BM6P6(@ &&&&&&%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%%%%%%%&&&'''$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%######$$$%%%%%%&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$#########$$$%%%&&&''''''%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$###&&&%%%###""""""###%%%&&&'''&&&&&&%%%%%%$$$$$$###&&&&&&&&&'''''''''(((((((((((((((((((((''''''''''''%%%$$$$$$&&&&&&%%%###&&&'''((())))))((('''&&&((((((((((((((((((((((((&&&'''(((******+++++++++++++++******)))*********++++++++++++++++++++++++++++++++++++++++++++++++...///000000000///---,,,---------------...///000111111111111111111111111333444555555555555444333111111222222222111111000000111111222222333444444666666666777888:::;;;<<>><<<<<<<<<===>>><<<>>>@@@BBBEEEFFFHHHHHHCCCBBB@@@???@@@CCCFFFHHHGGGDDDAAA??????AAADDDGGGGGGGGGFFFFFFEEEDDDCCCCCCHHHHHHGGGEEECCCBBBDDDEEEIIIKKKLLLLLLKKKKKKMMMNNNKKKJJJHHHGGGGGGHHHIIIJJJIIIHHHGGGIIIKKKMMMNNNMMMPPPOOONNNMMMKKKIIIEEEBBB>>>>>>@@@BBBGGGLLLPPPSSSRRRLLLEEEBBBCCCDDDDDDCCC===<<<<<<===>>>>>>===;;;999:::;;;===AAADDDHHHJJJ@@@<<<888666666666444111333333444444333333222111222222222333333222222222000000///............//////...,,,++++++,,,.../////////.........//////000////////////000000000000///...---+++***)))))))))************************...---+++***)))***++++++************************)))(((((((((***+++***))),,,,,,+++***))))))************))))))))))))******)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((''''''))))))*********((('''&&&))))))))))))))))))))))))******))))))((((((''''''''')))***,,,+++***(((''''''&&&'''))),,,,,,)))&&&+++***(((((((((((('''&&&++++++************++++++,,,,,,,,,+++++++++******((()))************))))))------------------------//////...------,,,++++++...------------...////////////000000111111222222111111000///...------,,,---......///000111111111((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%%%%%%%&&&'''$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%######$$$%%%%%%&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$'''&&&&&&%%%$$$$$$%%%%%%%%%&&&'''&&&%%%%%%%%%'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&%%%$$$$$$&&&%%%$$$######$$$%%%&&&''''''&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&(((((((((((('''''''''''''''&&&%%%%%%'''((('''&&&''''''((((((((((((''''''(((((((((((((((((((((((('''((()))************************)))******++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,---...///000000///...---...------------...///000111111111111111111111111000111222222222222111000111111111111111000000000222222222222222333333333444444555555666888999::::::::::::::::::999999888;;;===???AAACCCEEEFFFFFFCCCCCCBBBAAABBBCCCEEEFFFEEECCC@@@??????AAAEEEGGGGGGGGGFFFFFFEEEDDDDDDCCCHHHHHHGGGEEEBBBAAABBBDDDHHHIIIJJJJJJIIIIIIJJJKKKKKKJJJIIIHHHHHHGGGGGGGGGFFFFFFGGGHHHIIIKKKMMMNNNPPPOOONNNMMMKKKHHHEEEBBB>>>>>>???AAADDDIIIMMMOOOPPPLLLGGGCCCAAAAAAAAAAAA===<<<;;;<<<===>>><<<;;;;;;;;;;;;<<<===@@@BBBDDD???;;;777555555555333111333333444444333333222111111111222222222222111111......---,,,,,,,,,,,,---...---,,,++++++,,,---.....................///000000000//////......------...---,,,+++************************************...---,,,+++***++++++,,,++++++++++++++++++++++++***)))((()))+++,,,+++***,,,++++++******)))************))))))))))))******)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((''''''(((((()))***))))))''''''((((((((((((((((((((((((***)))))))))((((((((('''(((((()))***+++***)))((((((''''''(((++++++)))&&&+++***)))***++++++)))'''***))))))))))))))))))***,,,,,,,,,+++++++++******************************------------------------.........---,,,+++++++++,,,,,,,,,,,,,,,---....../////////000000000000000000//////......---------......///000000111222222)))((('''&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$''''''&&&&&&%%%%%%&&&&&&$$$&&&'''&&&%%%$$$%%%'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&&&&&&&%%%'''&&&%%%$$$$$$%%%&&&'''&&&&&&&&&&&&''''''''''''$$$$$$$$$%%%%%%%%%&&&&&&'''''''''''''''''''''''''''&&&%%%&&&((())))))(((((((((''''''''''''(((((((((((((((((((((((((((((((((((()))******)))))))))))))))))))))******+++,,,++++++++++++++++++++++++------------------------,,,,,,...//////000//////......------......//////111111111111111111111111///000000111111000000///222222111000000000000111333333333333222222222222333333333333444555777777666777999:::999888666444:::;;;===???AAACCCCCCDDDCCCCCCCCCCCCCCCCCCCCCCCCBBBAAA???>>>???BBBEEEGGGGGGFFFFFFEEEEEEDDDDDDDDDGGGHHHGGGEEEBBB@@@AAABBBEEEGGGGGGGGGEEEDDDEEEFFFIIIIIIIIIIIIHHHGGGFFFEEECCCEEEGGGGGGFFFGGGJJJNNNOOONNNNNNLLLJJJGGGDDDBBB>>>>>>>>>???AAADDDGGGIIILLLKKKHHHDDD@@@======>>><<<;;;:::;;;<<<===<<<:::<<<;;;:::::::::;;;<<<<<<===:::777555555444222111333333444444333333222111000111111111111111111000///...------,,,,,,------------++++++++++++---------------------...//////111000000///---,,,,,,+++------,,,+++++++++++++++************************...---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***)))***,,,,,,,,,***+++++++++*********************))))))))))))******)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((('''''''''((()))))))))(((((((((((((((((((((((((((((())))))))))))((((((((((((((((((((())))))*********)))((('''((())))))((('''******+++---......,,,)))))))))(((((((((((()))))),,,,,,,,,+++++++++******...---+++*********++++++------------------------...------,,,,,,++++++***,,,++++++++++++,,,------/////////...............------------------------//////000000111222222222((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%&&&'''''''''&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%%%%&&&''''''(((&&&&&&&&&'''''''''((((((&&&&&&'''''''''''''''(((&&&%%%%%%&&&(((***)))((()))((('''&&&&&&'''((()))((((((((((((((((((((((((((()))))))))))))))(((((((((((((((((()))+++,,,,,,************************,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,---///000111111//////............//////111111111111111111111111000111111111111111111000444333222222111222333333555555444333222222111111222222222222333444555666777888999:::999999777777999:::;;;===???@@@@@@AAA@@@AAAAAABBBBBBAAA@@@??????>>>>>>>>>@@@BBBEEEFFFFFFEEEEEEEEEDDDDDDCCCCCCFFFFFFFFFDDDAAA??????@@@CCCDDDDDDCCCAAA@@@AAABBBEEEFFFGGGHHHHHHGGGFFFEEEDDDGGGJJJIIIEEEDDDHHHLLLMMMNNNNNNLLLIIIFFFCCCBBB???>>>======>>>@@@BBBCCCEEEGGGGGGDDD???<<<<<<>>><<<:::999999;;;<<<;;;:::<<<;;;:::888888888888999<<<;;;999777666444333222333333444444333333222111000000111111111111000000111000000///////////////---,,,++++++++++++,,,------,,,,,,------...///000111000000///......---------,,,,,,+++++++++,,,,,,************************------------------------,,,,,,,,,,,,,,,,,,,,,,,,+++*********,,,---,,,+++******+++++++++*********+++******))))))******+++))))))))))))))))))))))))))))))))))))))))))))))))(((((())))))))))))((((((&&&''''''(((((()))))))))(((((((((((((((((((((((())))))))))))((((((((((((((((((''''''((()))***+++***)))''''''''''''(((((()))***,,,///111000...+++))))))(((((((((((()))))),,,,,,,,,+++++++++******000...,,,***)))***+++,,,,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,++++++++++++,,,,,,,,,+++,,,,,,---............------,,,,,,,,,,,,,,,,,,---------......000000111111222222222222%%%%%%%%%%%%%%%&&&'''(((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%$$$%%%&&&%%%$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&""""""###$$$%%%&&&&&&'''&&&&&&&&&'''''''''((((((%%%&&&&&&&&&''''''((((((%%%$$$$$$%%%''')))(((((()))((('''&&&&&&'''((()))(((((((((((((((((((((((((((((()))))))))(((((('''(((((((((((()))***+++,,,************************************************)))***+++,,,...000111222000//////.........//////000000000000000000000000000000000000000000000000555444444444555666666777666555555444333222111111333333333333444555666666999999888777777888999:::888999:::<<<===>>>>>>>>>======???@@@???>>>===<<<<<<<<<===>>>@@@BBBCCCEEEDDDDDDCCCCCCCCCCCCBBBBBBDDDDDDEEECCC@@@>>>>>>>>>@@@AAAAAA@@@>>>===>>>???AAABBBDDDGGGHHHHHHHHHHHHHHHKKKMMMJJJEEECCCFFFJJJLLLMMMNNNLLLHHHDDDBBBCCC>>>===<<<;;;;;;===???@@@@@@CCCDDDCCC???<<<===???;;;:::888888999::::::999::::::888888777888999:::<<<<<<;;;999777555444444333333444444333333222111000000111111111111000000111111000////////////000,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---...///000000000000000000000000000000------,,,,,,+++,,,,,,,,,************************,,,---------------------+++++++++++++++++++++++++++*********,,,---,,,+++)))******+++++++++******++++++************++++++))))))))))))))))))))))))(((((((((((((((((((((((((((((())))))))))))((((((&&&&&&'''''''''((())))))''''''''''''''''''''''''(((((((((((())))))))))))((((((''''''((()))******((((((((('''&&&''''''((()))***,,,///111111...,,,+++******))))))******+++,,,,,,,,,+++++++++******000...,,,******+++,,,---,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,,,,,,,+++---------------......///......------,,,,,,++++++++++++,,,,,,---.........111111111111111222222222$$$$$$$$$%%%&&&'''((()))%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$#########$$$%%%%%%###%%%&&&%%%$$$###$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&''''''''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%!!!""""""###$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&''''''((((((&&&%%%$$$%%%'''(((((('''((((((''''''''''''((((((((((((((((((((((((((((((''''''((())))))((((((((((((((((((((())))))***+++*********************************************************,,,---000111333000000//////......//////000000000000000000000000///......------......///333444555777888999999999666555555444333222222111444444444444444555666666888777555444444666888999888999:::;;;<<<<<<<<<<<<:::;;;<<<=========;;;;;;;;;;;;===>>>@@@AAABBBBBBAAAAAAAAAAAAAAAAAAAAAAAAAAABBBCCCBBB???>>>===>>>>>>???@@@???===<<<===>>>>>>@@@BBBDDDGGGHHHIIIJJJKKKMMMMMMKKKGGGEEEGGGIIIKKKMMMNNNLLLGGGCCCBBBCCC>>>===;;;;;;;;;===???@@@@@@AAAAAA@@@???>>>>>>???;;;999777666888999999999888888777777777888:::;;;;;;<<<===;;;888666555666333333444444333333222111000111111111111111111000000///......------......---------------------------------...///000111222000000000111111222222222......---,,,,,,,,,,,,,,,************************+++,,,,,,------------,,,************************+++***)))***,,,,,,,,,***((()))***,,,,,,+++******++++++************++++++))))))))))))))))))))))))(((((((((((((((((((((((('''(((((()))))))))))))))'''''''''&&&''''''((((((''''''''''''''''''''''''(((((((((((())))))))))))((((((((((((((((((((((((%%%'''(((((('''&&&((())))))***+++---///000...,,,++++++************++++++,,,,,,,,,+++++++++******---,,,+++++++++,,,------,,,,,,,,,,,,,,,,,,,,,,,,------------------------...------------...//////---------,,,,,,,,,,,,,,,,,,,,,------.........///111111111111111111111111%%%%%%%%%%%%%%%&&&'''(((%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&''''''&&&%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$%%%&&&&&&###%%%%%%%%%$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''&&&%%%$$$$$$%%%%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&'''((((((((('''&&&'''((()))((('''''''''((((((((((((''''''((((((((((((((((((((((((&&&&&&'''((())))))))))))))))))((((((((())))))************************************************************+++---///111222111111000///////////////000000000000000000000000//////...------.../////////111555888:::;;;;;;:::555555444444333333333222444444333333333444555555555555555555555666777777888999:::;;;;;;;;;;;;;;;999:::;;;<<<<<<<<<<<<<<<:::;;;===>>>@@@@@@@@@@@@??????????????????@@@@@@>>>@@@AAAAAA???>>>===>>><<<===???>>>======>>>??????@@@AAABBBDDDGGGIIIJJJKKKKKKJJJIIIIIIHHHIIIIIIJJJMMMNNNLLLFFFAAAAAACCC===<<<;;;;;;<<<>>>@@@BBBCCCAAA???>>>??????>>>===;;;888666555777888999999777666666555666777888999999;;;===;;;888555555555333333444444333333222111111111222222222222111111000//////........................//////..................///000111222333111111111111000000000000000///...---,,,+++++++++************************)))***+++---------,,,+++++++++++++++++++++++++++***)))((()))+++,,,+++***''')))***,,,,,,,,,***))),,,++++++******++++++,,,))))))))))))))))))))))))((((((((((((((((((((((((''''''((())))))))))))))))))((('''&&&&&&&&&'''''''''''''''''''''''''''''''''((((((((()))))))))***((())))))))))))'''&&&%%%"""%%%((()))((('''(((******))))))+++------,,,+++******))))))))))))******,,,,,,,,,+++++++++************++++++,,,,,,------++++++++++++++++++++++++........................------,,,,,,------...///,,,,,,,,,---------------..................//////000000000000000000000000''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&''''''&&&%%%%%%&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&'''(((###$$$%%%%%%######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$&&&%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''((((((((('''&&&%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&'''''''''(((((($$$$$$%%%%%%&&&'''((((((***)))(((((())))))((('''&&&'''((())))))((('''&&&((((((((((((((((((((((((%%%%%%'''((())))))))))))***))))))(((((((((((()))))))))))))))))))))))))))+++++++++++++++++++++++++++******+++,,,...111222111111000///////////////000000000000000000000000222111000//////000111222,,,///444999;;;<<<;;;:::555555444444444333333333333333333222333333444444444555777888999888777666888999:::;;;;;;;;;;;;;;;::::::;;;;;;<<<===>>>>>>:::;;;===>>>???@@@??????>>>>>>>>>>>>>>>?????????<<<>>>@@@@@@???>>>>>>>>>;;;===>>>>>>======???@@@AAAAAAAAAAAACCCEEEGGGIIIIIIHHHGGGGGGIIIKKKKKKJJJIIILLLOOOLLLEEEAAAAAACCC<<<<<<;;;;;;===???BBBCCCGGGCCC>>>===??????===;;;:::888555555666888999888777666555444555555777888777:::<<<;;;777444444555333333444444444333222222222222333333333333222222222222111000000000000000......////////////............//////000222333444222222111000///...------111000...---,,,++++++***************************((()))+++,,,---,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,)))(((((((((***+++***)))'''(((***,,,---,,,***))),,,++++++******++++++,,,))))))))))))))))))))))))((((((((((((((((((((((((''''''((()))))))))))))))***((('''&&&%%%%%%&&&''''''''''''''''''''''''''''''((((((((())))))******((()))******)))'''%%%######((()))((('''(((***+++)))((()))+++,,,+++***))))))(((((((((((()))))),,,,,,,,,+++++++++******((()))***+++,,,---------++++++++++++++++++++++++......//////////////////,,,,,,++++++,,,,,,---...,,,,,,,,,------.........////////////////////////000000000///////////////&&&&&&%%%$$$$$$%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$#########$$$&&&''')))&&&%%%&&&((()))'''%%%$$$######"""###$$$&&&'''&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$''''''&&&&&&%%%$$$######&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###&&&((((((%%%$$$%%%'''$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((((('''(((((((((((('''&&&%%%$$$'''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))+++)))((('''((()))+++,,,(((((()))***,,,...000111//////......---------,,,......---------...//////////////////////////////000111222333555666777777333555666777777555333222...///000111333333444444333444444555666777888888888888:::;;;<<<=========:::;;;===<<<;;;;;;<<<>>>=========>>>======<<<<<<;;;===>>>===;;;999999999:::;;;<<<===>>>>>>>>>>>>;;;;;;<<<======>>>>>>???BBBBBBBBBCCCDDDFFFHHHIIIIIIGGGEEEEEEGGGIIIJJJJJJNNNNNNLLLKKKHHHDDDAAA???CCC@@@===<<<>>>AAABBBCCCCCCBBBBBBBBBCCCAAA???<<<666666555555555555555666555555555666777888::::::;;;999777555333333333333333333333222111000//////000222333333222111222333111111111000111111222222333222000///---,,,,,,+++,,,,,,---///000222333333333333222222222222222222000//////...------,,,,,,,,,,,,,,,++++++*********+++*********+++,,,,,,---,,,,,,,,,+++++++++******++++++++++++++++++++++++++++++++++++++++++++++++*********++++++,,,,,,,,,...---+++)))((())))))***))))))(((((((((((())))))************************+++***((('''&&&&&&&&&'''(((((('''''''''&&&&&&&&&%%%&&&'''((())))))((((((((('''&&&%%%%%%&&&'''((())))))))))))((((((((((((************************(((((()))***++++++,,,,,,+++++++++***)))((((((''',,,+++)))''''''((()))***---,,,++++++++++++,,,---............------------------------------------,,,,,,---.../////////...///000111222333222222111444333222000///.........&&&&&&%%%%%%$$$%%%%%%&&&''''''&&&&&&&&&%%%%%%%%%%%%$$$#########$$$%%%&&&(((&&&$$$%%%'''((('''%%%&&&&&&$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%%%%%%%$$$$$$###"""""""""&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&((((((%%%$$$%%%'''%%%%%%&&&&&&&&&&&&&&&'''$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''''''''''''''''''''''''''&&&&&&%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''(((''''''''''''(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))***)))((('''((()))+++,,,*********+++,,,---...///000000000000/////////............---......///000000000000000000000000000000000111222333444555555333444555666666555333222///000111222333444444555333333444444555666777777777777999:::;;;<<<<<<<<<888999::::::999999:::;;;;;;<<<<<<======<<<<<<;;;;;;===>>>===;;;999999:::;;;;;;<<<===>>>>>>======;;;;;;;;;<<<===>>>???@@@BBBBBBAAABBBCCCEEEGGGHHHHHHFFFDDDDDDGGGJJJKKKKKKMMMMMMLLLKKKIIIFFFCCCAAACCC@@@===<<<>>>@@@AAAAAABBBAAA@@@@@@@@@???<<<:::666666555444555666777888777777777777888999::::::<<<:::888666444444333444333222222222111000000000000222444444333222333444333222222111111222222333333222000///---,,,,,,,,,,,,,,,---///000111222333111111111111111000000000/////////...---,,,,,,,,,,,,,,,,,,++++++*********++++++******++++++,,,---,,,,,,+++++++++*********++++++++++++++++++++++++++++++++++++++++++++++++******++++++,,,,,,,,,,,,---,,,+++)))))))))))))))))))))(((((((((((())))))************************+++***)))'''''''''''''''(((((('''''''''&&&&&&&&&''''''''''''(((((((((((((((((('''&&&&&&'''(((((())))))))))))((((((((((((************************))))))******+++,,,,,,,,,+++++++++***)))(((((((((,,,+++***))))))+++---......---,,,,,,,,,,,,---...000000000/////////......------------------------,,,,,,------...////////////000111333333333222111444333222000///.........&&&%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$$$$$$$%%%'''%%%$$$%%%&&&'''&&&$$$(((((('''%%%%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&((((((((('''&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&''''''&&&%%%%%%&&&''''''''''''&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&&&&%%%%%%###$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''&&&&&&%%%%%%%%%&&&''''''''''''&&&'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''(((&&&&&&&&&&&&''''''''''''))))))))))))))))))))))))))))))))))))))))))))))))***)))((((((((()))+++,,,,,,++++++++++++,,,,,,---///000000000000///.........---------......///000111111111111111111111111000000111111111222222222111222333444555444333222111111222333444444555555222222333333444444555555555666777888999::::::;;;777888:::999888888999;;;::::::;;;;;;<<<;;;;;;:::;;;===>>>===;;;:::::::::<<<<<<===============<<<;;;;;;::::::;;;===@@@AAAAAAAAA@@@@@@AAACCCDDDEEEFFFDDDBBBCCCGGGJJJLLLLLLLLLLLLLLLLLLJJJHHHEEECCCCCCAAA>>><<<===>>>>>>>>>???>>>=========<<<:::888777666444333444666888::::::999999888999999::::::<<<;;;999777555444333333222222111111111111111111111333555555444444555666444444333333333333333444222111000...---,,,,,,,,,,,,,,,---...000111222222000000000000/////////...///......------,,,,,,++++++++++++++++++*********++++++******++++++,,,,,,++++++++++++*********)))+++++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,+++***))))))))))))))))))((((((''''''(((((()))))))))))))))))))))))))))++++++)))((((((((((((((('''''''''''''''&&&&&&&&&))))))'''&&&&&&'''((((((((((((''''''''''''(((((((((((((((((())))))))))))************************++++++++++++,,,,,,,,,,,,+++++++++***))))))((((((++++++++++++,,,...000111///......------......///111111111000000000//////------------------------------,,,,,,---...000111111111222333333333222222333333111000////////////&&&%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$%%%%%%%%%%%%%%%((((((''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%)))))))))(((((('''''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&''''''&&&&&&&&&&&&'''''''''&&&%%%%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%"""###$$$%%%&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&&&&%%%$$$###$$$%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&'''''''''((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))(((((())))))***++++++++++++***+++,,,,,,---,,,------......---,,,,,,,,,,,,,,,,,,,,,---...///111111111111111111111111111111111111111111111111000111222333333333333333111111222222333444555555222222222333333333333333444444555555666888999999999:::;;;;;;::::::;;;===999::::::;;;;;;;;;;;;:::<<<===???>>><<<;;;;;;<<<===============<<<;;;;;;:::999888888999<<<@@@BBBAAA@@@@@@??????@@@BBBCCCCCCAAA@@@BBBFFFIIILLLMMMJJJKKKLLLMMMLLLIIIGGGEEECCCAAA===<<<<<<<<<;;;:::<<<:::::::::<<<<<<;;;999:::888555333333444777999;;;;;;:::999999999999999::::::888666555333222222111111111111111222222222222444666666666555666777666555555444444444444555111111///...---,,,,,,,,,,,,,,,---...///000111222111111000000///.........------------,,,,,,+++++++++++++++***************,,,++++++***++++++,,,,,,+++************)))))))))************************************************+++++++++,,,,,,,,,,,,,,,++++++***)))))))))))))))(((((((((''''''(((((((((((((((((((((((((((((((((++++++***)))))))))))))))''''''''''''''''''''''''+++***'''&&&%%%&&&'''((((((((((((((((((((((((((((((((((((((())))))))))))************************------,,,,,,,,,,,,,,,,,,+++++++++******))))))))),,,,,,,,,,,,---...000111000//////////////////000111000000000////////////,,,,,,,,,,,,,,,,,,,,,,,,...---,,,+++,,,...111222222222222333333333222222222222111000/////////000&&&%%%%%%%%%&&&&&&'''(((''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&''''''((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%&&&&&&''''''&&&%%%&&&%%%%%%%%%$$$#########$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%$$$"""###$$$%%%&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&%%%$$$$$$######%%%&&&''''''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''((((((((()))))))))(((((((((((((((((((((((((((((((((((((((((((((((()))))))))))))))******+++)))))))))***+++,,,---...+++,,,---......---,,,+++************+++,,,---...111111111111111111111111222222222222111111111111///000111222333333444444222222222222222333444555333333333333333333333222333333333333444666777888999;;;<<<<<<;;;:::<<<===999:::;;;;;;<<<<<<<<<;;;===???@@@@@@>>>======>>>>>>>>>>>>>>>===;;;::::::888777666666888<<>>>>>??????@@@@@@>>>>>>@@@DDDHHHKKKLLLIIIJJJLLLMMMLLLJJJGGGEEEBBB@@@===;;;;;;:::999777888777666888:::<<<<<<<<<;;;999555222111333555666;;;;;;:::999888888888888777777666555333222111000111111111111111222222222222444666777666666777888777666666555444444555555111000///---,,,,,,,,,,,,,,,,,,---...///000000111222111111000//////......,,,,,,,,,,,,,,,+++++++++************************,,,,,,++++++***++++++,,,*********)))))))))((((((************************************************++++++++++++++++++++++++************)))))))))(((((((((''''''''''''((((((''''''''''''''''''''''''***************)))))))))&&&'''''''''''''''''''''+++***'''&&&%%%&&&'''((())))))))))))))))))))))))'''((((((((()))))))))***************************------,,,,,,,,,,,,,,,,,,++++++++++++************,,,,,,,,,,,,,,,------...000000000000000000000000//////.........---------,,,,,,,,,,,,,,,,,,,,,,,,---,,,++++++,,,...111333333222222222222222222222111111000000000000000111%%%%%%%%%%%%&&&'''((()))''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$&&&'''&&&%%%$$$%%%'''$$$%%%&&&'''(((((((((((($$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&&&&'''&&&%%%%%%&&&''''''&&&$$$$$$$$$$$$$$$############$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%$$$$$$###$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$######$$$&&&&&&'''''''''%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&''''''''''''((((((((((((((()))))))))***((((((((((((((((((((((((((((((((((((((((((((((((((()))))))))************(((((())))))+++,,,---...,,,---///000000000...---)))))))))***+++,,,---...111111111111111111111111222222222111111111111111///000000111333444555555444444333222333444555666666666555555444444333333333333222222333555777888888999;;;:::999999:::<<<;;;;;;<<<===>>>>>>>>>>>>???AAABBBBBB@@@???@@@AAA@@@@@@???>>>===;;;999888777777777888:::>>>AAACCCBBBAAA@@@>>>======>>>>>>===<<<;;;===AAAFFFHHHIIIGGGIIILLLMMMLLLJJJGGGDDDAAA>>><<<::::::999777666666444444555888;;;;;;;;;999777555222111222333444999999888777666666666777444444444444333222111000222222111111111111111111222444666777777777888999777777666555444444444444000///...---,,,,,,,,,,,,,,,------...//////000000222222111000///......---++++++++++++++++++++++++)))))))))***************,,,,,,++++++******++++++))))))))))))((((((((((((***************************************************************)))))))))((())))))******)))(((((((((''''''&&&&&&''''''(((((((((((((((((((((((((((((())))))******)))((((((&&&&&&&&&'''''''''''''''))))))'''&&&&&&'''(((((())))))************))))))''''''(((((())))))******************************++++++++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,///000000111111000000///---------,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++,,,---///111222333222111111000000111111111000000000000000111222%%%%%%%%%&&&&&&'''((()))''''''&&&&&&&&&%%%%%%%%%$$$%%%&&&'''''''''&&&%%%%%%'''((('''%%%$$$&&&(((%%%%%%&&&'''''''''&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$######$$$%%%%%%((((((((((((((((((((((((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&'''''''''%%%$$$%%%((((((&&&$$$###$$$$$$$$$$$$$$$%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%###$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''((('''''''''((((((((())))))(((((((((((((((((((((((((((((((((((((((((((((((((((((()))*********************)))******+++,,,,,,+++,,,...000111000...---******++++++,,,...///000000000000000000000000000000000000000000000000000///000000111333555666777777666555444555666888999888888777777666555555444333333222222333555777888999;;;<<<<<<;;;:::<<<===<<<===>>>???@@@@@@@@@@@@AAABBBDDDDDDBBBBBBBBBCCCAAA@@@@@@>>><<<:::888777888999:::<<>>>>>======>>>@@@>>>>>>???AAAAAABBBBBBBBBBBBCCCEEEEEEDDDCCCCCCDDDAAAAAA@@@>>><<<:::888777999;;;===???BBBDDDFFFGGGDDDCCCAAA???============:::999888:::===AAADDDEEEFFFHHHKKKLLLKKKHHHDDDBBB>>><<<:::999999888666444666444222111222333333333000000000111222444555666444444333333333444444555111222444555666555444444444333333222111000//////111333555666666666888999777777666444444333333333///...------,,,,,,,,,,,,,,,------....../////////000//////...,,,+++************************++++++(((((())))))*********+++---,,,,,,+++*********+++)))(((((((((''''''''''''))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((('''''''''&&&'''((()))******)))(((((('''''''''&&&&&&'''''''''))))))))))))))))))))))))&&&'''((())))))(((''''''&&&&&&&&&'''''''''((((((%%%&&&'''((())))))(((((()))***+++,,,,,,+++***)))&&&''''''((()))******+++************************(((((()))***++++++,,,,,,++++++++++++++++++++++++((()))+++---...000000111...///000111111000///...------,,,,,,,,,+++++++++++++++++++++++++++++++++)))***,,,...///000111111222111000.........///000000/////////000111222333&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&((('''&&&%%%$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########""""""###$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&%%%%%%$$$###$$$$$$%%%%%%%%%%%%&&&&&&""""""!!!!!!""""""###$$$&&&&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%########################$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((''''''''''''&&&&&&&&&((((((''''''''''''(((((((((((((((((((((((((((((()))(((((((((((())))))***************************))))))))))))))))))))))))++++++++++++++++++,,,,,,******+++,,,------........./////////...------,,,,,,------......------,,,///000111222333444555555888888888888999::::::;;;<<<<<<;;;:::888666444333444333333333444666888999>>>@@@BBBBBBAAA?????????????????????>>>>>>======DDDEEEHHHIIIIIIGGGEEECCCBBBBBB@@@>>>===;;;:::999;;;===@@@CCCDDDCCCAAA@@@BBBAAA???===;;;:::999888::::::;;;<<<>>>AAADDDFFFFFFGGGHHHHHHGGGFFFEEEDDDAAA@@@>>>;;;888555222111111111111111111111111111111111111111000000000000333333333333333333333333333222111000000111222333222111///...------......///000222444666666666666999999888666333111///---++++++++++++,,,,,,---...,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++***************)))(((((()))************))))))))))))******222///,,,+++++++++***)))((((((((((((''''''''''''))))))))))))))))))))))))'''''''''&&&&&&'''''''''******)))((('''%%%###"""''''''(((((((((((('''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&'''''''''((((((((((((((((((((((((((((((***)))'''&&&&&&''')))***((((((''''''''''''(((((())))))))))))))))))))))))(((((((((''''''(((((((((*********)))))))))))))))))))))))))))))))))))))))************************------,,,++++++,,,,,,,,,,,,---...//////...---,,,******+++++++++,,,,,,,,,......---,,,++++++++++++------...///000111222222///............---------......//////000000111111$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''(((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&'''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######"""######$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&'''''''''&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((((((((''''''''''''((((((''''''''''''''''''''''''((((((((((((((())))))***************************************************+++++++++++++++,,,,,,,,,))))))******++++++,,,,,,...............---,,,,,,---------......---------//////000111222333444444777777666777888:::<<<===<<<<<<;;;999777555444333111111111222444666888:::===???BBBBBBAAA@@@@@@AAA@@@??????>>>>>>??????@@@EEEFFFHHHJJJJJJHHHFFFDDDCCCBBBAAA???===<<<::::::<<<===@@@BBBCCCCCCBBBAAABBBAAA???===;;;999888888777777777999;;;>>>@@@BBBEEEEEEFFFFFFFFFEEECCCCCCAAA@@@===;;;888555333222111111111111222222222222111111111111000000000000333333333333333333333333222111111000000111111222111000///------------...///000333555666666666666666555444222000...,,,***+++++++++++++++,,,---...,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++*********++++++++++++++++++++++++******))))))))))))******000...+++******+++***)))((((((((((((((((((((((((''''''''''''''''''''''''((('''&&&&&&&&&&&&'''((())))))(((((('''&&&$$$$$$''''''((((((((((((''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''(((((())))))))))))))))))))))))(((&&&%%%$$$$$$%%%&&&(((((((((''''''''''''(((((())))))))))))))))))))))))%%%%%%%%%$$$$$$%%%%%%%%%))))))******************))))))))))))))))))))))))++++++++++++++++++++++++---,,,,,,+++++++++,,,,,,,,,---...//////...---,,,*********+++++++++,,,,,,---,,,++++++++++++++++++------...///000111111222///............---------..................//////$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$############$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&'''%%%%%%$$$$$$$$$$$$######$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''''''''''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&'''''''''%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%&&&'''((()))***((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((()))))))))******************************************************+++++++++,,,,,,,,,---++++++++++++++++++++++++,,,------------,,,,,,+++------............------......///000111222333333555444444444777:::>>>@@@===<<<;;;999777444333222000000000111333666888:::<<<>>>AAABBBAAAAAABBBDDDAAA@@@???>>>>>>???AAABBBEEEGGGIIIKKKKKKIIIGGGFFFDDDCCCBBB@@@???===<<<;;;===>>>???@@@AAAAAABBBBBBAAA@@@>>><<<:::888777777555666666888:::<<<>>>???BBBCCCCCCCCCCCCBBBAAAAAA@@@???===;;;888666444333111111111222222333333333222222111111111000000000222222222222222222222222000111111222222111111000111000...---,,,,,,------///111333555666777666666333333222111///---+++***,,,++++++++++++,,,,,,---+++++++++++++++++++++++++++++++++++++++*********+++,,,---......---,,,+++******))))))))))))******---+++))))))*********)))))))))))))))))))))))))))'''''''''''''''''''''''')))(((&&&%%%%%%&&&((()))'''''''''(((''''''&&&%%%''''''(((((((((((('''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''))))))))))))))))))))))))'''&&&%%%$$$$$$%%%&&&'''((((((''''''''''''(((((())))))))))))))))))))))))(((''''''&&&&&&''''''((()))))))))***++++++,,,,,,))))))))))))))))))))))))++++++++++++++++++++++++,,,+++++++++++++++,,,,,,,,,------......------,,,*********++++++++++++,,,******************+++,,,,,,------...///000111111///............---------------------------,,,,,,&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&''''''''''''''''''''''''((('''&&&%%%%%%&&&'''(((%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&&&&''''''&&&&&&&&&&&&''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&'''(((((()))(((''''''&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''((()))))))))*********************************************************++++++,,,,,,---------............------------+++,,,,,,---,,,,,,++++++......////////////...............///000111111222333222111222555:::???BBB===;;;:::888555444333222111111000111222444666888:::<<>>???AAACCCGGGHHHJJJLLLLLLKKKIIIHHHEEEDDDCCCBBB@@@???>>>===>>>>>>=========???@@@AAA@@@???===;;;999888777666888888999:::<<<===?????????@@@@@@@@@@@@????????????>>>===;;;999777666555222222222222333333333444222222222111111111000000111111111111111111111111///000111222222111000///000///...,,,,,,,,,,,,---///000222444666666666666444444444333111///...---,,,+++++++++++++++,,,,,,++++++++++++************+++++++++***************+++,,,...//////...,,,+++******))))))))))))*********((('''((()))***)))((())))))))))))************'''''''''''''''''''''''')))(((&&&$$$$$$&&&((()))%%%&&&''''''((((((''''''&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((((((((((((((((((((()))(((''''''''''''((()))(((''''''&&&&&&''''''((((((((((((((((((((((((((())))))(((((((((((())))))((())))))***+++,,,,,,---))))))))))))))))))))))))************************+++************++++++,,,,,,,,,,,,------,,,,,,,,,************++++++++++++))))))((())))))***+++++++++,,,---...///000000111///............---------......------,,,,,,++++++&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''''''&&&%%%$$$$$$%%%&&&'''%%%%%%%%%&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&###$$$%%%%%%%%%$$$#########$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%&&&''''''$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((()))******************************************************************+++,,,------......//////..................++++++,,,,,,---,,,,,,+++...//////000000//////............///000000000111111000000111444999>>>BBB;;;:::888666444333333333444333222222222222444444999;;;===???@@@BBBEEEHHHIIIGGGCCC@@@???@@@AAABBBHHHIIILLLNNNNNNMMMKKKJJJFFFEEEEEECCCBBBAAA@@@??????>>><<<;;;;;;;;;===>>>===<<<;;;999888777777777999:::;;;<<<===>>>??????=====================>>>>>>===<<<;;;999888777777333333333333333333333333222222222222111111111111000000000000000000000000///000111222222111000///000///---,,,++++++,,,,,,...///111333555555555555444444444333222000///...,,,++++++******++++++++++++++++++******)))))))))************************)))+++,,,......,,,+++)))******))))))))))))******(((''''''''')))***)))'''((()))))))))*********+++(((((((((((((((((((((((()))(((&&&%%%%%%&&&((()))$$$%%%&&&'''((((((((((((&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''&&&''''''''''''''''''''''''(((((((((''''''(((((((((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&(((((()))***++++++,,,,,,))))))))))))))))))))))))(((((((((((((((((((((((()))))))))))))))***+++,,,,,,,,,,,,++++++,,,,,,,,,))))))*********+++++++++(((((((((((()))***++++++++++++,,,---...///000000///............---------.........------,,,,,,,,,$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$$$$######%%%%%%&&&&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$"""######$$$$$$$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&###$$$&&&'''''''''&&&%%%"""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%&&&&&&#########$$$%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&((()))************************************++++++++++++++++++++++++******+++,,,---...//////------------------------+++,,,,,,---------------//////000000000000//////.../////////000000000111111000000111444888<<>>;;;:::999888777777777777777888999999999:::;;;<<<======<<<<<<;;;:::999999:::;;;<<<===<<<<<<;;;;;;:::::::::999888777666555444222222111333333222222222111111111........................000000////////////000000...---,,,************++++++,,,...000111222222222////////////......---,,,,,,,,,+++***************+++******)))((((((''''''((()))))))))*********+++******++++++++++++************))))))))))))******)))(((((()))******(((&&&&&&&&&'''(((((()))******((((((((((((((((((((((((&&&&&&'''(((((('''&&&&&&%%%%%%&&&'''((((((((((((%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&''''''''''''''''''''''''%%%&&&&&&&&&&&&&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&))))))(((((((((((())))))((((((((((((((((((((()))))))))))))))))))))))))))(((((((((((((((((((((((((((''''''((()))***++++++,,,+++***))))))***+++,,,))))))))))))************++++++***)))))))))************+++,,,---......//////............---------++++++++++++,,,,,,,,,,,,&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&"""$$$%%%'''((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&(((***,,,,,,***(((&&&#########$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$&&&&&&&&&&&&$$$$$$###$$$%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&!!!$$$%%%%%%$$$$$$!!!"""###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''(((((('''''''''&&&&&&&&&((((((((((((((((((((((((%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&'''((())))))'''&&&&&&%%%%%%&&&&&&'''(((((((((((((((((((((((($$$%%%(((***++++++***)))************************++++++++++++++++++++++++******+++,,,---//////000---......///000111222222,,,------.../////////...000000111111111111000000000000000000111111111111111111222333444666777888777555444333333444666777555555444333444555666777666888999;;;<<>>>>>>>>======::::::999999999:::<<<===<<<<<<;;;;;;;;;:::::::::999999777666444222111000333333333222222222111111........................111000///......///000111...---,,,************+++***+++---///111111111111//////000000///......---,,,,,,+++***))))))******+++******)))(((''''''&&&(((((())))))*********+++,,,++++++******++++++,,,******))))))))))))******)))))))))*********'''%%%%%%&&&&&&'''((())))))***''''''''''''''''''''''''%%%&&&((())))))(((&&&%%%%%%&&&&&&'''((((((''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&'''''''''(((((('''''''''&&&&&&&&&((((((((((((((((((((((((''''''(((((((((((('''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&((((((((((((''''''''''''))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''((()))++++++,,,+++***))))))***+++,,,))))))))))))************,,,,,,+++***))))))******)))***+++,,,---....../////////.........---------))))))******+++++++++,,,%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$######$$$%%%&&&""""""###$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&((()))))))))((('''%%%%%%$$$#########$$$$$$%%%%%%$$$$$$%%%%%%&&&'''''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$''''''''''''''''''''''''''''''''''''''''''''''''&&&'''&&&$$$###"""$$$&&&%%%%%%%%%&&&&&&((())))))&&&&&&&&&%%%%%%$$$$$$$$$&&&''''''(((((((((((((((((((((((()))******++++++************************+++,,,,,,---.........---***+++,,,---............///////////////............------------...//////...//////000111111222222...//////111222333444444111111000000111222222333555555666555333333444666555555444555666777999;;;444666999<<<>>>@@@@@@@@@CCCDDDEEEFFFGGGHHHHHHHHHMMMNNNOOOOOOPPPPPPPPPOOOJJJJJJJJJIIIHHHGGGEEEEEEFFFEEEDDDBBB???===:::999999888777777666777777777999:::<<<===>>>???>>>>>><<<:::999777777888:::;;;<<<;;;:::999999:::<<<<<<999888888777666444222111444555555555444333333222000...---++++++,,,---...---...000///......///000---,,,,,,+++*********++++++***+++---000222333222/////////......---------((()))***++++++***)))(((***)))))))))))))))******)))))))))))))))))))))))),,,+++***((((((((()))***))))))))))))))))))))))))***)))(((&&&&&&''''''(((''''''(((***+++,,,---...,,,+++)))'''&&&%%%&&&&&&'''''''''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((()))((('''&&&%%%&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&'''''''''((((((((((((''''''''''''((((((''''''''''''((((((((((((''''''''''''((((((((((((&&&'''((())))))((('''&&&))))))))))))************,,,,,,+++***)))))))))***---,,,,,,++++++,,,,,,---***++++++***((('''((()))***++++++,,,,,,------...+++,,,---.........---,,,++++++++++++++++++++++++%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&'''''''''&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((((((&&&%%%$$$&&&(((%%%%%%%%%%%%&&&'''((()))(((((((((''''''&&&&&&&&&&&&''''''(((((((((((((((((((((((()))******+++++++++++++++++++++++++++++++++,,,,,,---......------+++,,,---.............../////////////////////......------------...//////000000000111222222333333222222222222222222222222222222111111111222333333444555666555333333555666:::999888777666777777888777888999;;;===???@@@AAAAAABBBCCCEEEFFFGGGGGGGGGKKKLLLMMMMMMNNNNNNNNNMMMJJJJJJJJJJJJIIIGGGFFFEEEEEEEEEDDDBBB@@@===;;;::::::999999888888888888888999:::<<<>>>?????????>>><<<;;;999888888999:::;;;;;;;;;:::::::::;;;===>>>;;;:::999777555333222111444444444444444333222222111000...---,,,---...///---...//////...---...///---,,,++++++******++++++,,,++++++---000222222111.........------,,,,,,,,,))))))************))))))******))))))))))))******)))))))))))))))))))))))),,,+++)))((((((((()))***))))))))))))))))))))))))***)))((('''&&&'''((((((''''''((()))***+++,,,,,,))))))((('''&&&'''((((((''''''((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''')))((('''&&&%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&'''''''''(((''''''''''''''''''(((''''''''''''((((((((((((''''''''''''((((((((((((''''''(((((()))((((((((())))))))))))************,,,+++******))))))******---,,,,,,++++++,,,,,,---)))***+++***)))((()))******++++++,,,,,,------...---...///000000///------++++++++++++++++++++++++%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&'''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$######"""&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$"""###$$$%%%%%%%%%$$$$$$%%%$$$$$$$$$%%%&&&''''''%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''''')))))))))((('''&&&((()))%%%%%%%%%%%%&&&'''((((((((((((((('''''''''''''''&&&''''''((((((((((((((('''(((((())))))******++++++++++++++++++++++++++++++,,,,,,---------------------......///...............//////////////////......------......///000111111222333333444444555666666555444333222222111444444333333222333333333555666666666444444666888===<<<;;;:::999999999999::::::;;;<<<>>>???@@@AAA???@@@BBBCCCEEEFFFGGGGGGIIIJJJJJJKKKKKKKKKKKKJJJJJJJJJJJJIIIHHHGGGFFFEEEDDDDDDCCCBBB@@@>>>===<<<;;;;;;;;;:::::::::999999:::;;;===>>>???@@@??????<<<;;;:::999888999999::::::::::::;;;;;;===>>>???>>><<<999666444333222222333333444444444333222222222111///.........