&&&&&&%%%'''&&&&&&%%%$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''###$$$%%%$$$"""!!!###%%%######$$$$$$%%%%%%%%%%%%"""############$$$$$$$$$$$$$$$#########$$$%%%&&&######$$$$$$$$$$$$####################################$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((((((((((((((((((((('''&&&&&&&&&&&&''''''(((((((((''''''''''''(((((('''''''''(((((('''''''''''''''''''''(((((((((((())))))))))))))))))))))))'''(((((()))******++++++++++++++++++++++++++++++(((***+++***)))((()))***)))))))))))))))))))))((('''''''''((())))))***+++))))))))))))************)))))))))))))))(((''''''''''''''''''&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''###$$$%%%%%%%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$%%%&&&&&&&&&&&&%%%###$$$%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$"""!!!"""%%%''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''"""$$$&&&%%%$$$$$$&&&)))""""""######$$$$$$$$$$$$"""############$$$$$$$$$%%%$$$#########$$$%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$########################!!!"""###$$$$$$###"""!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$"""###$$$%%%&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''###$$$&&&'''((('''&&&&&&(((((((((((((((((((((((('''&&&&&&&&&&&&'''(((((((((((((((((((((((((((((('''''''''''''''((()))***((()))***++++++***)))(((&&&'''((())))))((('''&&&''''''''''''((((((((()))))))))))))))))))))))))))'''(((((()))***+++++++++++++++++++++++++++++++++(((***+++***)))((()))***))))))))))))((((((((((((''''''''''''((()))++++++)))))))))))))))*********)))))))))))))))(((''''''(((((('''''''''&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%&&&'''))))))***'''&&&&&&%%%%%%&&&&&&'''"""###%%%%%%&&&%%%$$$###########################%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%###$$$%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$######$$$%%%(((***+++&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###!!! """%%%((((((&&&$$$%%%%%%&&&&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''""""""###$$$$$$$$$$$$###########################$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###""""""######$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$######""""""$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$######$$$%%%$$$###((('''&&&&&&%%%%%%%%%%%%'''&&&$$$######$$$&&&'''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&!!!!!!"""&&&***+++)))&&&(((((((((((((((''''''&&&((('''&&&&&&&&&&&&'''(((((((((((((((((((((((((((+++)))'''&&&%%%&&&'''((())))))))))))))))))))))))%%%&&&&&&''''''&&&&&&%%%''''''((((((((((((((((((+++++++++***************///...,,,*********,,,---$$$%%%(((***,,,,,,,,,,,,++++++************++++++))))))))))))))))))))))))++++++++++++++++++++++++))))))(((''''''''''''''''''''''''(((((((((((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''""""""###$$$$$$%%%&&&&&&###$$$%%%%%%&&&&&&&&&&&&((('''%%%$$$###$$$%%%%%%######$$$%%%%%%&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$''''''&&&%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###"""###$$$%%%&&&%%%%%%''''''((((((((('''(((((('''''''''&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$%%%&&&'''(((((((((((((((''''''&&&&&&''''''(((&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&((('''%%%$$$$$$%%%'''(((&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&)))'''&&&&&&'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&!!!!!!"""###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###""""""######$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$#########"""$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$######$$$%%%%%%$$$%%%$$$##################&&&%%%$$$######$$$%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&###""""""%%%((()))(((%%%&&&&&&'''(((((((((((((((+++***((('''&&&&&&&&&'''((((((((((((((((((((((((***)))'''&&&&&&&&&((((((((((((((((((((((((((((((&&&''''''((((((''''''&&&((((((((((((((('''''''''))))))))))))))))))))))))---,,,+++***)))******+++(((((()))***************++++++************++++++))))))))))))))))))))))))************************))))))((('''''''''''''''&&&&&&'''''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%$$$$$$$$$###$$$%%%%%%&&&&&&&&&%%%'''&&&%%%$$$$$$$$$%%%%%%######$$$%%%%%%&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$''''''&&&%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&'''(((%%%%%%&&&&&&&&&'''''''''((('''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&'''(((((((((''''''&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&'''&&&%%%$$$$$$%%%&&&'''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&'''%%%$$$$$$&&&'''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&& !!!!!!"""###"""""""""%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######"""#########$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$######%%%&&&%%%$$$##################$$$%%%%%%$$$###""""""###$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&$$$$$$$$$&&&'''&&&%%%$$$%%%&&&'''((()))******---+++)))'''&&&%%%%%%%%%((((((((((((((((((((((((***)))'''&&&&&&'''(((((((((((((((((((((((((((((('''(((((((((((((((((('''))))))(((((('''''''''&&&''''''''''''''''''''''''***************))))))))),,,+++***)))((((((((((((++++++************++++++))))))))))))))))))))))))(((((((((((((((((((((((())))))((('''''''''''''''%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''))))))(((&&&%%%$$$###"""$$$$$$%%%&&&&&&&&&%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%###$$$$$$%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%$$$$$$''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&'''(((&&&%%%$$$$$$$$$%%%&&&'''''''''''''''&&&&&&&&&&&&'''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$#########$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$######$$$%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&&&&$$$###$$$&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&!!!!!!"""###############%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$######%%%&&&&&&%%%&&&%%%%%%%%%&&&'''(((((($$$$$$###""""""###$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%%%%&&&&&&&&&%%%%%%&&&&&&'''((())))))+++***(((&&&%%%%%%%%%&&&(((((((((((((((((((((((()))(((''''''''''''((((((((((((((((((((((((((((((''''''(((((((((((('''''')))))))))(((''''''&&&&&&&&&&&&'''''''''''''''((()))******++++++***)))))),,,+++***((((((((())))))++++++************++++++))))))))))))))))))))))))(((((((((((((((((((((((())))))((('''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''***))))))'''&&&%%%$$$###$$$%%%%%%&&&&&&%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$%%%%%%&&&%%%###""""""###%%%'''&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$"""######$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&%%%$$$%%%'''))))))(((&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$###$$$%%%''''''&&&'''''''''''''''((()))***$$$##################$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%))))))((('''&&&&&&'''(((((('''&&&&&&&&&&&&''''''((('''&&&%%%%%%%%%&&&'''(((((((((((((((((((((((((((((('''''''''(((((((((''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%))))))(((((('''''''''&&&'''''''''(((((()))))))))******++++++,,,++++++******)))((((((((()))***+++++++++************++++++))))))))))))))))))))))))))))))))))))))))))))))))))))))((('''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((((((((''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%###""""""###%%%&&&%%%%%%&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%######$$$&&&'''((('''&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$#########"""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$###$$$&&&'''''''''&&&%%%%%%%%%%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&'''(((((('''&&&((())))))(((&&&%%%%%%%%%&&&'''((('''&&&%%%%%%&&&'''((((((((((((((((((((((((((('''''''''(((((((((((((((''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&%%%%%%((((((((((((((((((((((((((((((((())))))******+++*********++++++++++++,,,(((((((((((()))***,,,,,,++++++************++++++))))))))))))))))))))))))))))))))))))))))))))))))))))))((('''''''''''''''%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''''''''%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&&&&%%%$$$#########$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&'''''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&'''%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%&&&&&&&&&%%%%%%$$$%%%&&&''''''&&&%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%&&&&&&''''''&&&&&&$$$"""!!!"""$$$%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######""""""###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$###$$$&&&(((((('''%%%%%%$$$#########$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$ ###&&&'''&&&&&&''')))'''&&&%%%$$$$$$&&&'''(((+++***)))(((''''''((((((((((((((((((((((((((((((&&&''''''(((((((((((((((''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&&&&&&&''''''((()))))))))'''(((((())))))***++++++***))))))((()))***+++,,,'''((()))******+++++++++++++++************++++++))))))))))))))))))))))))''''''''''''''''''''''''))))))((('''''''''''''''&&&&&&'''''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&%%%%%%$$$######$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%$$$$$$###$$$$$$$$$###$$$&&&''''''&&&$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%&&&'''(((((()))***''''''''''''''''''''''''$$$$$$%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%###$$$%%%%%%&&&&&&&&&&&&$$$&&&'''(((((('''&&&$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&%%%###$$$%%%&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&""""""###$$$$$$$$$$$$###########################$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$###$$$&&&(((((((((&&&&&&%%%$$$############$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$ %%%'''&&&%%%&&&(((%%%%%%$$$###$$$&&&)))***///...,,,***((((((((((((((((((((((((((((((((((((&&&&&&'''((())))))((((((''''''''''''''''''''''''''''''((((((((((((''''''%%%%%%&&&'''((()))******'''''''''((()))******+++)))((('''&&&'''(((***,,,'''(((***++++++***))))))++++++************++++++))))))))))))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&))))))(((''''''''''''''''''''''''(((((((((((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$###"""###%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%$$$$$$######$$$$$$###$$$&&&''''''&&&$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&%%%$$$$$$%%%&&&&&&&&&&&&%%%$$$###$$$$$$$$$%%%%%%&&&&&&&&&###$$$%%%&&&''')))******''''''''''''''''''''''''%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&'''''''''%%%&&&&&&''''''&&&&&&%%%"""###$$$%%%&&&'''''''''%%%&&&((())))))(((&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&+++)))(((((()))))))))(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######"""%%%%%%%%%$$$$$$######### !!!"""###$$$%%%%%%%%%$$$###!!!!!!###$$$%%%###$$$$$$%%%%%%$$$$$$###'''&&&&&&%%%$$$###"""""""""###$$$%%%%%%$$$###"""######$$$%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$ !!!"""###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&&&&%%%$$$$$$&&&''''''''''''&&&%%%%%%%%%%%%&&&'''$$$$$$&&&'''(((((((((((()))(((&&&%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&'''(((((((((((((((((((((((((((((()))((('''&&&&&&'''((()))))))))(((((('''''''''&&&''''''''''''((((((((()))&&&%%%$$$$$$$$$&&&(((***))))))))))))******************))))))))))))******((()))************)))(((%%%""" ###)))---,,,)))))))))(((((('''''''''&&&)))(((((((((''''''''''''&&&'''''''''(((((())))))&&&''''''((((((((((((((("""%%%'''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%%%%%%%%%%%%%######$$$$$$%%%&&&''''''######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$ !!!###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((((((((((((((((((((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&''''''''')))(((&&&$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%))))))))))))))))))))))))$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%%%%&&&'''%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$###&&&&&&''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%&&&&&&''''''&&&&&&''''''''''''&&&%%%$$$###%%%%%%%%%$$$$$$#########%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$$$$$$$$$$%%%&&&&&&+++***((('''&&&&&&&&&'''$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###&&&%%%%%%$$$$$$###############$$$%%%%%%$$$############$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''&&&&&&&&&&&&#########$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&'''&&&$$$%%%&&&''''''&&&'''&&&%%%%%%%%%%%%&&&'''%%%&&&''''''((((((((((((((('''&&&&&&&&&'''((()))''''''&&&&&&&&&''''''((((((((((((((((((((((((((()))((('''&&&&&&'''((())))))((((((((('''''''''''''''''''''((((((((())))))%%%&&&''''''(((((((((((((((((()))))))))***************))))))))))))******++++++++++++++++++++++++)))&&&$$$%%%(((***)))'''))))))((((((((('''''''''))))))((((((((('''''''''''''''''''''((((((((()))&&&&&&'''(((((((((((((((###%%%''')))***)))(((&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%%%%&&&'''%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&&&&%%%%%%$$$#########%%%&&&''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&$$$%%%&&&&&&''''''&&&&&&''''''''''''&&&%%%$$$###%%%%%%%%%$$$$$$$$$######%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&''')))((('''&&&%%%%%%&&&&&&"""######$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$###)))(((((('''&&&%%%$$$$$$"""###%%%''''''%%%###"""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$%%%%%%%%%%%%$$$######$$$$$$$$$$$$######$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$((('''''''''&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&''')))'''&&&&&&'''''''''&&&'''&&&&&&%%%%%%&&&&&&'''''''''(((((((((((((((''''''&&&&&&'''''')))******(((''''''&&&&&&&&&''''''((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((''''''''''''''''''((((((((()))))))))%%%''')))******)))(((&&&(((((())))))))))))************))))))))))))******---,,,+++******+++,,,---***)))(((''''''((((((((())))))(((((((((((('''''')))))))))(((((((((''''''''''''''''''((((((((((((&&&&&&'''((((((((((((''''''(((***++++++***(((''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%)))(((&&&%%%$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&%%%$$$$$$!!!"""###%%%&&&''''''(((''''''&&&&&&&&&&&&''''''$$$%%%&&&&&&''''''&&&&&&&&&''''''&&&&&&%%%$$$###%%%%%%%%%$$$$$$$$$$$$###%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((((((''''''''''''&&&&&&&&&&&&&&&%%%&&&''''''(((&&&&&&%%%%%%%%%%%%%%%&&&#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$###""""""!!!"""###$$$%%%%%%$$$###"""###$$$$$$%%%%%%$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$"""######$$$$$$######""" !!!"""###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###""""""!!!!!!%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%&&&''''''***(((&&&&&&''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((((()))(((((('''''''''''''''''''''(((((()))(((((('''&&&&&&&&&&&&'''(((((((((((((((((((((((((((((((((''''''((((((((((((((((((((((((''''''''''''(((((((((((()))))))))'''((()))******)))((('''(((((((((((()))))))))*********))))))))))))******+++***(((''''''(((***+++'''((()))(((((((((***,,,))))))(((((((((((((((((()))))))))((((((((((((''''''''''''(((((((((((((((%%%&&&''''''((((((''''''$$$%%%'''(((((('''%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&+++)))&&&$$$###$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&"""###%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$"""###$$$%%%&&&''''''''''''''''''&&&&&&'''''''''$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&&&&&&&&&&'''&&&&&&&&&&&&'''((((((%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$############""""""""""""$$$###"""!!!!!!"""###$$$###$$$$$$%%%%%%$$$$$$############$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$"""######$$$$$$######"""!!!"""$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""!!! %%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%&&&''''''***(((&&&&&&&&&'''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''((((((((((((((('''&&&''''''''''''&&&&&&%%%%%%(((''''''&&&&&&&&&''''''(((((((((((((((((((((((('''((((((((((((((((((''''''''''''((((((((((((((((((((((((((()))))))))***)))((((((''''''(((******'''(((((((((((()))))))))******))))))))))))******+++***(((''''''(((***+++'''((()))((('''((()))+++(((((())))))))))))))))))***)))))))))((((((((((((((((((((((((((('''''''''%%%&&&&&&'''''''''''''''!!!"""###$$$%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%$$$$$$%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''((((((''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&"""###%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%%%%&&&''''''''''''&&&&&&%%%'''''''''&&&&&&'''''''''$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&'''''''''&&&&&&&&&%%%%%%$$$######"""###$$$$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%%%%$$$"""!!!!!!"""$$$%%%###$$$$$$%%%%%%$$$$$$############$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%######$$$%%%%%%%%%%%%$$$######$$$$$$$$$$$$###### !!!###$$$&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######"""""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&'''(((&&&%%%%%%&&&&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&'''''''''''''''&&&''''''''''''&&&%%%$$$###&&&&&&&&&&&&&&&'''((((((((((((((((((((((((((((((''''''(((((((((((('''''''''''''''(((((((((((((((((((((((()))))))))*********)))((('''(((***,,,...''''''(((((((((((())))))******))))))))))))******---,,,+++******+++,,,---+++***)))((('''''''''&&&(((((())))))))))))************)))))))))(((((((((((((((((((((((('''''''''%%%%%%&&&''''''''''''&&&"""###$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&(((((((((((('''''''''''''''&&&&&&&&&&&&%%%%%%%%%###$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%(((((((((((('''&&&%%%%%%''''''&&&&&&&&&&&&''''''$$$%%%&&&&&&''''''&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&''''''(((&&&&&&''''''''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$############$$$%%%######$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$#########$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&$$$######%%%&&&&&&%%%%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%&&&'''''''''&&&&&&&&&'''(((((('''&&&%%%%%%%%%%%%&&&'''((()))***((((((((((((((((((((((((&&&'''((())))))((('''&&&''''''''''''((((((((()))(((((()))))))))******************+++---...000000'''''''''((((((((())))))******))))))))))))******+++++++++++++++++++++++++++(((%%%&&&(((((('''%%%(((((()))))))))******************)))))))))(((((()))(((((((((''''''''''''$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$%%%%%%&&&"""######$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""$$$%%%''''''&&&%%%$$$%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&'''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&&&&%%%&&&&&&'''''''''&&&%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&$$$%%%&&&&&&''''''&&&&&&###$$$$$$%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%&&&&&&'''&&&&&&''''''&&&%%%$$$############$$$$$$%%%&&&&&&#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&((())))))(((&&&%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%######$$$%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$######!!! $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$###""""""$$$&&&&&&%%%%%%%%%&&&''''''&&&%%%%%%"""###$$$%%%&&&&&&'''&&&%%%&&&''')))))))))(((((($$$$$$%%%%%%'''(((***+++((((((((((((((((((((((((&&&'''((())))))((('''&&&&&&'''''''''(((((())))))))))))))))))************)))***---000222222222111''''''''''''((((((((()))******))))))))))))******((()))************)))(((((($$$!!!###))),,,***'''(((((())))))*********+++************))))))))))))))))))(((((('''''''''&&&$$$%%%&&&&&&''''''&&&&&&)))(((((('''&&&&&&%%%%%%'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$%%%%%%&&&!!!!!!"""###$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###%%%''''''&&&%%%$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''''''''&&&&&&%%%%%%%%%'''&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((((('''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&###$$$%%%%%%&&&&&&&&&&&&###$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%&&&&&&''''''&&&&&&###$$$$$$%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((%%%$$$$$$$$$$$$%%%&&&&&&%%%%%%&&&&&&%%%###"""!!!""""""######$$$$$$$$$%%%%%%%%%%%%%%%$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$###"""############$$$$$$$$$%%%$$$$$$%%%'''(((((('''$$$""""""$$$&&&&&&###$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$"""""""""!!!!!!!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%$$$$$$######%%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''%%%$$$%%%'''&&&&&&&&&''''''''''''((((((''''''&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&)))))))))))))))(((((((((%%%&&&'''(((((('''&&&%%%'''(((***++++++)))'''&&&***---333:::===999111)))******))))))))))))*********)))))))))))))))***+++************))))))))))))))))))))))))))))))))))))(((((())))))*********+++))))))))))))((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%)))'''&&&$$$$$$%%%&&&''''''''''''&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&######$$$%%%&&&&&&'''(((&&&&&&&&&&&&%%%%%%$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%''''''&&&%%%%%%%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&))))))))))))((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((''''''((('''%%%$$$###$$$%%%%%%(((((('''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((('''&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$(((''''''&&&&&&%%%$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$###############$$$$$$$$$$$$&&&$$$$$$$$$&&&'''&&&%%%$$$###"""###%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%############"""""""""!!!%%%%%%%%%$$$$$$$$$#########$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$###$$$&&&&&&&&&&&&''''''''''''((((((''''''&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''&&&&&&'''(((((('''&&&&&&'''((())))))***)))((((((+++000888>>>???999000******))))))(((((())))))***))))))(((((('''(((((())))))))))))(((((((((((('''))))))))))))))))))))))))(((((()))))))))*********))))))))))))((((((((('''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&)))((('''%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%)))'''&&&$$$$$$%%%&&&'''&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&((((((((((((((((((((()))&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''&&&%%%$$$$$$$$$%%%%%%(((''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((('''&&&%%%%%%%%%%%%%%%%%%&&&&&&'''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$######"""###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###############$$$$$$$$$%%%&&&%%%###$$$%%%%%%$$$"""&&&&&&%%%###"""###&&&((($$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%############""""""""""""%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%######$$$%%%&&&&&&&&&''''''''''''(((''''''&&&&&&&&&''''''(((&&&&&&''''''''''''&&&&&&$$$$$$$$$%%%&&&&&&''''''&&&&&&'''(((((('''&&&&&&''''''''''''((()))******---555???DDD@@@777///***))))))(((((((((((())))))))))))((('''&&&&&&&&&&&&((((((((((((''''''''''''))))))))))))))))))))))))(((((())))))))))))******)))))))))(((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&***)))(((&&&$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%$$$%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$#########"""%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&'''''''''((()))))))))((('''''''''&&&&&&%%%%%%(((''''''&&&%%%$$$$$$###&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&%%%$$$$$$$$$%%%%%%'''''''''&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%&&&'''''''''%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$######"""""""""!!!!!!###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%&&&%%%######$$$###""" %%%''''''%%%!!! """%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%########################%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%$$$$$$%%%&&&&&&&&&&&&''''''''''''((('''&&&&&&&&&&&&'''((((((&&&&&&''''''''''''&&&&&&######$$$%%%&&&&&&''''''&&&''''''''''''''''''&&&''''''&&&%%%&&&(((***,,,...999DDDGGG@@@555---***)))((((((''''''(((((()))***)))((('''&&&&&&&&&&&&))))))((((((((('''''''''(((((((((((((((((((((((((((((())))))))))))))))))))))))((((((((('''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&'''$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%&&&'''(((((())))))(((((((((''''''&&&%%%%%%(((''''''&&&%%%$$$######&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&######""""""!!!!!!!!! !!!"""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%&&&%%%############!!!"""%%%%%%"""!!!"""$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$##############################$$$$$$$$$$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&&&&%%%%%%&&&(((&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&'''((((((&&&&&&''''''''''''&&&&&&$$$$$$%%%&&&'''(((((()))'''''''''&&&&&&'''''''''((('''%%%%%%%%%(((***,,,...999CCCEEE<<<111+++***((((((''''''''''''((((((+++***)))(((''''''&&&&&&*********)))))))))(((((((((((((((((((((((((((((())))))((((((((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%%%%&&&''''''((($$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%&&&'''&&&&&&%%%$$$$$$$$$$$$%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&'''(((((()))(((((('''''''''&&&&&&&&&'''&&&&&&%%%$$$#########&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&"""""""""""""""!!!!!!!!! !!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%############""" !!!$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$######"""########################"""######$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&&&&&&&&&&''')))&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&'''((()))&&&&&&''''''''''''&&&&&&&&&&&&''''''(((((())))))((('''&&&&&&&&&&&&'''(((((('''&&&%%%%%%''')))+++...666>>>===666---******''''''&&&&&&&&&&&&''''''******)))(((''''''''''''************))))))))))))))))))))))))))))))))))))))))))((((((((((((''''''((((((((('''''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%&&&'''((())))))$$$$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%$$$#########%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&############$$$$$$$$$$$$!!!!!!"""######$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%######$$$$$$###!!!!!!$$$&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$########################"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""$$$%%%&&&%%%%%%'''(((&&&&&&&&&''''''''''''(((&&&%%%%%%&&&&&&((())))))&&&&&&''''''''''''&&&&&&'''''''''''''''(((((((((((('''&&&&&&&&&&&&'''(((((('''&&&&&&&&&'''((((((---111555444///***)))***'''&&&&&&&&&&&&&&&&&&'''(((((('''&&&&&&'''''''''***))))))))))))((((((((())))))))))))))))))))))))))))))((((((((('''''''''(((((('''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''''''''###$$$%%%%%%&&&&&&&&&%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%&&&'''(((&&&%%%$$$$$$###$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%&&&&&&''''''''''''''''''((((((((((((&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$######$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$%%%&&&&&&$$$############$$$%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&'''!!!""""""############"""$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%###$$$%%%%%%$$$###)))%%%!!! ###$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%&&&&&&""""""""""""""""""""""""######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&'''''''''#########$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!###$$$$$$$$$$$$&&&'''&&&&&&&&&'''''''''((((((%%%%%%%%%&&&'''((()))***&&&''''''''''''''''''&&&''''''''''''''''''&&&&&&((('''&&&%%%%%%&&&'''((((((''''''&&&&&&&&&'''''',,,...000...+++(((((()))'''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%%%%&&&'''''')))(((((((((''''''''''''))))))))))))))))))))))))))))))(((((('''''''''&&&(((((('''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$&&&%%%%%%$$$$$$#########$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$###$$$%%%%%%&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%&&&'''(((&&&%%%$$$$$$######$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%"""######$$$%%%&&&''''''(((((())))))******++++++&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$###"""###%%%&&&'''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&######""""""######$$$%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$#########%%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%"""######$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""""""""###%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$##################&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$"""###%%%'''(((((('''&&&)))((('''&&&&&&'''((())),,,+++***(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''')))***+++***((('''))))))))))))))))))))))))(((((('''''''''&&&&&&&&&)))))))))))))))******+++)))'''&&&'''***+++***(((''''''(((((())))))******''''''''''''''''''''''''((((((''''''''''''((((((&&&&&&''''''(((((())))))%%%%%%%%%&&&&&&'''''''''+++***)))'''&&&%%%$$$###'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%%%%%%%&&&'''+++***)))(((&&&$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$######$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$###$$$%%%&&&'''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%#########%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$'''''''''(((((((((((()))******))))))((((((''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%%%%%%%%%%'''&&&%%%$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$''''''''''''''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''%%%%%%%%%$$$$$$$$$######%%%%%%%%%$$$$$$$$$#########$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$#########&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%###$$$%%%&&&''''''''''''(((((('''&&&&&&'''((((((***))))))(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&((()))))))))'''&&&(((((((((((((((((((((((((((((('''''''''&&&&&&&&&)))(((((((((((()))******(((&&&%%%&&&(((***(((''''''((((((((((((((())))))''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''''''''((((((((((((%%%%%%%%%&&&&&&&&&''''''))))))((('''&&&%%%$$$$$$'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$$$$$$$$$$%%%&&&((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$######$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$######%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&'''''')))))))))(((((((((''''''&&&&&&&&&%%%$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&''''''''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''(((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''((('''&&&&&&(((((((((((((((((((((((('''''''''''''''&&&&&&&&&(((''''''''''''((())))))((('''&&&''')))***)))(((((((((((('''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''''''''''''''%%%%%%%%%&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%&&&''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$###$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%((((((((((((((('''''''''(((((('''&&&%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''((()))((('''&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&''''''((((((''''''$$$%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&(((((((((((((((((((((((('''''''''''''''''''''''''''&&&&&&&&&&&&'''((((((+++*********+++++++++***((((((''''''&&&&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&''''''&&&&&&&&&(((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$%%%&&&&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$############$$$$$$$$$$$$''''''''''''''''''''''''((((((''''''&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''')))******((('''%%%$$$%%%&&&''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###############$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&''''''((((((''''''%%%%%%%%%&&&&&&''''''''''''&&&%%%$$$%%%&&&'''(((%%%&&&&&&&&&&&&&&&&&&%%%###$$$%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((''''''''''''''''''''''''&&&'''''''''''''''''''''&&&&&&&&&&&&&&&''''''(((***+++++++++*********+++((((((''''''&&&&&&%%%%%%''''''''''''''''''''''''&&&'''(((((((((((('''&&&((((((''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&''''''((('''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&'''''''''&&&&&&&&&''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$######"""%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%'''(((******)))'''&&&$$$%%%&&&''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&''''''(((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&%%%%%%&&&&&&'''&&&&&&''''''''''''&&&&&&###$$$&&&'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''(((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&'''((((((((()))***)))'''&&&'''(((((((((((('''''''''''''''''''''''''''''''''''''''&&&'''((())))))((('''&&&'''''''''&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%###$$$$$$%%%&&&''''''''''''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''&&&%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&$$$%%%%%%&&&'''((())))))''''''''''''''''''''''''$$$$$$%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''((()))(((''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################!!!"""###$$$%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$############$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((((((&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&%%%&&&&&&'''&&&&&&%%%%%%&&&'''(((((((((((('''&&&$$$%%%'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&'''(((''''''''''''''''''''''''&&&&&&&&&'''''''''(((((('''''''''&&&'''(((((()))'''(((***(((&&&%%%&&&((('''((((((((((((((())))))''''''''''''''''''''''''%%%&&&((())))))(((&&&%%%%%%&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%&&&&&&&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&(((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&((('''&&&%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&''''''(((''''''''''''''''''''''''&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""!!!"""###$$$%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((())))))&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%%%%&&&&&&%%%%%%((((((((('''&&&&&&&&&%%%%%%&&&'''''''''&&&%%%$$$&&&'''((())))))((('''&&&%%%&&&((())))))(((&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&'''''''''''''''''''''''''''&&&&&&&&&'''''''''(((((((((''''''''''''((())))))(((***+++***'''&&&''')))''''''(((((())))))******''''''''''''''''''''''''$$$%%%'''(((((('''%%%$$$%%%%%%%%%&&&&&&''''''''''''''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%&&&&&&%%%$$$###$$$$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&(((((((((&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&)))((('''&&&%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%(((((((((((((((((((((((((((((())))))(((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((''''''%%%$$$$$$%%%''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######$$$%%%&&&%%%$$$$$$$$$######""""""$$$$$$######$$$&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%&&&&&&&&&%%%$$$###$$$%%%&&&$$$"""%%%%%%$$$$$$###$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$#########""""""$$$$$$############$$$$$$"""############$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########!!!"""$$$%%%&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((((()))''''''''''''''''''&&&&&&###$$$&&&'''((('''&&&&&&'''&&&$$$""""""$$$&&&(((&&&&&&&&&'''''''''((((((&&&%%%%%%%%%%%%&&&''''''"""###$$$&&&(((+++---...'''((()))******)))((('''))))))((((((''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$###$$$%%%%%%$$$"""######%%%%%%%%%%%%######&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&#########$$$%%%&&&'''(((((('''&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$'''''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&!!!""""""###%%%&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%)))((('''&&&%%%$$$$$$$$$%%%%%%%%%&&&'''(((((()))***++++++***((('''((()))(((''''''&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((())))))%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&&&&%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$#########$$$$$$$$$######$$$$$$%%%&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$#########%%%$$$$$$$$$$$$$$$$$$%%%############"""""""""!!!$$$$$$######$$$&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%%%%%%%%%%$$$###$$$%%%&&&$$$"""%%%%%%%%%$$$$$$%%%&&&&&&######""""""""""""######$$$$$$$$$#########""""""$$$$$$############$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((''''''''''''''''''&&&&&&%%%&&&''''''((((((((('''((('''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''(((%%%%%%&&&&&&((()))***+++(((((())))))))))))((((((((((((((((((''''''&&&&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%&&&'''(((&&&$$$%%%%%%&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&''''''''''''&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$(((((('''%%%%%%$$$$$$%%%$$$$$$%%%&&&&&&'''(((((()))***+++***)))((()))***(((((('''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%$$$&&&%%%$$$$$$######$$$$$$$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$$$$%%%$$$###$$$%%%&&&$$$"""%%%%%%%%%%%%%%%&&&'''(((""""""!!!!!!!!!!!!""""""$$$$$$$$$###############$$$$$$############$$$$$$############$$$$$$$$$%%%$$$############$$$%%%%%%$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###'''&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&''''''(((''''''''''''((())))))((()))*********((('''&&&'''''''''''''''&&&&&&&&&&&&&&&&&&%%%&&&&&&'''(((((((((''''''''''''(((((())))))(((((((((((())))))'''''''''''''''&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%&&&(((((('''%%%''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$########################%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$######((('''&&&%%%%%%$$$$$$%%%$$$$$$%%%%%%&&&'''''''''((()))******)))((()))+++***)))((('''&&&%%%%%%$$$%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&'''((((((&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$#########%%%%%%$$$$$$######$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&%%%%%%###$$$%%%&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$###"""$$$$$$###$$$%%%&&&$$$"""#########$$$%%%&&&'''(((######""""""""""""##############################$$$$$$############$$$$$$#########$$$$$$$$$%%%%%%######""""""######$$$%%%$$$######""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$)))(((&&&%%%$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&'''''')))((('''&&&&&&'''((()))((((((((((((((('''&&&%%%&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&'''(((((()))((((((''''''''''''(((***)))(((''''''((()))***''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$###%%%&&&'''%%%$$$''''''((((((((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$%%%%%%$$$$$$%%%&&&&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$'''&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&'''''''''(((%%%'''((((((''''''(((***,,,+++***)))(((''''''&&&%%%%%%%%%%%%%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%$$$######"""%%%%%%$$$$$$###$$$$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$###""""""$$$$$$###$$$%%%&&&$$$"""""""""""""""###$$$&&&&&&%%%$$$$$$######$$$$$$%%%########################$$$$$$############$$$$$$###$$$$$$$$$$$$%%%%%%%%%######""""""######$$$%%%$$$######""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$)))(((&&&%%%$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&&&&''''''((('''&&&%%%%%%%%%''''''(((&&&$$$###"""###$$$%%%###$$$%%%&&&''')))******'''&&&&&&&&&&&&'''(((((('''''''''''''''((())))))***)))(((''''''((()))***''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$###%%%''''''&&&$$$'''&&&&&&&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%'''''''''''''''(((((((((###%%%&&&&&&%%%%%%'''(((,,,,,,++++++***)))))))))&&&&&&&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&%%%$$$$$$###%%%$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$!!!!!!!!!!!!!!!"""""""""$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$###"""%%%$$$###$$$%%%&&&$$$""""""""""""""""""###$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%###############$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$############$$$%%%%%%$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%'''&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%%%%&&&&&&''''''''''''&&&%%%%%%%%%%%%&&&&&&$$$""" """%%%&&&###$$$%%%&&&''')))******''''''&&&&&&''''''((()))&&&&&&&&&'''''')))***+++))))))(((((((((((())))))'''''''''(((((((((((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''')))***)))'''&&&&&&%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$#########$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%&&&&&&(((''''''&&&%%%$$$######$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''%%%%%%$$$$$$$$$$$$%%%%%%''''''''''''''''''''''''$$$%%%&&&&&&%%%$$$%%%'''************************''''''''''''&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%(((((('''&&&%%%%%%$$$$$$'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&''''''%%%$$$$$$$$$$$$$$$$$$%%%!!!!!!!!!""""""#########$$$%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$######%%%$$$###$$$%%%&&&$$$"""$$$######"""######$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%""""""#########$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%###$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&###$$$$$$%%%&&&&&&'''''''''''''''''''''&&&%%%%%%$$$$$$######$$$%%%''''''&&&&&&&&&''''''''''''''''''''''''''''''(((((()))'''&&&&&&''''''((()))***(((((())))))))))))((((((((((((((()))))))))******((((((((((((''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''')))***)))(((&&&&&&%%%$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%$$$$$$######$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$###$$$$$$$$$%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&''''''''''''&&&%%%$$$###""""""$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((('''&&&%%%&&&'''&&&&&&''''''((()))))))))(((((((((((('''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&%%%$$$######$$$%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%&&&&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%$$$$$$%%%$$$###$$$%%%&&&$$$"""%%%%%%$$$$$$###$$$$$$$$$$$$$$$############$$$$$$""""""######$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%!!!"""$$$%%%&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&''''''######$$$%%%%%%&&&'''''''''((()))))))))(((&&&%%%###$$$&&&((())))))(((((())))))((('''&&&&&&%%%%%%'''''''''''''''((())))))(((((('''''''''(((((()))'''((()))******)))((('''(((((())))))******++++++)))(((((((((''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%(((((((((&&&'''&&&%%%$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$#########$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%""""""###$$$&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''###########################$$$%%%&&&&&&%%%$$$###$$$$$$%%%&&&&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&'''(((((($$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$###$$$$$$%%%%%%$$$#####################((()))***)))'''&&&&&&'''######$$$%%%&&&'''((()))))))))))))))((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&''''''(((&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$%%%%%%$$$#########$$$%%%%%%&&&$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$###"""""""""######$$$$$$%%%%%%$$$$$$###%%%$$$#########$$$%%%&&&&&&&&&%%%%%%$$$############$$$$$$$$$$$$###""""""########################%%%$$$#########$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&%%%$$$$$$###""""""%%%%%%%%%$$$$$$#########&&&&&&&&&&&&&&&&&&&&&&&&""" !!!%%%''''''%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%%%%$$$###"""&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$))))))((('''&&&%%%%%%$$$((((((((((((''''''''''''(((((((((((())))))))))))))))))(((((('''''''''&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&%%%&&&&&&''''''&&&&&&%%%'''''''''&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%###"""""""""######%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!###%%%'''((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&"""###$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%((((((((((((((((((((((((&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&(((((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''(((((($$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((())))))$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$#########$$$%%%&&&$$$$$$$$$$$$$$$#########$$$$$$$$$%%%$$$######"""######################## !!!###$$$%%%&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%"""!!! """%%%'''&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$((((((((('''&&&&&&%%%%%%'''''''''(((((()))))))))(((((((((((())))))))))))((((((((('''''''''&&&&&&'''&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&''''''&&&&&&%%%''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%###"""""""""###$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""######"""!!!%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&######$$$%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''***)))((('''&&&%%%$$$###%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%&&&'''''''''$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&''''''(((((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$######$$$$$$%%%&&&"""""""""############$$$%%%%%%%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$"""%%%'''&&&%%%$$$((((((''''''&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$######$$$%%%%%%&&&''''''%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""###%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$''''''''''''''''''''''''&&&&&&'''((()))***++++++(((((((((((())))))))))))(((((((((((('''''''''''''''''''''&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$############$$$$$$$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!"""$$$%%%&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&&&&&&&%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&***))))))(((''''''&&&&&&$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######"""######$$$###$$$$$$%%%%%%$$$$$$###$$$###$$$$$$$$$$$$%%%%%% !!!!!!"""######$$$$$$%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ ###$$$%%%%%%$$$###'''''''''&&&%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((''''''(((((()))******+++(((((((((((()))))))))))))))))))))))))))))))))(((''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((()))***)))))))))%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((()))******''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$######"""######$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$%%%%%%%%%%%% !!!"""###$$$$$$%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################%%%%%%%%%$$$$$$$$$#########$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((((((((()))))))))((((((((((((((((((((((((((())))))))))))************************''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%$$$$$$######""""""%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%'''((())))))***))))))((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&###$$$$$$%%%%%%$$$$$$###"""###$$$%%%%%%%%%%%%$$$!!!!!!""""""###$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%(((&&&%%%###"""######$$$###############$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&%%%$$$###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&'''''''''(((((()))((((((((('''''''''&&&(((((((((((())))))))))))************++++++++++++&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$***))))))(((''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''###$$$$$$%%%%%%$$$$$$###"""###$$$%%%%%%%%%$$$$$$"""#########$$$$$$%%%%%%$$$$$$$$$%%%$$$######"""%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%"""######$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&&&&%%%%%%!!!""""""######$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&&&&$$$###%%%'''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&''''''''''''(((((((((((())))))))))))((((((((())))))*********$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%&&&&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%$$$######$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$######%%%%%%&&&&&&'''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$%%%%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""""""""###$$$$$$%%%$$$$$$$$$%%%%%%$$$$$$$$$"""###$$$%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$###""""""%%%%%%%%%%%%%%%%%%%%%%%%"""$$$&&&((()))(((&&&%%%"""###$$$%%%&&&''''''(((%%%&&&&&&''''''&&&&&&%%% """###$$$%%%&&&#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""%%%'''&&&$$$###%%%((($$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$#########$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&''''''&&&$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''###$$$$$$%%%&&&'''(((((((((((((((((())))))))))))&&&'''''''''(((((())))))$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$%%%&&&&&&''''''&&&&&&%%%#########$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$"""###%%%&&&'''&&&%%%%%%######%%%''')))+++,,,---%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%(((((('''&&&%%%%%%$$$$$$&&&%%%%%%$$$$$$#########$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%$$$$$$###"""$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&&&&'''!!!!!!###$$$&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$#########$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$'''&&&%%%%%%$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&$$$"""$$$%%%%%%!!!"""#########""""""$$$&&&###%%%&&&&&&$$$######$$$%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###'''((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''((((((((((((%%%%%%&&&'''((((((((('''''''''((((((((((((''''''&&&&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$###$$$"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%%%%&&&'''((('''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&''''''''''''''''''''''''$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%'''&&&%%%$$$###$$$%%%%%%###$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''((((((''''''&&&&&&&&&%%%%%%%%%((('''%%%$$$$$$%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$#########$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$'''&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$###$$$$$$###!!!$$$%%%&&&$$$###"""$$$%%%!!!###%%%%%%$$$$$$%%%&&&%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&!!!$$$'''((('''%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''((((((((((((&&&&&&'''(((((((((''''''''''''((((((((((((''''''%%%%%%$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$###)))'''%%%$$$###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%&&&&&&''''''&&&%%%%%%$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''$$$%%%%%%%%%%%%%%%%%%&&&"""######$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''((('''&&&&&&%%%%%%&&&&&&'''&&&%%%$$$$$$$$$%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''''''(((''''''&&&&&&&&&%%%%%%%%%(((&&&%%%$$$$$$%%%&&&(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######"""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%$$$"""!!!!!!!!!&&&''''''&&&$$$######$$$ """$$$%%%%%%%%%&&&'''%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############"""%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))(((%%%#########%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''((((((((((((((((((((((((((('''&&&''''''(((((((((((('''''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%&&&''''''&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&&&&&&&''''''&&&%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&'''''''''''''''&&&&&&&&&%%%%%%%%%'''&&&%%%$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$"""%%%'''&&&"""!!!"""$$$###$$$&&&%%%$$$######$$$ """$$$%%%$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%)))(((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''%%%%%%''')))%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''(((((())))))))))))((('''&&&&&&&&&''''''((((((''''''&&&))))))((('''&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""!!!!!!"""$$$$$$ !!!"""#########""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################&&&&&&&&&%%%%%%$$$$$$$$$''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$&&&(((&&&###"""$$$''' ###$$$######$$$%%%###$$$&&&%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%)))(((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''&&&&&&''')))+++%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''(((((()))(((((('''&&&&&&&&&&&&''''''''''''&&&&&&)))((('''&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%!!!"""$$$&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$"""###$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$(((((('''&&&%%%$$$######$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$############"""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&%%%######%%%&&&"""#########$$$%%%###%%%&&&&&&$$$############$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&$$$%%%&&&''''''(((''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((('''%%%%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''''''''&&&%%%&&&&&&''''''''''''&&&&&&$$$$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%"""###$$$&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$"""###%%%&&&&&&&&&%%%$$$%%%%%%$$$$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$&&&&&&%%%$$$"""!!! $$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$###%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$"""#########$$$$$$$$$$$$"""###$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%$$$############""""""###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&'''$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%###!!!!!!"""$$$$$$### ###$$$$$$######$$$"""$$$%%%%%%$$$###$$$%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%$$$%%%&&&'''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''$$$%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%""""""""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%!!!""""""############"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$&&&'''''''''%%%$$$%%%$$$$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$$$$$$$#########%%%%%%%%%%%%&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$###$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$""""""######$$$$$$$$$$$$"""###$$$%%%&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%$$$############""""""###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&&&&'''&&&$$$$$$$$$$$$%%%%%%&&&'''%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%!!!"""