///000---...///...---,,,---...,,,,,,++++++******++++++---,,,,,,---///000000...,,,,,,,,,,,,,,,+++++++++*********))))))***************)))))))))))))))***((((((((((((((((((((((((+++***))))))((()))))))))))))))))))))))))))))))))***)))((('''''''''((((((''''''((((((((()))))))))'''''''''''''''((()))***'''''''''((())))))******&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&(((((('''&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((''''''''''''((((((((((((((((((((((((((()))******))))))))))))************++++++***)))))))))******,,,,,,++++++++++++,,,,,,((()))******)))(((***+++***++++++,,,,,,------...000000111111111///...---++++++++++++++++++++++++%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&''''''&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$"""######$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''((()))%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$############$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%&&&''''''''''''''''''''''''((()))***)))''''''((()))'''&&&&&&&&&''''''((()))&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''(((((((((((((((''''''(((((()))*********+++++++++++++++++++++++++++,,,,,,---------,,,,,,---......//////.....................////////////...............//////000222333333444444555666666888777777666555444333333666666555444444444444555777888999888777777888:::<<<<<<<<<<<<======>>>>>><<<===???@@@AAAAAAAAA@@@???@@@AAACCCEEEFFFGGGGGGHHHHHHIIIIIIIIIIIIIIIHHHHHHHHHHHHGGGFFFEEECCCCCCCCCCCCBBBBBBAAA???>>>===============<<<;;;;;;::::::;;;===???@@@@@@??????;;;:::999888888888888888999::::::;;;<<<>>>?????????===:::666333222222222222222333333333333222222222111000////////////000---...///...,,,++++++---,,,,,,++++++***++++++,,,...---,,,---......---,,,++++++++++++************,,,+++))))))))))))+++,,,+++***))))))))))))))))))((((((((((((((((((((((((******)))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((''''''''''''''''''''''''''''''''''''((((((((()))%%%&&&&&&'''((())))))***&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((''''''''''''&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((''''''''''''(((((((((((()))(((''''''((()))+++,,,((()))))))))******************))))))))))))******,,,,,,++++++++++++,,,,,,'''(((******))))))***,,,***++++++,,,,,,------...000111111111000///---,,,************************%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&''''''&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&'''((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&$$$$$$$$$%%%&&&'''((()))%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$############$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&'''(((((('''&&&'''((((((((((((((((((((()))***&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((((('''''''''((())))))******+++++++++++++++++++++++++++,,,,,,---,,,,,,++++++,,,---..................---.........//////000000///............///000000222333333444444555666666777666666666666666666666777777666666666666777777999:::;;;:::999:::;;;=========>>>??????@@@@@@@@@;;;>>>BBBEEEFFFDDDAAA??????@@@BBBDDDEEEFFFGGGGGGGGGGGGHHHHHHHHHHHHGGGFFFEEEEEEEEEDDDCCCBBBAAA@@@@@@@@@AAAAAA@@@@@@???>>>>>>?????????>>>===;;;;;;:::;;;<<<>>>????????????:::999999888777666666666888999:::;;;===>>>>>>>>>???===999666333222222222111111222222222222222111000000000///////////////...//////...,,,***+++,,,,,,++++++***++++++,,,,,,///---,,,,,,------,,,+++************************,,,+++***))))))***+++,,,++++++***)))(((((())))))(((((((((((((((((((((((()))))))))*********)))))))))))))))))))))))))))))))))))))))))))))((((((((('''''''''&&&&&&&&&&&&&&&(((((((((((((((''''''&&&$$$$$$%%%&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&''')))******&&&&&&''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&%%%$$$$$$&&&&&&&&&&&&''''''''''''''''''''''''(((((((((((()))((('''''''''(((***+++((()))))))))***************))))))((())))))******,,,++++++******++++++,,,'''(((******))))))***,,,***++++++,,,,,,------...//////000000///---,,,***************************%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&(((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''%%%$$$$$$$$$%%%&&&''''''%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$%%%%%%&&&&&&''''''''''''''''''''''''''''''$$$%%%''''''&&&&&&&&&''')))((((((((((((((())))))((((((((((((((()))))))))&&&''''''(((((((((((((((&&&''''''(((((())))))***************************,,,,,,,,,,,,,,,++++++******+++,,,---............------......///000000000//////......//////000111111111222333333444444555555555666666777777888888888888777777888888999::::::;;;<<<;;;;;;;;;===???@@@@@@AAAAAAAAA@@@???>>>;;;>>>BBBEEEFFFDDDAAA???AAAAAACCCDDDEEEEEEFFFFFFFFFFFFFFFFFFFFFEEEEEEDDDCCCCCCCCCBBBAAA@@@???>>>===>>>>>>???@@@@@@?????????@@@@@@@@@???===;;;:::999:::<<<===>>>???>>>>>>::::::999888777666666555888999:::;;;<<<<<<<<<<<<===;;;888555333222111111000000111222222222111111000000000000/////////...///000000///,,,******+++++++++******++++++,,,,,,...---++++++,,,---+++***)))))))))***************++++++************++++++,,,+++***)))(((((((((((((((((((((((((((((((((((((((((()))************)))))))))))))))))))))))))))))))))*********)))((('''''''''&&&&&&&&&&&&&&&&&&(((((())))))((('''&&&&&&$$$$$$$$$%%%&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&''')))******%%%&&&''''''((('''''''''((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&&&&'''''''''''''''''''''((((((((((((((((((''''''''''''(((((())))))))))))************))))))((((((((()))******++++++************++++++((()))******)))(((***+++***++++++,,,,,,------...------.........,,,+++***************************%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&((()))'''&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$$$$%%%&&&'''%%%%%%$$$$$$$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''''''((((((''''''''''''''''''''''''###%%%'''((('''&&&&&&'''''''''&&&&&&&&&&&&'''''''''((((((((()))))))))***&&&''''''(((((((((((((((&&&&&&''''''((())))))))))))))))))))))))))))))))),,,,,,,,,,,,,,,+++******((()))***,,,---.........------......///000000111///////////////000000111000000000111222222333333666666666666777777777777777777888888999:::<<<<<<999:::;;;;;;:::;;;===??????@@@AAABBBBBBBBBAAA@@@;;;<<<>>>@@@AAAAAAAAAAAAAAAAAABBBCCCCCCCCCCCCCCCCCCDDDDDDDDDCCCCCCBBBAAACCCCCCBBBBBBAAA???>>>===:::;;;<<<>>>>>>????????????@@@AAAAAA@@@===;;;:::888999;;;<<<============<<<;;;;;;:::999888777666777888:::;;;;;;;;;::::::999888777555444222111000///000000111222222111111111111111111111000000///111222222000---+++++++++++++++******++++++,,,------,,,++++++,,,,,,+++***)))))))))******+++++++++***++++++,,,,,,++++++***,,,+++***)))(((((((((((())))))))))))))))))))))))'''((()))***+++******)))))))))))))))))))))))))))))))))***+++***)))((('''&&&&&&&&&&&&''''''''''''&&&'''((())))))(((((('''%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''%%%%%%'''(((((((((''''''((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''$$$%%%&&&''''''&&&%%%$$$%%%%%%&&&&&&&&&'''''''''''''''''''''(((((((((((('''((((((''''''&&&%%%$$$))))))))))))************((((((((((((((()))******++++++************++++++)))***+++***)))((()))******++++++,,,,,,------...+++,,,---......---,,,+++************************%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&''''''&&&%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""$$$'''((()))(((&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$#########&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$#########$$$&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&'''((())))))''''''''''''''''''''''''###%%%(((((((((''''''(((&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''((((((&&&''''''(((((((((((((((&&&&&&''''''((()))))))))((((((((((((((((((((((((,,,,,,,,,,,,,,,+++***)))&&&''')))+++---......///---------...///000000111///////////////000111111...//////000111111222222777777777666666666666666777777888999:::<<<===>>>777999::::::999:::<<<>>>:::<<>>AAACCC@@@AAAAAABBBBBBAAAAAA@@@BBBBBBBBBBBBAAAAAA@@@???CCCCCCCCCBBBAAA@@@???>>>999:::;;;===>>>????????????@@@AAAAAA@@@===;;;999777888:::<<<======<<<<<<=========<<<;;;:::888777777888999:::::::::999888777777666555444222000/////////000111111111111111222333333333333222111111222222222000---++++++,,,+++*********+++,,,,,,---,,,+++***+++,,,,,,+++***))))))******+++++++++,,,***+++,,,------,,,+++***,,,+++***)))((((((((((((************************'''((()))+++++++++***))))))))))))))))))))))))))))))******++++++)))((('''&&&&&&&&&'''''''''((((((###%%%'''(((*********)))''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&))))))((('''&&&&&&%%%%%%$$$%%%'''(((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&'''''''''(((((($$$%%%'''(((((('''%%%$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''((((((((()))''''''(((((('''%%%###"""))))))))))))************((((((((((((((()))******++++++************++++++***++++++***((('''((()))***++++++,,,,,,---......+++,,,---.........---,,,))))))))))))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&&&&$$$$$$###"""%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$%%%'''((('''''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%%%%&&&&&&((('''''''''''''''((()))(((((('''''''''&&&&&&&&&%%%&&&&&&&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&***)))(((''''''((()))***(((((()))(((((('''&&&&&&(((((((((((((((((((((((('''(((((()))***++++++,,,***++++++,,,,,,------...////////////..................//////000000111111------......///111222333666777888999999999999999666666666666777777777777555666777777777777777666:::::::::;;;<<<>>>AAABBB===<<<;;;::::::;;;===>>>?????????>>>>>>>>>>>>>>>===>>>>>>>>>>>>======<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>===<<<<<<;;;;;;999999;;;===>>>??????@@@???>>>===<<<:::999888777777888888777555555666777666666555444333111///............////////////000000111111111222222222222444333111///---,,,++++++)))***+++,,,---...//////...---+++*********+++++++++++++++************))))))************+++++++++************))))))))))))'''(((((()))***+++++++++))))))))))))((((((((((((((()))))))))************(((((())))))))))))(((((($$$$$$%%%%%%'''(((******)))))))))(((((((((((((((&&&&&&'''''''''''''''&&&%%%%%%&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%(((((('''''''''&&&&&&&&&''''''''''''''''''&&&&&&((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((()))))))))(((&&&$$$#########$$$&&&&&&%%%$$$%%%&&&'''((('''((((((((()))))))))***''''''((()))))))))))))))&&&''''''((()))******+++))))))************))))))))))))***++++++++++++***+++***)))(((((()))***+++((())))))))))))************+++---//////...---,,,++++++++++++++++++++++++&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%$$$$$$###%%%%%%$$$######$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%$$$$$$$$$%%%&&&'''''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################&&&%%%%%%%%%%%%%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''((((((((((((((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&&&&&&&'''((())))))))))))))))))(((''''''(((((((((((((((((((((((('''(((((())))))***************++++++,,,---......111111000000000/////////....../////////000000000//////......///000111111444555666777777777777777555555555555666666666666555666666666666666555555888777888888:::<<<>>>???;;;::::::999::::::<<<<<<======>>>>>>======<<<;;;<<<<<<==================<<<======???AAACCCEEEFFF@@@@@@@@@??????>>>>>>>>>>>>>>>======<<<;;;;;;:::888999:::<<<===>>>??????===<<<;;;:::888777666666666777777666444444555666888888777555333000...---------........./////////000000000000111111111111111000///...------------))))))************++++++---,,,+++*********+++++++++++++++*********))))))))))))*********+++++++++*********)))))))))(((((()))))))))(((''''''&&&&&&******)))))))))((((((((((((((()))))))))*********(((((())))))))))))((((((&&&&&&&&&'''((()))***+++---+++)))'''&&&&&&(((((('''''''''(((''''''&&&&&&''''''((((((''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%((('''''''''&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&'''''''''(((***)))'''&&&%%%%%%&&&'''&&&&&&%%%%%%%%%&&&'''(((((((((((((((((()))))))))''''''((()))))))))))))))''''''(((((())))))******)))))))))******)))))))))))))))***++++++++++++***))))))(((''''''((()))))))))))))))************+++***+++---...///...---,,,++++++++++++++++++++++++&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''%%%$$$""""""$$$%%%'''$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&((('''&&&&&&$$$$$$###"""&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$#########$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''((())))))*********((('''&&&''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''((())))))*********)))(((((((((((((((((((((((((((((((((((((((((((((((((((((())))))***+++,,,---...///000000/////////..................///////////////000//////......//////000222333333444444444444444333333333333444444555555555555666555555444333222444444444555666888:::;;;999999999888999:::;;;;;;:::;;;=========<<<:::999::::::;;;;;;<<<<<<======999:::;;;>>>AAADDDGGGHHHBBBBBBAAA@@@???>>>>>>=========<<<<<<;;;:::::::::666777999;;;<<<=========;;;:::999888777555555444555666666555444333444555::::::888666333000...,,,,,,,,,,,,---------............/////////000000000......---------...//////++++++*********))))))))),,,,,,+++************+++++++++*********))))))))))))))))))*********++++++******))))))))))))((((((******)))(((((('''&&&&&&************))))))))))))(((((((((((())))))))))))'''(((((())))))(((((('''((((((((((((((()))******000---)))%%%$$$%%%''')))((((((((((((((('''&&&%%%''''''((((((''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&((((((&&&&&&&&&&&&'''(((&&&%%%%%%%%%%%%&&&'''(((((((((((((((((((((((((((''''''((()))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))))))))***++++++++++++***((((((''''''''''''(((((()))************+++++++++***+++---.........---,,,++++++++++++++++++++++++%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&'''&&&$$$""""""$$$&&&'''$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$'''&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''$$$%%%%%%%%%$$$$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&'''((()))***++++++***(((&&&$$$&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&''''''(((((())))))))))))((('''((((((((((((((((((((((((((((((((((((''''''''''''(((((()))+++,,,---...///------,,,,,,,,,+++++++++.......................................///000111111222222333333333222222000111111222222333333333555555555444333222111000222222333444555666777888888888999999::::::;;;;;;999:::<<<>>>===;;;999777888888999999:::;;;<<<===888999:::===???BBBEEEFFFCCCCCCBBBAAA???>>>======<<<<<<;;;;;;::::::999999555666888999;;;<<<<<<<<<:::999888777666555444444444666777666555333444555999999888666444111///...++++++,,,,,,,,,------------------.........//////---------,,,------...///,,,,,,,,,,,,++++++++++++++++++******************************))))))))))))))))))))))))***************)))))))))(((((((((((()))))))))******++++++++++++*********))))))))))))'''''''''((((((((())))))'''(((((((((((((((((('''((((((((('''(((((())))))---+++)))'''&&&&&&((((((((())))))(((((('''&&&%%%%%%%%%&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%$$$$$$###$$$%%%&&&'''%%%%%%%%%%%%&&&&&&'''''')))(((((((((((('''''''''''''''((()))))))))))))))))))))))))))(((((((((((()))))))))(((((()))))))))))))))***++++++++++++***((((((((((((((((((((((((************++++++++++++***+++,,,------------,,,************************%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&''''''&&&$$$######$$$&&&'''$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''(((((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%''''''''''''''''''''''''%%%%%%&&&&&&&&&'''''''''"""###$$$$$$%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$%%%&&&'''((())))))++++++***(((&&&$$$%%%%%%&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&''''''(((''''''&&&((((((((((((((((((((((((((((((((((((''''''''''''((())))))***,,,------...,,,,,,,,,,,,++++++++++++.........---------------++++++,,,---///000222333222222222333333222111111...//////000111222222222444444444444333222000000222222333444555666666777888999999:::;;;<<<<<<<<<999;;;===>>>>>><<<999777777777777777888999;;;;;;999999:::;;;===???AAABBBBBBBBBAAA@@@>>>===<<<<<<;;;;;;::::::999888888888555555777999:::;;;;;;;;;::::::999888777666666555555777888888666555555555666666666555444222111000+++++++++,,,,,,,,,,,,---,,,------------.........///...---,,,,,,+++,,,,,,******+++++++++,,,,,,,,,*********************************)))))))))(((((((((((()))))))))*********)))))))))((((((((((((''')))))))))))))))******************))))))))))))(((&&&''''''''''''(((((((((''''''(((((((((((('''''''''''''''&&&&&&'''(((((('''((())))))))))))(((((((((((())))))(((''''''&&&%%%%%%&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%$$$######$$$%%%'''(((%%%%%%%%%&&&&&&&&&&&&&&&((((((((('''''''''''''''''''''((()))))))))))))))))))))))))))(((((((((((())))))(((''''''((())))))))))))***++++++++++++***))))))))))))))))))))))))))))))*********++++++++++++++++++,,,,,,,,,,,,,,,************************%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""!!!%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&"""###$$$$$$&&&''''''(((%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''###$$$%%%%%%&&&&&&%%%%%%''''''''''''''''''''''''%%%&&&&&&&&&''''''''''''"""###$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$%%%&&&'''(((((()))))))))'''&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&'''''''''&&&&&&(((((((((((((((((((((((((((((((((((((((((((((((())))))******+++,,,,,,,,,//////.........------------------------,,,,,,,,,******+++,,,///111333444222222222222222222111000---......///000111222222333333444333333222111000222333444555666666666666777888:::;;;<<<<<<<<<<<<999:::<<<===<<<;;;999888777666555555666777888:::888888999999:::;;;<<<===??????>>>===<<<<<<;;;;;;:::::::::999888888777777444555777999:::;;;;;;;;;::::::999999888777777666555777999999777666555555444444444444333222111111+++++++++,,,,,,,,,------,,,,,,---------.........000///---,,,+++******)))((((((((()))))))))******((()))******+++***************)))))))))(((((((((((((((((()))))))))******))))))((((((((((((''''''))))))((('''%%%$$$######))))))))))))((((((((((((&&&&&&&&&&&&'''''''''(((&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&'''(((((($$$&&&(((++++++***)))((('''(((((())))))(((((((((''''''((((((''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&%%%&&&'''((()))$$$%%%&&&&&&''''''&&&&&&&&&&&&'''''''''(((((((((''''''((()))))))))))))))(((((((((((())))))))))))))))))''''''''''''))))))))))))***++++++++++++***))))))************))))))((())))))))))))*********++++++++++++,,,,,,,,,,,,************************$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$######""""""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&###$$$%%%&&&&&&&&&%%%$$$######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%''''''''''''&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&%%%$$$###"""%%%&&&&&&'''((((((''''''(((((((((((((((((((((((('''(((((())))))***************************++++++////////////............---------,,,,,,,,,+++++++++++++++,,,...000222333111111222222111000000///------...///000111222222222333333444333333222222222333444555666666555555666777888:::;;;;;;;;;;;;999999::::::999999888777777666555444444555666888666666666777888999:::;;;<<<;;;;;;;;;::::::999999:::999999888777777666666555666777999:::;;;<<<<<<:::999999888888777777777444666888888777555444444444444444333222000///...,,,,,,,,,,,,------------------------............///...---+++******))))))))))))))))))(((((((((((('''((()))***++++++***)))***)))))))))(((((((((((((((((((((((()))))))))***))))))((((((((('''''''''(((((('''%%%$$$###"""!!!(((((((((((('''''''''&&&%%%%%%&&&&&&&&&'''''''''&&&''''''((((((''''''&&&&&&&&&&&&&&&'''(((******'''((())))))***))))))(((&&&'''((())))))***))))))''''''((((((''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%%%%&&&&&&&&&###$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&'''''''''(((((('''&&&%%%&&&'''((()))$$$%%%&&&'''''''''&&&&&&$$$%%%%%%&&&'''((())))))''''''((()))))))))))))))''''''(((((())))))*********)))'''&&&&&&''')))***))))))***++++++++++++***(((((()))******)))((((((''''''((((((((()))))))))+++++++++++++++,,,,,,---************************$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''(((((('''%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""###%%%&&&'''&&&&&&%%%#########$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&'''''''''((((((''''''''''''&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$$$$&&&&&&%%%%%%%%%&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$"""!!!&&&&&&'''((())))))(((((((((((((((((((((((((((((('''(((((()))***++++++,,,+++++++++************)))......---------,,,,,,,,,---------,,,,,,+++++++++,,,,,,,,,---...///000111000000111111000///......------...///000111222333222222333444444444333333111222444555666555555444444555777999:::;;;::::::888888888777777777777777777666444333333444555666444444444555777888:::;;;999999999999999999999999999999888888777666666666555666888999;;;<<<<<<<<<999999888888777777666666333555777888666444333333555555444333111///---,,,,,,,,,------------......---------.........//////------,,,+++************------,,,+++***)))(((((('''((()))+++++++++***)))))))))))))))(((((((((((((((((((((((()))))))))))))))(((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((('''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&''''''''''''''''''&&&&&&&&&'''''')))***+++,,,+++***)))(((''''''((((((%%%&&&''')))************%%%%%%&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$%%%%%%&&&&&&&&&######$$$%%%%%%&&&''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((())))))&&&&&&$$$$$$$$$$$$%%%&&&$$$%%%&&&'''''''''&&&%%%###$$$%%%&&&''')))******'''(((((()))))))))))))))&&&''''''((()))******+++***((('''&&&&&&'''(((***))))))***++++++++++++***&&&'''((())))))((('''&&&''''''''''''((((((((((((++++++******++++++,,,---))))))))))))))))))))))))%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&&&&%%%$$$$$$%%%&&&&&&&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&''''''''''''''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$###$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$###"""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&'''''''''((()))))))))'''%%%###$$$''')))'''%%%&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&&&&&&&$$$%%%&&&((()))*********++++++,,,,,,---...////////////...---,,,,,,++++++++++++++++++++++++++++++---,,,,,,,,,---...000111.........///////////////+++,,,---...///000111222222333555777777666555444333333333444444444555555999777666666666666444333666666777777777777777666888666555333333444555666444555666777888999:::;;;<<<<<<;;;;;;999888666555777777666666777888888999666777999;;;<<<<<<<<<;;;============<<<:::888777555555444333333333333444555444222000///...//////---,,,,,,++++++,,,,,,---...---+++******+++---...------,,,,,,+++***))))))))))))))))))(((((((((((())))))))))))(((((((((((()))***+++***)))((()))***(((''''''(((******)))(((+++(((%%%###"""$$$&&&(((''''''&&&&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((%%%%%%%%%&&&&&&'''''''''&&&&&&%%%$$$%%%&&&'''(((&&&&&&&&&%%%%%%$$$$$$$$$'''&&&$$$######$$$&&&'''''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%&&&''''''(((''''''&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&''')))*********)))((((((((('''''''''&&&&&&&&&(((((())))))))))))((((((++++++***)))))))))))))))))))))))))))************+++++++++++++++*********,,,+++***)))((((((((((((******))))))******+++,,,))))))))))))))))))))))))&&&&&&&&&%%%%%%%%%%%%%%%###%%%&&&&&&%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&''''''''''''''''''((('''%%%$$$%%%'''((('''%%%&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&''''''(((%%%&&&'''((()))***************++++++,,,------...//////......---,,,,,,+++++++++++++++++++++++++++///...---------...///000////////////////////////------...///000000111222222333555666666666444444333333333444444444555555666555555555555555444444444555666666777777777777888777555444444444666666444555555777888999::::::;;;;;;:::999777666666555555555555666666777888999::::::;;;;;;;;;:::999888888999999999888666555444555444333333222222333333444222111///............---,,,,,,++++++,,,,,,---...---+++******+++---...---,,,,,,+++******))))))))))))))))))(((((((((((()))((((((((((((((((((((()))***+++***(((((((((***(((''''''(((******)))((()))(((%%%$$$###$$$&&&'''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%&&&'''(((&&&&&&%%%%%%%%%%%%%%%%%%'''&&&$$$######$$$&&&''''''&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&'''%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&'''((()))***)))(((((((((((('''''''''&&&&&&&&&(((((())))))))))))(((((()))(((((('''''''''''''''))))))))))))************%%%%%%&&&''''''((()))))),,,+++***)))((((((((((((***************+++,,,,,,************************&&&&&&&&&&&&&&&&&&&&&&&&###%%%&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&%%%&&&%%%$$$%%%'''((('''&&&&&&%%%%%%%%%%%%&&&''''''((('''&&&&&&&&&'''((()))'''((()))***************))))))******++++++,,,,,,/////////...------,,,,,,++++++++++++,,,,,,,,,,,,111000///.........///////////////////////////////////////000000000111111222333444555666555444333333333333444444444555555444444444444333333333333222333444555666777777777888777666555444555666666444555555666777888999999:::999777555555555555555444444444555666888999:::===>>>===<<<:::888555444555555666777666555444333333222222111111111111111111111///...---------------,,,,,,++++++,,,,,,---------++++++++++++------+++++++++******))))))((())))))))))))(((((((((((((((((((((((((((((((((((()))***+++***((('''((()))(((''''''(((******)))'''''''''&&&%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&'''(((((())))))(((((('''''''''''''''&&&&&&&&&'''(((((())))))(((((('''((((((''''''&&&&&&''''''))))))))))))************''''''(((((()))))))))***,,,+++***)))((((((((((((++++++******++++++,,,---************************&&&&&&&&&'''''''''''''''###%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%&&&'''''')))((('''&&&&&&''')))***)))******+++++++++******************++++++,,,,,,/////////......---------+++++++++,,,,,,,,,,,,,,,111000///......///000111000000000///////////////111111111111000000000000222222333444444444444333333333333444444444555555444444555333222111111111111222333555666777777777777666555444444444555555555555555666666777777777888666444333222333444555333333444555777999;;;<<<>>>>>>>>><<<:::777555333555666777888777777555555111111000////////////000//////...---,,,,,,,,,+++---,,,,,,++++++,,,,,,------,,,,,,++++++,,,,,,---*********)))))))))(((((())))))))))))(((((((((((('''''''''((((((((((((((()))***+++***(((''''''(((''''''&&&((()))***((('''&&&&&&&&&&&&&&&&&&%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&$$$%%%%%%%%%&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%&&&&&&'''((('''&&&&&&&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&''''''(((((((((((('''''''''''''''''''''''''''(((((((((((((((((('''***))))))((((((((())))))((()))))))))************,,,,,,+++***)))''''''&&&++++++***)))(((((())))))+++++++++++++++,,,,,,---************************&&&&&&&&&'''''''''((((((###%%%&&&&&&%%%$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$###%%%%%%&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&''''''(((''''''&&&'''((()))***)))***+++++++++++++++***++++++++++++,,,,,,,,,,,,...............---------++++++,,,,,,,,,---------......---...///111333444111111000000////////////111111111111000000000000111222222333333333333333333333333444444444555555666777777555111//////000111222333555666777777777555555555444444444444444555555555555555555666666666444222111111222444555333444555666888:::<<<>>><<<<<<<<<<<<;;;999777555666777888888888777666555000000///............///......------,,,,,,++++++---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,*********)))))))))))))))))))))))))))((((((((((((&&&&&&''''''((((((((())))))***+++)))'''&&&&&&''''''&&&&&&'''))))))((('''%%%%%%&&&''''''&&&&&&%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''''''''''''''(((((()))&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&''''''(((&&&'''''''''''''''''''''''''''((((((((((((''''''))))))(((((((((((())))))((()))))))))************))))))((('''%%%$$$######+++***))))))))))))))))))++++++******++++++,,,---************************%%%%%%%%%&&&''''''((((((###%%%&&&&&&%%%$$$$$$%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%'''&&&%%%%%%&&&(((&&&%%%%%%%%%%%%&&&''''''&&&&&&''''''((((((((((((((()))***++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,------------------------++++++,,,,,,------......,,,,,,,,,---///111333555222111111000000//////...000000000000000000000000111111111222222222333333333333333444444444555555777999999777222000000222222333444555666777777777555555555555555444444444555555555555555444444444333333222111111222333444333444555666888:::<<<===::::::;;;;;;;;;:::999888555666666777666555444333000000///...............---------------,,,++++++---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,************************))))))))))))((((((((((((&&&&&&&&&''''''(((((())))))***+++)))'''%%%&&&''''''&&&&&&'''))))))(((&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$######$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''''''''''''''(((((()))$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&&&&''''''''''''&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&'''''''''''''''&&&''''''((((((''''''&&&&&&&&&%%%%%%&&&&&&''''''))))))))))))************''''''''''''(((((())))))******)))))))))))))))*********))))))******+++,,,++++++++++++++++++++++++$$$$$$$$$%%%&&&'''''''''###%%%&&&&&&%%%$$$$$$%%%###$$$%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&''''''((($$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###""""""###$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&###%%%''''''%%%%%%&&&(((&&&%%%%%%%%%%%%&&&''''''$$$%%%'''(((((((((&&&%%%'''''')))***++++++++++++++++++++++++++++++******,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---......///,,,,,,,,,,,,...///111333222222111111000//////...////////////////////////111111111111111222222333333333333444444444555555555888:::888444222444777444555666666777777777777777777777777777666666555555555555444444333333333111111222222222333333333222222333444666888999:::999:::;;;;;;;;;:::999888666666666666555444222111000000///...............,,,---.........---,,,+++---,,,,,,++++++,,,,,,---+++,,,,,,------,,,,,,+++***+++++++++++++++++++++))))))))))))((((((((((((%%%%%%&&&''''''((()))))))))***+++)))'''%%%%%%&&&&&&&&&%%%'''((()))(((&&&%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%"""###$$$%%%&&&%%%%%%$$$''''''''''''&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&''''''$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%$$$$$$$$$%%%''''''&&&&&&&&&'''''''''((((((&&&''''''((((((''''''&&&&&&%%%%%%%%%%%%&&&'''((())))))))))))************))))))******+++,,,------******))))))))))))******))))))(((((())))))***+++++++++++++++++++++++++++######$$$%%%%%%&&&''''''###%%%'''&&&%%%$$$%%%%%%###$$$%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%$$$########################$$$$$$%%%%%%&&&'''(((((($$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%$$$######!!!!!!"""###%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&'''''''''###&&&((('''%%%$$$&&&)))&&&%%%%%%%%%%%%&&&''''''"""$$$&&&((()))'''%%%$$$&&&&&&((()))++++++,,,,,,*********)))))))))))))))++++++++++++++++++++++++++++++,,,,,,---...//////...---,,,,,,---...///000222222222111000//////.............../////////000111111111000111111222333333333333444444444555555333777:::999666555888<<<666666777777777777777666999999999999999888777777555555555444444333333222000111222333333444333333111111222222444555777888999:::;;;;;;;;;:::999888888888888888777555333111000000///............///,,,---.........---,,,+++---,,,,,,++++++,,,,,,---+++,,,,,,------,,,,,,+++++++++++++++++++++,,,,,,))))))))))))((((((((((((%%%%%%&&&&&&'''((())))))******+++)))&&&%%%%%%&&&&&&&&&%%%'''((()))'''&&&%%%%%%%%%%%%%%%&&&'''(((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%&&&"""###$$$%%%&&&%%%$$$$$$((((((((('''&&&&&&&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&'''''''''((((((&&&%%%$$$$$$$$$%%%&&&'''&&&&&&&&&'''''''''((((((&&&''''''''''''''''''&&&'''''''''''''''((()))***))))))))))))************)))))))))(((((((((((((((***)))))))))))))))******((((((((((((((())))))***++++++++++++++++++++++++&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&'''''''''((()))))))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$%%%''')))***%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$%%%'''''''''(((''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$&&&''''''((($$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&'''((('''%%%$$$%%%&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((((((((((((((((((((((((%%%&&&''')))***+++------------,,,+++***)))((('''******++++++***)))'''&&&+++,,,,,,,,,,,,,,,,,,---///...,,,,,,,,,///111333111111111111111000///...............////////////.........////////////000111111222222444666777888999999999999999999999999555666777999:::;;;;;;;;;>>>===;;;999888888888888888888999999888777666555444222///------000444777111222444666777888888888999:::<<<>>>===<<<999888777777777777777666555444222222111000///...------------............------,,,,,,+++******++++++,,,,,,,,,------,,,,,,+++***,,,+++******++++++)))'''''''''((((((((((((''''''(((((())))))******++++++******))))))((((((''''''(((((('''''''''&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''%%%$$$%%%'''&&&&&&&&&%%%%%%%%%$$$$$$&&&%%%$$$###$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$###"""!!!&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$######"""&&&&&&''''''&&&&&&%%%%%%&&&%%%%%%%%%%%%&&&'''''''''&&&&&&%%%%%%&&&&&&'''(((&&&$$$%%%&&&((())))))))))))))))))))))))((((((((()))+++,,,------,,,++++++***)))((('''''''''''',,,)))'''(((+++---,,,***)))))))))))))))******+++++++++++++++++++++++++++&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%&&&((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$###"""!!!$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&'''((('''%%%$$$%%%&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&''''''(((''''''''''''''''''''''''((((((((((((((((((((((((************************++++++***************)))((()))***+++++++++***)))+++,,,,,,,,,,,,---------...---+++++++++...000222111111222222111111000///////////////////////////////////////000000000000111111222333444666777888888888999999::::::;;;;;;999::::::;;;;;;:::::::::>>>===<<<:::999999888888888999:::::::::888777666888666333000000111333555222333444666777888999999777999;;;=========;;;:::999999999888777666444444111111000///...---,,,,,,---......//////......---,,,,,,+++++++++++++++,,,,,,,,,------,,,,,,+++***---,,,++++++,,,,,,***)))'''(((((())))))(((((('''&&&'''''''''((((((((())))))(((((((((''''''''''''(((((('''''''''&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%######$$$%%%%%%%%%%%%$$$$$$$$$######%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$###""""""%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&%%%$$$$$$######$$$$$$######$$$$$$$$$%%%%%%%%%%%%&&&'''''''''&&&%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''(((''''''&&&&&&''''''((('''%%%######%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%$$$((()))***,,,------,,,,,,,,,+++***)))((((((((((((***'''&&&&&&)))******((())))))(((((())))))***+++++++++++++++++++++++++++&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%$$$###!!! %%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% !!!"""$$$%%%&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&'''&&&%%%$$$%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&((('''&&&&&&$$$$$$###"""$$$$$$%%%%%%&&&'''((((((''''''''''''''''''''''''(((((((((((((((((((((((('''''''''''''''''''''''')))))))))******+++++++++((()))***+++,,,,,,,,,,,,++++++,,,,,,---------------,,,+++***+++---///000222222222222222222111000111111000000//////......////////////000000000111111222333444555777888888888888999:::;;;<<<======>>>>>>======<<<;;;999999<<<<<<======<<<:::888777999:::;;;;;;;;;:::999888;;;:::777555333333333333333444555666777999999:::666777:::<<<======<<<;;;::::::999999777666555444000000///...---,,,++++++......////////////......+++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++***---,,,+++,,,------+++)))((())))))******))))))(((''''''''''''((((((((((((((((((''''''''''''&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$$$$$$$%%%&&&$$$$$$$$$$$$############$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%$$$$$$######$$$$$$#########$$$$$$%%%%%%&&&###%%%'''(((((('''&&&%%%!!!"""###%%%&&&&&&''''''&&&%%%%%%%%%%%%&&&''''''(((((((((''''''((((((((((((&&&$$$$$$%%%&&&%%%$$$$$$%%%&&&&&&'''''''''''''''(((***,,,------------,,,,,,+++***)))))))))))))))'''&&&&&&((())))))((())))))(((((())))))***+++++++++++++++++++++++++++&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%(((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%$$$'''''''''&&&&&&$$$######%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###''''''''''''''''''''''''$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!"""###$$$%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$&&&'''&&&$$$$$$%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((((((((((((((((((((((((%%%%%%&&&'''((()))******))))))))))))************+++++++++,,,,,,---------++++++,,,,,,---............---,,,+++,,,---///000222222333333333222222111111111111000//////.............../////////000000111222333555666777888888:::::::::;;;;;;<<<<<<<<>>>>>===<<<::::::;;;<<<===>>>===;;;888777888999:::;;;;;;:::999999;;;:::999777666444333333444444555666777999:::;;;777888:::;;;<<<<<<;;;:::888999999999888777666666111000//////------,,,+++.........//////.........++++++,,,,,,,,,,,,,,,,,,+++,,,,,,,,,,,,+++******,,,+++***+++,,,,,,+++)))))))))************))))))))))))))))))************((((((((((((((((((((('''''''''''''''''''''''''''&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$&&&&&&&&&&&&((()))%%%%%%%%%$$$$$$$$$#########$$$%%%&&&'''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&%%%%%%$$$$$$###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$ """$$$&&&'''&&&$$$###!!!"""###$$$%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''((((((''''''''''''((((((***)))''''''(((((('''%%%%%%&&&'''((())))))))))))&&&(((***,,,---...------,,,+++***)))((((((((((((***)))((())))))***++++++((((((((((((((()))******************************&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&&&&&&&%%%$$$%%%&&&'''''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$####################################$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$######"""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&%%%$$$$$$%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%$$$''''''''''''''''''''''''(((((((((((((((((((((((((((((())))))***+++,,,,,,*********)))))))))((((((...------,,,,,,,,,++++++++++++,,,------.../////////......------...///000111222222333333333222222111000000000//////......------........./////////222333444666888888999888<<<<<<<<<;;;;;;:::::::::<<<======>>>======<<<<<<999;;;===>>>>>>;;;888666666777888:::::::::999999888888888777777666555444444444444555666888:::;;;:::;;;;;;;;;;;;999888777666666777888888888888777222111111000///...------------............------***+++,,,------------,,,++++++,,,,,,++++++***)))***)))((()))++++++***((())))))************))))))************))))))))))))))))))))))))))))))))))))&&&''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$&&&&&&&&&&&&((()))'''&&&&&&&&&&&&%%%%%%%%%###$$$%%%&&&'''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$############$$$%%%%%%%%%$$$$$$###$$$$$$%%%%%%'''&&&&&&%%%$$$###""""""!!!"""$$$&&&&&&&&&$$$###$$$$$$$$$%%%%%%$$$$$$###&&&%%%%%%%%%%%%&&&'''''''''&&&&&&%%%%%%&&&&&&'''***)))(((((()))((('''%%%###$$$%%%&&&'''''''''''''''(((***,,,------------***)))(((''''''&&&''''''))))))))))))))))))***+++((((((((('''((())))))***************************&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''$$$%%%&&&''''''&&&%%%$$$######$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%$$$######"""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""#########$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%%%%$$$$$$%%%&&&$$$$$$$$$$$$%%%%%%%%%%%%"""###$$$$$$&&&''''''((('''''''''&&&&&&%%%%%%$$$''''''''''''''''''''''''(((((((((((((((((((((((((((''''''&&&&&&%%%%%%$$$*********))))))(((((((((///...---,,,++++++++++++++++++,,,---...//////000//////.........//////000000111222222222222222222.........///////////////............////////////222333555777999999999999======<<<;;;:::999888888::::::;;;<<<=========<<<888:::<<<===<<<:::888666555666888999:::::::::999777777777777666666666666333333333333555777999:::<<<;;;;;;;;;:::888777666555666666777777777777777222222111000///...------,,,,,,------------,,,,,,***+++,,,.........------+++++++++++++++******)))((((((''')))***+++)))(((((())))))******))))))(((((((((((((((''''''''''''))))))************++++++&&&&&&&&&''''''''''''''''''&&&%%%$$$$$$%%%&&&'''&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$$$$$$$%%%&&&''''''''''''&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###############$$$%%%%%%$$$$$$######$$$$$$%%%%%%'''&&&&&&%%%$$$###""""""%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%$$$######&&&%%%%%%%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&'''&&&&&&&&&((('''&&&$$$%%%&&&'''(((((()))((((((((()))+++,,,------,,,+++))))))((('''&&&&&&&&&&&&&&&'''''''''&&&&&&(((***((((((''''''(((((()))***************************&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&((((((&&&%%%$$$######$$$%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%''''''''''''''''''''''''!!!""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%%%%%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$"""$$$%%%%%%$$$$$$%%%&&&###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''((((((((((((((((((((((((%%%%%%$$$$$$###""""""!!!((((((((()))))))))))))))---,,,+++******+++,,,,,,++++++,,,---...///000000........................///000111111222222111111,,,,,,------......//////000000000000111111111111222333666888::::::999999;;;;;;::::::999999888888888999:::;;;;;;;;;;;;:::888999:::;;;;;;999777666555777999:::<<<<<<<<<;;;999888777777666666777777333222222222333666888:::::::::::::::999999888888777777777666666555333333111111000///...------,,,***++++++,,,,,,++++++***)))***,,,...//////...---+++++++++++++++***)))))))))(((((()))++++++***)))'''(((((())))))((((((''')))((((((((('''''''''&&&((()))))))))************&&&&&&&&&'''''''''((((((((('''%%%$$$$$$%%%'''(((&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%######$$$%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&########################%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###############$$$$$$%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$((('''&&&%%%%%%%%%&&&'''$$$%%%%%%&&&&&&&&&&&&%%%&&&%%%%%%%%%%%%&&&''''''''''''&&&&&&&&&&&&''''''&&&%%%%%%'''(((((('''%%%(((((())))))***)))))))))******,,,,,,,,,,,,+++******)))(((''''''&&&&&&&&&%%%'''((('''%%%%%%'''***(((''''''''''''((())))))************************&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######%%%%%%&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$%%%'''(((((('''%%%$$$&&&&&&&&&&&&&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&'''''''''$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$###"""!!! $$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$"""###%%%%%%$$$$$$%%%&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%'''((()))***''''''''''''''''''''''''(((((((((((((((((((((((('''''''''(((((()))))))))&&&&&&'''((()))***+++++++++******)))***+++---...++++++,,,---...///000111------------------------...///000111111111111111***++++++,,,---...//////111222222222222333333333222444666999::::::999999999999999999999999999999999999999::::::999888888888888999999999888777666666888:::<<<============<<<:::999777666666777888222222111111222555888999999999999999999999::::::999888888666444222000///000000///...---,,,,,,+++*********++++++*********)))***---...//////...---***++++++++++++***)))))))))))))))***,,,,,,+++***''''''((((((((((((''''''++++++******)))))))))((('''((((((((())))))******&&&&&&&&&'''''''''((((((((('''%%%$$$$$$%%%'''(((&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''((('''%%%%%%%%%'''&&&&&&&&&%%%%%%%%%$$$$$$&&&%%%$$$###$$$%%%&&&'''########################%%%%%%&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########"""###$$$$$$%%%$$$#########$$$%%%%%%&&&!!!""""""$$$%%%&&&''''''(((&&&$$$"""""""""$$$%%%###$$$%%%&&&'''(((((((((&&&%%%%%%%%%%%%&&&''''''((((((''''''''''''((((((''''''''')))++++++)))(((%%%%%%%%%&&&%%%%%%$$$$$$++++++,,,---,,,+++***)))+++***)))(((((('''''''''''')))***)))''''''))),,,'''''''''''''''((())))))))))))))))))))))))))))))((('''&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''((('''&&&%%%$$$$$$%%%&&&&&&''''''((($$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&################################################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$#########$$$%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&&&&&&&###$$$$$$%%%&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%%%%$$$$$$#########%%%%%%$$$$$$%%%%%%&&&'''######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$###""""""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%(((((('''''''''&&&&&&&&&$$$%%%'''((((((((('''&&&'''&&&%%%$$$###"""""""""******))))))))))))******))))))))))))))))))******++++++,,,------...//////---------------------,,,///000000000111111111111,,,---------......//////000111111222222333444444777777777777666444333222777777888888888777777666888888888999999999888888888777777777777777888888777888999:::;;;;;;;;;;;;<<<;;;999777666555666666333444333111///000555999777888999:::::::::::::::666666666444333111///...///...---,,,++++++++++++,,,,,,,,,+++++++++******,,,++++++---...///...---//////...---,,,******)))++++++******))))))((((((''''''((((((((((((((((((***)))((('''&&&&&&'''(((%%%&&&'''(((((('''&&&%%%''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&''''''&&&%%%%%%$$$$$$$$$$$$)))(((&&&&&&''''''&&&%%%***'''%%%%%%''')))'''%%%%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###""""""###$$$$$$%%%%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&''''''%%%$$$###""""""###$$$%%%"""""""""!!!"""######$$$%%%%%%%%%&&&&&&&&&&&&'''$$$$$$%%%%%%%%%%%%&&&&&&(((%%%$$$%%%'''(((&&&$$$%%%%%%&&&&&&'''((((((((((((((((((((((((((((((((()))((('''''''''(((***+++************************%%%$$$###%%%''')))***)))((((((''''''&&&&&&&&&%%%***))))))(((((((((((()))''''''''''''((()))***+++''''''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&&&&%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$%%%&&&&&&'''&&&&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%%%%$$$$$$$$$######%%%%%%$$$$$$%%%%%%&&&'''######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$######"""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%''''''&&&&&&%%%%%%%%%%%%%%%&&&''''''(((''''''''''''&&&&&&&&&&&&''''''(((******))))))))))))***************)))))))))))))))***++++++,,,------......++++++++++++,,,,,,---.../////////000000000111111------........./////////000000111111222333333333666777777666666555444333666777777888888777777666555666777777888888888777888888777777777777888888888999::::::;;;;;;;;;;;;:::999777555444444444444555555555333000///111333666777888888999999999888666666555444222111///.........---,,,++++++++++++,,,,,,+++++++++*********,,,,,,,,,---//////...---+++******************************)))))))))))))))((((((((((((((('''''''''***)))((('''&&&&&&'''((('''((()))******)))((('''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&''''''&&&%%%%%%$$$$$$$$$%%%&&&$$$######$$$$$$###"""%%%###!!!"""$$$%%%$$$###%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%$$$"""!!!!!!"""$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&&&&'''%%%$$$###""""""###$$$%%%######""""""######$$$%%%###$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&'''&&&$$$%%%'''(((&&&$$$%%%%%%&&&&&&'''((((((((((((((((((((((((((((((((()))(((((('''((()))***+++************************&&&%%%$$$%%%(((*********++++++*********)))))))))))))))(((((((((((())))))***))))))(((((((((((((((&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&'''''''''''''''&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%$$$'''&&&%%%$$$###"""!!! $$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%%%%$$$$$$$$$$$$###%%%%%%$$$$$$%%%%%%&&&'''######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$'''&&&&&&&&&&&&'''((((((%%%%%%%%%&&&((()))+++,,,******))))))))))))******+++*********))))))((((((*********+++,,,,,,------,,,+++******+++---000111....../////////000000000........./////////////////////000111111222222333555555666666666666555555555666666777777777666666333444555666777888888888999888888777777888888888777777888888999888888888777666555444333222222222555666777555222...------555555666666777777666666444444444333222000///......------,,,,,,+++++++++,,,++++++++++++*********,,,---.../////////...---&&&&&&'''((()))***++++++((())))))))))))))))))***))))))(((((('''''''''&&&)))(((''''''&&&''''''''''''((())))))))))))((('''%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%$$$$$$$$$%%%%%%$$$###""""""######"""!!!"""!!! """#########%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$&&&$$$!!!!!!$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$$$$######"""$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$############$$$$$$$$$$$$######$$$$$$%%%&&&""""""###$$$$$$%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&'''&&&%%%%%%''''''&&&%%%%%%%%%&&&&&&'''(((((((((((((((((((((((((((((((((((((((((((((((()))******************************'''&&&%%%&&&)))***+++***++++++++++++************(((((('''(((((()))***+++,,,+++***((('''&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$%%%&&&'''(((&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%((('''&&&%%%$$$"""!!!!!!######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$%%%''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$###$$$$$$%%%&&&&&&&&&&&&%%%%%%$$$$$$######$$$$$$%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%'''((()))######$$$%%%''')))***+++******))))))))))))******++++++******)))((((((((())))))******++++++++++++///...,,,++++++---000222---............/////////////////////////////////...//////000000111111222333333444555666666555555444444555666666666666555222333444666777888999999999999888777777777888888444555555666666555555555666555444333333222222222444555666666444000,,,***333333444444444444444333222222222222111000///...------------,,,,,,+++***++++++++++++************+++---///000///...------&&&&&&''''''((()))******'''((((((((())))))******)))))))))(((''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%%%%&&&%%%$$$$$$%%%&&&%%%###""""""""""""$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%$$$'''%%%$$$""""""$$$%%%'''$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$#########$$$$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$%%%&&&&&&""""""###$$$%%%&&&&&&'''$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((((((((((((((((((((((((((((((((((((((((((((((())))))***************************((('''&&&''')))++++++***((((((((((((((((((((((((''''''''''''((()))++++++,,,+++***(((''''''&&&&&&%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$%%%&&&'''((($$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&%%%$$$$$$######$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''&&&%%%%%%'''((()))%%%%%%%%%&&&'''((()))*********))))))))))))******************))))))(((((())))))************++++++000///,,,***)))***,,,...,,,,,,---------.........///////////////.........------...//////000000111111222333444444444444444222333444555555555555555222333555777888:::::::::999888777777666666666777444555666666666666666666555555555555444333333222222333444555555333///---222222222333333222222111000111111111000//////...,,,,,,---------,,,+++***+++++++++*********))))))***---000111///---,,,---))))))))))))))))))))))))''''''(((((()))))))))***))))))(((((('''''''''&&&&&&&&&''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$%%%&&&'''&&&%%%######$$$$$$$$$%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&'''$$$$$$$$$%%%&&&''''''((($$$$$$$$$%%%%%%%%%&&&&&&%%%&&&&&&&&&&&&%%%&&&&&&%%%%%%&&&&&&'''((((((((())))))))))))))))))))))))'''(((((())))))))))))))))))))))))))))))))))))))))))'''&&&''')))*********''''''''''''''''''''''''''''''''''''((()))++++++))))))(((((((((((())))))&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''#########$$$%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&''''''((((((''''''&&&&&&&&&&&&&&&''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$######$$$%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$######$$$$$$%%%&&&###$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&'''''''''''''''((('''&&&&&&&&&&&&'''((((((((((((((((((((()))************))))))))))))******)))))))))))))))))))))***************************...,,,***(((''''''((()))+++,,,,,,,,,,,,---------...............---------,,,------......///000000000000111222222222222222111222333444444444444444333444555777888:::::::::888888777666555555555555666666777888999999999999555555666666555555444333222111222333555666444222111111222222222111000000/////////000//////......+++,,,---------,,,+++***+++************))))))))))))---111111...+++++++++++++++******))))))(((((('''(((((((((((((((((()))((((((((((((((((((((((((%%%%%%&&&''''''''''''&&&((((((''''''''''''(((((((((''''''&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%$$$$$$$$$%%%&&&&&&$$$###"""###$$$%%%$$$###"""###$$$$$$######%%%'''%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###""""""%%%%%%&&&&&&&&&&&&%%%%%%"""###%%%''''''%%%###"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%############$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$%%%%%%&&&'''%%%%%%&&&&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&''''''%%%%%%&&&'''%%%%%%&&&&&&'''((((((((())))))))))))))))))))))))''''''((())))))))))))))))))))))))))))))))))))))))))'''&&&&&&(((***))))))(((((((((((())))))))))))(((((('''(((((()))***+++''''''''''''((()))++++++''''''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&""""""######$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$###$$$$$$%%%&&&&&&&&&%%%%%%######$$$%%%%%%%%%%%%$$$%%%$$$$$$######$$$$$$%%%$$$$$$######$$$$$$%%%&&&######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%&&&''''''((('''''''''''''''''''''((()))***+++******))))))))))))******((((((((()))******++++++++++++++++++++++++++++++,,,,,,+++***))))))))))))++++++++++++,,,,,,,,,,,,...---------,,,,,,,,,,,,,,,,,,,,,---......////////////000000000000000///000111222333444444444444222333555666777888888888777666555444444333333333444444666888999:::::::::444555555666666555444333444222000111444777777666111111111111111000//////---....../////////......***+++---......---+++***************))))))))))))''',,,111111---))))))************)))))))))((((((((((((((((((((('''''''''&&&&&&''''''((()))))))))$$$%%%&&&'''''''''&&&&&&(((''''''&&&&&&''''''((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%$$$$$$$$$%%%%%%&&&'''###!!!!!!"""###$$$$$$######$$$%%%$$$""""""$$$&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$###%%%%%%&&&&&&&&&&&&%%%%%%"""###$$$$$$$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&'''$$$$$$%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$&&&((('''%%%$$$&&&'''%%%%%%&&&&&&'''((((((((())))))))))))))))))))))))&&&'''((()))***))))))((())))))))))))))))))))))))((('''%%%&&&''')))(((((((((((())))))************))))))(((((((((((())))))''''''''''''((()))***+++((('''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%&&&'''((('''&&&%%%&&&&&&%%%$$$$$$#########$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$%%%%%%&&&######$$$%%%'''((())))))%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$######$$$%%%%%%&&&&&&&&&&&&######$$$%%%%%%%%%%%%$$$%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&#########$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%'''((((((((('''&&&######$$$$$$&&&''')))*********))))))))))))******''''''((()))***+++,,,,,,,,,,,,++++++++++++++++++,,,---------------------******+++++++++,,,,,,,,,---------,,,,,,+++++++++++++++,,,------......///......////////////......///000111222333444444444222222444555666666777777777666555444333222222222000111333555666777888888333444555555555444333222777333000000444777999999111111111111111000//////,,,---......///.........***+++---......---+++***************))))))))))))&&&+++000111,,,(((((()))((((((((()))))))))))))))))))))(((((('''''''''&&&%%%%%%&&&'''((()))******###$$$&&&'''((('''&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$%%%%%%&&&'''###"""""""""$$$%%%%%%$$$%%%&&&'''&&&######%%%'''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$$$$%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######"""############$$$$$$$$$&&&&&&%%%%%%&&&&&&'''((($$$$$$&&&&&&&&&&&&$$$$$$$$$$$$######$$$$$$%%%&&&&&&&&&%%%$$$$$$######"""$$$$$$%%%%%%%%%&&&&&&&&&$$$&&&((('''%%%$$$%%%(((%%%%%%&&&&&&'''(((((()))))))))))))))))))))))))))&&&''')))*********)))((())))))))))))))))))))))))(((&&&%%%%%%'''(((((('''''''''(((((()))))))))******))))))(((((((((((()))((((((((((((((()))******))))))((('''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&%%%$$$######%%%&&&(((''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$!!!"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$###$$$&&&(((&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&''''''(((***)))(((''''''((()))***(((((((((((())))))))))))))))))))))))))))))))))))((()))))))))***,,,------++++++++++++++++++++++++---,,,,,,++++++,,,,,,---++++++++++++++++++++++++------------------------........................)))+++,,,...//////......////////////000000000000000222555777888777555444555555444333333222111111333333333333333444444444444333222444777999999888;;;888444111000222555777555333111000///111222444,,,,,,---......,,,+++***+++,,,------......------+++,,,,,,,,,,,,+++******)))***+++++++++)))((('''))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((('''&&&$$$$$$,,,***'''"""!!!###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!"""$$$%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$%%%&&&'''''''''%%%$$$$$$###$$$%%%'''(((&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$######%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$#########$$$%%%&&&######$$$$$$$$$%%%%%%%%%(((((('''''''''&&&&&&&&&(((''''''(((((()))***+++++++++++++++++++++++++++((((((((((((((()))******++++++)))(((((())))))***''''''((((((((((((''''''''''''''''''(((((((((((())))))(((((((((((())))))***************+++++++++)))(((((('''&&&&&&%%%%%%''''''((((((((((((''''''&&&%%%$$$###$$$%%%'''(((''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$"""###$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%######$$$&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%%%%%%%&&&''''''&&&%%%%%%%%%$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$##################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''((()))(((''''''''''''((()))'''((((((((())))))))))))((((((((((((((((((((((((%%%&&&((())))))((('''&&&++++++++++++++++++++++++,,,,,,++++++++++++,,,,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,------------------------***+++,,,...//////..................////////////000222555777777666555444555444444333222222111111000111111222222333444444555444444666888999888777:::888555222000111333444555555333222111000000000.........------,,,+++***+++,,,,,,---------------++++++,,,,,,++++++***)))))))))******)))(((((('''''''''''''''''''''''''''''''''''''''''''''''''''&&&'''''''''''''''&&&%%%))))))'''%%%"""###%%%'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$###"""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$######&&&&&&&&&%%%%%%$$$$$$$$$&&&$$$###$$$%%%&&&%%%###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&((('''''''''&&&&&&&&&&&&''''''''''''((()))***+++++++++++++++++++++++++++)))))))))))))))***++++++,,,+++)))((('''(((((()))''''''((((((((((((''''''''''''''''''(((((((((((())))))(((((((((((())))))(((((())))))))))))******((((((((('''&&&&&&%%%%%%''''''(((((((((((('''''''''&&&%%%%%%%%%&&&((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((((('''%%%###"""###$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%&&&''''''$$$$$$$$$$$$$$$############$$$$$$$$$$$$%%%%%%%%%############$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$######"""""""""!!!$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$%%%&&&&&&''''''((((((''''''&&&&&&''''''(((''''''((((((((()))))))))((((((((((((((((((((((((%%%&&&)))******(((%%%###++++++++++++++++++++++++++++++************++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++,,,---...............---------.........//////000222444666666666555444444444333333222222111111...//////000111222222333555555666777999999777555999777555222111000000111555555666555333111...,,,///...---,,,++++++***+++++++++,,,------------,,,++++++,,,,,,++++++***)))))))))(((''''''''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''''''''''''''%%%&&&&&&&&&%%%%%%''')))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$,,,)))$$$ !!!###%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%$$$&&&&&&%%%$$$$$$$$$%%%%%%##################$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%$$$$$$&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%&&&&&&&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&'''(((***+++,,,******************************))))))******++++++,,,***)))'''&&&&&&''''''''''''((((((((((((''''''''''''''''''(((((((((((())))))))))))))))))))))))'''''''''((((((((())))))(((((('''''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%'''&&&&&&&&&&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&&&&'''''''''&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''########################$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$###"""""""""$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$%%%&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((())))))((((((((((((((((((((((((((()))***++++++***)))(((************+++++++++++++++******))))))******+++***+++++++++++++++,,,,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,------........................////////////000000111333555555555444333333333333333222222111111///////////////000000000333333444666999999777555777666555333111///...---333555777888777333///---...---+++***)))***+++,,,******+++,,,,,,,,,,,,,,,+++++++++++++++***)))))))))(((&&&%%%%%%&&&'''((())))))))))))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&&&&!!!###%%%%%%$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$+++((($$$!!! !!!###%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$###'''&&&&&&%%%$$$$$$$$$$$$""""""######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$&&&'''&&&%%%########################""""""""""""""""""""""""$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&((()))+++,,,***************************)))))))))))))))******+++***((('''&&&&&&&&&&&&''''''((((((((((((''''''''''''''''''(((((((((((()))))))))******)))))))))'''''''''((())))))******'''''''''''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&''''''&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###%%%&&&&&&%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$$$$$$$%%%&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''(((%%%%%%&&&&&&&&&&&&%%%%%%''''''''''''((((((((((((''''''''''''''''''''''''+++***))))))***,,,---///)))))))))******++++++++++++******))))))******+++*********++++++,,,,,,,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,...------........./////////000000000000111111111000111222333444444444333333222222222222222111111111111000000///.........000000111444666888777666666666555333111///...---000333666888888666333111---,,,***))))))***+++,,,)))***++++++,,,,,,++++++***++++++++++++***))))))((('''&&&%%%%%%&&&'''((())))))))))))))))))))))))''''''''''''''''''''''''''''''''''''&&&%%%$$$###"""$$$&&&&&&$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&'''''''''''''''(((((((((%%%%%%%%%$$$$$$#########%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%$$$$$$######&&&&&&&&&&&&%%%$$$$$$######$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$&&&'''&&&%%%########################""""""""""""""""""""""""$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''')))***+++)))))))))))))))))))))))))))(((((('''''''''((((((+++***((('''&&&&&&&&&'''''''''((((((((((((''''''''''''''''''(((((((((((())))))************))))))((())))))***++++++,,,,,,''''''''''''''''''''''''''''''((((((((((((''''''%%%&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''(((((('''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%###$$$$$$%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&"""$$$&&&&&&%%%%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&&&&#########$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&""""""######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&''''''(((%%%&&&&&&''''''&&&&&&%%%&&&&&&'''''''''(((((((((''''''''''''''''''''''''***)))'''&&&'''***...000(((((())))))***+++++++++++++++************++++++*********++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,///......---......//////000000111111111222222222000000111222333333333333222222222222222222111111222222111111000000//////000000///111444666666555666555444333111000///......000222555666666666555///...---,,,+++*********))))))***++++++++++++*********++++++******)))((('''&&&&&&&&&&&&'''((((((''''''''''''''''''''''''''''''''''''''''''''''''((('''''''''%%%$$$###"""&&&'''((((((&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%'''''''''''''''(((((((((%%%%%%%%%$$$######"""""" """$$$&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$$$$###%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$""""""###%%%&&&&&&%%%######################################################""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))(((((((((((((((((((((((((((((('''&&&&&&&&&''''''***)))((('''''''''((()))''''''((((((((((((''''''''''''''''''((((((((((((((()))***++++++***)))((()))***++++++,,,---......''''''''''''''''''''''''''''''((((((((((((''''''$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&###%%%''''''%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$###$$$$$$%%%&&&$$$$$$$$$$$$%%%%%%%%%&&&%%%%%%%%%$$$$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''!!!""""""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&''''''(((%%%&&&'''(((((('''&&&%%%&&&&&&&&&'''''''''((((((''''''''''''''''''''''''***)))((('''((()))+++,,,((((((((()))***+++++++++,,,,,,++++++++++++,,,,,,)))******+++,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,------------------------000///...------...//////000000000000111111111111000000111111222333333333111111111111111111222222111111111222222333333333555333111000222444444444666555444222111111111111---......///111333444555666555333111...+++)))'''((())))))******************************))))))(((&&&&&&'''(((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$###&&&'''((('''%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''%%%%%%$$$$$$###""""""!!!!!!"""$$$%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$$$$$$$$$$$$$###$$$%%%&&&&&&&&&%%%$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&"""!!!!!!"""$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&'''''''''&&&&&&''''''((((((((((((((((((((((((((())))))((('''''''''''''''))))))((('''((()))***+++''''''((((((((((((''''''''''''''''''((((((((((((((()))+++,,,,,,+++)))(((******+++,,,---...//////&&&'''''''''''''''''''''%%%&&&&&&&&&&&&&&&&&&%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%''''''''''''''''''''''''$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%$$$############$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%'''((((((%%%###""""""$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$#########""""""""""""####################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%""""""###$$$%%%&&&&&&'''!!!""""""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''(((&&&&&&'''(((((('''&&&&&&&&&&&&&&&'''''''''((((((''''''''''''''''''''''''+++++++++++++++******)))'''(((((()))***+++++++++---,,,,,,++++++,,,,,,---))))))***+++,,,,,,------------------------------........................000///...------...///000////////////000000000000000000000111222222333333111111111111111111222222///000111222444555777777:::777333111111333333333777666444222111111222222------,,,+++---///222444;;;;;;999555111,,,'''%%%(((((()))******************************)))((((((%%%&&&((()))***)))((('''))))))))))))))))))))))))%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%###$$$%%%$$$######%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%%%%%%%$$$$$$###""""""!!!######$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$ !!!"""###$$$%%%%%%%%%"""###%%%&&&'''&&&&&&%%%%%%$$$$$$$$$######""""""$$$$$$$$$%%%%%%&&&&&&&&&!!! !!!###%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&(((((('''&&&&&&&&&&&&'''((((((((((((((((((((((((******)))((((((((((((((())))))(((((()))***+++---''''''((((((((((((''''''''''''''''''((((((((()))((()))+++,,,,,,+++)))((()))******,,,---...//////***''''''(((&&&$$$&&&+++(((%%%$$$%%%'''(((&&&$$$&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&''''''''''''&&&&&&&&&''''''&&&%%%%%%(((''''''&&&&&&%%%$$$$$$&&&&&&%%%$$$%%%&&&'''((('''&&&%%%%%%%%%%%%&&&'''"""###%%%'''((((((''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$'''''''''&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&'''''''''&&&%%%%%%$$$'''%%%###$$$&&&'''%%%###$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%%%%%%%$$$######&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$###"""!!!%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$"""!!!!!!"""$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&"""$$$)))''' """***$$$%%%''')))******))))))''''''(((******+++++++++)))************+++++++++++++++,,,,,,,,,,,,------,,,,,,++++++,,,...///000222111000//////......///111000///////////////000111000/////////000222222000000////////////000000111111222333222111000///222///,,,---///111111000111222222333444444444333222222222222444555666777555444333222000///...---......---,,,,,,+++******000000444;;;@@@<<<000&&&)))---(((%%%)))(((&&&---******)))(((((((((((((((******))))))((((((''''''((((((((((((((((((((((((%%%%%%%%%&&&&&&''''''''''''''''''''''''&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###"""!!! ######$$$$$$$$$%%%%%%%%%""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$###"""""""""###%%%%%%%%%%%%&&&&&&'''((())))))&&&&&&&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''###&&&))))))&&&%%%''')))))))))(((((('''''''''&&&''''''''''''''''''''''''((((((''''''''''''((((((&&&''''''((((((((((((((((((((()))************)))******+++,,,------......)))&&&&&&((()))&&&'''))))))'''%%%&&&((()))'''%%%&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&'''((('''&&&%%%%%%%%%%%%&&&'''###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$&&&&&&''''''&&&&&&%%%$$$'''%%%###$$$&&&'''%%%###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%%%%%%%$$$######$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$%%%%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&'''''''''&&&%%%%%%&&&((()))*********)))(((((()))***++++++******)))************++++++++++++++++++,,,,,,,,,---------,,,,,,+++,,,---/////////...............//////000///////////////000000111000000///000111222333111000000//////000000111111111222333333222111000222///---...000222222111222222333444444444444444333333333444555666777888666666444333111///...---...------,,,++++++************+++000444555000,,,'''...,,,))),,,)))&&&,,,******)))(((((((((((((((***)))))))))((((((((('''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''((((((''''''&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$######"""######$$$$$$$$$%%%%%%%%%"""######$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$###"""""""""###$$$%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&(((((('''''''''((()))((((((((('''''''''&&&''''''''''''''''''''''''((((((''''''''''''((((((&&&'''(((((())))))((((((((())))))***+++*********((((((((()))***+++++++++)))%%%$$$))),,,***(((((()))(((''''''))))))((('''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%$$$###&&&&&&''''''''''''&&&&&&$$$$$$%%%&&&&&&'''((((((&&&%%%%%%%%%%%%&&&'''((('''&&&&&&%%%%%%&&&&&&'''%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$&&&&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%&&&%%%$$$$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%$$$$$$###"""######$$$&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&''''''((('''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%((((((&&&(((,,,***###&&&'''((())))))))))))))))))******+++++++++******)))************+++++++++++++++++++++,,,,,,,,,,,,------,,,,,,,,,------...,,,,,,,,,,,,---...///000...............///000111111111000000111111222333111111111000000111111111000111222333333333222111222000//////111333444444333444555555555555555555444444444555666777999999888777555333111///---,,,------,,,,,,++++++******+++******+++///333777:::'''...+++)))///...,,,222******)))(((((((((((()))))))))))))))((((((((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&&&&'''((((((((('''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&%%%%%%######$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%""""""!!!!!!!!!""""""#########""""""######$$$%%%########################%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&((())))))((('''((((((((('''''''''''''''''''''''''''''''''''''''((((((''''''''''''((((((&&&'''(((((())))))(((((())))))***++++++++++++***''''''(((((())))))*********%%%%%%+++000...***(((((('''''''''((((((''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$###"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&%%%%%%$$$#########$$$%%%%%%&&&''''''%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%&&&((())))))'''%%%&&&'''''''''((((((((('''******++++++++++++******))))))*********+++++++++***++++++++++++,,,,,,,,,...------------,,,------------,,,,,,---...//////---,,,------...///000111111111111111111222222333222222111111111111222222000111222444444444333333222111000111222444555666555555666666666666555555555555555666777888999:::999888666444111///---,,,,,,,,,,,,,,,++++++******,,,,,,,,,+++---222;;;AAA333444,,,***333222,,,...+++***))))))(((((())))))))))))))))))((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&)))(((''''''&&&%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&''''''######$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""!!!!!!!!!!!!""""""##################$$$$$$$$$###############"""""""""%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''(((&&&%%%'''***+++)))&&&''''''''''''''''''''''''''''''''''''''''''''''''((((((''''''''''''((((((''''''((())))))))))))))))))******+++++++++++++++((()))))))))******++++++***&&&&&&---222000+++(((&&&&&&'''&&&&&&&&&&&&'''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&'''''''''&&&######$$$%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$###"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&'''"""###)))(((%%%''''''&&&&&&&&&&&&&&&&&&))))))***+++++++++******))))))*********+++++++++*********+++++++++,,,,,,------------------,,,,,,000///......------......,,,,,,,,,,,,---...000000000000111111222222222222222222111111111111222222000111333444555555555444222222222222222444666777555666666777666666555555555555555555666888999:::999888666333111...,,,+++,,,+++++++++++++++******''')))***)))(((+++222999>>>===666999GGGCCC111)))++++++***)))))))))))))))(((((((((((())))))))))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""""""""""""""###$$$%%%""""""######$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''(((&&&%%%'''***+++)))&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''((((((''''''''''''(((((('''(((((()))))))))))))))))))))***++++++++++++***)))))))))))))))************&&&'''---000---***)))%%%&&&'''&&&%%%$$$%%%'''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&''''''''''''"""###$$$%%%%%%&&&%%%%%%(((((('''&&&%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%&&&&&&''''''&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&%%%$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$"""######$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%###$$$%%%&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&'''######'''(((&&&&&&)))(((((('''&&&%%%%%%%%%&&&'''''')))******++++++***)))************+++++++++************++++++++++++,,,,,,---......------,,,111000///...------------,,,,,,,,,,,,,,,---.../////////000111111111111000111111111000000111111111000111333555666666666666333444444333222222444777666666666666666666555444333333333444555666888888777666444222000...,,,+++++++++++++++++++++******''')))******((())),,,000888<<>>:::===,,,+++******)))*********'''((((((((())))))******&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$########################$$$$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################""""""""""""###$$$%%%&&&!!!"""###$$$%%%$$$######!!!!!!"""###$$$%%%%%%&&&###$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''!!!$$$''''''$$$###%%%'''%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''((((((''''''''''''(((((((((((()))***************&&&''''''(((((((((((((((++++++++++++************%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%%%%&&&'''((((((((((((((((((((((((''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''(((((((((''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%'''((()))'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""!!!!!!"""###$$$######$$$$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''(((###+++---888gggxxxPPP---+++)))'''%%%%%%%%%&&&'''((((((((()))))))))***************************************************,,,------......------,,,------------------------...---,,,+++++++++,,,---------------------,,,,,,......//////000000000111000000000111222444555666444555666555333222333444111333666999999777333111000000000000000111111111000000///...------,,,,,,,,,,,,++++++++++++++++++++++++***)))(((((())))))******+++++++++,,,,,,,,,))))))))))))***************)))(((''''''&&&&&&''')))((('''&&&%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%$$$"""!!!!!!"""$$$%%%&&&%%%###"""""""""######&&&%%%%%%$$$#########$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$#########""""""!!!!!!&&&%%%$$$#########$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$############$$$$$$''')))+++***'''$$$###%%%########################%%%%%%%%%$$$$$$#########%%%%%%%%%$$$$$$#########$$$###!!! """$$$%%%$$$###""""""$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((()))******+++,,,,,,,,,,,,++++++***))))))((()))))))))((((((((()))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$%%%&&&((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$######""""""######$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&!!!)))'''(((IIIWWW888+++***)))''''''&&&&&&&&&(((((((((((())))))))))))************************************************,,,,,,------------,,,,,,------------------------///...---,,,+++,,,------------------------------000000000000//////////////////000000222333444555555666666555222111222333333333444555555444333222000000000000000111111111000000///......---,,,,,,,,,,,,,,,+++++++++++++++***))))))(((''''''(((((()))*********++++++++++++(((((()))))))))*********(((((('''''''''((()))))))))((('''&&&%%%%%%%%%%%%&&&''''''''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%$$$"""!!!!!!"""$$$%%%&&&%%%###"""""""""###$$$&&&%%%$$$$$$######$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$######""""""""""""%%%%%%$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$############$$$$$$!!!$$$&&&&&&%%%###$$$%%%########################%%%%%%%%%$$$$$$$$$######%%%%%%%%%$$$$$$$$$######$$$$$$###""""""###$$$%%%%%%#########$$$%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((())))))******+++,,,,,,,,,,,,+++******)))(((((((((((()))))))))((((((((('''''''''''''''''''''''''''''''''''''''&&&%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((((((((((((''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&)))$$$+++))) ///:::((((((((((((((((((''''''&&&))))))))))))((((((((((((************************************************++++++,,,,,,,,,,,,++++++------------------------///...---,,,,,,,,,------+++,,,,,,------.........111111111000//////............///000111222333333555666666444222000000111444333222111000000111111/////////000000111111111000000//////......---------,,,,,,,,,+++++++++***)))(((((('''''''''''''''((()))))))))))))))******(((((())))))))))))******'''''''''(((((()))***+++))))))((('''&&&&&&&&&&&&''''''((((((''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%$$$###""""""###$$$%%%%%%%%%$$$############$$$%%%%%%$$$$$$######$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$############"""%%%$$$$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$############$$$$$$ """$$$$$$######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%$$$$$$$$$$$$###$$$$$$##################&&&$$$###$$$%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((''''''((((((((()))))))))******+++,,,,,,,,,,,,+++******)))(((((((((((()))+++***)))''''''(((((()))''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&***$$$***+++###'''...(((&&&'''((())))))((('''&&&))))))))))))((((((((((((***************************************************++++++,,,,,,++++++***,,,,,,---------------------------,,,,,,,,,,,,,,,++++++,,,,,,---...//////000000//////////////////---...///000000111111111555666666444111//////000111111000//////...............//////000111111111000000000/////////......---------,,,,,,++++++***)))(((((('''''''''(((((((((((((((((((((((((((((((((((((((((()))))))))***((((((((((((((()))***+++)))(((((('''''''''(((((('''''''''''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$###""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&%%%$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$######"""!!!&&&%%%$$$$$$&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''((((((((('''(((((((((((()))))))))******+++,,,,,,,,,,,,+++++++++***))))))))))))***,,,***((('''&&&''')))***&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''!!!###(((&&&&&&)))'''%%%&&&((()))))))))((('''))))))))))))((((((((((((***************************************************++++++,,,,,,++++++***,,,,,,,,,---------......,,,,,,,,,,,,,,,++++++***++++++,,,,,,---...//////,,,,,,---...//////000000---...///000000000000000555555555333000......///---...///000///...,,,+++---......///000000111111000000000000000/////////......------,,,+++******)))))))))(((((()))******'''''''''''''''''''''''''''(((((((((((()))))))))******)))((((((((((((((((((((('''''''''(((((()))%%%&&&&&&&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$##################$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%$$$$$$###$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%######$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&%%%$$$$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""######""""""!!! &&&%%%$$$$$$&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''(((((((((((()))))))))*********+++,,,,,,,,,,,,+++,,,,,,+++************++++++***(((&&&&&&''')))***&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%)))%%%###&&&))))))'''(((''''''((((((((((((((('''(((((((((((())))))))))))************************************************++++++,,,,,,,,,,,,+++++++++,,,,,,------.........,,,,,,---------,,,+++***+++,,,,,,------.........)))***+++,,,---///000000---...///111111111000///333444444222000......///***,,,---//////...,,,+++------...///000000111111111111111111000000000000//////...---,,,+++*********))))))))))))******+++(((((((((''''''''''''&&&''''''(((((((((((())))))***)))(((''''''&&&&&&&&&&&&&&&&&&&&&'''((())))))%%%%%%&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#################################$$$%%%%%%&&&%%%%%%%%%$$$$$$######$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&""""""$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%"""  ###%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$######"""!!!!!!!!!&&&$$$###$$$%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&"""###%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''''''''((((((((()))))))))************+++,,,,,,,,,,,,+++,,,,,,+++************+++***)))(((&&&&&&''''''(((''''''''''''''''''''''''&&&'''((())))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&''''''''''''&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&%%%$$$#########$$$$$$$$$%%%%%%%%%###$$$&&&((((((&&&$$$###$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%))),,,'''$$$(((((('''))))))(((((('''''''''((((((&&&&&&'''((()))***++++++************************************************,,,,,,------------,,,,,,++++++,,,,,,---......///....../////////...---,,,------------------------))))))***+++,,,,,,------...///000222222111000///222333333222000...///000+++++++++,,,,,,---......,,,,,,---...///000111222111111111111111111111111//////...---,,,+++******((((((((((((((()))******(((((((((((('''''''''&&&'''''''''((((((((())))))((('''&&&&&&&&&&&&&&&'''%%%%%%%%%%%%&&&'''((()))&&&&&&&&&&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###############$$$$$$############$$$%%%&&&&&&&&&%%%%%%$$$$$$######$$$$$$%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&'''!!!"""$$$%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&###!!! ###&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%'''&&&%%%############$$$%%%#########$$$%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&!!!