$$$###!!! """%%%&&&%%%######### """$$$%%%%%%%%%&&&'''#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$$$$$$$$$$%%%&&&'''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###%%%''''''&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''######$$$%%%&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%"""""""""###$$$%%%''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%''''''''''''%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$&&&(((((('''&&&%%%$$$$$$$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%&&&''''''(((((()))&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%(((((('''&&&&&&&&&&&&'''%%%%%%&&&'''&&&%%%$$$######$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%###$$$$$$%%%%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$%%%###""" !!!###%%%'''$$$$$$$$$$$$$$$$$$$$$$$$$$$""" """%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$###"""!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$%%%&&&&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$#########%%%$$$$$$$$$###"""""""""!!!"""###%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###***)))&&&$$$$$$$$$%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&+++)))'''%%%$$$%%%&&&'''###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$(((((('''&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%''''''''''''%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&$$$###"""&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%$$$""" ######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""###$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&&&&%%%$$$###&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%&&&''''''((((((''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$######$$$$$$%%%&&&((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&''''''((('''''''''&&&&&&%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""" """$$$%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$#####################"""!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$###############$$$$$$$$$######"""%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$############### !!!"""###""""""!!!$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$%%%%%%%%%%%%$$$############$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%###$$$$$$%%%%%%$$$$$$###'''%%%###"""!!!!!!"""###$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&)))'''%%%#########$$$%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&%%%$$$$$$###""""""$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$######&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$###!!!!!!$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%&&&&&&'''''''''''''''&&&%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$$$$$$$%%%&&&&&&((('''&&&%%%%%%%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%!!!###$$$%%%%%%$$$"""!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$""" !!!###############$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######""""""#########"""!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%$$$###""""""$$$$$$$$$$$$######"""!!!$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###############$$$$$$$$$ !!!""""""""""""!!!$$$$$$$$$#########""""""$$$$$$$$$$$$%%%%%%%%%%%%$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%$$$###!!!!!!!!!""""""%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&&&&&&&'''''''''((('''%%%$$$######$$$%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''&&&&&&%%%%%%$$$$$$######"""$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%$$$#########%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%(((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&'''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&%%%$$$$$$'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%$$$"""!!!$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$""""""###$$$############$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########'''''''''&&&%%%$$$###"""$$$$$$############$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%"""""""""###$$$$$$$$$%%%"""#########$$$$$$$$$$$$%%%$$$$$$######""""""!!!$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$%%%%%%$$$$$$###''''''%%%%%%$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&'''''''''(((((()))((('''&&&&&&&&&&&&'''###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&'''''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%############%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%(((&&&%%%###"""""""""###%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&$$$$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###########################$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%$$$######$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&'''''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&'''(((((('''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$'''%%%$$$$$$%%%&&&%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%'''''''''&&&%%%$$$###"""%%%%%%$$$$$$$$$$$$%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%"""""""""###$$$$$$$$$%%%###############$$$$$$$$$$$$$$$$$$$$$######""""""$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$%%%%%%$$$$$$###(((''''''&&&&&&&&&&&&'''%%%%%%&&&&&&&&&'''''''''&&&&&&&&&'''''''''((((((((((((''''''&&&&&&&&&'''###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%''''''&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%############%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%###!!!!!!!!!!!!"""%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$###$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%$$$########################""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###########################$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&%%%$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&'''&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%''''''&&&&&&''''''((()))&&&&&&%%%%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%&&&'''((('''%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%&&&'''''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%&&&&&&'''$$$$$$$$$$$$######"""!!!&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%###############$$$$$$$$$!!!!!!!!! !!!""""""###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''''''''%%%&&&&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###""""""""""""###$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$%%%&&&'''((())))))%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&'''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&%%%&&&'''(((((('''&&&%%%'''&&&&&&&&&&&&'''((((((&&&&&&%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''((((((%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%!!!"""$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$%%%'''((('''&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$%%%%%%&&&''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&######$$$$$$$$$######"""%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$###############"""!!! !!!######$$$$$$$$$%%%&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&'''###$$$%%%%%%%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%###$$$$$$%%%%%%$$$$$$###$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%%%%%%%&&&'''''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%&&&''''''(((%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%&&&'''(((((('''&&&%%%&&&&&&%%%%%%&&&&&&'''(((%%%%%%%%%%%%%%%&&&'''(((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###'''((('''%%%###$$$$$$$$$$$$$$$$$$$$$$$$#########%%%'''((('''&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$#########$$$%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$$$$######""""""$$$###"""""""""###%%%&&&###$$$%%%%%%''''''((()))%%%%%%%%%&&&&&&&&&''''''"""###$$$%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%&&&'''''''''&&&&&&&&&&&&&&&'''''''''(((((($$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''(((((('''''''''$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%%%%%%%&&&'''''''''''''''''''''''''''%%%%%%'''(((((('''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&'''(((((('''&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%$$$###"""!!!######$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%&&&'''(((((($$$%%%''''''''''''%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%&&&((())))))(((&&&%%%&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%&&&'''(((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%"""###$$$%%%&&&''''''''''''&&&&&&%%%%%%&&&&&&'''!!!""""""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&((((((&&&%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###"""""""""###$$$!!!!!!!!!!!!""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$######"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!"""###$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((('''''''''&&&&&&&&&%%%&&&'''((((((&&&$$$######$$$&&&''''''&&&$$$###'''&&&%%%%%%%%%%%%&&&'''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!"""$$$%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&'''((())))))$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%###"""######$$$%%%%%%%%%%%%%%%%%%%%%%%%((((((((('''&&&%%%######&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''%%%%%%&&&'''(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''))))))((('''&&&$$$%%%&&&'''((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''))))))((('''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&&&&''''''&&&&&&'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&%%%$$$######'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%&&&''''''&&&&&&&&&$$$######""""""######$$$#########$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&&&&&&&%%%$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$"""""""""######"""""""""############$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%&&&'''((('''&&&$$$### !!!$$$&&&(((((('''''''''&&&%%%%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###$$$%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''(((''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''%%%%%%&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''((('''&&&%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%'''&&&&&&%%%%%%&&&&&&''')))(((((('''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&'''$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%'''''''''''''''&&&%%%%%%###""""""!!!!!!""""""###%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%$$$""""""%%%'''$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$###""""""""""""#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%&&&'''''''''&&&%%%$$$ """$$$&&&'''''''''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%&&&'''%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%$$$###&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%############$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''%%%%%%&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&'''''''''&&&&&&%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$""" !!!$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%###""""""!!!!!!############$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&%%%%%%%%%%%%&&&&&&&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''%%%%%%&&&'''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%$$$###"""###$$$%%%&&&'''''''''&&&&&&%%%%%%$$$'''&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%""""""###$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###""" !!!$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###"""!!!!!!"""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&""""""###$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%###$$$%%%&&&%%%###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%%%%&&&'''((((((((($$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''%%%%%%&&&'''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$$$$%%%%%%%%%$$$###"""###$$$%%%&&&'''''''''&&&&&&%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%% !!!"""$$$%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$###!!!!!!$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$###"""""""""""""""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&############$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%$$$$$$###&&&&&&&&&&&&''''''''''''$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''''''''(((%%%%%%%%%&&&&&&&&&&&&'''######$$$%%%%%%&&&''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%%%%&&&'''((()))***$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%$$$###$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$%%%&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''%%%%%%&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%"""###$$$$$$%%%%%%%%%%%%$$$$$$############$$$$$$############$$$$$$$$$$$$#########$$$$$$%%%%%%&&&##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%$$$######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%$$$###############$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&############$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&%%%%%%$$$######''''''''''''''''''''''''&&&%%%%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%&&&&&&''''''$$$$$$$$$$$$%%%&&&''''''%%%%%%&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$######$$$'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%&&&&&&'''''''''$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%$$$$$$###$$$&&&'''((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''%%%%%%&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%'''((((((((('''$$$$$$%%%&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&'''&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%""""""###$$$%%%&&&&&&'''##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""$$$&&&&&&$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$ !!!###$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&"""############$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((((('''&&&%%%$$$$$$$$$$$$%%%%%%&&&''''''&&&%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%(((******)))&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%&&&&&&''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&'''(((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&#########$$$$$$%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$###$$$&&&(((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''%%%%%%&&&'''(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%!!!###&&&(((******)))((($$$%%%&&&'''((('''&&&%%%###$$$$$$%%%&&&'''(((((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%&&&(((((()))'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########"""""""""!!!!!!$$$$$$%%%%%%%%%$$$############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%###$$$$$$%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$######%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%&&&'''''''''&&&%%%%%%$$$$$$$$$%%%&&&&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&)))((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$"""$$$%%%%%%%%%%%%&&&(((###%%%(((+++.../////////000111111000///,,,)))'''&&&$$$###$$$(((******(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%"""$$$&&&&&&%%%%%%&&&'''$$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$(((((('''%%%######%%%(((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''$$$%%%&&&''''''&&&%%%$$$%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########"""######$$$$$$$$$############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&$$$%%%%%%%%%%%%%%%%%%&&&%%%$$$###$$$%%%%%%%%%###&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&(((((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$###%%%&&&&&&%%%%%%&&&(((&&&(((+++...000000///...222222333333222000...---)))&&&$$$%%%'''))))))(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$&&&&&&%%%$$$%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&$$$###"""$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!!!!!!!!!!!!!!!!!!!######$$$$$$$$$%%%%%%%%%$$$$$$$$$######"""""""""$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%!!!!!!"""###$$$$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%%%%%%%%%%%%%$$$&&&%%%%%%%%%%%%%%%%%%$$$&&&$$$###$$$%%%&&&%%%###&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%'''''''''&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%&&&(((+++...111333333222///---000111222333444333222111,,,***'''%%%&&&(((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$########################$$$%%%'''&&&%%%$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%&&&%%%###"""###$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$######""""""$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&%%%%%% !!!"""$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%$$$$$$%%%&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&%%%%%%''')))000222555666555222///,,,+++,,,...000111222222222000---***'''&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&''''''%%%######$$$$$$$$$$$$%%%%%%%%%&&&&&&#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&&&&%%%###$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&'''%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%"""###$$$%%%&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%$$$$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&'''&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%&&&)))+++333444666777555222///,,,((()))+++---///111222222111000---)))'''%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''%%%######$$$$$$$$$$$$%%%%%%%%%&&&&&&#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###%%%''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&'''%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$%%%&&&'''''''''&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$&&&%%%%%%%%%%%%%%%%%%$$$'''%%%$$$%%%&&&'''&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&#########$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''###$$$&&&''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&&&&&&&(((+++...333444444444333111...---)))***+++---///111222333111111000,,,(((&&&%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$''''''''''''''''''''''''$$$%%%'''&&&%%%$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''((($$$%%%%%%&&&&&&%%%%%%$$$$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$&&&''''''%%%%%%&&&(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%&&&&&&&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%#########$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""#########$$$$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&$$$%%%%%%%%%%%%%%%%%%&&&'''%%%%%%%%%&&&'''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%"""$$$%%%''''''&&&%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%%%%&&&)))---111111111111000000///......***++++++,,,...///111222000111222///***&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&&&&%%%$$$%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%''')))******))))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%$$$###$$$&&&)))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%&&&&&&''''''$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%!!!!!!"""###$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''###$$$%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&'''&&&%%%%%%''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%$$$%%%%%%&&&'''''''''&&&&&&&&&%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######""""""""""""######"""###%%%'''''''''%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%&&&***///333000///......------......*********+++,,,---...//////111333111,,,'''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&########################$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%"""$$$&&&&&&%%%%%%&&&'''$$$$$$%%%%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%!!!""""""###$$$$$$%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###%%%(((***+++++++++***&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$""""""###&&&)))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%$$$%%%''''''''''''%%%$$$%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%$$$$$$#########%%%&&&''''''%%%######$$$&&&%%%%%%$$$###"""!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&&&&%%%$$$###"""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&'''&&&%%%$$$############'''''''''&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''''''''&&&###&&&&&&$$$&&&,,,//////333///***((())),,,...///...111///)))(((,,,,,,(((///000000---)))%%%######%%%%%%&&&&&&%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%'''&&&%%%%%%$$$$$$$$$%%%###%%%%%%$$$$$$$$$&&&&&&'''&&&%%%$$$###""""""###%%%&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%############%%%&&&$$$%%%&&&'''''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%((('''&&&&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&%%%$$$$$$''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%$$$$$$$$$######$$$&&&''''''%%%###$$$$$$&&&&&&%%%%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%$$$###""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%!!!"""###$$$%%%'''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%$$$############&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&''''''&&&&&&###&&&&&&$$$'''---111000222///+++)))+++---//////222333000***(((---///---...000111///+++'''%%%$$$%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%'''&&&&&&%%%$$$$$$$$$%%%###&&&)))******))))))***(((((('''&&&&&&%%%$$$$$$&&&&&&&&&&&&%%%$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%$$$$$$$$$$$$###$$$&&&'''&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$######"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&'''((()))%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$######%%%%%%$$$$$$$$$$$$######&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&###&&&&&&%%%(((///222222111...,,,+++---/////////333333///***))),,,//////---///222222...***'''&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%$$$&&&''''''&&&&&&''')))***)))'''&&&%%%&&&&&&'''''''''&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$############%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&%%%$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&'''((((((''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%'''&&&%%%$$$$$$%%%$$$$$$$$$$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%########################$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$###%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&&&&%%%%%%###%%%&&&%%%)))000444333000...------///000111000000///---+++***+++,,,,,,,,,///333333111---)))(((&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%###$$$$$$"""!!!!!!###%%%***(((&&&%%%$$$%%%&&&((($$$$$$######$$$&&&((()))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%$$$#########$$$%%%''''''''''''%%%$$$'''&&&$$$$$$$$$%%%''')))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$###%%%&&&&&&%%%$$$%%%&&&""""""######$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$############""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&%%%%%%$$$$$$###%%%&&&%%%)))000444333000...---...000222333222,,,---...000000---***))),,,///222333111---***(((&&&&&&'''''''''&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%&&&'''''''''&&&%%%&&&'''&&&$$$"""###%%%'''((('''%%%######$$$&&&'''$$$#########$$$&&&((()))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&%%%%%%%%%$$$$$$%%%''''''''''''%%%$$$'''&&&$$$$$$$$$%%%''')))$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''###$$$$$$$$$$$$%%%%%%%%%###$$$&&&&&&%%%$$$%%%&&&"""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$$$$!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&''''''&&&%%%$$$%%%%%%&&&&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######&&&&&&%%%(((///222222111///---...000333555555,,,---111666555000+++***,,,...111111///+++)))((('''''''''''''''&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$%%%'''(((((('''&&&&&&&&&&&&&&&%%%######%%%'''&&&&&&$$$$$$$$$$$$%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&%%%$$$%%%&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&%%%%%%$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''######$$$$$$$$$%%%%%%%%%"""$$$&&&&&&%%%%%%%%%&&&###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%% !!!###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&(((((('''%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$#########&&&&&&$$$'''---111000222000------000444666888---,,,000666666///+++,,,,,,...//////,,,)))'''&&&'''''''''''''''&&&&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$%%%'''((()))((('''&&&###$$$%%%$$$######$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&'''%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''#########$$$$$$%%%%%%%%%"""$$$&&&&&&%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&&&& !!!###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""###%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%########################$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$###""""""%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$$$$%%%'''(((((('''%%%$$$#########$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""###&&&&&&$$$&&&,,,//////333000------000444888999---+++---333222,,,***,,,,,,......---***'''&&&%%%''''''((((((''''''&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$%%%'''))))))((('''&&&$$$%%%''''''&&&%%%'''(((&&&&&&'''((((((''''''&&& !!!###&&&'''(((((('''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%############%%%&&&$$$%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&''''''(((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$$$$$$$%%%######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$%%%%%%&&&''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$######"""!!! &&&&&&&&&&&&%%%$$$######$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%'''&&&&&&%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&&&&&&&)))///333111111000000000000000000'''***...///...,,,++++++111000///---+++(((%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$######$$$&&&&&&$$$"""&&&%%%%%%$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%############%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%$$$###$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&''''''''''''&&&&&&)))((('''&&&%%%&&&&&&'''(((((((((((((((((((((((('''''''''&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%#########%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&(((''''''&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&)))((('''&&&%%%%%%&&&'''''''''&&&%%%%%%%%%%%%&&&)))(((&&&%%%$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&'''''''''&&&&&&%%%%%%%%%((('''%%%$$$###$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''&&&&&&&&&&&&%%%%%%%%%$$$###!!! $$$$$$%%%&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&''''''(((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&&&&(((---111222111111000///---,,,+++(((***,,,,,,++++++---...222111///,,,***'''%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&$$$###$$$%%%&&&%%%$$$'''&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######$$$%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&)))((('''&&&%%%&&&&&&'''########################&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%'''''''''''''''''''''''''''&&&$$$###"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&+++***)))(((''''''((()))''''''&&&%%%%%%%%%%%%&&&)))(((&&&%%%$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$###&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######'''''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%$$$###""" """###$$$%%%&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((((((((('''&&&&&&&&&&&&%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&&&&$$$$$$###"""&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&%%%%%%'''+++...222222222111///,,,)))''')))***+++******,,,///222333111...+++(((&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$(((&&&$$$###%%%&&&&&&&&&''''''&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%((((((''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&(((((('''&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''&&&&&&$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&''')))***%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&***)))(((((('''(((((((((''''''&&&%%%%%%%%%%%%&&&((((((&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''''''''''''''&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%((())))))))))))(((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%$$$$$$###"""###$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&(((***222333444333222...+++((()))+++,,,,,,,,,...000222333000---)))'''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%)))'''$$$###%%%&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%''''''''''''&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%''''''''''''&&&&&&''''''************************%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&%%%%%%$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&'''&&&%%%%%%&&&''')))+++%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''((()))******)))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$$$$############$$$$$$$$$%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%$$$$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''((()))+++,,,,,,"""###$$$%%%%%%&&&&&&&&&%%%&&&&&&&&&%%%%%%$$$###$$$$$$$$$%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&"""######$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$%%%&&&''''''///111333444444222000...***,,,///111000//////000000...+++(((&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%)))'''$$$###%%%&&&''''''%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%&&&'''(((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&((())))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%&&&########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#################################$$$%%%&&&((()))++++++"""###$$$%%%&&&'''''''''&&&&&&&&&&&&%%%$$$###"""######$$$$$$$$$$$$######&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&"""""""""###$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''&&&%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$$$$&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######%%%&&&%%%%%%+++---///222333333333222,,,///222333111...---,,,+++***(((&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&(((&&&$$$###%%%&&&&&&&&&$$$$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&''''''((('''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&'''''''''''''''(((''''''''''''&&&&&&&&&&&&&&&&&&'''(((((((((((('''''''''&&&%%%%%%%%%%%%&&&%%%&&&&&&''''''&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''''''''%%%%%%%%%&&&&&&&&&&&&'''%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%"""######$$$%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$###$$$$$$%%%%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&"""######$$$$$$%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$"""!!!"""%%%&&&%%%###&&&(((***,,,///000111222///111111000---***))))))&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&$$$###$$$%%%&&&%%%$$$$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&%%%$$$###$$$$$$$$$%%%%%%&&&&&&&&&###$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%'''(((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''((('''''''''&&&&&&&&&&&&!!!###%%%&&&'''&&&%%%$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&'''''''''((('''''''''&&&&&&&&&&&&%%%&&&'''(((((((((''''''''''''&&&%%%%%%%%%%%%&&&%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%""""""###$$$%%%%%%&&&&&&$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''(((((((((######$$$$$$$$$%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''$$$%%%&&&&&&''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%(((((('''''''''&&&&&&&&&((((((((('''&&&%%%############$$$%%%&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&''''''%%%%%%%%%&&&&&&'''''''''###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################$$$""" """%%%&&&%%%######$$$&&&(((***,,,...///222222000---)))''''''(((######$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$######$$$&&&&&&$$$"""%%%%%%%%%%%%&&&&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%######%%%%%%%%%%%%######$$$$$$$$$%%%%%%&&&&&&&&&###$$$%%%&&&'''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$#########&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&'''''''''(((((($$$%%%%%%&&&&&&%%%%%%$$$$$$%%%'''(((((((((''''''$$$$$$$$$$$$$$$$$$$$$$$$'''''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&!!!"""###$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((((('''''''''&&&&&&&&& ###&&&((('''&&&%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&(((((('''''''''&&&&&&&&&"""###%%%&&&'''&&&%%%%%%''''''&&&%%%%%%%%%%%%&&&$$$%%%&&&'''''''''&&&%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((%%%%%%%%%&&&&&&''''''''''''&&&%%%%%%%%%'''((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$############$$$$$$%%%$$$###""""""###$$$%%%$$$$$$############$$$$$$!!!###%%%&&&&&&&&&'''((("""###%%%&&&&&&%%%###"""$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$(((((((((''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&& !!!"""$$$%%%&&&''''''(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%))))))((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$#########&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''((((((''''''&&&%%%######$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%$$$$$$#########''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&''''''(((%%%&&&'''''''''&&&%%%$$$''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&%%%%%%$$$###%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&%%%$$$######%%%&&&&&&''''''&&&&&&%%%'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%(((''''''''''''((()))))))))((('''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''$$$$$$############$$$$$$%%%$$$###""""""###$$$%%%$$$##################$$$!!!###$$$$$$###"""###$$$"""###%%%&&&&&&%%%###"""%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&'''((())))))%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&%%%&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''&&&&&&%%%$$$%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%'''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''(((&&&&&&&&&&&&'''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&''''''(((''''''&&&&&&''''''((()))''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''(((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%&&&&&&&&&$$$$$$############$$$$$$$$$$$$############$$$$$$###########################$$$%%%%%%###"""""""""###$$$%%%&&&&&&%%%$$$###&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&'''((())))))%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&'''''''''&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''&&&%%%%%%&&&&&&'''''''''&&&&&&%%%#########$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%''''''&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%%%%&&&&&&(((((('''&&&&&&%%%$$$$$$&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&'''''''''$$$%%%%%%&&&'''((()))***&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&'''(((******&&&&&&&&&&&&&&&''''''(((&&&%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$#########$$$%%%'''&&&%%%$$$$$$%%%###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%'''''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&%%%%%%(((((((((((('''&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''((((((%%%%%%&&&&&&''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&'''((()))&&&%%%%%%%%%%%%&&&''''''$$$$$$$$$$$$%%%%%%&&&'''&&&&&&%%%%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&&&&&&&&&&%%%$$$$$$############$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$"""###$$$$$$$$$$$$###"""!!!###%%%&&&%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$%%%%%%&&&&&&%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''&&&%%%%%%$$$(((((((((((('''&&&%%%%%%((((((''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''######$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&'''''''''&&&%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((('''&&&&&&&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&''''''$$$$$$$$$$$$%%%%%%&&&''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&''''''&&&%%%%%%$$$$$$############$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$"""###$$$%%%%%%$$$###"""!!!###$$$$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&'''((())))))%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&'''''''''''''''''''''&&&%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$############&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$&&&&&&'''''''''&&&&&&%%%''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&''''''$$$$$$%%%%%%&&&'''(((((($$$#########$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''$$$%%%%%%&&&&&&''''''''''''''''''''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&&&&''''''''''''''''''(((((((((''''''&&&%%%$$$######"""&&&&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%&&&&&&'''''''''''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''&&&%%%$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&''''''(((&&&%%%%%%%%%%%%&&&&&&'''''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&''''''&&&%%%$$$$$$$$$############$$$$$$$$$$$$%%%&&&&&&%%%$$$$$$!!!###$$$%%%%%%$$$###!!! """$$$$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&'''((())))))%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$%%%&&&&&&&&&&&&&&&'''''''''((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$############"""&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%######$$$$$$%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%'''((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&''''''((('''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&'''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''((((((((((((''''''''''''''''''&&&&&&%%%%%%$$$$$$&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&''''''(((''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&''''''((()))''''''&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%'''(((((('''%%%$$$$$$$$$############$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$!!!"""$$$%%%%%%$$$"""!!!$$$&&&''''''%%%$$$$$$%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$%%%&&&&&&&&&&&&'''''''''((((((%%%&&&&&&''''''(((((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%$$$###&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$######$$$%%%&&&&&&&&&&&& """$$$&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&''''''&&&$$$$$$''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((''''''&&&&&&%%%%%%$$$''''''&&&&&&'''(((***+++''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''((((((''''''((((((''''''&&&%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%&&&(((((()))%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''))))))((((((''''''&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&'''((((((''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&'''((()))***(((''''''''''''((()))))))))(((''''''&&&&&&&&&&&&((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%'''(((((('''%%%$$$########################%%%%%%%%%$$$$$$$$$######!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""###$$$%%%&&&&&&%%%$$$###########################$$$$$$$$$%%%%%%&&&&&&&&&########################%%%$$$$$$$$$###""""""""""""$$$&&&%%%######&&&)))%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&'''''''''&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%''''''&&&&&&&&&&&&'''''''''&&&%%%%%%$$$$$$$$$$$$%%%$$$""" !!!"""###'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%'''&&&%%%%%%%%%%%%&&&'''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%((('''%%%$$$###$$$%%%%%%%%%%%%%%%&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######"""""""""###$$$$$$%%%%%%$$$$$$###!!!"""###%%%&&&'''(((((($$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%$$$###$$$%%%&&&'''(((%%%$$$%%%'''(((&&&$$$&&&&&&&&&%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''''''''(((((()))((('''&&&%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%'''&&&$$$######$$$&&&'''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''((('''&&&%%%$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$###############%%%%%%%%%$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########"""###$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############%%%&&&&&&%%%$$$$$$%%%&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%'''&&&$$$""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&&&&&&&%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%'''&&&%%%%%%%%%%%%&&&'''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$%%%%%%$$$$$$### !!!"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%&&&''''''&&&$$$%%%'''(((&&&$$$&&&&&&&&&%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&''''''((('''&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%'''&&&$$$######$$$&&&''''''''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&))))))((((((((('''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''((('''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$#########"""%%%%%%%%%$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$$$$$$$$$$((('''%%%%%%%%%%%%$$$###%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&'''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&((('''&&&%%%$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###""""""###$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%''''''&&&%%%%%%$$$######&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%&&&''''''&&&%%%%%%''''''&&&%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&$$$$$$$$$$$$&&&&&&((((((''''''''''''&&&&&&((('''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((('''''''''&&&%%%%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$######"""%%%%%%%%%$$$$$$$$$######&&&&&&&&&&&&%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""!!!!!!"""$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%)))&&&$$$%%%'''(((%%%"""%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%&&&'''((('''&&&&&&%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%&&&&&&'''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''&&&&&&&&&&&&(((((((((''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&'''((()))***''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''&&&''''''''''''''''''&&&&&&''''''''''''''''''&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$######%%%%%%%%%$$$$$$$$$######&&&&&&&&&&&&%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###""""""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%%%%&&&&&&$$$###%%%)))***'''$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%&&&'''&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$###&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###&&&''''''''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&&&&&&&&&&%%%&&&&&&'''''''''&&&&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&'''((()))***''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''&&&''''''''''''''''''&&&&&&''''''''''''''''''&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%'''))))))(((&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$%%%%%%%%%%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&######$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%###$$$%%%&&&&&&&&&%%%%%%%%%&&&''''''%%%%%%&&&'''''''''''''''&&&&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((((((((&&&&&&'''''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$&&&((()))((('''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$$$$%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%###$$$%%%&&&&&&&&&%%%%%%$$$&&&((('''%%%$$$&&&'''''''''''''''&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&###$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%&&&&&&''''''$$$$$$%%%%%%&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((())))))%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&''''''(((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$%%%&&&&&&'''(((%%%%%%%%%$$$$$$$$$######!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%''''''''''''%%%%%%########################!!!"""###$$$&&&'''((()))''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$(((++++++'''$$$$$$%%%%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%'''&&&$$$$$$$$$$$$&&&'''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$'''&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%&&&'''''''''&&&''''''''''''''''''''''''#########$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""###%%%&&&'''&&&%%%%%%#########$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%&&&'''((((((''''''''''''''''''''''''"""""""""######$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&''''''((((((''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%$$$$$$###&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%###$$$%%%&&&'''&&&%%%%%%$$$&&&((('''%%%$$$%%%((((((((('''''''''&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$%%%'''((()))(((''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&'''''''''(((((("""######$$$%%%&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&&&&''''''(((((((((((((((((((((((('''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''(((((('''''''''&&&&&&'''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''###$$$&&&'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&((('''%%%$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&'''&&&&&&%%%%%%&&&&&&&&&''''''''''''((((((((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&'''''''''((((((%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''(((''''''&&&&&&%%%$$$$$$%%%%%%&&&'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$%%%%%%""""""######$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$$$$%%%"""###$$$$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&'''''''''&&&%%%'''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''((((((&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''')))&&&$$$$$$&&&(((&&&$$$&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''&&&&&&&&&&&&&&&&&&'''''''''(((((("""###%%%&&&'''(((((((((%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&((('''%%%%%%&&&&&&%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&''''''%%%%%%&&&'''&&&%%%%%%%%%%%%&&&''''''''''''((((((((((((''''''((('''&&&%%%%%%&&&'''(((%%%%%%%%%&&&&&&&&&''''''!!!"""###%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''&&&&&&'''(((%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&'''&&&%%%$$$###$$$$$$%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$"""!!!!!!###%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%%%%"""#########$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$$$$$$$&&&&&&&&&'''(((((())))))%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''((('''&&&&&&'''&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&########################&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((&&&$$$$$$&&&'''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$#########&&&&&&&&&&&&'''''''''(((%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&(((&&&%%%%%%&&&'''%%%$$$%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&''''''%%%%%%&&&'''&&&%%%%%%%%%%%%&&&''''''&&&&&&''''''''''''&&&&&&((('''&&&&&&&&&&&&'''(((%%%%%%%%%&&&&&&&&&''''''###$$$%%%&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''&&&&&&'''(((%%%$$$###""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$#########$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$""" !!!$$$&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&'''''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%%%%############$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((((('''&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((&&&$$$######%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&$$$%%%&&&'''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$############""""""&&&&&&&&&&&&''''''''''''&&&'''''''''&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&(((&&&%%%%%%&&&'''&&&$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&''''''%%%%%%&&&'''&&&%%%%%%%%%%%%&&&''''''%%%%%%&&&&&&&&&&&&%%%%%%((('''&&&&&&&&&&&&'''(((%%%%%%%%%&&&&&&&&&''''''%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''&&&&&&'''((($$$###"""!!!"""###$$$&&&########################&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$"""!!!"""###%%%''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''######$$$%%%&&&&&&''''''((((((((((((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&'''''''''%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%$$$$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((((((''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&'''&&&%%%%%%&&&'''&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''%%%&&&''''''%%%%%%&&&'''&&&%%%%%%%%%%%%&&&''''''%%%&&&&&&''''''&&&&&&%%%'''''''''&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''&&&&&&&&&(((######"""""""""###%%%%%%########################&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&'''((()))))))))))))))))))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%$$$$$$$$$######"""!!!!!!!!!%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''((((((((('''&&&%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&""""""""""""""""""""""""&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''###%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&'''%%%%%%%%%''''''&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((&&&&&&&&&''''''(((((((((''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''%%%&&&''''''%%%%%%&&&'''&&&%%%%%%%%%%%%&&&''''''''''''((((((((((((''''''&&&''''''''''''''''''&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''&&&&&&&&&(((""""""###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&!!!"""$$$&&&&&&%%%$$$"""&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&'''((())))))***(((((()))))))))(((''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%$$$%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&%%%%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!"""%%%&&&'''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''"""$$$'''((('''&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%&&&'''''''''&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&&&&%%%$$$%%%'''''''''&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&'''(((((())))))''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&''''''%%%%%%&&&'''&&&%%%%%%%%%%%%&&&'''''''''(((((((((((((((((('''&&&&&&'''(((((('''&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''&&&&&&'''(((!!!"""$$$&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%&&&'''(((''''''&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&"""###$$$%%%%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''(((((((((%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""!!!!!!###$$$&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###%%%''''''&&&%%%$$$&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######%%%&&&&&&&&&%%%$$$%%%$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''!!!$$$'''((('''&&&&&&(((&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&'''''''''((($$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&&&&%%%$$$%%%'''((('''&&&###$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))))))))''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&''''''%%%%%%&&&'''&&&%%%%%%%%%%%%&&&''''''&&&''''''((((((''''''&&&&&&&&&'''(((((('''&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''&&&&&&'''((( """%%%(((((('''&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%'''(((((((((''''''######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$ """######$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%&&&'''%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''######$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$###!!! """$$$&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###%%%'''''''''%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###""""""###%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''' $$$((()))'''&&&&&&(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$((((((((('''&&&%%%###"""%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((())))))'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&'''''''''(((((($$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&&&&%%%$$$%%%'''((('''&&&######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))***''''''''''''''''''''''''&&&''''''''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&''''''%%%%%%&&&'''&&&%%%%%%%%%%%%&&&''''''%%%&&&&&&''''''&&&&&&%%%%%%&&&'''(((((('''&&&%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&'''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''&&&&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%'''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$#########%%%&&&&&&%%%######%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%&&&$$$!!!!!!$$$((()))(((&&&%%%$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&'''(((((($$$$$$&&&&&&&&&&&&$$$$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$$$$(((%%%""""""%%%'''&&&%%%&&&'''''''''&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$"""""""""$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&&&&'''&&&&&&%%%%%%%%%$$$$$$$$$'''&&&%%%%%%%%%%%%&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''((()))(((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&((())))))(((&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%'''&&&%%%%%%$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((((((((((((''''''''''''''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((((((((((())))))))))))&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((('''&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%((('''&&&%%%$$$%%%&&&''''''''''''''''''&&&&&&&&&(((((('''&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''+++(((&&&'''))))))'''%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!"""