###$$$&&&&&&&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((((((((((()))))))))***************+++,,,,,,,,,,,,++++++***))))))(((((())))))''''''''''''&&&&&&&&&&&&))))))))))))))))))))))))&&&'''((())))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((())))))&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&''''''((((((((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###%%%'''((((((''''''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######$$$%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######%%%%%%%%%%%%############$$$$$$$$$%%%%%%%%%###%%%'''******'''%%%###$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""+++''' """$$$###(((***)))(((&&&&&&&&&'''(((%%%&&&'''((()))***+++,,,************************************************,,,------......------,,,++++++,,,,,,---.../////////000111111111000...---------------------,,,,,,******************++++++...///111222333222000///111222222111/////////000,,,+++***)))***---///111,,,,,,---...///000111222111111111111111111222222000//////---,,,+++******'''''''''''''''((()))***))))))((((((((('''''''''''''''''''''((((((((()))%%%%%%%%%%%%%%%&&&'''((($$$$$$$$$%%%&&&'''((()))''''''((((((''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$$$$######"""###%%%&&&'''&&&%%%%%%$$$#########$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&'''''''''!!!"""$$$%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&)))&&&######%%%'''&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%***)))&&&$$$###$$$%%%&&&$$$###""""""$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&!!!"""$$$&&&&&&&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''((())))))***))))))))))))******************+++,,,,,,,,,,,,+++))))))((('''''''''''''''&&&&&&''''''&&&&&&%%%$$$'''''''''''''''((()))***'''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&'''''''''&&&%%%%%%$$$'''''''''&&&&&&%%%%%%%%%&&&%%%$$$###$$$%%%&&&''''''&&&&&&%%%%%%&&&&&&'''***(((&&&$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%((('''%%%$$$$$$%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$############$$$%%%%%%%%%%%%$$$###""""""###$$$%%%%%%&&&&&&########################%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$%%%%%%$$$$$$######$$$%%%&&&'''&&&%%%$$$&&&&&&&&&'''''''''((((((''''''''''''''''''''''''''''''''''''((((((((((((******+++++++++,,,,,,,,,+++++++++******))))))))),,,,,,,,,+++++++++***************+++,,,---...///000111111000000///...---,,,------------,,,+++***+++***((('''''')))+++,,,000222444555555333000///------............------,,,,,,,,,++++++*********,,,,,,------...//////000------......///000000000111111///---+++)))''''''))))))))))))************(((((('''&&&&&&&&&&&&'''((((((((('''&&&&&&%%%%%%''''''(((((('''&&&%%%%%%)))(((&&&%%%%%%&&&''')))(((((('''&&&&&&&&&&&&'''%%%%%%%%%&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$(((%%%###$$$''''''$$$!!!###$$$$$$%%%%%%$$$$$$###&&&&&&&&&%%%%%%$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((('''%%%$$$%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&######$$$%%%%%%&&&''''''%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$""" !!!############$$$$$$%%%%%%%%%##############################$$$%%%%%%%%%%%%$$$$$$$$$############$$$$$$%%%%%%$$$###""""""######$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%%%%&&&%%%%%%%%%$$$$$$#########$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&'''((())))))++++++******++++++,,,---************************))))))))))))((((((((((((%%%%%%%%%&&&&&&&&&''''''(((''''''''''''(((((()))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&''''''&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%&&&''''''&&&&&&%%%%%%&&&&&&'''%%%$$$"""!!!!!!"""###$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%((('''%%%$$$$$$%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''(((((((((((())))))%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$#########$$$%%%%%%%%%%%%$$$############$$$%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$#########$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''((((((((((((*********+++++++++,,,,,,,,,+++++++++************,,,,,,+++++++++******************+++,,,---...///000000111111000000//////......---,,,,,,+++******++++++***))))))***,,,---000111333444444222///...------............---------------,,,,,,,,,++++++,,,,,,,,,---...///////////////..................///...---,,,***((('''&&&(((((()))))))))*********))))))((('''''''''''''''&&&&&&''''''''''''''''''''''''(((((('''&&&&&&%%%((('''&&&%%%%%%&&&'''((((((((('''&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%$$$$$$$$$###$$$$$$%%%%%%$$$$$$###&&&%%%%%%%%%$$$$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&$$$###$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!""""""!!! !!!###%%%$$$$$$$$$$$$$$$$$$%%%%%%##############################$$$%%%%%%%%%%%%$$$$$$$$$############$$$$$$%%%$$$$$$###""""""########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%&&&&&&((())))))******))))))******+++,,,************************)))))))))(((((('''''''''%%%%%%%%%&&&&&&&&&'''''')))((((((''''''''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''%%%%%%$$$$$$%%%''')))***'''''''''''''''''''''''''''''''''''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$######$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$######$$$$$$%%%%%%$$$$$$###%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''''''''(((((((((((()))*********++++++++++++,,,,,,,,,++++++++++++***++++++++++++*********)))************+++---...//////000111111222111111111000///---+++************++++++++++++,,,,,,------...000111222222000...---------............------......------------,,,,,,+++,,,,,,------......////////////...---,,,,,,,,,,,,,,,+++***)))(((((('''(((((())))))))))))*********))))))((('''(((((((((%%%%%%&&&&&&'''(((((()))'''''''''(((''''''&&&%%%&&&&&&&&&&&&&&&&&&''''''(((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###&&&((('''###!!!###&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%$$$###"""###$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$ """#########$$$&&&)))%%%%%%$$$$$$$$$$$$$$$$$$##############################$$$%%%%%%%%%%%%$$$$$$$$$############$$$$$$%%%$$$######"""#########"""""""""###$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$$$$#########%%%%%%%%%$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&'''((()))((((((((((((((()))******))))))))))))))))))))))))))))))((('''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''***)))((('''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''((()))+++,,,&&&&&&&&&&&&&&&&&&&&&&&&''''''((())))))((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###""""""$$$&&&''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%###$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###&&&%%%$$$###$$$%%%&&&'''''''''&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((()))))))))************+++,,,,,,,,,++++++++++++++++++************)))))))))))))))******+++,,,.../////////000222222333333333222000---+++))))))******)))***+++,,,------,,,,,,---...///000000...---,,,,,,------......------,,,---------------,,,,,,,,,++++++,,,,,,------------...---------,,,,,,,,,+++++++++*********)))))))))(((((((((((()))))))))***))))))((('''''''''''''''&&&&&&&&&'''''''''((((((&&&'''''''''''''''&&&&&&%%%%%%&&&'''''''''&&&&&&((('''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###%%%&&&%%%###"""$$$&&&###$$$$$$%%%%%%$$$$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%$$$###"""###$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%&&&%%%&&&(((***%%%%%%%%%$$$$$$#######################################$$$%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$$$$###############$$$!!!!!!"""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&'''((()))''''''&&&&&&''''''((()))(((((((((((((((((((((((((((((('''&&&%%%%%%$$$###%%%%%%%%%&&&&&&&&&''''''***)))((('''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%&&&&&&'''''''''%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((()))***)))''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$"""!!!"""###%%%'''''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###&&&%%%$$$###$$$%%%&&&'''((((((((((((''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''(((((((((((((((((()))))))))*********++++++++++++++++++++++++*********)))))))))(((((()))))))))***+++,,,---......///000222222333333333222000---+++))))))******((()))***+++,,,,,,,,,,,,------.........---,,,+++,,,,,,------------,,,,,,+++++++++++++++,,,,,,,,,+++++++++,,,,,,,,,,,,,,,***+++++++++,,,,,,,,,---++++++++++++++++++++++++'''(((((((((((()))))))))''''''&&&%%%%%%%%%&&&&&&(((((('''''''''&&&&&&&&&&&&&&&'''''''''''''''&&&$$$$$$%%%&&&''''''&&&&&&''''''&&&%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$""""""$$$%%%%%%$$$###$$$$$$%%%%%%$$$$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###%%%&&&%%%$$$###$$$&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###%%%&&&&&&$$$$$$$$$%%%%%%%%%%%%$$$$$$#######################################$$$%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$###############$$$$$$!!!!!!"""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&'''((((((&&&&&&%%%%%%&&&&&&'''(((''''''''''''''''''''''''(((''''''&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&'''''')))((((((''''''''''''((('''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&'''&&&&&&%%%%%%&&&&&&'''((((((''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&(((******)))'''&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&########################$$$$$$$$$$$$$$$$$$%%%%%%#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%$$$$$$%%%%%%&&&&&&''''''((((((((()))))))))$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''(((((((((((((((((((((((()))))))))))))))************+++++++++))))))))))))(((((((((((())))))))))))***,,,---......///000111222222222222000///---+++************((())))))***+++,,,---------------------,,,,,,+++,,,,,,------------,,,,,,******++++++++++++,,,,,,++++++++++++++++++++++++)))))))))***+++,,,,,,,,,++++++++++++++++++++++++''''''(((((((((((())))))'''&&&%%%%%%$$$$$$%%%%%%)))(((((('''&&&&&&%%%%%%%%%&&&''''''((('''''''''$$$$$$%%%%%%&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''### $$$'''%%%######$$$$$$%%%%%%$$$$$$############$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$&&&%%%$$$$$$%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$###!!!  %%%%%%$$$$$$$$$$$$$$$$$$##############################$$$%%%%%%%%%%%%$$$$$$$$$############$$$$$$#########"""######$$$%%%"""""""""###$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$&&&''')))***###$$$$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%''''''&&&&&&&&&''''''(((&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''(((''''''''''''(((((()))''''''''''''''''''''''''(((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%'''((((((((('''&&&'''&&&&&&%%%%%%&&&&&&'''))))))))))))((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%((()))***)))'''&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$######$$$%%%%%%$$$%%%%%%%%%&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&'''((()))******%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''(((((((((((('''''''''((((((((())))))(((((()))))))))*********))))))((((((((('''''''''(((((())))))***,,,---......//////000111111111111......---,,,,,,+++******************+++---///000......---------,,,,,,,,,+++,,,,,,------,,,,,,++++++++++++,,,,,,,,,------+++++++++++++++*********))))))************************************))))))'''''''''((((((((())))))''''''&&&%%%%%%%%%%%%&&&''''''''''''''''''&&&&&&%%%&&&&&&'''((((((''''''%%%$$$$$$###$$$&&&'''((('''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%###!!!!!!"""$$$%%%&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%########################"""###$$$$$$######$$$&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$$$$"""  $$$$$$$$$$$$$$$$$$%%%%%%##############################$$$%%%%%%%%%%%%$$$$$$$$$############$$$$$$######""""""###$$$$$$%%%##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''((()))######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%(((''''''&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''%%%%%%%%%&&&&&&&&&'''''''''''''''''''''((()))***''''''''''''''''''''''''))))))))))))))))))))))))'''&&&&&&%%%%%%&&&&&&'''$$$%%%%%%&&&'''''''''&&&'''''''''&&&&&&%%%%%%%%%%%%%%%'''((((((((('''&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%%%%%%%%%%%%%$$$''''''''''''''''''''''''###%%%''')))***((('''%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&#########$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%&&&%%%$$$######$$$%%%&&&$$$$$$%%%%%%&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$#########""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$###$$$%%%&&&'''&&&%%%$$$###$$$%%%&&&''')))******''''''''''''''''''''''''''''''''''''((((((((()))''''''''''''((((((((()))''''''(((((()))))))))***)))(((((((((''''''''''''(((((())))))***+++---......//////000000000000///,,,------------,,,+++***,,,+++******+++...000222......------------,,,,,,+++,,,,,,------,,,,,,+++,,,,,,,,,------.........++++++******************++++++******))))))(((((())))))))))))((((((((((((''''''''''''((((((((()))(((((('''&&&&&&&&&&&&'''%%%%%%&&&&&&'''(((((((((%%%%%%&&&'''((((((((('''%%%$$$###"""###%%%((()))'''&&&%%%%%%$$$$$$%%%%%%#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""$$$$$$### %%%)))$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######################## """######""""""###%%%&&&%%%%%%$$$$$$%%%%%%&&&######$$$%%%%%%&&&''''''%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###%%%&&&&&&%%%##################$$$$$$%%%%%%&&&##############################$$$%%%%%%%%%%%%$$$$$$$$$############$$$$$$######""""""###$$$%%%%%%$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%&&&''''''#########$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&#########$$$$$$%%%%%%%%%(((''''''&&&&&&&&&''''''&&&&&&%%%%%%&&&&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''(((((()))%%%%%%%%%&&&&&&&&&''''''))))))))))))))))))))))))***)))((('''&&&&&&'''(((***)))((('''&&&%%%$$$$$$((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''(((((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((('''%%%$$$######$$$%%%(((((('''&&&&&&%%%$$$$$$&&&''''''''''''''''''&&&&&&&&&&&&&&&%%%$$$######&&&&&&&&&''''''''''''(((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################&&&&&&&&&&&&&&&&&&&&&&&&###########################$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''%%%$$$&&&)))***'''$$$$$$%%%&&&'''''''''&&&%%%&&&&&&&&&'''''''''(((((())))))))))))))))))))))))%%%&&&''')))************###$$$&&&(((((((((((((((************+++,,,---...++++++,,,,,,,,,---------,,,,,,,,,++++++*********+++,,,------......------,,,,,,++++++,,,,,,---...111111000000//////......++++++++++++++++++++++++******************++++++************)))))))))))))))((('''&&&%%%&&&&&&'''%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###""""""######%%%###  ###%%%""""""""""""""""""""""""######$$$%%%%%%%%%%%%$$$$$$$$$########################$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&(((%%%""""""%%%'''&&&%%%$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""###%%%''''''&&&%%%$$$$$$$$$%%%%%%&&&'''((((((%%%&&&'''(((((('''&&&%%%))))))))))))))))))))))))***)))((('''&&&''''''((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%&&&&&&''''''((((((((('''&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%&&&&&&&&&&&&%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""############$$$$$$$$$$$$$$$$$$$$$$$$(((((((((***,,,,,,***)))((((((((((((''''''&&&%%%&&&&&&&&&'''''''''(((((())))))))))))))))))))))))(((((()))))))))))))))(((%%%&&&'''((())))))((((((***************+++,,,---++++++++++++,,,,,,,,,,,,,,,++++++++++++++++++***+++,,,------...---------,,,++++++++++++,,,------111000000000//////......------,,,,,,++++++++++++******************************)))))))))(((((((((''''''((((((((('''&&&%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###""""""######%%%$$$""" """$$$%%%##############################$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((%%%######%%%&&&&&&%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&(((((('''&&&%%%$$$$$$%%%%%%&&&''''''(((&&&&&&''''''''''''&&&&&&(((((((((((((((((((((((())))))(((''''''''''''(((&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&'''(((((('''&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''((((((((((((((((((''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""""""""#########$$$%%%%%%%%%%%%%%%%%%%%%%%%###%%%'''(((((((((((()))++++++)))((('''&&&&&&&&&&&&&&&'''''''''((((((((()))))))))))))))))))))))))))*********))))))((('''(((((())))))***))))))(((******)))))))))******+++*********++++++++++++,,,*********+++++++++++++++++++++,,,---------------+++++++++++++++,,,------000000////////////////////////...---,,,,,,++++++************************)))(((((((((((('''''''''&&&(((***++++++)))&&&$$$%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######"""!!!!!!"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######"""#########%%%$$$############$$$%%%##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%###$$$%%%&&&&&&%%%$$$$$$######$$$$$$%%%&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((()))((('''&&&$$$%%%%%%&&&&&&''''''''''''''''''&&&&&&'''''''''((((((((((((((((((((((((((((((((('''''''''((((((&&&&&&&&&''''''''''''(((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&((((((((('''&&&'''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&'''(((((((((((($$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%!!!$$$''''''%%%%%%'''***+++***((('''&&&'''((((((''''''''''''(((((((((((((((((((((((((((((((((((())))))*********))))))(((******************))))))******))))))))))))))))))))))))*********+++++++++))))))******++++++,,,,,,++++++,,,------------,,,+++++++++***+++,,,,,,---......//////////////////111000///...---,,,+++++++++++++++***************(((((('''''''''&&&&&&&&&((()))***+++***)))'''&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########""""""#########$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%########################################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$######$$$$$$$$$$$$##############################$$$$$$###$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((''''''&&&%%%%%%%%%&&&&&&&&&''''''((('''&&&%%%%%%&&&'''(((((((((((((((((((((((((((''''''(((((((((((((((((((((''''''''''''&&&&&&&&&((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''''''''%%%$$$###%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&'''((((((((((((&&&&&&&&&&&&''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%(((******((((((+++...''''''&&&%%%&&&''')))***'''''''''((((((((())))))(((((((((((((((((((((((('''((()))***+++++++++++++++++++++*********************))))))))))))))))))))))))*********+++++++++)))))))))******+++++++++***+++,,,,,,------,,,,,,+++************+++,,,,,,------......//////000000111111000///---,,,+++++++++++++++*********))))))''''''''''''&&&&&&&&&&&&******)))(((((((((((((((%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&############$$$$$$$$$$$$################################################################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$""""""###$$$$$$###""""""########################$$$$$$#########$$$%%%&&&"""#########$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&((('''&&&%%%%%%&&&'''(((((((((((((((((((((((((((&&&'''(((((()))((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&&&&&&&&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$###"""%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&'''''''''((((((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%############################################################$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''((((((((('''''')))***%%%%%%%%%&&&'''(((******''''''((((((((()))))))))))))))))))))))))))))))))&&&''')))***+++,,,,,,,,,++++++*********++++++,,,******)))))))))******+++*********++++++++++++,,,)))))))))*********************+++,,,,,,,,,,,,,,,***************+++,,,,,,,,,,,,---...//////000000000000///...---,,,,,,+++,,,,,,++++++***)))))))))(((''''''''''''&&&&&&&&&+++)))((('''&&&'''((()))%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&"""###############$$$$$$################################################################################################$$$$$$$$$$$$$$$$$$$$$$$$#########"""######$$$%%%""""""############""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$#########$$$%%%&&&"""""""""######$$$$$$%%%#########$$$$$$$$$$$$$$$######$$$$$$%%%%%%&&&&&&###%%%'''&&&%%%$$$$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&'''''''''))))))))))))))))))))))))%%%&&&((()))))))))((((((&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%&&&&&&&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%$$$%%%&&&&&&%%%&&&'''(((((())))))))))))'''((((((((())))))))))))))))))))))))))))))))))))((()))***+++++++++++++++******))))))***+++,,,---***************+++,,,---++++++++++++,,,,,,,,,,,,************))))))))))))******+++,,,,,,,,,,,,+++***************++++++,,,++++++,,,---...000000111.........---------,,,,,,,,,,,,++++++***))))))((((((((((((''''''''''''&&&((((((((((((''''''&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&#########$$$$$$%%%%%%%%%################################################################################################$$$$$$$$$$$$$$$$$$$$$$$$######""""""###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""$$$&&&'''""""""###$$$$$$%%%&&&&&&""""""######$$$$$$%%%%%%"""######$$$%%%%%%&&&&&&"""%%%''''''%%%$$$$$$%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&************************%%%&&&((()))))))))(((((($$$$$$%%%&&&'''((()))***((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((('''&&&%%%%%%&&&'''(((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&%%%%%%&&&''')))***''''''((((((((((((((((((&&&''''''((((((''''''&&&&&&&&&&&&&&&%%%$$$######$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&...***'''&&&(((***(((&&&((()))***++++++***((('''(((((((((((())))))))))))))))))))))))))))))))))))***++++++++++++***))))))))))))(((((()))+++---...************+++,,,---...++++++,,,,,,,,,---------++++++******))))))((((((******+++,,,,,,,,,,,,+++*********)))***++++++,,,++++++,,,---...000111111------------------,,,,,,,,,,,,++++++***))))))((()))(((((((((((('''''''''%%%&&&((())))))'''%%%###%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%!!!"""###$$$$$$###"""!!!$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################""""""""""""""""""""""""""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$######""""""###$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""$$$&&&'''######$$$%%%%%%&&&''''''!!!!!!"""###$$$%%%%%%&&&""""""###$$$%%%%%%&&&&&&"""%%%((((((%%%###$$$&&&$$$$$$######$$$$$$%%%&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''(((((('''&&&%%%((((((''''''''''''((((((((((((((((((((((((((((((((((((((('''&&&&&&%%%%%%'''&&&$$$$$$$$$&&&((()))'''&&&%%%%%%%%%%%%&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''(((((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&&&&&&&&&&''''''''''''(((''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&'''''''''%%%%%%%%%$$$$$$#########$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%&&&'''((()))######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%)))'''&&&$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$#########$$$%%%&&&%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&'''((())))))'''''''''&&&&&&%%%%%%%%%))))))))))))))))))))))))))))))(((((('''''''''&&&(((((())))))))))))((((((******))))))))))))******000...,,,***))))))***+++***)))((()))++++++)))((()))***+++,,,,,,+++))))))(((((((((((())))))))))))******+++++++++******)))***+++,,,---------,,,+++------......///000000000000///...---,,,+++******))))))))))))((((((((((((((('''&&&%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&''''''''''''''''''###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$+++)))&&&&&&((((((%%%###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$$$$#########""""""!!!!!!!!!!!!!!!!!!!!!!!!%%%%%%%%%$$$###"""!!! ########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$"""!!!!!!"""$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%###"""!!!$$$$$$$$$######"""""""""%%%%%%%%%$$$$$$#########$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&%%%%%%$$$!!!"""###$$$%%%%%%&&&&&&(((''''''(((***)))'''%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''''''''(((((((((((((((((((((((((((((('''''''''''''''&&&&&&&&&'''&&&%%%$$$$$$&&&((()))'''&&&%%%%%%%%%%%%&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''''''''%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&%%%%%%'''''''''''''''(((((((((%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$%%%&&&'''((($$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%((('''%%%$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###"""""""""############$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&''''''((((((''''''&&&&&&&&&%%%%%%%%%'''''''''''''''''''''''')))(((((((((''''''''''''(((((())))))))))))((((((******))))))))))))******---,,,***)))(((((()))******)))))))))++++++)))((()))***++++++++++++***)))''''''((((((((()))))))))+++++++++,,,,,,++++++***++++++------------,,,+++------......//////000000000//////...---,,,+++***))))))))))))(((((((((((((((''''''&&&%%%%%%&&&&&&'''''''''&&&&&&&&&%%%%%%&&&&&&%%%%%%&&&&&&'''(((''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$''''''&&&&&&%%%%%%$$$$$$###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''%%%$$$$$$&&&'''%%%###$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###$$$$$$%%%%%%$$$$$$$$$#########""""""""""""""""""""""""""""""""""""###$$$$$$$$$$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$"""!!!!!!"""$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""%%%%%%$$$$$$$$$#########%%%%%%%%%$$$$$$$$$######$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$%%%&&&&&&'''(((((((((((('''&&&&&&((())))))'''%%%&&&&&&&&&&&&&&&&&&&&&&&&)))((((((''''''(((((()))((((((((((((((((((((((((&&&&&&&&&''''''''''''''''''&&&%%%%%%%%%&&&'''((('''&&&&&&%%%%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''''''''&&&&&&&&&%%%&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((''''''''''''&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&((('''&&&%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$###############&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###!!!"""$$$%%%%%%%%%$$$###%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''((((((((((((''''''''''''(((((())))))))))))((((((***))))))(((((())))))***+++***)))(((((()))***+++***))))))***++++++***((()))******+++++++++******(((((((((((())))))))))))+++,,,,,,---------,,,,,,+++,,,---......---,,,+++---------...//////000000000//////...---,,,++++++))))))))))))((((((((((((((((((''''''&&&&&&'''''''''''''''&&&&&&&&&&&&%%%'''&&&&&&&&&&&&'''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$''''''&&&%%%$$$###""""""###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###$$$&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$%%%$$$$$$$$$#######################################""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$###""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$############$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%&&&((()))'''&&&&&&&&&&&&&&&&&&&&&&&&&&&))))))(((((((((((())))))((((((((((((((((((((((((%%%%%%&&&&&&'''(((((()))''''''&&&&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&((((((((('''&&&&&&&&&%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''((((((((((((((((((((('''%%%%%%%%%$$$$$$#########%%%%%%%%%&&&&&&''''''''')))(((&&&%%%%%%&&&((()))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######"""""""""&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$&&&(((((('''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((((((((((((((('''''''''(((((())))))))))))(((((())))))(((((((((((()))))))))))))))))))))***+++,,,******)))***+++,,,***((()))*********++++++++++++)))************+++++++++,,,------............---,,,---.........---,,,+++,,,,,,---......//////000//////......---,,,,,,+++))))))))))))(((((((((((()))(((((('''''''''((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((&&&&&&&&&'''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&%%%%%%$$$$$$#########$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$###"""!!! $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$###""""""###$$$$$$###$$$$$$$$$$$$$$$%%%%%%&&&%%%######"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$""""""""""""############$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''&&&&&&%%%%%%$$$$$$%%%%%%%%%$$$######%%%$$$$$$%%%'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&))))))(((((((((((())))))(((((((((((((((((((((((($$$%%%%%%&&&'''((())))))((('''''''''&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''((((((((('''&&&&&&&&&%%%&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&''''''(((((((((((((((((((((%%%%%%%%%$$$$$$#########%%%%%%%%%&&&&&&''''''''')))(((&&&%%%%%%&&&((()))%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''''''''%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$######""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$&&&(((((('''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((('''''''''((((((((((((((((((((())))))))))))(((((())))))(((((((((((())))))************+++,,,,,,---+++***)))***,,,,,,***))))))))))))******++++++,,,++++++,,,,,,,,,---------,,,---...///////////////------...///...---,,,+++,,,,,,------.../////////......------,,,,,,++++++))))))))))))(((((((((((((((((('''''''''(((((()))(((((('''''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&'''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&''''''###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$"""#########$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%$$$#########%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$#########$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$###"""!!! $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$##################$$$#########$$$$$$%%%%%%%%%&&&%%%$$$######$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$"""#########$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''&&&&&&%%%'''((((((((((((((('''&&&&&&%%%$$$%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&***))))))(((((())))))***((((((((((((((((((((((((%%%%%%&&&&&&'''((())))))(((((((((((('''''''''&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%&&&''''''(((((('''''''''''''''&&&&&&&&&&&&&&&'''''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''(((((((((''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&((('''&&&%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###!!!"""$$$%%%%%%%%%$$$######$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%#########$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''))))))))))))))))))))))))'''''''''((((((((((((((((((((())))))))))))(((((()))((((((''''''(((((()))******++++++,,,,,,,,,,,,+++******+++,,,,,,+++)))))))))))))))***+++,,,---,,,,,,,,,------------...,,,---...///////////////......//////...---,,,+++,,,,,,,,,---......//////,,,,,,,,,,,,+++++++++***))))))))))))((((((((((((''''''&&&&&&''''''((((((((((((((('''''''''&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&%%%%%%&&&&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$######$$$%%%&&&'''((((((###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""""""""######$$$$$$%%%&&&%%%%%%$$$$$$######"""$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%###!!! %%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########################################################$$$$$$%%%%%%&&&%%%$$$$$$$$$$$$%%%%%%&&&$$$$$$$$$$$$%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&'''((((((((($$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''&&&&&&&&&&&&'''''''''''''''&&&((('''%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&******))))))))))))******((((((((((((((((((((((((%%%&&&&&&&&&''''''((((((((((((((((((((('''&&&&&&%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&'''(((((((((&&&&&&&&&'''''''''''''''''''''''''''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''(((((((((%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###"""""""""############$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%"""#########$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''((((((((((((((((((((((((''''''''''''((((((((()))(((((())))))))))))((((((((((((''''''''''''(((((()))******++++++++++++***+++******+++,,,,,,+++)))***))))))))))))+++,,,---++++++++++++,,,,,,,,,,,,+++,,,---...////////////...////////////---+++***+++,,,,,,------......///+++++++++************)))))))))))))))((((((((((((&&&&&&%%%%%%&&&''''''(((((((((((((((''''''''''''%%%%%%%%%%%%%%%&&&''''''%%%%%%&&&&&&'''(((((()))%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$%%%&&&&&&'''&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###%%%&&&%%%"""!!!"""$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$############""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#################################$$$$$$#########"""######$$$%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%#########$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&'''((((((((($$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&######$$$%%%&&&&&&&&&%%%+++)))&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&******))))))))))))******((((((((((((((((((((((((&&&&&&&&&'''''''''''''''(((((())))))((('''&&&&&&%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%&&&&&&'''((())))))%%%&&&&&&''''''(((((((((''''''''''''((((((((()))&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%$$$$$$#########$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$#########$$$%%%&&&#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%""""""######$$$$$$$$$$$$######$$$%%%%%%&&&''''''%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''&&&'''''''''(((((())))))(((((())))))))))))((((((((((((''''''''''''(((((())))))************)))))),,,+++***+++,,,---+++)))***))))))))))))+++---...))))))*********++++++++++++,,,---...///////////////////////////---+++***++++++,,,------......///*********)))))))))))))))))))))))))))((((((((((((%%%%%%%%%%%%%%%&&&'''((()))((((((((('''''''''''''''&&&&&&&&&&&&'''((((((%%%%%%&&&&&&'''((())))))%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$###############$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''(((((('''&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$''')))(((&&&%%%'''***&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$############""""""######$$$$$$$$$$$$########################%%%%%%%%%$$$###"""!!! %%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$$$$######""""""###$$$%%%%%%&&&&&&"""###%%%&&&'''&&&%%%%%%"""""""""######$$$$$$$$$#########$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$""""""###$$$%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&'''''''''&&&%%%&&&'''((())))))))))))---***'''&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&,,,,,,,,,,,,,,,+++***)))))))))))))))))))))))))))''''''(((((())))))******))))))))))))))))))))))))''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((((('''&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&'''((()))''''''&&&%%%$$$######"""%%%%%%&&&&&&'''&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$#########$$$$$$%%%%%%%%%%%%%%%$$$###$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$%%%&&&'''))))))***%%%%%%$$$$$$%%%'''(((***'''''''''&&&%%%$$$""""""%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&%%%%%%)))((('''&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&''')))+++,,,***((((((((((((((((((''''''''')))))))))***++++++,,,,,,,,,,,,,,,,,,+++***)))(((******))))))((((((''''''******+++,,,,,,---......---------....../////////111000///...,,,+++***)))*********++++++,,,,,,,,,,,,++++++++++++++++++,,,***************)))((('''(((((('''&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%&&&'''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$#########$$$%%%%%%%%%%%%$$$###$$$%%%&&&&&&%%%###"""%%%%%%$$$$$$###"""""""""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''%%%###""""""###%%%'''$$$$$$$$$$$$$$$$$$$$$$$$'''%%%$$$$$$%%%%%%###"""$$$$$$%%%%%%%%%%%%&&&&&&'''&&&$$$######$$$&&&'''%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&%%%$$$$$$$$$$$$$$$############"""$$$$$$$$$#########""""""######$$$$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%"""############$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###$$$$$$%%%%%%%%%%%%$$$###$$$%%%'''(((&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%'''((((((((('''''')))((((((''''''(((((()))+++)))(((&&&%%%%%%%%%&&&''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$+++++++++++++++***))))))))))))))))))))))))))))))(((((((((((())))))))))))((((((((((((((((((((((((&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&''''''''''''%%%%%%&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&'''((((((''''''&&&&&&%%%%%%$$$$$$&&&&&&&&&'''&&&&&&%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&'''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$&&&'''((($$$$$$%%%%%%$$$$$$######%%%%%%%%%&&&&&&&&&&&&'''%%%%%%&&&&&&&&&&&&&&&&&&(((((('''&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&%%%&&&''')))***((('''(((((((((((((((((((((''')))))))))***++++++,,,,,,---------,,,,,,+++***)))))))))))))))************))))))******+++,,,,,,---,,,,,,,,,------...............------,,,,,,++++++)))))))))*********++++++******))))))))))))******(((((()))))))))(((''''''(((((('''&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((())))))******$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$#########$$$%%%%%%%%%%%%$$$"""###$$$%%%%%%$$$########################$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$###$$$%%%%%%$$$############$$$$$$$$$%%%%%%'''&&&$$$######$$$&&&'''%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%$$$###"""$$$$$$$$$############"""$$$$$$$$$#########"""""""""######$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$"""############$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%$$$$$$$$$%%%%%%&&&'''&&&&&&&&&%%%%%%$$$$$$$$$###$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%***)))'''&&&%%%%%%%%%&&&''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&)))************))))))((())))))))))))))))))))))))))))))))))))((((((((((((''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((######$$$&&&'''((()))***'''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%$$$$$$%%%%%%&&&''''''''''''&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&###$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$ !!!"""###############$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$###"""!!!!!!%%%$$$$$$###$$$$$$%%%%%%!!!"""######$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&''''''((('''&&&&&&&&&&&&&&&&&&###$$$$$$%%%&&&'''((()))&&&%%%%%%&&&((((((&&&%%%''''''(((((((((((((((((()))))))))***++++++,,,,,,------------,,,+++******)))))))))***++++++,,,,,,(((((())))))***++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,((((((((())))))))))))***((((((''''''''''''((((((&&&&&&'''(((((((((''''''(((((('''&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$######""""""$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$#########$$$%%%%%%%%%%%%$$$!!!""""""######$$$$$$$$$!!!""""""###$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###%%%&&&&&&%%%###"""$$$$$$$$$$$$$$$$$$$$$$$$%%%#########%%%&&&%%%$$$""""""#########$$$$$$$$$&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%$$$###!!!!!!$$$$$$$$$############"""$$$$$$$$$###############""""""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$"""############$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$#########$$$$$$$$$%%%%%%&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$""""""$$$%%%&&&''''''''')))'''$$$""""""###$$$%%%''''''''''''''''''''''''(((((('''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&''''''(((((((((((())))))))))))((((((((((((((((((((((((((((((******))))))((((((''''''''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%'''''''''''''''''''''''''''''''''(((((((((((()))###$$$%%%&&&'''((()))***''''''&&&&&&&&&''''''(((&&&&&&&&&'''''''''((((((''''''''''''&&&%%%$$$###%%%&&&''''''((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$ !!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%""""""##################$$$$$$##################"""######$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&######$$$%%%&&&&&&''''''''''''&&&%%%%%%&&&&&&&&&$$$$$$%%%%%%&&&'''(((((((((&&&&&&&&&''''''&&&%%%''''''''''''(((((((((((()))))))))***++++++,,,,,,---------------,,,++++++)))*********************)))))))))*********++++++************++++++++++++++++++++++++++++++++++++))))))))))))))))))))))))(((''''''&&&&&&''''''(((%%%&&&'''((((((((((((((((((((('''&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%###!!!$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$#########$$$%%%%%%%%%%%%$$$!!!!!!!!!!!!"""###$$$%%%""""""#########$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$%%%%%%$$$$$$######$$$$$$$$$$$$$$$%%%%%%$$$###"""###%%%&&&&&&$$$############$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$###""""""$$$$$$$$$#########""""""########################!!!"""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$""""""#########$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$###############$$$%%%&&&'''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&&&&&&&&&&((('''&&&%%%%%%&&&&&&'''(((((())))))))))))((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''((())))))'''(((((()))))))))((((((((((((((((((((((((((((((******))))))((((((''''''''''''''''''''''''''''''''''''(((((((((((('''''''''''''''''''''''''''''''''''''''(((((((((((()))&&&&&&&&&''''''((((((((((((''''''&&&&&&&&&''''''%%%%%%&&&''''''(((((((((''''''''''''&&&%%%$$$###%%%&&&''''''((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$ !!!###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%############$$$$$$$$$$$$##################""""""%%%%%%%%%&&&%%%$$$$$$###$$$$$$$$$%%%%%%%%%&&&&&&######$$$$$$%%%&&&''''''&&&&&&%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&)))'''&&&&&&'''((('''&&&&&&'''''''''(((((()))))))))))))))***++++++,,,,,,,,,,,,------,,,,,,++++++++++++***)))((((((''''''*********+++++++++++++++************************,,,,,,,,,+++******))))))************************)))((((((''''''(((((()))&&&'''(((((())))))))))))(((((('''&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%$$$""""""!!!$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$#########$$$%%%%%%%%%%%%$$$!!!!!!!!!!!!"""