############"""''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$#########""""""$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###""""""%%%'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&'''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%(((%%%######%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&'''''''''''''''&&&&&&&&&%%%%%%'''&&&%%%%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%&&&&&&&&&'''&&&&&&''''''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$$$$%%%&&&&&&''''''&&&&&&((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((((((''''''''''''''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((('''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%'''&&&%%%%%%%%%%%%&&&'''&&&&&&''''''''''''''''''))))))(((''''''''''''''''''''''''&&&&&&'''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''***(((&&&'''((()))'''%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!!!!"""""""""""""""&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$###"""""""""###$$$&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$###$$$%%%&&&'''&&&%%%""""""###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&&&&&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&'''%%%###$$$%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""$$$%%%&&&'''''''''$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''%%%$$$$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''(((((((((((('''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%&&&'''(((***++++++%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&''''''''''''&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((('''&&&&&&&&&&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((''''''&&&%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&%%%%%%%%%&&&&&&'''%%%&&&&&&&&&'''((((((((((((((('''&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&'''''')))(((''''''(((((('''&&&$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((('''%%%######$$$%%%&&&''''''%%%$$$$$$%%%''''''%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######%%%&&&((('''$$$!!!"""%%%&&&%%%######$$$%%%&&&%%%%%%###"""%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&%%%&&&&&&&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&'''&&&%%%$$$$$$%%%%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&&&&&&&&&&###$$$&&&''''''&&&$$$###$$$$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&'''''''''%%%%%%&&&&&&'''(((((()))''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%&&&''')))***++++++&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&########################&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''(((((('''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''%%%%%%&&&&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%%%%&&&&&&''''''%%%%%%%%%&&&'''((())))))&&&&&&%%%%%%$$$%%%%%%&&&&&&''''''''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''((((((''''''((((((((('''$$$$$$$$$$$$$$$$$$$$$$$$########################$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((('''%%%######$$$%%%&&&''''''%%%$$$$$$%%%''''''$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&''''''$$$!!!"""%%%&&&%%%""""""###$$$%%%&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&$$$%%%%%%&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&'''$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$###$$$&&&''''''&&&$$$######$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&'''(((((()))&&&&&&&&&%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&''''''''''''&&&'''''''''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''&&&&&&%%%$$$%%%&&&&&&''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''((((((&&&&&&&&&%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''''''''''''''%%%%%%%%%%%%&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%&&&&&&'''''''''%%%%%%%%%&&&'''((())))))'''&&&&&&&&&&&&&&&''''''&&&&&&'''(((((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''((((((''''''(((((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$###"""""""""###$$$&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$###$$$%%%%%%$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$ !!!###$$$%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&######$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&###%%%'''&&&%%%$$$$$$%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&%%%%%%$$$###$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''((((((((('''&&&%%%###$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&''''''((((((&&&&&&%%%%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%'''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&'''''''''(((((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&$$$$$$%%%%%%&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((('''''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%&&&''''''''''''%%%&&&&&&&&&'''((((((((()))(((((((((((()))******%%%&&&'''(((((('''&&&%%%''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&'''((((((''''''((()))$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$#########""""""$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%''''''&&&%%%$$$###$$$%%%%%%$$$###$$$$$$%%%%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$ """$$$%%%&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&'''''''''$$$%%%%%%&&&&&&%%%%%%$$$!!!"""###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%"""%%%''''''%%%$$$$$$%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&$$$"""!!!""""""######$$$%%%%%%&&&$$$$$$$$$%%%&&&&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&$$$%%%&&&&&&''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&###$$$$$$%%%&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%&&&''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&'''''''''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''((((((''''''%%%&&&&&&''''''&&&&&&%%%###$$$%%%'''''''''''''''&&&&&&''''''''''''''''''((('''''''''(((((()))***%%%&&&((())))))(((&&&%%%''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''%%%''')))((('''&&&(((***$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%#########$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$#########%%%&&&&&&%%%######$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!###&&&(((((('''%%%###!!!$$$'''&&&###"""###&&&&&&&&&%%%$$$%%%&&&((()))%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$!!!"""%%%'''''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''(((((($$$$$$&&&''''''&&&$$$$$$ !!!"""$$$%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%$$$$$$$$$$$$"""%%%((((((%%%###$$$&&&$$$%%%%%%&&&'''''''''&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$###""" !!!!!!"""###$$$$$$%%%%%%######$$$%%%%%%&&&&&&'''(((((('''''''''&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&'''''''''&&&$$$%%%&&&&&&''''''&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&######$$$%%%%%%&&&''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''((((((((('''%%%&&&&&&''''''&&&&&&%%%"""$$$%%%'''(((((('''''''''''''''''''''&&&&&&&&&$$$$$$$$$$$$$$$%%%&&&'''%%%&&&((())))))(((&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%'''))))))'''&&&(((+++%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&%%%$$$$$$##############################$$$%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% """###%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$######""""""!!!#########$$$$$$%%%%%%%%%((('''%%%$$$$$$%%%'''(((######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''$$$&&&)))+++***'''$$$!!!$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$###"""###%%%&&&%%%$$$"""######$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%&&&&&&&&&%%%$$$###(((''''''''''''&&&&&&&&&'''&&&%%%$$$###$$$%%%%%%%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&'''((((((((('''%%%$$$$$$%%%'''(((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&'''((()))'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$%%%%%%&&&''''''((((((((((((((((((((((((%%%%%%%%%&&&&&&'''''''''******)))((('''&&&%%%%%%''''''&&&&&&&&&&&&'''''''''''''''''''''''''''''')))((('''''''''(((***+++%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$%%%%%%'''&&&%%%$$$$$$%%%&&&'''######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%&&&&&&''''''''')))+++------+++(((&&&''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&(((((('''&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$#########%%%&&&%%%$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&%%%&&&'''''''''&&&%%%%%%''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%&&&'''((()))%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((((((((('''%%%$$$$$$%%%'''(((''''''''''''''''''''''''%%%%%%%%%%%%&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$%%%%%%&&&''''''((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&''''''''')))))))))(((''''''&&&&&&'''''''''&&&&&&'''''''''''''''''''''''''''''''''((('''&&&&&&&&&'''))))))%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&'''((())),,,---.../////////...---,,,+++(((&&&%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&'''(((&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&(((((((((''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$###$$$%%%&&&%%%$$$(((((('''&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((((((''''''&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((()))***+++%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((('''&&&%%%$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((((((((())))))(((((((((%%%%%%%%%%%%%%%%%%%%%%%%))))))(((&&&&&&%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&'''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((((((((((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''&&&%%%%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$###$$$$$$%%%&&&&&&&&&%%%%%%########################""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""$$$%%%''''''&&&%%%$$$$$$$$$%%%%%%&&&''''''(((%%%%%%%%%$$$$$$#########$$$%%%&&&&&&&&&&&&%%%$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&'''((()))***...//////000000111111111111...+++'''%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&'''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$###$$$&&&'''&&&%%%'''&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&%%%%%%&&&&&&&&&'''((())))))***%%%&&&''''''((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((('''&&&%%%%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&'''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%(((((())))))))))))((((((&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''&&&''''''''''''''''''&&&&&&&&&'''''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''(((((())))))''''''(((((((((((('''''''''''''''''''''''''''''''''&&&%%%%%%%%%&&&((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%$$$$$$$$$###$$$%%%%%%&&&&&&&&&%%%##########################################$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%&&&'''(((((()))%%%%%%%%%$$$$$$#########$$$$$$%%%&&&&&&%%%$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&'''((()))+++,,,////////////000000111222333111,,,(((&&&%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$%%%$$$%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$###$$$&&&'''&&&%%%######$$$$$$%%%%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&''''''((()))))))))''''''((())))))(((''''''''''''''''''''''''''''''((('''&&&&&&&&&'''((()))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%######$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%%%%&&&'''((((((%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''')))+++,,,---............////////////333111...***'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$%%%&&&'''&&&%%%""""""###$$$$$$%%%&&&&&&###$$$$$$%%%%%%&&&&&&'''%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''(((((('''&&&%%%$$$$$$$$$$$$$$$%%%&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$###%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&((())))))'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((((((((((('''''''''''''''&&&'''''''''(((((())))))'''((()))******)))((('''''''''''''''''''''''''''((('''&&&&&&&&&'''))))))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&"""###$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######%%%&&&((($$$$$$%%%%%%&&&&&&&&&'''$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%$$$######$$$%%%&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&((()))+++---...---......///......---,,,222000...+++(((&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$%%%'''''''''&&&$$$$$$%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''(((((('''&&&%%%%%%%%%$$$$$$%%%&&&((()))&&&&&&&&&%%%%%%%%%$$$$$$###$$$%%%&&&&&&%%%$$$$$$%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''(((((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''''''''&&&&&&&&&''''''((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%'''''''''''''''''''''''''''''''''''''''''''''''')))((((((((('''''''''&&&'''''''''((((((((((((((('''((()))******)))(((''''''''''''''''''''''''''''''&&&%%%%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&'''''''''"""###$$$%%%&&&&&&'''&&&########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% """$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''%%%###""""""$$$''')))$$$$$$%%%%%%%%%%%%&&&&&&#########$$$$$$%%%%%%&&&&&&%%%###""""""###%%%&&&######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&(((***,,,...///---.../////////---,,,+++111000...,,,)))'''$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&''''''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&'''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$%%%'''((('''&&&(((''''''&&&&&&%%%%%%$$$######$$$%%%%%%&&&''''''%%%%%%&&&&&&'''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&((())))))(((&&&%%%&&&&&&%%%%%%&&&''')))***&&&&&&&&&%%%%%%%%%$$$$$$!!!"""$$$&&&''''''&&&&&&%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''(((''''''&&&&&&''''''(((((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%&&&'''((()))'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&'''''''''''''''''''''''')))((('''&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$))))))))))))((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&))))))(((((('''''''''&&&(((((((((((((((((((((((('''((()))++++++)))((('''''''''''''''''''''''''''%%%%%%$$$$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###"""!!!"""$$$%%%$$$###&&&%%%%%%$$$$$$%%%%%%&&&#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$(((((('''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&(((+++...///---,,,+++))))))))))))***,,,,,,,,,+++)))'''&&&%%%%%%%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%$$$%%%&&&&&&''''''''''''''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%&&&'''$$$###$$$&&&''''''%%%###$$$$$$$$$%%%%%%&&&&&&&&&'''''''''''''''''''''''''''$$$""""""%%%''''''&&&%%%$$$$$$%%%&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&'''''''''&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&'''(((((((((%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$###"""&&&&&&&&&''''''''''''(((%%%&&&&&&&&&'''(((((((((''''''&&&&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%)))(((&&&$$$$$$$$$&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%&&&'''''''''&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''&&&$$$###((('''%%%$$$$$$%%%'''(((%%%%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))&&&######&&&''''''%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''')))***))))))(((((('''''''''&&&((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''''''''&&&&&&&&&&&&''''''))))))))))))))))))))))))$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""###%%%%%%%%%$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$(((''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&)))+++...000---,,,***(((((()))******......---,,,***(((&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&'''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$%%%''''''&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''%%%"""###%%%'''&&&%%%&&&%%%%%%%%%&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%)))'''&&&$$$$$$%%%&&&'''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%%%%%%%&&&'''%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$((('''%%%$$$$$$%%%'''((((((((('''''''''(((((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))&&&$$$$$$&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''')))***)))(((((((((''''''''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''''''''&&&&&&&&&&&&''''''(((((((((((((((((((((((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''))),,,...000---,,,***(((((()))+++,,,111000///---+++((('''&&&###$$$&&&'''(((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%''''''&&&$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$$$$%%%&&&%%%$$$&&&&&&&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''''''''&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&&&&'''(((&&&&&&&&&''''''''''''((('''''''''''''''&&&&&&&&&''''''&&&&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%((('''&&&%%%$$$%%%&&&''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&'''&&&%%%$$$$$$%%%&&&'''(((((('''''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((&&&%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))((((((((((((''''''''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''''''''&&&&&&&&&&&&''''''(((((((((((((((((((((((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###$$$&&&'''&&&%%%###$$$$$$$$$$$$$$$$$$###%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''))),,,...000...---+++******,,,---///333222000---+++)))'''&&&!!!###%%%'''(((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''&&&%%%$$$###''''''''''''''''''''''''$$$$$$$$$%%%%%%%%%&&&&&&"""""""""$$$%%%''')))***&&&%%%$$$%%%'''((('''%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%%%%$$$$$$###%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''((((((((('''&&&&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%'''((()))&&&&&&&&&''''''''''''(((((((((((('''&&&&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%$$$$$$%%%&&&''''''&&&%%%%%%%%%%%%&&&'''&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((((('''&&&&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((((((((((('''''''''((((((((((((((((((((((((''''''''''''''''''''''''%%%&&&''''''((('''''''''''''''&&&&&&&&&&&&''''''(((((((((((((((((((((((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###$$$&&&'''&&&%%%###$$$%%%%%%%%%%%%$$$###%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&''')))+++---//////.........///000111111444222///,,,***((('''&&& """$$$&&&''''''%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&&&&%%%###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&"""""""""$$$%%%''')))***&&&%%%$$$%%%'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$ ###&&&&&&%%%%%%&&&(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''((((((((('''&&&&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%%%%&&&''''''&&&&&&&&&''''''''''''(((((((((((('''&&&&&&&&&%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%'''(((&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((('''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%&&&''''''((('''''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$%%%&&&&&&$$$$$$%%%&&&''''''&&&%%%$$$%%%%%%$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&(((***,,,---...///000222333333333333222000---***((('''&&&&&&!!!"""$$$%%%&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%'''&&&$$$%%%&&&(((((('''''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%''''''%%%$$$$$$%%% ###&&&'''%%%$$$&&&)))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''''''''&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&''''''''''''((('''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&'''%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%'''))))))'''&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&'''''''''((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((''''''&&&'''''''''(((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%&&&''''''((((((''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$###"""###%%%%%%%%%$$$$$$%%%'''(((((('''%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%''')))+++,,,,,,...111444555444333222///---+++(((&&&%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$###$$$$$$$$$(((((((((((((((((((((((($$$$$$%%%%%%%%%%%%&&&&&&'''&&&&&&%%%$$$$$$$$$$$$(((&&&$$$%%%&&&(((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&"""$$$''''''%%%$$$%%%&&&"""%%%((('''$$$"""$$$'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&((())))))'''%%%###&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&'''''''''&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%'''******(((&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''(((((('''&&&%%%''''''''''''''''''''''''$$$%%%%%%%%%&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%&&&&&&'''(((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((('''&&&%%%''''''''''''((((((((()))((((((((((((((((((((((((''''''''''''''''''''''''%%%&&&''''''((((((''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''###"""!!!"""$$$%%%$$$###%%%&&&((())))))(((&&&%%%#########$$$$$$%%%%%%&&&######$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&'''''''''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%&&&(((***+++***---111555666555222000---,,,)))&&&%%%$$$%%%&&&''''''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&$$$###"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$%%%%%%&&&'''(((&&&$$$%%%&&&((((((((((((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%% $$$''''''%%%$$$%%%'''%%%(((***(((### """$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&'''''''''&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''(((((((((%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''***++++++(((%%%###&&&&&&&&&'''''''''((((((%%%&&&&&&''''''(((((((((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&'''''''''$$$%%%&&&&&&'''''''''&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&'''''''''$$$%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&'''((('''&&&&&&%%%&&&&&&''''''&&&&&&%%%!!!!!!"""###$$$&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$(((******(((&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''(((((('''&&&%%%(((((((((((((((((((((((($$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''$$$%%%%%%&&&'''((())))))((((((((((((((((((((((((&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''&&&%%%&&&'''''''''(((((())))))((((((((((((((((((((((((((((((((((((((((((((((((%%%&&&''''''(((((('''''''''''''''&&&&&&'''''''''''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########""""""%%%$$$#########$$$%%%&&&&&&%%%###""""""###%%%&&&######$$$$$$$$$$$$######$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&''''''%%%######$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%%%%$$$%%%%%%&&&'''((()))&&&&&&&&&%%%%%%$$$$$$$$$((('''%%%$$$###$$$%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''(((((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%***+++---......---+++***))))))((('''&&&&&&%%%%%%(((((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$"""!!! !!!"""#########$$$%%%%%%&&&''''''((('''%%%$$$$$$%%%&&&'''))))))((('''''''''''''''&&&&&&''''''''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%))))))((('''''''''''''''''''''''''''''''''''''''***(((&&&&&&((((((&&&###%%%&&&&&&''''''&&&&&&%%%''''''&&&&&&&&&%%%%%%%%%'''''''''&&&&&&%%%%%%%%%'''''''''&&&&&&%%%%%%%%%'''''''''&&&&&&%%%%%%%%%((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&))))))(((((('''&&&$$$$$$$$$%%%&&&&&&%%%%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((('''&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&(((((('''''''''&&&&&&&&&''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''(((((($$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&'''''''''&&&%%%%%%$$$''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''$$$$$$$$$$$$%%%%%%&&&'''(((((('''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''''''''((((((((((((''''''))))))(((((((((''''''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''&&&'''''''''&&&%%%%%%$$$''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''((((((&&&'''''''''(((((())))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&&&&%%%%%%$$$$$$#########$$$%%%&&&&&&%%%###""""""###%%%&&&######$$$$$$$$$$$$######""""""#########$$$$$$$$$$$$&&&''''''%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%&&&&&&'''&&&&&&&&&$$$$$$$$$$$$%%%&&&'''(((&&&&&&&&&%%%%%%$$$$$$$$$'''&&&%%%%%%$$$$$$$$$%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""""""""############'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''')))******)))'''&&&&&&&&&&&&&&&'''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%###"""""""""###$$$$$$$$$$$$%%%%%%&&&&&&&&&((('''&&&%%%%%%&&&'''((()))(((((('''''''''''''''&&&&&&''''''''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%(((((('''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$%%%'''((('''%%%%%%&&&&&&&&&&&&&&&&&&%%%''''''''''''&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%(((((((((((('''&&&%%%%%%$$$%%%'''&&&&&&%%%'''(((''''''''''''''''''''''''&&&&&&''''''&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&(((((('''''''''&&&&&&&&&''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''%%%%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%&&&'''''''''&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''(((((('''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''&&&'''''''''&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&''''''(((''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''((((((''''''''''''((((((((()))''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((($$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$#########$$$$$$######$$$$$$%%%&&&&&&%%%$$$######$$$%%%&&&######$$$$$$$$$$$$######""""""#########$$$$$$$$$###%%%''''''%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&%%%%%%$$$###$$$$$$%%%&&&''''''''''''$$$$$$###$$$$$$%%%&&&'''&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&%%%$$$######$$$$$$&&&'''((()))***&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((((((&&&&&&&&&'''((())))))(((''''''&&&&&&''''''&&&&&&''''''''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''''''''&&&%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&%%%&&&''''''&&&%%%'''(((((((((((((((((((((((((((''''''&&&%%%%%%%%%&&&&&&''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&'''''''''''''''&&&&&&&&&''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&'''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%&&&''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&&&&''''''(((''''''''''''''''''''''''%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''&&&''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&&&&''''''(((''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''(((&&&&&&'''''''''(((((((((''''''''''''((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%############""""""""""""$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%&&&&&&&&&###%%%&&&'''&&&&&&&&&''''''&&&&&&%%%%%%$$$$$$###%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&%%%$$$#########$$$%%%&&&''''''''''''$$$#########$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%*********))))))(((((('''&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%######$$$%%%'''((())))))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$(((((('''''''''((())))))(((((('''&&&&&&&&&&&&'''%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&((((((((((((((((((((('''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((())))))))))))))))))))))))%%%&&&&&&'''((((((''''''%%%'''((('''&&&%%%'''(((((((((((((((((((((((((((((('''%%%$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''%%%&&&&&&''''''&&&&&&%%%(((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''''''''((((((''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''''''''(((((((((((('''''''''(((((((((((((((''''''''''''''''''''''''''''''(((((((((((())))))''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%######$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&###%%%''''''&&&&&&'''(((&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$$$$$$$$$$%%%&&&&&&%%%&&&&&&&&&%%%%%%$$$######$$$%%%&&&''''''''''''$$$$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$''''''''''''(((((())))))(((((('''&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%'''&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&%%%$$$$$$$$$$$$'''&&&%%%%%%%%%%%%&&&''''''(((((((((((((((((((((&&&&&&&&&'''''''''''''''%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((())))))))))))))))))))))))$$$%%%&&&'''((((((((((((&&&'''((((((&&&&&&&&&((('''''''''''''''''''''''''''&&&%%%$$$$$$%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''&&&%%%%%%&&&&&&&&&&&&'''''''''''''''''''''%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''''''''(((((((((((('''''''''((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&'''((((((''''''&&&(((((((((((((((((((((((((((((((((''''''(((((((((''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((('''''''''((((((((())))))((((((((((((((('''''''''''''''''''''''''''''''''&&&&&&'''''''''(((((((((((((((((((((((((((((((((************************$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$""""""#########$$$$$$$$$$$$&&&((((((&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%&&&''''''''''''%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$############%%%%%%%%%%%%$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''((((((((()))((('''&&&&&&%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((('''$$$###$$$%%%'''&&&%%%$$$$$$%%%&&&'''&&&''''''''''''(((((((((''''''''''''((((((((((((%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%&&&'''(((((((((''''''((()))(((&&&&&&&&&(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&'''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&&&&'''&&&&&&'''(((((((((((('''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%''''''''''''''''''''''''(((''''''&&&&&&''''''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&''''''(((((((((((((((((('''%%%%%%%%%&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&'''(((((((((((('''(((((((((((((((((((((((()))((((((''''''(((((()))''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''((((((((()))))))))((((((((((((((('''''''''''''''''''''''''''''''''&&&&&&&&&''''''(((((()))))))))))))))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%#########"""""""""!!!!!!"""###$$$%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$""""""#########$$$$$$$$$%%%'''((((((&&&%%%&&&&&&###$$$$$$%%%%%%&&&&&&'''$$$$$$$$$###$$$$$$%%%&&&######$$$%%%&&&&&&&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&'''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&'''(((((((((((('''&&&&&&%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%'''((('''%%%$$$&&&'''((('''%%%$$$$$$%%%'''(((%%%%%%&&&&&&''''''''''''&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''))))))((('''&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&'''''''''((((((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%&&&&&&&&&&&&'''''''''%%%%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&'''(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''&&&''''''((((((''''''&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&'''((((((((((((((((((((((((((((((((((((((())))))(((((((((((())))))''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''((((((((()))))))))))))))(((((((((''''''''''''''''''''''''''''''''''''&&&''''''((())))))******((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$"""###$$$%%%&&&%%%$$$$$$###$$$$$$%%%%%%$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&((()))(((&&&%%%%%%&&&"""###$$$%%%&&&&&&'''((($$$$$$######$$$$$$%%%&&&"""###$$$%%%&&&'''''''''&&&&&&&&&'''&&&&&&%%%%%%''''''&&&%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$###$$$%%%'''(((%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%"""""""""######$$$$$$$$$%%%%%%%%%$$$$$$$$$######''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&&&&''''''((($$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&'''''''''&&&######$$$%%%%%%&&&''''''###$$$%%%&&&''''''''''''''''''&&&%%%%%%%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%$$$#########$$$%%%%%%&&&''''''''''''''''''''''''###&&&((((((&&&&&&(((***((('''%%%$$$$$$%%%'''(((%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&'''''''''((((((((((((((((((((((((((((((((((((((((((((((((&&&'''''''''''''''&&&&&&((()))***)))'''&&&&&&'''''''''''''''''''''''''''###$$$&&&'''((('''&&&&&&''''''''''''''''''''''''&&&''''''''''''''''''&&&&&&&&&&&&'''''''''(((((('''''''''&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&'''(((((())))))((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''&&&&&&'''((())))))(((((('''''''''''''''''''''''''''''''''&&&&&&'''''''''''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&)))((('''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''%%%&&&&&&''''''&&&&&&%%%'''''''''((((((((())))))'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&'''((())))))((((((''''''''''''''''''''''''))))))(((((((((((())))))'''''''''&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''(((((((((((((((((())))))))))))))))))(((((('''''''''&&&'''''''''''''''''''''''''''(((((()))***+++++++++''''''''''''''''''''''''++++++++++++++++++++++++&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%&&&((()))((('''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$"""###%%%&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%$$$###'''&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$###%%%&&&''''''((((((''''''''''''&&&%%%%%%$$$######&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''&&&&&&'''((('''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((((('''&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$'''&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$'''&&&%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%&&&'''((((((((($$$$$$''')))'''&&&((((((((((((((((((((((((((('''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''(((((((((((((((((((((((((((((('''''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%&&&&&&%%%%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''&&&&&&&&&&&&&&&&&&''''''''''''((()))((('''&&&&&&'''((()))%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((())))))((('''&&&&&&''''''''''''''''''''''''))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''%%%&&&'''(((((('''&&&%%%''''''&&&%%%&&&'''((()))&&&&&&&&&'''''''''((((((((((((''''''''''''((((((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''((((((((((((''''''(((''''''''''''&&&&&&&&&%%%&&&''''''((((((''''''(((((())))))))))))(((((())))))))))))))))))))))))))))))(((((('''''''''&&&(((((((((((())))))))))))******))))))((((((((('''(((''''''''''''((())))))&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""###%%%&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''%%%######%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$###&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$%%%&&&''''''(((((('''''''''&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''&&&%%%&&&(((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&'''''''''&&&&&&&&&%%%%%%%%%$$$'''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&((($$$$$$''')))'''&&&((((((((((((((((((((((((((('''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''(((((((((((((((((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%'''&&&&&&%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&&&&''''''''''''(((((((((''''''''''''(((((($$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&''''''''''''&&&&&&%%%'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&'''&&&&&&%%%&&&'''((()))&&&&&&&&&'''''''''((((((((((((''''''''''''(((((())))))(((((((((((())))))((((((((((((((((((((((((''''''((((((((((((''''''(((''''''''''''&&&&&&&&&%%%&&&''''''((((((''''''(((((())))))))))))(((((((((((((((((((((((((((((()))(((((((((''''''''''''(((((((((((()))))))))))))))))))))(((((('''''''''''''''''''''((((((((((((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###"""!!!"""$$$%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&$$$$$$%%%&&&%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$&&&%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''&&&%%%%%%%%%&&&''''''((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%'''((('''&&&%%%&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&'''((('''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((('''&&&%%%%%%%%%%%%((($$$$$$''')))'''&&&(((((((((((((((((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''(((((((((((((((((((((((('''''''''''''''&&&&&&&&&((('''''''''&&&%%%%%%%%%''''''''''''''''''''''''%%%&&&''''''&&&%%%'''(((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$&&&&&&&&&''''''''''''(((''''''((((((((((((''''''$$$$$$%%%%%%%%%%%%$$$$$$'''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&&&&&&&&&&''''''''''''((('''''''''''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&&&&&&&'''((((((&&&&&&'''''''''(((((((((((((((''''''''''''(((((())))))(((((((((((())))))))))))))))))))))))))))))''''''((((((((((((''''''(((''''''''''''&&&&&&&&&%%%&&&''''''(((((('''''''''(((((())))))(((((('''((((((((((((((((((((((((((((((((((((''''''''''''(((((((((((())))))))))))((((((((('''''''''''''''%%%&&&((()))))))))((('''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$$$$%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&(((&&&$$$$$$%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''(((''''''&&&&&&%%%&&&''''''((('''''''''%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''(((((((((%%%&&&((())))))(((&&&$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%%%%%%%%%%((($$$$$$''')))'''&&&(((((((((((((((((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''(((((((((((((((((((((((('''''''''''''''''''''''')))(((((('''&&&%%%%%%$$$''''''''''''''''''''''''%%%'''((('''&&&%%%'''(((((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((%%%&&&((((((((((((&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$(((((((((((((((((((((((('''''''''''''''''''''''''''''''''''''''&&&&&&&&&(((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%&&&'''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''&&&&&&%%%%%%&&&&&&&&&''''''''''''(((''''''''''''''''''''''''((('''&&&%%%%%%&&&'''(((&&&&&&&&&&&&''''''((((((''''''''''''((((((((((((((((((''''''''''''((((((''''''&&&&&&&&&&&&''''''((((((((((((((((((((((((''''''((((((((((((''''''(((''''''''''''&&&&&&&&&%%%&&&''''''(((''''''''''''(((((((((((((((((('''((((((((((((((((((((((((((((((((((((((('''''''''(((((((((((())))))))))))''''''''''''''''''&&&&&&%%%&&&(((******)))'''&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%&&&'''((((((&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&%%%%%%&&&&&&$$$"""$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''(((''''''&&&%%%&&&''''''((('''''''''&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''&&&%%%$$$%%%'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''%%%%%%&&&'''''''''&&&%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''((((((((($$$&&&((())))))(((&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((($$$$$$''')))'''&&&(((((((((((((((((((((((((((''''''''''''''''''''''''(((''''''&&&&&&''''''(((((((((((((((((((((((((((&&&'''''''''''''''''''''))))))((('''&&&&&&%%%%%%''''''''''''''''''''''''&&&'''((((((&&&&&&&&&(((((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((%%%&&&'''(((((('''&&&%%%&&&&&&''''''''''''&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%&&&'''(((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&&&&''''''''''''(((''''''''''''''''''''''''((('''&&&%%%%%%&&&'''(((&&&&&&&&&''''''''''''''''''''''''((((((((())))))((((((''''''''''''((((((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''((((((((((((''''''(((''''''''''''&&&&&&&&&%%%&&&''''''((('''''''''''''''(((((((((((('''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((())))))))))))&&&&&&''''''''''''''''''%%%&&&(((******)))'''&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((&&&%%%$$$%%%&&&&&&$$$###$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%(((''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''&&&%%%&&&''''''(((((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&'''&&&%%%$$$%%%&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%!!!"""###$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&'''''''''$$$%%%'''(((((('''&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''$$$%%%&&&'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((((($$$$$$''')))'''&&&(((((((((((((((((((((((((((''''''''''''''''''''''''((((((''''''''''''((((((((((((((((((((((((((((((&&&&&&&&&''''''''''''''')))((((((((('''&&&&&&&&&'''''''''''''''''''''''''''((()))(((&&&&&&&&&(((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''(((&&&&&&''''''''''''&&&&&&''''''(((((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((('''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''(((((()))(((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''''''''''''''''''''''''''''''''&&&&&&'''''''''%%%&&&''''''((((((''''''''''''((((((((()))))))))((((((''''''''''''(((((())))))(((((((((((())))))''''''''''''''''''''''''''''''((((((((((((''''''(((''''''''''''&&&&&&&&&%%%&&&''''''((((((''''''&&&''''''((((((''''''&&&'''''''''''''''''''''''''''''''''((((((((((((((((((((((((((())))))))))))'''''''''''''''(((((((((%%%&&&((()))))))))((('''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""###%%%&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%&&&'''(((&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((((((((($$$$$$$$$%%%''''''%%%###$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&&&&%%%***)))(((&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''((((((''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!"""$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&''''''$$$%%%%%%%%%&&&&&&&&&&&&$$$%%%'''((()))((('''&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&'''((($$$$$$''')))'''&&&(((((((((((((((((((((((((((''''''''''''''''''''''''((((((''''''''''''((((((((((((((((((((((((((((((&&&&&&&&&'''''''''(((((((((((((((((('''''''''''''''''''''''''''''''''''''''))))))((('''&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''((('''&&&&&&%%%%%%&&&&&&'''&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&'''''''''((((((((()))&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''((((((''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((((((((&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&%%%&&&'''((((((((('''&&&'''((((((((())))))))))))((((((''''''''''''(((((())))))(((((((((((())))))''''''''''''''''''''''''''''''((((((((((((''''''(((''''''''''''&&&&&&&&&%%%&&&''''''((((((''''''&&&''''''((((((''''''&&&''''''''''''''''''''''''''''''''''''((((((((()))(((((((((((())))))))))))'''''''''(((((()))))))))''''''''''''((((((((((((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$%%%&&&'''(((&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&'''((())))))######$$$%%%'''(((&&&$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&&&&&&&+++***((('''%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&&&&%%%%%%&&&''''''((((((''''''))))))((('''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%'''))))))((('''&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$$$$$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))(((((('''&&&%%%%%%%%%%%%((($$$$$$''')))'''&&&(((((((((((((((((((((((((((''''''''''''''''''''''''((((((''''''''''''((((((((((((((((((((((((((((((&&&&&&&&&'''''''''(((((('''''''''(((((((((((((((''''''''''''''''''''''''((()))***)))'''&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&''''''(((((((((&&&&&&&&&'''''''''((((((''''''%%%$$$$$$%%%''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&'''''''''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''&&&%%%$$$$$$''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''((())))))&&&&&&&&&'''''''''((((((''''''''''''''''''''''''%%%&&&'''(((((('''&&&%%%%%%%%%'''((((((((('''&&&(((((((((((())))))))))))((((((''''''''''''((((((''''''&&&&&&&&&&&&''''''))))))))))))))))))))))))''''''((((((((((((''''''(((((('''''''''&&&&&&&&&%%%&&&''''''((((((''''''&&&''''''''''''''''''&&&''''''''''''''''''''''''&&&'''''''''(((((())))))(((((((((((())))))))))))'''((((((((())))))******(((''''''''''''((())))))$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''$$$&&&((()))***)))((('''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''((('''&&&&&&'''(((###$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&&&&%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&%%%$$$###"""!!!&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$'''''''''&&&&&&%%%%%%%%%)))%%%!!!!!!%%%)))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&''''''''''''(((((('''&&&&&&'''((('''&&&(((((())))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((('''''''''))))))))))))))))))))))))((((((((((((((((((''''''%%%&&&'''''''''&&&$$$###''''''''''''((((((((((((''''''((((((((((((''''''((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''))))))(((((('''''''''&&&%%%&&&&&&&&&'''(((((((((''''''''''''''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&((((((((((((((((((((((((&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((('''&&&%%%%%%&&&'''((()))''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%***)))(((&&&&&&&&&'''(((***)))&&&%%%$$$%%%&&&'''&&&&&&&&&''''''''''''(((%%%&&&&&&&&&'''((((((((('''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&&&&''''''&&&&&&&&&'''&&&&&&%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((''''''''''''(((((())))))))))))))))))))))))((((((((((((((((((((((((&&&&&&''''''(((((())))))++++++******)))'''&&&%%%''''''&&&&&&&&&&&&'''''''''((((((((('''&&&%%%%%%&&&&&&&&&''''''''''''((((((''''''''''''&&&&&&&&&''''''''''''''''''''''''(((((((((((((((((((((((())))))(((((('''''''''&&&(((((((((((((((((((((((())))))(((((((((((())))))%%%%%%&&&&&&'''((())))))(((((((((((((((((((((((($$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&'''))))))((('''&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''(((((((((((($$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%$$$######&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((((((''''''&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%'''&&&$$$######$$$&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&''''''''''''(((((('''&&&&&&'''((('''&&&((((((((((((((('''&&&%%%(((((((((((((((((((((((('''''''''(((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&%%%%%%''''''''''''((((((((((((''''''((((((((((((''''''(((((((((((((((((((((((())))))))))))))))))))))))(((((((((((((((((((((((()))((((((((('''''''''&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&&&&'''''''''((((((((((((((((((((((((&&&&&&&&&''''''''''''(((''''''''''''''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&'''))))))''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&)))(((''''''&&&&&&''''''***)))(((''''''((())))))&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''''''''(((''''''&&&&&&''''''(((''''''&&&&&&&&&&&&''''''&&&&&&'''(((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((''''''''''''((((((''''''''''''''''''''''''(((((((((((((((((((((((('''''''''((((((((((((((((((((())))))))))))((((((''''''&&&&&&&&&&&&''''''''''''((((((''''''&&&%%%&&&&&&&&&''''''''''''((((((''''''''''''&&&&&&&&&''''''''''''''''''''''''(((((((((((((((((((((((())))))((((((((('''''''''(((((((((((((((((((((((())))))(((((((((((())))))%%%%%%&&&''''''(((((()))(((((((((((((((((((((((($$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&'''''''''&&&%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((&&&$$$&&&***,,,***(((%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&'''((((((''''''&&&&&&&&&%%%%%%%%%&&&&&&'''''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&''''''''''''(((((('''&&&&&&'''((('''&&&&&&''''''''''''&&&%%%%%%((((((((((((((((((((((((&&&&&&''''''(((((())))))((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&))))))((('''''''''''''''''''''''''''((((((((((((''''''((((((((((((''''''(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))(((((((((''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''''''''''''''&&&''''''''''''(((((((((((((((((((((((((((((((((&&&&&&&&&''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''((())))))''''''''''''''''''''''''))))))))))))))))))))))))''''''''''''''''''''''''&&&''''''''''''&&&&&&%%%((((((((((((((()))))))))&&&&&&&&&''''''''''''((('''''''''''''''&&&&&&&&&(((((((((''''''(((((((((''''''&&&&&&&&&&&&''''''&&&&&&'''((())))))))))))''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((''''''''''''((((((''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((((('''''''''%%%&&&'''((()))*********''''''&&&&&&&&&&&&''''''''''''((((((((('''&&&&&&&&&&&&&&&''''''''''''((((((''''''''''''&&&&&&&&&''''''''''''''''''''''''(((((((((((((((((((((((())))))((((((((((((''''''(((((((((((((((((((((((())))))(((((((((((())))))&&&&&&&&&''''''(((((()))(((((((((((((((((((((((($$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$###%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%)))%%%###&&&+++...,,,)))&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%############$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&''''''(((&&&&&&'''&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%'''((())))))((('''%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&''''''''''''((((((&&&&&&&&&'''((('''&&&%%%&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''((()))******(((((((((((((((((((((((('''''''''(((((((((((((((+++***((('''''''''((()))''''''''''''((((((((((((''''''((((((((((((''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''((((((((('''&&&&&&&&&%%%''''''''''''''''''''''''&&&&&&'''''''''(((((((((((((((((((((((((((((((((&&&&&&&&&''''''''''''(((''''''''''''''''''''''''(((((((((((((((((((((((())))))((((((((()))))))))''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%'''''''''&&&%%%$$$$$$$$$%%%&&&'''''''''&&&&&&&&&&&&''''''''''''(((((((((((('''&&&&&&&&&%%%((((((''''''''''''((((((''''''&&&&&&&&&&&&''''''$$$%%%&&&(((((()))))))))''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((''''''''''''(((((())))))))))))))))))))))))(((((((((((((((((((((((())))))((((((''''''&&&&&&%%%%%%'''((())))))******''''''&&&&&&&&&&&&''''''''''''((((((((((((''''''&&&&&&&&&''''''''''''((((((''''''''''''&&&&&&&&&''''''''''''''''''''''''(((((((((((((((((((((((())))))(((((((((((((((((((((((((((((((((((((((((())))))(((((((((((())))))&&&&&&''''''((((((((()))(((((((((((((((((((((((($$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$######%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%)))%%%###&&&+++...,,,)))''''''&&&%%%%%%&&&&&&'''%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''&&&'''''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%############$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&&&&''''''&&&&&&'''''''''&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&''''''''''''((((((&&&&&&&&&'''((('''&&&%%%%%%&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''((()))******'''''''''''''''''''''''''''''''''((((((((())))))+++***)))''''''((())))))''''''''''''((((((((((((''''''((((((((((((''''''((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''((((((((('''&&&&&&&&&%%%''''''''''''''''''''''''%%%&&&&&&&&&&&&'''''''''((((((((((((((((((((((((&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((())))))))))))))))))((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''''''''%%%%%%###$$$%%%&&&''''''&&&&&&&&&&&&&&&''''''''''''(((((((((((('''&&&&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&&&&''''''###$$$%%%&&&'''(((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((''''''''''''(((((())))))))))))))))))))))))(((((((((((((((((((((((())))))((((((''''''&&&&&&''''''((((((((((((''''''''''''&&&&&&&&&&&&''''''''''''((((((((((((((('''&&&&&&&&&''''''''''''((((((''''''''''''&&&&&&&&&''''''''''''''''''''''''(((((((((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))'''''''''((((((((((((((((((((((((((((((((((((((($$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((&&&$$$&&&***,,,***(((((((((&&&%%%%%%%%%&&&'''%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&'''%%%%%%&&&&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&&&&&&&'''%%%&&&'''''''''&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&%%%$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''''''''''''''&&&&&&&&&''''''''''''(((((('''&&&&&&'''((('''&&&%%%%%%&&&''''''''''''&&&((((((((((((((((((((((((&&&&&&''''''(((((())))))''''''''''''''''''''''''$$$$$$%%%%%%&&&'''''''''******)))(((((((((((((((''''''''''''((((((((((((''''''((((((((((((''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&''''''''''''''''''''''''%%%%%%&&&&&&&&&'''''''''((((((((((((((((((((((((&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((((((((()))))))))(((''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''''''''&&&'''''''''''''''(((((((((&&&&&&&&&''''''''''''((('''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&''''''$$$$$$%%%&&&'''''''''&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((''''''''''''((((((''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((((('''''''''((((((((((((((('''&&&%%%''''''&&&&&&&&&&&&''''''''''''((()))))))))((((((&&&&&&&&&''''''''''''((((((''''''''''''&&&&&&&&&''''''''''''''''''''''''(((((((((((((((((((((((((((((())))))))))))******))))))))))))))))))))))))))))))(((((((((((())))))(((((((((((((((((((((((((((((((((((((((((((((((($$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&'''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''(((((((((((()))(((&&&%%%%%%%%%&&&'''%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%###$$$%%%%%%&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&'''((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&%%%$$$######&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&&&&&&&&&&%%%&&&'''((((((&&&$$$###&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&)))((((((((('''''''''&&&&&&&&&&&&''''''''''''(((((('''&&&&&&'''((('''&&&%%%&&&'''((((((((((((((((((((((((((((((((((((((('''''''''(((((((((((((((''''''''''''''''''''''''$$$$$$%%%%%%&&&''''''((((((((())))))(((((('''&&&''''''''''''((((((((((((''''''((((((((((((''''''((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''&&&&&&&&&'''''''''''''''''''''''''''''''''''''''&&&''''''''''''(((((((((((((((((((((((((((((((((&&&&&&&&&''''''''''''(((''''''''''''''''''''''''(((((((((((((((((((((((('''(((((()))((('''&&&%%%''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&''''''((())))))((('''&&&&&&&&&'''(((&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&'''''''''''''''&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((''''''''''''((((((''''''''''''''''''''''''(((((((((((((((((((((((('''''''''(((((((((((((((''''''((((((''''''&&&%%%''''''&&&&&&&&&&&&''''''''''''((()))))))))))))))&&&&&&&&&''''''''''''((((((''''''''''''&&&&&&&&&''''''''''''''''''''''''(((((((((((((((((((((((((((((()))))))))*********))))))))))))))))))))))))))))))(((((((((((()))))))))((((((((((((((((((((((((((((((((((((((((((((($$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&''''''%%%%%%%%%%%%&&&&&&'''(((%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''((('''&&&&&&'''(((***)))'''%%%%%%%%%'''(((%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%###$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$&&&'''(((((())))))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&'''''''''&&&&&&&&&%%%$$$###"""!!!&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&&&&&&&&&&&&&%%%&&&'''((((((&&&$$$###(((((((((''''''&&&&&&%%%%%%%%%%%%&&&&&&'''''''''&&&&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&))))))(((((('''''''''&&&&&&&&&&&&'''''''''((((((((('''&&&&&&'''((('''&&&&&&&&&'''((())))))((((((&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((('''''''''''''''''''''''''''''''''&&&&&&''''''((()))******'''((()))))))))(((&&&%%%''''''''''''((((((((()))''''''((((((((((((''''''(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))%%%%%%%%%&&&&&&'''''''''%%%&&&&&&''''''(((((((((''''''''''''''''''''''''(((((((((((())))))))))))((((((((((((((((((((((((&&&&&&&&&'''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''((((((((('''%%%$$$''''''''''''''''''''''''))))))))))))))))))))))))))))))))))))))))))))))))((('''&&&&&&'''((()))***((('''%%%###"""###%%%&&&&&&&&&&&&'''''''''((((((%%%&&&&&&''''''(((((((((((((((''''''''''''(((((('''''''''&&&&&&'''''''''((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((''''''''''''(((((())))))))))))))))))))))))((((((((((((((((((((((((&&&'''''''''(((((())))))&&&&&&'''''''''''''''&&&'''''''''&&&&&&'''''''''''''''((()))))))))))))))&&&&&&&&&'''''''''(((((((((((('''''''''&&&&&&&&&''''''''''''''''''''''''(((((((((((((((((((((((((((((())))))*********+++))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))((((((((((((((((((((((((((((((((((((%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%&&&&&&'''((())))))%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&)))&&&######%%%'''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&'''((('''&&&&&&######$$$$$$$$$$$$######%%%&&&''''''%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%'''''''''%%%###"""$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&###$$$&&&'''((('''&&&&&&&&&'''((()))(((&&&$$$"""''''''&&&%%%%%%%%%&&&&&&'''(((((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((())))))))))))''''''((()))*********)))((('''&&&%%%&&&(((***+++***(((''''''(((((('''%%%''''''((()))))))))))))))''''''''''''''''''''''''$$$%%%%%%%%%&&&'''''''''(((((())))))))))))((((((&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&&&&&&&&&&&&&******)))(((((((((((((((''''''(((((())))))******))))))))))))))))))))))))(((((('''''''''&&&&&&&&&))))))((((((''''''&&&&&&((((((((((((((('''''''''%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&'''((()))((('''&&&%%%%%%&&&'''(((''''''((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''&&&&&&&&&%%%%%%%%%(((((('''''''''&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&&&&''''''''''''&&&%%%&&&'''((()))***)))'''%%%$$$$$$$$$%%%''''''''''''''''''''''''(((((((((((((((((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&)))(((((('''''''''((((((((((((((((((((((((((((((((('''&&&&&&'''((('''%%%&&&'''((())))))((('''&&&&&&&&&&&&''''''''''''(((((((((((((((((((((((((((+++***)))((('''&&&%%%%%%''''''''''''((((((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))(((((())))))))))))))))))))))))''''''((((((((((((''''''%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&'''(((((()))%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%%%%&&&&&&&&&&&&+++)))&&&%%%&&&'''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$&&&'''&&&%%%$$$%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''&&&$$$$$$%%%'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''')))(((((((((''''''''''''(((''''''&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%&&&''''''%%%###"""$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((&&&&&&''''''''''''&&&&&&''''''''''''&&&&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%&&&&&&'''''''''&&&)))***+++,,,+++***((('''((('''&&&&&&&&&&&&&&&&&&''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((()))))))))$$$%%%&&&&&&&&&&&&&&&&&&+++***(((&&&%%%&&&'''(((***(((''''''(((((('''&&&&&&&&&'''(((((((((((((((((((((((((((''''''''''''''''''((((((((((((((((((((())))))******))))))((((((((((((((((((((((((((()))((('''&&&&&&&&&&&&'''******)))((((((((((((((('''((((((((()))))))))***''''''''''''''''''''''''(((((('''''''''&&&&&&&&&((((((((((((((('''''''''((((((((((((((((((((((((%%%%%%&&&&&&&&&'''''''''(((''''''&&&&&&&&&'''''')))(((''''''''''''((()))''''''((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''''''''&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%(((((((((((((((((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&&&&'''''''''&&&&&&%%%&&&'''((()))((('''&&&%%%%%%%%%&&&'''''''''''''''''''''''''''''''''''''''''''''''''''(((((('''''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''((((((''''''''''''(((((('''''''''''''''''''''''''''&&&%%%&&&'''((('''&&&%%%&&&'''(((((('''&&&%%%&&&&&&&&&''''''''''''(((((((((((((((((((((((((((((((((((('''''''''''''''''''''''''''((((((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))((((((((((((((((((((((((((((((''''''((((((((((((''''''%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''***(((&&&%%%&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$%%%&&&%%%$$$###$$$&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&%%%$$$###%%%&&&%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''(((((((((((('''''''''''')))(((''''''&&&&&&&&&&&&"""######$$$&&&''''''((($$$%%%&&&'''&&&%%%$$$###$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((&&&&&&''''''''''''&&&&&&((((((((('''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))***+++,,,---,,,++++++)))(((''''''&&&&&&&&&'''''''''((((((((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((((((((()))))))))(((''''''+++***((('''&&&&&&'''''')))(((''''''(((((('''&&&%%%&&&&&&'''''''''''''''(((((((((((((((((((((((())))))((((((((((((((((((((())))))******))))))((())))))))))))))))))))))))((((((''''''&&&&&&''''''******)))((((((((((((((((((((((((((())))))))))))''''''''''''''''''''''''(((((((((''''''''''''&&&'''''''''(((((((((((((((((((((((((((((((((((((((&&&&&&&&&'''''''''''''''))))))(((&&&&&&%%%%%%%%%(((''''''&&&&&&''''''(((''''''((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((((((((((((''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%))))))((((((''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&'''''''''&&&&&&&&&&&&'''((((((&&&%%%%%%%%%%%%&&&'''((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''(((((()))))))))''''''''''''''''''''''''((((((''''''''''''((((((''''''''''''''''''''''''&&&%%%%%%&&&((()))((('''%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&''''''''''''(((((((((((((((((((((((((((%%%%%%&&&&&&'''''''''(((''''''''''''((((((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))((((((''''''''''''''''''''''''''''''((((((((((((''''''%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&'''''''''&&&%%%%%%$$$%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&)))(((&&&%%%$$$%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%###$$$%%%%%%######$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%"""$$$%%%%%%$$$###$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%$$$###############$$$%%%%%%&&&''''''$$$%%%&&&&&&&&&%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&)))(((((((((((('''''''''%%%%%%%%%&&&&&&&&&&&&'''((('''&&&%%%%%%&&&'''((('''((()))+++,,,,,,,,,,,,******)))(((''''''''''''&&&'''((((((((((((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((***************)))((('''''''''&&&&&&'''((()))***)))(((''''''((()))(((&&&%%%&&&''''''((((((''''''&&&'''''''''''''''((((((((((((''''''&&&&&&%%%%%%'''(((((())))))(((((('''((((((((((((((((((((((((((((((''''''''''''((((((***))))))((((((((((((((((((((((((((())))))))))))''''''''''''''''''''''''((((((((('''''''''''''''&&&&&&''''''(((((())))))((((((((((((((()))))))))'''''''''''''''''''''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((((((((((((((((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%$$$#########''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''(((((())))))&&&&&&&&&'''''''''''''''(((''''''''''''(((((()))''''''''''''''''''''''''&&&%%%$$$&&&((())))))(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((((((((((((((((((%%%%%%%%%&&&&&&&&&&&&'''''''''''''''((((((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))((((((''''''''''''''''''''''''''''''((((((((((((''''''%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$$$$$$$%%%%%%&&&'''%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''###$$$%%%%%%&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&***)))(((&&&&&&&&&'''((($$$$$$%%%%%%%%%%%%$$$$$$###$$$%%%%%%######$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%!!!###%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%%%%%%%((('''&&&%%%$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&)))(((((((((((('''''''''%%%%%%&&&&&&&&&''''''''')))(((&&&%%%%%%&&&'''(((&&&'''(((***+++------...,,,+++***)))((((((((((((&&&&&&'''((((((((((((((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&'''''''''(((''''''''''''&&&%%%%%%$$$&&&&&&&&&'''(((((()))***((('''&&&'''((()))((('''''''''((())))))))))))(((%%%%%%&&&&&&&&&'''''''''(((((((((''''''&&&&&&%%%&&&''''''((((((''''''&&&))))))))))))))))))))))))(((((('''''''''(((((()))***))))))((((((((((((((())))))))))))((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&''''''(((((())))))(((((((((((())))))******((((((((((((((((((((((((&&&&&&&&&&&&&&&'''(((((('''''''''(((((('''''''''''''''((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''(((((((((((((((((((((''''''''''''((((((((((((''''''&&&%%%$$$#########''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&''''''(((''''''&&&&&&&&&&&&''''''&&&&&&&&&'''''''''''''''((('''''''''&&&%%%$$$$$$''''''''''''''''''''''''''''''''''''''''''''''''&&&'''''''''''''''''''''%%%%%%&&&&&&&&&'''''''''&&&&&&&&&'''''''''(((((('''''''''''''''((())))))''''''''''''''''''''''''&&&%%%$$$&&&((())))))((((((''''''''''''''''''(((&&&&&&&&&''''''''''''((((((((((((((((((((((((((('''&&&&&&&&&&&&%%%%%%%%%''''''''''''((((((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))((((((''''''''''''''''''''''''''''''((((((((((((''''''%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$%%%&&&''''''%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&###%%%'''((('''&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&)))(((''''''''''''''''''$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%&&&%%%$$$###$$$&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%!!!###&&&&&&&&&%%%%%%&&&%%%%%%%%%&&&''''''((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&'''''''''''')))(((''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((&&&&&&''''''''''''&&&&&&((((((((('''''''''&&&&&&%%%&&&&&&&&&'''''''''''')))(((''''''''''''''''''(((((()))***,,,---...///---,,,+++***)))(((((((((%%%&&&'''((())))))))))))))))))(((((('''&&&&&&&&&&&&&&&'''''''''(((((((((''''''(((((((((''''''&&&)))))))))(((''''''&&&&&&((('''&&&'''((()))(((''''''(((((()))))))))))))))%%%%%%&&&&&&'''(((((((((******))))))))))))))))))&&&''''''((((((''''''&&&************************((((((''''''(((((())))))******)))((((((((((((((())))))))))))(((((((((((())))))))))))))))))))))))'''(((((((((((()))))))))'''''''''((((((((((((((('''(((((())))))******+++))))))))))))((((((((((((%%%%%%%%%&&&&&&((()))))))))******++++++******)))''''''((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&''''''''''''(((((((((((((((((((((((()))))))))))))))((((((''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''''''''((((((''''''&&&&&&&&&&&&''''''%%%&&&''''''((((((''''''((((((((('''&&&%%%###"""''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((((((((''''''&&&''''''((()))***&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&((()))(((''')))(((''''''''''''((()))&&&&&&&&&''''''''''''(((((((((((((((((((((((((((((('''''''''&&&&&&%%%%%%''''''''''''((((((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))((((((''''''''''''''''''''''''''''''((((((((((((''''''%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&#########$$$$$$$$$%%%%%%###%%%''''''$$$"""###$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$&&&'''&&&%%%$$$%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!###&&&((('''&&&&&&'''%%%%%%&&&&&&'''(((((((((%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&'''''''''(((''''''&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&'''$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%&&&'''((((((%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&''''''''''''&&&&&&''''''''''''&&&&&&&&&%%%&&&&&&&&&&&&''''''''''''((((((((((((((('''&&&&&&''''''((((((***+++,,,---...---,,,+++***)))))))))%%%&&&'''((()))))))))))))))))))))((('''&&&&&&&&&''''''((((((((()))))))))((())))))************))))))))))))(((((('''&&&%%%((('''&&&''')))))))))(((&&&'''(((((())))))(((((('''''''''((()))*********)))))))))))))))*********(((((())))))))))))((((((************************((((((((((((((()))************)))(((((((((((((((***)))))))))((((((((('''(((((((((((((((((((((((('''((((((((())))))))))))(((((((((((((((''''''''''''(((((()))******++++++*********)))))))))((((((''''''&&&&&&&&&''''''(((((()))***++++++***)))(((''''''((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((%%%%%%&&&&&&''''''''''''''''''''''''(((((())))))((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((''''''''''''((((((''''''&&&&&&&&&&&&''''''%%%&&&'''((((((((('''&&&&&&&&&'''''''''&&&$$$###''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((((((''''''&&&&&&%%%%%%%%%%%%&&&&&&'''(((((()))&&&&&&&&&''''''((()))***&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%&&&'''((('''&&&((('''&&&&&&&&&&&&'''(((&&&&&&&&&''''''''''''((((((((((((((((((((((((((('''''''''''''''(((((((((''''''''''''((((((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))((((((((((((((((((((((((((((((''''''((((((((((((''''''%%%$$$$$$$$$$$$$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&""""""#########$$$$$$$$$!!!$$$%%%$$$ &&&&&&&&&&&&&&&&&&&&&&&&!!!"""$$$%%%&&&%%%%%%$$$&&&''''''''''''''''''&&&%%%&&&''''''%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%!!!$$$'''(((((('''''''''%%%%%%&&&&&&'''((())))))%%%%%%%%%&&&&&&&&&''''''#########$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&######$$$%%%&&&&&&'''(((%%%$$$$$$$$$%%%%%%&&&'''$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$%%%'''((())))))%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''(((((('''((()))))))))(((&&&%%%$$$$$$%%%%%%&&&((()))***///...---+++***)))))))))%%%&&&'''((())))))))))))***))))))((('''&&&&&&&&&(((((((((((())))))))))))%%%%%%&&&''''''(((''''''%%%&&&'''((())))))))))))'''&&&&&&''')))***)))(((%%%&&&''''''((((((''''''((())))))***+++,,,,,,,,,&&&&&&''''''(((((())))))******++++++++++++******''''''''''''''''''''''''((((((((((((((()))************)))(((((((((((((((******))))))(((((((((''''''''''''''''''''''''''''''((((((((())))))******))))))(((((('''''''''&&&'''(((((()))***++++++++++++*********))))))(((((()))((('''&&&&&&&&&&&&&&&%%%&&&'''(((((('''&&&%%%''''''((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&'''''''''((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((''''''''''''(((((('''''''''&&&&&&'''''''''%%%%%%'''((((((((('''&&&$$$%%%&&&'''''''''&&&%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((******)))((('''&&&&&&%%%%%%%%%&&&&&&'''((())))))&&&&&&&&&'''''')))******&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&&&&'''((('''%%%'''&&&%%%%%%%%%%%%&&&'''&&&&&&&&&'''''''''((((((((((((((((((((((((((((((%%%%%%&&&'''((()))***+++''''''''''''((((((((()))((((((''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))(((((())))))))))))))))))))))))''''''((((((((((((''''''&&&&&&&&&%%%%%%$$$$$$$$$''''''''''''&&&%%%$$$$$$############$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&'''(((((((((%%%&&&&&&&&&%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$###"""&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&((('''&&&%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''******((('''%%%%%%$$$$$$&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&***)))((('''&&&%%%%%%%%%''''''''''''''''''''''''((((((((((((((((((((((((&&&'''''''''''''''''''''&&&'''((())))))((('''&&&''''''''''''''''''''''''((((((***++++++***)))((('''((()))))))))))))))(((''''''((((((((((((''''''++++++***)))((('''&&&&&&'''((()))******)))((('''''''''''''''((((((((()))******))))))((((((''''''))))))))))))))))))))))))(((((((((((())))))))))))************************((((((((((((((('''''''''---,,,***)))))))))***+++''''''(((((())))))******,,,+++)))((('''((()))***+++***(((&&&&&&''')))***''''''((((((((((((''''''((())))))***************((()))+++,,,,,,***'''%%%((()))***++++++***)))(((((()))***++++++***)))((('''((()))******)))((('''''''''''''''''''''''''''))))))))))))))))))))))))'''(((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((((((((((('''&&&%%%%%%&&&'''(((''''''''''''''''''''''''((((((((((((((((((((((((***)))((('''&&&%%%%%%%%%%%%''')))***((('''''''''((((((''''''&&&&&&&&&%%%'''&&&&&&%%%%%%%%%&&&&&&'''''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&'''&&&&&&''''''(((((())))))(((((((((((((((((((((((('''''''''''''''''''''''')))(((((('''''''''((((((''''''''''''''''''''''''((('''&&&%%%%%%%%%%%%%%%''''''''''''''''''''''''((((((((('''&&&&&&%%%%%%((('''&&&%%%%%%&&&'''((()))((('''&&&&&&'''((()))''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''''''''((()))))))))))))))'''''''''((((((((((((((((((((((((((())))))))))))''''''''''''((((((((()))((((((((((((((((((((((((&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$!!!!!!!!!!!!"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&((('''&&&%%%%%%%%%%%%&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''(((''''''&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))(((((('''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''((((((''''''''''''''''''&&&&&&'''(((((('''&&&&&&'''''''''''''''''''''''''''((()))***+++******)))(((((()))))))))))))))(((''''''((((((((((((''''''++++++******))))))(((((((((((())))))))))))(((((('''''''''((((((((())))))******))))))(((((((((((())))))))))))))))))))))))''''''''''''(((((((((((())))))))))))))))))))))))((((((((((((((((((((((((+++******)))(((((())))))(((((((((((())))))))))))******)))((()))+++---......---+++***)))***+++,,,'''(((((())))))(((((('''&&&&&&'''(((((((((((('''(((***+++,,,,,,***(((&&&)))))))))******))))))))))))))))))******)))))))))'''((()))******)))((('''(((((((((((((((((((((((((((((((((((((((((((((((('''''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&))))))((((((''''''&&&&&&((('''&&&&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((()))((('''&&&&&&&&&&&&&&&%%%'''((((((&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''''''''&&&%%%%%%&&&'''''''''''''''(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((((((''''''''''''((((((''''''''''''''''''''''''(((((('''&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''&&&&&&&&&((('''&&&&&&&&&&&&'''((()))((('''&&&&&&'''((()))''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''(((((((((((())))))))))))''''''((()))))))))))))))((((((''''''''''''''''''(((((((((((())))))))))))'''''''''((((((((())))))************************&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%$$$$$$######&&&''''''''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%''''''&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&'''((()))***%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''&&&''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&)))))))))(((((('''''''''%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''&&&'''(((***++++++++++++))))))))))))))))))))))))'''(((((())))))(((((('''+++++++++***************))))))(((((((((((())))))''''''((((((((()))))))))***))))))))))))((((((((())))))))))))))))))))))))&&&&&&&&&'''''''''(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))((('''))))))))))))((((((((((((((((((((()))***---///000///...---+++******++++++((())))))******))))))(((%%%&&&&&&''''''''''''''')))***,,,,,,,,,+++)))(((***))))))(((((())))))******))))))(((((())))))***'''(((((())))))(((((('''))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&***))))))((('''&&&%%%%%%(((''''''&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((((((''''''&&&&&&&&&''''''%%%&&&'''&&&$$$$$$&&&''''''''''''&&&&&&&&&&&&%%%'''&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''&&&%%%%%%&&&''''''((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((((((''''''''''''((((((''''''''''''''''''''''''((((((((((((''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''((('''&&&&&&&&&&&&'''(((((((((''''''''''''((((((''''''&&&&&&&&&&&&''''''(((((((((((((((((((((((((((((((((((())))))))))))''''''((()))))))))))))))((((((((('''&&&&&&&&&%%%(((((((((((())))))))))))''''''((((((((()))))))))************************%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%%%%%%%%%%'''''''''''''''((())))))%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""$$$%%%'''(((******%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&'''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$&&&''''''(((''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%(((''''''''''''&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&'''((()))***$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&&&&'''''''''''''''((())))))''''''''''''''''''''''''''''''''''''''''''''''''*********)))((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&'''((()))***+++,,,,,,******))))))))))))))))))(((((())))))))))))(((((()))))))))******+++++++++***)))(((''''''((()))***'''(((((((((((()))))))))))))))))))))))))))))))))(((((((((((((((((((((((('''''''''(((((((((((()))))))))))))))))))))))))))(((((())))))))))))******((()))***++++++***)))(((******))))))((((((''''''''''''((()))***,,,...///---,,,***)))(((''''''((())))))************))))))''''''((())))))))))))))))))***+++,,,,,,+++***)))***)))(((''''''((()))******)))(((''''''((()))***((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''(((((((((''''''&&&&&&&&&((((((''''''''''''((((((''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&'''((()))'''''''''%%%$$$$$$''')))'''''''''''''''''''''''''''&&&&&&&&&&&&''''''(((''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''))))))((((((''''''&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''(((''''''''''''(((((()))''''''''''''''''''''''''(((((()))))))))(((((((((''''''''''''''''''''''''%%%%%%&&&&&&'''(((((()))'''''''''&&&&&&'''''''''(((((((((''''''(((((((((''''''&&&&&&&&&&&&''''''))))))))))))))))))))))))&&&&&&&&&&&&''''''''''''''''''((())))))))))))))))))(((((('''&&&%%%%%%$$$(((((((((((())))))))))))'''(((((((((((()))))))))''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&''''''&&&&&&%%%$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%'''((()))***%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&'''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''(((&&&&&&''''''(((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((&&&$$$"""###$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&'''$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&''''''((($$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&'''''''''''''''''''''((()))***((((((((((((((((((((((((((((((((((((((((((((((((******))))))(((((((((''')))(((((((((((((((((()))((((((((((((((((((((((((''''''((((((***+++,,,---,,,+++***)))((()))))))))(((((())))))))))))((((((''''''(((((()))************)))(((''''''((()))***(((((((((((()))))))))***))))))))))))************((((((((((((((((((((((((((())))))))))))*********************************))))))))))))******++++++)))***+++,,,---,,,+++*********))))))((((((''''''((((((((((((((()))*********))))))((('''&&&&&&&&&))))))************))))))'''(((((()))***))))))))))))******+++++++++***)))***)))(((''''''((()))******)))(((''''''((()))***((((((''''''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$%%%&&&'''((())))))''''''''''''''''''''''''%%%%%%&&&&&&''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&'''((()))((((((((('''%%%&&&(((***(((((((((((((((((())))))&&&&&&&&&&&&&&&'''((()))''''''''''''''''''''''''''''''''''''''''''''''''))))))((((((''''''&&&&&&(((((((((((((((((((((((('''''''''''''''''''''''''''''''''''''''((())))))''''''''''''''''''''''''(((((()))******))))))((((((((((((((((((((((((((($$$%%%%%%&&&'''((())))))&&&''''''''''''''''''&&&'''(((((((((((((((((('''''''''&&&&&&&&&&&&''''''))))))))))))))))))))))))&&&&&&&&&&&&''''''''''''''''''((()))))))))))))))))))))((('''&&&&&&%%%%%%(((((((((((())))))))))))(((((((((((()))))))))***''''''''''''''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&'''''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((())))))%%%%%%&&&''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%)))+++,,,)))%%%###$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&''''''$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&''')))((('''&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$%%%%%%&&&&&&'''''''''((('''''''''((())))))***(((((((((((((((((((((((())))))))))))))))))))))))((((((((((((((((((((((((***))))))(((((())))))***(((((((((((((((((((((((((((((((((((()))***,,,,,,---,,,***)))(((((()))***((())))))******))))))(((''''''(((((()))))))))***))))))(((((((((((())))))((((((((()))))))))******)))))))))************+++))))))))))))))))))))))))))))))*********+++++++++************************)))))))))***++++++,,,,,,++++++,,,,,,---,,,,,,,,,))))))))))))(((((((((((()))))))))((((((''''''''')))))))))))))))(((((((((((())))))******))))))(((&&&''''''((((((((((((((((((((()))************))))))((((((''''''(((((())))))((((((''''''(((((()))(((''''''&&&&&&''''''(((''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&&&&'''((()))******''''''''''''''''''''''''$$$$$$%%%&&&'''(((((()))'''(((((())))))(((((('''((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&'''((()))'''((()))((('''&&&((()))((((((((((((((()))))))))&&&&&&&&&&&&'''((())))))''''''''''''''''''''''''&&&'''(((((((((((('''&&&((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&''''''((()))***''''''''''''''''''''''''&&&''')))*********)))(((((((((((((((((((((((((((%%%%%%&&&&&&'''((())))))&&&&&&'''(((((('''&&&&&&''''''((((((((((((''''''''''''&&&&&&&&&&&&''''''(((((((((((((((((((((((((((((((((((())))))))))))''''''((())))))))))))))))))))))))(((''''''&&&&&&(((((((((((())))))))))))((((((((()))))))))******************************$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&%%%$$$$$$(((((('''''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&%%%$$$######"""&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$'''***,,,***%%%###%%%(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((######$$$%%%&&&'''((((((%%%%%%%%%%%%%%%&&&'''((($$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&$$$$$$%%%%%%&&&''''''((()))((((((((((((((())))))(((((((((((((((((((((((())))))))))))))))))))))))&&&&&&&&&'''(((((())))))***)))(((''''''((()))***(((((((((((((((((((((((())))))(((((((((***+++,,,...,,,***)))(((((()))***))))))************))))))))))))))))))))))))******(((((())))))))))))(((((((((((()))))))))*********))))))*********+++++++++))))))))))))))))))))))))))))))))))))************************************))))))******+++,,,,,,---++++++******++++++,,,---(((((((((((()))))))))))))))))))))))))))(((''''''((())))))***************'''(((((())))))((((((''''''(((((()))))))))))))))''''''(((((())))))))))))'''((((((((((((((((((''''''(((((((((((((((((('''((('''&&&&&&&&&&&&'''(((''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&''''''''''''((()))******)))((('''''''''''''''''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&''''''(((%%%'''(((((('''&&&&&&'''&&&&&&&&&&&&'''''''''(((&&&&&&&&&&&&'''((()))***''''''''''''''''''''''''&&&'''((())))))((('''&&&'''''''''(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&''''''((()))***''''''''''''''''''''''''%%%&&&(((******)))((('''((((((((((((((((((((((((%%%&&&&&&&&&''''''((((((&&&&&&'''(((((('''&&&&&&&&&'''((())))))((('''&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''(((((((((((())))))))))))''''''((()))))))))))))))))))))))))))))))))(((((((((((((((((())))))))))))(((((()))))))))*********************************$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%$$$###"""%%%$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%$$$$$$######$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$###''')))((($$$"""%%%(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((!!!"""###$$$&&&'''((((((%%%%%%%%%%%%%%%&&&'''((($$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&''''''(((&&&''''''((((((''''''&&&$$$$$$%%%%%%&&&'''(((((())))))(((((((((((())))))))))))))))))))))))))))))(((((((((((((((((((((((($$$%%%%%%&&&'''((()))))))))((('''&&&&&&'''((()))))))))))))))))))))))))))******)))(((((()))***+++...---+++)))(((((()))***))))))************))))))************************'''((()))******)))((('''))))))))))))************))))))******++++++++++++))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))))))))***+++,,,,,,------+++***)))))))))***,,,---''''''(((((())))))******))))))************))))))&&&'''((())))))******)))''''''((((((((((((''''''******+++,,,,,,,,,,,,,,,&&&'''''''''(((((())))))&&&'''((())))))((('''&&&&&&'''((())))))((('''&&&((('''&&&%%%%%%&&&'''((())))))))))))))))))))))))))))))))))))))))))))))))+++***)))((('''&&&%%%%%%((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&%%%'''((()))******)))((('''%%%%%%%%%%%%%%%%%%%%%%%%(((((((((((((((((((((((((((''''''&&&&&&&&&''''''###&&&(((((('''%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&'''''')))******''''''''''''''''''''''''&&&'''((())))))((('''&&&&&&'''''''''(((((())))))((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&'''''')))******''''''''''''''''''''''''$$$&&&((()))***)))((('''))))))))))))))))))))))))&&&&&&&&&'''''''''''''''%%%&&&'''(((((('''&&&%%%&&&'''((())))))((('''&&&'''''''''&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&&&&'''''''''((('''(((((()))))))))))))))))))))))))))************(((((((((((())))))))))))))))))))))))************((((((((((((((((((((((((&&&%%%%%%$$$#########$$$'''''''''&&&&&&%%%%%%%%%######$$$$$$$$$%%%%%%%%%#########$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%%%%$$$%%%%%%&&&'''((())))))(((((('''&&&%%%$$$$$$#########$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%######$$$%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&///---***'''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&'''(((((((((%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((('''&&&%%%$$$%%%&&&'''(((((('''&&&%%%$$$$$$###%%%&&&&&&'''((()))******'''''''''''''''''''''''',,,***((('''&&&''')))***&&&&&&''''''((()))))))))&&&'''''''''&&&%%%%%%$$$%%%&&&''''''(((((('''''')))((('''&&&&&&&&&&&&&&&+++***(((&&&%%%&&&'''(((************))))))))))))++++++******))))))(((((((((((((((((('''''''''''''''((()))******)))((('''))))))))))))))))))))))))(((((())))))))))))((((((*********)))))))))))))))************************+++******+++,,,,,,***((((((((((((((()))***+++,,,***+++,,,,,,+++***)))(((***************************************************++++++***((()))+++---******++++++++++++******++++++************++++++,,,+++)))((((((((()))***))))))(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))******))))))((((((''''''(((((())))))******++++++(((((((((((()))))))))))))))(((&&&&&&''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((((((((((('''''''''&&&&&&&&&))))))((((((''''''&&&&&&((('''&&&%%%%%%&&&'''((((((((())))))))))))((((((((('''&&&&&&'''((('''%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))***+++,,,))))))(((((((((((())))))((((((((((((((((((((((((%%%&&&&&&&&&'''(((((((((''''''''''''((((((((((((''''''''''''''''''''''''((((((((('''&&&&&&&&&%%%&&&&&&&&&'''''''''((((((%%%%%%&&&'''((((((((('''(((((((((((((((((((((((())))))))))))))))))))))))&&&'''((('''&&&&&&'''((((((((((((((((((((((((((('''''''''''''''''''''''''''''''''''''''''''''''')))(((&&&%%%%%%&&&((()))''''''''''''(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************(((((((((((())))))))))))))))))))))))))))))))))))&&&%%%%%%$$$######$$$$$$''''''&&&&&&&&&%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%############$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&(((((((((''''''&&&&&&&&&######$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%!!!""""""###$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%$$$###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%%%%&&&''''''''''''&&&&&&%%%%%%$$$%%%%%%&&&&&&''''''(((((('''''''''''''''''''''''''''&&&%%%$$$###$$$$$$%%%((('''''''''''''''''''''&&&'''''''''&&&&&&%%%$$$%%%&&&''''''(((((('''''')))((('''&&&&&&&&&&&&'''+++***(((''''''((()))***))))))))))))))))))))))))*********)))))))))))))))*********************)))(((((()))******)))((((((************************((())))))))))))))))))(((************************************************)))((('''((()))***)))(((+++******)))))))))************+++++++++***)))(((************************++++++++++++++++++++++++)))******)))((((((***,,,******++++++++++++******,,,++++++******++++++,,,,,,+++)))((((((((()))***))))))(((((((((((())))))))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((((((((())))))(((((((((((()))))))))))))))(((&&&&&&'''(((&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((((((((((('''''''''&&&&&&&&&((((((((((((((('''''''''(((((('''&&&&&&'''(((((((((((())))))))))))((((((((('''&&&&&&'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&))))))(((((((((((())))))((((((((((((((((((((((((&&&&&&&&&'''''''''''''''&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%&&&&&&&&&&&&'''''''''&&&&&&''''''((('''''''''((((((((((((((((((((((((((((((((((((((((((((((((&&&'''((('''&&&&&&'''(((((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''((('''&&&%%%%%%&&&'''(((''''''''''''(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))''''''''''''(((((((((((((((((((((((()))))))))***((((((((((((((((((((((((&&&%%%%%%$$$$$$$$$$$$$$$'''&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$###############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$''''''''''''''''''&&&&&&###$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%""""""######$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$############%%%&&&(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%((((((''''''&&&%%%%%%$$$&&&''''''''''''&&&%%%%%%&&&&&&'''(((((((((((('''((((((''''''&&&&&&''''''******)))(((((()))+++,,,(((((((((((())))))))))))))))))))))))************************************((())))))******))))))(((************************))))))************))))))************************++++++++++++++++++++++++---+++******,,,.........---,,,+++***)))))))))))))))************)))((((((++++++++++++++++++++++++++++++++++++++++++++++++)))******)))(((''')))+++******++++++++++++******,,,,,,++++++++++++,,,,,,,,,+++***)))((()))*********))))))(((((())))))***))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))(((((((((((())))))))))))((((((''''''''''''''''''(((((((((((()))))))))))))))'''&&&'''(((((('''%%%((((((((((((((((((((((((&&&''''''((((((((((((((((((((((((''''''''''''&&&'''''''''((((((((((((((()))((((((''''''(((((()))'''(((((())))))(((((('''(((&&&%%%&&&'''((('''&&&'''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%)))((((((''''''(((((()))(((((((((((((((((((((((('''''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''%%%%%%%%%%%%&&&&&&&&&&&&'''''''''(((''''''&&&&&&((((((((((((((((((((((((((((((((((((((((((((((((&&&'''((('''&&&&&&'''(((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))''''''''''''((((((((((((((((((((()))))))))******((((((((((((((((((((((((&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%((((((&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''')))***%%%%%%&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&%%%%%%%%%&&&&&&''''''%%%%%%%%%&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((())))))(((((('''&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&'''(((((((((((((((((((((''''''''''''(((((((((((((((((()))***+++,,,((((((((((((((()))))))))(((((())))))******++++++((((((((((((((()))))))))))))))))))))))))))))))))************************)))******++++++******)))*********+++++++++++++++++++++++++++++++++++++++...,,,******,,,///000111---,,,+++***************))))))))))))))))))))))))++++++++++++++++++++++++++++++++++++++++++++++++***+++,,,+++)))(((***+++***++++++,,,,,,++++++***++++++************++++++,,,+++***)))))))))***+++***))))))))))))))))))***))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((())))))))))))((((((((((((((((((((((((''''''(((((())))))******)))((((((''''''&&&&&&&&&(((((((((((()))))))))))))))'''&&&'''((()))'''&&&((((((((((((((((((((((((&&&''''''(((((((((((((((((((((((('''''''''''''''&&&&&&''''''(((((())))))))))))(((((((((((())))))'''((((((((((((((((((''''''&&&%%%&&&(((((((((&&&((((((((((((((((((((((((&&&&&&'''(((((()))******(((((((((''''''(((((((((((((((((((((((((((((((((((((((((('''&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''%%%&&&&&&&&&'''((((((((($$$$$$$$$%%%%%%%%%&&&&&&'''((((((((('''&&&%%%%%%((((((((((((((((((((((((((((((((((((((((((((((((&&&'''((('''&&&&&&&&&((((((((((((((((((((((((((())))))))))))))))))))))))''''''''''''''''''''''''&&&&&&'''(((((('''&&&&&&''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))************(((((()))))))))*********))))))))))))))))))))))))&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%))))))(((&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&'''(((((((((&&&&&&&&&&&&&&&'''''''''$$$$$$%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&'''''''''$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''((((((%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%%%%&&&&&&'''''''''$$$%%%%%%&&&&&&'''''''''((((((((('''''''''''''''''''''''''''''''''''''''&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&'''((((((''''''&&&&&&'''(((((())))))(((((((((((('''''''''(((((()))&&&&&&&&&'''((()))***+++'''((((((((())))))******(((((())))))******++++++'''((((((((()))))))))*********))))))))))))************************************++++++++++++*********+++++++++,,,,,,,,,---++++++++++++++++++++++++***(((&&&&&&(((+++,,,,,,+++++++++++++++,,,------))))))))))))))))))******++++++++++++++++++++++++************************,,,---...---+++***+++,,,++++++,,,,,,,,,,,,++++++******))))))))))))******---,,,***)))))))))***+++******))))))))))))******************************************************(((((((((((((((((((((((((((((((((((())))))))))))((((((((((((((((((((((((''''''(((((())))))******)))))))))(((((('''''''''(((((((((((()))))))))))))))'''&&&'''))))))((('''))))))))))))))))))))))))&&&''''''(((((((((((((((((((((((((((((((((((((((&&&&&&''''''(((((())))))(((((())))))))))))((((((''''''(((((((((((('''''''''&&&%%%&&&((()))((('''((((((((((((((((((((((((&&&&&&''''''(((((())))))((((((''''''''''''((((((((((((((((((((((((((((((((((((((('''&&&&&&&&&%%%&&&'''''''''((((((((((((''''''''''''''''''''''''%%%&&&&&&&&&'''((((((((($$$$$$$$$%%%%%%%%%&&&&&&'''((((((((('''&&&%%%%%%((((((((((((((((((((((((''''''''''''''''''''''''&&&'''((('''&&&&&&&&&((((((((((((((((((((((((((())))))))))))))))))))))))''''''''''''''''''''''''&&&&&&'''(((((('''&&&&&&''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))************))))))))))))************************************%%%%%%%%%%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%)))((('''&&&&&&%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''$$$%%%%%%&&&'''((()))***(((((((((((((((((((((((($$$$$$%%%&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&''''''''''''%%%%%%%%%&&&&&&''''''''''''(((((((((((((((((((((''''''''''''''''''''''''((((((((((((''''''''''''$$$%%%%%%&&&''''''((((((&&&&&&'''(((((((((((('''''''''((())))))))))))(((((((((''''''(((((())))))%%%&&&&&&'''((()))))))))(((((())))))******++++++))))))))))))************)))******++++++,,,,,,,,,+++******))))))******+++++++++++++++++++++++++++++++++,,,,,,,,,,,,+++++++++++++++,,,,,,------...,,,,,,,,,,,,,,,,,,,,,,,,+++)))((((((***,,,,,,,,,++++++++++++,,,---...///*********)))******+++,,,,,,,,,,,,,,,,,,,,,,,,,,,************************---...000///---++++++,,,++++++,,,,,,,,,,,,+++++++++******************+++---,,,+++***)))***+++++++++******))))))******+++************************++++++++++++++++++++++++))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))(((((((((((()))))))))))))))))))))((((((((((((((((((((((((((())))))))))))(((''''''''')))***)))((())))))))))))))))))))))))&&&''''''((((((((((((((('''(((((((((((()))))))))'''''''''((((((((((((((('''(((((())))))(((((('''&&&''''''((((((''''''&&&&&&%%%%%%&&&((()))((('''''''''''''''''''''''''''(((''''''&&&%%%$$$######(((''''''&&&&&&''''''((((((((((((((((((((((((((('''''''''''''''&&&&&&&&&'''''''''((((((((())))))''''''''''''''''''''''''&&&&&&&&&'''''''''''''''%%%%%%%%%%%%&&&&&&&&&&&&'''''''''(((''''''&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''&&&'''((('''&&&&&&'''(((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))''''''''''''(((((((((((()))))))))*********++++++++++++++++++++++++++++++%%%%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%&&&&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''%%%%%%%%%&&&&&&''''''''''''''''''&&&&&&%%%%%%%%%$$$%%%&&&&&&'''&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&''''''(((%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%'''''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((((((''''''''''''''''''''''''+++***)))((('''((())))))'''''''''''''''''''''(((&&&&&&'''(((((((((((((((''''''((()))))))))))))))((((((((((((((()))******&&&'''((())))))))))))))))))))))))***+++,,,,,,,,,*********))))))))))))))))))******++++++,,,------++++++***))))))***++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,++++++++++++,,,,,,---.........,,,,,,,,,,,,,,,,,,,,,,,,...---,,,---...///...---------,,,,,,,,,------...,,,+++*********+++---...,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,...000///---+++***++++++,,,,,,------,,,,,,+++---,,,,,,++++++,,,,,,------,,,+++*********+++++++++******))))))******+++************************************************))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))((((((((((((''''''''''''''''''(((((((((((((((((())))))))))))(((''''''''')))***)))(((((((((((((((((((((((((((&&&''''''((((((((((((((('''((((((((())))))))))))((((((((((((((('''''''''&&&'''(((((((((((('''&&&&&&''''''((((((''''''&&&&&&%%%$$$&&&((())))))(((&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&$$$######"""(((''''''&&&&&&''''''(((((((((((((((((((((((((((&&&&&&&&&'''''''''''''''&&&&&&&&&'''''''''(((((('''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%&&&&&&&&&&&&'''''''''&&&&&&''''''((('''''''''((((((((((((((((((((((((''''''''''''''''''''''''&&&'''((('''&&&&&&'''(((((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''((('''&&&%%%%%%&&&'''(((''''''''''''(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))''''''''''''(((((((((((())))))*********+++++++++************************%%%%%%%%%%%%%%%&&&'''(((%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''#########$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%#########"""######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$###$$$%%%&&&'''&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$######"""!!! $$$%%%&&&&&&''''''&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''###$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''(((((($$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''"""$$$%%%'''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''((((((''''''''''''''''''''''''(((&&&$$$###"""###%%%&&&)))))))))(((''''''&&&&&&&&&&&&'''((())))))(((((('''(((((()))))))))))))))((((((((((((((()))******((())))))************)))))))))***+++,,,,,,------++++++******))))))(((((('''(((((()))******++++++,,,+++***))))))***+++,,,+++++++++++++++++++++++++++,,,,,,------,,,,,,+++++++++,,,,,,---...//////,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++,,,------+++)))//////...---,,,,,,,,,,,,,,,,,,+++++++++,,,...///,,,,,,,,,,,,,,,,,,,,,,,,........................,,,---///...,,,***)))***+++,,,,,,------,,,,,,+++///......------......///---,,,+++*********+++,,,++++++************++++++************************))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))******))))))((((((''''''%%%%%%%%%&&&&&&'''''''''(((((((((((())))))))))))(((''''''((()))******)))((((((((((((((((((((((((&&&''''''((((((((((((((('''((((((((())))))******))))))(((((('''''''''&&&%%%&&&'''(((((('''&&&%%%&&&''''''''''''''''''&&&&&&%%%$$$&&&((())))))(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&'''''''''((((((((((((((((((((((((%%%&&&&&&''''''(((((((((%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''(((((((((''''''&&&&&&%%%&&&&&&&&&'''''''''((((((%%%%%%&&&'''((((((((('''((((((((((((((((((((((((''''''''''''''''''''''''&&&'''((('''&&&&&&'''((((((((((((((((((((((((((('''''''''''''''''''''''''''''''''''''''''''''''')))(((&&&%%%%%%&&&((()))''''''''''''((((((((()))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************)))************+++++++++))))))))))))))))))))))))(((((((((''''''&&&&&&&&&&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%$$$$$$''')))&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&((())))))'''%%%%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$#########%%%%%%$$$%%%&&&(((***+++$$$%%%&&&'''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''&&&$$$""""""###$$$%%%'''$$$""" """$$$'''&&&%%%%%%%%%%%%&&&'''(((%%%&&&&&&''''''&&&&&&%%%((((((((((((((((((((((((%%%%%%%%%&&&&&&&&&''''''((((((((((((((((((((((((******))))))((((((''''''))))))))))))))))))))))))''''''''''''((((((((()))+++)))(((&&&&&&((()))+++))))))))))))))))))))))))%%%&&&&&&'''((()))************))))))))))))******)))))))))***+++++++++,,,***+++,,,------,,,***)))...,,,++++++,,,,,,***))),,,,,,,,,++++++***((((((,,,,,,,,,,,,,,,---------------------------......000//////...---,,,+++***////////////////////////........................//////------------//////.........---------,,,,,,,,,,,,,,,,,,,,,,,,------+++,,,------............------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++,,,---......---,,,+++************))))))))))))++++++++++++++++++++++++))))))))))))))))))))))))(((((()))***************''''''(((((())))))************)))''''''&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%))))))))))))))))))))))))+++*********))))))(((((())))))))))))))))))))))))***)))(((''''''((()))***))))))))))))))))))))))))&&&&&&&&&'''''''''((((((''''''''''''''''''''''''(((((((((''''''&&&&&&&&&%%%&&&'''(((((('''&&&%%%(((((((((((('''&&&%%%$$$$$$%%%&&&'''(((((((((((()))((('''&&&&&&&&&&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&''''''(((((((((((((((((((((((((((&&&&&&&&&''''''''''''(((&&&&&&'''((())))))((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''))))))(((((('''''''''&&&''''''''''''''''''''''''&&&'''''''''(((((())))))(((((('''''''''&&&&&&&&&(((((((((((())))))))))))******))))))((((((''''''+++*********))))))(((((((((((((((((())))))))))))************************+++,,,,,,,,,,,,,,,,,,---'''''''''&&&&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&'''((('''&&&$$$###%%%'''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$#########%%%%%%###"""%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&&&&%%%%%%&&&%%%%%%&&&'''(((***+++'''&&&&&&'''((((((&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%$$$###$$$%%%&&&((('''%%%######%%%'''(((&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((%%%%%%&&&&&&&&&'''''''''(((((((((((((((((((((((((((((((((((('''''''''&&&))))))))))))))))))))))))'''''''''((((((((())))))***)))(((''''''((()))***))))))))))))))))))))))))'''(((((())))))***************))))))))))))******************++++++++++++***+++++++++++++++******,,,+++***+++,,,,,,+++******++++++,,,,,,,,,++++++,,,,,,------------.....................//////////////////...------,,,,,,////////////////////////......//////////////////000///............///000////////////............------------------------,,,,,,---.........------........................------------------------,,,,,,,,,,,,,,,,,,,,,,,,)))***++++++++++++***)))++++++++++++************++++++++++++++++++++++++************************(((((()))***************(((((((((((())))))******)))((('''&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''))))))))))))))))))))))))******)))))))))((((((((())))))))))))))))))))))))))))))(((((((((((())))))((((((((((((((((((((((((&&&&&&&&&'''''''''((((((((((((((((((((((((((((((''''''''''''&&&&&&&&&%%%&&&&&&'''(((((('''&&&&&&&&&&&&'''''''''''''''&&&$$$%%%&&&'''(((((((((((((((((('''&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&'''((((((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&&&&'''''')))(((((((((''''''''''''''''''''''''''''''''''''''''''''''''((((((((()))(((((('''''''''&&&&&&&&&(((((((((((()))))))))))))))))))))***************************)))))))))((((((((((((((()))))))))*********************************++++++++++++,,,,,,&&&&&&%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&((()))(((&&&$$$###$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%'''%%%$$$$$$%%%&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''&&&&&&&&&&&&&&&&&&&&&'''((()))***+++***(((%%%&&&''''''%%%"""&&&&&&&&&&&&&&&&&&&&&&&&)))(((&&&%%%%%%%%%&&&'''((('''&&&&&&&&&&&&'''(((&&&'''((()))))))))((('''''''''&&&&&&&&&&&&''''''((((((((((((((((((((((((%%%&&&&&&&&&&&&'''''''''((((((((((((((((((((((((''''''''''''&&&&&&&&&&&&((((((((((((((((((((((((''''''((((((((()))))))))))))))(((((((((((())))))))))))))))))))))))))))))******************************))))))))))))******+++++++++++++++*********+++***************++++++,,,+++***+++,,,---,,,+++)))***+++,,,------...---------------......//////////////////000000111111////////////////////////000000000000000000000000///000000000111111222222111111000000000000111111111111111000000000//////.................................///......------................................................++++++++++++++++++++++++******++++++++++++******---,,,,,,,,,,,,+++++++++++++++++++++++++++++++++************************(((((()))***************((((((((())))))))))))***'''&&&%%%$$$$$$$$$$$$$$$###$$$%%%&&&'''((())))))))))))))))))))))))))))))))))))((((((((((((((('''))))))))))))))))))))))))((((((((())))))(((((((((((((((((((((((((((((((((&&&&&&'''''''''((((((((())))))))))))))))))))))))'''&&&&&&&&&&&&%%%%%%%%%&&&&&&'''(((((('''&&&&&&$$$%%%&&&'''((((((((((((%%%%%%&&&'''(((((((((((((((((('''&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((((((((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((''''''''''''&&&(((((((((((())))))))))))((())))))***+++,,,,,,,,,************))))))))))))((((((((()))))))))******************************)))))))))******+++++++++$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((('''%%%$$$%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%######$$$$$$$$$%%%%%%%%%(((&&&$$$###%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$'''''''''((()))******++++++'''$$$$$$'''(((%%%"""&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%&&&&&&'''%%%%%%&&&&&&&&&&&&%%%%%%$$$&&&((()))***)))'''&&&((('''&&&%%%%%%&&&'''(((((((((((((((((((((((((((&&&&&&&&&&&&''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''(((((((((((((((((((((((('''(((((((((((()))))))))(((((())))))))))))((((((((((((((((((((((((((((((******************))))))+++******))))))******+++,,,,,,,,,++++++*********+++***)))((()))***+++,,,---,,,++++++,,,---,,,*********+++,,,------------,,,------......////////////000000111111222222222000000111111222222222222111111222222222222222333222222333333444555555555444444444333333444444444333222222222111111111111///////////////.........000000000000000///...---.......................................---------,,,,,,,,,,,,,,,,,,,,,,,,------------------------,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++************************(((((()))***************))))))))))))))))))))))))'''&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&'''(((((()))((((((((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((&&&'''((())))))((('''&&&((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''''''''''''''&&&$$$%%%&&&'''((((((((((((%%%&&&&&&'''((((((''''''(((''''''&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((())))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''(((((((((((((((''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((('''''''''''''''(((((((((((()))))))))))))))))))))******+++++++++*********)))))))))))))))(((((()))))))))*********************************))))))******++++++,,,,,,$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%%%%%%%&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&'''&&&&&&'''(((&&&%%%%%%$$$$$$%%%%%%&&&###########################$$$%%%%%%&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%###!!! """#########%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''((())))))*********(((&&&###$$$&&&'''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%###%%%'''(((((((((&&&%%%'''''''''&&&&&&'''''''''((((((((((((((((((((((((&&&&&&&&&'''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((()))))))))***(((((())))))))))))(((((((((((((((((((((((((((((()))))))))))))))))))))(((++++++************++++++---,,,,,,,,,++++++******+++***)))))))))***,,,---///...,,,,,,,,,,,,+++)))+++,,,,,,,,,,,,,,,,,,+++------......///000111111111111222222333444555555333333444444555555666666444444555555666666666666666666777777888888888999777777888888888888777777555555444444444333333333111111111000000/////////222222222222222111000/////////////////////////////////......---------,,,,,,,,,,,,,,,,,,,,,,,,,,,------------------------,,,++++++++++++*********++++++++++++++++++++++++************************(((((()))***************************))))))))))))(((''''''&&&&&&&&&&&&'''''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((&&&'''((())))))((('''&&&'''''''''''''''''''''''''''''''''((((((((())))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&'''''''''&&&&&&''''''''''''&&&&&&%%%&&&''''''((('''''''''''''''&&&&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((((((((())))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((''''''&&&&&&&&&&&&'''''''''''''''(((((((((((((((''''''''''''''''''''''''((((((((((((((('''''''''(((((((((((((((((((((((((((((((((((())))))))))))******)))))))))((((((((())))))))))))))))))******))))))))))))******************************************++++++,,,------...###$$$$$$$$$$$$%%%%%%%%%'''&&&%%%$$$$$$%%%&&&'''''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$!!!