###$$$%%%$$$$$$$$$#########""""""######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%###""""""###%%%&&&#########$$$$$$%%%%%%%%%$$$###"""###%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$#########""""""########################!!!"""###$$$%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%""""""#########$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$$$$#########$$$$$$%%%&&&'''&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$!!!###%%%((((((((('''&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''((())))))'''(((((()))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((('''''''''''''''''''''''''''(((((((((((((((((('''''''''''''''''''''''''''&&&&&&'''''''''(((((((((((((((((('''''''''''''''(((((('''&&&&&&&&&&&&'''%%%%%%&&&&&&'''''''''(((''''''''''''&&&%%%$$$$$$%%%%%%&&&''''''''''''&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$######$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%'''&&&&&&%%%$$$###"""""""""######$$$$$$$$$######&&&&&&&&&&&&&&&%%%$$$###$$$$$$$$$$$$%%%%%%%%%%%%######$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&%%%%%%%%%)))'''&&&&&&'''(((((('''&&&&&&''''''((())))))))))))))))))***++++++,,,,,,+++++++++,,,,,,++++++***,,,+++***)))(((&&&%%%%%%++++++++++++++++++++++++***************))))))))),,,,,,++++++***)))((((((++++++************))))))))))))(((((((((((())))))''''''((()))))))))(((((((((((('''&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&'''((()))***$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$#########$$$%%%%%%%%%%%%$$$!!!""""""######$$$$$$$$$%%%%%%$$$$$$###""""""!!!######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%&&&&&&''''''%%%###!!!!!!###%%%'''#########$$$$$$%%%%%%&&&%%%#########%%%&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$############"""###############$$$$$$$$$######$$$%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%"""############$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&&&&%%%%%%$$$######'''((('''%%%###%%%&&&'''(((((('''&&&%%%###$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&''''''(((((('''((())))))*********)))))))))))))))))))))))))))(((((((((((())))))))))))((((((((((((((((((((((((&&&''''''((((((''''''&&&''''''''''''''''''''''''%%%&&&&&&&&&''''''''''''((((((((('''''''''''''''(((((('''&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&'''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$#########$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$#########!!!"""###%%%%%%%%%%%%$$$###$$$$$$%%%%%%%%%%%%$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%&&&&&&&&&&&&&&&&&&'''%%%$$$$$$&&&(((((((((&&&&&&''''''((())))))***)))))))))***++++++,,,,,,)))******++++++******)))++++++******)))(((''''''************************+++++++++******)))))))))******************))))))******)))))))))((((((((())))))(((((((((((())))))''''''((((((((('''&&&&&&(((((('''&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&!!!"""###$$$&&&((())))))$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$#########$$$%%%%%%%%%%%%$$$"""###$$$%%%%%%$$$######$$$$$$########################$$$$$$$$$%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%$$$######$$$%%%%%%"""######$$$%%%%%%&&&&&&&&&$$$###$$$%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$#########$$$%%%$$$$$$$$$############"""""""""#########$$$$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######""""""""""""######"""############$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&&&&'''&&&%%%%%%$$$$$$$$$%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%&&&&&&&&&%%%%%% ###%%%&&&%%%$$$###'''((()))******)))((('''"""###$$$&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&(((((()))***************))))))))))))))))))))))))''''''(((((())))))******))))))))))))))))))))))))%%%&&&&&&''''''&&&&&&%%%((((((((((((((((((((((((%%%%%%%%%&&&&&&&&&''''''''''''''''''(((((()))))))))((('''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$############$$$%%%&&&'''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%% !!!"""###$$$%%%&&&&&&!!!"""$$$%%%&&&&&&&&&%%% !!!"""###$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&'''###$$$$$$%%%&&&'''((((((%%%###"""###%%%'''((((((&&&&&&&&&'''((())))))***)))))))))***++++++,,,,,,((())))))*********))))))+++++++++***************))))))))))))((((((((((((,,,+++++++++******))))))'''(((((()))***+++++++++))))))(((((('''''''''&&&((((((''''''''''''((((((''''''''''''&&&%%%$$$$$$(((((('''&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$######$$$%%%%%%%%%%%%$$$###$$$%%%&&&&&&%%%###""""""""""""###$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%######$$$%%%%%%&&&''''''###$$$%%%%%%%%%%%%$$$###""""""###$$$%%%%%%&&&&&&'''%%%$$$$$$%%%%%%###""""""############$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$((('''%%%###""""""######$$$$$$$$$############"""""""""######$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!!!! !!!!!!"""############$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$%%%''''''((('''%%%$$$###$$$%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&"""###$$$%%%&&&'''''''''%%%%%%%%%%%%%%%%%%&&&&&&$$$%%%'''(((((('''%%%$$$!!!"""$$$&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%$$$'''(((***,,,,,,***((('''+++******)))(((''''''&&&)))))))))))))))***++++++---,,,+++)))((('''''''''******))))))((((((((('''(((((((((((((((((((((((('''&&&&&&&&&&&&'''((((((''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&''''''((((((''''''&&&'''&&&%%%%%%$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%$$$######$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!$$$&&&((((((&&&$$$!!!########################&&&''''''%%%######$$$%%%######$$$$$$$$$%%%%%%%%%'''&&&&&&&&&&&&'''(((((('''&&&&&&&&&'''(((***+++((((((((((((((((((((((((''''''''''''(((((((((((())))))(((((((((((())))))+++*********))))))((((((************************)))************+++++++++,,,+++++++++******))))))))))))************)))))))))))))))))))))))))))))))))((('''&&&&&&&&&&&&&&&(((''''''&&&&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%)))((('''&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&########################!!!!!!"""############"""%%%%%%%%%%%%&&&'''((((((&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$#########$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%&&&&&&''''''###$$$%%%&&&&&&$$$###!!!""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&'''''''''%%%### &&&%%%$$$"""!!!!!! """"""#########$$$$$$$$$&&&&&&&&&&&&%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$$$$%%%&&&'''$$$%%%&&&&&&''''''&&&&&&&&&''''''((())))))((((((%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&''''''''''''&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''((()))***++++++***)))(((+++******)))(((((('''''')))(((((((((((()))***++++++***))))))))))))))))))((('''''''''&&&&&&&&&&&&(((((((((((((((((((((((('''&&&&&&&&&&&&'''((((((''''''&&&&&&&&&&&&''''''(((((((((''''''(((((((((''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$######'''&&&%%%%%%$$$$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""$$$&&&''''''&&&$$$"""$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&'''%%%######$$$&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%&&&''''''((('''&&&&&&&&&&&&''')))***''''''''''''''''''''''''&&&''''''''''''((((((((())))))(((((((((((())))))************)))))))))(((************************(((((()))))))))*********)))))))))(((((((((''''''(((((())))))))))))(((((((((((((((((((((((((((((((((((('''&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%''''''&&&&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""""""""#########$$$$$$""""""###$$$&&&(((***+++&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!!!!"""######$$$$$$###$$$%%%&&&&&&$$$###!!!########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&%%%$$$""" !!!!!!""""""###$$$$$$"""######$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###%%%%%%$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$%%%&&&'''$$$%%%&&&&&&''''''&&&&&&))))))(((&&&$$$""" $$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&''''''''''''&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''))))))))))))))))))))))))*********))))))(((((('''((((((''''''(((((())))))))))))(((((()))***++++++''''''''''''&&&&&&&&&&&&(((((((((((((((((((((((('''&&&&&&&&&&&&'''((((((''''''&&&&&&&&&&&&''''''))))))))))))))))))))))))''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$$$$%%%&&&'''((()))***'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$###$$$&&&%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((((()))))))))******))))))(((((((((((())))))************))))))))))))))))))))))))))))))))))))'''''''''((((((((())))))))))))((((((((((((''''''''''''((((((((((((''''''(((((((((((((((((((((((((((((('''&&&&&&&&&&&&''''''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''&&&&&&%%%&&&&&&%%%%%%%%%&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$%%%&&&######$$$$$$%%%'''((()))%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$######$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!!!!""""""######$$$$$$%%%&&&%%%$$$###"""########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$$$$$$$###"""!!!"""#########""""""###$$$%%%&&&%%%$$$$$$%%%%%%%%%%%%%%%$$$$$$###%%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&$$$%%%&&&&&&''''''&&&&&&######$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&******))))))))))))***************)))))))))((((((((((((''''''''''''(((((()))))))))))))))******+++)))))))))))))))((((((((((((((((((((((((((((((((('''&&&&&&&&&&&&'''((((((''''''&&&&&&&&&&&&''''''((((((((())))))(((((((((''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&'''(((((()))'''''''''&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$###%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&'''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&******+++++++++,,,,,,,,,))))))(((((((((((())))))*********)))))))))))))))((((((((((((((((((((((((''''''((((((((()))))))))******************))))))&&&''''''''''''''''''&&&(((((((((((((((((((((((((((''''''&&&&&&&&&''''''))))))(((((((((((())))))''''''''''''''''''''''''%%%%%%&&&&&&'''&&&&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######%%%'''(((((('''&&&%%%$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$###"""########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""############"""!!!"""###$$$$$$### """###%%%&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%$$$$$$###&&&%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%######""""""""""""######%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$%%%%%%$$$%%%&&&&&&''''''&&&&&&######%%%&&&(((((())))))$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&******))))))))))))******************))))))))))))((((((''''''''''''((((((+++******)))))))))))))))((((((((()))))))))))))))(((((((((((((((((((((((('''&&&&&&&&&&&&'''((((((''''''&&&&&&&&&&&&''''''&&&''''''((((((''''''&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&''''''((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''######$$$$$$$$$$$$######%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$############$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&%%%$$$$$$%%%'''$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&)))))))))*********++++++))))))(((((((((((())))))))))))))))))))))))******''''''''''''''''''''''''((((((((()))))))))******))))))))))))))))))******&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&''''''((((((''''''&&&&&&''''''(((''''''''''''''''''''''''$$$%%%%%%&&&'''''''''&&&***)))(((&&&%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''%%%$$$######%%%'''(((((('''&&&%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""!!!!!! $$$%%%%%%%%%### """###$$$%%%%%%%%%$$$$$$######$$$%%%%%%$$$$$$$$$%%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&******))))))'''&&&%%%$$$&&&&&&&&&&&&''''''''''''&&&%%%%%%%%%%%%&&&''''''''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))************************))))))((((((''''''((((((++++++***)))(((((())))))&&&&&&&&&'''''''''''''''(((((((((((((((((((((((('''&&&&&&&&&&&&'''((((((''''''&&&&&&&&&&&&''''''%%%&&&'''(((((('''&&&%%%''''''&&&&&&&&&&&&''''''&&&&&&&&&'''(((((())))))''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$########################$$$%%%&&&%%%$$$$$$&&&'''#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&'''%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((())))))(((((((((((())))))))))))))))))************(((((((((((((((((((((((((((((()))))))))*********&&&&&&''''''''''''((((((&&&&&&''''''''''''&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&'''((((((%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&''''''''''''+++***((('''&&&%%%$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$########################%%%%%%$$$$$$$$$%%%&&&'''$$$$$$###$$$$$$%%%&&&'''#########$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&###$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###""""""!!!!!!######$$$$$$###"""!!! """"""#########$$$$$$$$$"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&&&&%%%$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%''''''''''''((((((((((((&&&%%%%%%%%%%%%&&&''''''''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%((()))***++++++***)))(((************************+++***)))(((((((((((()))))))))))))))))))))***+++&&&&&&&&&&&&'''''''''((((((((((((((((((((((((((('''&&&&&&&&&&&&'''((((((''''''&&&&&&&&&&&&''''''&&&'''((())))))((('''&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&'''((()))))))))''''''''''''''''''''''''&&&&&&&&&'''''''''''''''$$$%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((())))))******))))))(((%%%$$$$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$&&&((($$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%&&&''''''(((%%%%%%'''((()))(((((('''''''''''''''''''''''''''&&&&&&&&&'''''''''(((((())))))(((((((((((())))))((()))))))))************(((((((((((((((((((((((('''''''''((((((((())))))&&&&&&&&&'''''''''((((((''''''((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&'''((((((&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&''''''''''''))))))((('''''''''((((((&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%############$$$%%%&&&'''"""#########$$$$$$$$$$$$######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%&&&%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$"""#########$$$$$$$$$%%%###"""!!! !!!"""$$$%%%""""""###$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%""""""!!!!!!!!!!!!""""""%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&$$$%%%&&&&&&''''''&&&&&& !!!###%%%'''((())))))&&&&&&&&&'''''''''((((((&&&%%%%%%%%%%%%&&&''''''''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%''')))***,,,,,,***)))'''******************++++++++++++***)))))))))))))))''''''(((((()))+++,,,---'''((((((((())))))******(((((((((((((((((((((((('''&&&&&&&&&&&&'''(((((('''''''''&&&&&&''''''''''''((()))++++++)))(((''''''''''''&&&&&&'''''''''&&&&&&&&&'''((())))))***''''''''''''''''''''''''$$$%%%%%%&&&'''((())))))###$$$$$$%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&"""###%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&$$$$$$$$$$$$%%%%%%&&&'''&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%$$$######$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$$$$$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%###%%%%%%%%%$$$$$$&&&(((%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&'''(((((($$$%%%''')))******))))))(((((((((((((((((((((((())))))))))))************))))))(((((((((((())))))(((((())))))*********+++))))))))))))))))))))))))&&&&&&&&&'''''''''(((((('''((((((((())))))******''''''((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&'''((()))))))))(((((((((((())))))%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''''''''''''''''''''((((((***++++++&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%%%%$$$$$$&&&%%%$$$$$$######$$$$$$""""""######$$$$$$$$$$$$######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&#########$$$$$$%%%%%%%%%&&&%%%%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&'''%%%$$$$$$######$$$%%%%%%###""" !!!###%%%!!!"""###$$$$$$$$$$$$$$$""""""###$$$%%%&&&&&&'''######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((((('''&&&$$$%%%&&&&&&''''''&&&&&&&&&'''''''''&&&&&&%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&''''''''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%******+++++++++,,,,,,,,,************************)))))))))))))))*********(((((((((((())))))))))))******)))((('''&&&%%%%%%(((((((((((((((((((((((((((((((((((())))))))))))''''''''''''''''''''''''***)))(((''''''((()))***((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''((((((''''''&&&%%%######$$$$$$%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$###"""###$$$&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###############$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$########################$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""###$$$%%%&&&&&&%%%$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$###""""""%%%%%%%%%%%%%%%%%%%%%%%%(((((('''''''''&&&&&&&&&)))'''&&&(((++++++)))'''(((((((((((())))))))))))((((((((((((((()))******(((((((((((((((((((((((()))(((((()))******)))''')))'''&&&(((+++,,,***'''&&&&&&&&&'''''''''(((((())))))))))))))))))))))))(((''''''&&&&&&&&&''''''((((((''''''''''''((((((((((((((('''&&&&&&&&&%%%'''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%''')))******)))&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$%%%%%%$$$$$$###"""""""""%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$"""!!!!!!!!!"""###""""""###$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$##################$$$%%%&&&'''(((%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%""""""""""""###$$$%%%&&&"""############$$$$$$$$$!!!!!!!!!!!!!!!!!!!!!!!!########################$$$$$$######"""!!!!!!!!!!!!$$$%%%$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&''''''(((((('''''''''''''''&&&&&&%%%%%%%%%$$$%%%''''''''''''%%%$$$*********+++++++++,,,,,,************************)))))))))))))))))))))***))))))))))))(((((((((((((((((()))))))))*********((((((((((((((((((((((((&&&&&&&&&'''''''''((((((''''''''''''''''''''''''***)))(((''''''((()))***''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''((((((''''''&&&%%%$$$$$$$$$%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&''''''%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%(((((('''''''''&&&&&&&&&'''%%%%%%'''***+++)))'''(((((((((((())))))))))))((((((((((((((()))*********************************)))(((((())))))((('''((('''&&&(((***+++)))'''&&&&&&&&&'''''''''(((((())))))))))))))))))))))))---,,,***)))'''&&&&&&&&&((((((''''''''''''(((((('''''''''''''''&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&((())))))((('''&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%##################$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$###""""""%%%%%%%%%$$$$$$$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%""""""!!!!!!!!!!!!""""""$$$$$$###############$$$"""############$$$$$$$$$################################################""""""""""""############"""###$$$$$$######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&'''''''''''''''''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$))))))*********+++++++++++++++++++++++++++++++++******))))))))))))))))))******))))))((((((''''''''''''((((((((()))))))))(((((((((((((((((((((((($$$%%%%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''')))((((((''''''(((((()))''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''((((((''''''&&&%%%%%%%%%%%%&&&''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&&&&&&&&&&&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%%%%%%%$$$%%%$$$$$$$$$$$$$$$$$$%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((((((''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''&&&&&&&&&%%%%%%%%%''')))***)))'''(((((((((((())))))))))))((((((((((((((()))******************************,,,***''''''((((((((('''''''''&&&'''))))))((('''&&&&&&'''''''''((((((((()))))))))))))))))))))))),,,+++***((('''&&&&&&&&&((((((''''''''''''((((((&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$%%%'''((((((&&&'''&&&&&&%%%$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$$$$!!!""""""###$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%%%%%%%$$$######%%%%%%%%%%%%$$$###""""""%%%%%%%%%$$$$$$$$$$$$###%%%%%%&&&&&&%%%$$$######%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%&&&%%%$$$###"""""""""""""""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################!!!!!!""""""###$$$$$$%%%$$$%%%%%%$$$######&&&((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$&&&&&&&&&&&&%%%%%%$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%)))))))))*********++++++++++++++++++++++++++++++*********)))))))))))))))******))))))((((((''''''(((((('''&&&%%%$$$######(((((((((((((((((((((((($$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''''''''(((''''''&&&%%%&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&'''&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$&&&%%%$$$######$$$%%%&&&######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''''''''(((((()))(((((('''(((((((((((())))))))))))((((((((((((((())))))***************************---***'''&&&'''((((((((('''''''''(((((((((''''''''''''''''''((((((((((((((((((((((((((((((((((((&&&&&&%%%%%%%%%&&&''''''(((''''''&&&&&&''''''(((%%%&&&&&&&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###$$$&&&'''&&&%%%%%%$$$$$$$$$######""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&############""""""""""""""""""#########$$$$$$$$$%%%$$$$$$######$$$$$$%%%###$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""###$$$$$$"""!!! """"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$###%%%$$$$$$######$$$$$$%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%$$$$$$###""""""######""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################"""""""""######$$$$$$$$$###$$$%%%$$$###$$$%%%'''$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$&&&&&&&&&&&&%%%$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&$$$$$$$$$$$$&&&''')))************+++++++++++++++++++++++++++++++++************))))))((((((***)))))))))((((((((('''(((((('''&&&%%%$$$######((((((((((((((((((((((((%%%&&&&&&&&&''''''''''''((((((((((((((((((((((((''''''((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''''''''(((''''''&&&%%%&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&'''''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&'''''''''''''''''''''++++++++++++)))((('''&&&(((((((((((())))))))))))((((((((((((((())))))***))))))))))))))))))))))))---***'''&&&'''((()))((('''((())))))(((''''''''''''''''''((((((((())))))((((((((((((((((((((((((%%%%%%%%%%%%%%%&&&''''''''''''&&&&&&&&&&&&''''''%%%&&&&&&&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###$$$&&&&&&%%%$$$"""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&""""""""""""""""""""""""$$$$$$$$$#########""""""%%%$$$$$$######$$$$$$%%%#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################""""""###$$$$$$"""!!! """"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%######""""""""""""############""""""###$$$$$$%%%""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$$$$$$$######"""""" """%%%&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%&&&&&&&&&%%%%%%$$$###$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%&&&'''(((******+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++******)))(((((((((((((((((()))))))))))))))''''''((((((((()))))))))((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''((((((''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&''''''''''''&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&''''''###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&########################$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###############$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''&&&%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''&&&&&&&&&'''''''''''''''+++------,,,)))'''''''''(((((((((((())))))))))))((((((((((((((()))******((((((((((((((((((((((((+++)))''''''((()))))))))((()))******((('''((((((''''''((((((((()))))))))))))))))))))))))))))))))***)))((('''&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&'''''''''''''''%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$&&&&&&%%%$$$!!!!!!"""###$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&#########$$$$$$$$$%%%%%%%%%%%%$$$$$$###""""""!!!%%%$$$$$$######$$$$$$%%%#########$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%%%%%%%$$$######%%%%%%%%%%%%$$$###""""""###$$$$$$$$$$$$%%%%%%%%%""""""""""""###%%%&&&'''%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%""""""""""""###$$$%%%&&&"""############$$$$$$$$$################################################&&&%%%%%%$$$######"""""""""%%%'''&&&$$$######$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''((((((''''''''''''((((((+++,,,,,,,,,,,,---------,,,,,,,,,,,,,,,,,,,,,,,,++++++******)))(((((('''''''''(((((())))))******(((((()))))))))*********((((((((((((((((((((((((&&&'''''''''((((((((((((((((((((((((((((((((((((&&&&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''((((((''''''&&&%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%''''''((('''&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&''''''''''''&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&%%%%%%&&&&&&&&&&&&''''''######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&''''''######$$$%%%%%%&&&''''''&&&&&&&&&'''''''''(((((((((***,,,+++)))'''(((***(((((((((((())))))))))))((((((((((((((()))******))))))))))))))))))))))))((('''&&&''')))+++***)))(((+++,,,,,,)))'''(((***'''((((((((())))))))))))))))))))))))))))))))))))))))))((('''&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&''''''''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''%%%$$$%%%&&&'''&&&$$$"""######$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""###$$$%%%&&&&&&$$$$$$##################%%%$$$$$$######$$$$$$%%%"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$###""""""######$$$$$$$$$%%%%%%%%%%%%###"""!!!!!!###%%%'''%%%$$$$$$######$$$$$$%%%'''''''''&&&&&&'''''''''$$$###############$$$$$$"""############$$$$$$$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$"""$$$&&&&&&%%%$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!###%%%&&&''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$%%%%%%%%%%%%######$$$%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''&&&''''''''''''''''''&&&,,,,,,,,,---------......,,,,,,,,,,,,,,,,,,,,,,,,+++++++++***)))(((((('''&&&&&&'''((()))***++++++******)))((('''&&&%%%%%%((((((((((((((((((((((((&&&&&&&&&'''''''''(((((())))))))))))))))))))))))%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''((((((''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''')))))))))((((((%%%%%%%%%&&&&&&&&&''''''&&&''''''''''''''''''&&&(((((('''''''''&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&###$$$%%%&&&&&&%%%$$$#########$$$$$$$$$%%%%%%%%%######$$$%%%%%%&&&'''''''''''''''(((((((((((((((######$$$%%%%%%&&&''''''&&&&&&&&&'''''''''(((((($$$'''******(((((()))+++(((((((((((())))))))))))((((((((((((((()))******************************&&&&&&&&&(((+++,,,+++)))))),,,---,,,***((()))***(((((((((((())))))))))))))))))))))))))))))))))))#########$$$%%%&&&'''((('''&&&&&&%%%%%%&&&&&&'''(((((((((''''''&&&&&&%%%%%%%%%%%%&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%''''''&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%"""""""""###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%""""""###$$$%%%%%%&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$"""!!!!!!!!!"""###""""""###$$$%%%%%%%%%%%%#########$$$$$$%%%%%%%%%(((%%%""" !!!$$$&&&%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%&&&%%%$$$###"""""""""""""""############$$$$$$$$$#########################################################$$$$$$%%%&&&&&&%%%&&&&&&%%%$$$%%%''')))$$$$$$$$$$$$$$$$$$$$$$$$!!!"""%%%'''''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$"""###$$$%%%&&&'''''''''$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''$$$##################$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&'''''''''$$$%%%''''''''''''%%%$$$+++++++++,,,,,,---------------,,,,,,+++***))))))***++++++++++++***))))))))))))))))))))))))))))))((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((''''''''''''''''''&&&&&&(((((())))))))))))(((((('''''''''''''''((())))))***(((%%%%%%'''(((&&&$$$'''((((((((())))))******''''''''''''''''''''''''%%%&&&&&&&&&''''''((((((&&&&&&''''''''''''&&&&&&(((''''''''''''&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$''''''''''''&&&%%%$$$###$$$$$$######$$$$$$%%%&&&&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$#########""""""###$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''(((((((((((((((((((((((((((((((((''''''''''''(((((((((((())))))))))))(((((()))))))))))))))))))))))))))((('''&&&&&&'''((())))))((('''&&&&&&'''((())))))&&&$$$%%%'''(((%%%!!!(((((((((((())))))))))))%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''''''''########################$$$$$$$$$############"""$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$$$$####################################$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%########################$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$%%%%%%%%%%%%$$$###%%%&&&''''''%%%%%%&&&'''######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$###""""""$$$###"""""""""###%%%%%%%%%$$$$$$######$$$$$$%%%$$$######"""!!!!!!!!!"""########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&(((''''''&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&++++++,,,,,,,,,------------,,,,,,,,,+++************************)))(((((())))))))))))))))))))))))(((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&'''''''''''''''((())))))***(((%%%%%%'''((('''%%%'''''''''((((((((())))))'''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&''''''''''''&&&&&&'''&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&%%%$$$###"""%%%%%%%%%%%%%%%%%%&&&'''&&&&&&%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$###$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$######$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''(((((((((((((((((((((((((((((((((''''''''''''(((((((((((())))))))))))(((((((((((((((((((((((((((((()))((('''&&&&&&'''((())))))(((''''''''''''((()))***)))((()))******(((&&&((((((((('''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$%%%%%%%%%%%%$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$##################$$$########################$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$%%%%%%%%%%%%$$$######$$$%%%$$$###"""###%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$######"""$$$###"""""""""###$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%''''''%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&,,,,,,,,,---------------,,,,,,,,,,,,++++++++++++)))))))))***)))(((((('''))))))))))))))))))))))))(((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&'''''''''&&&''''''((())))))'''&&&&&&'''''''''&&&&&&&&&&&&''''''''''''(((''''''''''''''''''''''''((((((((('''&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%$$$###""""""%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$######$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%$$$$$$######""""""######$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((((((((((((((((((((((((''''''''''''(((((((((((())))))))))))((((((((((((((((((((((((((((((((((((''''''''''''(((((())))))(((((((((((())))))''')))*********))))))***'''''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$########################%%%$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%&&&&&&%%%%%%%%%##############################$$$$$$$$$%%%%%%%%%######""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$%%%%%%%%%%%%$$$###"""###$$$###"""""""""$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$###############""""""######$$$%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&((((((&&&%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&######$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&---------------.........++++++,,,,,,,,,,,,,,,,,,***************)))(((((())))))))))))))))))))))))(((((((((((((((((((((((())))))(((((((((((())))))((((((((((((((((((((((((''''''''''''(((((((((((((((((())))))))))))(((((('''''''''&&&&&&''''''(((((('''&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%$$$######$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$###$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''((((((''''''&&&%%%%%%%%%&&&&&&&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((((((((((((((((((((((((''''''''''''(((((((((((())))))))))))(((((((((((((((((((((((((((((((((((((((''''''((((((((())))))))))))))))))))))))"""%%%((((((&&&%%%'''***((((((''''''&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$######### %%%%%%$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$%%%%%%%%%%%%$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$%%%%%%%%%%%%$$$######$$$%%%%%%######$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$########################$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%$$$$$$$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%'''(((((('''&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''((((((''''''&&&&&&%%%%%%######$$$%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&........................,,,,,,,,,,,,,,,,,,------++++++,,,,,,++++++***))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((()))))))))(((((((((((((((((((((((('''''''''((((((((())))))(((((())))))))))))((((((''''''&&&&&&&&&&&&'''''''''''''''&&&&&&&&&'''(((&&&&&&&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%&&&'''((())))))&&&&&&''''''''''''&&&&&&''''''''''''&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&%%%%%%$$$######$$$%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&(((((())))))))))))((((((%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((((((((((((((((((((((((((((((((''''''''''''(((((((((((())))))))))))(((((('''''''''''''''''''''''''''(((((((((((((((((('''(((((())))))))))))(((((( ###&&&'''%%%$$$&&&)))((((((((('''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$$$$####################################$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$%%%%%%%%%%%%$$$######$$$%%%%%%######$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$###""""""######$$$$$$$$$$$$$$$$$$############$$$$$$###$$$$$$%%%%%%%%%$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%'''(((((('''&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$###$$$%%%&&&'''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''///////////////.........------------,,,,,,,,,,,,,,,,,,------,,,,,,+++***))))))))))))))))))))))))))))))))))))))))))))))))(((''''''&&&&&&''''''((((((((((((((((((((((((((('''''''''(((((())))))***&&&&&&''''''''''''&&&&&&((('''&&&&&&%%%&&&&&&&&&&&&'''''''''&&&&&&''')))'''&&&&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''###$$$%%%&&&''')))******&&&&&&''''''''''''&&&&&&(((((('''''''''&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&''''''&&&&&&%%%"""###$$$%%%&&&%%%$$$###&&&&&&''''''''''''&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$######$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%%%%%%%%%%%%%$$$&&&%%%%%%%%%%%%%%%%%%&&&###$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&((((((((())))))(((((((((%%%%%%%%%&&&&&&&&&'''''''''''''''''''''(((((((((&&&&&&&&&''''''''''''(((((((((((((((((((((((((((((((((''''''''''''(((((((((((())))))))))))((((((''''''''''''''''''''''''''''''((((((((((((''''''''''''((((((((((((''''''###$$$&&&'''''''''((()))''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$''''''''''''''''''''''''%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################"""######$$$$$$######"""##############################$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$%%%%%%%%%%%%$$$###"""###$$$###"""""""""$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$#########""""""""""""#########$$$&&&'''''''''&&&%%%########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&((((((&&&%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&''''''&&&%%%$$$$$$%%%%%%&&&&&&'''''''''000000000/////////...............---,,,,,,,,,++++++,,,,,,,,,,,,+++******))))))))))))))))))))))))))))))))))))))))))))))))((((((''''''''''''((((((((((((((((((((((((((((((&&&''''''((())))))******&&&&&&''''''''''''&&&&&&((('''&&&&&&%%%%%%%%%&&&%%%'''((('''%%%%%%(((***''''''''''''&&&&&&&&&%%%''''''''''''''''''''''''$$$%%%%%%&&&'''((())))))&&&&&&''''''''''''&&&&&&'''''''''&&&&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%"""###%%%&&&'''&&&%%%$$$%%%&&&'''(((((('''&&&%%%%%%%%%%%%%%%&&&&&&&&&'''$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&''''''&&&$$$###$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&'''''''''((((((((()))&&&&&&&&&''''''''''''(((((((((((((((((((((((((((((((((''''''''''''(((((((((((())))))))))))((((((''''''''''''''''''''''''&&&'''((())))))((('''&&&%%%&&&'''(((((('''&&&%%%&&&%%%%%%'''((()))((('''%%%%%%%%%&&&''''''((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$#################################$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$%%%%%%%%%%%%$$$######$$$%%%$$$###"""###%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%$$$$$$###$$$##################$$$"""###%%%&&&'''&&&%%%$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%''''''%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&$$$%%%&&&'''&&&$$$"""!!!$$$$$$%%%%%%&&&''''''(((111111000000/////////...//////...---,,,,,,++++++***++++++++++++***))))))))))))))))))))))))))))))))))))))))))))))))))))))******))))))))))))******((((((((((((((((((((((((&&&''''''((()))******+++(((((())))))))))))((((((((('''&&&&&&%%%%%%%%%%%%$$$&&&((('''%%%%%%(((***(((((((((''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&''''''''''''''''''&&&''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%%%%%%%$$$$$$###$$$&&&(((((('''&&&%%%%%%&&&'''(((((('''&&&%%%&&&&&&&&&'''''''''((((((###$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&''''''&&&$$$###$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$#########$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$############$$$$$$#########$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&'''''''''(((((())))))&&&&&&&&&'''''''''((((((((((((((((((((((((((((((((((((''''''''''''(((((((((((())))))))))))((((((''''''''''''''''''''''''&&&'''((())))))((('''&&&$$$%%%&&&''''''&&&%%%$$$'''$$$###%%%((()))'''$$$"""###$$$%%%&&&&&&'''(((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$############$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$%%%%%%&&&&&&%%%%%%$$$##############################$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$%%%%%%%%%%%%$$$###%%%&&&''''''%%%%%%&&&'''######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%$$$######%%%$$$$$$$$$$$$$$$$$$%%% """$$$$$$$$$"""!!!########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''###%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''((((((((($$$%%%&&&&&&%%%### $$$$$$%%%%%%&&&'''((((((222000......///000///.........---------,,,,,,,,,---,,,++++++******++++++************************************************))))))*********+++++++++(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))***))))))((((((((())))))'''''''''&&&&&&%%%%%%%%%((((((''''''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&%%%%%%$$$%%%&&&((()))$$$$$$######$$$$$$%%%&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%'''((('''%%%$$$###%%%''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$&&&'''&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%$$$######$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$#########&&&""""""&&&'''###$$$)))'''&&&&&&&&&&&&'''(((((())))))((('''&&&%%%%%%$$$(((((('''&&&&&&&&&&&&'''((((((''''''&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((('''(((((())))))))))))((((((%%%%%%%%%&&&&&&&&&''''''******)))'''&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$###"""!!! &&&%%%###"""!!!"""###$$$&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$""""""###$$$%%%%%%$$$######%%%%%%$$$"""""""""""""""""""""""""""!!!###%%%&&&'''&&&$$$###%%%$$$"""!!!!!!"""$$$%%%$$$######"""###$$$&&&'''$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((&&&$$$###%%%%%%$$$$$$###"""!!!!!!###$$$%%%&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%$$$###"""!!!"""###$$$%%%&&&&&&&&&&&&$$$######%%%&&&&&&&&&###$$$%%%%%%&&&&&&&&&%%%%%%### !!!###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&'''((((((777555222000000///---,,,......---------------------,,,++++++***+++++++++************************))))))))))))))))))))))))))))))*********+++++++++(((((((((((((((((((((((((((((((((((((((((((((((('''''''''''''''''''''''')))((((((''''''(((((()))'''''''''&&&&&&%%%%%%%%%(((''''''''''''''''''(((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&'''(((%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&'''''''''&&&$$$$$$%%%'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$&&&'''&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$######"""""""""###%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&%%%&&&######&&&'''$$$%%%*********)))((('''''''''((('''''''''''''''&&&&&&&&&(((''''''&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&((((((((()))((((((''''''%%%%%%%%%&&&&&&&&&''''''###$$$$$$%%%&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########%%%$$$""" !!!"""###$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%((('''%%%######$$$%%%&&&'''%%%$$$%%%''''''&&&%%%##############################%%%&&&&&&&&&%%%$$$&&&$$$###""""""###$$$&&&&&&%%%$$$#########$$$%%%###############$$$%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((('''&&&$$$###&&&&&&%%%%%%$$$######"""######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$$$$$$$###"""""""""###$$$%%%%%%%%%%%%%%%###"""###$$$%%%%%%$$$$$$$$$%%%%%%&&&%%%%%%%%%(((&&&$$$""""""###$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%&&&&&&&&&&&&>>>:::555222000///...------------...............------,,,+++++++++++++++++++++++++++++++++++++++)))))))))))))))))))))))))))))))))************+++((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''((('''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((''''''&&&''''''&&&$$$$$$%%%''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$&&&'''&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$#########$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&&&&&&&&&&&&&''''''$$$$$$'''(((&&&'''***---,,,+++)))((((((''''''&&&&&&&&&'''''''''(((((('''''''''&&&''''''((((((%%%%%%&&&''''''(((((()))(((((((((((((((((((((((('''''''''''''''&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((('''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''!!!!!!"""