$$$&&&'''&&&&&&((()))&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&$$$######$$$%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''((((((((((((&&&'''((())))))))))))(((&&&&&&%%%$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&''''''((())))))(((''''''$$$$$$&&&'''''''''&&&%%%&&&'''(((((((((((('''&&&((((((((((((((((((((((((&&&&&&'''''''''(((((((((((((((((((((((((((((((((((((((((()))))))))))))))((((((((((((((((((((((((((((((((()))))))))******))))))(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))++++++************++++++,,,,,,,,,,,,,,,+++++++++************+++,,,------///...,,,,,,------+++***---------...------,,,,,,//////000111222333444444444444555666777888888999777777777888888999999999888888999999:::;;;;;;;;;<<<<<<<<<<<<;;;;;;;;;;;;;;;;;;<<<<<<<<<<<<;;;;;;999999888888888777777777444444444333333222222111444444444555444444333333111111111111111111111111000000000///......------------------------------,,,,,,++++++++++++,,,,,,++++++++++++************++++++++++++++++++++++++++++++++++++++++++++++++(((((()))***************+++************))))))))))))((((((''''''(((((((((((((((((('''''''''&&&&&&))))))))))))))))))))))))'''(((((((((((()))))))))))))))))))))))))))))))))'''''''''(((((('''''''''''''''''''''''''''''''''''''''((((((((()))))))))''''''''''''''''''''''''&&&&&&&&&''''''''''''(((((('''&&&&&&&&&&&&'''(((&&&'''''''''''''''&&&&&&&&&&&&'''''''''''''''&&&'''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$%%%%%%&&&'''((((((((((((((((((((((((((((((&&&&&&&&&''''''''''''((((((((((((((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((''''''&&&&&&&&&&&&'''''''''''''''(((((((((((((((''''''''''''''''''''''''(((((((((((((((''''''''''''(((((((((((()))))))))(((((((((((())))))))))))******))))))(((''''''&&&))))))))))))************)))))))))*********++++++******************************+++,,,---......///$$$$$$$$$$$$%%%%%%&&&&&&'''&&&$$$######$$$&&&'''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$"""$$$'''''''''&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&((('''&&&'''))))))'''&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((()))%%%&&&'''((()))(((''''''&&&((((((%%%!!!!!!$$$(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''%%%&&&(((******(((&&&%%%((((((((((((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((('''''''''((((((((())))))))))))))))))))))))))))))(((((()))))))))************)))(((''''''((()))***))))))))))))))))))))))))((())))))******+++++++++,,,++++++******++++++,,,++++++,,,,,,,,,,,,,,,,,,******+++,,,---.........---++++++,,,...///...------...///000000000000000333333444555666777888888888999:::;;;<<<======>>>:::;;;;;;;;;;;;;;;;;;;;;<<<<<<======>>>??????@@@AAA@@@@@@??????>>>>>>===>>>??????@@@@@@??????>>>>>>============<<<<<<<<<999999888777777666555555555555666777777777666666555555555555555555555555333333222111111000//////////////////////////////---,,,++++++++++++,,,------,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++(((((()))***************+++++++++*********)))))))))((((((''''''(((((()))''''''''''''(((((((((((())))))))))))))))))))))))((((((((()))))))))******))))))))))))))))))))))))(((''''''&&&&&&''''''((('''''''''''''''''''''''''''((((((((())))))))))))'''''''''''''''''''''''''''''''''((((((((())))))((('''&&&&&&&&&&&&'''(((%%%%%%&&&'''((((((((((((&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&'''((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&'''((((((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''''''''''''''((((((((()))'''''''''''''''''''''''')))((((((((('''''''''''''''((((((((())))))))))))(((((((((((())))))))))))***)))))))))))))))))))))((()))))))))************))))))*********+++++++++************************))))))***+++,,,---......$$$$$$$$$%%%%%%&&&&&&&&&'''&&&$$$######$$$&&&'''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$&&&(((((('''%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''$$$$$$%%%&&&&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''$$$$$$$$$&&&''''''%%%"""%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&'''((((((((('''&&&'''***+++&&& """'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))((((((&&&%%%$$$$$$$$$$$$%%%&&&(((''''''''''''((())))))$$$&&&)))++++++)))&&&$$$((((((((((((((((((((((((''''''''''''((((((((()))((((((((((((((((((((((((&&&&&&&&&'''''''''((((((************************))))))))))))************+++)))(((&&&&&&((()))+++))))))))))))))))))))))))))))))***+++,,,,,,------,,,++++++******++++++,,,+++++++++,,,,,,---------)))+++,,,...//////......***))))))+++...000111000---...000111333444444444666666777888999:::;;;;;;<<<<<<===>>>???@@@AAAAAA========================>>>??????@@@AAAAAABBBBBBDDDCCCCCCBBBAAA@@@???>>>@@@@@@BBBBBBBBBBBB@@@@@@AAAAAAAAA@@@@@@@@@@@@???<<<<<<;;;;;;:::999888888555666777888888999888888888888888888888888888888555555444444333222111111000000000000000000000000///...------------...///......---------,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++(((((()))***************++++++++++++******))))))(((((('''''''''(((((()))%%%&&&&&&'''((()))******))))))))))))))))))))))))(((((())))))******++++++))))))))))))))))))))))))((('''&&&%%%%%%&&&'''(((''''''''''''''''''''''''(((((((((((())))))))))))))))))))))))))))))))))))'''((((((((())))))******((('''&&&%%%%%%&&&'''((("""###%%%'''((()))******&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&'''((()))((((((((((((((((((((((((''''''''''''''''''''''''(((((((((((((((((((((((((((''''''&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((&&&&&&'''((()))))))))((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''&&&&&&'''''''''&&&'''''''''(((((())))))''''''''''''''''''''''''))))))(((((('''''''''&&&'''((((((((())))))******(((((((((((()))))))))))))))))))))***++++++,,,,,,(((((())))))*********+++)))************+++++++++************************'''((()))***+++,,,------$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&''''''''''''&&&&&&'''&&&'''((())))))&&&$$$%%%$$$$$$$$$$$$%%%&&&'''(((''''''''''''&&&&&&&&&###$$$&&&&&&&&&&&&$$$############$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%***)))'''%%%$$$$$$$$$$$$%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%%%%%%%&&&''''''''''''&&&%%%%%%$$$$$$###$$$$$$%%%&&&'''(((((('''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&((())))))((((((''''''((((((((((((''''''(((((('''''''''&&&&&&&&&&&&&&&&&&'''((())))))***))))))))))))))))))))))))&&&((())))))(((''''''(((***)))((('''&&&&&&'''((((((((((((((())))))))))))))))))))))))))))))))))))(((((((((((())))))))))))++++++,,,,,,,,,---------+++++++++***************///......---------------.........---------,,,,,,))),,,///111111000000111333333333333444555666777777777888:::<<<>>>===<<<:::;;;>>>AAABBBCCCBBBBBBBBB@@@>>>===>>>>>>===<<<;;;===@@@CCCEEEFFFFFFFFFFFFFFFFFFEEEDDDBBBAAA@@@FFFEEECCCDDDEEEGGGGGGFFFCCCBBBAAAAAACCCDDDCCCBBB???????????????>>>===<<<:::::::::::::::999999999===<<<999777666666777888;;;888555444555555555444555444222222333222111//////////////////000111111///...---,,,++++++++++++,,,,,,,,,++++++++++++++++++++++++************)))************************))))))))))))))))))))))))))))))))))))))))))))))))&&&&&&&&&&&&''''''''''''******))))))((((((''''''(((((((((((((((((((((((())))))))))))))))))))))))******))))))((((((''''''''''''''''''''''''''''''(((((((((((())))))))))))((((((((((((((((((((((((''''''((((((((((((''''''))))))(((((('''''''''&&&''''''''''''''''''''''''))))))))))))))))))))))))''''''''''''''''''''''''(((((('''''''''&&&&&&&&&'''((()))))))))(((&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''((((((((((((''''''&&&&&&&&&&&&&&&%%%%%%%%%''''''&&&&&&&&&&&&''''''''''''''''''((((((((()))))))))(((((((((((())))))))))))(((((((((((()))))))))***+++,,,,,,+++))))))******))))))))))))******)))+++------------///111$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&''''''''''''&&&&&&$$$#########%%%%%%###"""%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&'''(((%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%&&&''''''&&&&&&&&&&&&&&&'''''''''%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''((((((''''''&&&''''''((((((((((((''''''(((((('''''''''&&&&&&&&&&&&&&&''''''((())))))***))))))))))))))))))))))))&&&((())))))(((''''''(((***)))((('''''''''(((((())))))))))))************))))))))))))))))))))))))((((((((()))))))))******++++++++++++,,,,,,,,,---++++++++++++++++++++++++---,,,,,,+++++++++,,,,,,///////////////////////////222555666666666666666777777777777888999:::;;;;;;;;;;;;<<<>>>@@@@@@@@@@@@AAACCCDDDEEEEEEDDDCCCCCCBBBAAABBBCCCCCCBBB@@@AAACCCGGGJJJMMMNNNNNNMMMKKKJJJJJJIIIHHHFFFEEEDDDFFFDDDCCCDDDFFFGGGFFFFFFIIIHHHHHHHHHIIIIIIHHHFFFDDDDDDDDDDDDDDDCCCCCCBBB============<<<<<<<<<<<<===<<<;;;:::999:::;;;;;;>>><<<:::999::::::999888777555444444555555444222222111000000/////////000...------,,,,,,,,,------------,,,,,,,,,,,,,,,,,,++++++++++++************************************))))))))))))))))))))))))))))))))))))))))))))))))))))))*********+++++++++)))(((((((((''''''''''''(((((((((((((((((((((((())))))))))))))))))))))))***)))))))))((((((((('''''''''''''''''''''''''''(((((((((((())))))))))))))))))))))))))))))))))))(((((())))))))))))(((((()))(((((((((''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''(((((('''''''''&&&&&&&&&%%%&&&'''''''''&&&%%%$$$''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((((((((((((((((((''''''((((((((((((''''''((((((((((((((((((((()))(((''''''''''''''''''((('''''''''((((((((())))))))))))(((((((((((())))))))))))(((((((((((()))))))))***++++++++++++***)))******))))))))))))******+++,,,............///111$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&''''''''''''&&&&&&&&&%%%###$$$%%%&&&&&&%%%$$$%%%&&&'''((('''&&&&&&''''''''''''&&&&&&&&&&&&(((''''''&&&&&&''''''((((((''''''&&&%%%%%%&&&&&&$$$%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%&&&&&&''''''$$$$$$$$$$$$%%%&&&'''(((%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%&&&''''''%%%&&&&&&'''(((((())))))''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&%%%%%%''''''(((((((((((('''''''''''''''''''''&&&&&&&&&&&&''''''(((((())))))***))))))))))))))))))))))))&&&((())))))((('''((((((***)))(((((('''(((((((((************++++++++++++))))))))))))))))))))))))((())))))))))))***************+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,------//////000000111222222333333555888999999999999:::===<<<<<<<<<===>>>???@@@@@@@@@@@@@@@AAABBBDDDDDDGGGHHHIIIIIIIIIHHHGGGFFFEEEFFFGGGJJJLLLLLLJJJHHHHHHJJJNNNRRRTTTUUUUUUUUUQQQQQQPPPOOONNNLLLJJJJJJIIIHHHGGGHHHIIIJJJIIIHHHJJJIIIJJJLLLNNNNNNLLLJJJGGGGGGGGGGGGFFFFFFFFFEEEAAABBBBBBBBBAAA@@@@@@???@@@@@@????????????@@@@@@AAA@@@???@@@@@@@@@>>><<<999777666666777888777666777666555333222111111111...------------...//////------------------------,,,,,,,,,+++++++++******++++++++++++++++++++++++))))))))))))))))))))))))))))))))))))))))))))))))+++++++++,,,,,,,,,------((((((''''''''''''&&&&&&(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))((((((((((((''''''''''''''''''''''''(((((((((((())))))))))))************************))))))************))))))(((((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$''''''&&&&&&&&&&&&''''''(((''''''''''''''''''(((((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''))))))))))))))))))))))))(((((((((''''''''''''&&&&&&&&&&&&''''''''''''((())))))))))))))))))))))))''''''((((((((((((''''''((((((((())))))*********)))((((((''''''(((((()))''''''((((((((()))))))))***))))))(((((())))))******))))))(((((())))))***)))******+++++++++************))))))))))))******,,,---//////......///111$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%(((%%%######%%%'''''''''$$$%%%'''))))))((('''&&&'''''''''&&&&&&&&&%%%%%%((('''&&&%%%%%%&&&'''((((((''''''&&&&&&&&&''''''$$$$$$%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%(((''''''&&&&&&&&&&&&&&&%%%&&&''''''((('''''''''%%%%%%&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&'''''''''''''''((((((((())))))&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((''''''''''''''''''''''''''''''''''''(((((())))))))))))(((((((((((((((((((((((('''(((******((('''((()))***))))))))))))))))))))))))))))))*********++++++)))))))))))))))))))))))))))))))))*********++++++*********+++++++++,,,,,,++++++,,,,,,,,,,,,---------,,,,,,---...///000000000000111222444555666777777999<<<=========>>>???@@@@@@AAAAAABBBCCCDDDEEEFFFGGGGGGFFFFFFGGGIIIJJJMMMMMMNNNOOOOOOOOONNNNNNKKKMMMOOOSSSVVVVVVTTTRRRPPPRRRVVVYYY[[[[[[ZZZYYYWWWWWWVVVUUUTTTRRRPPPOOOQQQPPPOOOPPPQQQQQQPPPNNNIIIJJJLLLOOOSSSTTTSSSRRRLLLLLLKKKJJJJJJJJJJJJJJJHHHHHHHHHHHHGGGFFFDDDCCCEEEEEEEEEDDDDDDDDDDDDDDDCCCCCCCCCCCCDDDCCC@@@>>><<<:::888888999::::::999;;;;;;999888777666666666111000000/////////000000---------...............---,,,,,,,,,++++++++++++++++++++++++++++++++++++************************)))))))))))))))))))))))))))))))))*********++++++((((((((((((((((((((('''(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))((((((((((((''''''''''''''''''''''''(((((((((((())))))))))))))))))))))))))))))))))))((())))))******))))))(((((((((((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((('''''''''''''''&&&&&&&&&&&&''''''((((((''''''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((((('''''''''''''''&&&&&&&&&''''''''''''(((((((((((((((((((((((((((''''''((((((((((((''''''%%%&&&&&&'''((())))))***))))))(((((((((((())))))'''(((((((((((()))))))))***))))))))))))))))))******))))))))))))))))))***)))*********+++++++++++++++******))))))******+++,,,---///...------...000$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$""" """$$$$$$$$$$$$%%%'''))))))((('''&&&'''&&&&&&&&&&&&%%%%%%%%%'''&&&%%%$$$$$$%%%&&&'''&&&%%%%%%&&&'''((())))))$$$$$$%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&((((((''''''&&&%%%$$$$$$))))))((((((''''''&&&&&&%%%&&&''''''((('''''''''%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''))))))((((((((('''''''''$$$$$$%%%%%%&&&'''(((((())))))))))))))))))))))))'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''$$$$$$$$$%%%&&&''''''(((''''''((((((((((((''''''&&&'''''''''''''''''''''((((((((()))))))))))))))((((((((((((((((((((((((''')))******)))(((((()))))))))******************((((((((()))))))))******************************************++++++++++++******+++++++++,,,,,,,,,+++++++++,,,,,,,,,------,,,,,,---...///111222333222222333555777999::::::<<<>>>AAABBBCCCDDDFFFGGGEEEGGGIIIKKKLLLMMMMMMMMMPPPRRRSSSRRRPPPPPPRRRTTTTTTUUUVVVXXXZZZ[[[[[[\\\XXXXXXZZZ]]]aaabbbaaa___\\\___bbbeeefffdddbbb`````````___^^^\\\ZZZXXXWWWZZZYYYXXXYYYYYYXXXVVVTTTOOOPPPQQQUUUXXXZZZZZZYYYVVVUUUTTTRRRQQQPPPPPPPPPPPPPPPPPPPPPOOOMMMKKKIIIIIIHHHGGGFFFEEEEEEEEEEEEGGGFFFEEEFFFFFFEEEBBB??????===;;;:::;;;<<<<<<<<<<<<;;;;;;:::::::::::::::666555444222111111000000///............---------------------,,,,,,,,,+++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,************************((((((((())))))))))))***))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((())))))))))))(((((((((((((((((((((((((((((((((((())))))))))))(((((((((((((((((((((((('''(((((())))))((((((''''''''''''(((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&'''''''''''''''''''''))))))((((((''''''''''''''''''&&&&&&&&&&&&''''''((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''((((((((((((''''''%%%&&&&&&'''((())))))***))))))(((((((((((())))))(((((((((((()))))))))*********))))))))))))************))))))))))))******)))))))))******++++++,,,++++++************+++++++++,,,......------...000$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$###"""###%%%&&&&&&%%%$$$%%%&&&'''((('''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$%%%&&&((()))***$$$%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&''')))(((((('''&&&%%%$$$$$$&&&&&&'''(((((((((((('''%%%&&&''''''((((((''''''$$$%%%%%%&&&&&&'''''''''&&&'''(((((((((((('''&&&))))))(((((('''&&&&&&%%%###$$$$$$%%%&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''#########$$$%%%'''((()))''''''((((((((((((''''''&&&&&&&&&'''''''''''''''))))))))))))))))))))))))))))))))))))))))))))))))''')))******)))(((((()))))))))***++++++++++++***'''((((((((())))))))))))******************************+++++++++,,,,,,,,,++++++,,,,,,,,,---------+++,,,,,,------.........------...///111333555666666777888:::;;;===>>>???===@@@BBBDDDEEEGGGJJJMMMPPPSSSXXX\\\^^^^^^]]]\\\```cccfffeeebbb```aaaccccccdddeeehhhjjjlllnnnoooiiihhhggghhhkkknnnnnnnnnlllnnnrrruuuuuussspppnnnmmmmmmlllkkkiiifffdddccceeedddccccccbbb```]]]ZZZVVVVVVVVVXXX[[[]]]^^^]]]```^^^\\\YYYWWWVVVVVVVVVYYYZZZZZZZZZYYYVVVSSSQQQLLLKKKIIIGGGGGGHHHIIIJJJNNNMMMKKKKKKJJJIIIFFFDDDEEEBBB???===>>>?????????<<<<<<;;;;;;:::;;;;;;;;;;;;:::888666444333222222222111111000///...------......---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,************************)))))))))************+++))))))************++++++))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))(((((((((((((((((((((((((((((((((((())))))))))))''''''''''''''''''''''''''''''(((((((((((('''''''''''''''(((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''''''''&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&''''''(((''''''''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((()))))))))&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''((((((((((((''''''((((((((())))))*********)))((((((''''''(((((()))((((((((()))))))))******+++******))))))******++++++******))))))******+++))))))))))))***+++,,,---++++++************++++++***,,,............000222$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%''')))***)))(((%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&&&&''''''(((&&&&&&&&&'''''''''''''''%%%&&&'''''''''&&&%%%$$$%%%&&&''''''((((((''''''$$$$$$%%%%%%&&&''''''(((&&&'''((())))))((('''&&&'''''''''&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''%%%%%%$$$$$$$$$%%%'''(((''''''((((((((((((''''''&&&&&&&&&'''''''''(((((())))))))))))))))))))))))))))))))))))))))))))))))((()))++++++)))((()))***)))***+++,,,,,,,,,++++++(((((()))))))))*********************************+++++++++,,,,,,,,,,,,---,,,,,,---------.........---......///000000111111111111222444666888;;;<<<<<<<<<>>>???AAABBBCCCDDDBBBDDDGGGJJJLLLOOOSSSVVV___dddkkkqqquuutttqqqooossswww|||{{{wwwttttttvvvwwwwwwyyy{{{}}}{{{xxxtttsssuuuxxx{{{}}}wwwzzz~~~}}}}}}|||zzzxxxvvvtttssssssrrrpppooommmjjjfffbbb]]]\\\\\\___dddiiilllmmmooommmiiifffcccaaaaaaaaacccdddddddddbbb___\\\ZZZSSSQQQNNNMMMNNNQQQUUUWWWZZZWWWTTTRRRQQQPPPMMMLLLKKKHHHDDDBBBBBBBBBBBBBBBAAAAAA???>>>============<<<;;;:::888777666666666666555444333111///...---............------------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++************************)))))))))*********++++++((()))))))))************))))))))))))))))))))))))))))))))))))))))))))))))'''((((((((()))))))))***(((((((((((((((((((((((((((((((((((())))))))))))(((((((((((((((((((((((((((((())))))))))))((((((''''''''''''((((((((()))''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&'''''''''((((((((('''&&&%%%$$$%%%%%%&&&''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((())))))))))))&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''((((((((((((''''''((((((((((((((((((((()))(((''''''''''''''''''((((((((()))))))))*********+++******))))))******++++++******))))))******+++***))))))))))))+++,,,---,,,++++++******++++++,,,+++---///000000111444666$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$""""""###%%%((((((&&&$$$%%%%%%$$$$$$$$$%%%&&&'''&&&&&&&&&%%%%%%%%%$$$$$$%%%&&&'''(((((('''&&&%%%&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((((((''''''''''''(((((($$$$$$%%%&&&'''((()))***(((((((((&&&$$$"""%%%&&&''''''((((((''''''$$$$$$%%%%%%&&&'''((((((&&&'''((())))))((('''&&&$$$$$$%%%%%%&&&'''''''''''''''&&&&&&&&&%%%%%%%%%'''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''(((((((((((((((((((((((('''&&&%%%$$$$$$$$$%%%&&&''''''((((((((((((''''''&&&&&&&&&'''''''''((((((*********)))))))))))))))))))))))))))))))))))))))((()))++++++)))((()))***)))***+++,,,---,,,,,,+++)))************+++++++++************************++++++,,,,,,,,,------------------........./////////000000111222333333333666666888999<<>>>>>AAAFFFJJJMMMLLLJJJKKKPPPRRRQQQ[[[^^^ccciiinnnppprrrrrryyy~~~~~~{{{zzzzzz{{{zzzwwwvvv{{{}}}yyyuuuppprrrrrroooiiieeecccdddbbb___[[[ZZZ^^^fffnnntttqqqmmmgggccc___\\\YYYVVVWWWTTTOOOJJJFFFDDDDDDDDDEEEFFFGGGGGGGGGEEECCCAAA===<<<;;;:::999999999999999999888777777777777777333333111000////////////------...------,,,+++***************+++,,,---...++++++******)))((((((((())))))))))))))))))******))))))))))))))))))******************************((()))******)))(((***+++)))((('''''''''(((***+++000---***'''&&&(((***,,,)))((('''&&&&&&'''((()))+++***)))(((((()))***+++******))))))((((((''''''))))))))))))************''''''''''''''''''''''''***)))(((((()))+++---...))))))))))))))))))))))))(((((((((((())))))))))))&&&'''((())))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&***))))))((('''&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&&&&''''''''''''''''''''''''''''''''''''(((((((((((()))(((((('''''')))***+++******))))))((((((''''''''''''''''''''''''''''''''''''''''''((((((((((((''''''''''''((((((((()))************************)))************+++++++++++++++++++++++++++++++++++++++******++++++,,,---,,,,,,+++++++++,,,------...------000333666888999''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''&&&%%%%%%%%%&&&&&&((('''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%'''&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%)))'''&&&%%%%%%&&&''')))((('''%%%%%%%%%&&&((()))&&&'''((())))))((('''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%'''''''''((((((((((((((())))))))))))))))))))))))(((((())))))******++++++))))))))))))))))))))))))))))))************))))))(((((())))))))))))))))))++++++***))))))***+++,,,))))))***+++++++++++++++*********++++++++++++,,,---,,,,,,,,,,,,,,,------,,,,,,,,,---...000111222111444777888888888999:::>>>;;;<<<@@@BBBDDDIIIOOOYYY^^^```^^^]]]```cccccckkkooouuu{{{}}}xxxyyyyyywwwsssooollljjjgggeeecccccchhhoooxxx}}}|||xxxrrrmmmiiifffbbb```]]]\\\YYYUUUPPPLLLIIIHHHHHHHHHIIIJJJIIIHHHFFFDDDBBBBBB@@@???>>>===<<<<<<;;;::::::999999888999999777666555333222111000000............------------------,,,,,,,,,,,,------)))))))))***************************))))))))))))************))))))))))))************************)))***+++***)))((()))***)))))))))))))))***++++++...---***((('''(((***+++)))(((''''''''''''((()))***)))(((''''''((()))******)))))))))(((((((((''''''(((((((((((()))))))))''''''''''''''''''''''''))))))(((((()))+++,,,---(((((((((((((((((((((((((((((((((((())))))))))))&&&'''((())))))((('''&&&''''''''''''''''''''''''***))))))(((''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((('''''''''((()))******)))))))))((((((((('''''''''''''''''''''''''''''''''''''''(((((((((((('''''''''((((((((())))))************************)))************+++++++++++++++++++++++++++++++++++++++******++++++,,,---,,,,,,,,,+++,,,,,,---...,,,---///222666999:::;;;''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%$$$%%%%%%&&&&&&((('''&&&%%%%%%%%%%%%&&&$$$$$$$$$%%%&&&'''''''''%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''(((''''''&&&&&&%%%$$$$$$&&&&&&&&&&&&'''((()))***&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((('''&&&%%%%%%&&&'''((('''&&&%%%%%%%%%&&&((()))$$$%%%&&&'''((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((''''''''')))))))))))))))))))))))))))))))))))))))*********))))))))))))))))))))))))******++++++++++++*********************************************+++,,,---***************+++,,,,,,++++++,,,,,,,,,---------......---------------...,,,,,,---...000222444555666888;;;<<<<<<===>>>???BBB???AAAEEEIIINNNVVV___mmmvvv|||zzzuuuuuuxxxyyyyyy}}}~~~|||}}}wwwrrrllllllkkkmmmrrryyy}}}wwwrrrmmmiiieeebbbaaabbbaaa]]]WWWQQQMMMKKKNNNOOOOOOOOOMMMKKKIIIHHHHHHHHHFFFDDDCCCAAA@@@???<<<<<<<<<;;;;;;;;;;;;;;;;;;:::999777555444444333000000///.........//////111000///...---,,,,,,,,,((())))))***++++++,,,,,,++++++*********)))))))))++++++*********)))))))))))))))))))))))))))))))))***+++,,,+++)))(((((()))))))))***+++++++++++++++,,,,,,***))))))))))))))))))((((((''''''(((((())))))((((((''''''(((((()))))))))))))))((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((()))((((((((()))***+++,,,(((((((((((((((((((((((((((((((((((())))))))))))''''''((((((((((((''''''(((((((((((((((((((((((()))))))))(((''''''&&&&&&'''''''''''''''''''''''''''''''''((((((((())))))''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((''''''&&&&&&''''''((()))))))))))))))((((((((((((''''''''''''''''''''''''''''''''''''((((((((((((''''''((((((((()))))))))************************)))************+++++++++++++++++++++++++++++++++++++++******++++++,,,---,,,,,,,,,,,,,,,---......,,,...111555888;;;<<<===''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%&&&&&&'''(((''''''&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%'''''''''''''''((())))))&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((((('''&&&&&&&&&&&&'''(((&&&&&&%%%%%%%%%&&&'''(((&&&&&&''''''((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%&&&&&&'''(((((()))(((((((((((((((((((((((((((((((((((((((((((((((())))))((((((''''''&&&&&&((((((((((((((((((((((((*********)))))))))))))))(((((((((((((((((((((((()))******++++++******)))+++************)))))))))))))))******+++,,,------,,,+++***)))***+++,,,---++++++,,,,,,,,,---------......------------.........//////000222444666777:::<<>>>>>>>>=========<<<<<<:::999888888888888444333111///.........///000000///...------------*********+++++++++,,,,,,,,,++++++******))))))(((,,,++++++******))))))(((((((((((((((((((((((((((+++,,,---+++)))(((((()))((()))***+++,,,+++***)))***************)))(((((()))(((((((((((((((((()))))))))(((((((((((())))))))))))))))))(((((((((((('''''''''((((((((())))))))))))))))))))))))))))))(((((((((((())))))******(((((((((((((((((((((((((((((((((((())))))))))))'''(((((((((((((((((('''''''''''''''''''''''''''))))))((((((''''''''''''''''''''''''''''''''''''&&&'''''''''((((((((((((&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((&&&&&&&&&&&&'''''''''((())))))))))))((((((((((((''''''''''''''''''''''''''''''''''''(((((((((((('''(((((((((((()))))))))************************))))))*********+++++++++++++++++++++++++++++++++++++++******++++++,,,------,,,,,,,,,---...///000---000444888:::;;;<<<<<<''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&''''''((()))***&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''(((((())))))((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&'''''''''%%%%%%%%%%%%%%%&&&''''''***))))))(((((('''''''''''''''''''''''''''''''''(((''''''&&&&&&''''''(((''''''''''''''''''''''''$$$%%%%%%&&&'''((())))))((((((((((((((((((((((((''''''''''''''''''''''''))))))((((((''''''&&&&&&((((((((((((((((((((((((*********)))))))))))))))(((((((((((((((((((((((((((((())))))))))))(((((())))))))))))))))))))))))))))))***+++,,,---------,,,+++*********+++---...+++++++++,,,,,,,,,,,,---...------------...//////222333333444555777888999<<>>??????@@@@@@@@@??????<<<;;;;;;::::::;;;;;;;;;888777555222000///...---......------------......---,,,,,,,,,+++++++++***,,,+++++++++******)))))),,,+++++++++******))))))((((((((((((((((((((((((,,,------,,,)))(((((()))&&&''')))*********)))((())))))*********)))((('''((())))))))))))))))))(((************************(((((((((((())))))))))))(((((()))))))))*********))))))))))))))))))))))))''''''(((((()))))))))(((''''''''''''''''''''''''(((((((((((())))))))))))(((((((((''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&&&&'''''''''&&&&&&&&&'''''''''((((((((((((((((((((((((((((((''''''''''''((((((((((((%%%&&&&&&'''''''''''''''(((((((((((())))))))))))((((((((((((((((((((((((''''''''''''(((((((((((((((((((((((()))))))))***))))))))))))))))))))))))))))))*********+++++++++++++++++++++++++++++++++++++++******++++++,,,---------------...///000111///333777:::::::::;;;===''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((())))))&&&&&&''''''&&&&&&%%%$$$'''''''''&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%'''((())))))***)))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%%%%%%%&&&&&&&&&&&&++++++)))((((((''''''(((''''''''''''''''''''''''((((((''''''''''''((((((''''''''''''''''''''''''%%%%%%&&&&&&'''((())))))((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%(((((((((((((((''''''''')))))))))))))))))))))))))))))))))))))))*********))))))))))))))))))))))))(((((())))))))))))((((((((((((((()))))))))******)))***+++,,,---------,,,+++++++++++++++,,,------+++++++++,,,,,,,,,---------------...///000222222777777888999;;;===???@@@AAADDDHHHLLLPPPUUUZZZ^^^______bbbfffiiiooo|||~~~tttuuuwww~~~}}}vvvpppkkkgggbbb___aaadddfffeee```___cccgggnnnllliiifffbbb___\\\[[[VVVUUUTTTQQQNNNJJJFFFDDD@@@AAABBBDDDDDDCCCBBBAAA======<<<<<<<<<<<<======;;;:::999888555333000///......---------......///......---,,,,,,+++******++++++++++++++++++++++++++++++++++++++++++++++++))))))))))))))))))))))))+++,,,---,,,***))))))***''''''((()))))))))))))))((())))))******)))((((((((())))))******))))))(((***++++++,,,,,,++++++***(((((((((((())))))))))))))))))))))))************((((((((((((((((((((((((''''''((((((((((((''''''''''''''''''''''''''''''(((((((((((())))))))))))((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&&&&'''%%%%%%&&&&&&'''(((((((((((((((((((((((((((((((((''''''''''''((((((((((((&&&&&&'''(((((((((((('''(((((((((((())))))))))))((((((((((((((((((((((((''''''''''''((((((((((((((((((((()))))))))******)))))))))))))))))))))))))))************+++++++++++++++++++++++++++++++++++++++******++++++,,,------------...///000111222111555:::<<<;;;<<<>>>AAA''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&)))((((((''''''''''''(((&&&&&&'''''''''&&&%%%$$$'''''''''&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''((((((''''''&&&&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))&&&''''''''''''''''''&&&$$$$$$%%%%%%&&&&&&&&&&&&))))))((('''''''''((()))''''''''''''''''''''''''((((((''''''''''''((((((''''''''''''''''''''''''%%%&&&&&&&&&''''''((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((((((((())))))))))))))))))))))))(((((())))))******++++++)))))))))))))))))))))))))))))))))******)))))))))'''((())))))***+++,,,,,,***+++,,,------,,,,,,+++***+++,,,,,,------,,,,,,,,,------------...............///000222444666777999:::<<>>======<<<<<<;;;<<<======<<<999666444111111000///............---------------,,,,,,,,,)))******++++++,,,,,,---)))******++++++,,,,,,---***************************+++,,,,,,*********,,,))))))(((((())))))***+++))))))(((((())))))))))))((()))************)))((()))***++++++++++++***)))'''((((((((()))))))))***((((((((())))))))))))***''''''''''''''''''''''''&&&'''((((((((('''&&&&&&''''''''''''''''''''''''(((((((((((()))))))))))))))((('''&&&&&&'''((()))'''''''''''''''''''''''''''(((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''%%%%%%&&&&&&'''(((((()))((((((((((((((((((((((((''''''''''''((((((((((((&&&'''((()))))))))(((((('''((((((((()))))))))***((((((((((((((((((((((((''''''''''''(((((((((((((((((()))))))))*********)))))))))))))))))))))))))))************+++++++++++++++++++++++++++++++++++++++******++++++,,,------------...///000222333222777<<<>>>>>>@@@EEEIII''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&&&&&&&&&&&&&%%%&&&'''''''''&&&%%%$$$%%%&&&&&&''''''(((((()))%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&###$$$%%%&&&&&&&&&%%%%%%'''&&&%%%%%%&&&''')))***''''''''''''''''''''''''((((((''''''''''''((((((''''''''''''''''''''''''&&&&&&&&&'''''''''''''''((((((((((((((((((((((((************************&&&'''''''''(((((())))))))))))))))))))))))))))))'''(((((()))***++++++,,,))))))))))))))))))))))))******++++++++++++******(((((()))***,,,---...///+++,,,---------,,,+++******+++,,,---...---,,,+++............/////////000///000111222444777999::::::<<>>===<<<;;;;;;===@@@AAAAAA???<<<999555444222000///......---+++,,,,,,------......///))))))***+++,,,------...))))))***+++,,,------...***************************+++,,,,,,+++***+++---+++***)))))))))***,,,---))))))(((((((((((()))***((()))***++++++***)))(((((()))***++++++***)))((('''((((((((())))))******''''''''''''((((((((()))''''''''''''''''''''''''&&&'''((((((((('''&&&%%%''''''''''''''''''''''''(((((((((((()))))))))))))))((('''&&&&&&'''((()))(((((((((((((((((((((((('''''''''(((((((((((((((''''''''''''''''''''''''''''''''''''((((((((()))%%%%%%&&&&&&'''((())))))))))))))))))))))))))))))''''''''''''((((((((()))&&&''')))*********)))((('''((((((((())))))******))))))))))))))))))))))))''''''''''''((((((((()))))))))))))))************)))))))))))))))))))))))))))************+++++++++++++++++++++++++++++++++++++++******++++++,,,---------......///111222333222777<<>>>>>AAAEEEIIINNNVVV```gggqqqqqqsssuuuyyy~~~~~~{{{wwwvvvuuutttsssuuussspppllleee\\\RRRKKKLLLMMMOOOPPPPPPOOONNNMMMJJJHHHEEECCCBBBAAA???===>>>???@@@AAAAAAAAA@@@???<<<;;;888666444222111111.........---------,,,,,,+++++++++---......,,,***......------,,,+++******+++***)))(((((()))***+++))))))))))))))))))))))))+++*********))))))(((((())))))))))))))))))))))))************************&&&'''((((((''''''(((***))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''((((((((((((***)))'''%%%$$$%%%&&&'''&&&&&&&&&''''''((()))***((((((''''''''''''((((((''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&'''''')))((('''&&&&&&'''((()))((((((((((((((((((((((((((((((((((((((((((((((((++++++++++++*********)))))))))))))))))))))))))))))))))))))))))))))))))))&&&''''''((()))******++++++***(((&&&&&&''')))***((()))***++++++***)))(((*********++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,......---------,,,,,,,,,---///000000000000333555===;;;<<<@@@DDDIIIRRR[[[&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''(((((('''''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&'''''''''&&&&&&%%%$$$''''''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))((((((''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%&&&'''((()))''''''''''''''''''''''''((((((((((((((((((((((((((('''''''''''''''&&&&&&%%%%%%&&&(((******(((&&&&&&&&&''''''''''''&&&&&&(((''''''&&&'''((()))***(((((('''&&&%%%%%%$$$$$$(((''''''''''''((())))))((())))))'''%%%$$$''')))))))))((((((''''''''''''))))))************))))))))))))))))))))))))))))))))))))***+++++++++++++++***++++++++++++,,,,,,,,,,,,,,,,,,+++++++++******+++,,,---...///......---444333111111111333555666777999;;;<<<===>>>@@@BBBFFFIIIOOOUUU\\\fffqqqxxx~~~{{{xxxuuurrrppprrrpppnnnlllhhhbbb[[[VVVUUUVVVXXXXXXWWWUUURRRQQQOOOLLLIIIFFFDDDCCC@@@>>><<<===>>>???@@@??????>>>@@@???===;;;888666444333//////...............///,,,++++++---......,,,***------,,,,,,++++++******+++***)))(((((()))***+++************************************)))))))))((())))))))))))))))))))))))))))))))))))))))))))))))&&&'''((((((''''''(((***))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''(((((((((((()))(((&&&%%%%%%&&&'''((())))))((('''''''''''''''((((((''''''''''''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&''''''((()))((('''&&&&&&'''((()))((((((((((((((((((((((((((((((((((((((((((((((((***))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&''''''((())))))******+++***(((''''''(((***+++))))))************))))))))))))*********+++++++++,,,,,,,,,,,,,,,,,,,,,,,,---------------------------...000111111222444666???===>>>BBBFFFLLLXXXddd%%%%%%'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((''''''&&&&&&''''''((('''''''''''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&''''''''''''&&&%%%%%%''''''''''''''''''''''''######$$$$$$%%%&&&''''''''''''''''''''''''''''''(((''''''&&&&&&%%%%%%$$$'''''''''''''''''''''''''''&&&&&&&&&&&&'''(((((((((((((((((((((((((((((())))))))))))))))))))))))'''''''''(((((((((((((((%%%$$$$$$%%%((()))((('''&&&&&&''''''''''''&&&&&&(((''''''''''''((())))))***)))((('''%%%$$$###"""((((((''''''(((((()))***((()))***)))((('''((())))))(((((((((((('''''''''))))))************)))))))))))))))))))))))))))))))))******+++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++---......///000/////////222111111111222444777888>>>???AAACCCDDDEEEHHHKKKNNNRRRYYYbbbmmmyyy|||wwwsssppppppnnnmmmmmmllljjjfffcccbbbcccddddddbbb^^^ZZZWWWUUURRRNNNKKKIIIEEEBBB???;;;<<<>>>???@@@@@@@@@???DDDCCCCCCAAA???<<<999777222111000/////////000111---,,,,,,---......---++++++++++++++++++++++++++++++***))))))))))))***+++************************************))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((&&&((())))))(((''')))***))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''((((((((((((((('''&&&%%%%%%&&&((()))++++++)))(((&&&&&&%%%%%%((((((''''''''''''((((((''''''''''''''''''''''''''''''&&&&&&''''''((()))((((((''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''&&&&&&(((((((((((((((((((((((((((((((((((((((((((((((('''''''''(((((())))))***+++***)))(((((()))++++++*********))))))*********))))))))))))************+++++++++++++++++++++++++++,,,,,,------.........,,,...111222333444666999??????AAACCCGGGPPPcccsss$$$%%%'''))))))((('''%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''$$$%%%%%%&&&'''((())))))''''''''''''''''''''''''###$$$$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((''''''''''''''''''''''''))))))))))))))))))))))))&&&&&&''''''((((((((()))%%%###"""###&&&((())))))&&&&&&''''''''''''&&&&&&''''''''''''((((((((()))(((((((((((())))))))))))((((((((('''((())))))***((()))*********)))))))))************************++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++)))***++++++,,,,,,+++++++++++++++,,,,,,,,,------..................---------......///000000000000000000111333666:::>>>@@@DDDFFFHHHKKKMMMPPPTTTXXXWWW[[[bbbmmmyyy~~~~~~|||yyyvvvtttrrrrrrrrrqqqooommmmmmooopppooolllgggbbb___[[[XXXTTTPPPMMMIIIDDDAAA===>>>@@@BBBCCCCCCCCCCCCCCCDDDDDDDDDCCC@@@===<<<777666333111/////////000///...------......---+++******++++++++++++++++++*********************************************************)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))&&&((())))))(((((()))***(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((''''''''''''((((((((((((&&&&&&&&&&&&&&&'''((()))+++***)))(((&&&&&&&&&&&&((((((''''''''''''((((((''''''''''''''''''''''''(((''''''''''''((())))))(((((((((''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''&&&&&&&&&(((((((((((((((((((((((((((((((((((((((((((((((('''''''''((((((((())))))+++******)))******+++,,,,,,+++))))))))))))+++,,,******************++++++******************************+++,,,---...///000,,,///222444555666999;;;>>>>>>AAADDDIIIVVVmmm$$$%%%'''))))))((('''%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&'''''''''''''''''''''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&&&&'''((((((''''''&&&''''''''''''''''''''''''%%%%%%&&&&&&'''((())))))''''''''''''''''''''''''######$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))%%%%%%%%%&&&&&&''''''(((%%%$$$"""###%%%((()))***&&&&&&''''''''''''&&&&&&&&&''''''(((((((((((((((&&&&&&'''((()))***+++,,,((((((((((((((()))******)))))))))***++++++***)))************++++++++++++++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++******+++,,,,,,,,,,,,+++++++++,,,,,,,,,---------........................------...///000111222333555555777:::???DDDIIILLLMMMOOOSSSVVVYYY^^^cccgggfffiiioooyyy|||wwwvvvsss}}}~~~{{{zzzxxxxxxxxxwwwsssnnniiifff```]]]YYYVVVRRRMMMHHHEEE???AAACCCDDDFFFFFFFFFFFFAAABBBDDDEEEEEECCCAAA@@@===;;;888444111///......000///------...///---,,,++++++++++++++++++,,,,,,******++++++++++++******************************))))))))))))))))))******))))))))))))))))))))))))************************'''((())))))(((((()))+++(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((''''''''''''((((((((((((&&&&&&&&&&&&''''''((((((((((((''''''''''''((((((((((((''''''''''''((((((''''''''''''''''''''''''(((''''''''''''((())))))'''(((((((((((((((((('''(((((((((((((((((((((((((((((((((((((((((((((((()))))))))(((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((***************++++++,,,,,,+++***))))))***+++,,,,,,,,,,,,,,,,,,,,,,,,,,,******************************+++,,,...///000000---000333666777999;;;<<<<<<===@@@FFFMMM^^^xxx%%%%%%'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&'''''''''''''''%%%%%%&&&&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((('''''''''''''''''''''''''''$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%###$$$&&&((())))))&&&&&&''''''''''''&&&&&&&&&''''''((()))(((((((((''''''''''''''''''''''''))))))(((((())))))***+++***)))((()))***+++***)))((((((((())))))))))))***))))))************))))))***************************++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,------------,,,,,,,,,,,,---------------......000222444666777999:::<<>>CCCKKKTTT]]]eeejjjrrrsssuuuvvvxxx|||{{{zzz{{{}}}wwwqqqooogggeeecccaaa___[[[VVVRRRKKKLLLNNNOOOOOOOOONNNNNNIIIIIIHHHHHHGGGGGGFFFFFFBBBBBBBBB@@@===999666444333111///......///...---///......------,,,,,,,,,***++++++,,,,,,++++++***++++++++++++++++++++++++((()))))))))************))))))))))))))))))))))))************************''')))******))))))***+++))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''((((((((((((''''''''''''''''''&&&&&&&&&&&&&&&''''''(((******((((((''''''''''''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&''''''(((&&&'''((())))))((('''&&&((((((((((((((((((((((((((((((((((((((((((((((((*********)))))))))((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((()))***************++++++,,,,,,++++++***---------,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---...//////000333777:::;;;;;;<<<===>>>???EEERRRcccxxx'''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&'''''''''&&&&&&&&&'''''''''((((((%%%%%%&&&&&&'''((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))(((((('''''''''''''''''''''''')))((((((''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&''''''(((''''''''''''''''''''''''%%%%%%'''((((((((('''&&&(((((((((((((((((((((((((((((((((((((((((((((((())))))(((((('''''''''&&&((('''&&&'''))))))((('''&&&''''''''''''''''''&&&%%%&&&((()))))))))(((''')))))))))***************)))))))))))))))******++++++(((%%%%%%(((***+++*********++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,,,,------,,,,,,,,,,,,,,,---------.............../////////000000000000111444777;;;>>>@@@BBBFFFMMMXXXeeerrr}}}yyyssspppiiihhhfffeeeccc```[[[WWWSSSTTTUUUVVVVVVUUUUUUTTTOOONNNLLLJJJIIIHHHGGGGGGBBBCCCDDDDDDBBB???;;;888444222///......//////...000000///...------,,,,,,***+++,,,------,,,+++***++++++++++++++++++++++++(((((())))))*********+++))))))))))))))))))))))))))))))))))))))))))))))))''')))******))))))***+++))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''((((((((()))'''((((((((('''&&&%%%%%%'''''''''''''''((())))))((((((''''''''''''((((((''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&''''''&&&'''((())))))((('''&&&(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))(((((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&((()))***************+++,,,------,,,+++***,,,,,,,,,++++++*********,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,------.........111444888;;;;;;<<<<<<===AAAAAAHHHXXXkkk(((&&&$$$$$$$$$$$$""" !!!"""$$$&&&''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''&&&%%%&&&'''((()))######$$$%%%&&&'''((()))&&&&&&&&&''''''''''''(((''''''''''''''''''&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''###$$$$$$%%%%%%$$$$$$###%%%&&&''''''(((((('''''''''&&&&&&%%%%%%&&&&&&'''((((((((((((((((((((((((((((((''''''''''''((((((,,,***)))'''&&&&&&&&&&&&''''''''''''''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&&&&'''''''''(((((()))***++++++,,,))))))))))))))))))))))))''')))***)))((('''((()))))))))************))))))+++++++++*********))))))+++***(((***,,,---***(((&&&(((***+++++++++,,,------.........---,,,,,,+++------------...///000000......---...//////...,,,222333444777<<>>EEEFFFNNN^^^uuu)))'''&&&'''(((((('''%%%"""###%%%'''((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%'''&&&&&&%%%&&&'''((()))&&&&&&&&&&&&&&&'''''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%$$$$$$%%%&&&''''''(((((('''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''***)))((('''&&&&&&''''''''''''''''''''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''&&&&&&''''''(((((())))))))))))))))))))))))))))))'''((())))))''''''((()))))))))************))))))+++++++++*********))))))+++***)))***,,,,,,***(((''')))+++++++++***+++,,,------......------,,,+++,,,,,,,,,,,,,,,---...///000000000111333444555555666777999<<>>>>>@@@EEEKKKTTT[[[```kkknnnuuu}}}~~~uuusssuuuyyy|||~~~|||tttooonnnmmmmmmmmmnnnnnnllljjjjjjiiihhhiiijjjlllnnnoootttwwwyyyzzzzzzyyyzzz{{{{{{}}}~~~~~~}}}{{{{{{||||||{{{zzz|||zzz{{{}}}|||~~~|||~~~}}}xxxwwwvvvvvvvvvsssooolll```[[[TTTNNNKKKJJJIIIHHHFFFEEEEEEFFFHHHIIIIIIGGGEEEDDDAAA>>>:::777444333222000......//////...---,,,,,,,,,,,,,,,,,,,,,,,,++++++************++++++))))))************))))))))))))))))))))))))))))))))))))))))))************************************************))))))))))))************)))))))))))))))((((((''''''''''''''''''(((((()))))))))((((((((((((((((((''''''''''''''''''((()))))))))))))))(((((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((&&&&&&'''''''''((((((((())))))))))))))))))))))))''''''''''''''''''''''''''''''((((((((()))))))))((((((''''''''''''(((((((((((((((((())))))))))))'''(((((())))))******+++------------------,,,++++++++++++++++++,,,------......---,,,,,,,,,------,,,,,,,,,---///111444555888:::<<<===>>>@@@CCCEEEPPPXXXfffttt&&&$$$$$$%%%&&&'''&&&%%%&&&''''''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''(((((()))(((((((((((('''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&%%%&&&''''''(((''''''''''''&&&&&&%%%%%%&&&&&&''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''(((((())))))''''''''''''''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''))))))))))))))))))((((((((((((((((((((((((((((((((()))******(((((()))***))))))************))))))*********************************+++++++++***)))***+++---,,,+++******+++,,,------...------,,,,,,///////////////000111111...///000222555:::AAAEEEHHHHHHKKKPPPWWWaaaiiinnnvvvzzzxxxqqqooosssxxx|||}}}zzzwwwxxxwwwvvvrrrlllgggdddcccggggggiiikkkmmmoooooooooooonnnmmmjjjiiikkkooorrrsssxxx}}}|||}}}~~~~~~~~~|||{{{~~~||||||~~~~~~zzzxxxzzzxxxzzz}}}}}}{{{yyyvvvssshhhccc\\\WWWSSSOOOLLLJJJGGGFFFFFFGGGIIIKKKKKKJJJIIIHHHFFFCCC???<<<999888555222000///000///...---------------------------,,,++++++******++++++,,,)))******++++++******)))))))))))))))))))))))))))(((((())))))******++++++*********************************)))))))))))))))*********))))))))))))))))))(((((('''''''''(((((('''''''''''''''&&&&&&&&&((((((((((((((('''''''''''''''((()))))))))))))))((((((((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((''''''''''''(((((((((((())))))))))))))))))))))))''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))((((((''''''''''''(((((((((((((((((())))))))))))''''''(((((()))))))))***------------,,,+++******++++++++++++,,,,,,------///...---,,,,,,,,,,,,,,,,,,,,,---...000333666888;;;<<<<<<===>>>BBBHHHLLLYYYdddsss~~~&&&%%%$$$$$$%%%%%%$$$"""''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((('''&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((((((((()))&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&''''''((((((''''''&&&%%%&&&''''''(((''''''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''((((((''''''''''''((((((&&&&&&'''(((((()))))))))''''''''''''''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''))))))))))))(((((((((((((((((((((((((((((((((((()))***++++++))))))***+++))))))************))))))************************)))***+++++++++************,,,------+++******+++,,,,,,------...------,,,............///000111222333444777:::>>>EEEMMMTTTWWWXXXZZZ^^^dddlllsssxxxzzz~~~|||zzzvvvtttvvv{{{|||vvvrrrooolllkkkhhhhhhgggddd```___```bbbbbbdddgggjjjmmmoooqqqrrrqqqpppmmmjjjhhhkkkpppttttttzzz|||{{{}}}~~~~~~}}}|||~~~|||vvvtttuuuqqqtttzzz|||zzzqqqmmmiiiddd```ZZZTTTPPPMMMKKKJJJKKKLLLNNNNNNNNNKKKJJJIIIGGGDDDAAA???===888666333222111111///...------------------------,,,,,,++++++++++++,,,,,,******++++++++++++******))))))))))))))))))))))))(((((())))))******++++++))))))))))))))))))))))))))))))))))))))))))******))))))))))))))))))******)))))))))(((((()))******((('''''''''&&&&&&&&&''''''''''''(((((((((((((((''''''((()))))))))))))))'''''''''(((((((((((((((''''''''''''''''''''''''&&&''''''''''''''''''''''''''''''((((((((())))))''''''''''''(((((((((((())))))))))))))))))))))))'''''''''((((((((())))))((((((((((((((((((((((((******)))(((((()))******(((((((((((())))))))))))((((((''''''''''''(((((((((((((((((())))))))))))(((((((((((())))))))))))+++++++++++++++***)))(((++++++,,,,,,------------///...---,,,,,,,,,,,,,,,,,,------///222555888:::<<<<<<<<<<<<@@@FFFNNNTTTcccnnn|||((('''%%%%%%&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))((('''&&&%%%&&&''''''((((((''''''&&&&&&&&&''''''(((((((((&&&&&&&&&''''''''''''(((%%%%%%&&&&&&'''(((((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&%%%&&&''''''(((((('''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''(((((((((&&&&&&'''((())))))((((((''''''''''''''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&)))))))))))))))))))))))))))***++++++))))))***+++))))))************))))))***************+++++++++)))***,,,,,,***)))***+++***+++------,,,++++++,,,,,,,,,------......------,,,,,,,,,---///000222333444888>>>CCCIIIRRR]]]eeemmmmmmmmmnnnqqqtttwwwyyyyyy||||||yyyxxx{{{{{{tttooollljjjhhhgggdddeeedddaaa^^^^^^aaaeeeeeeiiimmmqqqsssvvvyyy|||yyyvvvrrroooooorrrvvvxxx}}}{{{wwwxxxrrrvvv|||}}}zzzsssssstttvvv|||}}}|||sssqqqnnnkkkgggaaa[[[VVVRRRPPPMMMLLLMMMNNNNNNNNNOOOOOONNNLLLJJJFFFCCCBBB<<<999666444444222111///------------------------,,,,,,++++++++++++,,,,,,******++++++++++++******))))))))))))))))))))))))))))))))))))************))))))))))))))))))))))))))))))))))))************))))))))))))***************))))))))))))******+++***))))))(((((()))******'''''''''(((((((((((((((''''''((()))))))))))))))'''''''''(((((((((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''''''''''''''(((((())))))***''''''''''''((((((((((((((((((((((((((((((((((((''''''((((((((()))))))))))))))))))))))))))))))))******((((((((((((******''''''((((((((()))))))))((((((''''''''''''(((((((((((((((((()))))))))))))))))))))))))))))))))))))))***************)))(((++++++,,,---------------......---,,,,,,,,,---------...///000333777:::<<<<<<<<<<<<===BBBLLLWWW___oooxxx'''&&&%%%&&&'''((('''&&&%%%$$$$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&((())))))(((&&&%%%%%%&&&'''((((((((('''&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((%%%%%%&&&&&&'''(((((()))''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''&&&&&&&&&%%%&&&''''''(((((('''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&''''''(((&&&'''((())))))(((((('''''''''''''''''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''$$$%%%%%%&&&&&&'''''''''))))))))))))))))))))))))''')))***)))((('''((()))))))))************))))))))))))*********+++++++++(((***,,,,,,***)))***+++)))+++------,,,,,,---...+++,,,------......------,,,---...///111444666777:::@@@IIIRRR[[[fffsss|||{{{xxxvvvuuurrrssstttuuuwwwwwwxxxxxx~~~xxxvvvtttrrrqqqooollljjjdddfffgggdddbbbccchhhmmmqqquuu{{{~~~}}}~~~|||yyywwwpppppprrruuuzzzvvvtttqqqooonnnkkkgggddd\\\YYYUUUSSSSSSSSSRRRRRRUUUUUUTTTRRRNNNJJJFFFDDD???===999777666444222000........................---,,,,,,++++++,,,,,,---***++++++,,,,,,++++++***))))))))))))))))))))))))*********)))))))))))))))))))))))))))))))))))))))((()))))))))************((()))))))))************((((((((((((((()))******))))))(((((((((***+++,,,''''''''''''((((((((()))''''''((()))))))))))))))''''''''''''((((((((()))''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&''''''((())))))******''''''''''''(((((((((((('''''''''''''''''''''''''''((((((((()))))))))))))))))))))))))))))))))))))))((('''&&&&&&'''((()))&&&&&&'''''''''(((((((((((((((''''''''''''(((((((((((((((((())))))))))))************************))))))***+++++++++******+++,,,---.........---,,,------,,,,,,,,,---......//////000222444777:::<<<=========???FFFRRR```jjj{{{$$$######%%%''')))((((((#########$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%'''(((((('''%%%$$$%%%%%%'''((((((((('''&&&)))((('''&&&%%%$$$######&&&&&&&&&'''''''''((((((%%%%%%&&&&&&'''((())))))''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''(((((('''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&'''((())))))((('''&&&''''''''''''''''''''''''(((((((((((((((((((((((('''''''''&&&&&&'''''''''&&&&&&''''''((()))******))))))))))))))))))))))))&&&'''((('''&&&%%%&&&((())))))************))))))))))))******++++++++++++(((***---,,,***(((***+++(((***,,,---,,,,,,---///+++,,,,,,---.........---///000111333666888;;;<<>>;;;888777555333111........................---,,,,,,++++++,,,,,,---***++++++,,,,,,++++++***))))))))))))))))))))))))++++++******))))))(((((())))))))))))))))))))))))(((((())))))*********+++(((((())))))*********+++'''''''''''''''((()))***'''&&&&&&&&&'''(((***+++&&&'''''''''(((((())))))'''(((((()))))))))))))))&&&'''''''''(((((())))))''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&''''''((()))******+++''''''''''''((((((((()))''''''''''''''''''''''''(((((((((((())))))))))))))))))))))))))))))))))))((('''%%%$$$$$$%%%'''(((&&&&&&&&&&&&'''''''''(((((((((''''''''''''(((((((((((((((((())))))))))))+++++++++***************)))***+++,,,,,,,,,,,,,,,+++,,,---.........---,,,,,,,,,,,,,,,------...///000000111222555888;;;<<<>>>>>>>>>AAAIIIWWWgggqqq''''''''''''''''''''''''&&&&&&''''''(((((())))))''''''''''''(((((())))))))))))))))))((((((((((((''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&''''''''''''&&&&&&((('''&&&%%%%%%&&&'''(((%%%&&&&&&&&&'''(((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&%%%%%%''''''&&&&&&&&&&&&''''''(((((('''''''''&&&&&&&&&((((((''''''&&&&&&&&&%%%%%%'''(((((('''&&&&&&'''&&&'''''''''(((((())))))(((((((((((())))))))))))))))))(((((((((((()))))),,,+++*********+++------''')))+++------+++)))'''++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,---------......///......///000000...---...000333555777:::>>>AAAJJJUUUeeesss}}}|||rrrllleee^^^\\\dddmmmrrryyy|||zzzyyyyyyzzz|||}}}}}}{{{zzzzzz{{{zzz|||}}}xxxmmmoooooonnnmmmpppvvv|||{{{tttrrrtttqqq{{{|||}}}{{{rrrmmmjjjiiifffdddhhhgggddd]]]UUUMMMHHHEEEFFFBBB???>>>@@@>>>888333000///...///000000///---///...---,,,+++,,,------,,,,,,,,,,,,,,,,,,,,,,,,))))))))))))))))))))))))++++++++++++++++++++++++******))))))((((((''''''))))))))))))))))))))))))))))))))))))((((((((((((''''''(((((())))))******)))))))))))))))))))))))))))(((((((((((((((&&&$$$))))))''''''''''''))))))''''''''''''''''''''''''++++++******))))))(((((((((((((((((((((((((((((())))))))))))))))))))))))))))))))))))(((((((((((()))((('''&&&&&&'''((()))))))))))))))))))))))))))))))))))))))******************))))))((((((''''''&&&'''((()))***+++,,,---))))))))))))************(((((())))))))))))(((((())))))))))))))))))))))))++++++++++++++++++++++++---------............///+++,,,------,,,,,,...000444444555777:::<<<======<<<>>>???CCCPPPbbbpppvvv''''''''''''''''''''''''''''''''''''((((((((((((''''''((((((((()))))))))))))))((((((((('''''''''''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&''''''''''''&&&&&&'''&&&%%%%%%%%%%%%&&&'''&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&''''''''''''(((((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''(((((('''''''''&&&&&&&&&((((((((('''''''''&&&&&&&&&((())))))(((''''''(((%%%%%%&&&&&&''''''''''''(((((((((((())))))))))))))))))(((((((((((()))))),,,++++++***+++,,,---...,,,++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++,,,,,,---------.........,,,,,,,,,---///000000///000222444666:::???EEEJJJVVVaaappp|||}}}sssmmmgggbbbbbbkkkuuu|||~~~|||yyyvvvrrrpppnnnmmmkkkmmmppprrrsssuuuwwwzzz{{{zzzyyyvvvuuuwwwzzz}}}|||{{{{{{{{{}}}zzzxxxrrrmmmlllpppoooyyy}}}|||~~~~~~xxxsssooolllrrrqqqnnnhhh___UUUMMMIIIFFFCCCAAABBBCCCBBB===888333222000000000000///---......------,,,---------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++***************)))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((()))))))))))))))))))))))))))))))))))))))))))))***++++++***)))((('''&&&%%%%%%&&&'''(((''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))(((((((((''')))((('''&&&&&&'''((()))((((((((((((((((((((((((((((((((())))))******+++***)))))))))((((((((('''&&&&&&''''''((()))******((((((((()))))))))******(((((())))))))))))((((((************************++++++++++++++++++++++++---------............///---.........------///111222333444777:::<<<======AAADDDHHHMMMZZZkkkwww|||''''''''''''''''''''''''(((((((((''''''''''''''''''''''''(((((((((((()))(((((('''''''''&&&&&&&&&(((((((((((((((((((((((('''''''''''''''&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&%%%$$$$$$%%%&&&&&&'''''''''''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''''''''(((((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''(((((((((''''''''''''&&&))))))((((((((((((''''''''')))******)))(((((()))''''''''''''(((((((((((((((((((((((())))))))))))))))))(((((((((((()))))),,,++++++++++++,,,------...,,,)))''''''))),,,...------------------------,,,,,,,,,,,,,,,,,,,,,,,,------------.........///+++,,,,,,...000111333444666777:::===AAAHHHPPPUUUaaalll{{{{{{rrrnnnooonnnqqq{{{{{{zzzwwwtttqqqmmmkkkiiieeegggkkkooosssxxx~~~~~~}}}}}}|||zzzxxxyyy{{{|||~~~|||yyyvvvtttssssss|||~~~xxxsssmmmiiikkkpppuuu~~~~~~}}}}}}~~~}}}yyyvvvvvvyyy{{{yyyyyywwwssslllcccXXXNNNHHHFFFEEEDDDFFFHHHGGGBBB>>>999666333111000000...---------...............---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++******++++++++++++++++++))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))(((((((((((())))))))))))))))))))))))'''((()))***++++++++++++''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%(((((((((((((((((((((((()))))))))))))))))))))))))))))))))(((((((((''''''((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''((())))))***++++++))))))))))))((((((((((((&&&&&&&&&&&&'''''''''(((''''''((((((((()))))))))((())))))******))))))(((++++++++++++++++++++++++++++++++++++++++++++++++---------............///...///000///......000222333444777:::<<<>>>???@@@FFFMMMUUU]]]jjjyyy''''''''''''''''''''''''(((((((((''''''&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&%%%%%%%%%))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''&&&&&&&&&%%%''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&''''''''''''(((%%%%%%%%%&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''(((((((((''''''''''''''')))))))))))))))((((((((('''(((******((('''((()))******************++++++(((((((((((())))))))))))))))))(((((((((((())))))************++++++,,,,,,,,,***'''%%%%%%'''***,,,------------------------,,,,,,,,,,,,,,,,,,,,,,,,---............////////////000000000111333666888;;;???DDDIIIOOOUUU\\\```iiirrr~~~}}}vvvsssttt}}}|||||||||zzzwwwsssooommmkkkmmmppptttxxx}}}{{{xxxssspppoooppppppqqqyyy~~~~~~|||vvvssswww~~~~~~{{{{{{}}}~~~xxxuuusssuuu~~~~~~zzztttkkkbbbXXXNNNHHHFFFFFFGGGIIIKKKJJJFFFCCC???;;;666222111///...---,,,---...000000///......------------------------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++)))*********++++++,,,,,,))))))))))))))))))))))))))))))))))))((((((((((((******))))))((((((''''''((((((((((((((((((((((((&&&''')))))))))((()))))))))(((((((((((((((((()))''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))((((((((('''''''''(((((((((''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((()))***++++++))))))))))))((((((((((((''''''''''''''''''''''''''''''''''''(((((((((((()))))))))******)))))))))++++++++++++++++++++++++***+++++++++++++++,,,,,,---------............///.../////////...///111222777999<<<>>>???@@@BBBCCCIIITTT```lllyyy''''''''''''''''''''''''((((((''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%))))))))))))))))))))))))&&&'''''''''''''''''''''&&&&&&''''''''''''&&&&&&''''''((((((((((((''''''((((((((('''&&&&&&&&&%%%''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''((((((((((((((((((((((((((((((((()))))))))))))))%%%'''(((((('''&&&''''''++++++++++++++++++******(((((((((((())))))))))))))))))(((((((((((())))))((())))))***************+++***))))))))))))***+++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,........./////////000000222333333222222555999===@@@GGGQQQZZZbbbggglllooosssyyy|||xxxtttvvv|||~~~||||||}}}~~~}}}yyyuuurrruuuvvvwwwxxxyyy|||~~~yyyuuurrrpppooooooooopppyyy|||yyywwwxxx}}}|||yyywwwxxx}}}tttkkkccc\\\TTTOOOHHHIIIJJJLLLMMMLLLIIIGGGDDD@@@;;;666333111///...---...///000000000///...------------------------++++++++++++++++++++++++++++++++++++++++++++++++((())))))******+++++++++))))))))))))))))))))))))))))))))))))((((((((((((******))))))((((((''''''(((((((((((((((((((((((((((***+++***(((''''''((((((((())))))))))))(((((((((((((((((((((((((((((())))))))))))))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''''''''(((((((((((((((((('''''''''''''''''''''''''''&&&''''''((())))))******(((((((((((()))))))))))))))))))))(((((((((((((((''''''''''''(((((((((((())))))************))))))++++++++++++++++++++++++*********++++++,,,,,,,,,---------............///,,,.../////////000222444999<<<>>>??????@@@CCCFFFNNN[[[jjjwww'''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$''''''&&&&&&&&&%%%%%%%%%((((((((((((((((((((((((&&&&&&&&&'''''''''''''''&&&&&&''''''''''''&&&&&&(((((())))))))))))(((((('''''''''''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&''''''''''''(((&&&&&&''''''((()))))))))''''''&&&&&&&&&&&&'''''''''(((((((((((()))))))))''''''(((((((((((())))))%%%'''(((((('''&&&&&&'''))))))))))))(((((((((((((((((((((((())))))))))))))))))(((((((((((())))))((()))******+++*********+++,,,------------,,,+++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,////////////000000000000111333555555777<<>>>>>>>>@@@FFFKKKWWWeeeuuu''''''''''''''''''''''''%%%&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&''''''''''''&&&&&&''''''((())))))(((''''''&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&'''''''''(((&&&&&&&&&''''''''''''(((&&&&&&''''''((())))))***''''''&&&&&&&&&&&&'''''''''((((((((())))))))))))&&&&&&'''''''''(((((((((&&&'''))))))'''&&&'''((())))))((((((((('''''''''(((((((((((())))))))))))))))))(((((((((((()))))))))***+++,,,---,,,,,,+++++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,------------------------//////000000000111111111///333888<<>>???@@@EEENNNVVVeeerrr''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''))))))((((((((('''''''''(((((('''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&''''''''''''''''''&&&%%%&&&'''(((((('''&&&%%%%%%&&&&&&''''''(((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&&&&'''''''''(((((($$$$$$%%%%%%&&&'''(((((('''''''''&&&&&&''''''''''''((((((((())))))******%%%&&&&&&&&&''''''((((((''')))******)))(((((()))+++*********))))))(((((((((((((((((())))))))))))))))))(((((((((((())))))+++,,,---...///...------))))))(((''''''((())))))------------------------------------------------000000000000111111111111000555<<>>@@@AAADDDKKKWWW```ooo{{{'''&&&%%%%%%%%%%%%&&&'''&&&&&&%%%&&&'''***---///'''''''''(((((((((((()))&&&&&&''''''''''''&&&&&&))))))((('''&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''&&&&&&'''((()))))))))(((&&&%%%%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&***))))))(((''''''&&&&&&))))))((((((''''''&&&&&&'''&&&&&&&&&&&&'''((((((''''''''''''(((((((((((())))))))))))))))))))))))''''''''''''((((((((()))(((((())))))******++++++((((((''''''''''''((((((++++++******)))(((((((((++++++************++++++++++++******************,,,,,,++++++,,,,,,---...//////.........---------111...******---......,,,,,,,,,,,,...111333333333888>>>EEENNNYYYjjj}}}{{{kkkggg```]]]^^^eeennntttzzzwwwvvvuuurrrooonnnpppsssttttttuuuxxxzzz}}}|||||||||yyyxxxyyyyyyvvvssspppwwwwwwnnniiidddbbbbbbbbb```^^^YYYVVVSSSOOOLLLHHHDDD@@@999777333111111111///....../////////...------,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,)))((((((((()))***++++++)))))))))))))))))))))))))))))))))))))))))))))))),,,***'''%%%%%%'''***,,,))))))))))))))))))))))))******+++******+++---///444333333222111000//////.........+++(((&&&'''((())))))))))))))))))))))))))))))(((((((((((())))))((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&'''''''''((((((((((((''''''''''''((((((***)))(((''''''((()))***&&&&&&&&&&&&'''''''''(((%%%&&&'''((())))))))))))***)))(((''''''((()))***,,,,,,+++***)))(((''''''++++++,,,,,,,,,---------******+++++++++,,,,,,,,,---------...............111///...222999???BBBBBBCCC@@@???CCCIIISSSbbbppp((('''&&&&&&&&&&&&'''(((((((((&&&&&&&&&(((***+++&&&&&&'''''''''(((((((((&&&&&&''''''''''''&&&&&&(((''''''&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''(((((()))((('''&&&%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((''''''''''''&&&&&&&&&&&&'''((((((''''''''''''(((((((((((())))))))))))))))))))))))'''''''''((((((((()))))))))))))))))))))*********)))(((((('''''''''((((((,,,++++++++++++*********++++++************++++++++++++******************,,,,,,++++++,,,,,,---...//////.........---------///---+++,,,///000000////////////000222444555555<<>>BBBDDDDDDDDDBBBDDDPPPbbbyyy(((''''''''''''''''''((()))((('''%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&''''''(((((())))))))))))((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&'''''''''''''''((((((((('''''''''&&&&&&((('''&&&%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((()))))))))&&&&&&''''''(((((())))))'''&&&&&&&&&&&&'''((((((''''''''''''(((((((((((((((((((((((((((((((((((('''(((((((((((()))))))))++++++******))))))((((((+++***)))(((''''''''''''%%%&&&&&&'''((()))))))))++++++************++++++******+++++++++++++++,,,,,,,,,++++++,,,,,,---...........................------...///000111111111444555666777:::???DDDHHHLLLUUUdddttt~~~ggg\\\ZZZ___aaafffooozzzxxxtttrrrsssyyy|||zzzxxxwwwwwwvvvtttqqqssstttwww}}}~~~{{{wwwrrrnnnooommmjjjgggaaaZZZQQQKKKEEECCC???<<<:::777444111111111000//////.........------------------------------------------------------,,,+++*********+++++++++++++++++++++++++++)))))))))))))))))))))))))))))))))******)))))))))))))))))))))))))))))))))(((((()))+++...000111222//////.........///000111111111000...+++))))))***(((((((((((((((((((((((())))))(((((((((((())))))((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((''''''''''''(((((())))))(((((((((((())))))((())))))))))))*********)))))))))))))))((('''''')))***+++,,,,,,+++***)))(((((())))))************))))))*********++++++++++++++++++,,,,,,,,,------------......//////000000000333666;;;@@@BBBCCCCCCEEEDDDJJJ[[[rrr&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&''''''((())))))((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&'''''''''(((((((((''''''&&&&&&&&&&&&&&&((('''&&&%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((&&&&&&''''''(((((())))))'''&&&&&&&&&&&&'''((((((''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((()))))))))***++++++******))))))((((((******)))(((((((((((((((%%%%%%&&&'''((())))))***++++++************++++++******++++++,,,,,,,,,,,,,,,,,,++++++,,,,,,---...---.....................---.../////////000111222333555888;;;@@@FFFNNNTTTYYYbbbqqqtttaaa\\\^^^bbbgggoooyyy{{{uuusssrrrsssrrryyy~~~|||zzzxxxvvvzzz}}}|||xxxrrrpppnnnjjjeee^^^VVVPPPGGGEEEAAA???===:::777444555444222111000/////////,,,,,,,,,,,,,,,,,,,,,,,,------------------------------,,,+++*********+++************************))))))))))))))))))))))))((()))***++++++***)))((())))))))))))))))))))))))(((((((((+++000222222111000///......///000222333111111111...+++))))))***(((((((((((((((((((((((())))))(((((((((((())))))(((((((((((((((((((((((((((((((((((((((((((((((('''''''''((((((((())))))((((((''''''''''''(((((((((((())))))))))))(((((())))))))))))*********+++''''''((()))******)))))))))***+++,,,,,,+++***)))((((((((()))******++++++))))))*********+++++++++++++++,,,,,,,,,---------------......///000000111000333888===@@@BBBCCCCCCDDDFFFQQQhhh%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&''''''''''''&&&&&&''''''''''''&&&&&&###$$$$$$$$$%%%%%%&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&'''(((((((((((('''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%'''''''''((((((((((((((('''&&&&&&&&&&&&'''((((((''''''''''''(((((((((((())))))))))))))))))))))))((((((((()))))))))******************))))))))))))***))))))(((((())))))***(((((()))******+++,,,,,,++++++************++++++******++++++,,,---------,,,,,,++++++,,,,,,---...---------..................///000000///111444666666:::@@@EEEJJJQQQZZZaaahhhppp~~~kkk```aaafffpppsssyyyyyyvvvxxxxxxvvvrrrooonnnnnnpppqqqnnnuuu~~~wwwuuuqqqmmmhhhaaaYYYTTTIIIGGGEEEDDDCCC@@@===::::::888666333111000000000,,,,,,,,,,,,,,,,,,,,,,,,------------------------,,,++++++************+++)))))))))))))))))))))))))))))))))))))))))))))))))))******++++++******)))))))))))))))))))))))))))***((())),,,111444333111111000.........000222333111111000...+++))))))***))))))))))))))))))))))))))))))(((((((((((())))))((((((((((((((((((((((((((((((((((((((((((((((((''''''((((((((()))))))))((((((''''''''''''(((((((((((())))))))))))(((((())))))))))))************&&&'''((()))************)))******************)))(((((())))))*********+++*********++++++++++++,,,,,,,,,,,,,,,------------------...///000000111222111555:::>>>@@@AAACCCEEEDDDHHHWWWqqq%%%&&&'''(((((('''&&&%%%&&&&&&''''''''''''&&&&&&&&&&&&'''''''''(((((((((&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%&&&&&&'''(((((()))((('''&&&%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''''''''(((((((((((((((''''''''''''&&&&&&&&&&&&'''((((((''''''''''''(((((((((((())))))))))))))))))))))))(((((()))))))))*********)))))))))))))))*********(((((((((((()))***++++++)))******++++++,,,,,,,,,++++++************++++++******++++++,,,------...,,,,,,++++++,,,,,,---...---------.........//////...///000000111444:::???CCCIIIPPPVVV[[[bbbjjjqqqttt{{{zzzqqqhhhffflllsss~~~zzzyyyvvvqqqooopppmmmllljjjiiiiiijjjkkkllliiioooyyy|||wwwqqqkkkccc\\\WWWMMMLLLKKKJJJJJJIIIEEECCC>>><<<999555222111000000------------------------........................******)))))))))***++++++************************))))))))))))))))))))))))************************))))))))))))))))))))))))+++))))))---222555333///111000...,,,---...000222000111000---***((()))***))))))))))))))))))))))))))))))(((((((((((())))))(((((((((((((((((((((((((((((((((((((((((((((((('''((((((((())))))))))))((((((''''''''''''(((((('''((()))******)))((('''((((((((()))))))))******((())))))*********))))))***))))))(((((())))))***)))))))))))))))*********++++++++++++,,,,,,,,,,,,,,,,,,,,,------------...------...///000111222222333777<<>>@@@AAACCCGGGJJJOOOPPP[[[sss~~~xxxvvvvvvwww''''''''''''(((((((((((((((((((((((((((((((((((($$$$$$$$$%%%%%%%%%&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''+++***)))''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''''''''((())))))(((''''''&&&&&&''''''(((((())))))(((((('''''''''&&&&&&&&&((('''%%%$$$$$$&&&)))***((((((''''''''''''((((((%%%&&&&&&'''((()))******))))))(((((('''''''''&&&)))((('''&&&&&&'''((()))''''''(((((())))))******&&&&&&'''((()))***++++++))))))(((((((((***+++,,,))))))************))))))''''''((())))))***))))))******+++++++++,,,,,,,,,,,,++++++***+++,,,...///,,,,,,,,,---------......,,,...000111000000111222111222666:::999:::FFFUUUbbbqqq{{{zzz|||~~~}}}}}}~~~}}}uuujjjbbbZZZ___gggnnntttzzz|||wwwvvvnnnnnnnnnnnnlllkkkiiihhhggghhhiiigggcccaaadddgggeeekkkuuuzzzrrrjjjbbb]]][[[VVVQQQRRRXXXZZZXXXSSSLLLHHHBBB>>>;;;999666555000000000222333222000.........---------,,,,,,,,,........................+++++++++++++++++++++++++++++++++*********))))))************************))))))))))))))))))))))))'''(((+++---000111222333222111///.........//////222111000///---+++***))),,,,,,+++***)))((('''&&&))))))***))))))((('''&&&))))))))))))))))))))))))******))))))((((((''''''))))))))))))))))))))))))++++++******))))))(((((())))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))*********)))))))))))))))*********))))))))))))))),,,,,,,,,+++++++++******+++,,,------//////000000............000333666888;;;;;;<<>>DDDTTTeeezzzzzzvvvqqqnnnllljjjfffccceeekkksssyyy}}}vvvqqqooojjjkkklllllljjjfffcccaaabbbbbbbbbaaa______bbbeeejjjqqq|||{{{vvvqqqkkkfffccc]]]XXXXXX]]]___]]]ZZZWWWRRRKKKDDD???;;;666444222111000000111111///.../////////.........------+++++++++++++++++++++++++++++++++++++++++++++++++++++++++*********))))))************************))))))))))))))))))))))))((()))***,,,///111222333222222000/////////000000333222000...,,,***))))))))))))))))))))))))))))))((())))))))))))(((((('''))))))))))))))))))))))))***)))))))))((((((((('''))))))))))))))))))))))))*********)))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))***))))))))))))))))))))))))))))))))))))***************++++++,,,,,,,,,------------,,,------...............///111444777999:::;;;===BBBGGGKKKNNNOOOTTT[[[hhhyyyyyysssooommmmmm''''''''''''((((((((((((((((((((((((((((((((((((&&&''''''''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((('''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&%%%&&&&&&'''(((&&&%%%$$$$$$$$$$$$%%%&&&(((((((((((((((''''''''''''''''''''''''&&&&&&&&&$$$%%%'''((()))((('''&&&''''''&&&&&&&&&&&&'''''''''''''''((((((((((((((((((((((((((('''''''''''')))((('''&&&&&&'''((()))(((((((((((())))))))))))'''(((((()))***+++,,,,,,***)))((((((((((((((()))))))))************)))))))))))))))***))))))(((((()))))))))*********++++++,,,------------,,,,,,+++,,,------------............000111111111111222333222444888>>>DDDQQQeeewwwssslllbbb[[[\\\aaagggkkkvvv{{{zzznnniiihhhjjjlllnnnnnnlllfff```\\\^^^]]]\\\\\\\\\___bbbdddnnnwww~~~}}}|||wwwsssoooiiicccbbbeeehhhfffddd```[[[TTTLLLFFF???:::666555222000////////////...000000000/////////......************************,,,,,,,,,,,,,,,,,,,,,,,,+++++++++***************************************))))))))))))))))))))))))))))))***+++---///222333333333222111111111111222444222///,,,***)))))))))&&&&&&'''((()))******+++'''(((((())))))))))))((())))))))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))************))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))******(((((())))))******++++++))))))***+++,,,---......111000...---------............///000222555888999:::<<<@@@EEEKKKPPPSSSUUUWWWaaaooo~~~{{{sssnnnlllkkk''''''''''''((((((((((((((((((((((((((((((((((((%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))&&&&&&&&&%%%&&&&&&''''''&&&&&&&&&&&&&&&'''(((((('''&&&$$$######$$$&&&'''))))))((((((''''''&&&&&&''''''''''''''''''''''''%%%&&&''''''((('''''''''&&&&&&%%%%%%%%%%%%&&&&&&((((((((((((((('''''''''((((((((((((((('''''''''(((((('''&&&&&&''')))***(((((((((((())))))))))))******+++,,,,,,---......***))))))(((((('''''''''))))))************))))))***************)))((('''((())))))))))))*********------.........---+++***------------...............///111111000111333444888:::===BBBLLL]]]ssszzzjjjcccYYYTTTXXXdddrrr{{{~~~pppgggeeeeeemmmooossstttpppiiiaaa\\\\\\ZZZYYYYYY[[[```cccfffqqq{{{|||wwwqqqnnnpppqqqpppnnnfffbbb\\\UUUNNNHHHAAA<<<999555111......//////...000000000/////////......------------------------,,,,,,,,,,,,,,,,,,,,,,,,************************************************))))))))))))))))))))))))+++***))))))+++...111222333333333222222222222333444111---***((('''((()))%%%%%%&&&'''((()))******&&&'''((())))))***))))))(((((((((((((((((((((((())))))))))))(((((((((((((((((((((((((((((((((((((((((())))))******++++++(((((((((((((((((((((((((((((((((((()))))))))))))))))))))))))))))))))))))))))))))))))))*********''''''((()))***++++++,,,******++++++,,,------...222111///......///111222...///000111444666999::::::>>>CCCHHHMMMRRRWWWZZZ]]]gggvvv|||tttooommmlll''''''''''''((((((((((((((((((((((((((((((((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))''''''''''''''''''(((((('''&&&&&&&&&&&&'''(((((()))'''&&&$$$$$$&&&''')))))))))((((((''''''&&&&&&&&&'''''''''''''''''''''((('''%%%%%%%%%&&&(((***&&&&&&%%%%%%%%%%%%&&&&&&(((((((((((((((''''''''''''''''''(((((((((((((((((('''&&&&&&'''((()))***))))))))))))(((((((((((())))))******+++,,,,,,,,,******)))))))))(((''''''))))))************))))))******+++******)))((((((((())))))))))))*********---......///...---+++***---------.........//////---///000000000222555777:::???DDDJJJVVVkkkuuummm___\\\YYYYYYaaaooozzzooogggcccccceeejjjmmmppprrroooiiiaaa\\\XXXXXXWWWWWW[[[aaagggkkkyyy~~~{{{zzzzzzxxxvvvrrrnnnhhhaaaZZZQQQIIIDDD===999444000/////////////////////.........------////////////////////////,,,,,,,,,,,,,,,,,,,,,,,,************************************************))))))))))))))))))))))))+++***))))))***,,,///111222222222222222222222222222///,,,)))''''''((()))''''''''''''((((((((((((&&&'''((())))))***))))))(((((((((((((((((((((((((((((((((((())))))))))))(((((((((((((((((((((((((((((())))))******++++++(((((((((((((((((((((((((((((((((((())))))))))))************************(((((())))))************''''''((()))***++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,...............000111222...///111333555888:::;;;<<<@@@DDDHHHLLLRRRXXX\\\bbbkkkwww}}}}}}||||||}}}zzzrrrnnnllllll''''''''''''((((((((((((((((((((((((((((((((((((''''''((((((((()))))))))&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((()))(((((('''''''''((((((''''''&&&&&&''''''((())))))(((''''''''''''((()))((((((((((((((('''''''''&&&&&&&&&''''''''''''''')))'''%%%$$$$$$&&&)))+++''''''&&&&&&&&&&&&'''''''''''''''((((((((((((((('''''''''(((((((((((((((''''''&&&&&&'''((()))***))))))))))))(((((((((((('''''''''((((((((()))))))))************))))))((())))))************))))))*********+++******)))))))))))))))*********++++++---............------,,,------........./////////...000111222333555999<<<<<>>888444222222111000/////////.........------------------------------,,,,,,,,,,,,,,,,,,,,,,,,***************+++++++++************************))))))))))))))))))))))))******))))))***,,,---...///000111111222111111111...---***(((''''''((())))))))))))((((((''''''''''''(((((())))))))))))((())))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))************))))))))))))))))))))))))(((((((((((())))))))))))************************((((((((()))******++++++(((((())))))******++++++...---------,,,,,,,,,+++***+++,,,---...//////000...000222444777999;;;<<<>>>AAAEEEHHHKKKRRRZZZaaagggmmmuuuyyywwwtttrrrqqqwwwxxxpppmmmkkkkkk''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))'''''''''''''''''''''''''''''''''''''''''''''''')))(((''''''&&&&&&&&&&&&'''''''''''''''(((((()))(((((((((((((((((((((((('''''''''(((((((((((((((&&&&&&&&&'''''''''(((((('''&&&&&&%%%&&&'''((()))(((''''''''''''''''''(((&&&&&&''''''(((((())))))''''''''''''((((((((()))''''''&&&&&&'''(((***+++***)))))))))(((((((((''''''''''''((((((((((((((()))***+++,,,,,,++++++***))))))************))))))))))))***+++++++++******************+++++++++,,,...------------......///............////////////000222333555666:::???BBBDDDOOO[[[eeeuuu|||lllccc```]]]ccckkkttt{{{~~~wwwppphhhbbb^^^^^^___``````^^^^^^^^^___^^^```ccceeeeeedddbbbaaa```ffflllppptttyyysssjjj```VVVOOOEEEAAA<<<888666444222111000000000/////////......------------------------------------------------))))))*********+++++++++************************))))))))))))))))))))))))))))))******++++++,,,,,,------///000000000//////******)))(((((((((((()))******)))))))))(((((((((((())))))))))))(((((('''))))))))))))))))))))))))'''((((((((()))))))))***))))))))))))))))))))))))*********)))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))************************'''(((((()))******++++++)))))))))))))))*********,,,,,,,,,---------------+++,,,...000000000.........000222555888:::<<<===>>>AAAEEEGGGKKKTTT___hhhnnnqqquuuyyyyyywwwtttrrrwww{{{sssooommmmmm''''''''''''((((((((()))((((((((((((((((((((((((&&&&&&&&&&&&'''''''''((((((((((((((((((((((((((('''''''''''''''''''''''')))((('''&&&%%%$$$$$$$$$'''''''''''''''((())))))''''''((())))))(((''''''&&&'''''''''(((((())))))&&&&&&&&&'''''''''((((((%%%&&&'''((((((((('''&&&((((((''''''''''''((((((%%%&&&&&&'''((()))******&&&'''''''''(((((())))))'''&&&&&&&&&'''(((***+++******))))))((((((((('''***************+++++++++)))***+++,,,------,,,+++))))))************))))))((()))***+++++++++++++++***++++++++++++,,,,,,,,,...---,,,,,,---...000111............/////////000222333555777999===CCCGGGMMMYYYfffppppppccc___```eeelllvvv~~~}}}uuunnnhhhccc___\\\YYY\\\______^^^\\\[[[[[[```aaaccceeeggghhhhhhhhhllluuu~~~}}}{{{wwwrrrkkkcccYYYSSSGGGDDD???;;;999666333111111111111111000000000000........................------------------------))))))******++++++++++++************************))))))))))))))))))))))))((()))***++++++++++++++++++,,,---/////////...---((((((((()))))))))))))))))))))))))))************))))))***))))))(((''''''))))))))))))))))))))))))'''((((((((())))))******))))))))))))))))))))))))++++++******))))))(((((())))))))))))))))))))))))(((((((((((())))))))))))************************'''(((((()))***+++++++++*********)))))))))))))))***++++++,,,---.../////////111333444444222000...///000333666999;;;<<<===>>>AAAEEEGGGLLLVVVdddnnnuuuvvvyyy||||||zzz}}}wwwsssqqqqqq((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&'''''')))((('''&&&&&&&&&&&&&&&)))&&&%%%&&&((()))'''%%%''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&'''''''''''''''&&&&&&***)))(((''''''&&&''''''***))))))((('''&&&&&&&&&'''((()))******)))((('''''''''((((((((((((''''''((()))*********)))((('''((((((((((((((('''''''''******************++++++***((('''&&&'''(((***+++---------,,,,,,+++++++++))))))***+++,,,,,,---------------.........//////333///...000111//////111444555888;;;>>>CCCKKKSSS___iiiuuu|||ooofffaaaaaabbbmmmuuu|||yyytttnnngggbbb]]][[[XXX[[[]]]\\\YYYXXX[[[^^^```dddiiinnnppprrruuuwww}}}yyyssspppnnnggg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bbblllrrr|||xxxsssrrr((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''(((((('''&&&&&&&&&&&&&&&(((&&&%%%&&&((()))(((&&&''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&'''''''''''''''&&&&&&(((((('''''''''(((((()))***))))))(((''''''&&&&&&'''((()))******)))((('''''''''((((((((((((''''''%%%%%%'''(((((((((((('''(((((())))))))))))******))))))******+++++++++,,,+++***)))((()))***,,,---+++++++++*********)))))))))******+++,,,,,,---------------.........//////111...---111222111111444777999===AAAEEEKKKUUU]]]jjjsss~~~yyysssjjjdddbbbeeekkkoooyyy}}}~~~uuuuuusssnnnggg```[[[ZZZXXXZZZ\\\\\\[[[]]]bbbfffrrrwww||||||}}}}}}|||}}}xxxssspppllldddYYYQQQKKKIIIEEEBBB???<<<999888777222000333333111///111333111...---...///...------------,,,,,,,,,++++++,,,,,,,,,++++++*********************************(((((((((((())))))******))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))'''((((((((()))))))))***)))((((((''''''(((((()))***)))))))))((((((((('''***)))((('''''''''(((((())))))))))))))))))))))))))))))******)))(((((('''''''''(((((())))))************))))))))))))******))))))(((((())))))***+++++++++************++++++++++++,,,,,,---............///000///......000222222444777999;;;<<<>>>@@@CCCFFFKKKTTT```lllwww}}}~~~}}}((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''(((((('''&&&&&&&&&&&&''''''%%%%%%&&&((()))((('''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&'''''''''''''''&&&&&&&&&&&&''''''(((******)))))))))(((''''''&&&&&&(((((())))))))))))(((((('''(((((())))))((((((''''''((()))+++,,,,,,,,,,,,)))))))))***++++++,,,,,,((())))))***+++,,,---------,,,+++***+++,,,---...++++++++++++******************++++++,,,,,,------------.........////////////,,,---111333222444777<<>>???@@@BBBAAAEEENNNZZZhhhuuu((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''(((''''''&&&&&&&&&''''''&&&%%%%%%&&&'''(((((((((''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((%%%&&&''''''(((''''''''''''''''''''''''((())))))))))))((((((''''''''''''(((((())))))))))))(((((((((((())))))))))))(((((()))******+++,,,---------************++++++++++++(((((()))***,,,---......---,,,,,,+++,,,---......------------------------+++++++++,,,,,,,,,------............////////////...,,,...222444444777<<>>HHHSSSiiiyyy{{{rrrjjjbbbZZZXXXZZZ[[[cccqqq~~~uuupppmmmkkklllttt{{{}}}zzzuuussssssrrrtttvvvyyy}}}uuurrrnnnkkkjjjiiigggeeeXXXUUUTTTXXX^^^aaa___\\\RRRIIIAAA===888333111333555333111000000111111000............---------,,,,,,,,,,,,,,,,,,---------************************+++************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((())))))))))))))))))))))))))))))))))))(((((((((((()))((((((''''''(((((()))(((((((((((())))))))))))'''((()))*********))))))))))))))))))))))))))))))******++++++,,,+++++++++******************************))))))))))))******(((''''''''''''((())))))++++++************++++++,,,,,,---......//////000---...000000000222444777777:::===@@@BBBDDDHHHKKKSSSYYYdddrrr|||uuurrrwww~~~((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&'''(((((('''((()))(((%%%$$$%%%'''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((($$$%%%&&&'''(((((((((((()))(((((('''''''''(((((('''(((((((((((((((((((((***)))(((''''''((()))***))))))************)))))),,,,,,+++++++++,,,------)))******+++,,,------...+++++++++,,,,,,---------******+++,,,,,,,,,,,,,,,+++++++++,,,,,,,,,------------------------------.../////////000000000000444333666;;;@@@HHHVVVddd}}}ssshhhaaaZZZUUUXXX___dddlllyyy{{{uuunnnrrrqqqlllgggfffeeebbbdddjjjqqqvvvyyyzzz{{{|||~~~}}}}}}zzzrrrnnnooopppmmmkkkccc___]]]```hhhlllkkkggg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jjjxxx|||sssrrrrrrpppsssrrruuu{{{)))(((((((((''''''''''''''''''''''''''''''''''''''''''''''''((((((((()))(((((((((((((((((((((((('''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&'''((()))((()))***)))%%%###$$$&&&''''''''''''((((((((()))(((((((((((((((((((((((((((((((((((((((((((((((($$$%%%&&&'''((((((((((((''''''&&&''''''((()))***'''''''''(((((((((((((((***)))(((''''''((()))***))))))************)))))))))((((((((()))+++---...((()))***,,,...000111222,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,,,,------,,,,,,---------....../////////------------------------////////////000000000000555555888===DDDOOOaaappptttkkkbbb]]]YYYWWW]]]gggqqqwwwwwwmmmfff]]]```aaa^^^^^^___]]]YYY___cccjjjrrrzzz~~~yyyzzz}}}xxxtttuuuwwwtttpppnnniiifffiiipppuuutttqqqfff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bbbhhhssslllbbbcccfffhhhxxxzzz((((((((((((((((((((((((((((((((((((''''''''''''))))))(((((('''''''''&&&***(((''''''(((((('''%%%''')))***++++++***)))'''&&&&&&&&&&&&&&&&&&%%%%%%'''''''''((((((((())))))***)))'''%%%%%%%%%''''''((((((((((((((((((((((((&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''''''''''''''((((((((((((((('''&&&''')))++++++***++++++***)))((('''&&&&&&(((((((((((())))))))))))&&&'''((()))))))))))))))*********++++++,,,,,,,,,------------------------+++,,,,,,---...///000000,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,.../////////...---000///...///000111111111777777<<>>:::777555333111111000///---//////...------------...------------------------************************++++++,,,,,,+++***(((''',,,***((())),,,---+++))),,,,,,,,,++++++++++++***))))))))))))))))))))))))******))))))((((((''''''))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))(((((((((((((((((((((((((((((())))))))))))(((((())))))***+++,,,,,,------,,,+++***))))))***+++,,,,,,+++++++++***)))))))))******+++++++++,,,,,,,,,...------------.../////////000111222333555999<<<>>>???@@@CCCHHHNNNTTTXXXfffrrrwwwcccUUURRR\\\jjjxxx(((((((((((((((((((((((((((((((((((('''''''''''')))((((((((('''''''''''')))(((''''''(((((('''%%%'''(((***++++++***(((''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''((())))))((((((''''''&&&(((((((((((((((((((((((('''''''''(((((('''''''''''''''''''''''''''''''''''''''''''''((((((((((((***((('''(((***+++++++++))))))))))))(((((((((((((((((((((((()))))))))***))))))***+++++++++++++++******+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------------......---------,,,,,,,,,,,,,,,,,,---.../////////......111000000111222444555666999:::???GGGPPP```yyyhhhaaa]]]aaagggmmmwwwtttjjjbbb[[[VVVUUUSSSTTTWWWXXXWWWZZZ```dddjjjsss|||~~~uuufffZZZQQQKKKDDD???999666333111000000...---000///......------......,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++&&&''')))***+++*********,,,***))))))+++,,,***(((*********))))))))))))((())))))))))))))))))))))))***)))))))))((((((((('''))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((()))******(((((((((((((((((((((((())))))))))))))))))))))))*********++++++,,,,,,,,,++++++***************************)))))))))))))))***++++++++++++,,,,,,,,,...------------.../////////000222333444666:::===@@@AAACCCEEEHHHOOOWWW]]]qqqnnn^^^TTTUUUaaannn~~~((((((((((((((((((((((((((((((((((((''''''''''''((((((((((((''''''''''''((('''&&&&&&''''''&&&%%%&&&'''((())))))((('''&&&''''''''''''''''''''''''%%%%%%&&&&&&&&&''''''''''''(((***++++++)))'''&&&(((((((((((((((((((((((('''(((((())))))(((((('''''''''''''''''''''''''''''''''''''''((((((((((((,,,***))))))+++,,,+++***''''''(((((())))))******((((((((()))))))))***************+++++++++++++++***++++++++++++,,,,,,,,,++++++++++++++++++++++++---------,,,,,,+++++++++------------------------,,,---...////////////............///111444666777<<<>>>DDDPPP^^^qqquuubbb```bbbiiirrr{{{{{{oooeee]]]WWWTTTTTTRRRTTTXXXZZZ\\\bbbhhhsssyyytttggg\\\RRRHHHBBB<<<999555222111111000///000000///...............++++++++++++++++++++++++++++++++++++++++++++++++***+++,,,---............---+++******++++++)))(((*********))))))))))))((())))))))))))))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))((('''((()))***+++((((((((((((((((((((((((***))))))(((((())))))*********+++++++++++++++++++++++++++++++++***)))(((((((((((()))))))))))))))++++++++++++,,,,,,,,,,,,......------......///000///111333444555777;;;===AAADDDGGGGGGIIIPPP[[[ddd|||wwwcccWWWUUU\\\iiiuuu((((((((((((((((((((((((((((((((((((''''''''''''(((((((((((((((''''''''''''&&&%%%%%%&&&'''&&&%%%&&&&&&'''(((((('''&&&&&&'''''''''((((((((((((((((((((((((((())))))))))))'''((()))***))))))''''''(((((((((((((((((((((((((((((())))))))))))((((((''''''''''''''''''''''''''''''''''''((((((((((((,,,***))))))***+++***)))(((((((((((())))))))))))(((((()))))))))*********)))))))))))))))))))))***++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++---------...............---......///////////////...///000000222555888;;;BBBDDDKKKYYYjjj~~~vvveeeaaaeeemmmwww}}}rrriiiaaaZZZVVVTTTSSSVVV\\\bbbgggpppyyy|||pppcccVVVKKKCCCAAA===888555333333222111111000//////......//////,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,000000//////...------,,,,,,,,,+++*********)))(((,,,,,,,,,+++++++++******))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))((((((((((((((((((((((((***)))((('''((()))+++,,,((((((((((((((((((((((((******)))(((((()))******++++++++++++***************+++,,,,,,+++***((('''(((((())))))******+++++++++++++++,,,,,,,,,------...............//////000///111444666777999<<>>@@@BBBFFFKKKMMMOOOXXXgggsss|||kkkZZZWWW```ooo))))))))))))))))))))))))(((((((((((('''''''''''''''''''''((((((((((((((('''&&&%%%&&&'''((('''&&&''''''''''''''''''''''''&&&&&&&&&''''''(((((()))&&&&&&'''''''''(((((((((((('''%%%$$$$$$&&&(((***(((((((((((((((((((((((('''(((((())))))(((((('''((((((((((((((((((((((((''''''''''''((((((((((((***(((''''''((())))))(((******))))))(((((('''''')))))))))*********++++++...---,,,******+++,,,,,,,,,,,,,,,++++++++++++***,,,,,,,,,,,,,,,,,,,,,,,,((()))***+++,,,------...,,,,,,,,,---......////////////......//////000111///111444666888===EEEKKKTTTZZZ```gggppp|||uuulllfffdddeeeeeeooo|||~~~rrrfff]]]\\\^^^fffsssvvvjjj^^^TTTOOOFFFCCC>>>;;;888666222000222111111000000000000000........................------------------------))))))))))))***+++,,,---)))***++++++***)))***+++*********))))))))))))((())))))))))))))))))))))))(((((((((((())))))))))))(((((((((((((((((((((((()))))))))))))))))))))))))))))))))))))))))))))))))))))))))*********++++++)))))))))))))))))))))))))))******++++++******)))))))))***************************+++++++++******+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,------------//////......//////000111000333777999;;;===???AAABBBGGGLLLPPPVVV```nnnyyywwwiii\\\]]]iiizzz))))))))))))))))))))))))((((((((((((''''''''''''''''''''''''((((((((()))'''&&&%%%&&&((()))((('''(((''''''''''''''''''((($$$%%%%%%&&&''''''((((((&&&'''''''''(((((((((((('''''''''''''''(((((()))(((((((((((((((((((((((('''''''''(((((('''''''''((((((((((((((((((((((((''''''''''''(((((((((((()))((('''((()))++++++***(((((((((((())))))))))))))))))*********+++++++++///...,,,******+++,,,---,,,,,,,,,+++++++++******++++++++++++++++++++++++***+++++++++,,,,,,------+++++++++,,,---.........000///.........///111111---222777:::>>>EEEPPPXXX^^^fffkkklllnnntttvvvuuuqqqjjjbbb[[[ZZZ___hhhooozzzzzzooohhhkkknnnxxx}}}yyyrrriii```XXXTTTLLLJJJFFFDDDAAA===888444222222111000000000111111........................------------------------,,,+++++++++,,,---...///''')))++++++***)))+++---*********))))))))))))((())))))))))))))))))))))))'''((((((((()))))))))***))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))''')))***,,,,,,+++***)))))))))))))))))))))))))))((()))+++------+++)))((((((((())))))******++++++))))))))))))***+++,,,,,,,,,,,,,,,+++++++++++++++,,,,,,,,,------------...///////////////000000111000333777;;;<<<>>>@@@BBBDDDHHHMMMTTT^^^jjjvvv~~~pppfff^^^bbbppp)))))))))))))))))))))))))))(((((((((''''''''''''&&&'''''''''(((((())))))(((&&&&&&''')))***)))(((((((((''''''''''''(((((($$$$$$%%%%%%&&&'''(((((())))))))))))************%%%''')))***+++***)))(((((((((((((((((((((((((((&&&&&&''''''''''''&&&&&&))))))))))))))))))))))))''''''''''''((((((((()))***(((((()))+++,,,---,,,&&&&&&'''((()))***++++++)))************+++++++++---,,,***(((((()))***+++,,,,,,,,,++++++*********))))))))))))))))))))))))---------,,,,,,,,,++++++******+++,,,,,,---......000///.........///111222333999???DDDJJJSSS___hhheeennnsssooolllnnnnnnkkkgggaaaZZZXXXZZZcccppp{{{xxxsssyyy}}}{{{xxxwwwvvvtttnnnfff___YYYVVVSSSQQQOOOLLLIIIDDD>>>:::333222111111000111111111------------------------........................---,,,***)))(((((()))***&&&)))++++++******,,,///,,,,,,,,,++++++++++++***))))))))))))))))))))))))'''((((((((())))))******************************))))))))))))))))))))))))))))))))))))))))))))))))'''(((+++------,,,***((())))))))))))))))))))))))'''))),,,......,,,)))''''''(((((()))***++++++,,,))))))(((((()))+++---...,,,+++++++++***))))))))),,,,,,,,,---------......///////////////000111111000444888;;;===???AAACCCFFFIIINNNXXXcccppp{{{kkkccc___eeettt))))))))))))))))))))))))(((((((((((((((''''''&&&))))))))))))(((((((((((())))))(((((((((((())))))+++(((&&&&&&((()))(((&&&&&&'''''''''(((((()))))))))*********(((''''''((((((((((((((()))))))))))))))))))))(((''''''&&&&&&(((((((((((((((((((((((('''&&&&&&&&&&&&'''((((((''''''''''''((((((((((((************++++++++++++)))))))))))))))))))))))))))))))))))))))))))))))))))***+++,,,,,,,,,,,,,,,++++++************++++++,,,,,,++++++++++++++++++---------............///+++)))(((+++///111111///111000111333222///111666>>>???EEEQQQ___jjjppptttzzz|||zzzuuuppplllhhheee______^^^___dddnnnzzz||||||~~~|||wwwrrrsssqqqoookkkhhheeebbbaaa```]]][[[[[[XXXPPPEEE???===:::777444111000////////////.........---------//////...---,,,,,,++++++************))))))))))))++++++++++++++++++++++++++++++++++++++++++++++++(((((((((((())))))))))))))))))))))))))))))))))))((()))***)))''''''((()))))))))(((((((((((()))))))))************+++++++++++++++++++++***((('''&&&))))))))))))))))))))))))***+++,,,---...---,,,,,,))))))))))))))))))))))))************************,,,------,,,******,,,---,,,,,,,,,,,,,,,,,,,,,,,,---.........---...111333666555777===AAAAAAAAADDDIIIMMMVVVcccnnnwww~~~~~~iiiffffffkkkuuu))))))))))))))))))))))))(((((((((((((((''''''&&&))))))))))))(((((((((((()))((((((''''''(((((()))$$$###!!!###&&&(((((('''''''''''''''((((((((()))((()))***)))'''&&&'''((('''((((((((())))))))))))'''''''''((((((((((((((((((((((((((((((((((((((((((''''''''''''((())))))''''''''''''(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((()))***************++++++************++++++++++++++++++++++++,,,,,,---------............///000...,,,---///000...,,,...---///222111///222888AAAJJJZZZmmm}}}}}}vvvpppjjjfffeeeeeefffggglllsss}}}yyyuuuwwwyyyuuuqqqpppoooppprrrvvv|||~~~}}}xxxsssqqqqqqpppooommmkkkiiihhhgggfffhhhiiiggg^^^QQQHHHEEEAAA;;;666333222111111//////.........---------///......---,,,,,,++++++++++++++++++************++++++++++++++++++++++++++++++++++++++++++++++++(((((((((((()))))))))***))))))))))))))))))))))))(((((()))))))))))))))((())))))(((((((((((())))))))))))*********+++++++++******+++******)))((('''))))))))))))))))))))))))***+++,,,---------,,,,,,************************************************,,,------,,,++++++,,,...---------------------------............///111444888666999???BBBCCCEEEJJJQQQUUU^^^iiirrryyy~~~yyyjjjiiikkkqqqxxx))))))))))))))))))))))))(((((((((((((((''''''&&&(((((((((((())))))))))))(((''''''''''''''''''(((&&&%%%%%%&&&)))******)))''''''''''''(((((((((((('''((()))(((&&&&&&&&&(((''''''((((((((()))))))))&&&&&&''''''((())))))***((((((((((((((((((((((((((((((((((((((()))******''''''''''''(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((()))******************++++++************++++++******++++++,,,,,,---------------............///222000//////000000...---,,,,,,///333222111666<<>>BBBHHHLLLTTTdddsss}}}************************(((((((((((((((''''''&&&''''''(((((())))))******(((''''''''''''''''''(((###%%%((())))))))))))***((((((((((((((('''''''''&&&'''(((((('''&&&((()))&&&&&&'''''''''(((((((((***))))))(((''''''&&&&&&((((((((((((((((((((((((&&&&&&&&&&&&&&&'''((((((''''''''''''(((((((((((((((((((((((())))))))))))************************))))))))))))))))))))))))++++++++++++++++++***)))++++++************++++++++++++,,,,,,------......---------............///...000000///---,,,---...000111333666666<<>>???GGGJJJOOO\\\hhh~~~wwwooohhheeejjjoooqqqqqqyyy{{{~~~...---,,,+++***)))))))))))))))((((((((('''''''''(((((())))))))))))))))))((('''%%%&&&(((***++++++***)))))))))((()))))))))(((((((((((((((((((((((('''''''''''''''((())))))$$$%%%&&&((())))))******(((((())))))(((''''''&&&'''''''''''''''((())))))(((((()))************)))))))))))))))))))))))))))((((((((()))))))))******))))))))))))************)))************+++++++++++++++,,,,,,,,,---------,,,,,,,,,,,,,,,,,,,,,,,,,,,---------------,,,,,,------......///000000000///000111000//////111333777:::>>>CCCKKKYYYjjjwww{{{rrrnnnmmmqqqzzz~~~nnnmmmmmmooowww|||mmm]]]TTTKKKBBB<<<<<<777444111000000000///...///...............------......------,,,++++++******************))))))(((******************************++++++++++++******************))))))))))))******************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))******++++++++++++******)))************+++++++++******+++,,,,,,,,,,,,++++++,,,,,,------,,,,,,+++,,,,,,++++++,,,,,,------.........//////////////////111333555666999<<>>AAAAAAJJJNNNUUUbbbmmm}}}vvvpppkkkiiijjjnnnuuu~~~||||||)))))))))*********))))))))))))((((((((((((((((((((()))***++++++)))((('''%%%(((******'''%%%&&&((('''&&&%%%$$$$$$%%%'''((((((((((((((((((((((((((('''''''''''''''((())))))***)))'''&&&&&&'''(((((((((((()))))))))((((((''''''''''''''''''((())))))'''(((((())))))))))))))))))))))))))))))))))))))))))*********++++++++++++((()))))))))************))))))*********++++++++++++++++++,,,,,,,,,------------------------------,,,,,,------......------.........///000000111111...000222333555777;;;===@@@EEENNNVVV]]]eeelllqqquuuxxxxxxqqqiiidddeeeggglllvvv}}}sssfffZZZQQQJJJEEECCC@@@<<<777333222111000///222111000///...---,,,+++......------,,,,,,,,,,,,++++++,,,,,,++++++***)))******************************++++++++++++******)))***************++++++******************************)))))))))((((((((()))))))))))))))))))))))))))))))))))))))))))))))))))******++++++******)))))))))*********+++++++++---,,,+++*********,,,,,,+++,,,,,,------,,,,,,+++***+++,,,---...---,,,+++.........///000000111111222444666888999<<>>IIIWWW```lllrrrzzzzzzvvvjjjgggeeefffhhhjjjqqqyyy|||||||||}}}zzzwwwwww{{{sssqqqqqquuu{{{}}}yyyxxxxxxyyyvvvmmm```XXXVVVTTTQQQLLLGGG@@@:::777555333222//////////////////000000......------------------,,,------------,,,++++++******************************++++++++++++******))))))******+++,,,,,,,,,++++++++++++++++++++++++)))))))))***+++,,,,,,,,,))))))))))))))))))))))))))))))))))))))))))))))))'''((((((((((((((((((''')))************+++++++++...---,,,+++***)))))))))+++,,,,,,------,,,,,,+++++++++,,,,,,------,,,,,,......///000000111222222333555888;;;===AAAEEEHHHJJJRRRVVV\\\eeeeeejjjyyyvvvmmmaaabbblll}}})))***,,,---,,,+++***((((((((()))))))))*********((('''&&&&&&''')))+++,,,,,,***(((((()))***+++***%%%''')))***++++++***)))(((((((((((((((((((((((('''''''''''''''((())))))$$$%%%&&&((())))))******(((((()))***************'''''''''''''''((())))))&&&'''(((((())))))(((((())))))))))))))))))))))))((((((((()))))))))******))))))))))))************)))************+++++++++))))))*********+++++++++........................,,,---...///000000000000/////////000111111222222444555888@@@PPPggg~~~~~~tttmmmjjjooosssvvvzzzyyyqqqlllkkkmmmlllnnnpppnnnmmmqqqzzz~~~~~~~~~}}}~~~sssnnnjjjlllpppvvv}}}}}}wwwvvvyyyuuuuuunnnddd^^^___```^^^WWWQQQHHH@@@;;;777444333////////////////////////------..................---------------,,,,,,+++******************************++++++++++++******))))))***++++++,,,------++++++++++++++++++++++++)))))))))***************))))))))))))))))))))))))))))))))))))))))))))))))(((((())))))))))))(((((()))************+++++++++***++++++,,,,,,++++++++++++,,,,,,------,,,,,,+++,,,,,,++++++,,,,,,---------...///000111222333333555777;;;>>>AAAEEEJJJMMMMMMUUUWWW[[[bbb___```lllmmmyyyuuujjjaaaaaaiiixxx***+++---------,,,***((((((((())))))*********+++)))(((&&&&&&'''***...000333...)))((()))***(((&&&###%%%(((***+++***((('''(((((((((((((((((((((((('''''''''''''''((())))))'''((()))))))))(((&&&%%%(((((()))***************'''''''''''''''((())))))&&&''''''((((((((((((((())))))))))))))))))))))))(((((((((((())))))))))))))))))))))))************)))************+++++++++******+++++++++,,,,,,,,,........................+++,,,---.../////////////////////000111111222222333555<<>>888555222111111111111000////////////............,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++...,,,)))((()))******)))************************)))))))))))))))))))))))))))******+++++++++***************++++++*********+++++++++***************))))))))))))))))))))))))++++++************++++++)))))))))***************++++++++++++,,,,,,,,,,,,+++++++++,,,------......000///......///222444666<<<>>>CCCIIIOOOSSSWWWXXXUUUWWW___llluuuxxxzzz|||zzzwwwnnnqqquuuwww{{{,,,,,,+++************+++*********+++++++++******(((((())))))*********+++*********)))))))))(((((((((((((((((((((((((((((())))))))))))))))))))))))******)))(((((('''(((((((((((()))))))))*********(((((((((((((((((((((((())))))))))))))))))))))))'''((()))******)))((('''((((((((((((((((((((((((************************))))))*********+++++++++*********++++++,,,,,,+++)))******++++++,,,,,,,,,,,,,,,------------,,,,,,............///////////////000222333333444666888===GGGXXXnnn{{{rrrqqqyyy|||sssooohhhccc```___```aaakkkrrr~~~{{{tttpppmmmjjjfffbbb\\\YYYVVVTTTUUUWWWXXXXXX\\\^^^```bbbeeeiiinnnrrrssstttwww{{{~~~}}}zzzvvvssskkkhhhccc``````___^^^\\\]]]___aaadddfffggghhhhhhdddcccbbb```]]]ZZZWWWVVVTTTSSSSSSSSSUUUWWWZZZ\\\\\\YYYYYYZZZZZZYYY^^^dddsssuuu}}}~~~}}}{{{oooeeeccchhhqqq~~~mmm___TTTMMMGGGCCC:::777444222111111000///////////////............------------------------++++++++++++++++++++++++...,,,***)))*********)))************************))))))))))))))))))))))))((()))***+++++++++++++++,,,,,,------------,,,,,,************************))))))))))))))))))))))))++++++************++++++***************+++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---.........111111000000111444777999<<>>;;;666333111111000///////////////............------------------------++++++++++++++++++++++++---+++***)))***+++***(((************************************************((()))***++++++++++++++++++,,,,,,------,,,,,,+++************************))))))))))))))))))))))))++++++************+++++++++++++++,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,------...//////000000000000222555888:::===@@@EEEJJJOOOVVV]]]bbbkkkqqqzzz------,,,+++++++++++++++******+++,,,,,,***)))((())))))))))))))))))******++++++*********)))))))))((((((((((((((((((((((((''''''''''''''''''''''''***))))))(((((((((((()))''''''''''''(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))((())))))******))))))((())))))))))))))))))))))))++++++++++++++++++++++++)))************+++++++++***+++,,,,,,++++++,,,...,,,+++++++++,,,,,,---...------............------............////////////---...///000111333777:::BBBNNN___pppqqqkkknnnsssvvv|||{{{rrrooosss||||||uuujjjeee___\\\[[[ZZZWWWTTTTTTQQQMMMLLLLLLLLLLLLLLLLLLMMMPPPQQQRRRTTTWWWYYY[[[]]]___cccgggllloooqqqsssxxxsssooojjjeeeaaa]]]XXXVVVQQQPPPMMMJJJHHHHHHHHHHHHFFFFFFGGGHHHJJJKKKMMMMMMKKKKKKKKKJJJHHHGGGEEEDDDEEEEEEEEEFFFHHHLLLOOOQQQWWWUUUUUUWWWVVVSSSVVVZZZ^^^bbbkkkvvv~~~zzzvvvrrrqqqoooooottt{{{|||sssjjjiiimmmwwwpppcccYYYOOOIIIEEE@@@:::666333222000///////////////............------------------------,,,,,,,,,,,,,,,,,,,,,,,,+++***)))***+++,,,+++)))++++++++++++++++++++++++************************)))******+++++++++******)))))))))******)))))))))***************+++++++++))))))))))))))))))))))))++++++************++++++++++++,,,,,,---.........------------,,,,,,,,,,,,,,,,,,,,,---......//////---...///111333666888999>>>BBBHHHLLLQQQXXXaaagggxxx------,,,++++++++++++,,,)))***,,,,,,,,,***)))'''************************+++++++++*********))))))))))))))))))))))))))))))(((((((((((((((((((((((()))(((((((((((())))))***'''(((((((((((()))))))))))))))))))))))))))))))))))))))))))))))))))))))))***))))))))))))))))))***************************++++++++++++++++++++++++)))************+++++++++)))+++------++++++,,,......---,,,,,,,,,---...///------............------............///////////////000111222333666:::>>>EEEQQQaaaooo~~~wwwlllfffgggmmmrrr|||vvvoooccc___[[[ZZZ[[[[[[XXXUUUTTTRRROOONNNNNNMMMLLLJJJJJJKKKMMMNNNOOOPPPRRRTTTUUUUUUWWWZZZ^^^bbbfffhhhlllooottt{{{{{{xxxhhhccc^^^XXXUUURRRNNNLLLJJJIIIGGGEEECCCCCCEEEFFFCCCCCCCCCCCCDDDEEEEEEFFFEEEEEEEEEEEEEEEDDDCCCBBBCCCBBBBBBCCCFFFIIILLLNNNSSSRRRSSSUUUTTTQQQSSSWWWVVVZZZdddooouuuyyy}}}yyytttqqqqqqrrrqqqpppuuu}}}xxxqqqooorrrwwwvvvkkk```WWWPPPLLLGGG@@@:::666444222111////////////....................................,,,,,,,,,,,,,,,,,,,,,,,,)))((((((***,,,---,,,***++++++++++++++++++++++++******************************+++++++++***))))))'''(((((())))))(((((('''))))))*********+++++++++))))))))))))))))))))))))++++++************++++++******+++,,,,,,---............---------,,,,,,,,,,,,,,,------.../////////...///222555888999::::::AAAEEEKKKOOOSSS[[[eeemmm...---,,,,,,++++++,,,,,,)))***,,,---,,,***((('''+++++++++***************+++++++++************)))************************))))))))))))))))))))))))(((((('''(((((()))***+++))))))))))))************))))))))))))))))))))))))))))))))))))))))))))))))+++***)))(((((()))***+++************************++++++++++++++++++++++++)))************+++++++++))),,,...---+++***,,,/////////------,,,---...///------............------............/////////000333444555666777:::???BBBHHHTTTcccnnnxxx|||uuulllffffffkkkrrrvvvtttmmmaaa___\\\\\\^^^___\\\YYYVVVTTTRRRQQQQQQPPPMMMKKKJJJLLLNNNOOOPPPPPPRRRTTTSSSSSSUUUWWWZZZ^^^bbbdddhhhiiilllppptttuuusssrrraaa]]]WWWRRROOOMMMKKKIIIHHHGGGFFFDDDCCCDDDFFFHHHEEEDDDDDDCCCCCCDDDDDDDDDBBBCCCCCCDDDCCCCCCBBBBBBBBBAAAAAABBBEEEHHHKKKMMMPPPOOOQQQSSSRRROOOQQQUUURRRVVV___iiioooqqqvvv~~~zzzssspppsssrrrsssuuuuuutttyyyyyyqqqoooqqq}}}wwwnnnfff]]]XXXQQQLLLDDD===999666444333000/////////....................................,,,,,,,,,,,,,,,,,,,,,,,,(((((((((***,,,---,,,+++++++++++++++++++++++++++************************+++++++++++++++***)))((())))))************))))))))))))******++++++++++++))))))))))))))))))))))))++++++************++++++))))))***+++,,,,,,------.........------,,,,,,,,,,,,,,,------.../////////000333666:::===>>>>>>>>>CCCHHHNNNQQQVVV^^^iiiqqq111///---------...---,,,++++++++++++++++++++++++******))))))))))))******++++++*********+++---...))))))))))))))))))))))))))))))(((((('''''''''&&&(((((((((((())))))))))))))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((******))))))))))))******)))))))))))))))))))))))))))************+++++++++,,,,,,++++++***+++++++++)))***,,,...////////////,,,------......------,,,,,,,,,---.../////////......000222222000000000111111111333666:::???DDDGGGOOOWWW```gggmmmsssxxx{{{ooooooooonnnooosssxxx}}}yyyuuulllgggbbbbbbeeefffccc```\\\[[[YYYXXXXXXWWWTTTQQQTTTSSSRRRQQQRRRSSSUUUWWWUUUUUUUUUUUUXXX[[[^^^___```bbbeeeggghhhfffdddbbbWWWVVVSSSOOOMMMKKKJJJJJJMMMKKKHHHFFFDDDEEEFFFGGGDDDBBBAAAAAABBBBBBAAA???AAAAAABBBCCCCCCCCCCCCCCCEEEDDDBBBAAABBBDDDGGGIIILLLMMMOOOPPPQQQRRRSSSSSSWWWWWWZZZ___eeekkknnnooowww}}}uuurrrqqqqqqqqqpppssswwwxxxyyy{{{yyyppplllqqq|||}}}wwwnnnddd\\\YYYTTTLLLEEE???:::555222444222000000111111///---//////.........---------------------------------+++***)))***,,,,,,***)))************************(((((())))))******++++++))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************)))************++++++++++++++++++***************,,,++++++******++++++,,,.........------,,,,,,,,,,,,,,,------.../////////111333555777999;;;???BBBFFFLLLRRRUUUWWW]]]hhhqqq111///---------...---,,,++++++++++++++++++++++++******))))))))))))************)))))))))***+++,,,))))))))))))))))))))))))''''''''''''&&&&&&%%%%%%((((((((()))))))))******))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))******))))))))))))******)))))))))))))))))))))))))))************+++++++++,,,,,,++++++***++++++,,,)))***+++---............,,,------......------,,,.........///......------///000222222111000111222444444666<<>>888555333222000000111111///...//////.........---------------------------------,,,+++***+++------+++***************************)))))))))))))))*********))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************)))************+++++++++***************+++++++++,,,++++++******++++++,,,---------,,,,,,+++++++++,,,,,,---......//////000///111333555777999===@@@IIIOOOUUUYYY\\\cccoooxxx|||111///---------...---,,,******************************))))))))))))******)))))))))((())))))***+++))))))))))))))))))))))))((((((((((((''''''''''''))))))))))))************))))))))))))))))))))))))******************************************************))))))))))))******)))))))))))))))))))))))))))************+++++++++,,,++++++***++++++,,,,,,((()))+++,,,------------------............------////////////...---,,,,,,///000222222111111222333777777<<>>AAAIIIOOOVVV\\\aaaiiittt}}}}}}{{{111///---------...---,,,,,,,,,,,,,,,,,,,,,,,,,,,+++******))))))******+++******)))))))))*********))))))))))))))))))))))))++++++******************))))))))))))*********+++((((((((((((((((((((((((******************************************************))))))))))))******))))))))))))))))))))))))))))))*********+++++++++++++++******++++++,,,,,,))))))***+++,,,,,,------------............------...////////////......