$$$%%%'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%&&&&&&%%%$$$###"""!!!"""###$$$###############$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$((('''%%%$$$$$$%%%&&&&&&"""!!!!!!"""$$$%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$######$$$%%%&&&'''&&&%%%$$$###########################$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###'''&&&&&&%%%%%%$$$$$$############$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&''''''&&&$$$###'''&&&&&&%%%%%%$$$$$$$$$#########""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$$$$$$$###""""""######$$$%%%%%%%%%%%%###"""!!!"""$$$%%%$$$###$$$%%%%%%%%%%%%%%%$$$$$$((('''&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''((('''&&&&&&IIICCC:::444111111111222.............../////////------,,,++++++++++++,,,++++++++++++++++++++++++))))))))))))))))))))))))))))))))))))************(((((((((((((((((((((((((((((((((((((((((((((((('''''''''''''''''''''''''''&&&&&&&&&&&&''''''((('''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''(((''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&'''((((((&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%&&&'''&&&%%%$$$&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$###$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$&&&'''&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&#########$$$$$$%%%%%%%%%&&&%%%&&&'''(((((()))+++,,,+++***)))((((((((((((''''''''''''''''''''''''''''''&&&''''''((())))))(((((((((((())))))))))))''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''(((((((((''''''''''''&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%&&&'''###############$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################&&&%%%%%%$$$$$$$$$%%%&&&!!! !!!###$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$%%%&&&&&&&&&%%%%%%$$$&&&&&&%%%%%%$$$$$$$$$$$$$$$###"""!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$#########"""###$$$%%%%%%%%%%%%%%%###""""""###%%%%%%$$$###$$$%%%%%%%%%%%%$$$######$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''')))++++++***)))'''[[[SSSFFF<<<666333333444////////////////////////...---,,,,,,++++++,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&'''((((((''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%$$$''''''&&&&&&''''''((()))''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$&&&''''''%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$###$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$&&&'''&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$(((''''''&&&$$$###!!!!!!%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&#########$$$$$$%%%%%%%%%%%%&&&&&&&&&'''***++++++(((((('''''''''(((((())))))(((((('''&&&&&&%%%%%%&&&&&&&&&'''((()))***+++---,,,,,,+++***))))))(((&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''(((((('''&&&%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&''''''$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##########################################$$$$$$%%%$$$$$$%%%''')))(((((($$$$$$$$$$$$$$$$$$$$$$$$###""""""""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$############$$$###"""!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################$$$######$$$%%%%%%%%%$$$$$$$$$######%%%&&&'''%%%$$$$$$$$$$$$%%%%%%$$$######"""###$$$%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''')))++++++***)))'''ooofffYYYKKKAAA:::666333111000000000////////////...------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,***)))))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))&&&&&&&&&&&&'''((())))))'''''''''''''''(((((((((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&'''''''''&&&%%%%%%'''&&&&&&&&&&&&'''((((((((((((((((((''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$###%%%''''''&&&%%%&&&'''%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$&&&'''&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$""" %%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&&&&&&&&&&&&&'''$$$&&&'''%%%&&&***,,,***&&&&&&&&&&&&&&&'''((((((***)))((('''&&&%%%$$$$$$&&&&&&&&&'''(((***+++,,,......---,,,***)))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&#########$$$%%%%%%&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$$$$############$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###############%%%$$$$$$%%%'''((('''&&&$$$$$$$$$$$$$$$$$$$$$$$$"""""""""############$$$$$$$$$%%%%%%%%%%%%$$$$$$!!!"""###%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%&&&''''''########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%""""""###$$$&&&'''((((((#########$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%#################################""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""###$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$&&&''''''&&&$$$"""######$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''((('''&&&&&&xxxrrriii^^^SSSGGG===666333222111111000///............---,,,,,,,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++******))))))((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''((()))***+++&&&'''''''''((((((((()))(((''''''''''''''''''(((''''''''''''''''''''''''''''''''''''''''''''''''$$$%%%&&&'''''''''&&&%%%&&&&&&%%%%%%&&&&&&'''((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$###%%%'''((('''&&&&&&'''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$&&&'''&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$"""!!! %%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&%%%"""&&&'''$$$%%%+++,,,***''''''&&&&&&&&&&&&&&&&&&((((((''''''&&&&&&&&&%%%%%%%%%&&&'''(((***,,,---,,,,,,+++***)))(((((('''''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&'''(((((($$$%%%&&&''''''(((''''''%%%%%%%%%&&&&&&&&&''''''######$$$$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#################################$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$$$$###############$$$%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$$$$$$$$$$###"""!!!"""###$$$###"""########################"""###$$$%%%&&&%%%%%%$$$###$$$$$$$$$$$$$$$$$$#########$$$%%%%%%%%%$$$###$$$############$$$%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$%%%%%%&&&''''''$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""###$$$$$$$$$$$$$$$%%%%%%$$$$$$############%%%''''''%%%""" !!!"""$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%%%%%%%&&&&&&&&&&&&xxxvvvrrrkkkaaaSSSFFF<<<444333222111000...------......---,,,,,,,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,******************************))))))((((((((('''(((((((((((((((((((((((((((((((((((((((((((((((('''''''''''''''''''''''''''''''''((((((***++++++&&&'''''''''(((((())))))((((((''''''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''###$$$&&&'''((('''&&&&&&&&&%%%%%%%%%%%%&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%"""%%%'''((('''&&&&&&'''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$&&&'''&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&'''((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$#########!!!&&&&&&###%%%+++,,,)))***)))((('''&&&%%%%%%%%%&&&&&&&&&''''''''''''(((%%%%%%&&&''')))+++,,,---)))))))))(((((((((((((((((((((((((((((((((((((((&&&&&&&&&'''''''''((((((&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&((((((((()))***++++++,,,$$$$$$&&&'''((()))))))))%%%%%%%%%&&&&&&&&&''''''########################$$$$$$$$$$$$$$$$$$$$$$$$"""""""""""""""""""""""" !!!"""###$$$%%%&&&&&&###$$$%%%&&&&&&&&&&&&&&&"""""""""""""""######$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%%%%%%%%%%&&&%%%###$$$%%%%%%$$$###""""""""""""""""""""""""###$$$&&&(((((('''&&&%%%"""######$$$$$$######"""$$$%%%&&&&&&%%%$$$"""!!!"""""""""!!!"""######$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%$$$$$$%%%%%%%%%$$$$$$###!!!!!!"""$$$&&&&&&###!!! """###%%%%%%&&&&&&###############$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&&&&'''&&&'''''''''''''''''''''''''''&&&&&&&&&&&&'''((((((|||xxxqqqeeeUUUIII===:::777444222///---+++,,,---.........---,,,,,,,,,,,,,,,,,,,,,+++***))),,,,,,,,,+++++++++******++++++************++++++***)))(((''''''((()))***))))))))))))))))))))))))))))))))))))))))))))))))'''''''''''''''''''''''''''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&((())))))(((&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&+++)))(((&&&%%%%%%%%%&&&''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$'''&&&%%%$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&''''''&&&$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((())))))&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&'''(((***++++++)))&&&%%%'''+++///222***))))))((('''&&&&&&&&&''''''''''''''''''''''''%%%&&&&&&&&&'''((((((((((((((('''''''''&&&&&&&&&###$$$$$$%%%&&&'''((((((&&&'''''''''&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$#########%%%%%%%%%$$$$$$###############""""""######$$$%%%&&&&&&%%%$$$###"""!!! #########$$$$$$%%%%%%%%%########################$$$$$$$$$$$$######""""""%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$#########$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$&&&&&&''''''""""""#########$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$$$$########################$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$#########""""""""""""""""""""""""###$$$$$$$$$%%%""""""#########$$$$$$$$$$$$$$$$$$############"""###$$$%%%%%%&&&&&&%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''***(((&&&&&&&&&'''&&&$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%}}}yyyqqqfff^^^LLLDDD:::555444444111...///.........---......///---------------,,,++++++,,,,,,,,,+++++++++******++++++************++++++***)))(((((((((((()))***))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''''''''''''''(((''''''''''''((())))))&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&))))))'''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''((()))******)))'''&&&'''***---///***))))))(((''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''''''''#########$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$######%%%%%%%%%$$$$$$$$$############""""""######$$$%%%!!!!!!"""$$$%%%'''((()))$$$$$$$$$$$$$$$$$$%%%%%%########################$$$$$$$$$$$$#########"""%%%$$$$$$######$$$$$$%%%&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$$$$$$$$$$$$$########################""""""#########$$$$$$$$$&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$""""""#########$$$$$$$$$""""""######$$$$$$$$$%%%###$$$%%%%%%&&&&&&%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&''')))'''&&&&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%{{{vvvrrr]]]PPP???666555555222...111000............000111---............------,,,,,,,,,,,,+++++++++******++++++************+++++++++***))))))))))))***+++))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''''''''''''''((((((((((((((()))******''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%&&&'''(((((((((((((((''''''&&&&&&&&&''''''%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%&&&&&&&&&%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$$$$$$$%%%########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''###$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((()))))))))(((((()))((((((''''''(((***+++)))))))))(((''''''&&&&&&'''''''''''''''''''''''''''''''''''''''&&&&&&&&&!!!!!!"""###$$$%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$######$$$%%%&&&%%%%%%%%%&&&''''''((((((%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%$$$$$$$$$$$$#########""""""######$$$%%%'''&&&&&&$$$###"""!!!!!!%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$######"""""""""###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%################################################&&&%%%%%%$$$$$$$$$$$$%%%########################"""############$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$ !!!"""###$$$%%%&&&&&&###$$$$$$%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%&&&((()))***%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''$$$"""!!!"""%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%{{{}}}zzzxxxlll```PPPDDD===999444111000000000///////////////------.........------,,,,,,,,,,,,+++++++++******++++++************+++++++++******************+++((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''((((((''''''(((((()))***((((((((((((((((((((((((((('''&&&&&&&&&&&&'''((((((((((((((((((((((((((($$$%%%&&&'''((((((((((((&&&&&&&&&&&&''''''(((((($$$$$$%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$!!!###%%%'''''''''%%%$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&'''((()))******)))(((''')))(((((((((''''''''''''))))))((((((''''''''''''''''''''''''''''''''''''((((((((('''&&&&&&&&&%%%$$$$$$%%%&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&$$$###""""""$$$&&&'''%%%%%%&&&&&&'''((())))))%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%***)))&&&### %%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$####################################%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%########################%%%%%%%%%%%%%%%%%%%%%%%%#################################$$$$$$$$$$$$$$$%%%$$$$$$$$$###"""""""""########################!!!""""""###$$$$$$%%%%%%######$$$%%%%%%%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%&&&&&&'''((()))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''$$$###"""###%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%sssxxx~~~{{{yyyuuupppgggZZZLLLAAA;;;888000000111222111///---,,,,,,,,,------------,,,,,,,,,,,,,,,+++++++++******++++++************++++++*********++++++*********((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&&&&''''''((()))((((((((((((((((((((((((((('''&&&&&&&&&&&&'''((((((((((((((((((((((((((($$$%%%&&&'''((((((((((((%%%%%%&&&''''''((((((((($$$$$$$$$%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$!!!###%%%'''''''''%%%$$$$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''((()))*********)))((()))))))))((('''&&&&&&%%%((((((((((((''''''''''''((((((((((((((((((((((((((((((((('''&&&&&&&&&%%%((((((((((((((('''''''''$$$$$$%%%%%%&&&'''((((((%%%%%%&&&&&&'''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$###""""""$$$&&&'''%%%%%%&&&&&&'''((())))))%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%!!!!!!!!!!!!!!!"""""""""%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$%%%&&&&&&'''########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$######$$$$$$%%%########################%%%%%%%%%%%%%%%%%%%%%%%%########################""""""""""""######$$$$$$%%%$$$$$$$$$###"""""""""################################################"""###$$$$$$%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''')))(((&&&&&&((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%kkkpppvvv|||~~~|||sssuuurrriiiYYYKKKAAA>>>444444444333222///---+++++++++,,,------------,,,,,,,,,,,,+++++++++******++++++************++++++))))))***++++++***))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((&&&&&&&&&&&&&&&'''((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%&&&'''((((((((((((%%%%%%&&&'''((((((((('''$$$$$$%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&'''((())))))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$%%%%%%&&&&&&&&&&&&%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''((()))************)))))))))(((''''''&&&&&&((((((((((((((((((''''''(((((((((((((((((((((((('''''''''''''''&&&&&&&&&''''''''''''&&&&&&&&&%%%###$$$$$$%%%&&&'''((()))%%%%%%&&&&&&''''''&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&$$$############%%%&&&'''%%%%%%%%%&&&''''''(((((($$$$$$############$$$$$$###$$$$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%######""""""######$$$%%% !!!"""###%%%&&&'''(((%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$########################"""###$$$%%%&&&'''(((((($$$$$$$$$#####################$$$$$$$$$%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''$$$############$$$$$$%%%########################$$$$$$$$$############"""#########$$$$$$$$$$$$$$$!!!!!!!!!"""######$$$$$$$$$$$$$$$###############$$$$$$$$$###############$$$$$$$$$#########"""""""""######$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%!!!!!!!!!!!!!!!!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&&&&%%%$$$###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''''''%%%$$$$$$%%%&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%jjjjjjmmmssszzz~~~~~~}}}sssuuuwwwrrrhhhZZZNNNGGG<<<:::666333000/////////,,,,,,---...............,,,,,,,,,+++++++++******++++++************++++++((())))))******))))))((())))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((('''''''''''''''(((((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&%%%&&&'''((((((''''''&&&$$$%%%%%%&&&''''''((((((''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((()))+++,,,---******)))((('''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&'''''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$"""######$$$$$$%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$############$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%######""""""######$$$%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$%%%%%%%%%&&&$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$%%%%%%%%%&&&$$$$$$$$$#########""""""""""""###$$$%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&###############$$$%%%%%%########################$$$$$$$$$#########""""""$$$$$$$$$$$$%%%%%%%%%&&&!!!!!!"""######$$$%%%%%%###############$$$$$$$$$$$$$$$$$$#########""""""###############$$$$$$$$$""""""###$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''$$$"""!!!"""$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%llliiigggkkkssszzz{{{zzzzzz{{{||||||wwwlll___UUUCCC>>>888222//////222444------...///000000//////,,,,,,,,,+++++++++******++++++************++++++'''((()))******)))((('''))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((()))******&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&((())))))(((&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((''''''&&&&&&&&&&&&'''(((((('''&&&%%%%%%%%%&&&&&&'''((())))))''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$''''''%%%$$$$$$$$$$$$%%%$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%((((((((('''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%###$$$&&&'''((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&'''((())))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&''')))+++...///+++***)))'''''''''((()))'''''''''((((((((((((((())))))))))))))))))))))))%%%&&&&&&''''''((((((((($$$%%%%%%&&&'''((())))))''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&'''''''''&&&&&&&&&&&&%%%%%%$$$$$$$$$!!!"""###%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$#########$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%#########"""###$$$$$$%%%###############$$$$$$$$$#########$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%#########$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$###############$$$$$$$$$$$$######""""""!!!!!!"""###%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%######""""""###$$$%%%%%%########################&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&""""""###$$$%%%%%%&&&&&&""""""######$$$$$$$$$%%%$$$$$$$$$$$$######""""""!!!!!!"""###$$$%%%%%%&&&""""""###$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%#########$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%'''***,,,---,,,&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%rrrnnnhhheeegggmmmtttzzzvvv|||{{{rrriii\\\LLL===777444000///111/////////---,,,,,,...000...---,,,,,,++++++,,,,,,+++++++++************)))++++++******))))))(((((())))))))))))************(((((((((((((((((((((((()))((('''&&&&&&'''((()))'''''''''''''''&&&&&&&&&''''''''''''''''''''''''))))))))))))(((((((((((('''''''''''''''((()))***'''''''''''''''&&&&&&&&&''''''&&&&&&&&&&&&''''''(((''''''&&&&&&''''''(((&&&&&&'''((()))))))))((($$$%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&)))((((((''''''&&&%%%%%%))))))((('''&&&&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''&&&&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%&&&'''&&&%%%%%%'''''''''&&&&&&%%%%%%%%%''''''((((((((((((''''''$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$'''&&&%%%$$$###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''$$$""""""%%%)))&&&%%%%%%%%%%%%&&&''''''%%%&&&&&&&&&&&&&&&%%%%%%'''&&&&&&)))---111333444(((((('''''''''(((((()))***)))((('''''''''''''''&&&'''((()))************&&&&&&&&&'''''''''((((((''''''&&&&&&&&&%%%%%%%%%"""%%%'''((('''&&&&&&&&&$$$%%%&&&''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$$$$'''&&&&&&%%%%%%$$$$$$###%%%%%%%%%$$$$$$#########%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%$$$$$$###$$$$$$$$$$$$$$$######$$$$$$%%%&&&&&&&&&%%%$$$$$$######"""""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######""""""##############################$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$#########""""""!!!!!!########################!!!!!!""""""##################$$$$$$$$$$$$######"""######$$$$$$######"""###################################################$$$%%%&&&&&&%%%$$$###"""############$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&'''''''''%%%$$$######$$$&&&'''sssppplllhhhfffjjjqqqwwwzzzzzzssskkk\\\LLLAAA999111///111//////...---++++++,,,---,,,+++******)))*********+++++++++************)))*********)))))))))))))))(((((((((((())))))))))))(((((((((((((((((((((((()))(((''''''''''''((()))%%%%%%&&&&&&'''''''''(((''''''''''''''''''''''''))))))))))))(((((((((((('''&&&&&&&&&&&&''''''(((&&&&&&''''''''''''''''''))))))(((((((((((())))))&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&'''&&&&&&&&&''''''&&&&&&''''''(((((($$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%$$$$$$$$$)))(((((('''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''((((((&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$#########&&&&&&''''''''''''&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%$$$######$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$######&&&(((&&&&&&&&&&&&&&&''''''(((''''''((((((((((((''''''%%%%%%$$$'''+++...000111'''&&&&&&%%%%%%%%%&&&&&&))))))((('''''''''''''''*********))))))'''&&&&&&&&&&&&&&&'''''''''(((((('''''''''&&&&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%'''(((%%%&&&''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&'''&&&&&&&&&%%%%%%$$$$$$###$$$$$$%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######""""""##############################$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$##################"""###########################""""""""""""###$$$$$$######$$$$$$$$$$$$############$$$$$$$$$$$$######################################################"""######$$$$$$######""""""############$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&''''''((('''&&&$$$$$$%%%'''(((ssstttsssnnniiiiiimmmsss{{{~~~zzznnn___QQQCCC888333333111000///...---,,,,,,,,,,,,,,,+++***************+++++++++************)))))))))))))))************'''''''''((((((((())))))(((((((((((((((((((((((()))((((((''''''(((((()))$$$$$$%%%&&&'''((())))))''''''''''''''''''''''''))))))))))))(((((((((((('''&&&&&&%%%%%%%%%&&&&&&%%%&&&&&&&&&'''((((((((())))))(((((((((((())))))&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&'''&&&&&&%%%%%%***)))((('''&&&'''((()))$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&((((((((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$&&&''')))***+++&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$######%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$(((&&&$$$###%%%&&&&&&&&&&&&&&&'''''''''(((((((((''''''(((((()))(((((('''&&&%%%%%%'''***---//////((('''&&&%%%%%%%%%%%%%%%((((((((('''''''''''''''*********)))((('''%%%$$$&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&%%%&&&&&&&&&$$$###$$$'''***&&&&&&'''(((((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$###########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&%%%$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$%%%&&&"""######$$$%%%%%%&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######""""""##############################$$$$$$######$$$$$$%%%&&&&&&%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$#########"""###$$$$$$$$$$$$$$$%%%%%%########################$$$######""""""$$$%%%&&&######$$$$$$$$$$$$######$$$$$$$$$%%%%%%$$$$$$$$$###################################################""""""""""""""""""###"""############$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&''''''***)))'''&&&%%%&&&&&&'''ooouuuzzzxxxqqqmmmnnnqqqxxx~~~yyyooobbbRRRDDD<<<999444333111000000000///.........---,,,,,,,,,,,,---+++++++++*********))))))(((((())))))******++++++(((((((((((())))))))))))(((((((((((((((((((((((()))(((((((((((((((((()))&&&&&&''''''((())))))***''''''''''''''''''''''''))))))))))))(((((((((((((((((('''&&&%%%%%%%%%%%%%%%%%%%%%&&&'''((())))))''''''&&&&&&&&&&&&''''''((((((''''''''''''((((((((()))))))))((('''&&&&&&***)))'''&&&%%%&&&'''(((''''''''''''''''''''''''%%%%%%&&&&&&'''((())))))(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&""""""$$$%%%'''(((******&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))&&&######&&&((('''%%%&&&''''''(((((((((((((((&&&''''''((((((((((((((((((''''''))),,,...///...+++***)))((('''&&&&&&&&&'''''''''''''''''''''&&&''''''((((((((((((((('''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&%%%&&&&&&%%%$$$%%%''')))''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%&&&#########$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######""""""##############################$$$$$$######$$$$$$%%%&&&&&&&&&%%%%%%$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$######"""$$$$$$$$$%%%%%%&&&&&&&&&########################%%%$$$###"""###$$$&&&'''######$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$################################################$$$###"""!!!!!!"""###$$$""""""#########$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########"""&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''***)))'''&&&%%%%%%%%%%%%llluuu{{{tttrrrtttvvv||||||qqqbbbSSSFFF>>>777444111000111111111//////...------,,,,,,------+++++++++*********))))))(((((())))))******++++++))))))*********+++++++++))))))))))))))))))))))))((())))))))))))))))))(((******))))))))))))))))))(((((((((((((((((((((((())))))))))))(((((((((((())))))((('''&&&&&&&&&'''%%%%%%%%%&&&'''((())))))''''''&&&&&&&&&&&&'''''')))((((((''''''(((((()))((()))))))))((('''&&&&&&)))(((&&&%%%%%%%%%&&&&&&''''''''''''''''''''''''$$$%%%%%%&&&'''((())))))'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&''''''(((&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((())))))***&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))&&&###$$$'''((('''$$$&&&'''(((((())))))(((((((((((()))***************(((''''''))),,,---,,,++++++***)))((('''&&&&&&&&&%%%&&&''''''((('''&&&&&&&&&''''''((((((((((((''''''''''''''''''''''''&&&(((((('''''''''&&&&&&&&&###%%%'''((('''&&&&&&&&&'''''''''&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$#########$$$$$$%%%&&&$$$$$$######$$$$$$%%%&&&%%%%%%%%%$$$$$$$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######""""""##############################$$$$$$######$$$$$$%%%&&&&&&&&&%%%%%%$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%&&&&&&&&&'''########################%%%$$$#########$$$%%%&&&######$$$$$$$$$$$$#########$$$$$$%%%%%%$$$$$$###################################################%%%$$$###""""""###$$$%%%""""""#########$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''((('''&&&%%%$$$$$$$$$###nnnvvv{{{xxxxxxwww}}}}}}qqqdddTTTGGG>>>888222//////111000///---,,,,,,++++++++++++++++++++++++************)))))))))))))))*********************+++++++++,,,,,,))))))))))))))))))))))))((())))))******))))))(((+++*********))))))))))))(((((((((((((((((((((((())))))))))))(((((((((((())))))((('''''''''((((((%%%&&&&&&&&&'''((((((((())))))(((((((((((())))))''''''&&&&&&&&&&&&''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%$$$$$$$$$%%%&&&'''######$$$$$$$$$$$$%%%%%%&&&&&&''''''''''''&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&'''((()))))))))(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%&&&'''''''''%%%%%%&&&'''((()))(((''''''******+++,,,------------&&&&&&&&&''')))***)))'''((('''&&&%%%%%%%%%%%%%%%$$$%%%&&&(((((('''&&&&&&((((((((((((''''''&&&%%%'''''''''''''''&&&&&&&&&((((((((('''''''''&&&&&&"""$$$((()))(((&&&%%%&&&'''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&%%%%%%$$$#########$$$$$$$$$$$$%%%%%%%%%&&&%%%$$$######$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%%%%############$$$%%%&&&&&&$$$$$$######$$$$$$%%%&&&&&&&&&%%%%%%$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######""""""##############################$$$$$$######$$$$$$%%%&&&&&&%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%&&&&&&#################################$$$$$$$$$$$$$$$######$$$$$$$$$$$$###############$$$$$$#########################################################%%%%%%$$$$$$$$$$$$%%%%%%"""############$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$###tttxxx|||}}}}}}}}}zzz||||||zzz|||}}}vvvhhhZZZJJJBBB888222111111000///------,,,++++++++++++,,,+++++++++************)))*********))))))))))))))))))************+++++++++))))))))))))))))))))))))((()))************)))((((((((((((((((((((())))))(((((((((((((((((((((((())))))))))))((((((((((((''''''&&&&&&&&&'''((((((&&&&&&''''''''''''''''''))))))(((((((((((())))))''''''&&&&&&&&&&&&''''''%%%%%%&&&&&&'''&&&&&&&&&$$$%%%'''(((((((((&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%$$$$$$$$$%%%&&&'''#########$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&''''''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%'''(((((('''&&&&&&'''$$$%%%'''(((((((((&&&%%%((()))***+++,,,,,,,,,,,,&&&&&&&&&'''))))))'''%%%'''&&&&&&%%%%%%%%%&&&&&&###$$$&&&(((((('''&&&%%%&&&''''''(((((('''&&&&&&(((((('''''''''&&&&&&&&&((((((((((((''''''''''''$$$%%%''''''&&&%%%&&&'''&&&%%%$$$$$$$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%########################%%%$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%$$$###""""""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$############$$$%%%&&&'''$$$$$$######$$$$$$%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######""""""##############################$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$######################## !!!###$$$%%%$$$###"""######$$$$$$$$$$$$######!!!""""""######""""""!!!######################################################$$$$$$$$$$$$######"""############$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&'''%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&&&&&&&%%%%%%yyyyyyyyyzzz{{{}}}{{{zzzvvvqqqrrrzzzxxxkkkUUUKKK???666444444222000//////...------------...+++++++++************)))++++++******))))))(((((())))))))))))************))))))))))))))))))))))))((()))***++++++***)))((($$$%%%%%%&&&'''((())))))))))))))))))))))))))))))))))))))))))((((((((((((%%%%%%%%%%%%&&&&&&'''((('''''''''''''''&&&&&&&&&''''''&&&&&&&&&&&&''''''))))))(((((((((((())))))&&&&&&'''((()))))))))(((###%%%(((***+++***(((&&&((((((((((((((((((((((((&&&&&&&&&'''''''''((((((&&&'''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$###$$$%%%&&&'''%%%%%%%%%&&&&&&'''''''''$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%&&&&&&&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$'''***)))&&&%%%&&&(((###$$$&&&(((((('''&&&%%%%%%%%%&&&(((((()))))))))((((((((()))+++***(((&&&(((((('''''''''(((((()))###$$$&&&(((((('''&&&%%%"""###%%%'''((()))******(((((('''''''''&&&&&&&&&)))(((((((((''''''''''''&&&&&&&&&$$$###$$$'''***%%%%%%############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$%%%%%%&&&'''###$$$$$$%%%%%%&&&&&&'''#########$$$$$$%%%%%%%%%$$$###""" """###$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$############$$$%%%&&&'''$$$$$$######$$$$$$%%%&&&#########$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###"""#################################$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&&&&'''(((%%%%%%%%%$$$$$$################################# ###%%%%%%$$$""" ######$$$$$$$$$$$$######!!!!!!""""""""""""!!!!!!################################################!!!"""###$$$$$$###"""!!!"""############$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$ """$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''((('''''''''vvvtttuuuxxxyyyxxx{{{~~~vvvmmmgggjjjttt}}}zzzjjj\\\JJJ;;;555333222000000...------///000000000,,,,,,+++******+++++++++************************(((((())))))))))))((((((***************)))(((((())))))((((((((('''''''''(((((((((((((((((((((((())))))))))))************,,,111333000)))%%%(((,,,))))))))))))((('''%%%%%%(((((())))))))))))((((((((((((((((((((((((((((((%%%&&&&&&&&&'''(((((((((&&&'''((())))))((('''&&&''''''(((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%'''((()))))))))((((((''''''&&&&&&%%%&&&''''''%%%%%%&&&'''%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%$$$###"""###$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''###$$$&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''*********))))))((('''&&&((()))))))))'''&&&&&&'''&&&&&&&&&&&&&&&'''(((((('''((((((((())))))******))))))(((&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&)))&&&%%%&&&((((((%%%"""""""""""""""""""""""""""$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$###""""""%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&'''''''''%%%$$$$$$######$$$$$$%%%###$$$$$$%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!!!!""""""##############################&&&%%%%%%$$$#########$$$$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$""""""""""""""""""""""""%%%###"""$$$&&&'''$$$"""""""""###$$$$$$$$$$$$######$$$%%%%%%######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&%%%###"""###$$$#########$$$$$$%%%%%%%%%%%%%%%$$$######$$$$$$$$$''''''''''''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%uuussstttwwwxxxvvvyyy}}}~~~wwwmmmeeedddiiiooouuu|||vvvhhhTTTDDD;;;666222000111///......///000///......---,,,+++++++++++++++************************))))))************))))))***************)))(((((((((((((((''''''&&&&&&&&&(((((((((((((((((((((((((((((()))))))))************---///---)))(((***---((()))))))))((('''&&&&&&'''(((((())))))(((((('''((((((((((((((((((((((((&&&&&&&&&'''''''''''''''&&&''''''((((((''''''&&&''''''(((((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$%%%&&&((((((((((((((((((''''''''''''%%%&&&''''''%%%%%%&&&'''%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$###$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''$$$%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''&&&&&&((())))))))))))))))))******)))((('''''')))'''&&&&&&&&&&&&&&&'''''''''''''''(((((()))))))))******(((''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$%%%''''''%%%"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$###"""###$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$$$$######$$$$$$$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%######$$$&&&&&&$$$"""""""""###$$$$$$$$$$$$###"""###$$$$$$###"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&%%%$$$######%%%######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%tttqqqrrruuuvvvuuuvvvyyy~~~yyypppfff___^^^___iiisss}}}tttbbbRRRGGG>>>777333222111//////000000...,,,000///...---,,,+++++++++++++++++++++++++++++++++***++++++++++++++++++************+++******)))((())))))((((((((((((''''''(((((((((((((((((((((((((((((())))))))))))******(((((()))******++++++,,,'''((((((((((((((('''''''''''''''(((((('''''''''(((((((((((((((((((((((('''''''''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&''''''''''''(((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&''''''''''''''''''(((((((((%%%'''''''''&&&%%%&&&'''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''$$$%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''%%%&&&'''((()))))))))))))))***+++***(((((((((***((('''&&&&&&&&&&&&&&&''''''''''''''''''(((((((((******)))(((''''''''''''%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%''''''&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$############$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$######""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$%%%&&&$$$"""""""""###$$$$$$$$$$$$###"""###$$$###"""!!!"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&%%%$$$###$$$%%%###$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%rrroooooosssuuutttuuuxxx~~~}}}vvvlllaaaZZZWWW```hhhrrryyy~~~~~~yyynnnbbbWWWKKKAAA:::444333111111222111000...111111///...,,,,,,++++++++++++++++++++++++++++++******++++++++++++***************++++++******)))************************(((((((((((((((((((((((((((((((((((()))))))))***(((&&&%%%'''***,,,+++)))&&&'''((((((((((((((('''&&&&&&''''''''''''&&&&&&((((((((((((((((((((((((((((((((('''&&&&&&&&&%%%'''&&&$$$$$$$$$$$$&&&'''&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&''''''(((((((((&&&'''((('''&&&%%%&&&((('''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''"""###%%%&&&&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&''''''(((((((((((('''&&&%%%%%%((()))***)))((('''((()))))))))(((''''''''''''(((&&&&&&''''''''''''''''''))))))((('''''''''''''''$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''((((((((('''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$%%%%%%%%%$$$###""""""###$$$$$$$$$$$$###"""$$$%%%$$$###"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%sssnnnlllpppttttttuuuxxx|||~~~}}}uuujjj```ZZZYYYZZZaaammmyyy}}}}}}{{{wwwpppfffXXXJJJAAA999777444333333444333111222111///...---,,,,,,,,,++++++++++++++++++++++++)))******************)))******++++++++++++******))))))))))))))))))))))))))))))))))))))))))))))))'''(((((((((((()))))))))***'''%%%&&&***+++)))&&&&&&'''((((((((((((((('''&&&&&&''''''''''''&&&&&&((((((((((((((((((((((((((((((((('''&&&&&&&&&%%%&&&%%%$$$######$$$%%%&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''((((((&&&'''((((((&&&&&&'''((('''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''###$$$%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&########################%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&'''''''''((((((''''''&&&%%%$$$&&&'''((('''&&&&&&'''(((******)))))))))))))))***''''''''''''''''''&&&&&&''''''&&&%%%%%%%%%&&&&&&$$$%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###############%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!"""###$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###$$$$$$%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%%%%$$$$$$$$$""""""###$$$$$$$$$$$$###$$$%%%&&&&&&$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ """###"""!!! !!!###$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%yyyqqqmmmooorrrssstttwwwyyy}}}~~~uuukkkdddVVVQQQRRR```oooxxx{{{{{{{{{|||}}}yyyoooaaaSSSJJJCCC???999666555555555444111000///...---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,))))))************)))))))))***++++++,,,+++++++++&&&&&&''''''''''''(((((())))))))))))))))))))))))''''''(((((((((((())))))+++(((&&&''')))***(((%%%'''((((((((((((((('''''''''''''''(((((('''''''''(((((((((((((((((((((((('''''''''''''''&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&''''''((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&'''''''''&&&'''(((((('''&&&'''(((&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$$$$''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''''''''&&&&&&&&&&&&''''''###$$$%%%&&&''''''''''''$$$&&&''''''&&&%%%&&&((()))))))))))))))***++++++((((((((('''''''''''''''&&&&&&%%%%%%%%%%%%%%%&&&$$$%%%&&&((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&& """$$$$$$###""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$############$$$$$$$$$$$$###"""""""""""""""%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%% !!!"""############%%%%%%%%%%%%$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%""""""######$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$###########################$$$$$$######$$$$$$%%%%%%###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%% #########$$$$$$$$$$$$$$$########################"""$$$&&&%%%$$$###$$$%%%""""""###$$$$$$$$$$$$###%%%&&&'''&&&%%%$$$%%%'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!""""""!!! """###%%%%%%%%%$$$$$$$$$$$$###!!!"""$$$%%%&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$#########$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%xxxooooooqqqqqqrrrtttvvvzzz|||ssslll[[[SSSOOOWWWaaahhhoootttwwwzzz|||{{{tttkkkaaa[[[NNNHHH@@@999666555444444///......---,,,,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,******++++++++++++******)))***++++++,,,,,,,,,+++'''''''''(((((()))))))))))))))))))))))))))))))))'''''''''((((((((()))))))))((('''((()))))))))(((((()))))))))((('''&&&&&&'''(((((())))))(((((('''((((((((((((((((((((((((&&&&&&&&&'''''''''''''''%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&'''((((((''''''''''''''''''''''''''''''###$$$&&&''''''''''''&&&'''&&&&&&&&&&&&&&&&&&%%%&&&((()))((('''&&&''')))%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%((('''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%########################&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''''''''&&&&&&&&&&&&''''''###$$$%%%&&&&&&'''&&&&&&%%%&&&''''''&&&&&&''')))&&&&&&''''''((()))***+++)))))))))(((((('''''''''&&&&&&%%%%%%%%%&&&&&&'''$$$%%%'''((()))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&!!!$$$%%%%%%###!!!"""###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%%%%$$$######""""""######%%%%%%%%%%%%%%%%%%%%%%%%((('''%%%$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%!!!"""###$$$%%%%%%$$$###&&&&&&&&&&&&%%%%%%%%%$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%!!!!!!!!!!!!!!!!!!!!!!!!"""#########$$$$$$$$$$$$"""""""""""""""""""""""""""$$$&&&&&&$$$######%%%""""""###$$$$$$$$$$$$###$$$%%%&&&&&&$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""######""""""###%%%%%%%%%%%%$$$$$$$$$######!!!"""$$$&&&''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%}}}rrrooopppoooppprrruuuxxx~~~wwwqqqdddZZZSSSTTTVVVYYYbbbkkkrrruuuyyyyyyvvvrrrmmmkkkWWWOOODDD;;;666444333333...