---///000222222111222333555777;;;HHH]]]tttzzzqqqllljjjhhhiiikkkpppvvvtttjjjnnntttxxxzzz|||~~~}}}zzzwwwvvvuuutttqqqppppppmmmjjjgggfffggghhhjjjkkkhhheeebbbbbbcccfffhhhjjjkkkkkkkkkiiifffcccaaabbbbbbcccccceeefffgggggggggddd___YYYTTTQQQNNNMMMJJJIIIGGGFFFHHHIIIIIIHHHJJJKKKKKKKKKKKKJJJJJJIIIIIIIIIHHHGGGGGGGGGGGGGGGHHHIIIJJJKKKKKKKKKKKKKKKMMMQQQWWW___gggkkkkkkjjjkkklllnnnssszzzyyysssqqqoooooorrrvvvyyy|||xxxqqqhhhbbbaaa___fffpppzzzwwwqqqmmmrrr|||}}}zzzzzz||||||vvvmmmbbbWWWLLLBBB<<<666333111000111111000///////////////............------------------------,,,++++++,,,------,,,***************************++++++******))))))(((((())))))))))))))))))))))))))))))))))))))))))))))))((()))))))))************))))))*********+++++++++))))))******+++,,,------,,,++++++******++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,---------...//////000000111333555777:::>>>CCCGGGMMMSSSZZZaaahhhrrr}}}~~~111///---------...---,,,------------------------++++++************+++++++++++++++++++++++++++***))))))))))))))))))))))))******++++++++++++++++++((())))))))))))*********(((((((((((((((((((((((())))))))))))))))))))))))******************************))))))))))))******))))))))))))))))))))))))))))))*********++++++++++++*********++++++,,,---************+++,,,,,,------......//////......---,,,---...///000000000000///000222222111333555777:::EEE[[[xxxzzztttrrrooopppsssssszzzzzzmmmdddfffhhhjjjlllooosssvvv}}}zzzxxxtttqqqpppqqqsssuuuxxxvvvssspppnnnoooqqqrrruuuuuuuuuuuusssqqqnnnmmmmmmnnnoooqqqssstttuuuvvvrrrooojjjccc]]]WWWTTTRRROOOMMMJJJJJJLLLMMMNNNMMMOOOOOOPPPPPPPPPPPPOOOOOOMMMMMMMMMLLLKKKJJJIIIHHHGGGHHHIIIIIIIIIIIIIIIHHHKKKNNNUUU^^^gggmmmoooooonnnlllkkkmmmrrryyy{{{uuuqqqpppqqqsssvvvzzzzzzsssiii```\\\[[[aaagggmmmttt{{{rrrrrrzzz~~~zzz|||~~~wwwnnnbbbUUUIIIAAA999666333111111111000000000000/////////.........------------------------+++*********,,,,,,***)))************************++++++******))))))(((((())))))))))))))))))))))))))))))))))))))))))))))))((()))))))))************))))))*********+++++++++))))))***+++,,,------...,,,++++++******++++++,,,---------...............------......///000000111222444777999===BBBHHHLLLTTTYYYaaajjjttt|||111///---------...---,,,------------------------++++++************+++++++++,,,,,,,,,,,,+++******))))))))))))))))))))))))(((((((((((())))))))))))(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))******************************))))))))))))******)))))))))))))))))))))))))))************+++++++++************+++,,,------+++++++++++++++,,,------......////////////......+++,,,---///000111222222000111222222222444777:::AAAQQQnnn}}}}}}zzzzzz~~~yyyuuuiii``````___```bbbhhhpppvvv~~~~~~~~~{{{yyyxxxuuuvvvyyy}}}~~~zzzuuunnnfff```[[[YYYUUUSSSPPPPPPRRRTTTUUUUUUUUUUUUVVVWWWWWWWWWWWWWWWTTTTTTTTTTTTRRRPPPNNNLLLIIIIIIJJJJJJJJJIIIHHHHHHJJJLLLRRR[[[fffpppvvvyyyssspppmmmlllmmmppprrrssssssuuuwwwvvvssspppnnnmmmnnnqqqvvv{{{wwwkkk___YYYWWW[[[aaagggoooyyy}}}xxxyyy}}}xxxnnn___QQQGGG===:::666333222222111000000000000/////////......------------------------******)))***+++,,,***(((************************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************)))************+++++++++******++++++,,,,,,------,,,++++++******++++++,,,............////////////---......//////000111111111333666:::>>>EEELLLQQQVVV\\\eeeqqqsss111///---------...---,,,++++++++++++++++++++++++,,,++++++******++++++,,,***+++,,,,,,+++***)))((())))))))))))))))))))))))'''''''''((((((((())))))&&&'''''''''(((((((((((())))))))))))))))))))))))************************))))))))))))))))))))))))******))))))))))))******)))))))))))))))))))))))))))************+++++++++************+++,,,---...---,,,,,,++++++,,,---.........////////////......,,,---...000000111111111000111111222222444888;;;GGGZZZyyyzzznnneee]]]\\\[[[\\\aaajjjuuu}}}~~~xxxpppiiicccaaa\\\ZZZWWWWWWXXX[[[\\\\\\[[[\\\]]]^^^___`````````[[[\\\]]]\\\ZZZWWWTTTRRRLLLMMMMMMMMMLLLLLLKKKJJJJJJKKKPPPYYYfffsss}}}|||wwwtttsssqqqnnnkkkiiikkknnnnnnllllllnnnpppqqqwww~~~vvvjjjddd]]]aaahhhpppzzz||||||wwwiiiYYYNNNBBB>>>999555333222111000000000000000/////////...------------------------+++******+++,,,,,,+++)))************************)))))))))))))))*********))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************)))************+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++******++++++,,,---------.........//////.........///000000111111333555888<<>>CCCRRRbbb|||{{{vvvmmmeee```\\\YYY\\\eeennnxxx|||tttkkkfffffffffdddbbbbbbeeegggggggggggghhhiiikkkmmmoooooollljjjiiiiiigggbbb^^^VVVUUUUUUTTTRRROOOLLLJJJMMMIIIIIIPPP]]]mmm~~~ooonnnkkkkkkoooqqqssswww|||yyyiiiYYYHHHAAA;;;888555111000222222111000///............//////.........---------------------------------(((((((((((()))+++,,,---++++++++++++++++++++++++))))))))))))))))))))))))*********************************++++++,,,,,,,,,,,,+++***((((((((())))))******+++++++++,,,,,,,,,///...,,,*********,,,------.........---,,,,,,+++(((+++///222222111222222444666<<>>GGGUUUdddrrr|||}}}yyyzzz////////////...---,,,+++------------,,,,,,,,,,,,------,,,+++++++++,,,,,,************+++,,,------,,,---------,,,+++)))'''************************))))))(((((((((((())))))(((((()))***************))))))))))))))))))))))))************************+++++++++,,,,,,,,,------++++++++++++++++++++++++++++++++++++++++++++++++------,,,,,,,,,---...///.........------,,,,,,,,,............////////////111111000000000111111222111222333444888AAAMMMVVV]]]cccjjjqqqtttuuuuuuuuummmnnnrrrzzz{{{~~~{{{vvvsssqqqvvv{{{vvvrrrppppppwwwwwwxxxyyyzzzzzzzzzzzz|||zzzwwwtttsssrrrqqqqqqppplllhhheeebbb^^^YYYTTTOOOMMMLLLMMMNNNTTTbbbqqqzzzyyy|||}}}pppdddTTTDDD>>>===999333000111111000000000000000111........................++++++++++++++++++++++++------,,,,,,,,,,,,,,,---++++++++++++++++++++++++***************************************************************+++++++++(((((())))))***+++,,,,,,,,,,,,,,,,,,------------...---,,,,,,,,,,,,------------............---------...//////000222666999<<>>IIIYYYhhhqqquuuvvvvvv{{{}}}111000///.........///000......---,,,++++++******,,,,,,,,,,,,,,,---...///......---,,,++++++++++++++++++++++++************((()))************)))((())))))(((((((((((())))))(((((()))***************))))))))))))))))))))))))************************))))))))))))*********+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,***++++++,,,,,,,,,,,,,,,,,,,,,------------------------......///000000111......///000111222444555666:::@@@EEEIIINNNVVV[[[cccfffhhhfffbbb```bbbeeennnvvv}}}zzzwwwwwwyyy~~~|||yyytttoookkkhhhgggcccdddeeegggkkktttuuujjjbbb[[[VVVSSSQQQOOOMMMLLLNNNRRRVVVXXXbbbppp~~~|||~~~zzzpppfff___WWWOOOMMMLLLJJJJJJMMMWWW^^^hhhppprrrpppnnnnnnpppqqqxxx{{{nnnaaaXXXOOOEEE>>>;;;555444333111000//////...---------.........//////,,,,,,,,,,,,,,,,,,,,,,,,***************+++,,,---++++++++++++++++++++++++++++++++++++++++++++++++************************+++*********)))))))))((())))))+++,,,,,,,,,,,,++++++++++++,,,,,,,,,------,,,------...............------...///////////////...000222333444666:::===@@@NNNaaannnsssuuuvvvxxx~~~{{{222111///...---...000111------------------------+++++++++,,,---...///000++++++++++++,,,---......***************+++++++++)))***+++,,,,,,+++***)))))))))(((((((((((())))))(((((()))***************))))))))))))))))))))))))************************))))))*********+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,)))***+++,,,,,,,,,++++++,,,,,,,,,------.........---------...///000000111/////////111222444666777;;;@@@HHHMMMPPPTTTZZZ^^^]]]```bbbaaa```bbbiiioooyyy~~~xxxrrrrrrvvv{{{zzz}}}yyyuuujjjgggddd___[[[WWWUUUSSSSSSTTTVVVXXX]]]gggttt}}}uuukkkeee]]]VVVRRRNNNLLLJJJFFFEEEDDDEEEGGGKKKOOORRRVVVeee}}}uuujjj___UUURRRPPPMMMJJJJJJOOORRRYYY```ccccccccceeejjjkkkrrrwwwoooiiiooo{{{nnncccXXXKKKCCCBBB666555333111000///......---------.........//////------------------------......---,,,,,,,,,------++++++++++++++++++++++++++++++++++++++++++++++++************************+++*********))))))(((((()))***+++,,,---,,,+++***,,,,,,,,,---------......,,,,,,---.../////////...------...///000000//////...000222444555777:::===BBBRRRfffsssvvvvvvyyy}}}{{{{{{000///...---------------,,,,,,------,,,,,,+++***))))))))))))***+++,,,---111///---+++++++++***((()))(((((()))***++++++***)))))))))))))))))))))))))))************+++++++++(((((((((((())))))))))))(((***+++***)))((()))***************************)))***+++++++++)))((('''******+++++++++,,,,,,,,,+++---------+++***+++------------,,,,,,+++++++++,,,,,,------...////////////000111000......///111333///111666666333666>>>@@@SSS]]]^^^cccaaa___dddddd^^^]]]bbbfffiiipppyyyvvvllljjjnnnsssuuu|||xxxuuuxxx}}}xxxsssmmmddd]]]XXXVVVRRRNNNKKKJJJIIIIIIKKKJJJJJJLLLSSS\\\eeejjjzzz}}}~~~zzzsssnnnnnnpppnnnqqqxxx~~~yyyrrrjjjbbb^^^RRRQQQNNNKKKIIIFFFEEEDDDBBBBBBBBBCCCDDDEEEFFFGGGTTTXXXfff|||vvvkkk^^^TTTQQQPPPNNNMMMNNNPPPTTTYYY]]]```cccdddhhhmmmsssyyyzzzpppiiieeehhhvvvzzzrrrfffXXXJJJAAA>>>888333444555111//////000000///...............,,,,,,,,,,,,,,,,,,,,,---++++++++++++++++++++++++)))***+++,,,,,,,,,,,,,,,************************,,,,,,,,,++++++***************+++++++++,,,,,,,,,******+++++++++,,,,,,,,,------------------------///////////////.........000000000000////////////000///000333555555;;;BBBIII[[[ppp|||||||||111000//////............---------------,,,++++++***)))))))))***+++,,,,,,000...++++++++++++***)))((('''&&&'''((()))(((''')))))))))))))))))))))))))))************+++++++++))))))))))))************(((***+++***)))((()))+++++++++++++++++++++++++++***************)))((((((******+++++++++,,,,,,,,,,,,---......---,,,---///...---------,,,,,,,,,+++,,,,,,------...////////////000111000......000111333///111666666555>>>JJJXXXlllvvvvvvvvvooohhhjjjeeebbbccciiiooossszzz|||pppfffdddggglllnnntttsssttt{{{~~~xxxpppjjjeee___WWWQQQOOOMMMJJJGGGDDDCCCCCCCCCCCCBBBBBBDDDHHHNNNUUUYYY```cccdddaaa[[[VVVWWWXXXXXX[[[```hhhmmmnnnkkkggggggfffccc___ZZZVVVRRROOONNNLLLJJJHHHFFFDDDCCCCCCAAAAAAAAABBBBBBCCCEEEEEEKKKNNNZZZlllxxxiii]]]WWWSSSOOOLLLMMMOOOSSSWWW\\\___bbbccchhhlllrrrwww}}}~~~ppphhhdddeeemmmvvvzzzpppbbbSSSJJJBBB;;;555555555222000000000000///............///,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++******+++,,,,,,,,,,,,,,,************************,,,,,,,,,+++++++++***************+++++++++,,,,,,***++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,........................000000000000////////////000///000444666888???GGGUUUeeeyyy333222111000///.........---............---,,,,,,++++++*********++++++,,,---,,,******++++++***))))))(((''''''((()))(((&&&)))))))))))))))))))))))))))************+++++++++************++++++++++++)))***+++***))))))***+++,,,,,,,,,,,,,,,,,,,,,,,,++++++***))))))))))))*********+++++++++,,,,,,,,,***,,,------,,,,,,...///.........---------------,,,,,,------...////////////000111000///...000222222000222666666:::KKK___}}}zzzyyynnnmmmooouuu|||{{{sssggg___^^^aaagggkkkmmmpppvvv~~~yyyuuulllfff^^^XXXTTTPPPJJJFFFFFFEEEBBB@@@>>>>>>>>>>>>AAAAAAAAAAAACCCGGGJJJLLLMMMOOOPPPNNNJJJGGGGGGIIIJJJLLLOOOTTTXXXYYYXXXVVVTTTRRRPPPNNNLLLKKKJJJJJJIIIIIIGGGFFFDDDCCCCCCCCCBBBBBBBBBBBBCCCDDDDDDEEEFFFHHHPPP\\\iii{{{uuuhhh___XXXRRRNNNNNNPPPSSSXXX\\\```dddeeehhhlllqqquuuzzzvvvlllfffccceeeiiiuuu{{{~~~vvvjjj[[[PPPHHH@@@888666666333111333111000//////......//////......------,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,***++++++,,,,,,,,,,,,,,,++++++++++++++++++++++++,,,,,,,,,++++++++++++***))))))*********+++++++++++++++++++++,,,,,,,,,,,,++++++++++++++++++++++++,,,,,,------......//////////////////000000000000000///111555888<<>>>>>>>>>>>AAAAAABBBBBBCCCEEEFFFFFFFFFHHHIIIIIIFFFEEEEEEFFFHHHHHHJJJLLLOOOQQQQQQQQQNNNNNNNNNNNNNNNNNNNNNNNNIIIHHHGGGFFFFFFEEEEEEFFFEEEEEEDDDDDDDDDEEEFFFFFFGGGIIIMMMTTT[[[ggg}}}}}}pppfff]]]WWWSSSRRRSSSVVVZZZ___dddgggjjjjjjmmmqqqtttwww}}}zzzpppiiiiiinnnyyy}}}{{{qqqcccXXXOOOEEE;;;888666333222333111000000///...///////////////...---,,,++++++***,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---,,,,,,+++++++++++++++++++++++++++++++++++++++++++++++++++)))))))))*********+++++++++++++++,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,---...//////////////////000000000000000000333777999???JJJVVViiisss555444222000///...------......//////......---,,,,,,,,,+++++++++++++++++++++***((()))***++++++***---+++******++++++***((())))))))))))))))))))))))))))))*********+++++++++((((((((()))))))))******)))+++,,,+++***)))***+++)))))))))))))))))))))))),,,+++***))))))***+++,,,******+++++++++,,,,,,,,,'''(((************,,,---........................,,,,,,------...////////////000111000///000111333222222555999===KKKjjjuuuiii^^^ZZZZZZ\\\ccclllqqqwww|||yyyqqqmmmhhhccc___ZZZUUURRRNNNKKKHHHEEEDDDDDDCCCCCCAAAAAA@@@@@@@@@@@@@@@@@@======???@@@AAAAAAAAAAAA@@@AAACCCCCCBBBBBBBBBCCCCCCDDDEEEFFFGGGJJJLLLNNNLLLMMMPPPRRRRRRQQQOOONNNKKKJJJIIIHHHGGGGGGGGGGGGGGGFFFFFFEEEEEEEEEEEEFFFGGGHHHLLLQQQTTT\\\mmm|||wwwlllccc\\\XXXTTTVVVXXX\\\aaafffkkkmmmmmmpppssstttvvvzzzyyy|||zzzmmmbbbTTTIII???:::777333222333111111000/////////////////////...------,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------,,,,,,+++++++++++++++++++++++++++++++++++++++++++++++++++)))************+++++++++++++++,,,,,,,,,---------........................+++++++++,,,---...//////.../////////000000000111111222444888<<>>???@@@AAABBBBBBBBB>>>???@@@AAAAAABBBAAAAAAAAABBBDDDEEEFFFIIIMMMPPPQQQSSSVVVYYYYYYXXXUUUSSSPPPOOONNNLLLKKKJJJJJJJJJHHHGGGFFFEEEEEEEEEEEEEEEDDDEEEIIINNNQQQWWWcccooo{{{}}}rrrhhh```\\\WWWXXX[[[___dddiiinnnqqqrrrtttvvvvvvwwwzzz~~~qqqfffZZZOOODDD>>>:::555333444222111000000//////000000//////......------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------------,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,***++++++++++++,,,,,,,,,******+++++++++,,,,,,,,,,,,,,,,,,,,,------------........................,,,,,,------......//////......//////000000111111111222666;;;@@@JJJ\\\mmmwww}}};;;999777555333111000000---------------,,,+++++++++++++++++++++,,,---......,,,******+++,,,,,,+++***(((((((((***+++***))))))))))))))))))))))))))))))************+++++++++(((((()))))))))************+++,,,,,,******+++,,,)))))))))))))))))))))))))))***++++++,,,,,,,,,+++******+++++++++,,,,,,,,,,,,---......---,,,---///+++,,,,,,,,,------------,,,,,,------...////////////000111111000111333555666444888@@@KKK^^^{{{lll___]]]]]]]]]eeeppp}}}xxxxxxwwwvvvvvvvvvvvvvvvwwwuuuqqqkkkeee^^^YYYVVVTTTQQQMMMKKKJJJHHHGGGEEEDDDDDDDDDDDDCCCCCCCCCDDDBBBBBBBBBCCCCCCBBBBBBBBBAAAAAABBBCCCDDDDDDDDDDDDBBBBBBCCCDDDEEEFFFEEEEEEDDDGGGIIIKKKLLLPPPUUUYYY^^^___aaacccdddcccbbbaaaZZZYYYWWWUUURRRQQQPPPOOOLLLLLLJJJIIIHHHHHHHHHHHHHHHGGGHHHMMMPPPTTT]]]eeesss{{{}}}tttkkkeeebbb]]]^^^```dddiiioootttxxxwwwyyyzzzyyyxxxzzztttiii___TTTIIIDDD???999555555222111000000//////000000...............---------------------------------------......---,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,******+++++++++,,,,,,,,,+++,,,,,,,,,,,,---------,,,,,,,,,------------............................................................///000111111111000222888???FFFSSSiii}}}===<<<:::777555333222111,,,,,,------,,,,,,+++************+++,,,---...//////---++++++,,,,,,,,,++++++***)))***,,,------,,,)))))))))))))))))))))))))))************+++++++++)))************+++++++++***+++,,,,,,******+++,,,************************(((***+++,,,---,,,,,,+++******+++++++++,,,,,,,,,+++---...---+++++++++---+++++++++,,,,,,---------,,,,,,------...//////000///000111111000111333555888555888CCCOOOccczzzkkk```aaaccceeennn|||}}}wwwqqqnnnhhhhhhiiiiiiiiiiiiiiiiiifffdddaaa]]]XXXUUURRRPPPMMMKKKHHHFFFGGGGGGFFFEEEFFFGGGHHHHHHFFFDDDDDDDDDDDDDDDEEEEEEEEEDDDDDDCCCAAAAAAAAAAAAAAABBBBBBBBBEEEDDDEEEFFFHHHHHHHHHFFFGGGJJJMMMPPPQQQUUU[[[___gggggghhhhhhiiijjjlllllldddbbb```]]]ZZZXXXVVVVVVRRRQQQPPPNNNMMMMMMMMMMMMQQQMMMKKKMMMPPPSSSYYY___mmmvvvzzzssslllhhhfffddddddgggjjjpppvvv{{{~~~zzz||||||{{{zzz{{{zzzooocccXXXMMMGGGBBB;;;777666222111111000000000000000---------...............---------------------------.........---,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,*********++++++,,,,,,,,,,,,,,,,,,---------......,,,,,,,,,---------......------------------------///////////////.........---......///000111111222///222999AAAJJJZZZsss|||AAA@@@???===999555111...------------------------+++++++++*********)))))),,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,((()))***++++++***)))(((************************,,,***((()))+++,,,+++((())))))***++++++++++++***((()))))))))******************+++++++++,,,,,,,,,++++++,,,,,,,,,,,,------***+++,,,---...---,,,+++,,,,,,,,,---...///000111......---,,,---...///000...000222333333333444555444666<<>>777444333222000000111111///......------,,,,,,------...)))***++++++------...///+++,,,------......---------------,,,,,,+++++++++************************,,,,,,++++++,,,,,,---...+++++++++,,,,,,,,,------,,,,,,,,,---------......///////////////.........000/////////000111222222333666999???OOOggg||||||>>>>>><<<;;;:::888666444///......------,,,---------,,,,,,,,,+++++++++***,,,,,,,,,,,,,,,,,,,,,,,,************************((()))***++++++***)))(((************************,,,***((()))+++,,,+++)))))))))***+++++++++++++++))))))))))))************))))))*********+++++++++++++++,,,,,,,,,,,,------++++++,,,------------,,,---------------...///000//////.........///000111...000222333222222333444444777>>>KKK\\\qqq|||uuuvvv|||xxxooorrrvvv{{{}}}yyyppplllfff```\\\YYYVVVTTTUUUTTTRRRQQQRRRSSSUUUVVVUUUUUUTTTRRRQQQPPPNNNNNNNNNOOOOOOPPPPPPPPPPPPPPPTTTSSSRRRSSSTTTTTTRRRPPPPPPPPPOOOOOONNNMMMLLLKKKHHHIIIJJJIIIHHHIIIJJJLLLPPPNNNMMMNNNQQQTTTWWWXXX___bbbfffhhhkkkooowww|||~~~zzzwwwrrrmmmjjjgggdddaaa___^^^\\\ZZZXXXWWWVVVTTTTTTVVVYYY]]]```gggppp||||||vvvrrrooommmiiidddeeeiiilllppptttvvvwwwyyy}}}}}}}}}xxxvvvvvvuuurrrsssxxx}}}tttgggYYYRRRKKKAAA:::777555333111111222111000//////......------......///+++++++++,,,,,,------...+++,,,------......---------,,,,,,,,,,,,,,,,,,+++************************+++++++++++++++,,,------,,,,,,,,,,,,------------,,,,,,---------.........////////////////////////000000///000000111222333444777;;;CCCUUUmmm@@@>>>;;;::::::999777666222111///---,,,,,,,,,---------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,************************))))))***++++++***))))))************************+++***)))***++++++***))))))******+++++++++++++++******************))))))(((((()))))))))*********++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,------.........---------......///000////////////000111111///111222222111111333444666:::BBBOOO___ppp~~~|||tttnnnooouuu{{{yyy|||~~~vvvpppgggccc___[[[XXXUUURRROOOOOOOOONNNOOOPPPRRRTTTUUUVVVWWWWWWXXXXXXXXXXXXXXXUUUVVVXXXYYYZZZ[[[[[[[[[___]]][[[[[[\\\]]]\\\[[[ZZZZZZZZZYYYWWWTTTQQQPPPRRRSSSSSSRRRQQQQQQSSSUUUZZZYYYYYYZZZ^^^ccciiillluuuzzz~~~{{{tttqqqmmmjjjgggeeebbb___^^^]]][[[ZZZZZZ\\\]]]___hhhppp{{{yyysssmmmiiifffeeecccaaadddjjjpppuuuzzz}}}~~~|||tttnnnjjjhhhfffcccbbbfffjjjnnnuuu|||~~~pppbbbYYYRRRHHHAAA>>>777555333222222222000///000//////////////////000,,,,,,,,,,,,,,,,,,,,,---+++,,,------......------+++,,,,,,,,,,,,,,,,,,---+++++++++++++++++++++++++++************+++,,,,,,,,,------------.........,,,------------.........////////////////////////000000000000111222333444555888===III^^^uuuEEEAAA<<<999888777555333444333000...,,,,,,---------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,************************************************+++************+++******)))***++++++,,,,,,++++++++++++************))))))))))))))))))*********++++++++++++,,,,,,,,,------------,,,++++++---...//////......---------......///////////////000000000///111222222111111333555999>>>FFFRRR___lllvvv|||zzzxxxuuuoookkkmmmsssyyy{{{rrrllldddbbb___]]]\\\YYYVVVTTTQQQSSSTTTVVVXXX[[[___aaacccdddfffggghhhiiiiiihhhcccdddgggiiikkkmmmnnnnnnnnnkkkiiihhhiiijjjjjjiiiiiihhhhhhfffbbb___[[[YYY\\\]]]]]]\\\\\\]]]```cccfffhhhkkknnnrrrxxx~~~}}}yyyuuuqqqnnnkkkggggggeeedddcccdddddddddlllsss}}}~~~vvvpppjjjeeebbbaaa______dddkkksssxxx~~~{{{uuummmhhhccc^^^[[[^^^aaaccchhhmmmzzzwwwiii```YYYOOOGGGDDD999777444222222111000...000//////......//////000......------,,,,,,,,,,,,+++,,,------......------+++++++++,,,,,,---------++++++++++++++++++++++++******))))))******+++,,,---------.........//////------------............///////////////000000000000000000111222333444555555888@@@NNNdddyyy|||JJJDDD<<<888777777555222555444222000...---------+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++************++++++******************************+++************+++******+++,,,,,,,,,,,,++++++++++++************************+++++++++,,,,,,+++++++++,,,,,,,,,------...---,,,+++,,,---...//////......---------......------........./////////000111222222111222555777:::???GGGQQQ[[[ccciiilllnnnooonnnlllkkknnnuuuzzz}}}wwwppplllbbb```^^^^^^^^^]]][[[YYYXXX[[[___bbbeeeiiioootttxxxyyy{{{|||||||||{{{zzzwwwxxxzzz}}}}}}||||||}}}|||{{{|||{{{yyyvvvrrrnnnjjjgggcccdddeeeeeefffiiinnnqqquuuzzz~~~{{{ttttttrrrqqqqqqqqqrrrrrrrrrxxx|||vvvqqqjjjeeeaaa___^^^]]]cccjjjsssyyywwwnnnddd]]]XXXXXXYYYZZZ\\\___gggrrr~~~pppggg^^^SSSIIIEEE<<<888444222111000///...///..................//////......------,,,,,,++++++,,,------......------+++++++++,,,,,,---------++++++++++++++++++++++++******))))))******+++,,,---------.........//////---------.........//////////////////000000111111000000111111222444555666555:::BBBQQQfffyyy|||ssszzzOOOGGG===888999:::888666555444333222000///...---++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,************************,,,+++************+++,,,************************)))+++++++++***)))***+++***++++++,,,,,,,,,,,,,,,*********+++++++++,,,,,,***++++++++++++,,,,,,,,,++++++,,,,,,,,,,,,---------------------......///......---------......///,,,------...///.........000111222222222444888:::;;;???FFFNNNTTTYYY\\\]]]ccceeehhhjjjlllqqqxxx~~~}}}}}}{{{vvvrrrooogggeeeddddddeeeffffffeeecccfffkkkooottt{{{~~~zzzwwwuuummmnnnoooppprrrvvv|||~~~|||{{{zzz{{{|||}}}|||~~~zzzvvvsssmmmhhhdddccc```___dddkkktttzzzuuulllccc[[[YYYYYYWWWVVVXXXXXX```mmmyyy|||{{{zzzwwwuuuuuuvvvxxxzzzxxxoooeeeWWWKKKEEE???;;;666333222111///...///......------......//////.........------,,,,,,+++,,,------......------+++,,,,,,,,,,,,,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,+++************+++,,,,,,,,,------------.........------........./////////...//////000000111111222000111111222333555666777777===FFFRRReeeuuu{{{yyyrrr{{{XXXNNNAAA;;;;;;;;;999666333444444444333111...---,,,,,,,,,,,,---------...,,,,,,,,,,,,,,,,,,,,,,,,************************,,,++++++******++++++,,,************************)))+++,,,+++)))(((***,,,***+++,,,,,,------,,,,,,))))))******+++,,,------************++++++++++++++++++,,,,,,,,,,,,------,,,------...............---------------...///000,,,---...///000//////...000111222333444666;;;>>>AAADDDIIINNNRRRTTTUUUUUU[[[```eeejjjooovvv|||xxxwwwxxxzzz|||||||||wwwuuusssqqqoooppprrruuuwwwwwwssswww|||}}}~~~~~~{{{yyyvvvtttooolllkkkiiigggkkkrrrwww}}}xxxnnnccc```^^^ZZZWWWWWWSSSXXX___fffooo{{{~~~yyyqqqkkkhhhggghhhiiiooo~~~wwwnnn```SSSMMMCCC???999666444333111000000//////......//////000...............---------+++,,,------......---------,,,,,,,,,,,,,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++,,,------,,,,,,,,,,,,------------............////////////...//////000111111222222111111111222444555777888;;;AAAJJJTTTbbbqqqxxxxxx}}}aaaVVVGGG>>><<<;;;888444222333555555444222///------------.........//////,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---,,,+++******+++,,,---************************(((+++,,,,,,)))(((***,,,***+++,,,,,,------,,,,,,(((((()))***,,,---...///))))))))))))************++++++,,,,,,,,,---------+++,,,.../////////...---,,,,,,,,,---...///000111---...000111111111000//////111222333444888<<<@@@GGGJJJNNNQQQTTTTTTTTTSSSYYY___fffmmmsss{{{vvvtttqqqqqqtttwwwyyyyyy~~~{{{{{{xxxvvvwwwzzz~~~~~~|||zzzzzzvvvtttsssqqqppptttzzzzzz~~~sssgggbbb___ZZZWWWVVVVVVXXXZZZ\\\aaakkkxxx~~~rrrhhhbbb`````````eeeppp{{{uuuiii]]]WWWFFFBBB<<<888666444333222111111000000000000111111........................+++,,,------......---------------,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---...+++++++++,,,,,,,,,------............/////////000...//////000111222222222111111111222444666777888===DDDMMMUUU```nnnvvvxxxlll[[[JJJBBB@@@<<<888666777666444444444333000..................---------///...,,,***(((&&&%%%$$$******+++,,,,,,,,,,,,++++++++++++*********))))))++++++++++++++++++++++++)))************+++++++++---------,,,,,,+++++++++...---,,,++++++---...000))))))))))))***+++,,,,,,,,,,,,,,,---------.....................---------............/////////////////////000111111222222///111333444666<<>>:::666222000222222111000//////.........,,,,,,,,,------.........------------------------,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++++++++++++++++++++,,,,,,---------+++,,,------......------------......///000000000000000000000111111111111333333333333555888<<>>:::888777555444444444333111//////............---------------,,,,,,,,,,,,------)))***++++++,,,,,,+++++++++++++++*********))))))))))))))))))))))))))))))************++++++++++++,,,,,,,,,++++++*********---,,,+++******,,,---...,,,++++++*********++++++,,,,,,,,,---------......------............................../////////////////////000111111222222111222444555999BBBPPPZZZfffiiihhhbbb```cccffffffiiijjjnnnuuuxxx{{{}}}uuupppfffggghhhjjjpppzzz}}}tttmmmfff```[[[YYYVVVTTTRRRRRRUUUYYY[[[gggooo{{{tttmmmddd___]]]^^^eeettt}}}ppp\\\PPPCCC===888444222333222111000//////......///,,,------------------...------------------------,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++++++++++++++++++++,,,,,,---------+++,,,------......------------......///000000000000000000000111111111111222222333333666:::???BBBIIILLLUUUbbbjjjppp{{{kkk\\\MMMFFFCCC???<<<:::666555333333444333222000/////////.........------,,,,,,,,,,,,---...000000)))***++++++,,,,,,+++++++++++++++***************))))))))))))))))))))))))************+++++++++,,,++++++***************))),,,+++***)))***+++,,,---...---,,,++++++*********,,,,,,,,,---------......,,,---------.../////////............/////////////////////000111111222222222444666888???OOOfffwwwzzzrrrrrrwwwzzzyyyyyytttrrrvvv{{{~~~|||uuunnnhhhbbbccceeekkkvvv~~~vvvnnnfff```]]]YYYUUUPPPNNNNNNPPPQQQXXX___iiisssyyynnnfffcccbbbmmmqqq```LLLAAA;;;666444444222222111000////////////.........---------------------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,------+++,,,------......------------......///000000000000000000000111111111111111222333444666:::@@@EEEKKKSSS```lllrrrxxxiii\\\OOOIIIFFFAAA===;;;777555444333444444333111000000//////......------...---,,,+++************))))))***+++++++++++++++************************++++++++++++++++++++++++*********+++++++++,,,,,,++++++++++++************+++++++++***+++,,,------...---,,,,,,+++++++++,,,,,,,,,,,,---------......,,,,,,,,,---...///000000............/////////////////////000111111222222222555999>>>JJJbbb~~~vvvxxx~~~zzzssskkkfffcccdddiiirrr~~~tttkkkddd]]]ZZZUUUPPPMMMMMMOOOPPPQQQVVV]]]eeeppp}}}sssmmmiiixxxpppVVVGGG???:::555444333222111000//////////////////......------,,,,,,------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++,,,------......------------......///000000000///000000000111111111111111222333333444999@@@EEELLLYYYiiiuuuzzzhhh^^^SSSOOOKKKDDD>>><<<:::777555444555555444333111000000///......------///...,,,+++)))((((((((())))))***++++++++++++***************************++++++++++++++++++++++++***++++++++++++,,,,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------...,,,+++++++++,,,,,,---...,,,,,,,,,---------......,,,,,,,,,---...///000000............/////////////////////000111111222222222666===GGGYYYuuu|||}}}|||uuummmhhhfffiiippp{{{{{{pppiii]]]ZZZTTTOOOMMMLLLNNNOOOPPPSSSWWW]]]eeesssvvvppp~~~bbbPPPFFF===777444333222111000000//////////////////......---------------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++,,,------......------------......///000000000///000000000111111111111111333444333333777???EEENNN]]]ppp{{{lllddd]]]ZZZTTTKKKCCC???===;;;777666666666555444222111000000///...------------,,,,,,,,,,,,,,,---((()))******++++++*********************+++++++++))))))))))))))))))))))))++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,---------,,,,,,---------.........************+++,,,---...,,,,,,,,,---------......,,,---------.../////////............/////////////////////000111111222222333888AAAPPPfff|||tttooolllpppxxx|||xxxxxx}}}uuummm___[[[UUUOOOKKKJJJJJJKKKOOOQQQTTTXXX^^^iiivvv~~~ooo\\\NNNBBB:::777333333222111000000000000/////////...............------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,,,,+++++++++,,,------......------------......///000000000000000000000111111111111000333444333333777AAAIIITTTcccuuusssmmmiiiggg```TTTJJJEEEAAA>>>:::777777777666555222222111000///...------------,,,------...///000((())))))***************))))))*********+++++++++))))))))))))))))))))))))+++++++++,,,,,,,,,------******++++++,,,,,,,,,,,,++++++,,,---------------++++++*********++++++,,,,,,,,,,,,---------......------............................../////////////////////000111111222222555999DDDWWWpppzzzvvvyyy}}}uuuppprrrwww|||wwwnnnaaa]]]WWWQQQMMMLLLLLLMMMOOOQQQUUUXXX\\\dddnnnvvv{{{hhhXXXHHH>>>:::333333222111000000000000............////////////------------------------,,,,,,,,,,,,,,,,,,,,,,,,---------------------------------,,,,,,++++++++++++,,,------......------------......///000000000000000000000111111111111///222555555555;;;FFFOOO\\\jjj{{{~~~xxxtttqqqpppiii[[[OOOJJJCCC@@@;;;999888777666555222222111000///...------------,,,,,,,,,------...(((((()))***************))))))******++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,---------))))))******++++++++++++******+++,,,,,,,,,,,,+++,,,,,,+++***)))))))))))),,,,,,,,,---------.....................---------............/////////000/////////000111111222222666;;;FFFZZZtttuuummmmmmrrrvvvyyyuuulllbbb^^^YYYTTTQQQQQQRRRSSSOOOSSSWWWYYY]]]ccclllsssqqq^^^LLLAAA===444333222111000000000000------......//////000000------------------------,,,,,,,,,,,,,,,,,,,,,,,,---------------------------------,,,,,,++++++++++++,,,------......------------......///000000000000000000000111111111111---111555666777>>>KKKUUUbbbooo~~~zzz}}}xxxoooeeeXXXNNNGGGBBB===;;;;;;:::777444444333111111111111000///......---,,,,,,,,,,,,------------,,,,,,,,,++++++---,,,***)))((()))******...---,,,***)))((((((((())))))***+++,,,,,,------,,,,,,,,,,,,++++++***)))++++++,,,,,,---...//////...------,,,,,,------.../////////......------------------.........//////111000000///...---------...///111111000000222333666???NNN```rrrvvvqqqpppnnnpppuuu}}}ppplllccc___[[[XXXWWWVVVTTTSSSUUUVVVXXXZZZ\\\aaafffjjj{{{fffTTTIII<<<888555222000000111111000//////.........---------//////.........---------.........------,,,,,,,,,---,,,,,,++++++,,,,,,---,,,---......//////......---------............///////////////////////////000000000000111222333444111222777;;;>>>DDDRRRaaasss|||{{{yyy|||vvvjjj]]]RRRHHHCCC>>>;;;:::999666444555444333333444333111//////...------,,,,,,------,,,,,,,,,+++++++++******---,,,++++++++++++++++++***************++++++,,,*********++++++,,,,,,---,,,,,,,,,,,,,,,,,,+++******+++++++++,,,---------,,,++++++******++++++,,,---,,,,,,,,,++++++++++++---------........./////////000000000000000000000,,,...///000000000222444888@@@OOO___ooo}}}yyytttoooqqqxxx~~~qqqllljjjgggdddbbbaaa^^^ZZZWWWVVVXXXZZZ[[[^^^bbbgggjjjttt}}}rrrmmmjjjiiiiiilllppprrrvvvlllYYYNNNAAA:::777444222111222111111//////.........---------//////.........---------------------------,,,,,,---,,,,,,++++++,,,,,,---,,,,,,---............------------............///////////////////////////000000000000111222333444222444777;;;???FFFWWWfffzzzwwwvvv{{{~~~rrreeeYYYLLLGGGAAA>>>===;;;888555666555555555666555333000///...------,,,---------++++++++++++************++++++,,,---------,,,,,,***************+++,,,,,,+++++++++++++++++++++++++++,,,,,,------------,,,++++++++++++++++++++++++,,,++++++******++++++,,,,,,,,,++++++++++++******------........./////////...//////000111222222333---///000111000111444666;;;DDDQQQ___kkkttt{{{wwwqqquuu~~~vvvpppnnnmmmkkkkkkkkkggg```ZZZYYY[[[]]]^^^```ccchhhkkkuuusssfff^^^[[[WWWVVVXXX[[[]]]___hhhqqq~~~rrraaaUUUGGG===:::666333222222111111/////////.........------...............---------,,,,,,------------------------,,,,,,,,,,,,------++++++,,,------------------------............///////////////////////////000000000000111222333444444555777;;;@@@JJJ^^^ooosssttt{{{yyylllaaaUUUOOOHHHCCCAAA???;;;888666555555666777666333000//////...---------------,,,,,,,,,+++++++++******)))***,,,---------,,,,,,...---,,,+++************,,,,,,+++++++++++++++++++++,,,,,,---............,,,,,,,,,+++++++++++++++...------,,,,,,------...---------------------,,,............////////////...//////000000111222222222333333333222333555888???GGGSSS___hhhmmmqqqsssxxxxxxrrrxxxwwwqqqpppqqqsssuuuqqqiiibbb___```bbbcccdddfffiiilllxxxtttfff]]]XXXRRRPPPPPPRRRSSSTTTZZZbbbooo{{{wwwpppnnnrrrxxx~~~uuufffZZZLLL???<<<777444333222111///////////////....................................,,,,,,,,,------.........------,,,,,,,,,,,,------***+++,,,,,,------,,,,,,---------............///////////////////////////000000000000111222333444555555777;;;AAANNNeeeyyyzzzzzz~~~uuuwwwqqqggg]]]WWWNNNGGGCCC@@@<<<999666555555666666555333111//////...------------......------------,,,,,,,,,((()))***,,,,,,,,,+++***------,,,+++************,,,,,,+++++++++++++++++++++,,,,,,---............------------,,,,,,,,,,,,...------,,,,,,------...------------------------........./////////000000////////////////////////333444444333222333666888@@@GGGQQQ[[[bbbfffiiikkkoooyyy||||||yyysss{{{~~~tttrrrrrrvvv{{{zzztttmmmfffgggiiiiiihhhiiikkklllttt{{{vvvfffZZZTTTOOOKKKJJJLLLLLLLLLPPPVVV^^^hhhzzzvvvkkkcccbbbeeehhhlllqqqxxxvvviii^^^NNNBBB>>>999555333111///...000000/////////.........---.....................,,,,,,,,,------............------,,,,,,------...***+++,,,,,,------,,,,,,---------............///////////////////////////000000000000111222333444555444666;;;CCCSSSmmmvvvsssvvv{{{|||xxxmmmfff^^^SSSKKKFFFAAA<<<888888666555555555555444333000///......------..................------------))))))***+++++++++******************+++---...///+++++++++++++++++++++++++++,,,,,,------------,,,------------------------,,,++++++******++++++,,,++++++,,,,,,,,,,,,------....../////////000000000////////////............222222222222222444777:::AAAGGGNNNVVV[[[```dddfffhhhppp}}}vvvuuuzzz~~~}}}|||~~~{{{vvv~~~sssooolllooovvvyyyuuupppnnnooopppooommmkkklllmmmqqqvvv~~~{{{jjjZZZQQQPPPLLLJJJKKKKKKJJJLLLPPPTTTYYYgggzzzxxxlllaaa[[[YYYXXX[[[^^^cccsssuuukkkaaaQQQEEEAAA;;;777444222000...000000000/////////......---------...............,,,,,,------------------......------------......++++++,,,------------------------............///////////////////////////000000000000111222333444555555777>>>HHHZZZuuu{{{ooonnnuuu|||wwwpppggg\\\QQQKKKEEE???;;;;;;999666555555666666666000//////.....................---------,,,,,,,,,,,,,,,+++*********++++++*********+++,,,---...///*********++++++,,,,,,---,,,,,,,,,,,,,,,,,,+++***+++++++++,,,,,,------...,,,++++++******++++++,,,,,,,,,,,,------............/////////000000000000.........///000000111111000111222333555999>>>BBBHHHKKKPPPUUUYYY^^^dddgggjjjooowwwzzzooommmqqqvvvwwwyyy|||zzzzzzwwwooohhhiiipppvvvvvvsssuuuvvvvvvtttpppnnnmmmmmmnnnpppvvv}}}rrraaaVVVSSSNNNKKKLLLLLLKKKKKKOOOMMMNNNVVVgggyyyttthhh^^^YYYQQQUUUXXXYYYcccxxxtttmmmnnnuuuvvvoooeeeVVVIIIEEE???:::777444111///000000000000/////////...---------.........//////------------------,,,,,,......------------......,,,,,,---............------------............///////////////////////////000000000000111222333444666666:::BBBMMM```|||{{{pppqqq{{{yyypppcccXXXPPPJJJDDD???>>>;;;777555666777888888000000///...............---------,,,,,,,,,++++++///...,,,+++***+++,,,,,,------,,,+++++++++,,,,,,))))))***+++,,,,,,------,,,,,,,,,,,,++++++***)))))))))***+++,,,,,,------...------,,,,,,------.../////////000000000111111////////////000000000000------...000111333444444000222444777:::@@@FFFKKKPPPRRRTTTWWWZZZ```fffkkkrrrtttxxxuuukkkhhhkkkooosssxxx~~~yyyyyy}}}wwwmmmlllsss{{{}}}{{{yyyzzzyyywwwrrrooommmmmmggghhhjjjoootttwwwyyyyyyxxxxxxxxxwwwvvvwwwzzz|||wwwfff[[[RRRMMMJJJKKKKKKIIIIIILLLJJJHHHLLLZZZlll}}}qqqeee___RRRWWWYYYWWW[[[hhhwwwzzzpppfffccceeeiiisss|||wwwrrriiiYYYLLLHHHBBB===999666333111000000000000////////////---------.........//////.........------,,,,,,,,,......------------......,,,---......//////......---------.........//////////////////////////////000000000000111222333444777888<<>>;;;888666777888999888555444333111000///.........---,,,++++++,,,---...++++++***))))))***+++++++++++++++++++++++++++++++++++++++,,,,,,---------......---,,,,,,+++*********************)))((('''***+++++++++,,,------------------............///000000111111000//////...222222111000000000111111222333444888@@@OOO```kkkoooooopppqqqsssuuuxxxzzz{{{zzzyyy{{{|||tttmmmhhhgggfffhhhooowww|||xxxtttmmmgggccc\\\YYYUUUTTTUUUWWWXXXYYYUUUUUUTTTSSSSSSUUUYYY]]]dddmmmwww~~~|||qqqeeeYYYUUUPPPNNNOOONNNLLLIIIIIIDDDEEENNNUUU^^^ppp~~~tttjjjbbb\\\]]]```aaaeeejjjgggbbb^^^\\\YYYWWWZZZ___gggmmmvvvyyy|||ttteeeUUUKKKDDD===888666444333222111000/////////.........---------,,,,,,...................................................,,,+++,,,......---+++............////////////........./////////000000222111000111222444444444555999>>>GGGZZZsssuuummmeeeYYYPPPLLLCCC???:::888888999999999888777444222///.........---,,,,,,++++++,,,,,,---------,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,---------,,,+++...------,,,,,,++++++***++++++******)))'''&&&%%%,,,------------------------------............///222111111000000000000000444333222111111000000111444444777???OOOeee|||}}}}}}~~~yyyqqqjjjfffeeefffgggqqq||||||vvvooohhhaaa\\\RRRPPPLLLKKKKKKKKKJJJIIIJJJJJJIIIHHHGGGIIIMMMQQQVVV```mmmwww}}}|||tttjjj\\\XXXSSSPPPPPPNNNKKKHHHHHHDDDDDDJJJNNNRRR___nnn~~~{{{qqqhhhhhhjjjiiifffeee```ZZZUUUTTTSSSUUU]]]fffssszzz|||xxxzzzxxxgggZZZNNNBBB:::888444333222111111111111111.........------------,,,................................................///---,,,---...///...---............////////////....../////////000000000111111111111222333444555666:::AAANNNbbbwww{{{tttmmmeee\\\WWWHHHDDD>>>999888999999:::;;;999666333000/////////,,,,,,,,,++++++,,,,,,,,,.........------.........,,,,,,,,,,,,,,,,,,,,,,,,***+++---......---+++***---------,,,,,,+++++++++,,,,,,,,,,,,,,,+++***)))...............------------------............///222111000/////////111111333333222222111222222222444666;;;III___|||{{{rrrjjjeeeeeegggmmmxxx~~~~~~~~~~~~~~~}}}}}}||||||{{{{{{|||{{{yyyxxxxxxxxx|||yyypppiiiaaaYYYTTTMMMKKKIIIHHHHHHGGGEEECCCGGGGGGFFFEEEEEEFFFJJJMMMQQQ[[[hhhrrryyy{{{uuulll^^^YYYTTTPPPPPPNNNKKKHHHKKKGGGGGGJJJKKKMMMTTT^^^hhhrrrxxxyyy}}}}}}uuunnnddd]]]UUUSSSSSSXXXdddppp~~~~~~xxxiiiXXXGGG<<<999333222222111111111222222............------------,,,,,,,,,,,,,,,,,,,,,,,,........................///........./////////...............////////////...////////////000000000000111222222222333555777888;;;EEEWWWlll{{{~~~zzzuuuoooggg```PPPJJJBBB<<<999999999999===;;;888555222000//////,,,,,,,,,,,,,,,,,,,,,,,,*********++++++*********++++++++++++++++++++++++***+++---......---+++***------,,,,,,,,,,,,++++++++++++,,,---............///.....................---------............///000///...------...000111111111111111222333444555555888BBBTTTnnn}}}uuulllhhhjjjnnnyyy}}}zzzxxxuuurrrpppmmmkkkkkkkkkmmmmmmlllkkkjjjjjjiiiiiihhhhhhggggggfffiiilllnnnnnnooopppqqqssstttuuuwwwxxxyyyyyyyyy{{{|||}}}}}}{{{xxxtttrrrkkkjjjgggeeeddddddeeefffhhhkkkmmmnnnnnnnnnooopppnnnnnnooopppqqqssstttuuuuuuwwwyyy{{{}}}~~~{{{zzzzzzzzzzzztttjjjccc[[[SSSMMMJJJIIIGGGGGGHHHGGGEEECCCEEEFFFFFFEEEDDDEEEHHHJJJLLLVVVbbbkkkssswwwssslll___ZZZUUURRRQQQPPPMMMIIILLLJJJIIIJJJJJJKKKNNNSSSYYY___iiisss}}}}}}kkkaaaWWWRRRSSSZZZhhhvvvwwwcccNNN@@@<<<222111111000000000111111//////.........---------,,,,,,,,,,,,,,,,,,,,,,,,........................///////////////...//////............////////////////////////000000000111000111333333222333555888999===JJJ___ttt~~~~~~{{{vvvnnneeeYYYRRRHHH@@@;;;:::::::::<<<;;;:::777555222000///,,,------......------,,,++++++,,,,,,,,,,,,++++++************************+++,,,---------,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,((()))***,,,------......---.....................---------............///...............//////000/////////000222333555666666<<>>>>>::::::;;;;;;999666222///---...///000000///...---******,,,,,,,,,,,,******,,,,,,,,,,,,,,,,,,,,,,,,...---,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------,,,,,,+++++++++,,,,,,---...//////---------.........//////...///000222222222111000111000000000000000111111:::EEEYYYsss}}}}}}{{{yyyyyyyyy}}}~~~~~~zzzyyyxxxwwwvvvvvvvvvvvvuuuvvvwwwxxxxxxwwwvvvvvvssstttuuuwwwxxxyyyyyyyyyzzzyyyxxxwwwvvvwwwxxxxxxwwwwwwwwwwwwwwwvvvwwwwwwuuutttsssqqqooommmkkkjjjiiiiiihhhfffdddbbb```___[[[ZZZXXXVVVSSSQQQOOONNNLLLMMMMMMLLLJJJHHHIIIIIIHHHFFFFFFGGGIIIJJJIIIHHHEEEEEEEEEFFFFFFGGGGGGHHHIIIIIIIIIHHHGGGGGGJJJLLLKKKLLLMMMOOOOOOPPPPPPPPPNNNNNNMMMMMMMMMLLLLLLLLLLLLJJJHHHFFFEEEEEEFFFGGGIIIJJJJJJIIIGGGFFFFFFGGGGGGHHHIIIJJJKKKKKKKKKKKKHHHIIIKKKLLLLLLNNNQQQSSSTTTTTTUUUVVVWWWXXXXXXXXXUUUWWWZZZ\\\]]]\\\[[[ZZZ\\\\\\\\\[[[YYYXXXXXXYYYXXXWWWUUUTTTTTTUUUVVVXXXXXXXXXZZZ[[[]]]```bbbccciiimmmttt}}}{{{lllbbb]]]YYYSSSNNNNNNKKKHHHGGGGGGGGGFFFEEEEEEFFFFFFFFFDDDDDDFFFHHHEEEKKKQQQWWW```iiikkkiiikkkgggdddccceeefffdddbbbYYYXXXTTTPPPNNNNNNLLLIIIJJJIIILLLSSSWWWZZZcccnnnsssyyytttaaaUUURRRZZZeee~~~tttZZZIIIDDD777666555333222111111111000/////////............,,,,,,,,,,,,,,,,,,,,,,,,........................,,,...000///,,,,,,---000............/////////000000000000000111111111111...222555444222222777;;;:::BBBUUUnnnzzzppphhh[[[OOOGGGCCCAAA@@@???@@@@@@>>>:::555222111000///...---,,,------......------,,,,,,++++++***+++++++++,,,,,,---------+++,,,,,,,,,,,,+++******------------------------******)))+++,,,---+++******++++++,,,---...//////000---,,,---000111000......//////000000000000000111222222222111333555888BBBNNNbbbxxx~~~|||{{{zzz{{{|||}}}}}}|||zzzwwwvvvwwwwwwwwwvvvuuutttrrrqqqkkkllllllmmmmmmmmmmmmmmmllllllkkkkkkkkkkkkllllllmmmlllkkkkkkkkklllnnnooonnnmmmlllkkkkkkkkkkkkkkklllkkkkkkjjjiiihhhhhhggggggdddbbbaaabbbbbb___\\\ZZZYYYXXXVVVUUUSSSRRRRRRNNNMMMLLLJJJIIIHHHHHHHHHJJJIIIHHHGGGEEEEEEEEEEEEBBBBBBBBBCCCDDDDDDEEEEEEEEEEEEEEEDDDEEEEEEFFFFFFGGGFFFEEEEEEEEEGGGJJJKKKIIIIIIIIIIIIIIIIIIIIIIIIGGGFFFEEEFFFGGGHHHGGGFFFIIIIIIHHHHHHGGGGGGFFFFFFFFFFFFFFFFFFFFFGGGGGGGGGGGGGGGGGGGGGHHHHHHHHHHHHEEEGGGIIIKKKLLLMMMMMMMMMNNNOOOOOOPPPQQQQQQQQQPPPOOOQQQSSSVVVXXXYYYZZZZZZXXXWWWWWWXXXXXXVVVTTTRRRWWWSSSPPPPPPTTTWWWYYYXXXZZZ[[[]]]^^^___ccchhhkkkooottt|||tttjjjeeebbb]]]ZZZTTTRRROOONNNMMMMMMKKKIIIIIIIIIIIIGGGFFFEEEFFFGGGIIILLLQQQXXX___eeekkkmmmlllkkkjjjkkklllmmmlllkkkccc]]]VVVQQQOOONNNLLLJJJJJJKKKLLLNNNRRRXXX___dddmmmmmmsss}}}ttt___SSSUUU\\\qqqzzzdddQQQFFFBBB;;;555333111---,,,---000000000000////////////......------------......------------.........///...------------.../////////////////////.........////////////000000000000333111000111333666888999BBBKKK\\\mmmyyy~~~}}}wwwnnn```SSSJJJDDDAAA???@@@AAAAAA???<<<888555333111000...------------...,,,,,,,,,,,,,,,,,,,,,---,,,,,,,,,---------------***++++++,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,+++///......///111111000///---------------------...///...,,,---000111000......//////000000000000000333444555444444666999;;;FFFTTTiii}}}~~~|||{{{yyywwwvvvyyyzzzzzzzzzxxxuuusssqqqqqqqqqpppnnnllljjjhhhfffaaaaaabbbccccccccccccccccccbbbbbbaaaaaabbbbbbccccccbbbaaaaaaaaabbbddddddcccbbbaaa````````````aaa______^^^^^^]]]\\\\\\\\\YYYWWWUUUTTTUUUUUURRRPPPOOOOOONNNMMMLLLJJJJJJIIIJJJIIIIIIHHHGGGGGGGGGGGGHHHGGGGGGFFFFFFFFFFFFGGGDDDDDDDDDEEEEEEEEEFFFFFFGGGFFFFFFFFFFFFGGGGGGHHHIIIHHHGGGGGGGGGIIIKKKLLLJJJJJJJJJJJJJJJJJJJJJJJJJJJHHHGGGHHHIIIJJJIIIHHHIIIHHHHHHHHHGGGGGGFFFFFFGGGGGGGGGHHHHHHHHHHHHIIIIIIIIIIIIIIIJJJJJJJJJJJJIIIJJJLLLMMMNNNNNNNNNMMMMMMNNNOOOPPPQQQQQQQQQQQQQQQRRRTTTVVVXXXXXXXXXXXXWWWWWWWWWXXXYYYYYYWWWVVVZZZWWWUUUVVVZZZ^^^``````ccceeehhhkkknnnsssyyy}}}zzzuuuqqqkkkgggbbb^^^ZZZWWWUUUTTTRRRPPPMMMMMMMMMKKKIIIHHHHHHIIIIIILLLQQQWWW^^^dddiiilllmmmkkkjjjkkklllmmmkkkjjjddd^^^XXXSSSQQQPPPOOOMMMMMMNNNPPPQQQTTTXXX^^^bbbiiijjjooowww}}}qqq___ZZZ^^^lllzzzfffTTTJJJ???888444333222///...000000000000000///////////////..................///------........./////////...------------...///////////////////////////...000000000000111111111111333222111111333666999:::CCCNNN]]]kkkvvv~~~wwwiii[[[PPPHHHBBB???AAAAAAAAA@@@===;;;888777222111000...------......***++++++,,,------......---------------,,,,,,,,,)))***+++,,,,,,------,,,---,,,,,,,,,++++++******...------...///000///............---------,,,,,,///...---...///000000......///000000111111000000000111222111222444777:::JJJ[[[qqq~~~}}}|||{{{yyywwwuuurrrpppooorrrrrrqqqpppmmmjjjgggeeefffeeedddaaa^^^[[[YYYWWWSSSSSSTTTUUUUUUUUUUUUTTTUUUUUUTTTTTTTTTTTTUUUUUUVVVUUUUUUUUUUUUVVVWWWXXXUUUTTTTTTSSSSSSSSSSSSTTTQQQQQQQQQPPPOOOOOONNNNNNLLLJJJIIIHHHIIIIIIGGGFFFGGGFFFFFFEEEDDDDDDCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDCCCCCCCCCDDDDDDEEEEEEEEECCCDDDDDDDDDDDDDDDEEEEEEFFFEEEEEEEEEFFFFFFGGGHHHIIIHHHGGGFFFGGGHHHIIIJJJIIIIIIIIIIIIIIIIIIIIIIIIJJJIIIHHHHHHJJJJJJIIIHHHHHHHHHHHHHHHGGGGGGGGGGGGGGGGGGGGGHHHHHHHHHIIIIIIJJJJJJJJJJJJJJJJJJJJJJJJKKKLLLMMMNNNNNNNNNNNNMMMOOOPPPRRRSSSUUUUUUVVVVVVWWWXXXZZZ[[[[[[[[[[[[ZZZZZZ[[[]]]___```aaaaaaaaabbbaaa```cccgggkkknnnoootttwww||||||wwwqqqkkkfffccc___]]]WWWVVVUUUSSSQQQPPPNNNMMMMMMPPPTTTZZZ```fffjjjlllnnnlllkkkkkklllllljjjiiiddd```[[[WWWUUUUUUTTTSSSTTTVVVYYY[[[]]]```dddgggkkklllqqqwww{{{ggg[[[[[[bbbxxxxxxfffVVVMMMAAA:::666666555111000111000000000000////////////////////////////////////....../////////000000000...------------...//////......//////////////////111111111111222222222222222222222222444777:::<<>>===:::999444333111///............,,,,,,,,,,,,------......------,,,,,,++++++******((()))***,,,---............------,,,,,,+++++++++...,,,+++,,,---///...---...............---------............///000////////////000111111111111000...///000000111333888;;;JJJ\\\sss{{{yyyzzz}}}{{{yyyvvvtttrrrooollliiigggfffeeeeeedddaaa^^^[[[XXXWWWXXXWWWVVVTTTRRROOOMMMKKKGGGHHHHHHIIIIIIIIIIIIIIIJJJJJJIIIIIIIIIIIIJJJJJJLLLLLLLLLLLLMMMMMMNNNNNNKKKKKKJJJJJJJJJJJJJJJKKKIIIIIIHHHHHHHHHGGGGGGGGGFFFEEEEEEEEEEEEEEEDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDCCCDDDDDDDDDDDDDDDCCCCCCEEEEEEEEEFFFFFFFFFFFFFFFFFFFFFFFFFFFGGGGGGGGGGGGHHHHHHHHHHHHIIIJJJKKKKKKKKKJJJJJJIIIIIIJJJKKKKKKMMMMMMMMMMMMMMMMMMMMMMMMNNNLLLLLLLLLNNNOOONNNMMMNNNNNNNNNNNNMMMMMMMMMMMMKKKKKKLLLLLLMMMNNNNNNNNNOOOOOOOOOOOOOOOOOOOOOOOOPPPQQQRRRSSSTTTUUUVVVVVVWWWXXXZZZ]]]___```aaaaaacccdddeeeggggggggggggffffffhhhjjjlllnnnoooqqqsssrrrrrrtttwww{{{zzztttqqqhhhfffccc```^^^[[[XXXVVVWWWYYY\\\```eeejjjmmmoooooommmkkkkkklllkkkjjjhhheeeccc___\\\[[[[[[[[[\\\]]]```eeehhhjjjmmmpppssssssvvv{{{mmm]]]ZZZXXXeeexxxzzzrrrcccVVVOOOFFF@@@;;;999777222000111000000000000//////////////////000000000000//////////////////000000000000...------------...//////............////////////000000000111111111222222222222333333555888;;;>>>EEEUUUeeennnttt}}}~~~vvvhhhZZZNNNFFFAAA???======>>>>>>;;;999666555333000///..................------,,,,,,,,,,,,,,,++++++******))))))((()))+++,,,---...////////////......------------000...------///000000///,,,,,,---......///000000---...///////////////000///000000111111111111111222222333333555888===AAAHHHYYYnnn{{{|||xxxtttsssrrrzzz}}}}}}}}}~~~~~~{{{vvvrrrmmmkkkhhhdddaaa^^^]]]\\\ZZZYYYWWWUUURRRPPPMMMLLLKKKKKKKKKJJJIIIGGGFFFEEEAAAAAABBBCCCCCCCCCCCCBBBDDDDDDCCCCCCCCCCCCDDDDDDDDDEEEEEEFFFFFFFFFFFFFFFEEEDDDDDDCCCDDDDDDEEEEEEEEEEEEEEEEEEDDDDDDDDDDDDCCCDDDDDDDDDDDDDDDEEEEEECCCDDDDDDEEEEEEFFFGGGGGGIIIIIIJJJJJJJJJIIIHHHGGGLLLLLLMMMMMMMMMLLLKKKJJJKKKKKKLLLMMMMMMNNNNNNOOOPPPPPPPPPPPPQQQRRRSSSTTTQQQQQQQQQQQQQQQRRRRRRRRRVVVVVVVVVVVVVVVVVVVVVVVVVVVUUUUUUVVVXXXYYYYYYXXXYYYXXXXXXWWWWWWVVVUUUUUUVVVVVVVVVWWWXXXYYYYYYYYYYYYYYYZZZZZZZZZ[[[[[[[[[\\\]]]^^^```bbbeeeggghhhggghhhkkknnnpppssstttuuutttvvvxxxzzz{{{||||||{{{zzz||||||vvvqqqnnnjjjfffcccbbbccceeehhhkkknnnpppqqqqqqooommmmmmnnnmmmllljjjhhhgggfffdddcccdddeeegggiiilllppprrrtttvvvxxxyyy}}}wwwccc]]]VVVXXX```mmm{{{xxxrrrlllaaaWWWQQQIIIBBB;;;999666222111333000000000000//////////////////000111111000//////////////////000000000000...------------...//////---.........//////000000/////////000000000111111111333444555555888===AAAFFFXXXjjjrrrwww}}}tttooorrr}}}yyygggVVVKKKCCC@@@======??????<<<:::888666444222000///......//////......---,,,,,,+++++++++++++++************)))***+++---......//////..................//////...,,,******,,,---...---+++,,,---...///000111111---...//////......///111///000111111222222111111111222222333555999???DDDIIIVVVgggsssvvvuuusssssspppxxx}}}{{{zzzzzz{{{wwwwwwwwwxxxxxxtttoookkkcccaaa^^^ZZZVVVTTTRRRRRRQQQPPPNNNLLLKKKIIIHHHGGGCCCCCCCCCDDDCCCCCCBBBAAA>>>???@@@@@@AAAAAA@@@@@@AAA@@@@@@@@@@@@@@@@@@AAA??????@@@AAAAAAAAAAAAAAAAAAAAA@@@@@@AAAAAABBBBBBDDDDDDDDDDDDDDDDDDDDDDDDAAACCCDDDDDDDDDDDDEEEGGGDDDEEEFFFGGGIIIJJJKKKKKKLLLMMMNNNOOOOOONNNMMMMMMRRRSSSTTTTTTSSSRRRQQQPPPQQQQQQRRRSSSUUUVVVWWWWWWXXXXXXXXXYYYZZZ[[[\\\]]]ZZZZZZ[[[[[[\\\]]]]]]]]]bbbbbbbbbbbbbbbbbbbbbbbbaaaaaaaaacccfffhhhhhhhhhfffeeedddcccaaa```______bbbbbbcccdddeeefffgggggggggggghhhiiijjjkkkllllllnnnnnnppprrruuuyyy{{{}}}{{{vvvsssnnnooopppqqqrrrssstttttttttsssrrrrrrrrrrrrqqqpppmmmnnnooonnnnnnoooqqqtttuuuxxx{{{|||}}}~~~ggg]]]ZZZUUUTTTYYYaaaiiissszzzxxxqqqllleee]]]YYYMMMDDD<<<999666222222555000000000000////////////......000000000000............/////////000000000...------------...//////------......///000000000.../////////000000000000000333555666666999???CCCKKK]]]mmmsssyyyuuummmeeetttrrr]]]OOOEEEBBB>>>>>>@@@AAA>>>;;;999888555222000///.....................---------,,,,,,,,,,,,,,,---------***+++,,,---............,,,,,,------.../////////,,,)))'''''')))+++++++++------......//////000000,,,...000///...---///111000000111222222222222111000000111111444999???DDDNNNWWWcccnnntttvvvwwwwwwuuu|||}}}yyyzzz}}}}}}|||zzzxxxxxxxxxxxxyyyuuusssqqqooommmjjjfffccc[[[XXXUUUPPPMMMKKKJJJJJJHHHGGGFFFEEEDDDDDDCCCCCC??????@@@@@@@@@??????>>>===>>>>>>??????????????????>>>>>>======>>>>>>???===>>>???@@@AAA@@@@@@???BBBBBBBBBBBBBBBCCCDDDDDDGGGGGGGGGGGGGGGGGGGGGGGGDDDFFFHHHIIIHHHHHHJJJMMMLLLLLLNNNPPPRRRSSSUUUVVVUUUVVVYYY\\\]]]^^^]]]]]]___```bbbcccccccccaaa``````aaabbbdddfffhhhjjjjjjkkkkkkkkklllmmmnnnooopppnnnooopppqqqssstttttttttwwwwwwwwwwwwwwwwwwwwwwwwxxxxxxxxx{{{}}}|||yyyxxxvvvuuuyyyyyyzzz{{{|||}}}~~~~~~}}}}}}|||||||||{{{{{{{{{zzzxxxwwwxxxyyyyyyxxxwwwtttvvvxxxyyyyyyzzz}}}pppaaa]]]VVVQQQRRRTTTWWW```jjjsss~~~wwwtttoooiiiggg[[[PPPEEE===888333333555000000000000////////////,,,---///000000///---,,,------........./////////...------------...//////------......///000000111//////000000000111111111000333666777777999@@@EEERRRaaammmqqqyyy{{{sss^^^oooyyyaaaQQQHHHCCC??????BBBBBB???<<<:::999666333111//////...,,,,,,------.../////////---------....../////////++++++,,,---............***++++++,,,---.../////////---******,,,.../////////////////////.........,,,...000000...---///111000000111222222222222111444444444555888===DDDIIITTTYYYbbbkkksssxxxzzz{{{{{{~~~tttppprrrvvvzzz{{{xxxxxxwwwvvvvvvvvvwwwxxxyyywwwsssmmmhhheeebbb```^^^VVVSSSOOOKKKHHHFFFFFFFFFAAA@@@@@@?????????@@@@@@>>>>>>???>>>>>>===<<<<<<<<<======>>>>>>>>>>>>>>>======<<<<<<<<<<<<======???@@@AAABBBCCCBBBAAAAAAEEEEEEEEEEEEEEEFFFGGGHHHJJJJJJJJJJJJJJJJJJJJJKKKIIILLLOOOOOONNNOOOQQQTTTUUUVVVXXXZZZ\\\^^^``````dddfffjjjnnnqqqrrrssssssqqqsssuuuxxxyyyyyyxxxwwwuuuvvvxxxzzz}}}}}}|||{{{|||~~~~~~~~~|||yyy||||||jjj^^^WWWRRRPPPOOONNNVVV```hhh{{{~~~{{{xxxsssqqqlll___PPPDDD;;;444222444000000000000////////////,,,---///000000///---,,,------------.........///...------------...//////---------...///000000111000111111111111222222222000333777777777:::@@@FFFXXXeeemmmnnnwwwxxx[[[jjj|||fffXXXJJJCCC???@@@AAA???>>>???===999555222111111000///......---------,,,,,,,,,------------------------+++,,,---...////////////........................,,,,,,,,,---------.........000111000...------...////////////000111333333000000000000000111111111555333111333:::CCCKKKQQQeeeccceeemmmwww~~~}}}xxxooojjjhhhmmmsss{{{}}}xxxuuuuuuuuuuuuvvvwwwvvvtttrrrpppmmmiiiddd```[[[UUUQQQLLLKKKIIIGGGEEEDDDDDDCCCBBBAAA@@@???>>>============<<<<<<;;;<<<>>>???AAA??????>>>>>>>>>>>>??????===>>>?????????>>><<<;;;DDDEEEFFFFFFEEEDDDEEEGGGLLLKKKIIIFFFEEEGGGLLLPPPOOOQQQSSSTTTSSSRRRSSSTTTRRRUUUXXXZZZ[[[\\\]]]^^^```bbbdddgggjjjooouuuzzzyyy}}}}}}kkkbbb[[[TTTQQQOOONNNQQQVVVcccooo}}}ttt```MMM@@@999777777333111//////000111000///111111000......---------////////////////////////////////////////////////////////////000000000000000000000000111111111111222222444666777999DDDOOObbbfffmmmxxxxxxWWWdddyyy~~~iiiZZZLLLEEE@@@@@@AAA???===>>><<<999555333333222000///.........---------,,,,,,------------------------+++,,,---...////////////........................,,,,,,,,,---------......---...//////---,,,,,,---///...............//////111111111111222222222222333444555777<<>>======;;;999666555444333111///.........------------,,,------------------------+++,,,---...////////////........................,,,,,,,,,---------......---///000///...------...000000///...............222222222222333333444444222555888<<>><<<===:::999777666666444111///............------------------------------------+++,,,---...////////////........................,,,,,,,,,---------......///111222222111000000111111000000000000000111222111111222222333333444444444666:::CCCSSSkkkzzzrrrmmmlllsss{{{}}}{{{yyy|||{{{{{{~~~~~~yyyuuuqqqooolllkkkkkkjjjiiihhhccc```\\\YYYXXXXXXXXXWWWUUUTTTRRRPPPMMMLLLKKKJJJEEEEEEEEEEEEEEEDDDDDDCCCFFFFFFFFFGGGHHHHHHIIIJJJKKKKKKJJJJJJJJJJJJKKKKKKMMMMMMMMMNNNPPPRRRUUUWWWWWWZZZ^^^```bbbcccfffgggiiilllooorrrssstttvvvwwwpppeeeYYYTTTQQQNNNNNNQQQaaatttlllXXXHHH>>>999444222000000111111000///111111000///......//////////////////////////////////////////////////////////////////000000000000000000111111111222222222444444777<<<@@@HHHWWWeeeqqqxxxyyyzzz|||~~~XXXXXX___sss|||zzzyyy{{{ooo]]]RRRHHHDDDAAA>>><<<===:::999777777777555222000//////.........---------------------------------+++,,,---...////////////........................,,,,,,,,,---------......///000222222111000000111.........///000222333444000000111111222333333444777777<<>>===>>>;;;999777777777666444222/////////.........------------------------------+++,,,---...////////////........................,,,,,,,,,---------......,,,---//////...---...///++++++,,,---///111222333///000000111222333444444::::::BBBVVVuuu|||wwwwww~~~~~~~~~||||||xxxwwwwwwwwwyyy}}}|||wwwssskkkgggbbb___^^^^^^]]]]]]\\\ZZZZZZ[[[^^^aaabbbbbb___^^^]]]\\\[[[ZZZZZZZZZXXXYYYZZZZZZZZZXXXWWWVVVWWWXXXYYY[[[]]]^^^_________^^^^^^]]]]]]^^^^^^___cccdddgggjjjnnnrrruuuwwwxxx}}}ooo\\\RRRNNNLLLNNNQQQeeeyyysss___LLL???888666444222111111111000///111000000//////000000000////////////////////////////////////////////////////////////000000000000111111111222222222222333444444777>>>FFFRRRfffvvv~~~~~~xxxxxxttt{{{|||pppiii___WWW[[[lll|||yyy{{{yyy|||}}}~~~}}}vvviii]]]PPPIIIDDD???===???===:::777666666666555444////////////............------------------------+++,,,---...////////////........................,,,,,,,,,---------......+++,,,......------...///,,,,,,,,,---...000111222000000111222333444555555:::???KKKaaa}}}zzzyyy{{{zzzyyyxxxxxxzzz||||||wwwpppkkkeee```ZZZVVVTTTTTTTTTTTTTTTTTTUUUXXX]]]```aaaaaabbbbbbcccdddeeeggghhhiiihhhiiikkkmmmnnnnnnmmmllllllmmmooopppqqqppppppooopppoooooonnnnnnoooooopppsssuuuyyy~~~fffWWWPPPLLLMMMOOO[[[mmmxxxdddQQQBBB;;;666444222111111111000///111000000000000000111111////////////////////////////////////////////////////////////000000000000111111111222222222333333555555999AAAJJJXXXmmm~~~zzzyyyxxx{{{xxxkkkvvviiiZZZUUU___rrr}}}~~~|||}}}wwwmmm```RRRJJJEEE@@@>>>???>>>;;;777555555666666555000/////////............------------------------+++,,,---...