------,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,------,,,,,,+++)))***+++,,,,,,,,,,,,,,,******++++++,,,,,,,,,,,,))))))))))))))))))))))))''''''''''''((((((((()))''''''((()))))))))******))))))))))))((('''%%%%%%(((((())))))))))))((((((((((((((((((((((((((((((%%%&&&&&&''''''(((((((((%%%%%%'''(((((('''%%%%%%%%%%%%&&&'''((((((((('''''''''''''''''''''''''''"""###%%%'''(((((('''''''''''''''&&&&&&%%%%%%%%%'''((()))((('''&&&''')))%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&%%%$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''((('''&&&%%%$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%########################&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&'''''''''''''''&&&&&&'''''''''&&&&&&&&&&&&%%%$$$######%%%'''((((((''''''(((***$$$$$$$$$%%%'''(((***+++******))))))((((((((('''''''''&&&&&&&&&''''''((($$$%%%'''))))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%''')))(((%%%###$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%***(((&&&%%%%%%%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((()))((('''&&&'''''''''&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$%%%%%%&&&""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################""""""######$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&"""$$$'''&&&$$$"""###%%%""""""###$$$$$$$$$$$$######$$$%%%%%%######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###%%%%%%$$$$$$%%%&&&%%%%%%%%%$$$$$$#########"""###&&&((((((((('''&&&########################$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%yyynnnnnnpppoooooorrrxxx}}}}}}xxxiiieee]]]TTTNNNOOOTTTYYYbbbfffoooxxx}}}zzzqqqiii```TTTEEE===888333///,,,000000///...,,,+++***))),,,,,,,,,,,,,,,,,,,,,,,,---,,,+++******+++,,,---+++++++++************))),,,+++***))))))***+++,,,))))))))))))))))))))))))''''''((((((((((((''''''((((((((((((((((((((((((&&&'''((())))))((('''&&&''''''''''''''''''''''''******))))))((((((''''''&&&'''''''''(((((())))))((((((((((((((((((''''''&&&&&&''''''''''''&&&&&&******))))))((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''&&&%%%%%%$$$'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&'''''''''(((((((((((('''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%$$$"""###&&&)))***(((%%%$$$%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%$$$$$$###%%%$$$$$$$$$$$$%%%&&&'''&&&%%%%%%%%%%%%&&&''''''%%%%%%''''''''''''%%%%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''&&&&&&''''''&&&&&&%%%$$$)))'''&&&(((,,,---+++)))&&&'''''''''(((((())))))***(((&&&&&&&&&'''&&&%%%%%%%%%&&&'''&&&%%%###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%###!!!!!!###%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#################################&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$###"""!!! """!!!!!!!!!"""###$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$############$$$$$$ !!!"""###############%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%$$$###############$$$$$$%%%%%%%%%%%%%%%$$$###""""""##############################$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%qqqllljjjkkknnntttyyy{{{{{{|||~~~{{{rrrjjj```YYYVVVUUUSSSQQQXXX\\\eeeooowwwxxxtttpppggg[[[LLL???777333111000222111000///...---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++******+++,,,,,,++++++++++++************++++++***))))))***++++++))))))))))))))))))))))))(((((())))))))))))(((((((((((((((((((((((((((((('''(((((())))))(((((('''''''''''''''''''''''''''***)))))))))((((((((('''''''''''''''((((((((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&((('''''''''''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&'''''''''&&&&&&%%%$$$'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&'''''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%$$$###$$$&&&)))***'''%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&%%%%%%%%%%%%&&&''''''###$$$$$$%%%%%%$$$$$$###%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$'''%%%%%%'''***+++)))'''&&&&&&''''''(((((((((((()))(((&&&&&&''''''&&&%%%%%%&&&&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%###""""""###%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$###$$$$$$%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######""""""!!!!!!!!!!!!""""""######$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$#######################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&xxxlllgggiiinnnvvvyyyyyywwwyyy}}}}}}yyyoooccc___aaa___WWWOOOPPPTTT[[[eeennnuuuwwwwwwrrrhhhXXXGGG;;;555444444333222111000///.........,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,,,,+++++++++************++++++***))))))***++++++))))))))))))))))))))))))))))))************))))))))))))))))))))))))))))))***))))))(((((())))))***''''''''''''''''''''''''))))))))))))((((((((((((''''''''''''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&''''''''''''&&&%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&&&&'''$$$$$$&&&''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&$$$###$$$&&&))))))&&&$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''''''''(((((('''&&&%%%$$$&&&%%%%%%%%%%%%&&&''''''###$$$$$$%%%%%%$$$$$$###%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$%%%$$$$$$%%%'''((('''&&&&&&&&&&&&''''''''''''(((((('''&&&&&&'''((('''%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$############$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######""""""!!!!!!!!!!!!""""""%%%$$$###""""""######$$$%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%"""###$$$%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$########################$$$$$$%%%&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''sssiiijjjppptttwwwxxxvvvwww|||~~~|||xxxpppgggeeeggggggaaaZZZTTTVVV[[[aaaiiiqqqvvvyyyzzzuuugggTTTEEE<<<777444333222111000/////////000------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++*********+++******************+++))))))))))))))))))))))))*********++++++*********))))))))))))))))))))))))+++***)))(((((()))***+++''''''''''''''''''''''''))))))))))))(((((((((((('''''''''((((((((((((((('''''''''(((((((((((((((&&&&&&''''''''''''&&&&&&$$$$$$$$$%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''&&&&&&''''''''''''&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&%%%$$$%%%''')))(((&&&$$$$$$%%%'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%'''((((((&&&$$$###&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%&&&&&&'''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%&&&(((((('''&&&'''&&&%%%$$$###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&'''(((((('''&&&%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$############$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$###"""!!!!!!!!!"""########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$############$$$$$$%%%###!!!!!!"""%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%######$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%$$$$$$#################################$$$%%%%%%&&&'''&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&&&&''''''qqqkkknnnppptttwwwwwwyyy||||||yyyvvvrrrmmmjjjiiihhhgggfffbbbcccdddfffjjjnnnrrruuu|||}}}uuueeeUUUIII>>>555444333111///......///000------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++************++++++*********))))))))))))))))))))))))******++++++++++++******))))))))))))))))))))))))+++***)))(((((()))***+++(((((((((((((((((((((((((((((((((((())))))))))))(((((((((((((((''''''''''''''''''((((((((())))))&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&''''''((((((''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&'''((((((''''''&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''&&&%%%%%%'''((((((&&&$$$$$$%%%'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$ !!!$$$&&&'''&&&%%%$$$&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$%%%%%%'''''''''&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%'''))))))(((&&&&&&%%%$$$###$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$######""""""######$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############"""$$$$$$###"""!!!!!!!!!"""########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$############$$$$$$%%%###!!!  !!!"""%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$%%%%%%%%%$$$$$$###"""%%%%%%%%%$$$$$$#########%%%$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&'''''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%&&&''''''|||ooollllllrrrvvvwwwyyy|||zzzvvvwwwvvvtttoooiiifffgggiiimmmnnnoooooonnnnnnoooqqqyyy~~~}}}rrrfff[[[JJJ;;;666555222///......//////------------------------,,,,,,------------,,,,,,,,,,,,,,,,,,++++++++++++)))***++++++++++++***)))))))))))))))))))))))))))******++++++++++++******))))))))))))))))))))))))***))))))(((((())))))***(((((((((((((((((((((((((((((((((((())))))))))))((((((((((((((('''''''''$$$$$$%%%%%%&&&'''''''''&&&&&&''''''''''''&&&&&&''''''''''''((((((((((((''''''''''''''''''''''''%%%%%%&&&&&&'''(((((((((&&&&&&'''((((((((((((''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%'''''''''&&&&&&%%%######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''$$$&&&''''''&&&&&&'''((()))&&&$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%$$$###### """$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''%%%$$$$$$######$$$$$$%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''&&&&&&''''''&&&&&&%%%$$$%%%'''(((((('''&&&''''''&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%''')))***((('''%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%&&&&&&%%%$$$###$$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$######""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%######""""""""""""############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$######""""""%%%%%%$$$$$$###$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######""""""!!!!!!!!!!!!""""""&&&%%%$$$#########$$$%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$###"""!!!%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%&&&&&&zzzssskkkqqquuuvvvxxx{{{zzzvvvuuuvvvvvvrrrlllgggeeeeeeooorrrvvvvvvtttqqqpppppprrr{{{~~~yyytttlllYYYFFF:::888444111///...///000........................,,,,,,---......---,,,,,,------,,,,,,,,,+++++++++)))***++++++++++++***)))))))))))))))))))))))))))))))))************))))))(((((((((((((((((((((((('''(((((())))))(((((('''(((((((((((((((((((((((('''((((((((()))))))))***)))(((((((((''''''''''''$$$$$$%%%%%%&&&''''''(((&&&&&&''''''''''''&&&&&&((((((((('''''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&'''(((((()))&&&&&&'''((((((((((((((('''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''$$$&&&(((((('''&&&'''(((***'''%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&''''''%%%$$$$$$######$$$$$$%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$%%%''')))(((&&&%%%&&&'''%%%%%%%%%%%%$$$$$$$$$#########%%%'''******)))'''###$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&%%%%%%%%%######$$$$$$%%%&&&''''''"""######$$$%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$"""#########$$$$$$$$$$$$"""#########$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!""""""###$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%######""""""""""""############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######""""""!!!!!!!!!!!!""""""%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%######$$$$$$$$$######"""$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%|||lllqqqttttttvvvzzzzzzwwwqqqsssuuutttpppkkkfffccclllqqqwwwyyywwwtttrrrqqqmmmwww}}}|||{{{vvvdddOOO===:::666222000///000111........................,,,,,,---......---,,,,,,---------,,,,,,,,,++++++)))***+++,,,,,,+++***)))))))))))))))))))))))))))))))))************))))))((((((((((((((((((((((((&&&'''((())))))((('''&&&))))))))))))))))))))))))'''((((((((())))))******))))))(((((('''''''''&&&&&&&&&''''''((()))******&&&''''''''''''''''''&&&(((((((((''''''&&&&&&&&&''''''''''''''''''''''''%%%%%%&&&&&&'''((())))))&&&&&&'''((())))))(((((('''&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%######$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%$$$&&&(((((('''&&&'''(((***(((%%%$$$%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&'''%%%%%%$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%&&&''''''''''''%%%%%%%%%%%%''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$&&&)))(((%%%$$$%%%'''%%%%%%%%%$$$$$$###############%%%'''***+++)))'''"""###%%%&&&'''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&""""""###$$$&&&'''((((((""""""###$$$%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""!!!!!!########################""""""######$$$$$$$$$$$$""""""######$$$$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!""""""###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%######""""""""""""############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$ !!!"""###$$$%%%&&&&&&"""!!!!!!!!!"""###$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$############$$$$$$"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%!!!"""###$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&$$$$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%""""""""""""""""""""""""#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&''''''((((((''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$xxxvvvsssrrrtttvvvxxxxxxvvvuuuttttttuuussspppmmmmmmrrrwwwyyyvvvsssqqqqqqpppsssvvvzzzsssbbbJJJAAA777333444444222...111///......//////---,,,------------------------,,,,,,,,,+++++++++******++++++++++++++++++++++++++++++++++++++++++++++++)))))))))))))))))))))))),,,+++)))((((((((()))***'''&&&&&&&&&'''(((***++++++***)))((('''''''''((())))))))))))))))))))))))))))))((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((***(((&&&%%%%%%%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%((('''&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&((((((((((((((((((((((((&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''$$$$$$%%%&&&&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''''''''&&&%%%$$$$$$$$$%%%&&&'''###%%%)))++++++***'''%%%(((((('''&&&%%%%%%$$$$$$%%%'''(((((('''&&&&&&'''''''''''''''''''''''''''%%%&&&&&&&&&'''(((((((((''''''''''''''''''''''''(((&&&$$$$$$%%%'''''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%###""""""$$$%%%%%%$$$'''''''''&&&&&&%%%%%%%%%(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''%%%$$$&&&)))***(((&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$######$$$$$$%%%&&&#########$$$$$$%%%%%%%%%########################&&&&&&%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$######""""""###$$$&&&''''''&&&&&&$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######%%%&&&&&&%%%$$$$$$%%%########################""""""""""""""""""""""""%%%%%%$$$###""""""##############################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################"""############$$$$$$$$$#########$$$$$$%%%%%%%%%######$$$$$$$$$$$$######$$$$$$######"""######### !!!"""$$$$$$%%%%%%%%%"""###$$$%%%&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%|||yyywwwvvvtttttttttsssuuuvvvvvvtttrrrkkknnnssstttrrrooonnnnnnqqqqqqpppsss{{{vvviiiXXXMMM>>>555222222111000...,,,,,,---...///...---------------------------,,,,,,,,,++++++++++++***++++++++++++++++++++++++************************))))))))))))))))))))))))+++******)))))))))))))))''''''&&&&&&'''(((***+++)))(((((((((((()))))))))))))))))))))))))))))))))))))))((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&%%%%%%$$$%%%'''***+++'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''''''''&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&'''$$$&&&((()))***(((&&&%%%'''''''''&&&&&&%%%%%%$$$$$$&&&''''''&&&%%%%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''%%%$$$$$$&&&''''''&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&%%%$$$$$$&&&''''''&&&(((((('''''''''&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###%%%'''(((&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""""""""###$$$$$$######$$$$$$$$$%%%%%%%%%########################'''&&&%%%$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###!!!"""###%%%%%%%%%%%%%%%$$$$$$$$$#########""""""###########################$$$$$$%%%%%%$$$$$$######%%%&&&&&&%%%$$$$$$%%%################################################%%%$$$###""""""""""""###################################################$$$$$$$$$$$$$$$$$$$$$$$$########################"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%$$$$$$#########$$$$$$!!!"""###$$$$$$$$$$$$$$$"""###$$$%%%&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%}}}wwwssspppooooooppprrrrrrqqqpppiiikkklllllljjjhhhhhhhhhnnnmmmkkkkkkqqqwwwvvvqqqfffZZZHHH:::444333333333///---------//////...---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++))))))))))))))))))))))))))))))))))))))))))))))))***************)))((((((''''''''''''((()))******'''''''''((()))******+++))))))))))))))))))))))))))))))((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&(((***+++((((((((((((((((((((((((''''''''''''''''''''''''(((((('''''''''&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$%%%%%%&&&'''(((((('''&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%%%%%%%#########$$$%%%&&&'''(((&&&&&&&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###%%%&&&&&&%%%$$$$$$%%%(((((('''''''''&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$&&&'''((('''%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%((('''%%%&&&((())))))(((((((((((((((''''''''''''&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###""""""###%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###############$$$%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%!!!!!!###$$$$$$$$$$$$$$$$$$$$$$$$##########################################$$$$$$%%%%%%$$$$$$######%%%&&&&&&%%%$$$$$$%%%################################################$$$###""""""""""""""""""########################""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$########################"""############$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%######$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%~~~vvvqqqooommmmmmmmmnnnmmmllljjjjjjiiifffdddaaa```___gggiiijjjhhhhhhkkkqqquuuoooeeeUUUEEE;;;666555555444222000000000000...,,,,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,+++++++++++++++++++++++++++++++++************************))))))))))))))))))))))))))))))***++++++)))((('''''''''((((((((())))))***''''''((()))))))))))))))(((((((((((((((((((((((())))))((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''((((((((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$$$$""""""###$$$%%%'''((((((&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&###%%%&&&&&&%%%%%%%%%&&&((((((((('''&&&&&&%%%%%%'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$%%%&&&((((((&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((('''%%%&&&((())))))(((''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########$$$$$$%%%%%%%%%%%%&&&&&&#########$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!"""###%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&""""""###$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$&&&&&&$$$###$$$%%%######################################################"""!!!!!!""""""###################################################$$$$$$$$$$$$$$$$$$$$$$$$########################""""""#########$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%}}}wwwtttpppoooooopppooooooooommmiiieeeaaa^^^[[[YYY]]]dddkkkiiiaaa___gggpppsssnnncccUUUGGG===666444555333222222222222000...---------------------------------,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++++++++))))))))))))))))))))))))))))))***++++++)))((('''((((((((())))))))))))))))))))))))***)))((('''&&&(((((((((((((((((((((((())))))((('''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((('''''''''&&&&&&&&&''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$###""""""###%%%&&&'''((((((&&&%%%$$$$$$$$$$$$%%%&&&%%%%%%&&&&&&&&&&&&&&&&&&$$$%%%'''((('''&&&'''((((((((('''''''''&&&&&&&&&''''''&&&&&&%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$%%%&&&((((((&&&$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$%%%&&&(((''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""!!! $$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""###$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%&&&&&&'''$$$$$$$$$$$$%%%%%%%%%&&&########################%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###"""$$$%%%%%%$$$######$$$######################################################""""""""""""##############################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""#########$$$$$$$$$%%%%%%%%%$$$$$$###############$$$$$$$$$$$$######%%%$$$$$$$$$%%%%%%&&&'''&&&%%%$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%~~~{{{vvvssssssssssssssstttqqqlllhhhddd___[[[WWWVVV]]]fffggg___YYY^^^gggqqqqqqoooeeeWWWHHH>>>999888666555555666666555333........................------------,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++))))))))))))))))))))))))***************)))((((((((())))))******))))))((()))************(((&&&%%%))))))))))))))))))))))))))))))((('''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&'''((())))))&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%$$$%%%&&&'''''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''$$$$$$%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###"""###$$$%%%&&&'''''''''%%%$$$$$$$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&((((((''''''((()))''''''''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&'''((('''%%%$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%###$$$%%%'''&&&&&&$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&'''''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&((('''&&&%%%$$$""""""!!!###$$$$$$%%%%%%&&&&&&'''%%%&&&((('''%%%$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###############$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%######"""""""""%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%&&&&&&###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###"""$$$%%%%%%$$$######$$$########################$$$$$$$$$$$$$$$$$$$$$$$$##################$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################"""############$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$"""######$$$$$$######"""$$$######$$$$$$%%%&&&'''&&&%%%$$$######$$$%%%&&&'''&&&&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%|||zzzxxxwwwwwwtttooollliiiddd___ZZZTTTUUU[[[aaa___ZZZYYY]]]ffflllrrrpppeeeXXXOOOKKKFFFCCCAAA???>>><<<999777000000000000000000000000...------------,,,,,,,,,++++++++++++++++++++++++************************))))))))))))))))))))))))+++******)))))))))))))))((()))************)))((('''((()))******)))'''&&&))))))))))))))))))))))))))))))((('''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$%%%'''(((((())))))''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&'''(((((((((''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%###$$$&&&'''((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$###$$$%%%&&&&&&&&&&&&%%%######$$$%%%&&&'''(((((('''''''''&&&&&&%%%%%%$$$"""$$$&&&'''&&&&&&'''(((%%%%%%&&&&&&'''(((((((((%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''%%%$$$$$$&&&''''''&&&###$$$&&&''''''&&&$$$###$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%###$$$%%%''''''&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&((((((((((((''''''''''''######$$$%%%%%%&&&''''''$$$'''((('''%%%###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""""""""###$$$$$$%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%&&&%%%$$$######$$$%%%%%%""""""#########$$$$$$$$$""""""""""""""""""""""""###$$$$$$%%%%%%$$$$$$###"""###%%%%%%###"""###$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&################################################$$$$$$$$$$$$$$$$$$$$$$$$########################"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%###$$$$$$%%%%%%$$$$$$###"""""""""######%%%&&&&&&%%%$$$#########%%%'''(((((('''&&&%%%$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%xxxuuuqqqooommmiiiccc^^^UUUPPPRRR[[[```]]]XXXWWWZZZdddppptttooofff```^^^VVVSSSNNNIIIEEE@@@;;;777000000000000000000000000......---------,,,,,,,,,++++++++++++++++++++++++)))))))))))))))))))))))))))))))))))))))))))))))),,,+++)))((((((((()))***((()))***++++++***)))(((%%%&&&(((***+++***)))((())))))))))))))))))))))))))))))((('''''''''''''''))))))))))))))))))))))))''''''''''''''''''''''''((((((((((((((((((((((((''''''((((((''''''&&&%%%((((((((((((((((((((((((''''''''''''''''''''''''$$$%%%%%%&&&'''((())))))&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%###$$$&&&(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''(((''''''&&&&&&%%%%%%$$$''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&&&&%%%$$$###$$$%%%&&&&&&&&&%%%$$$"""###$$$&&&'''((())))))(((((('''&&&%%%%%%$$$$$$!!!###%%%&&&%%%%%%&&&'''$$$%%%%%%&&&'''((())))))$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%(((&&&$$$$$$%%%'''''''''###$$$&&&''''''&&&$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%'''%%%$$$$$$&&&''''''&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$&&&''''''&&&$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&!!!!!!"""######$$$%%%%%%######$$$%%%%%%&&&''''''$$$&&&((('''$$$######%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$######$$$$$$%%%&&&%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%% !!!"""###&&&(((***+++%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%$$$###""""""###$$$$$$""""""######$$$$$$$$$$$$!!!!!!!!!!!!!!!!!!!!!!!!$$$$$$$$$%%%%%%$$$$$$$$$"""###%%%%%%###"""###$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$%%%&&&&&&'''########################""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$########################"""############$$$$$$$$$#########$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$""""""""""""###$$$%%%&&&%%%$$$#########%%%((()))((('''&&&%%%$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%~~~wwwqqqpppnnniiieeedddUUUTTTSSSSSSSSSSSSQQQOOOMMMYYYhhhqqqrrrqqqpppqqqkkkhhhaaaWWWPPPJJJ@@@666444222111111111000...,,,//////...------,,,++++++***++++++,,,,,,++++++***+++,,,,,,+++******+++---))))))))))))))))))))))))++++++******))))))((((((***)))(((''''''((()))***************))))))))))))&&&''''''((()))******+++''''''((((((((((((''''''((((((''''''''''''((((((''''''''''''''''''''''''******)))((('''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''(((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''%%%&&&&&&&&&'''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%))))))(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&'''(((######$$$%%%'''((())))))((($$$!!!"""''')))'''$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%$$$%%%&&&%%%""" """"""#########$$$$$$$$$'''((()))******(((&&&$$$&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&'''&&&%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%%%%###$$$&&&''''''&&&$$$###########################$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%"""###$$$%%%&&&'''''''''###$$$$$$%%%%%%$$$$$$###%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%$$$$$$#########%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$#########$$$%%%""""""#########$$$$$$$$$######################## $$$''''''$$$  """$$$%%%$$$###""""""""""""""""""#########$$$%%%%%%$$$"""!!!###$$$!!!"""$$$%%%&&&''''''''')))((('''&&&%%%&&&&&&'''###$$$$$$%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########%%%%%%%%%&&&&&&'''''''''zzzqqqpppoookkkgggeeeYYYUUUQQQNNNMMMLLLKKKJJJFFFPPP```mmmuuuxxxxxxxxxuuutttnnneee___XXXNNNEEE<<<999555333222222111000//////.........---------++++++,,,,,,,,,,,,++++++***+++,,,+++***)))+++,,,************************))))))((((((''''''''''''***)))(((((((((((()))*********)))))))))((((((((('''''''''((()))*********''''''((((((((((((''''''((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((((((&&&&&&&&&'''''''''(((((((((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%)))((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%&&&'''((((((''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%&&&((())))))***&&&"""!!!%%%'''%%%"""%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&"""######$$$%%%&&&''''''$$$######$$$&&&&&&%%%###$$$$$$$$$%%%%%%%%%&&&&&&''''''((((((((('''&&&%%%&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%###$$$&&&''''''&&&$$$###########################$$$$$$%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$%%%%%%&&&&&&###$$$$$$%%%%%%$$$$$$###%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%&&&%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$$$$%%%################################################!!!"""$$$%%%%%%$$$"""!!! !!!###%%%&&&%%%$$$$$$$$$$$$$$$######"""""""""!!!"""######""""""$$$&&&###$$$$$$%%%&&&'''((())))))((('''&&&%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$##################$$$$$$$$$$$$rrrooopppnnnjjjhhhaaa[[[SSSLLLHHHGGGFFFEEEBBBIIIUUUeeettt}}}~~~}}}vvvpppjjj```WWWGGGBBB:::444111000000000/////////...............++++++,,,,,,,,,,,,++++++)))+++++++++))))))***+++************************)))(((((((((((('''''''''***))))))(((((())))))***)))))))))(((((((((''''''''''''(((((())))))******'''(((((())))))(((((('''((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''''''''''''''''''''((((((((())))))(((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%((((((((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&""""""###$$$%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%%%%&&&&&&''''''((()))******%%%### !!!$$$&&&%%%###%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&!!!""""""###$$$%%%&&&'''$$$###"""###%%%''''''&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$$$$$$$%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$##############################$$$$$$$$$$$$#########$$$$$$%%%%%%$$$$$$###%%%$$$###""""""###$$$%%%###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%$$$$$$$$$$$$$$$$$$$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$%%%%%%$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$&&&&&&&&&%%%%%%'''&&&&&&%%%$$$###"""!!!!!!""""""""""""%%%'''%%%%%%%%%%%%&&&''')))***((('''&&&&&&%%%&&&&&&&&&%%%%%%$$$######"""!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$##################"""""""""tttnnnoooooollljjjiiicccZZZRRRLLLHHHEEECCCEEEFFFMMM[[[mmmzzzzzzvvvmmmeeeXXXPPPEEE:::444111000000........................+++,,,,,,,,,,,,,,,,,,+++)))***++++++***)))***+++************************************************))))))))))))))))))))))))(((((((((((('''''''''''''''((((((((()))))))))***(((((())))))))))))((((((((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&+++***)))(((&&&%%%######&&&'''''''''(((((((((((((((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&(((******)))((('''&&&&&&''''''((((((((()))'''%%%###$$$&&&((('''&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%$$$$$$$$$$$$&&&$$$""""""$$$&&&'''&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$########################"""######$$$$$$######"""%%%&&&&&&''''''&&&&&&%%%&&&%%%###!!!!!!"""###$$$###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%$$$############$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$ !!!""""""!!!"""$$$&&&&&&%%%$$$###$$$&&&(((***'''&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$#########"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$#########xxxoooooonnnlllkkklllhhhbbb\\\VVVOOOIIIEEEJJJGGGHHHQQQaaarrr}}}}}}wwwqqqkkkbbbUUUHHH???888444111............------------,,,,,,,,,------,,,,,,,,,(((***,,,,,,+++)))******************************************++++++++++++))))))************))))))((((((((((((''''''''''''(((((((((((())))))))))))(((((())))))))))))((((((((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&******)))'''&&&$$$######%%%%%%&&&&&&&&&'''''''''(((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''((((((''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&(((******)))((('''&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%)))&&&$$$###$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################"""######$$$$$$######"""%%%&&&&&&''''''&&&&&&%%%'''%%%###!!!!!!!!!###$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$############%%%%%%$$$$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%!!!!!!"""$$$%%%&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$###$$$&&&((((((&&&$$$############$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&'''"""###$$$###!!!!!!"""$$$%%%$$$"""""""""$$$&&&(((%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$#########sssooommmmmmmmmmmmkkkhhheee```YYYQQQLLLMMMLLLKKKNNNXXXgggxxx{{{uuunnnbbbUUUJJJ???666000000000//////...------,,,,,,,,,------------,,,,,,)))+++------,,,+++***+++++++++++++++++++++++++++((((((((())))))))))))***)))******++++++******))))))))))))(((((((((''''''(((((((((((())))))))))))((())))))******))))))(((((((((''''''''''''((((((''''''''''''''''''''''''%%%%%%&&&&&&&&&'''''''''%%%%%%%%%&&&&&&&&&&&&'''(((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&""""""###$$$%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%&&&'''(((((())))))'''%%%%%%%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&!!!"""###$$$%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%##############################$$$$$$$$$$$$#########$$$$$$%%%%%%$$$$$$###&&&%%%$$$###""""""###$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$%%%%%%%%%$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""$$$%%%%%%%%%%%%%%%!!!"""###$$$%%%''''''(((%%%%%%%%%%%%%%%%%%%%%%%%"""$$$&&&((((((&&&$$$"""###############$$$$$$$$$"""###$$$%%%&&&''''''((($$$%%%%%%$$$"""!!!"""$$$$$$###"""""""""$$$%%%&&&$$$%%%%%%&&&&&&&&&&&&%%%###$$$$$$%%%&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%###############"""""""""yyyqqqmmmmmmpppppppppnnnmmmjjjeee^^^YYYTTTUUUUUUSSSSSS]]]nnn||||||xxxoooeeeYYYKKK>>>666444333222111000...------,,,,,,------------,,,,,,))),,,...///---,,,++++++++++++++++++++++++++++++(((((()))))))))*********)))***++++++++++++***)))******)))))))))((((((((())))))))))))(((((((((((())))))************))))))((((((''''''''''''(((((((((((((((((((((((((((((($$$$$$%%%&&&&&&'''((((((&&&&&&&&&&&&''''''''''''(((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%((((((''''''&&&&&&&&&%%%$$$$$$%%%$$$$$$$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$%%%&&&'''((((((&&&%%%%%%$$$$$$%%%%%%&&&######$$$%%%&&&''''''((('''&&&%%%&&&''''''%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%###$$$%%%'''''''''&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&& !!!###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######&&&%%%%%%$$$$$$%%%%%%&&&########################$$$$$$%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""""""""###$$$%%%&&&$$$$$$######$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""$$$%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%######$$$$$$%%%%%%&&&&&&$$$$$$%%%$$$######%%%'''######$$$$$$$$$$$$%%%%%%###$$$%%%&&&'''&&&&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%############$$$$$$$$$$$$}}}sssnnnnnnrrrvvvuuutttsssrrrnnniiifff[[[___```YYYRRRUUUdddsss~~~vvvjjj[[[KKKBBB777666555333111000///...,,,------......------,,,***,,,///000...---,,,,,,++++++++++++++++++++++++******++++++,,,,,,,,,,,,)))***+++,,,,,,+++***)))************))))))))))))))))))))))))(((((((((((())))))************))))))((((((''''''''''''(((((())))))))))))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((()))(((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&'''((()))))))))(((''''''&&&&&&&&&'''''''''&&&&&&((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&"""###$$$%%%'''((())))))&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$&&&((()))'''%%%$$$$$$$$$%%%%%%%%%&&&&&&###$$$&&&(((((((((&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&& !!!###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########&&&%%%%%%$$$$$$%%%%%%&&&########################$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!""""""###$$$&&&&&&######""""""###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""$$$%%%&&&&&&%%%%%%''''''&&&%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%###""""""###%%%&&&'''&&&&&&%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%%%%$$$%%%''')))$$$$$$%%%&&&&&&&&&%%%%%%"""###%%%&&&'''&&&&&&%%%%%%%%%$$$$$$###"""""""""$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&'''''''''}}}rrroooppprrrrrrsssttttttsssqqqooojjjkkkkkkhhh```\\\dddooo~~~}}}wwwlll]]]RRRCCC???888333111111000///---------,,,++++++,,,...------,,,,,,,,,,,,++++++******++++++++++++******))))))))))))))))))))))))************************)))))))))))))))))))))))),,,,,,+++***)))(((''''''(((((())))))))))))(((((((((''''''&&&&&&((()))***''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''(((((())))))((('''&&&&&&&&&%%%$$$###$$$%%%&&&''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%'''(((******)))'''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((())))))''''''&&&&&&&&&%%%%%%%%%#########$$$%%%&&&(((((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$"""!!! !!!"""$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&%%%###""" %%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%&&&###$$$%%%%%%######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&***(((&&&&&&&&&&&&$$$"""&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&!!!"""$$$&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%###""""""!!!$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$###!!!!!! $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$######"""#########%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%$$$######$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%$$$$$$#########%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$$$$%%%&&&&&&$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&sssnnnooorrrvvvzzzzzzxxxvvvuuuuuurrrqqqrrrpppkkkgggllltttvvvjjjaaaSSSLLLBBB:::555333222111/////////...---,,,,,,---------,,,,,,,,,,,,++++++******++++++++++++******************************************************))))))))))))))))))))))))''''''''''''&&&&&&&&&&&&(((((())))))))))))(((((((((((('''&&&'''((()))***''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''((((((((((((((('''&&&&&&%%%%%%%%%%%%%%%&&&''''''(((((((((''''''&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%'''((()))))))))'''%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((((()))''''''&&&&&&&&&%%%%%%%%%######$$$$$$%%%'''((()))&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$"""""""""###%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&''''''&&&&&&&&&%%%%%%%%%###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&''''''%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''(((&&&%%%%%%&&&&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###""""""###$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$###""""""&&&&&&&&&&&&%%%$$$######%%%$$$$$$$$$############&&&&&&&&&%%%%%%%%%$$$$$$""""""##################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&xxxnnnmmmlllrrryyy{{{xxxuuuuuuwwwvvvuuuvvvxxxwwwtttuuuyyyyyyssshhh```SSSGGG>>>888444222111111000///...---,,,,,,------,,,,,,,,,,,,++++++******++++++++++++******************************************************))))))))))))))))))))))))((((((((()))))))))******(((((())))))))))))(((((((((((('''''''''((()))***''''''''''''''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''(((((((((((((((''''''&&&%%%&&&&&&'''''''''''''''((((((((((((((('''''''''&&&&&&''''''''''''&&&&&&(((((((((((('''%%%$$$"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&'''))))))&&&&&&%%%%%%%%%%%%&&&&&&%%%&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######%%%&&&'''$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$'''&&&&&&&&&&&&%%%%%%%%%#########$$$%%%'''))))))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&''''''%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%&&&''''''(((&&&$$$###$$$%%%&&&%%%###$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$############$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######"""""""""''''''&&&&&&%%%###"""!!!$$$$$$#########"""""""""&&&&&&&&&&&&&&&%%%%%%%%%#########$$$%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$######"""$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&tttmmmhhhlllrrrwwwyyyxxxwwwuuutttrrrtttzzz}}}{{{{{{|||~~~yyyrrreeeXXXLLLBBB999444111000///.........,,,+++------,,,,,,,,,+++++++++***++++++,,,,,,++++++***************************************************((((((((((((((((((((((((************************(((((())))))))))))((((((((((((((((((((()))))))))''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&'''''''''(((((((((((((((''''''%%%&&&((()))))))))((('''((((((''''''''''''''''''&&&&&&''''''''''''&&&&&&&&&'''''''''&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%&&&'''((())))))&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$###$$$%%%''')))+++%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$######$$$%%%%%%######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%"""######%%%&&&'''(((((($$$###"""###%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&######$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%#########$$$%%%&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$#########"""%%%%%%%%%%%%%%%$$$###"""#########""""""""""""!!!%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!""""""###$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&~~~tttooommmmmmttt}}}|||vvvpppnnnqqqyyy~~~}}}tttiii]]]OOOBBB:::333111...---......---+++------,,,,,,,,,+++++++++++++++,,,,,,,,,,,,++++++************************************************(((((((((((((((((((((((())))))((('''&&&&&&%%%%%%(((((())))))))))))((((((((((((((()))))))))))))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''((((((((((((((('''&&&'''((()))***)))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((''''''&&&$$$$$$%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&'''((()))%%%%%%%%%$$$$$$%%%%%%%%%######$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###############$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$%%%&&&((()))%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$$$$###$$$%%%%%%######$$$%%%########################""""""###$$$%%%''''''(((###""""""###%%%&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########"""""""""$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%""""""""""""###%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$"""######$$$%%%%%%%%%%%%#########""""""""""""!!!##################$$$$$$ !!!""""""$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&########################$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&xxxpppkkkppp{{{|||uuuqqqnnnpppxxx}}}~~~wwwlll^^^QQQHHH<<<777111...//////...---------,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++************************))))))))))))))))))))))))+++******)))((('''&&&%%%(((((())))))))))))(((((('''((()))*********))))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&'''((((((((((((((((((&&&''''''(((((((((((((((%%%%%%%%%&&&&&&&&&&&&&&&''''''((((((((((((''''''$$$$$$%%%&&&'''((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%&&&''''''(((%%%%%%$$$$$$$$$$$$%%%%%%######$$$$$$$$$$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&''''''%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%&&&&&&'''$$$######$$$&&&'''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&+++)))'''%%%###"""!!!!!!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%""""""""""""###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%% !!!"""