////////////........................,,,,,,,,,---------......,,,...///000///...///000000000000000000111222222111111222333555666666777999BBBSSShhh~~~xxxwwwxxx}}}|||{{{zzzzzz|||~~~}}}yyyrrrjjjddd___ZZZTTTOOOMMMMMMNNNMMMNNNNNNQQQUUUZZZ^^^___^^^eeefffhhhkkknnnrrruuuwwwzzz|||~~~~~~}}}}}}}}}}}}~~~~~~qqq^^^SSSNNNMMMOOOSSSccczzz{{{iiiVVVHHHBBB777555222111222111000///111000000000000000111111////////////////////////////////////////////////////////////000000000000111111222222222333333333666666;;;CCCMMM[[[qqquuufffooo[[[UUUVVV^^^ppp{{{yyyllldddYYYOOOHHHCCC???===???:::777777666444444888111111000000//////.........------,,,,,,------...---------------------------...///000000///...---///............---------///////////////.........000///...---...///111333222333444444333222333555999DDDWWWmmm}}}zzzyyyxxx}}}}}}{{{zzzyyyzzz~~~}}}zzzvvvqqqjjjccc^^^YYYUUUQQQNNNNNNNNNNNNNNNKKKLLLMMMOOOSSSWWW[[[^^^ffffffiiiooowww~~~wwwbbbXXXQQQNNNOOOTTTYYYiii|||mmmXXXGGG@@@888555222111111111000///////////////////////////---------.........//////...///////////////......000000000000111111111111111222333333222222444666:::999<<>>999999888444111111333333222111000000//////......------------......------------............------------------------,,,,,,------...//////000............////////////222222111000000111222333000111222222222333666999EEEOOO___mmmvvv{{{zzzyyyzzz{{{{{{}}}~~~~~~{{{xxxvvvuuurrrpppnnnkkkhhhddd___[[[WWWVVVTTTTTTSSSQQQMMMJJJKKKJJJIIIJJJKKKNNNPPPRRRQQQWWW^^^dddjjjsss~~~{{{rrrkkkgggeeeaaa^^^]]]ZZZ[[[^^^```aaahhhoooyyy}}}zzzxxxrrrmmmkkknnnpppooopppssstttvvvzzz}}}wwwcccWWWQQQPPPPPPNNNPPPUUU]]]kkkyyytttrrrlll```TTTNNN@@@<<<888555444333222111////////////////////////.............../////////...//////000000000000//////000000000111111111111111222333333222222444666888888===IIIWWWgggzzzwwwjjjxxxjjj[[[PPPNNNPPP[[[kkk}}}jjjYYYIIIAAA:::::::::777444444444444333222111000/////////......------......///---------......////////////..................///........................---.........//////000000222222111111111111111111222333333333333444777999EEEPPP___lllrrrvvvyyy|||{{{xxxxxxyyyzzz|||~~~{{{vvvrrrpppnnnllljjjhhhfffccc___[[[YYYXXXXXXXXXWWWUUUQQQOOONNNMMMLLLLLLMMMOOOQQQRRRWWWXXX[[[aaaiiiqqqwwwzzzvvvooofff___\\\YYYUUURRRQQQNNNMMMOOOOOOPPPUUU[[[bbbmmm~~~~~~~~~}}}}}}}}}}}}}}}zzz|||}}}~~~}}}zzzxxxuuurrrkkkeeebbbdddeeecccdddfffggghhhmmmqqqssszzz~~~hhh[[[WWWUUUSSSPPPNNNOOOQQQYYYiiiyyyvvvooommmjjjaaaVVVPPPBBB>>>999555333222222111000000000000000000000000////////////////////////......///000111111000000///000000000111111111111111222333333222222444666999999@@@NNN^^^ooozzzmmmccc}}}nnn]]]PPPJJJIIIQQQ^^^tttwwwgggRRRGGG>>><<<<<<999777666666555444333222000////////////............//////---------...//////000000000///............///000//////.........---------------......///000000000111111111111111000000000333444444444444666:::===EEEPPP___jjjooossswwwzzz~~~yyyxxxyyyzzz{{{{{{}}}~~~zzzuuuqqqooommmkkkiiigggfffdddaaa___]]]\\\[[[\\\\\\[[[XXXUUUUUUTTTRRRRRRSSSTTTWWWXXX\\\\\\___fffnnnvvvyyyzzztttmmmccc\\\YYYUUUQQQNNNMMMJJJIIIJJJIIIHHHKKKPPPSSS^^^nnn}}}~~~}}}|||{{{{{{|||}}}~~~}}}}}}xxxuuunnnhhhdddddddddaaa```bbbbbbbbbeeeiiikkkooozzz|||{{{~~~lll___[[[ZZZUUUQQQNNNMMMMMMQQQ[[[fff~~~xxxxxxnnnlllkkkdddYYYRRREEE@@@:::555333222111111000000000000000000000000000000000////////////.........///000111111111111000000000000111111111111111222333333222222444666888999BBBRRReeewww~~~wwwooofff```rrraaaTTTMMMJJJKKKUUUgggvvv\\\OOOBBB===<<<:::777777666666555333222111000/////////............//////---------...///000000000///...------------...///---------...............------......///000000111000111111111000000///...111222333444666999???BBBJJJUUUcccmmmqqqtttyyy~~~~~~{{{~~~zzzxxxyyyzzz||||||{{{}}}}}}yyyvvvuuurrrpppnnnmmmmmmllliiigggdddcccbbbcccddddddbbb``````___^^^^^^___```cccdddeeeiiiooouuu{{{xxxqqqggg___ZZZVVVRRRNNNLLLIIIHHHIIIGGGDDDEEEJJJKKKTTTaaannnzzzxxxsssrrrooojjjhhhiiihhhffffffiiijjjjjjooovvv}}}~~~ooodddbbbaaa]]]VVVOOONNNMMMNNNTTT[[[jjjxxx}}}|||rrroooooohhh]]]VVVHHHCCC<<<777444333333222000000000000000000000000000000000000/////////.........///111111222222111000000000000111111111111111222333333222222444666:::<<>>888666444444333000000000000000000000000111111000000/////////.........///111111222222222000000000000111111111111111222333333222333555666===???JJJ^^^tttvvvjjjbbb```aaa}}}wwwooo```RRROOOLLLSSSkkkkkk]]]KKK@@@>>>>>>:::666777777777666444222///...////////////////////////////////////////////////......//////...---,,,,,,---------.........//////---...///...---,,,---.../////////000111111222222444111333666888;;;FFFSSSaaahhhqqqyyy}}}uuunnnnnnqqqtttyyy}}}}}}{{{zzzxxxwwwxxxzzz|||~~~|||zzzxxxwwwqqqsssuuutttrrrrrruuuwwwyyywwwuuuuuuwwwyyyyyyyyy{{{uuullleee___YYYUUUSSSMMMGGGFFFDDDBBBDDDHHHEEEHHHOOOWWW___jjj}}}~~~zzztttooonnnmmmllllllyyy|||{{{vvvrrrtttyyyvvvpppooonnndddYYYRRRNNNKKKLLLOOO```hhhvvvuuu~~~{{{vvvwwwvvvoooggg[[[PPPCCC:::777666444111222111111000000000000000000000000000000000000000............/////////000000000000000111111111111222333444444444555777999<<>>:::666777777777666555222000...//////////////////////////////////////////////////////000000//////...------------.........//////---...//////------.../////////000000111111222222444333444777999>>>MMM]]]mmmsss{{{wwwpppjjjkkknnnrrryyy|||zzzxxxvvvuuuuuuvvvyyy|||~~~{{{||||||{{{yyyyyy|||~~~~~~}}}~~~~~~~~~}}}wwwnnnfff___ZZZSSSMMMIIIHHHFFFDDDEEEHHHEEEGGGLLLTTT[[[eeexxxyyyuuusssqqqpppwwwyyymmmgggbbbcccfffkkkttt|||yyy}}}}}}zzzttthhh[[[SSSNNNKKKLLLQQQ```lll~~~vvv{{{~~~xxxrrrcccWWWGGG<<<888666444222222111111000000000000000000000000000000000000000........./////////000000000000000000111111111111222333444444444555888:::<<>>999666444222111111000000000000000////////////////////////...////////////000000000000000111111111222222222222333444444555777;;;>>>@@@OOOddd{{{sssddd^^^]]]wwweeeUUUQQQTTT___vvvzzzvvvtttssspppeeeVVVJJJDDD@@@===999888888888888777555333111////////////////////////////////////////////////---......//////................../////////000000777777777555222000///000000000000111222222333333000444777:::CCCYYYvvvyyyuuussstttvvv|||zzztttpppnnnnnnoooqqquuuzzz}}}}}}|||{{{{{{~~~~~~tttjjjaaa]]]XXXPPPIIIFFFHHHEEEEEEGGGJJJPPP[[[fffrrrqqqbbbXXXPPPKKKHHHHHHGGGFFFIIINNNPPPVVV___gggmmmuuu}}}xxxppprrr|||rrr___RRRKKKKKKQQQYYYwww|||xxx```MMMAAA;;;777444222111111000000000000000////////////////////////////////////000000000111111111111111222222222222222333444444555888<<<@@@FFFUUUlllsssfff```___kkkZZZTTTSSSWWWjjj~~~xxxuuusssrrroooeeeWWWLLLEEEAAA>>>;;;888888999888777666444333////////////////////////////////////////////////,,,------...................../////////000000000777888777555222/////////000000111111222333333333000555999>>>LLLggg|||xxxzzz~~~yyysssooonnnnnnoooqqqvvv{{{}}}zzzxxxvvvvvvxxx}}}sssiiiddd___WWWOOOLLLJJJGGGFFFHHHJJJLLLSSS[[[eeeppp{{{rrrjjjaaaVVVNNNKKKGGGEEEFFFFFFDDDFFFJJJFFFKKKQQQWWW[[[```gggmmmyyyuuusssvvvuuuaaaSSSLLLKKKQQQYYYuuu}}}}}}~~~fffRRREEE===888444222111111000000000000000000000000000000000000000/////////000000000111111111111111222222222222333333333444444555999>>>BBBKKK[[[rrr}}}pppeee``````nnn]]]XXXUUUTTTaaattt|||yyyvvvtttrrrmmmdddXXXLLLEEEAAA>>>===888999999999888666444333////////////////////////////////////////////////------...///////////////.../////////000000000000333444444222000//////000000111111222222333333444222777;;;CCCVVVttt~~~}}}wwwrrrooommmmmmnnnqqquuu{{{~~~}}}|||{{{uuusssqqqqqqsssuuuxxxyyy~~~vvvnnnhhh^^^UUUQQQLLLIIIHHHJJJJJJJJJNNNTTT\\\dddrrrzzzrrrkkkaaa[[[YYYUUUNNNIIIJJJGGGEEEGGGFFFCCCDDDGGGAAAEEEIIILLLMMMPPPVVVZZZeeekkkttt}}}yyyuuuwww{{{fffVVVMMMKKKPPPVVVhhh~~~iiiUUUGGG???888444222111111000000000000000000000000000000000000000//////000000000111111111111111111222222222333333333333444444666:::???CCCOOO___uuu|||uuukkkddd___^^^nnn^^^[[[WWWSSS[[[lll|||yyywwwuuurrrllldddWWWMMMFFFAAA???===888999999999888777555444////////////////////////////////////////////////......///000000111000000////////////000000000000...///000000///...///000000111111222222333444444444999===GGG]]]|||zzzuuuqqqooollllllmmmppptttzzz~~~{{{yyyxxxxxxuuusssrrrqqqssstttttttttrrr|||yyyooocccXXXSSSNNNKKKJJJLLLLLLJJJLLLPPPXXX^^^iiivvvzzztttpppmmmhhheeebbb[[[SSSOOOOOOOOOKKKHHHGGGDDDBBBDDDBBB???>>>AAAAAADDDGGGHHHGGGIIIMMMQQQRRRVVV^^^gggpppwww{{{~~~uuuqqq|||jjjYYYOOOKKKNNNTTT\\\}}}kkkVVVIII@@@888333222111111000000000000000000000000000000000000000000000000000111111111111111111222222222333333333333333444444666:::@@@DDDPPPaaawww~~~wwwooohhhbbb^^^\\\|||pppgggccc[[[SSSWWWccc{{{}}}||||||uuukkk\\\OOOHHHCCC@@@>>>@@@===;;;999999777555333//////000111111000......////////////000000000000////////////////////////000000000000000000000000............///////////////000000000000111444666888888@@@TTTnnn~~~xxxrrrnnnlllkkkmmmoooqqqssswww{{{}}}zzzwwwuuusssrrrpppooonnnnnnkkkjjjnnnrrr|||yyymmm```WWWTTTPPPLLLJJJKKKMMMOOOOOOSSSVVV\\\dddnnnxxx{{{{{{wwwpppllljjjeee___\\\WWWRRROOOPPPPPPNNNKKKHHHFFFCCCBBBBBBBBBAAA???DDDDDDDDDEEEFFFGGGHHHIIILLLPPPTTTXXX]]]bbbhhhlllooosssyyyzzzoooqqqzzznnn]]]QQQLLLMMMRRRZZZpppnnn\\\MMMCCC<<<888555444222111111111111222000000000000000000000000111111111111111111111111111111222222222333333333333222444777777888>>>FFFMMM```ttt|||yyysssmmmiiiccc]]][[[]]]|||rrrjjjeee[[[RRRUUU___tttzzzooo___QQQIIIDDD@@@===???===;;;::::::888555333///000111111111000///...////////////000000000000////////////////////////000000000000000000000000/////////000000000111111000000111000000111444666888;;;FFF[[[sss}}}}}}}}}}}}|||yyytttpppmmmmmmkkkmmmppprrrtttxxx{{{~~~~~~zzzvvvtttpppnnnkkkiiiiiigggeeeccccccfffooo|||vvvggg]]]VVVSSSOOOMMMMMMOOOOOOOOOPPPRRRUUU[[[aaahhhnnnqqq|||~~~}}}~~~~~~|||{{{~~~}}}|||}}}|||uuuqqqnnniiibbb^^^ZZZUUUSSSSSSSSSQQQNNNLLLIIIEEECCCCCCDDDCCCCCCAAAAAAAAABBBBBBCCCEEEEEEGGGJJJMMMPPPSSSWWW[[[^^^bbbeeejjjoootttyyypppmmmrrruuucccVVVNNNMMMQQQZZZmmm{{{kkk[[[MMMCCC;;;777555444333111111111111222000000000000000000000000111111111111111111111111111111222222222333333333333222444777777777>>>FFFPPPbbbvvv}}}tttqqqlllgggeeeaaa\\\[[[]]]}}}vvvpppiii]]]RRRRRRZZZnnnxxxgggXXXNNNGGGAAA>>>???>>>===<<<;;;999666333111111111111111000///...////////////000000000000////////////////////////000000000000000000000000000000000111111111222222111222222111000111333666777???OOOdddyyy|||tttsssxxxxxxvvvsssooommmmmmnnnjjjmmmqqqtttvvvyyy|||~~~}}}xxxssspppkkkhhhdddaaa___]]]ZZZXXXZZZ[[[bbbmmmyyypppdddYYYVVVSSSPPPPPPPPPOOONNNNNNNNNOOOPPPSSSVVVYYY[[[hhhnnntttwwwuuurrrqqqqqqnnnnnnpppssswwwyyyyyyyyyvvvxxx{{{|||}}}~~~{{{}}}zzzwwwrrrooommmlllkkkiiihhhkkkmmmooorrrxxx{{{xxxsssllleeeaaa\\\ZZZZZZZZZWWWTTTQQQMMMHHHEEEEEEEEEFFFFFF@@@@@@@@@@@@AAABBBCCCCCCEEEGGGIIIJJJKKKMMMQQQSSSXXX[[[^^^aaadddgggkkkmmmoooqqqtttvvvyyy|||vvvnnnmmmttt~~~lll^^^SSSOOOPPPYYYiiiwwwjjj\\\OOOEEE===888666555333222111111111222000000000000000000000000111111111111111111111111111111222222222333333333444333444666666777===EEESSSdddwww}}}|||}}}~~~rrriiieeeaaa^^^___]]]ZZZZZZ^^^{{{wwwpppcccVVVRRRVVVdddyyyssscccWWWMMMEEE@@@@@@???>>>======:::666333222222222111111000000///////////////000000000000////////////////////////////////////////////////000000000111111111222222222333333222111111444666777DDDXXXmmm|||{{{sssrrrxxxwwwtttooolllkkkmmmooojjjmmmrrruuuwwwyyy{{{}}}|||uuuoookkkeeeaaa]]]YYYVVVSSSPPPNNNPPPQQQVVV^^^iiixxxvvvjjj\\\YYYUUURRRQQQPPPNNNMMMMMMLLLKKKKKKLLLMMMNNNOOO[[[aaagggkkkkkkiiigggfffcccbbbccceeeiiikkkllllllkkknnnqqqtttvvvyyy}}}zzzyyypppsssuuuwwwxxxzzz}}}~~~zzznnnjjjeeebbbaaa```___^^^^^^aaadddgggjjjqqqzzz{{{ppplllgggdddcccbbb___\\\XXXSSSLLLGGGFFFEEEFFFFFFBBBBBBBBBBBBBBBCCCDDDDDDGGGHHHJJJKKKKKKMMMOOORRRVVVYYY\\\^^^___```ccceeeccceeegggiiijjjmmmqqqtttwwwzzzuuunnnnnn|||ttteeeXXXRRRRRRXXXcccyyy~~~|||uuukkk___TTTJJJAAA;;;666555444222111111111222000000000000000000000000111111111111111111111111111111222222222333333333555333444666666777>>>FFFVVVfffwww|||xxxwwwyyy|||zzznnnccc\\\XXXWWWYYYZZZYYY[[[___yyymmm___VVVTTTWWWiiioooaaaTTTIIIBBBAAA@@@>>>>>>===;;;888555444333333222111000000000////////////000000000000000000000000000000000000/////////////////////////////////000000000111111222333333222222222555777888HHH___rrr{{{}}}|||{{{zzz{{{ttttttzzzxxxtttnnnjjjiiikkknnniiimmmqqquuuwwwyyy{{{}}}}}}|||ssskkkfff___[[[VVVQQQNNNLLLIIIGGGEEEFFFJJJQQQYYYeeexxx~~~qqq___[[[VVVSSSQQQOOONNNLLLKKKJJJIIIIIIIIIJJJLLLMMMRRRUUU[[[^^^^^^\\\ZZZYYY[[[ZZZYYYZZZ\\\___``````^^^aaaeeehhhjjjnnnrrrtttyyy}}}}}}sssmmmlllgggiiilllnnnoooppprrrttttttwwwzzz|||{{{xxxsssooogggccc^^^[[[ZZZZZZZZZYYY[[[^^^bbbeeehhhooowww~~~yyyrrrmmmkkkiiieeebbb]]]WWWPPPJJJGGGFFFEEEDDDDDDDDDCCCCCCDDDDDDEEEEEEFFFHHHJJJKKKLLLNNNQQQTTTTTTWWWZZZ\\\]]]^^^```bbb```aaacccccccccdddfffhhhkkkmmmpppqqqrrrtttvvvxxx{{{sssmmmuuuyyykkk^^^XXXWWWXXX___nnnzzzwwwssskkkbbbYYYMMMCCC<<<777666444222111111111222000000000000000000000000111111111111111111111111111111222222222333333333555444444777777888@@@IIIXXXiiizzz~~~vvvtttvvvzzzrrrhhhZZZVVVUUUWWWYYYYYY]]]bbbyyylll^^^UUUSSS^^^rrr}}}mmm^^^PPPFFFDDDAAA???======;;;999777555555333222111111111111////////////000000000000000000000000000000000000000000000000000000000000/////////000000000111111222222333333333444777999<<>>>>>@@@CCCBBBCCCKKKUUU[[[mmm{{{hhhbbbZZZSSSRRRSSSTTTUUUWWWVVVSSSPPPNNNLLLLLLKKKKKKJJJKKKLLLNNNOOONNNNNNKKKIIIGGGGGGKKKPPPSSSUUUXXXYYYZZZZZZZZZZZZ[[[\\\fffkkkrrrxxx}}}uuullleee]]]YYYYYYVVVWWWYYYYYYWWWUUUTTTTTTVVVXXX\\\```dddgggiiijjjccc___YYYVVVVVVXXXYYYYYY\\\aaahhhooouuu~~~vvvnnnjjjhhhfff[[[YYYUUUSSSSSSRRRQQQOOONNNMMMMMMLLLLLLLLLMMMMMMQQQSSSUUUWWWXXXZZZ]]]```dddgggjjjlllkkkjjjjjjkkkbbbdddffffffffffffggghhheeeeeedddbbb___]]]^^^___]]]^^^```bbbgggnnnvvv|||uuurrrtttjjjeeefff___^^^\\\^^^eeesss{{{tttwwwzzzzzzyyywwwsssjjj]]]OOOEEE999888666333222111111111000000000000000000000000111111111111111111111111111111222222222333333333666444555999;;;???HHHSSSjjj|||{{{wwwzzzooohhh```]]]]]]^^^dddkkk{{{iiiZZZSSSVVVgggyyypppeeeVVVKKK???:::===???<<<888777666555333222111000000000000000000000000000000000000000000000000000000//////000000111111111111111111111000000000000000555222222333333444999AAAPPP___nnnssstttwww|||~~~}}}|||xxxwwwxxxrrroookkkfffdddcccdddeeekkkmmmooorrrtttvvvyyy{{{}}}yyyqqqlllhhheeebbbaaacccgggjjjkkkkkkmmmppprrrqqqnnnjjjhhh___]]]YYYUUUQQQMMMKKKJJJHHHGGGEEECCCAAA@@@@@@???>>>>>>???AAABBBDDDFFFGGGUUU\\\kkk~~~yyynnn___SSSRRRTTTRRRTTTZZZVVVYYYYYYUUUTTTUUUSSSOOOMMMLLLLLLMMMNNNNNNLLLJJJJJJJJJKKKLLLMMMOOOQQQQQQVVVXXXYYYYYYXXXVVVUUUVVV___dddkkkrrrxxx}}}vvvjjjaaa[[[WWWUUUSSSTTTTTTUUUTTTSSSQQQPPPTTTSSSTTTZZZbbbfffeeeccc```^^^ZZZWWWVVVXXX[[[]]]]]]bbbjjjrrryyywwwlllfffbbb___YYYYYYXXXWWWVVVUUUUUUUUUUUUTTTSSSQQQPPPPPPOOOOOOSSSUUUXXX[[[^^^bbbhhhkkkppppppppppppppppppppppppmmmkkkiiiiiijjjkkklllkkkiiiiiihhhgggeeebbb```______```aaa___]]]aaaiiippp}}}ttt~~~uuunnnhhhcccccc^^^ZZZZZZ[[[aaaooo|||vvvooosss{{{vvvlll[[[KKKAAA:::444555666444333444111111111111111111111111111111000000111111222333333333222222333333444555666888555888>>>===EEEZZZuuuzzzyyy{{{rrrfff]]][[[___fffkkksss[[[SSSSSSaaaqqq|||vvvmmm[[[OOOBBB<<<===>>><<<888777666555333222111000000000000000000000000000000000000000000000000000000000000000000000111111111111111111111000000000000555333333444555666===EEE\\\hhhtttwwwxxx}}}{{{xxx~~~|||yyyyyypppnnnjjjgggfffgggiiijjjnnnooorrrtttuuuvvvwwwxxxxxxzzz}}}}}}zzztttnnniii^^^[[[VVVTTTUUUXXXYYYZZZXXXYYY[[[]]]\\\YYYVVVTTTOOONNNKKKHHHFFFDDDCCCBBBBBBAAAAAA@@@@@@@@@AAAAAA=========>>>@@@AAACCCDDDKKKQQQ]]]mmm{{{|||mmm```UUUTTTSSSQQQTTT\\\]]]```aaa]]][[[[[[YYYTTTQQQPPPNNNNNNNNNMMMKKKIIIJJJKKKKKKLLLNNNPPPRRRTTTVVVXXXYYYXXXVVVTTTSSSTTT[[[```hhhpppvvv|||yyynnnfff___ZZZWWWRRRSSSSSSSSSRRRQQQPPPOOOTTTSSSTTTZZZaaaeeedddbbb___\\\YYYVVVUUUWWWZZZ\\\^^^ccckkksss{{{yyynnngggdddbbb]]]]]]\\\[[[[[[[[[[[[\\\\\\[[[ZZZYYYXXXXXXWWWWWWXXX[[[^^^aaadddiiinnnrrrxxxxxxyyyyyyyyyxxxwwwvvvsssrrrppppppqqqrrrrrrqqqnnnnnnnnnlllkkkiiigggfffeeefffeeeaaa^^^___eeekkktttxxx}}}zzzssslllfff```[[[WWWVVVVVVZZZfffrrrvvvnnnjjj}}}xxxeeeTTTDDD<<<555555666444333333111111111111111111111111111111000000111111222333333333222222333333444555555777666999??????HHH]]]xxx~~~~~~wwwkkkbbb___aaafffjjj|||___UUURRR[[[fffooo||||||vvvdddWWWGGG>>>===>>><<<999888777555333222111111111////////////////////////000000000000000000000000111111111000000000000000111111111111111111111111555333333555666999BBBLLLjjjuuu~~~}}}}}}|||yyynnnllljjjhhhhhhjjjmmmoooqqqsssuuuwwwxxxwwwuuutttrrrtttuuuuuurrrlllgggcccVVVRRRMMMJJJJJJJJJJJJJJJKKKKKKLLLLLLLLLJJJHHHGGGDDDDDDCCCBBBAAAAAAAAAAAA???>>>>>>>>>>>>>>>??????>>>>>>>>>>>>>>>???@@@AAADDDGGGPPP\\\fffrrr~~~lll```WWWUUURRROOOTTT]]]dddhhhiiifffdddccc^^^YYYWWWUUURRRPPPOOONNNKKKIIIKKKKKKLLLMMMPPPSSSUUUWWWWWWXXXYYYWWWTTTQQQPPPPPPTTTZZZcccmmmtttzzz}}}tttllleee___[[[UUUUUUUUUTTTSSSRRRRRRQQQUUUUUUVVVZZZ```cccccc```]]]ZZZWWWTTTTTTVVVYYY\\\___dddlllttt~~~}}}}}}tttnnnkkkiiidddcccbbbbbbbbbccceeeeeedddccccccbbbaaa```_________bbbeeeiiilllqqqwww{{{}}}{{{xxxwwwvvvwwwxxxyyyxxxvvvuuuuuuuuutttsssrrrqqqppppppooommmgggbbbaaadddgggllluuu|||yyypppiii^^^YYYUUURRRQQQSSS]]]gggwwwvvvmmmdddssssss^^^JJJ???777666666555333333111111111111111111111111111111000000111111222333333333222222333333444555333777666:::AAAAAALLLbbb|||~~~}}}{{{qqqhhhddddddhhhkkk|||fffZZZSSSWWW___fffrrr{{{nnn```OOOCCC>>>>>><<<:::888777555444222111111111////////////////////////////////////////////////111111111111000000000000000111111111111111222222333222333555777<<>><<<;;;888777666444333222111111000000000000000000000000////////////////////////111111111000000000000000000000111111222222222333111000222555888???OOO^^^xxxzzzrrrlllkkkiiihhhiiilllppprrrtttuuuwwwzzz|||zzzuuuqqqooonnnkkkgggaaa\\\WWWTTTOOOMMMJJJIIIIIIIIIHHHFFFDDDCCCBBBAAAAAA@@@@@@@@@>>>>>>===<<<<<<=========AAA@@@???>>>>>>>>>>>>>>>BBBAAA@@@@@@??????@@@@@@CCCDDDHHHNNNRRRZZZhhhuuu}}}jjj```WWWTTTOOOJJJPPPZZZfffmmmsssttttttrrrkkkccc___\\\XXXVVVTTTSSSQQQOOOMMMLLLLLLMMMPPPTTTWWWZZZXXXZZZ[[[ZZZUUUPPPLLLJJJJJJQQQ[[[fffooowww}}}|||tttmmmgggbbbaaa^^^\\\[[[[[[\\\]]]]]]^^^___aaacccdddcccbbb\\\ZZZVVVTTTTTTVVVYYY[[[```dddkkkrrr}}}wwwmmmlllooowww|||uuusssqqqpppooooooppprrrtttsssrrrqqqooommmjjjhhhfffiiilllpppuuuyyy~~~zzzyyyyyy{{{}}}~~~|||xxxtttqqqqqqqqqnnnssszzz~~~pppdddXXXTTTOOOMMMKKKLLLUUU___xxxwwwnnnbbblllvvvYYYJJJ;;;777777555333222111111111111111111111111111111000000111111222333333333222222333333444555444888777:::AAADDDTTToooyyywwwzzzxxxvvvuuuxxxvvvrrrlllhhhiiimmmqqqzzznnn```TTTPPPPPPRRR]]]kkkyyy}}}ppp^^^NNNDDD@@@===<<<888888666444333222222222000000000000000000000000000000000000000000000000///000000000111111111111000000111111222333333333111111333666:::CCCVVVggg{{{vvvnnnkkkjjjhhhhhhjjjnnnrrrtttvvvvvvwwwzzz|||zzztttooommmkkkfffaaa[[[VVVRRRQQQJJJIIIHHHHHHIIIIIIHHHFFFDDDDDDCCCCCCBBBAAAAAAAAA@@@@@@???>>>>>>===>>>>>>>>>>>>>>>???@@@BBBCCCDDD@@@@@@???>>>>>>>>>>>>>>>???@@@CCCGGGJJJOOO[[[gggrrrnnnaaaWWWTTTOOOKKKOOOWWWfffoooxxx|||~~~|||uuunnnccc```[[[XXXVVVUUUSSSQQQMMMLLLKKKLLLNNNRRRVVVXXXXXX[[[^^^^^^YYYRRRLLLHHHGGGMMMWWWaaakkkttt|||}}}vvvqqqgggeeebbb___^^^^^^```aaadddeeefffgggggggggffffff___\\\YYYVVVUUUWWWYYY[[[```ccchhhnnnyyytttkkkhhhhhhnnnwwwzzz{{{yyyvvvtttssstttuuuwwwwwwxxxwwwvvvtttrrrooommmnnnqqquuuzzz~~~}}}|||~~~}}}{{{zzzzzzuuuxxx{{{sssfffVVVQQQMMMJJJHHHIIISSS]]]wwwyyyooo```gggxxx```OOO>>>777777666333222111111111111111111111111111111000000111111222333333333222222333333444555444888777:::BBBIII]]]{{{{{{uuutttyyyyyyqqqooooooppppppnnnjjjhhhjjjpppvvv}}}sssdddVVVPPPKKKJJJTTT```ooozzzuuucccRRRGGGAAA>>><<<999888666555333222222222222222222222222222222222000000000000000000000000......///000111222222333000000111222222333444444222222555888===HHH]]]pppssskkkiiihhhhhhiiilllqqqvvvyyy{{{yyywwwyyyzzzxxxrrrlllhhhfffaaa[[[WWWSSSQQQPPPJJJIIIIIIJJJKKKKKKIIIGGGHHHHHHHHHHHHHHHFFFEEEEEEDDDCCCCCCBBBAAAAAABBBBBB>>>>>>???@@@AAACCCEEEFFFAAA@@@@@@????????????@@@>>>???BBBEEEEEEHHHQQQ\\\gggtttsssdddXXXTTTRRRMMMOOOUUUcccmmmyyy~~~vvvhhhddd___ZZZXXXUUUSSSQQQMMMLLLJJJJJJLLLPPPSSSVVVWWW\\\aaabbb]]]UUUMMMHHHEEEJJJSSS\\\fffpppyyyzzzmmmkkkgggcccbbbccceeefffjjjkkklllmmmllljjjjjjiiibbb___[[[XXXVVVXXXZZZ\\\___aaaeeejjjtttssskkkfffcccfffnnnzzz|||xxxvvvvvvwwwxxxvvvwwwyyyyyyyyyxxxvvvuuusssvvv{{{~~~{{{lllZZZTTTNNNJJJGGGIIISSS^^^ttt|||nnn```cccpppeeeSSS???888777666333222111111111111111111111111111111000000111111222333333333222222333333444555444888777;;;EEEPPPiii{{{uuuuuuxxx}}}yyyuuu}}}vvvnnnlllllllllmmmlllhhhfffiiiqqqxxxxxxiiiZZZRRRKKKGGGOOO[[[gggtttxxxfffUUUIIIBBB???===999888666555333333222222222222222222222222222222000000000000000000000000------...000111222333444000000111222333333444444333444777:::???KKKbbbvvv|||qqqjjjgggggghhhjjjnnnuuuzzz~~~~~~{{{xxxxxxyyyvvvoooiiidddaaa]]]XXXTTTRRRQQQPPPNNNMMMMMMNNNPPPOOOMMMJJJIIIIIIJJJJJJJJJHHHFFFEEEBBBBBBAAAAAAAAAAAABBBBBBAAAAAAAAA@@@AAAAAABBBCCCCCCCCCBBBBBBAAABBBBBBCCCAAAAAADDDFFFFFFFFFNNNXXX```kkkxxxwwwgggYYYVVVTTTPPPPPPTTT___kkkxxxyyymmmhhhbbb\\\XXXUUURRRPPPMMMKKKJJJIIIKKKNNNRRRTTTWWW\\\ccceee```WWWNNNHHHDDDHHHPPPXXXbbbmmmwww}}}sssppplllhhhfffgggjjjkkkmmmoooppppppnnnmmmlllllleeebbb]]]YYYXXXXXXZZZ\\\^^^```cccgggppprrrllleee```bbbiiivvv{{{xxxxxxyyyyyyssstttwwwyyyzzzzzzyyyxxxwww{{{~~~sss```ZZZRRRMMMIIIJJJTTT```rrr}}}mmmdddccclll~~~hhhUUU@@@888777666333222111111111111111111111111111111111000111222222333333333222222333333444555444888777;;;GGGUUUqqq{{{xxxyyywww}}}~~~yyyppppppzzzwwwooommmmmmllllllkkkhhheeeiiirrryyywwwcccVVVPPPNNNQQQVVVcccooo~~~}}}lll[[[NNNEEE???<<<888888666555333333222222000000000000////////////000000/////////111222333////////////000000000000000000000000000000111222111666999:::@@@PPPjjj~~~}}}qqqjjjiiihhhhhhjjjooouuuyyy{{{zzzzzzyyyyyywwwsssmmmhhhaaa[[[UUUSSSTTTVVVTTTQQQPPPPPPOOONNNNNNOOOQQQRRROOONNNLLLIIIHHHIIIJJJKKKIIIHHHEEEBBBAAA@@@AAABBBCCCCCCCCCCCCDDDDDDDDDEEEBBBBBBBBBBBBBBBBBBBBBBBBAAAAAAAAABBBEEEJJJNNNQQQYYYbbbooo|||yyylll^^^WWWSSSPPPQQQSSSaaalllxxx~~~}}}qqqiii```ZZZXXXUUUQQQMMMLLLIIIGGGIIIJJJKKKQQQYYYWWW^^^cccdddaaa[[[PPPFFFCCCFFFJJJRRR]]]hhhrrrwww~~~zzztttkkkggggggiiikkkkkknnnnnnooorrruuutttoookkkgggccc^^^ZZZZZZZZZZZZZZZ]]]___cccgggjjjsssuuujjjeee```aaaeeepppzzzzzzzzzxxxuuuuuuvvvwwwyyy{{{}}}~~~yyykkkaaaWWWPPPKKKJJJRRRZZZxxx{{{jjjhhhqqqnnnZZZEEE<<<:::777333000000000000000000000000000111111111111111111111111222222333444444555555666555888<<>>999999777666444333333333111111000000000/////////111000000//////000111222////////////000000000111222111111111111222222333222555999===FFFYYYqqq|||pppjjjiiihhhhhhjjjooouuuyyyzzzvvvuuusssrrrppplllgggccc^^^YYYTTTSSSUUUVVVUUURRRTTTSSSRRRRRRRRRSSSTTTTTTVVVTTTRRRPPPNNNNNNOOOPPPLLLKKKHHHEEECCCBBBCCCCCCCCCCCCDDDDDDDDDEEEEEEEEECCCCCCCCCCCCCCCCCCDDDDDDDDDCCCCCCCCCEEEHHHKKKNNNTTT]]]iiiuuurrrccc[[[VVVRRRRRRTTT___jjjvvv~~~~~~ssskkkaaaZZZWWWTTTPPPMMMLLLIIIGGGIIIJJJKKKQQQYYYWWW]]]ccccccaaa[[[PPPFFFEEEFFFIIIOOOYYYdddnnnttt|||yyypppjjjiiikkklllmmmsssssstttwwwyyyxxxtttpppjjjfff```\\\\\\]]]]]]]]]___```ccceeegggooovvvkkkeee```___bbbkkk}}}|||zzzzzzwwwuuuttttttvvvxxxzzz}}}ooofff[[[SSSNNNLLLSSS[[[ssspppoooyyyppp\\\GGG===:::777444222111111111111111111111111111111111111111111111111222222333444444555555666555888<<<@@@GGG]]]zzzvvvsssuuu{{{}}}vvvnnniiikkkiiigggfffjjjrrryyysssbbbRRRHHHGGGKKK\\\kkk~~~qqqbbbVVVLLLDDD@@@;;;:::999777555444444444111111111000000000000///222111000000///000000111/////////000000000111111222222222222222333444444444555888@@@NNNcccyyyzzzooojjjhhhggghhhkkkpppuuuxxxyyyrrrpppnnnkkkiiifffbbb___[[[XXXVVVVVVYYYZZZYYYWWWYYYXXXWWWWWWWWWXXXZZZ[[[]]][[[YYYWWWUUUUUUUUUUUURRROOOLLLIIIGGGEEEEEEFFFDDDDDDDDDEEEEEEEEEFFFFFFEEEEEEEEEEEEEEEEEEEEEEEEGGGFFFEEEDDDDDDFFFHHHJJJPPPXXXcccnnnzzz{{{kkk```YYYTTTSSSUUU[[[ggguuu}}}yyyqqqfff]]]YYYVVVRRRPPPLLLIIIGGGIIIIIIKKKQQQXXXXXX^^^ccccccbbb\\\QQQFFFGGGGGGHHHLLLTTT___jjjqqq{{{~~~wwwpppmmmmmmnnnoooxxxyyy{{{~~~|||yyyqqqlllfffaaa```aaabbbbbbbbbbbbcccddddddjjjyyywwwkkkddd^^^\\\^^^eeeuuu{{{yyyvvvsssqqqqqqsssuuuxxx{{{~~~wwwnnncccZZZSSSPPPTTT\\\ppp{{{zzzsss___III>>>;;;777444333111111111111111111111111222222222222222222222222222222333444444555555666555888===AAAIII```yyyyyyzzz}}}zzzuuunnnjjjiiihhhfffggglllsss{{{|||lllZZZKKKHHHKKKWWWiiixxxkkk^^^QQQGGGAAA===<<<:::888777555555555222222111111111000000000222222111000000///////////////000000000111111111222222111222222333444555777666999DDDVVVjjj{{{vvvmmmiiihhhggghhhlllqqquuuwwwwwwrrroookkkhhhfffccc```^^^[[[ZZZYYY[[[^^^___^^^]]]\\\\\\[[[\\\]]]___aaaccccccbbb```^^^\\\[[[[[[ZZZWWWUUUQQQMMMJJJHHHHHHHHHEEEEEEEEEFFFFFFFFFFFFGGGFFFFFFFFFFFFEEEEEEEEEEEEGGGFFFEEEEEEEEEFFFGGGHHHNNNUUU```kkkwwwrrrfff]]]VVVTTTUUUYYYeeesss}}}zzznnnddd]]]YYYVVVTTTMMMJJJHHHIIIJJJKKKQQQXXXZZZ```dddfffeeeaaaUUUJJJIIIGGGFFFIIIQQQ]]]jjjrrr|||~~~~~~uuupppooopppqqqzzz||||||vvvnnnhhheeeeeeeeeeeedddcccbbbcccbbbgggtttxxxjjjddd]]]ZZZ[[[aaappp~~~{{{wwwtttrrrnnnnnnnnnpppsssxxx|||~~~}}}|||{{{~~~yyymmmcccZZZTTTVVV\\\ooorrr___JJJ???:::777444444111111111111111111111111222222222222222222222222222222333444444555555666666888===BBBKKKccc{{{~~~|||xxxtttoookkkggggggfffhhhmmmttt|||uuucccRRRLLLMMMNNNbbb~~~tttfffWWWJJJBBB>>>===;;;999777666555555222222222222111111111111111111111111000000//////000000000000111111111111000000000111111333444444888888;;;HHHZZZlllxxx}}}ssskkkhhhhhhhhhjjjnnnsssvvvwwwvvvqqqmmmiiifffeeecccaaa___[[[[[[[[[]]]___aaaaaa```^^^^^^^^^```bbbeeegggiiihhhgggfffdddcccbbbaaaaaa\\\ZZZUUUQQQMMMJJJIIIIIIFFFFFFFFFGGGGGGGGGGGGHHHFFFFFFFFFFFFEEEEEEDDDDDDEEEEEEEEEEEEFFFGGGHHHIIILLLRRR\\\fffsssyyylllbbbZZZUUUVVVYYYeeerrr|||vvvkkkbbb[[[XXXVVVNNNKKKIIIJJJKKKKKKQQQYYY^^^cccgggjjjkkkggg\\\OOOIIIGGGEEEHHHPPP]]]kkksss|||~~~zzztttqqqqqqsssxxx|||xxxqqqllljjjhhhhhhfffcccbbbbbbaaadddooo{{{zzziiiccc\\\YYYYYY^^^lllyyy|||vvvsssrrrlllkkkjjjkkknnnsssxxx{{{{{{zzzwwwvvvwww{{{uuujjj___XXXXXX]]]iii~~~zzz{{{{{{yyyooo^^^KKK@@@;;;666333333111111111111111111111111222222222222222222222222222222333444444555555666777999===CCCMMMddd~~~~~~zzzwwwtttrrrooolllffffffgggjjjooouuu|||nnn\\\QQQNNNLLL^^^yyy{{{mmm]]]NNNDDD>>>===;;;999777666555444333333333222222222111111000111111111111000000///000000000111111111222222000000000000111333444555888999???LLL]]]kkkqqqssstttzzz{{{pppjjjhhhhhhiiilllpppuuuwwwwwwvvvooommmiiigggfffeeecccaaa]]]]]]]]]^^^___```aaabbbaaaaaaaaabbbdddfffiiijjjkkkkkkjjjiiihhhgggffffff```]]]XXXSSSNNNKKKJJJIIIGGGGGGGGGHHHHHHHHHHHHIIIGGGGGGGGGFFFEEEEEEDDDDDDDDDDDDEEEEEEFFFHHHIIIIIIIIINNNVVV___kkk~~~tttiii___XXXWWWYYYdddpppzzz~~~rrrggg^^^YYYVVVPPPMMMKKKLLLLLLMMMSSSZZZ```dddiiimmmpppnnnbbbVVVJJJHHHFFFHHHPPP]]]kkksssyyy}}}xxxttttttuuuxxx}}}yyytttpppmmmkkkhhhdddaaa```___aaajjjttt|||jjjccc\\\XXXWWW[[[hhhttt}}}xxxvvvuuummmkkkiiihhhjjjooossswww}}}~~~~~~wwwuuurrrppppppssswwwyyy~~~wwwmmmbbb[[[ZZZ___bbbpppxxxtttrrrppplll]]]LLLBBB<<<777444444222222222222222222222222333333333333333333333333222222333444444555555666888999===CCCNNNeeexxxuuurrroooooonnnmmmlllffffffhhhkkkpppvvv{{{|||gggWWWPPPOOO[[[qqq~~~qqqaaaQQQGGG>>>===;;;999777555444444444333333333333222222222//////111111222111000000000000111111111222222222111111111111333444555666666:::CCCQQQ```jjjmmmmmmmmmsss|||}}}tttmmmjjjjjjiiijjjnnnrrrwwwyyyxxxvvvqqqooommmllllllkkkhhhfffccccccbbbaaaaaabbbdddfffeeedddccccccccceeefffggghhhhhhhhhhhhggggggffffffbbb___YYYTTTOOOKKKIIIHHHHHHHHHHHHHHHIIIIIIIIIIIIIIIIIIHHHHHHGGGFFFFFFEEEEEEEEEEEEFFFFFFGGGHHHHHHIIIMMMSSSYYYdddvvv{{{pppddd\\\ZZZYYYcccmmmvvv{{{nnnddd]]]ZZZRRROOOMMMNNNNNNNNNTTT[[[aaaeeeiiinnnsssrrrgggZZZKKKIIIFFFHHHOOO[[[gggoootttyyy}}}xxxwwwxxx{{{{{{vvvrrroookkkfffaaa___\\\\\\ccckkk|||{{{kkkddd]]]WWWTTTWWWbbbnnn~~~{{{zzzzzzpppnnnjjjhhhiiilllqqqtttwwwxxxxxxxxxyyy{{{{{{sssqqqmmmkkkjjjllloooqqqtttvvvyyy{{{~~~|||ssskkkccc]]]]]]bbbaaafffsss}}}tttooommmiii\\\NNNFFF@@@999555555222222222222222222222222333333333333333333333333222222333444444555555666999999===CCCNNNeee{{{ooollliiiggghhhiiijjjiiifffgggiiilllqqqvvv{{{}}}qqq]]]SSSMMMUUUfff~~~ssscccSSSIII>>>===;;;999666555444333444444444333333333222222...///000111222222111000000111111111111222222222222222222333444555777777444:::EEETTTaaaiiikkkjjjkkkpppyyyvvvooolllkkkkkkjjjkkkoootttxxxzzzxxxwwwtttsssrrrrrrrrrqqqnnnllljjjiiihhheeedddeeehhhkkkhhhgggeeedddcccbbbccccccccccccddddddddddddccccccccc___ZZZTTTNNNKKKHHHHHHHHHHHHHHHIIIIIIIIIJJJJJJKKKKKKJJJIIIHHHHHHGGGGGGFFFFFFFFFFFFFFFFFFFFFFFFLLLOOOSSSXXXaaaqqquuuhhh```\\\YYYaaakkksss}}}uuujjjbbb^^^TTTPPPNNNOOONNNOOOUUU\\\```dddiiiooouuutttiii\\\LLLJJJGGGHHHNNNYYYdddlllpppuuu}}}{{{zzzzzz~~~{{{vvvsssmmmgggaaa]]]ZZZXXX]]]dddooo|||wwwmmmeee]]]WWWRRRSSS]]]hhhyyy~~~}}}}}}sssppplllhhhiiilllpppssspppqqqrrrqqqqqqssswwwzzz}}}yyyqqqnnnjjjgggggghhhkkkmmmmmmnnnppprrruuuzzz|||vvvoooiiiccc^^^___dddddddddkkk|||yyyzzzxxxqqqooohhh\\\PPPHHHBBB;;;777666222222222222222222222222333333333333333333333333222222333444444555555666999:::===CCCNNNdddvvviiifffcccbbbdddfffggggggfffgggiiimmmqqqvvvzzz}}}|||jjj\\\OOOQQQYYYjjjuuudddTTTKKKDDDBBB===999888999777555222333333333333222111111000000000000000000000000000111111222333333444444111222444444333333444555<<<<<>>CCCLLL```qqqbbb^^^]]]___``````cccggggggjjjmmmppprrruuuyyy{{{lll\\\RRRRRRVVVeeezzzzzzjjjZZZQQQEEEBBB===:::::::::888666333333333333333222111111111111111111111111111111111111111111222222222222111222444333222222444555===AAAOOObbbooosssvvvzzz{{{uuullljjjjjjiiiggghhhmmmssszzz~~~~~~zzz{{{{{{zzzxxxwwwwwwxxxtttrrrooollljjjiiiiiiiiikkkfff```\\\ZZZYYYYYYXXXYYYYYYXXXWWWVVVUUUUUUTTTXXXVVVSSSPPPMMMKKKJJJJJJKKKKKKKKKKKKJJJJJJJJJJJJJJJJJJIIIIIIHHHHHHGGGGGGHHHHHHIIIHHHGGGHHHKKKMMMLLLLLLOOOTTTZZZeeevvvvvvmmmeee^^^XXXXXX\\\fffrrrzzzvvvlllcccZZZSSSQQQQQQSSSWWW\\\ggglllpppsssuuuuuulllcccUUULLLDDDEEEKKKSSS^^^gggooosssxxx}}}{{{vvvmmmddd___\\\WWWWWWYYY^^^fffsss~~~|||wwwjjjbbbZZZUUUQQQRRRYYYbbbqqq{{{tttllliiijjjlllkkkjjjnnnooopppppppppqqqtttvvv}}}|||{{{{{{|||zzzwwwuuurrrnnniiiggggggiiiiiiiiijjjkkkllllllmmmrrryyy~~~|||nnnccc^^^\\\[[[ZZZ]]][[[___nnnvvvlllhhhssszzzqqqllleeeXXXLLLAAA:::555333222222111111111111222222222222222222222222222222222222444666777888999999888:::???EEENNN___|||yyylll___[[[ZZZ]]]^^^^^^bbbfffgggjjjmmmppprrruuuxxx{{{ppp___VVVRRRRRR\\\oootttcccWWWGGGCCC>>><<<<<<;;;999777333333444444333333222111111111111111111111111111000111111111111111111111222333333333222222444555;;;EEEVVViiissswww{{{}}}|||~~~~~~|||qqqiiigggggggggggghhhmmmttt{{{}}}~~~}}}}}}~~~{{{zzzwwwtttpppmmmjjjhhhiiieee___ZZZWWWVVVUUUSSSUUUTTTSSSRRRQQQPPPPPPOOOTTTRRRPPPNNNLLLKKKJJJJJJLLLLLLKKKKKKKKKJJJJJJJJJJJJJJJJJJJJJIIIIIIIIIIIIIIIJJJKKKJJJIIIJJJMMMOOOMMMMMMOOOSSSXXXaaaqqqxxxlllddd]]]XXXTTTTTTXXX```llltttzzzzzzkkkaaaWWWTTTSSSTTTYYY___iiimmmrrruuuxxxyyyrrriiiWWWNNNFFFFFFKKKRRR]]]fffmmmqqqwww{{{~~~yyyooofff```[[[VVVTTTVVVWWW\\\fffrrr{{{}}}yyyttthhh```XXXSSSPPPPPPVVV^^^kkkzzzyyyqqqmmmlllmmmlllkkkooopppqqqppppppqqqtttvvvzzzyyyyyyyyyyyywwwssspppqqqnnnkkkiiiiiiiiihhhggghhhiiiiiijjjlllpppvvv{{{}}}vvvhhh___ZZZXXXWWWYYYXXX[[[iii}}}vvvhhh___gggzzztttlll___PPPDDD<<<888666222222111111111111222222222222222222222222222222333444666888:::<<<===>>>;;;===BBBHHHOOO^^^wwwuuuggg[[[WWWVVVYYY[[[\\\```eeegggiiimmmppprrrtttwwwzzzwwwgggYYYQQQMMMTTTfff{{{nnn]]]LLLDDD>>>======;;;888777444444444444444333333222111111111111111111111111...//////000111111222222222333333333222222555777===JJJ]]]llltttyyy||||||}}}vvvmmmgggeeefffhhhhhhjjjooovvv}}}}}}xxxqqqlllhhhgggccc^^^ZZZWWWVVVTTTSSSTTTTTTSSSRRRQQQPPPOOOOOOPPPPPPOOONNNMMMLLLKKKKKKKKKKKKKKKJJJJJJJJJIIIIIIIIIIIIIIIIIIIIIJJJJJJJJJJJJKKKKKKKKKJJJKKKNNNQQQPPPOOOPPPTTTWWW^^^mmm{{{~~~ooobbbZZZUUURRROOONNNQQQXXXcccllltttrrrggg\\\WWWUUUVVVZZZ```hhhmmmqqqtttyyy{{{vvvnnn[[[RRRIIIHHHLLLRRR\\\eeelllpppvvvzzz~~~~~~zzzqqqgggaaa\\\UUURRRTTTXXXZZZ```jjjtttxxxuuupppeee^^^WWWRRRNNNMMMSSSZZZeeesssxxxssspppppppppoooqqqqqqrrrqqqpppqqqsssuuuyyyyyyyyyyyyyyyvvvrrroooooonnnmmmkkkjjjiiigggfffjjjjjjjjjjjjlllpppuuuxxx|||~~~rrreee\\\WWWUUUUUUSSSVVVaaattt{{{jjj^^^aaa||||||tttgggWWWIII???;;;999333333222111111111222222222222222222222222222222666777888;;;===@@@BBBDDDCCCCCCEEEIIIPPP]]]uuurrreeeWWWSSSRRRUUUXXXYYY^^^dddgggjjjnnnqqqssstttwwwyyy~~~qqq]]]RRRKKKPPP___tttiiiTTTHHH???>>>>>>:::777777444555555555555444333333111111111111111111111111,,,---...///111333444444222333333333333444777:::EEESSSdddooowww~~~vvvrrrkkkfffeeegggiiikkkmmmrrrxxxxxxqqqllliiifffaaa]]][[[ZZZWWWVVVUUUUUUTTTSSSRRRQQQPPPPPPNNNNNNMMMMMMMMMLLLKKKKKKJJJJJJJJJIIIIIIIIIHHHHHHHHHHHHHHHHHHIIIIIIIIIIIIIIIJJJJJJJJJJJJKKKNNNQQQQQQPPPQQQSSSUUU[[[hhhuuuwwwgggZZZSSSPPPMMMKKKHHHIIIPPPZZZccclllzzzwwwlllaaaZZZXXXWWW[[[```gggkkkooorrrxxx{{{wwwppp^^^TTTJJJHHHKKKPPPYYYaaalllpppvvvzzz~~~zzzqqqhhhccc]]]WWWTTTUUUYYYYYY\\\eeennnsssqqqmmmccc]]]VVVRRRNNNKKKPPPWWWaaannn~~~~~~wwwtttrrrrrrrrrsssttttttsssqqqrrrtttvvv{{{{{{{{{||||||yyyuuuqqqooooooooonnnllljjjiiiiiinnnmmmlllmmmooorrruuuwwwzzz|||~~~~~~mmm```WWWTTTPPPOOOQQQZZZjjj}}}pppaaa```vvvyyymmm]]]MMMAAA;;;999444333333222111111222222222222222222222222222222777888:::===@@@DDDGGGIIILLLJJJHHHJJJOOO]]]sssnnn```UUUQQQPPPRRRUUUWWW]]]cccgggkkkooorrrtttuuuwwwxxxzzzeeeXXXNNNOOOZZZlll{{{```PPPBBB@@@???:::777888555555666666555555444333222222222222222222222222------...000222333444555222333333333444777;;;>>>JJJXXXhhhsss}}}{{{xxxqqqmmmiiieeeeeegggkkknnnrrruuuzzzzzzvvvpppmmmhhhdddbbb___]]]ZZZWWWVVVUUUUUUSSSSSSRRRQQQMMMMMMNNNNNNMMMMMMLLLKKKKKKJJJJJJJJJIIIIIIIIIIIIIIIIIIHHHHHHHHHHHHHHHHHHHHHIIIJJJJJJJJJKKKNNNQQQQQQPPPQQQSSSTTTXXXeeeqqq}}}rrrcccWWWPPPMMMKKKIIIDDDEEEJJJRRRZZZdddrrr{{{pppeee___\\\ZZZ]]]bbbhhhlllooorrrxxx}}}zzzsss___UUUKKKGGGIIIMMMVVV^^^kkkooouuuyyy}}}zzzrrrkkkgggbbb\\\ZZZ[[[XXXYYY\\\cccjjjooonnnmmmbbb\\\VVVRRRMMMJJJNNNTTT^^^jjjzzz{{{wwwuuuuuuvvvxxxxxxxxxwwwuuuuuuwwwyyy}}}}}}~~~zzzvvvrrrrrrsssqqqooonnnnnnoootttrrrppppppqqqtttuuuuuuvvvxxx{{{~~~vvveeeXXXRRRLLLLLLMMMTTTbbbuuuwwwgggbbbooo~~~|||ssseeeSSSDDD;;;777555444333222222111222222222222222222222222222222666777999<<<@@@EEEIIILLLQQQLLLIIIIIINNN[[[ppp}}}lll]]]UUUQQQOOOQQQTTTVVV\\\bbbhhhlllqqqtttuuuvvvxxxyyyppp```SSSQQQUUUbbb}}}lllXXXGGGCCCAAA;;;888:::666666666666666555444444222222222222222222222222000000111111222333333333222333444444666999>>>BBBQQQ```rrr{{{vvvssskkkiiifffdddcccfffkkkooowwwyyy{{{{{{wwwqqqmmmhhhddd```]]]ZZZYYYYYYXXXWWWVVVUUUUUUQQQQQQRRRRRRRRRQQQPPPOOOLLLLLLLLLLLLKKKKKKKKKKKKKKKKKKJJJJJJIIIIIIHHHHHHHHHIIIJJJJJJJJJLLLOOOQQQUUUTTTTTTVVVVVVZZZfffrrr{{{pppbbbVVVOOOLLLJJJIIIEEEEEEGGGMMMSSS[[[iiivvv~~~tttjjjdddaaa^^^```ccclllooorrruuuzzz}}}wwwcccYYYNNNJJJKKKNNNVVV^^^jjjmmmsssxxx{{{~~~{{{tttnnnkkkhhhcccbbbccc^^^```dddgggjjjlllllllllbbb\\\WWWSSSNNNJJJLLLRRR\\\fffvvv|||zzz{{{}}}~~~~~~~~~|||zzzzzz|||~~~~~~{{{vvvwwwwwwvvvsssssstttwwwxxxuuurrrqqqssstttsssrrrtttvvvzzz}}}lll\\\SSSJJJJJJKKKPPP\\\ooopppfffkkkwww|||ppp]]]KKK???999555555444333222222222222222222222222222222222222333444666999>>>DDDHHHKKKNNNJJJGGGHHHLLLWWWjjj{{{pppbbbWWWRRROOOQQQSSSVVV[[[bbbjjjmmmrrrvvvwwwxxxxxxyyyxxxgggXXXRRRRRR[[[tttuuu^^^KKKEEECCC<<<999<<<666666666666666555555444222222222222222222222222444333333333222222111111222333444555777;;;@@@DDD\\\mmm|||wwwsssppphhhgggdddbbbbbbfffkkkooozzz{{{|||~~~xxxrrrmmmgggbbb___^^^]]]]]]\\\[[[ZZZYYYXXXVVVWWWXXXXXXXXXVVVUUUTTTNNNNNNNNNNNNMMMMMMMMMMMMMMMMMMLLLKKKJJJIIIIIIHHHIIIJJJKKKKKKKKKMMMPPPRRRZZZYYYYYY[[[[[[___jjjvvvzzzpppaaaVVVPPPMMMKKKIIIGGGFFFFFFKKKOOOVVVcccpppwwwwwwmmmhhhdddaaabbbeeeooorrruuuwww}}}{{{hhh]]]RRRNNNNNNRRRYYYaaahhhlllqqqvvvyyy}}}|||vvvpppooommmiiigggiiihhhkkkmmmnnnllljjjjjjjjjbbb\\\WWWSSSNNNJJJLLLQQQZZZdddttt~~~~~~}}}yyyzzz{{{yyywwwwwwyyy}}}zzzwwwsssrrrssstttrrrppptttvvvzzzrrr```VVVIIIIIIIIINNNYYYlllwwwjjjjjjqqqyyyfffRRRDDD>>>666555444333222222222222222222222222222222222222111222333777<<>>:::;;;888777777666666666666777444444444333333222222222111111111000111111222333333666333444999888CCCZZZnnn{{{{{{uuurrrnnnkkkdddcccbbbaaacccgggkkkmmm{{{zzz{{{yyysssnnniiifffbbb```^^^]]]]]]^^^\\\[[[XXXVVVUUUUUUVVVVVVUUUSSSTTTRRRQQQQQQQQQQQQPPPOOOQQQNNNKKKKKKMMMLLLJJJGGGIIIJJJJJJJJJJJJLLLPPPSSSWWW[[[_________dddoooxxx{{{oooccc[[[TTTMMMIIIIIIDDDDDDDDDEEEJJJSSS^^^eeennn{{{yyynnnddd```bbbgggkkksssxxx{{{|||qqqdddUUUMMMKKKLLLTTT[[[gggjjjmmmqqquuuyyy~~~{{{yyywwwuuusssqqqnnnqqqqqqqqqpppooommmjjjiiibbb^^^XXXQQQLLLJJJJJJKKKYYYcccqqq}}}|||zzzxxxxxxxxxzzzzzz|||xxxuuutttuuuuuusssqqqrrrvvv{{{fffSSSLLLIIIHHHLLLTTTbbbvvv~~~ooojjjooo{{{qqqZZZFFF:::777555333333444444333222333333222111111222333333666777888888999;;;???CCCFFFBBBAAAEEELLLVVVeeerrrxxxlll\\\VVVRRRQQQQQQSSS[[[ccclllpppvvvzzz{{{zzzyyyxxxsss___SSSOOOQQQaaarrr{{{bbbLLLFFFDDD???;;;<<<888777777666666666666666444444444333333222222222111111111111111222222333222555222444:::<<>>CCC??????CCCJJJTTTcccqqq~~~wwwlll[[[VVVQQQQQQQQQSSSZZZcccnnnrrrxxx{{{|||{{{zzzzzzxxxeeeXXXPPPOOO[[[kkkwwwbbbNNNGGGEEE???<<<===888888777666666666666666444444333333333333222222111111111111111222333333111444222444<<>><<<<<>><<<:::999888666555555555555222222333333333333444444222222222222222333444444222666444555;;;BBBXXXxxxyyymmmdddbbbaaaaaacccggglllrrruuu{{{~~~xxxtttqqqooommmkkkjjjhhhfffffffffeeecccaaa^^^___```___]]]\\\]]]^^^\\\___bbbdddfffhhhkkknnnssswww}}}uuuhhh___XXXPPPKKKKKKDDDCCCAAA???>>>AAAFFFKKKWWW```kkkrrrxxx{{{yyytttllliiieee```^^^]]]^^^___fffkkkpppsssxxxuuugggWWWLLLEEEBBBDDDHHHSSSZZZdddmmmrrrtttuuuuuu|||~~~|||vvvpppnnnnnnlllgggbbb___[[[UUUOOOKKKJJJJJJKKKRRR^^^ooo~~~ooo^^^RRRNNNKKKKKKMMMSSSaaannn~~~||||||yyylllYYYKKK???<<<777444444444444333111222222333333222222111000222333333333222444555888999<<>>EEE\\\}}}{{{ssshhh```[[[\\\^^^bbbiiirrryyy~~~~~~|||{{{yyyvvvtttqqqtttuuutttqqqppprrrtttzzz}}}~~~pppfff^^^UUUOOONNNIIIHHHEEEAAA???@@@CCCGGGFFFPPP\\\gggrrryyyyyytttlllhhhbbb\\\XXXVVVWWWWWW[[[```ccceeejjjssswwwwwwtttfffVVVKKKDDD@@@AAAFFFIIIQQQ\\\fffnnntttwwwyyyqqqwww}}}~~~||||||{{{tttooojjjkkknnnlllfff___```\\\VVVOOOKKKHHHHHHIIIPPP\\\nnn|||nnn^^^VVVRRRQQQQQQQQQTTT]]]hhhooo{{{}}}{{{zzzqqq___QQQBBB===888555444444444444111222333444444333222111222444777888777888999:::777888<<<@@@CCCMMMaaasssxxxpppfff[[[[[[gggxxxwwwsssqqqllleee\\\XXXUUUUUUWWW[[[dddmmmvvvxxx|||~~~lllhhhmmm~~~yyynnn\\\IIIAAACCC===;;;888888888999888777555444333333222222333333777555111///...000222444444444666888;;;IIIddd|||}}}uuummmfffaaa]]]]]]___dddkkkttt|||wwwiii___XXXSSSOOOLLLJJJGGGCCC@@@?????????CCCKKKSSS\\\iiiuuuxxxsssppphhhaaa\\\WWWSSSSSSWWWWWWYYY]]]bbbhhhmmmppprrrpppdddWWWNNNGGG@@@???AAAHHHOOOYYYcccjjjooorrruuuwwwyyy|||{{{uuuooonnnmmmkkkiiifffdddbbb^^^ZZZUUUOOOKKKJJJJJJJJJPPP[[[lll~~~}}}|||nnn^^^WWWRRRPPPTTTXXXYYY[[[___fffppp|||xxxgggXXXFFF>>>888666444111111333111111111111111111111111222333444444333333555777777888;;;@@@EEEOOObbbttt|||hhh```YYY\\\kkk|||xxxsssnnnooopppfffbbbZZZUUUVVVZZZ^^^eeelllppptttyyy{{{{{{|||~~~xxxmmmfffxxxsss```LLLBBBBBB>>><<<999888888999888777555444333333222222333333666555333111111222444555444444666888;;;IIIddd{{{}}}|||zzzsss}}}|||wwwpppiiiaaa]]]]]]]]]___ccckkkttt}}}zzzlllbbb[[[TTTPPPLLLJJJFFFCCC@@@???>>>>>>@@@GGGOOOWWWdddpppuuurrrqqqiiiaaa\\\WWWRRRRRRUUUUUUVVVZZZ___dddjjjnnnpppnnnbbbUUUMMMEEE@@@???AAAEEELLLWWWaaahhhnnnrrruuuyyyzzz|||~~~~~~}}}{{{tttooommmmmmllljjjhhhfffdddccc^^^[[[UUUPPPLLLJJJJJJJJJPPP[[[lll~~~}}}}}}tttdddZZZUUUSSSWWWZZZZZZZZZ\\\ccckkkuuu}}}|||ppp{{{}}}kkk[[[III@@@999777555222222444222222222222222222222222222333444444333333555777888999<<<@@@FFFQQQeeexxx}}}jjj```XXX]]]mmm{{{tttqqqmmmpppqqqiiibbbZZZUUUWWWZZZ___eeelllppptttxxxzzz{{{{{{~~~mmm```pppyyygggTTTHHHDDD???===:::888999999888777555444444333333333333333444444333333333444555555444555666888;;;IIIddd{{{{{{yyyqqqggglllwww}}}yyyxxxuuuqqqllleee___\\\]]]]]]^^^cccjjjttt~~~qqqfff^^^WWWRRRLLLJJJFFFBBB???>>>===>>>>>>BBBHHHPPP\\\jjjqqqrrrrrrjjjbbb]]]WWWPPPOOORRRQQQRRRUUUZZZ```eeejjjmmmkkk___SSSJJJDDD>>>>>>@@@BBBIIITTT^^^gggmmmrrruuu{{{|||}}}~~~~~~}}}}}}~~~zzzvvvrrrmmmiiijjjjjjiiihhhgggeeedddccc___\\\VVVPPPLLLJJJJJJJJJPPP[[[lll~~~~~~~~~}}}lll\\\WWWUUUXXX[[[YYYXXXXXX___fffooovvvzzzsssdddjjj{{{ooo___MMMCCC:::777666333222444333333333333333333333333222333444444333333555777999999;;;@@@FFFSSSiii|||lllaaaYYY___rrrtttnnnmmmkkkpppssskkkbbb[[[VVVWWW[[[___fffmmmqqqssswwwyyyyyy{{{|||~~~~~~eee]]]lllooo]]]OOOGGGAAA>>>;;;999999999888777555555444333333333333333222222333444444555555444444555777999<<>>LLLgggrrrgggbbbhhhqqqrrrzzzxxxuuuwwwwwwuuupppiiiccc```___\\\]]]```eeellluuu~~~wwwlllbbbZZZUUUMMMJJJGGGBBB???===============@@@GGGRRR^^^kkkttttttmmmfff```YYYPPPLLLMMMLLLMMMNNNRRRXXX___fffjjjhhh]]]QQQHHHBBB===<<>>======>>><<>><<<:::999888666666666555444444444444444333333333333333222222222444555999<<>>>>>>>><<<>>>EEEMMMVVVdddrrruuuoooiiieee]]]SSSNNNNNNIIIHHHIIILLLRRR[[[ccchhhlllaaaTTTKKKDDD>>>===???@@@FFFOOOZZZccckkkrrrwwwzzz{{{|||}}}rrrmmmfffaaa___^^^^^^^^^```````````````___^^^^^^YYYVVVRRRNNNKKKKKKLLLMMMVVV```ppp|||kkkXXXPPPOOONNNMMMMMMSSS[[[fffrrr~~~mmmddd```pppwww```OOO???888888666555444222222222222222222222222222333444444333333555777888888;;;???CCCNNNbbbttt|||kkkhhhhhhrrrxxxkkkgggiiiiiiqqquuunnnbbb\\\YYY^^^eeellluuu}}}~~~{{{xxxvvvwwwwwwuuusssrrrccc^^^```rrrkkkXXXFFFCCC???<<<;;;999888666666666555444444444444555666555444333333333333333333555999===DDDTTTqqqrrriiiggglllwwwvvvggg___^^^```\\\___eeekkkqqqvvvyyy{{{~~~sssjjjaaa[[[PPPNNNJJJEEEBBB@@@???>>>>>>;;;===EEELLLTTTbbbpppuuupppjjjfff^^^TTTOOONNNGGGGGGGGGIIIPPPYYYbbbgggnnncccUUULLLEEE???===@@@???EEENNNXXXaaaiiiqqquuu{{{{{{{{{|||}}}rrrmmmgggcccaaaaaaaaaaaa````````````___^^^]]]]]]WWWTTTPPPMMMKKKKKKLLLMMMWWWaaaqqqttt^^^RRROOONNNMMMMMMSSS\\\hhhuuummmccc^^^kkkvvvcccRRRAAA::::::888666666333333333333333333333333222333444444333333555777::::::===@@@DDDNNN```qqq|||jjjiiikkkuuuwwwjjjgggiiijjjsssxxxqqqbbb]]]ZZZ___fffnnnxxx}}}yyywwwwwwwwwtttrrrxxxbbbYYYWWWeee|||uuufffVVVHHH=========888777;;;888888777777666666555555333555666777777666444333333777;;;===EEE\\\~~~lllccchhhuuurrrfff```\\\[[[[[[___dddiiimmmqqquuuxxx~~~|||tttlllddd^^^SSSNNNHHHDDDCCCBBB???<<<>>><<<===BBBHHHPPP___lllrrruuussskkkbbbZZZSSSLLLIIIGGGFFFHHHKKKQQQ]]]iiiooojjj___RRRGGG@@@>>>???CCCHHHQQQ[[[dddkkkppprrrzzzzzzzzzzzzzzzzzzzzzzzz}}}~~~~~~tttpppkkkhhhffffffeeeddddddbbb```_________]]][[[ZZZVVVRRRQQQMMMHHHJJJNNNTTT```qqqgggWWWQQQOOONNNOOOTTT\\\lll}}}yyyfffYYYddd|||~~~kkkWWWDDD===:::777444555222222222222222222222222111222444555666777777777:::999:::???DDDMMM^^^mmmxxxkkkhhhmmm}}}rrrjjjbbbbbbjjjrrrrrrppp```]]]\\\bbblllvvvzzz{{{~~~{{{xxxwwwwwwwwwxxxvvvbbbWWWRRR\\\ooosss]]]LLL???===>>>999777999888888777777666666555555333333222222222222333333333777:::>>>IIIcccmmmgggooovvviiiaaa]]]\\\[[[^^^dddiiimmmrrrvvvyyy~~~~~~}}}uuummmeee^^^TTTNNNHHHEEEDDDCCC@@@===>>>===>>>BBBGGGPPP]]]jjjrrrvvvvvvnnneee]]]UUUNNNKKKGGGFFFGGGJJJOOO\\\hhhqqqlllbbbTTTHHHAAA???@@@BBBGGGPPPZZZdddkkkooorrryyyyyyyyyyyyyyyzzzzzzzzz}}}~~~xxxtttooolllkkkjjjjjjjjjhhhfffdddccccccaaa___]]]ZZZVVVRRRQQQMMMIIIJJJOOOWWWbbbssssssaaaWWWQQQNNNOOOTTT\\\mmm{{{hhh[[[cccxxxppp\\\GGG>>>:::666444555222222222222222222222222222333333444555666777888:::999:::>>>CCCLLL\\\kkk}}}xxxhhhfffmmm|||ppphhhaaaaaaiiioooooolll^^^[[[[[[```kkkuuuzzz{{{}}}{{{zzzyyyyyyzzzvvvdddWWWNNNSSS```tttgggSSSAAA>>>???;;;777777888888777777666666555555777666444333333444666777333666999???NNNlllmmmkkkxxxwwwhhh```\\\[[[ZZZ^^^dddjjjnnnsssxxx{{{}}}|||}}}yyyvvvtttrrrvvv|||xxxpppeee^^^SSSOOOIIIEEEEEEDDDAAA??????===>>>CCCGGGNNN[[[hhhrrrwwwxxxrrriiiaaaXXXOOOMMMHHHFFFFFFGGGNNN[[[hhhtttoooeeeWWWIIIAAA@@@AAAAAAFFFOOOZZZdddkkkppprrrwwwwwwxxxxxxyyyyyyyyyzzz|||~~~}}}}}}|||vvvrrrqqqrrrrrrrrrnnnllliiihhhgggeeebbb```ZZZVVVRRRQQQMMMJJJLLLPPPYYYeeeuuuqqq```TTTOOOOOOSSSZZZkkk}}}mmmaaaeeeuuuwwwdddMMM@@@:::666444444333333333333333333333333444333333333444666888999:::999:::>>>AAAIIIYYYhhhwwwtttcccdddmmm||||||llleee______eeeiiihhheeeZZZXXXYYY^^^iiisssyyy|||~~~}}}|||zzzgggZZZPPPQQQZZZggg}}}pppXXXDDD???@@@<<<777666888888777777666666555555666555444444444555666777555666888@@@RRRsss{{{lllooorrrddd]]]ZZZYYYZZZ___eeejjjoootttyyy}}}}}}{{{zzz|||}}}wwwtttqqqnnnlllpppvvv}}}{{{rrrfff]]]SSSNNNHHHEEEEEEDDDBBB???@@@>>>???CCCGGGMMMYYYeeeqqqwwwyyyuuummmdddZZZQQQOOOJJJFFFEEEFFFLLLYYYfffuuurrriii[[[KKKBBB???AAAAAAFFFPPPZZZdddlllqqqsssuuuuuuvvvwwwwwwxxxyyyyyy|||}}}{{{zzz|||{{{zzzzzzzzzyyytttqqqnnnkkkiiigggdddaaaZZZVVVRRRQQQMMMJJJMMMSSS[[[fffvvvkkkXXXQQQQQQPPPVVVgggtttiiikkkxxx~~~lllTTTCCC:::666555444333333333333333333333333555444333333444666999::::::999:::===@@@HHHVVVdddqqqmmm^^^bbbmmm|||~~~xxxhhhbbb\\\\\\```bbb```]]]VVVUUUWWW^^^hhhrrrxxx{{{~~~|||iii\\\SSSSSSXXX```pppsss[[[EEE@@@AAA===888777888888777777666666555555...///111222222222111000666666999BBBWWWxxx{{{qqqzzz|||kkk___[[[ZZZ[[[[[[```fffkkkpppuuuzzz~~~zzzyyyxxx{{{}}}wwwrrrnnnkkkhhheeelllqqqyyy~~~tttggg^^^SSSNNNHHHEEEEEEDDDAAA>>>???>>>???CCCFFFLLLWWWcccmmmtttxxxuuunnnfff\\\TTTQQQLLLGGGFFFFFFKKKXXXeeetttssslll___OOOCCC???@@@BBBHHHQQQ[[[eeelllqqqssssssssstttuuuvvvwwwxxxyyy{{{||||||yyyxxxzzz|||}}}~~~xxxuuuqqqmmmkkkgggccc```ZZZVVVRRRQQQNNNKKKOOOUUU\\\gggwwwsss]]]TTTTTTPPPUUUeee{{{qqqsssrrrZZZFFF;;;777666444333333333333333333333333555444333333444666999;;;:::999:::===@@@GGGUUUbbbnnn}}}~~~cccZZZbbbooo||||||ttteee```ZZZXXXZZZ[[[YYYVVVSSSTTTXXX___iiiqqqxxx{{{~~~~~~lll___TTTSSSUUUZZZgggvvvqqq[[[GGGAAAAAA<<<888999888888777777666666555555...000222444555444222111777777:::EEE[[[|||}}}qqqddd\\\[[[\\\^^^]]]aaagggmmmqqqvvv{{{~~~yyyxxxxxx{{{~~~|||}}}|||{{{|||~~~{{{uuupppllliiieeecccfffkkksss~~~~~~uuuiii___VVVQQQJJJGGGFFFDDDAAA>>>>>>===???CCCFFFKKKVVVaaakkkrrrvvvtttnnnhhh```XXXSSSNNNJJJHHHGGGKKKWWWcccssstttqqqeeeTTTFFFAAAAAACCCHHHQQQ[[[dddkkkppprrrpppqqqrrrtttuuuwwwxxxxxxzzz|||~~~~~~}}}xxxuuuvvvwwwyyy~~~{{{xxxsssoookkkgggbbb___[[[VVVRRRQQQNNNLLLPPPWWW___jjjzzzxxxbbbXXXWWWTTTWWWeee~~~vvv{{{}}}uuu___HHH<<<999777444333333333333333333333333555444444444555777999:::999999:::>>>AAAGGGTTTbbbmmm{{{|||nnn\\\WWWcccrrr~~~yyyoooddd___XXXTTTTTTTTTSSSQQQQQQUUU[[[ccckkkrrrwwwzzz|||~~~ssscccVVVQQQQQQUUUcccssskkkXXXGGGBBB@@@;;;999;;;888888777777666666555555444444555666777777777777666666;;;IIIaaaxxxxxx||||||sssggg]]]YYYYYY\\\^^^___ccchhhmmmrrrvvvzzz~~~xxxxxxxxx{{{~~~||||||yyyxxxvvvvvvxxxyyyzzzyyy{{{{{{wwwvvvxxx{{{~~~|||}}}}}}~~~|||wwwrrrnnnkkkgggdddcccfffmmmyyy}}}uuukkkcccZZZTTTMMMIIIHHHFFFBBB???===<<<>>>BBBFFFKKKVVVaaaiiipppuuusssoookkkddd]]]TTTPPPLLLJJJIIILLLWWWbbbrrrvvvvvvkkkZZZKKKDDDCCCCCCHHHPPPYYYbbbiiimmmnnnooopppqqqrrrtttvvvwwwxxxyyy{{{~~~{{{{{{{{{~~~}}}vvvrrrrrrsssuuuyyy~~~zzzuuuppplllgggbbb^^^[[[VVVRRRQQQNNNMMMRRRXXXcccnnn}}}zzzfff\\\[[[UUUWWWccc{{{yyy|||vvvaaaJJJ>>>;;;888444444444444444444444444444444444555666777888999999999888;;;>>>AAAGGGUUUbbbmmm|||~~~sssaaaXXXVVVddduuuxxxllleee^^^WWWQQQOOOOOOOOONNNPPPVVV___gggooossswwwxxxzzz{{{}}}zzziiiXXXPPPOOOTTTccctttzzzgggVVVGGGCCC@@@:::999===888888888777666666555555555444333222333555777999555666<<>>BBBFFFKKKVVVaaaiiipppuuusssppplllgggaaaUUUQQQMMMLLLKKKMMMVVVaaarrrxxxyyyppp^^^NNNGGGEEEBBBGGGOOOXXX```fffjjjlllnnnoooppprrrtttvvvwwwxxxyyy{{{~~~|||yyywwwwwwyyy}}}uuuppppppqqqrrrwww||||||wwwrrrmmmhhhbbb___[[[VVVRRRQQQNNNNNNRRRYYYhhhrrr{{{iii___]]]UUUVVVaaawwwzzzwwwcccLLL???<<<999444444444444444444444444444333444555777888888888888888888;;;???BBBHHHUUUbbbnnn~~~{{{ggg[[[XXXVVVeeevvvwwwjjjeee___VVVOOOMMMMMMMMMMMMPPPWWWaaajjjqqqtttvvvwwwyyyzzz{{{}}}~~~rrr^^^TTTOOOPPP___pppzzziiiYYYHHHBBBBBB@@@======;;;:::888777555444444444555444444444444555666666555<<>>AAAGGGTTTbbbnnn{{{|||dddWWWTTTWWWiii{{{zzzlllccc\\\UUURRRPPPMMMMMMPPPOOOUUU___jjjtttxxxxxxwww{{{{{{yyyyyyyyyyyy{{{{{{xxxdddYYYSSSSSS```ppp{{{iiiYYYHHHBBBAAA>>><<<;;;999888777666666555666666555444444444444555666666555:::@@@LLLccc}}}~~~zzzmmmffflllsssnnnfff^^^WWWWWWXXXXXXZZZ]]]dddggglllrrrwwwyyyzzz{{{}}}{{{zzz{{{}}}|||||||||{{{xxxuuurrrpppjjjooorrrqqqssswwwzzzyyy{{{zzzxxxwwwyyy}}}~~~zzzxxxyyyzzz{{{|||{{{{{{|||wwwsssmmmgggbbb```bbbdddhhhooozzz~~~xxxsssnnnhhhccc```ZZZRRRLLLJJJHHHEEEBBB???@@@AAAAAAEEEMMMYYYaaaiiiooosssrrrqqqnnnggg```[[[UUUPPPOOOOOOOOOUUU[[[iiixxxqqq^^^SSSKKKDDDEEEGGGLLLUUU___fffjjjjjjmmmpppsssuuuuuuuuuvvvwww|||}}}~~~yyysssrrrpppooottt~~~{{{tttvvvvvvrrruuu|||zzzwwwsssooollliiidddbbbZZZVVVSSSQQQOOONNNUUU^^^nnnxxxtttiiieeeaaa```bbbjjjvvvwww}}}|||}}}uuucccQQQBBB999555444555444444333333444444555333444555666777888888999:::999;;;>>>AAAGGGUUUbbbnnn|||{{{cccVVVTTTXXXiiiyyy{{{ooohhh___WWWSSSPPPMMMNNNQQQSSSXXXbbbnnnvvv{{{{{{zzzzzzyyyxxxxxxxxxxxxyyyzzzmmm```WWWUUU```ooo{{{iiiZZZJJJCCC@@@===:::999777777666666666666777777555555444444555555666777888:::@@@NNNdddzzzwwwvvv~~~uuujjjdddlllsssnnnbbb[[[VVVVVVXXXYYY\\\aaafffjjjoootttyyy{{{||||||}}}|||{{{{{{}}}~~~}}}|||||||||{{{zzzwwwsssooommmgggmmmrrrsssuuuyyy{{{zzzzzzyyywwwwwwyyy~~~|||{{{|||~~~~~~}}}|||~~~~~~zzzuuunnnfffaaa^^^___aaadddjjjsss~~~~~~xxxsssnnnhhhdddaaa\\\TTTOOOMMMJJJGGGCCC???@@@AAAAAADDDLLLXXX```gggmmmrrrrrrqqqoooiiibbb___XXXSSSRRRQQQQQQUUU[[[gggvvv|||qqq___SSSKKKEEEDDDGGGLLLUUU^^^eeehhhiiilllnnnrrrttttttuuuvvvwwwzzz{{{|||~~~zzztttqqqnnnlllpppyyyxxxyyyxxxuuuwww}}}sssqqqnnnllljjjhhheeebbbYYYUUURRRPPPNNNPPPXXXbbbrrr{{{{{{qqqmmmkkkhhhdddffflllvvvuuuuuu~~~|||uuudddRRRCCC999555333555444444333333444444555444555555666777888999::::::999;;;>>>AAAHHHVVVcccooovvv___UUUTTT\\\lll{{{}}}ssskkkbbbYYYTTTQQQOOOPPPSSSTTT[[[eeepppxxx{{{||||||zzzyyyxxxwwwwwwxxxyyyzzzsssdddYYYVVV___kkkyyykkk\\\MMMEEEBBB===::::::888777777666666666666666555555555555555666666777:::;;;BBBRRRhhhyyy~~~|||zzzqqqooovvvqqqiiieeelllrrrmmm```ZZZVVVVVVXXXYYY]]]ccchhhkkkoootttxxxzzz{{{{{{yyyxxxyyyzzz}}}}}}|||{{{zzzzzzyyyxxxuuupppmmmjjjfffnnntttvvvyyy}}}~~~|||zzzyyywwwwwwyyy~~~{{{{{{}}}{{{|||}}}xxxpppgggaaa]]]^^^___aaafffnnnxxx~~~xxxtttoooiiieeebbb\\\VVVQQQOOOLLLGGGCCC@@@AAAAAAAAADDDLLLWWW___ffflllrrrssssssrrrmmmfffbbb\\\VVVTTTRRRQQQUUUZZZeeerrryyyppp```TTTKKKFFFEEEHHHNNNVVV^^^dddhhhiiilllnnnrrrttttttuuuwwwyyyzzz{{{|||~~~zzzuuuooollljjjmmmttt~~~{{{zzzyyyvvvxxx||||||uuullljjjhhhggggggfffdddbbbZZZVVVRRRPPPNNNPPPZZZdddsss|||~~~vvvrrrsssnnngggdddfffmmmuuuzzzuuuooovvvvvvfffUUUFFF===888666555444444333333444444555555555666777888999::::::999999;;;???BBBIIIWWWdddrrrmmmYYYSSSUUUbbbrrr|||rrrggg___XXXUUUSSSPPPQQQSSSUUU\\\fffpppwwwzzz{{{{{{{{{zzzyyyxxxxxxyyyzzz{{{wwwgggZZZWWW^^^hhh|||vvvlll___PPPIIIDDD>>><<<<<<:::999888666555555444444666555555555555666777777::::::CCCWWWlllyyyzzzwwwwwwmmmkkkppp~~~|||ooojjjgggnnnrrrkkk```[[[WWWXXXXXXYYY^^^dddhhhkkkooosssvvvwwwwwwwwwrrrsssuuuyyy|||~~~}}}|||xxxxxxwwwuuussspppmmmllljjjrrryyy{{{}}}{{{zzzxxxxxxzzz~~~|||||||||yyy|||zzzrrriiiccc^^^^^^^^^___cccjjjrrryyy|||uuuqqqlllgggcccaaa\\\WWWSSSQQQMMMGGGCCCAAAAAAAAAAAACCCKKKVVV^^^fffmmmsssuuuvvvwwwrrrllleee^^^XXXVVVSSSQQQSSSXXXbbbmmmtttoooaaaTTTKKKFFFFFFIIIPPPWWW^^^cccgggjjjlllooorrrtttuuuwwwyyy|||{{{|||~~~{{{vvvpppmmmkkklllrrr{{{}}}zzzyyywwwwwwyyy{{{qqqkkkdddcccbbbbbbcccdddcccaaa]]]XXXTTTRRRPPPRRR[[[eeerrr{{{~~~zzzvvvtttoooiiicccccchhhpppvvvyyyooommmzzzvvvhhhXXXIII???999777555444444333333444444555555555666777888999::::::888888;;;???BBBIIIXXXfffuuuxxxbbbSSSQQQUUUeeevvvvvvkkk^^^YYYUUUUUUTTTQQQPPPRRRVVV^^^iiirrrxxxzzz{{{|||}}}|||{{{{{{{{{{{{|||}}}zzziii\\\YYY```hhh~~~xxxtttlll```SSSKKKEEE@@@===>>>;;;:::888777555444444333666666555555666666777888777999FFF\\\pppyyy{{{zzz{{{mmmjjjllluuuxxxooommmkkkppprrriii___[[[YYYYYYYYYZZZ```hhhkkkmmmqqqtttuuuuuutttsssnnnpppsssyyy~~~}}}xxxwwwvvvtttsssrrrrrrrrrrrryyy~~~|||zzzyyy{{{~~~}}}zzz|||{{{ssskkkfff```___^^^^^^```fffnnnttt~~~wwwrrrnnniiieeeaaa]]]XXXUUUSSSNNNHHHCCCAAABBBBBBAAACCCJJJTTT]]]eeelllsssvvvyyyzzzvvvppphhhaaa[[[XXXUUURRRSSSWWW^^^hhhooommmaaaSSSJJJFFFEEEJJJPPPWWW\\\aaafffiiilllooorrrtttuuuxxx{{{}}}|||}}}zzzrrrpppnnnooossszzzzzzxxxwwwwwwwww{{{qqqhhhbbb^^^]]]]]]^^^```aaaaaa```^^^ZZZVVVUUUSSSUUU]]]gggsss|||}}}zzzuuuooolllgggcccbbbfffmmmrrr}}}ssskkkrrrzzzkkk[[[LLL@@@999666555444444333333444444555444555555666777888999:::888888:::???CCCJJJYYYgggyyynnnZZZNNNPPPVVVfffwwwzzzpppfffZZZTTTQQQRRRRRRPPPPPPRRRYYYbbbmmmvvvzzz{{{}}}~~~}}}}}}~~~}}}mmm```^^^eeelll{{{vvvsssjjj___SSSKKKEEE???===???999999777666555555555555666666666666666777777888777<<>>===;;;888666666555555555666666555555666888;;;@@@OOOkkkyyyvvvuuuyyy}}}||||||ooo```]]]ZZZYYY]]]dddlllqqqwww{{{|||{{{zzz|||}}}|||}}}}}}|||{{{}}}}}}}}}|||{{{vvvooojjjbbbaaa``````bbbfffkkknnnjjjooovvv|||~~~yyytttoookkkhhheeebbb^^^YYYTTTNNNJJJCCCBBBAAA@@@AAAGGGNNNTTT[[[___eeejjjlllmmmooopppooommmiiibbb[[[VVVTTTTTTVVVYYY[[[[[[WWWOOOFFFAAA@@@BBBEEEJJJPPPUUUZZZ\\\bbbfffjjjnnnqqqtttwwwzzz~~~~~~{{{vvvsssttt{{{zzzmmmbbbYYYSSSPPPOOONNNOOOPPPRRRVVVYYY[[[\\\[[[[[[\\\bbbmmmyyyyyylll^^^XXXUUUXXX^^^eeeqqq{{{~~~rrrqqqsss}}}iiiTTTCCC:::888666444333444444333222444555777777666666888999:::;;;===@@@CCCKKK[[[kkkppp]]]WWW[[[bbbwwwqqqaaaUUUOOOMMMRRRXXXaaammmwwwzzzzzz{{{|||{{{}}}}}}~~~xxxkkkggglllzzz}}}qqq```SSSJJJEEEAAA===>>>===:::888777666666777555666666666555777999<<<@@@UUUxxxzzzuuuuuu|||{{{kkk```]]]ZZZYYY\\\bbbiiinnnvvvzzz~~~{{{zzzyyy|||~~~}}}|||||||||||||||~~~}}}zzzyyyzzzuuunnniii^^^]]][[[[[[^^^ccchhhllljjjooowww|||~~~yyysssoookkkhhhccc^^^YYYTTTNNNKKKBBBBBB@@@@@@AAAFFFLLLRRRXXX[[[```dddfffhhhjjjkkklllkkkhhhbbb\\\WWWUUUTTTUUUVVVXXXXXXTTTMMMFFFAAA>>>@@@CCCHHHNNNSSSXXX[[[```dddhhhlllooosssvvvyyy}}}wwwsssrrrxxx{{{nnnbbbYYYRRROOONNNMMMLLLLLLNNNRRRVVVYYYZZZZZZZZZ]]]eeeqqqqqq```ZZZVVVYYY```lll{{{rrrpppqqq~~~kkkVVVEEE;;;888666444444444555444222444555777777666666888999;;;;;;>>>AAACCCJJJ[[[jjjttt```YYY___fffyyy|||zzz{{{}}}tttcccWWWPPPMMMRRRYYYdddooozzz}}}|||}}}}}}{{{}}}}}}}}}}}}jjjaaa^^^hhh|||uuufffXXXNNNHHHCCC@@@<<<;;;:::888888888999999555666777777666888:::===BBB\\\vvvtttwwwuuueee]]][[[XXXXXXZZZ```gggkkktttyyy~~~|||xxxvvvvvvzzz~~~~~~~~~}}}}}}}}}}}}~~~}}}{{{yyywwwzzz{{{}}}~~~zzztttmmmhhh\\\ZZZXXXWWWYYY^^^dddhhhlllrrrzzz~~~xxxsssnnnjjjeee```[[[UUUOOOKKKBBBBBBAAA???@@@DDDJJJNNNUUUXXX]]]```bbbccceeefffffffffeeeaaa\\\XXXUUUUUUSSSTTTUUUTTTPPPJJJEEEAAA>>>???BBBGGGMMMSSSXXX\\\```ccchhhkkknnnqqquuuwww}}}~~~xxxtttqqqvvv}}}}}}qqqdddZZZSSSPPPMMMLLLJJJIIIKKKNNNSSSVVVUUUVVVYYY]]]fffsssuuubbb\\\XXX\\\eeesssqqqoooooo}}}mmmYYYGGG===888666444444555555444333444555777777666666888999;;;;;;>>>AAACCCJJJ[[[jjjwwwccc\\\bbbkkk}}}yyyssssssuuuxxxmmm___VVVOOOMMMRRRZZZcccooozzz}}}}}}~~~~~~|||~~~}}}|||}}}}}}ggg[[[XXX^^^rrr{{{mmm```UUULLLFFFBBB<<<;;;999888888999::::::555666777777777888;;;>>>GGGeee}}}uuuyyynnn```ZZZYYYWWWWWWZZZ```gggkkksssxxx}}}~~~yyyuuurrrrrrvvv|||~~~~~~~~~~~~zzzxxxvvvvvvtttvvvxxx{{{~~~zzzuuummmggg]]]ZZZWWWUUUVVVZZZ```ccclllsss||||||vvvpppmmmhhhccc^^^WWWPPPLLLDDDCCCAAA??????AAAFFFJJJPPPTTTZZZ^^^```aaabbbcccbbbcccccc```\\\WWWUUUTTTQQQQQQPPPOOOKKKGGGCCC@@@===>>>AAAEEELLLRRRXXX\\\aaadddhhhkkknnnpppsssvvvyyy|||zzzvvvrrruuuzzzsssfff[[[UUURRRMMMLLLJJJHHHIIILLLOOOQQQQQQSSSWWW]]]fffrrryyyeee___[[[```iiivvvrrroooooo|||}}}qqq]]]JJJ???999777555444555555444333444555777777666666888999:::;;;===@@@CCCKKK[[[kkk}}}ggg```hhhsssvvvlllhhhjjjggg```XXXSSSOOONNNTTT[[[bbbnnnxxx{{{{{{|||}}}||||||~~~}}}||||||~~~hhh[[[VVVZZZmmmwwwiii[[[PPPHHHCCC===<<<;;;999888888999999555777777888888999<<>>???CCCFFFJJJPPPWWW]]]aaabbbcccddd```aaabbb___ZZZUUURRRPPPMMMLLLKKKIIIFFFCCC@@@>>><<<===???DDDJJJQQQXXX\\\bbbeeeiiilllmmmooorrrttttttyyy~~~|||yyyrrrtttzzztttfff\\\UUUSSSNNNLLLJJJIIIIIIJJJLLLMMMNNNQQQWWW^^^gggrrr}}}yyyhhhbbb___ccckkkvvvuuupppmmm~~~{{{xxx|||vvvaaaMMMAAA999777555444555555555333444555777777666666888999999:::===@@@CCCKKK\\\lllmmmgggppp|||}}}rrrccc[[[\\\UUURRRPPPQQQPPPPPPVVV^^^cccmmmvvvxxxwwwxxxzzzzzzyyy|||}}}||||||lllaaaVVVXXXkkk~~~ooo```SSSHHHCCC@@@>>><<<:::888777777777666777888888888:::===???MMMmmmvvvxxxwwwhhh```WWWVVVVVVXXX]]]dddkkkpppuuuzzz}}}wwwqqqnnnmmmrrrwww{{{}}}xxxtttrrrrrrsssnnnqqquuuzzz~~~}}}{{{vvvmmmfffZZZVVVQQQMMMLLLOOOSSSWWWccclllxxxzzzrrrpppmmmiiiccc[[[RRRLLLFFFEEECCC@@@>>>>>>AAADDDFFFLLLUUU]]]bbbdddeeefff```aaabbb___YYYSSSOOOMMMJJJIIIHHHFFFCCC@@@===<<<;;;<<<>>>BBBIIIPPPWWW[[[cccfffjjjlllmmmoooqqqsssqqqwww}}}}}}{{{sssuuuzzz~~~tttfff\\\VVVTTTNNNMMMKKKIIIIIIIIIJJJKKKMMMQQQXXX___hhhrrr{{{vvvjjjdddbbbeeellltttxxxrrrlll{{{}}}{{{~~~zzzdddPPPCCC999777555555555666555444444555777777666666888999888999<<<@@@CCCLLL]]]mmmrrrlllvvvzzzmmm[[[QQQQQQIIIIIILLLPPPQQQRRRXXX```dddnnnuuuvvvtttvvvwwwwwwwwwzzz~~~}}}}}}|||