$$$%%%%%%&&&&&&$$$$$$#########"""""""""""""""""""""############""""""######$$$$$$%%%%%%###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%&&&&&&$$$$$$######$$$$$$%%%&&&#################################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&yyyppppppwww|||zzzuuusssqqqqqqvvvyyyzzz~~~wwwlllaaaYYYJJJBBB888333222222000...------,,,,,,,,,,,,+++++++++,,,,,,------,,,,,,+++++++++++++++++++++++++++************************)))))))))))))))))))))))),,,+++++++++******))))))(((((())))))))))))(((((('''((()))***+++***))))))''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&'''(((((((((((((((''''''&&&&&&''''''((()))&&&&&&&&&&&&'''''''''(((''''''((((((((((((''''''&&&&&&&&&&&&'''((())))))''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%&&&''''''%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%$$$%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&)))(((&&&$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""###$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$#########$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$$$$$$$$$$$$$%%%$$$$$$$$$############""""""#########$$$$$$$$$&&&&&&&&&'''''''''''''''######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&########################$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$######$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&|||wwwyyy|||}}}{{{uuurrrrrrssstttuuu|||}}}|||uuulllgggUUUKKK???777555444222000---------,,,,,,,,,+++++++++,,,,,,------,,,,,,+++++++++++++++++++++++++++************************))))))))))))))))))))))))''''''''''''(((((((((((((((((())))))))))))(((((('''((()))++++++******)))''''''''''''''''''''''''(((((((((((((((((((((((('''''''''&&&&&&'''''''''&&&&&&'''((())))))((((((''''''&&&%%%%%%'''((()))&&&'''''''''(((((())))))''''''(((((((((((('''''')))(((((('''''''''((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%'''''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&'''''''''!!!"""$$$%%%&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''###$$$%%%%%%######$$$%%%''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$%%%'''&&&%%%%%%''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&######"""###$$$&&&)))***%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%% !!!"""###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%##########################################$$$$$$######$$$$$$$$$######"""%%%%%%%%%$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%######""""""""""""""""""######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################&&&&&&%%%$$$$$$#########$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$######$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&zzzyyyqqqqqqqqqqqqrrrtttxxx{{{{{{||||||~~~~~~wwwpppfffYYYHHH;;;555333000...000///......///000...---++++++++++++++++++++++++)))))))))***+++++++++,,,************************))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))(((((((((((())))))))))))************(((((())))))))))))((((((***)))((((((((((((((()))'''''''''''''''&&&&&&&&&%%%&&&&&&'''((()))******''''''''''''''''''&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$%%%&&&'''''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&& !!!"""$$$%%%&&&''')))&&&!!!$$$'''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$)))&&&$$$###$$$%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%$$$###$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$###"""!!!"""$$$%%%%%%$$$###%%%&&&%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$###"""!!! $$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%!!!###%%%$$$###"""###$$$$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$###"""!!!!!!%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""""""""$$$'''(((&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%###$$$$$$%%%%%%$$$$$$###""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%yyysssrrrrrrrrrrrrrrrrrrtttuuuxxxyyy{{{~~~~~~xxxmmmbbbSSSEEE<<<777333000000...---.../////////---,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++,,,,,,,,,************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((()))))))))*********(((((())))))))))))((((((''''''&&&&&&'''((())))))''''''''''''''''''''''''&&&&&&''''''(((((())))))''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$$$$%%%%%%'''%%%###"""!!!"""$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$'''&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%)))))))))))))))(((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%$$$$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&###$$$$$$%%%%%%%%%$$$$$$"""$$$%%%%%%$$$###%%%&&&%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$"""$$$%%%%%%$$$######$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$$$$%%%&&&(((***%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%###$$$$$$%%%%%%$$$$$$############$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$yyynnnoooooooooooooooooopppppptttuuuyyy||||||xxxzzzvvvooobbbTTTGGG<<<555222///...------...//////...---------------------------------,,,,,,,,,,,,,,,************************))))))))))))))))))))))))************************))))))))))))(((((((((((((((((())))))))))))******(((((())))))))))))((((((%%%%%%%%%%%%&&&((()))***(((((((((((((((((((((((('''''''''(((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&'''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%$$$$$$###$$$%%%&&&&&&&&&%%%$$$###&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%'''((((((&&&$$$"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%$$$$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$#########$$$$$$$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%'''&&&%%%$$$$$$%%%&&&'''######$$$%%%&&&''''''&&&"""$$$%%%%%%$$$###%%%&&&%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$#########%%%&&&&&&$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$%%%&&&((()))$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%########################%%%%%%%%%$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%$$$$$$#########zzztttrrrooonnnoooqqqrrrrrrooorrrvvv{{{xxxppppppwww|||xxxoooaaaQQQBBB888444000...,,,,,,...//////...------------------------------,,,,,,+++++++++***************************))))))))))))))))))))))))************************))))))))))))(((((((((((((((((((((((()))))))))***(((((())))))))))))((((((&&&&&&&&&&&&'''(((((()))(((((((((((())))))))))))((((((((((((((('''''''''&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&%%%%%%$$$$$$###$$$%%%&&&&&&%%%$$$"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&'''%%%$$$######%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&######$$$%%%&&&&&&%%%%%%"""$$$%%%%%%$$$###%%%&&&%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$#########%%%'''&&&%%%$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$###""""""yyytttsssssstttsssmmmppptttyyy}}}vvvkkkgggkkkrrrzzz~~~|||vvvjjjZZZJJJ===777222000------.../////////,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++******))))))************************************************************************))))))))))))(((((((((((('''(((((((((((()))))))))(((((())))))))))))((((((******)))((('''''''''((('''((((((((())))))******((((((((((((((('''''''''&&&&&&&&&'''''''''((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''$$$$$$######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%###!!!!!!###%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''(((((((((''''''$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%$$$""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%###$$$&&&''''''&&&$$$###$$$$$$$$$$$$$$$###"""""""""$$$%%%%%%$$$###%%%&&&%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$###%%%'''&&&%%%$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$###""""""~~~yyyuuuqqqmmmmmmooossswww|||xxxjjjaaa```bbbpppzzz}}}yyypppdddTTTFFF===666333///....../////////,,,,,,,,,,,,,,,,,,,,,,,,++++++******************************************************************************************))))))))))))((((((((((((''''''(((((((((((())))))(((((())))))))))))((((((,,,+++***)))''''''''''''&&&''''''(((((())))))***'''''''''(((((((((((((((%%%%%%&&&&&&'''(((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''(((((($$$$$$###""""""###%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&### ###'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%%%%%%%#########$$$$$$$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%"""###$$$%%%%%%$$$###"""$$$$$$$$$$$$###"""!!!!!!"""$$$%%%%%%$$$###%%%&&&%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$###%%%&&&&&&$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&%%%$$$###""""""###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%$$$$$$#########yyyrrroooppprrrvvvzzz~~~zzzlll___XXXUUUbbbnnn{{{}}}zzzuuummm```QQQGGG999666222////////////...------------------------******++++++++++++++++++************************************************))))))))))))))))))))))))))))))))))))(((((((((((('''''''''((((((((())))))(((((())))))))))))((((((***)))((('''''''''''''''%%%&&&&&&'''(((((())))))&&&&&&''''''(((((())))))%%%%%%&&&&&&'''(((((()))((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%&&&&&&''''''$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$''')))'''###!!!$$$'''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%$$$###!!! !!!###$$$$$$$$$$$$%%%$$$$$$######"""$$$%%%%%%$$$###%%%&&&%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$$$$######"""$$$%%%%%%$$$######$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&'''&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%###$$$$$$%%%%%%$$$$$$############$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$pppqqqrrruuuyyy}}}|||ooo```TTTNNNVVVdddsss{{{~~~}}}zzzxxxssshhhYYYMMM;;;888333000/////////...////////////////////////+++++++++,,,,,,---------************************************************(((((((((((((((((((((((())))))))))))((((((((((((''''''''''''((((((((()))(((((())))))))))))((((((''''''&&&&&&&&&''''''(((%%%%%%%%%&&&'''(((((()))%%%&&&&&&'''((()))******%%%%%%&&&&&&'''((())))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%&&&$$$$$$&&&'''''''''&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###''',,,+++'''$$$%%%'''######$$$%%%%%%&&&''''''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$######$$$$$$$$$%%%%%%%%%'''$$$$$$'''######$$$%%%&&&&&&&&&&&&"""$$$%%%%%%$$$###%%%&&&%%%%%%%%%$$$$$$$$$######%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""###$$$&&&'''&&&&&&&&&&&&&&&&&&&&&&&&""""""############""""""!!!###%%%%%%###"""###$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$######$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$""""""""""""""""""""""""#########$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$%%%%%%$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%}}}vvvrrrtttvvvxxx|||~~~wwwlll]]]QQQPPP[[[mmm}}}|||zzz}}}~~~~~~}}}{{{vvvlll```YYYHHHAAA777000.........---//////.........---------......---,,,,,,,,,,,,---((((((((()))******++++++***+++++++++,,,,,,,,,,,,))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((('''&&&&&&%%%%%%''''''''''''''''''''''''&&&''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%&&&''''''((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%'''(((((('''%%%$$$$$$%%%&&&&&&''''''&&&&&&###%%%&&&&&&%%%%%%'''((((((((((((((((((((((((((('''((()))))))))(((&&&%%%$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$########################%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%$$$%%%%%%&&&&&&&&&''''''''''''&&&&&&)))((('''&&&&&&&&&&&&&&&''''''''''''&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''(((((($$$%%%%%%&&&&&&%%%%%%$$$!!!$$$''''''$$$$$$%%%'''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$%%%%%%$$$$$$###$$$!!!!!!######"""$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$############&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$###"""###&&&(((&&&&&&%%%%%%%%%%%%$$$$$$%%%&&&''''''%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''%%%###!!!!!!###%%%'''%%%%%%%%%&&&&&&&&&''''''######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$#########$$$%%%&&&(((%%%""""""$$$$$$"""%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$#########""""""""""""###$$$%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$###""""""######$$$%%%%%%&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$%%%%%%&&&&&&%%%%%%$$${{{tttsssuuuvvvxxx{{{}}}~~~xxxoooaaaTTTMMMUUUfffvvv~~~}}}|||~~~}}}}}}~~~}}}yyyqqqggg```OOOGGG<<<333//////......//////.........---------......---,,,,,,,,,,,,---+++++++++++++++*********'''((((((((()))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((('''&&&&&&%%%%%%''''''''''''''''''''''''&&&&&&'''(((((((((((('''((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''&&&&&&&&&%%%''''''&&&&&&&&&%%%%%%%%%%%%&&&''''''((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&$$$&&&'''&&&%%%%%%&&&'''''''''''''''''''''''''''&&&'''''''''&&&&&&%%%$$$$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&(((''''''&&&%%%%%%&&&&&&'''''''''&&&&&&$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%'''))))))'''&&&''')))&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$%%%### !!!###%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$""""""$$$&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%&&&'''&&&%%%%%%%%%'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######$$$%%%&&&%%%%%%%%%&&&&&&&&&&&&'''######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$#########$$$%%%&&&$$$######$$$%%%&&&%%%$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&&&&&&&'''%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######""""""$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$uuupppqqqrrrsssuuuxxx}}}~~~zzzsssfff[[[NNNRRR]]]lllwww{{{|||~~~}}}}}}}}}xxxpppjjjYYYQQQDDD888222//////////////////.........------......---,,,,,,,,,,,,---...------,,,++++++******************++++++++++++))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((('''&&&&&&%%%%%%''''''''''''''''''''''''&&&&&&'''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''(((((()))((('''%%%%%%'''&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%'''''''''%%%$$$%%%&&&''''''''''''''''''''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$%%%&&&$$$$$$$$$$$$############%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&'''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$&&&'''&&&$$$$$$$$$&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%&&&$$$######%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###$$$$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&'''&&&%%%###"""###$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$&&&'''&&&%%%$$$%%%'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$######$$$$$$%%%&&&###%%%&&&&&&%%%%%%&&&'''%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$&&&''''''(((&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%%%%$$$$$$$$$######$$$$$$############$$$$$$$$$$$$$$$$$$############%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&&&&&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$tttjjjjjjmmmooorrrsssyyy}}}}}}{{{wwwlllbbbTTTRRRVVVcccooovvvzzz|||}}}~~~{{{uuuqqqccc[[[MMM???666111//////////////////..................---,,,,,,,,,,,,------,,,,,,,,,+++++++++***+++++++++,,,,,,,,,------))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''&&&&&&&&&'''''''''''''''''''''''''''(((((()))***)))))))))((((((((((((((((((((((((((((((((((((((((((((((((%%%'''(((******)))'''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((('''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$%%%&&&&&&''''''&&&&&&&&&'''((('''%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$######$$$%%%&&&$$$%%%&&&&&&$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%$$$$$$$$$%%%%%%'''''''''''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$#########$$$&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%$$$%%%&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%############$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''%%%$$$###$$$%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%''')))'''###!!!"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&'''''''''&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$vvvhhheeeiiinnnrrrpppuuuyyyzzz{{{yyyqqqhhhXXXQQQPPPYYYgggrrryyy~~~~~~~~~}}}xxxtttkkkdddXXXIII===555111000000000/////////...............---,,,,,,,,,,,,---************++++++,,,,,,(((((((((((())))))))))))))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''''''''&&&&&&&&&''''''''''''''''''''''''))))))***++++++++++++***((((((((((((((((((((((((((((((((((((((((((((((((###%%%''')))******)))(((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((('''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$%%%&&&&&&''''''&&&&&&&&&'''((('''%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&'''$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&'''((((((((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$((('''&&&%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%###$$$%%%%%%%%%%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%############$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&&&&%%%%%%&&&'''&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%&&&%%%$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''(((((('''%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$#########$$$$$$%%%%%%%%%%%%$$$&&&'''%%%""" !!!###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%$$$#####################$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&$$$######""""""######$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$~~~lllfffggglllqqqooosssvvvwwwxxxyyytttmmm[[[QQQKKKQQQ]]]kkkwww~~~~~~~~~}}}zzzwwwqqqlllcccVVVHHH<<<555222000000000/////////............---,,,,,,,,,,,,---)))))))))***+++,,,,,,---)))))))))*********++++++))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''''''''''''''''''''''''''''''''''''''))))))***+++++++++++++++((((((((((((((((((((((((((((((((((((((((((((((((###%%%&&&((()))))))))(((%%%%%%%%%&&&&&&&&&&&&'''%%%&&&''''''((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%'''''''''%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''((($$$%%%&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''(((((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&$$$######$$$&&&'''&&&&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%!!!###%%%%%%$$$$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""$$$&&&'''&&&&&&'''(((&&&&&&%%%%%%%%%%%%$$$$$$###%%%&&&%%%$$$###$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&''''''&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%######$$$$$$$$$$$$######"""###$$$%%%%%%%%%%%%$$$!!!###$$$$$$######$$$%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$############"""###############$$$$$$!!!"""###$$$%%%&&&&&&'''$$$$$$############$$$$$$&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$xxxmmmhhhjjjnnnooorrrtttsssuuuxxxuuupppbbbVVVLLLKKKSSS___nnnzzz}}}|||}}}~~~}}}{{{uuusssnnnbbbSSSDDD:::666000000000000/////////.........---,,,,,,,,,,,,---+++++++++,,,,,,,,,,,,,,,++++++,,,,,,,,,---------))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''''''''''''''''''''''''''''''''''''''(((((()))*********))))))((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&''''''((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&$$$&&&'''&&&%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&'''''''''''''''$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''''''''&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%&&&''''''(((%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''$$$%%%%%%&&&&&&%%%%%%$$$###!!!"""%%%&&&%%%&&&&&&&&&&&&'''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%$$$$$$!!!###&&&&&&%%%###$$$&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%###%%%''''''&&&%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$###%%%%%%%%%$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%######$$$$$$$$$$$$######"""###$$$%%%%%%%%%$$$$$$$$$###"""###%%%%%%%%%$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$$$$$$$$$$%%%%%%#########$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$######"""$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$sssjjjhhhkkkppprrrsssqqqssswwwuuuqqqjjj]]]OOOIIILLLUUUdddqqq{{{{{{|||~~~~~~wwwxxxtttjjjZZZJJJ>>>999000000000000////////////......---,,,,,,,,,,,,---///......------,,,,,,+++(((((()))))))))*********))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))&&&'''''''''''''''''''''''''''''''''''''''''''''&&&''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((***)))'''&&&$$$$$$$$$$$$%%%%%%%%%&&&&&&'''''''''%%%&&&''''''((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%'''(((((('''%%%$$$$$$%%%&&&&&&''''''&&&&&&$$$%%%&&&&&&%%%%%%'''((($$$$$$$$$$$$$$$$$$$$$$$$###$$$&&&'''((('''&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&########################'''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$&&&'''((('''&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&'''((()))######$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''(((((($$$%%%%%%&&&&&&%%%%%%$$$&&&### !!!%%%)))))))))&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&'''''''''###$$$$$$%%%%%%$$$$$$###!!!$$$''''''%%%$$$%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$############$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%''')))(((&&&$$$$$$$$$&&&&&&&&&%%%%%%%%%$$$$$$###$$$%%%%%%######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%######$$$$$$$$$$$$######"""###$$$%%%&&&%%%$$$$$$***'''$$$$$$&&&&&&### #########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%&&&&&&'''(((&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$###&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$$$$###"""!!! ######$$$%%%%%%&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&'''''''''$$$%%%%%%&&&&&&%%%%%%$$${{{pppiiiccchhhooorrrqqqppprrrttttttmmm```TTTNNNLLLOOO[[[iiiuuu~~~zzzzzz~~~zzz{{{yyytttmmmbbbOOO???;;;444...///000......///000000///...,,,+++***)))------,,,,,,,,,,,,++++++,,,,,,,,,+++++++++******************************(((((())))))))))))(((((())))))))))))))))))))))))(((((())))))))))))((((((((((((((((((((((((((((((,,,+++)))'''&&&%%%%%%&&&&&&&&&''''''''''''&&&&&&'''''''''((((((((())))))))))))))))))***************)))((('''&&&%%%%%%%%%$$$$$$&&&'''(((((())))))&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''((('''&&&%%%%%%$$$$$$$$$$$$'''&&&%%%$$$$$$%%%&&&'''%%%&&&&&&'''''''''''''''&&&'''((('''%%%$$$%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%&&&'''((()))&&&&&&&&&%%%%%%$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&$$$&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%''''''&&&%%%%%%'''((()))%%%%%%%%%&&&&&&'''''''''''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%$$$$$$###"""###$$$%%%&&&'''(((((((((&&&'''''''''&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$###&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%########################%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%""""""""""""""""""""""""#########$$$$$$%%%%%%%%%"""###%%%'''((((((''''''#########"""""""""!!!!!!((('''%%%$$$###$$$%%%%%%%%%%%%&&&''''''&&&%%%%%%&&&%%%$$$#########$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&""""""""""""""""""""""""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$####################################$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%###"""%%%***+++((($$$%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&rrrkkkgggkkkqqqtttrrrqqqssstttrrrqqqggg[[[SSSMMMLLLUUUaaannnyyy}}}yyyzzz~~~~~~~~~zzztttkkk\\\MMM???666000111222000......//////......---,,,++++++------,,,,,,,,,,,,++++++,,,,,,,,,+++++++++******************************(((((())))))))))))(((((())))))))))))))))))))))))'''(((((())))))(((((('''((((((((((((((((((((((((+++***)))'''&&&&&&&&&&&&''''''((((((((((((''''''%%%%%%%%%&&&&&&&&&''''''''''''((((((((())))))))))))((('''&&&&&&&&&&&&&&&%%%%%%&&&'''((((((((((((&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''((('''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&'''((()))(((&&&%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&''''''(((&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&'''&&&&&&%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%$$$######""""""###$$$$$$$$$######%%%%%%&&&&&&%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$###&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$%%%%%%###$$$%%%'''''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$$$$$$$%%%%%%%%%%%%&&&''''''&&&%%%%%%%%%%%%$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&###"""%%%)))***'''############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%wwwpppllllllqqqsssqqqqqqssstttrrruuuooofff[[[PPPJJJNNNVVVeeepppwwwvvvxxx~~~zzzuuuiii^^^GGG<<<333222444222///---.........---------,,,,,,------,,,,,,,,,,,,++++++,,,,,,,,,+++++++++******************************((())))))******))))))((())))))))))))))))))))))))'''(((((())))))(((((('''(((((((((((((((((((((((())))))((('''''''''''''''(((((())))))))))))((((((%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((((((''''''&&&&&&&&&''''''&&&&&&'''''''''''''''&&&&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''((('''&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$%%%&&&&&&'''&&&&&&&&&'''((()))((('''&&&&&&((($$$%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%''''''%%%%%%%%%&&&'''''''''''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%''''''&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$###&&&&&&%%%%%%%%%%%%$$$$$$'''&&&&&&%%%$$$###""""""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$######$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$((('''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$###%%%((((((&&&###!!!"""###$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$vvvooojjjmmmooonnnooosssuuusssvvvuuuooocccVVVLLLLLLPPP^^^gggoooppprrrzzz}}}{{{xxxppphhhSSSEEE777333444222000///---------...............------,,,,,,,,,+++++++++,,,,,,,,,+++++++++******************************)))))))))******)))))))))((((((((((((((((((((((((((())))))******))))))((((((((((((((((((((((((((((((((('''''''''((((((((())))))************))))))((((((((((((((((((((((((&&&&&&'''''''''(((((((((''''''&&&&&&&&&''''''(((''''''(((((('''&&&&&&%%%&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''((('''&&&&&&%%%%%%%%%&&&&&&$$$%%%&&&''''''&&&%%%$$$%%%%%%&&&'''''''''''''''&&&(((((('''&&&%%%&&&'''$$$$$$%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###%%%'''&&&%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%''''''&&&%%%%%%'''&&&&&&%%%%%%$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&''''''&&&%%%%%%&&&'''''''''''''''&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%&&&&&&%%%%%%%%%$$$&&&&&&&&&&&&''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###########################$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''%%%$$$%%%&&&'''%%%###""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$sssiiikkkkkkiiilllsssvvvuuutttvvvsssjjj^^^UUUQQQOOOYYYaaaggghhhkkkrrr|||}}}zzzyyytttnnnaaaQQQ???777444222111111---------.........//////------,,,,,,,,,+++++++++,,,,,,,,,+++++++++******************************))))))************))))))(((((((((((((((((((((((()))******++++++******)))))))))))))))))))))))))))'''''''''((((((((((((((())))))************))))))((((((((((((((((((((('''''''''((((((((()))))))))''''''&&&&&&&&&''''''((((((((((((((('''&&&%%%$$$&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''(((&&&&&&&&&%%%%%%&&&''''''$$$%%%&&&''''''&&&%%%$$$&&&&&&'''(((((((((((('''%%%&&&'''&&&$$$###$$$%%%$$$$$$%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&#########$$$%%%'''((()))%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&&&&%%%$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%'''((((((((('''&&&&&&&&&&&&%%%%%%$$$$$$###&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%&&&''''''&&&&&&&&&!!!!!!###$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###########################$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&~~~rrrqqqmmmhhhkkkrrrvvvvvvqqqttttttnnnfff```YYYSSSUUU\\\bbbeeefffkkkvvv~~~~~~|||{{{xxxtttlll^^^LLLAAA999333222333..................//////------,,,,,,,,,,,,++++++,,,,,,,,,+++++++++******************************)))******++++++******))))))))))))))))))))))))))))))******++++++******)))))))))))))))))))))))))))&&&'''((((((((((((((('''))))))************))))))&&&&&&&&&&&&&&&%%%%%%%%%''''''((((((((()))))))))(((''''''&&&&&&&&&'''''''''((((((((('''&&&%%%%%%&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&'''(((%%%&&&&&&''''''&&&&&&%%%%%%&&&''''''((((((''''''$$$%%%&&&%%%#########$$$$$$%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&(((***,,,---$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$&&&&&&$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''%%%&&&''''''((((((''''''%%%%%%%%%%%%$$$$$$$$$$$$&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%!!!"""###%%%&&&&&&''''''%%%%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%%%%%%%%%%&&&&&&""""""###$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%""""""$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%############$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%&&&%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&uuullllllqqqtttssspppssstttpppnnnjjjaaaVVVPPPXXXaaaeeeeeefffnnnvvv|||}}}~~~|||yyysssiii[[[OOOBBB666222444////////////............------,,,,,,,,,,,,++++++,,,,,,,,,+++++++++******************************)))******++++++******)))))))))))))))))))))))))))(((((())))))))))))(((((())))))))))))))))))))))))'''(((((())))))((('''&&&((())))))))))))))))))(((''''''&&&&&&&&&%%%%%%%%%&&&&&&'''''''''((((((((()))((('''&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&'''((((((&&&&&&&&&%%%%%%&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%&&&'''&&&$$$###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''')))***+++$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&'''&&&&&&%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$&&&&&&$$$###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%&&&&&&'''((($$$$$$$$$$$$$$$%%%%%%%%%&&&%%%$$$$$$###$$$$$$$$$######$$$%%%%%%%%%%%%%%%%%%&&&&&&'''(((((((((((($$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$%%%%%%&&&&&&&&&#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$#########%%%&&&'''((('''&&&&&&%%%$$$#########$$$%%%&&&&&&&&&%%%%%%%%%%%%$$$######$$$%%%%%%!!!"""$$$%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######"""""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$######$$$&&&'''$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%}}}pppmmmqqqsssqqqooossssssqqqrrrpppfffXXXLLLUUUaaagggfffdddiiipppxxx}}}~~~}}}~~~{{{vvvooofffZZZIII:::333444000000//////............---------,,,,,,,,,++++++,,,,,,,,,+++++++++************************************++++++++++++******))))))))))))))))))))))))&&&&&&''''''''''''&&&&&&))))))))))))))))))))))))'''((()))))))))(((&&&%%%(((((())))))))))))(((((())))))((((((((('''''''''%%%%%%%%%&&&&&&&&&''''''***)))((('''&&&%%%%%%%%%&&&&&&'''''''''''''''&&&&&&&&&&&&'''''''''((((((&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&'''((()))''''''%%%$$$$$$%%%''''''""""""###$$$$$$$$$$$$###&&&'''((('''%%%$$$%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&############$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''###$$$$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$"""$$$&&&%%%$$$###$$$%%%((((((((((((((((((((((((%%%%%%%%%&&&&&&'''''''''&&&%%%$$$###$$$%%%&&&'''#########$$$$$$%%%%%%&&&&&&%%%$$$$$$######$$$$$$"""###$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$######"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&######""""""###%%%'''((())))))(((&&&%%%$$$###""""""###%%%&&&'''&&&%%%%%%&&&%%%$$$######$$$%%%&&&!!!"""$$$%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""!!!!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$&&&)))""""""###$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$${{{rrrnnnnnnppppppppppppqqqqqqooojjjggg___ZZZ\\\gggnnnmmmjjjkkktttwww|||{{{yyytttiiiYYYHHH;;;444222222222222111000...---......//////////////////+++,,,,,,------,,,,,,+++++++++++++++++++++++++++******************************++++++++++++******))))))))))))))))))))))))(((((((((((())))))))))))++++++******)))((((((((())))))))))))))))))))))))))))))(((''''''''''''''')))(((((('''''''''(((((())))))))))))))))))))))))$$$$$$%%%&&&'''((()))***)))))))))(((''''''&&&&&&((((((((('''&&&&&&&&&%%%&&&&&&&&&'''''''''(((((((((((((((((('''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&''''''''''''***(((&&&%%%&&&''''''&&&(((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%&&&'''''''''''''''&&&&&&%%%%%%%%%(((((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&'''&&&&&&%%%$$$###""""""%%%%%%%%%&&&&&&&&&''''''((((((&&&%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%'''(((((('''%%%$$$)))(((&&&%%%%%%&&&((()))&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%''''''((((((((((((''''''(((((((((((((((((((((((())))))(((((('''''''''&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$###&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((((((((((((((((((((((("""$$$&&&''''''&&&$$$###!!!!!!"""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''%%%""" """%%%'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###!!!!!!$$$%%%$$$"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&((('''&&&%%%%%%%%%%%%%%%(((((('''&&&&&&&&&&&&'''&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%wwwooojjjlllllllllnnnpppqqqooommmddd```aaajjjpppooommmnnnpppssswww|||~~~|||{{{wwwooobbbRRRCCC:::666555333111000///---,,,........................+++,,,,,,------,,,,,,+++++++++++++++++++++++++++************************************************))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))******))))))))))))))))))))))))))))))((('''''''''''''''((((((''''''''''''(((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((('''''''''''''''&&&&&&&&&&&&&&&&&&'''''''''((((((&&&&&&''''''(((((())))))'''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''&&&&&&&&&)))(((&&&&&&''''''&&&%%%'''''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$#########%%%%%%%%%%%%&&&&&&&&&&&&'''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''&&&$$$######$$$&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&&&&%%%%%%$$$###&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%$$$$$$$$$%%%&&&&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%(((&&&$$$######$$$&&&(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$''''''((((((((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$"""!!!"""$$$%%%$$$"""%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&((('''&&&%%%%%%%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%xxxmmmlllkkkjjjlllooorrrssssssmmmiiiiiiooossssssrrrrrrkkklllpppvvv|||~~~{{{~~~}}}zzzvvvnnn```PPPDDD;;;888444111///...---+++......------------------+++,,,,,,------,,,,,,+++++++++++++++++++++++++++******************************((((((((((((******(((((((((((((((((((((((((((((((((((())))))))))))''''''((())))))***++++++))))))))))))))))))))))))))))))((('''''''''''''''((((((''''''''''''((((((''''''''''''''''''''''''))))))((('''&&&%%%%%%$$$&&&&&&''''''((())))))***&&&&&&&&&'''''''''''''''&&&&&&&&&'''''''''''''''$$$%%%&&&'''((()))******&&&&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%((('''&&&'''((((((&&&$$$&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$&&&''''''(((((('''%%%$$$$$$%%%'''(((&&&%%%$$$######$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&%%%$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%$$$%%%%%%%%%""""""######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""###%%%&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%|||sssoookkkiiilllpppsssuuutttqqqqqqtttwwwxxxxxxwwwiiigggfffllluuu|||~~~|||}}}zzzxxxtttjjj\\\QQQAAA<<<555111000000...------------------,,,,,,,,,+++,,,,,,------,,,,,,+++++++++++++++++++++++++++************************+++)))'''&&&&&&''')))+++(((((((((((((((((((((((((((((((((((())))))))))))(((((((((((())))))******))))))))))))))))))))))))))))))((('''''''''''''''(((''''''''''''(((((()))''''''''''''''''''''''''))))))((('''&&&%%%%%%$$$''''''''''''(((((())))))%%%&&&&&&&&&'''(((((((((''''''''''''''''''''''''%%%%%%&&&''''''((())))))&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%$$$$$$'''&&&&&&((()))(((&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&'''''''''&&&%%%%%%%%%%%%&&&'''((('''&&&&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((&&&%%%######$$$%%%&&&!!!"""""""""#########$$$#################################$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""############""""""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&'''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%{{{tttlllffffffkkkpppsssvvvvvvvvvwwwyyy||||||{{{kkkeee```ccclllwww}}}{{{wwwvvvuuupppfff^^^JJJBBB888222111222111000......---------,,,,,,,,,+++,,,,,,------,,,,,,+++++++++++++++++++++++++++************************+++)))'''&&&&&&''')))+++(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))((((((''''''))))))))))))))))))))))))))))))(((''''''''''''''''''''''''''''''((())))))(((((((((((((((((((((((('''''''''''''''''''''&&&))))))((((((''''''''''''%%%&&&&&&&&&'''((((((((('''''''''''''''''''''&&&'''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%$$$$$$&&&&&&&&&((())))))'''$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&''''''######$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%'''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''''''''''')))'''%%%###"""###%%%&&&%%%%%%%%%&&&&&&&&&&&&&&&########################"""###$$$$$$$$$$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&'''&&&''''''((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%qqqgggdddgggmmmqqqssswwwyyyxxxzzz~~~}}}qqqiiiaaa___dddoooxxx}}}|||zzzwwwwwwvvvsssmmmhhhUUUKKK===555333333222111//////......---,,,,,,,,,+++,,,,,,------,,,,,,+++++++++++++++++++++++++++******************************((((((((((((******(((((((((((((((((((((((((((((((((((())))))))))))******)))(((((('''&&&&&&))))))))))))))))))))))))))))))((('''''''''''''''''''''&&&''''''((()))***))))))))))))))))))))))))%%%&&&&&&&&&'''(((((((((***))))))(((''''''&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&%%%'''((()))'''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&''''''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&''''''$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&'''((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%'''(((((('''%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&)))'''%%%#########%%%&&&$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''&&&$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&''''''&&&'''((()))((('''&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$""""""""""""""""""""""""%%%%%%%%%%%%%%%%%%%%%%%%pppgggfffjjjmmmnnntttxxxxxx{{{}}}wwwpppggg``````gggpppvvvxxxyyy{{{{{{zzzvvvrrrooobbbUUUDDD888444444111///000000//////...------,,,+++,,,,,,------,,,,,,+++++++++++++++++++++++++++************************************************))))))))))))))))))))))))(((((((((((())))))))))))((((((((((((((((((''''''))))))))))))))))))))))))))))))((('''''''''''''''&&&&&&&&&''''''((()))***((((((((((((((((((((((((&&&&&&&&&'''''''''(((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''&&&&&&&&&'''&&&%%%%%%'''(((((('''%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&'''''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&###$$$%%%'''((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&$$$######$$$$$$""""""""""""""""""""""""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&'''&&&###"""###%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&'''(((%%%&&&'''((((((&&&%%%###$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$########################%%%%%%%%%%%%%%%%%%%%%%%%{{{lllggghhhjjjjjjrrrxxxxxxzzz}}}|||vvvlllccc___bbbiiiooouuuzzz~~~yyyuuurrrkkk\\\III;;;555333000---111111000///......------+++,,,,,,------,,,,,,+++++++++++++++++++++++++++******************************++++++++++++******************************(((((((((((())))))))))))&&&&&&''''''((()))))))))))))))))))))))))))))))))))))))((('''''''''''''''&&&&&&&&&'''''')))******''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&''''''((()))))))))(((((((((''''''&&&&&&%%%(((((('''''''''&&&&&&&&&###$$$$$$%%%&&&'''(((((($$$$$$$$$%%%&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&''''''''''''(((&&&$$$$$$&&&((()))(((&&&&&&&&&''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&''''''"""###$$$&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&&&&'''(((((('''%%%$$$$$$%%%'''(((&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&###$$$%%%%%%&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%$$$$$$######&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%###%%%'''&&&###!!!###%%%%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&&&&''''''((($$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&'''((($$$%%%&&&''''''%%%###"""$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%sssiiihhhhhhjjjiiimmmuuuzzzzzzyyy{{{}}}zzzwwwqqqggg^^^^^^cccpppuuuzzz|||~~~}}}xxxooogggYYYIII;;;333111222222111/////////...,,,+++......//////......---,,,***+++,,,+++)))))))))***)))))))))***++++++,,,,,,++++++***)))))))))))))))))))))))))))))))))))))))((()))***++++++***)))((())))))))))))))))))))))))))))))))))))))))))))))))''''''(((((())))))******))))))((('''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((%%%&&&((()))))))))((('''(((((('''&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&((('''%%%$$$$$$%%%'''(((((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''(((((('''&&&%%%$$$$$$###''''''&&&&&&&&&%%%%%%%%%(((((((((((((((((((((((('''''''''''''''''''''''''''&&&$$$######$$$&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&''''''((((((''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&''''''''''''(((''''''''''''''''''&&&&&&(((&&&%%%%%%&&&((((((((()))((('''&&&%%%&&&&&&'''&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%%%%""""""#########$$$$$$$$$((('''&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&'''((((((&&&$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$######$$$%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""!!!%%%%%%$$$$$$%%%%%%&&&'''&&&&&&'''((('''&&&$$$###&&&&&&&&&&&&&&&&&&&&&&&&$$$#########$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%$$$######$$$%%%&&&zzzlllgggeeejjjhhhlllsssxxxxxxxxxyyy{{{{{{zzzvvvlllaaa___cccjjjsss{{{|||{{{||||||zzzrrrlll___PPPBBB999444222333111000///000000...---,,,,,,------,,,,,,+++******+++,,,+++***))))))+++++++++******************))))))((('''''''''''''''))))))))))))))))))))))))'''''''''(((((('''''''''))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))((('''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))%%%&&&'''((()))((((((''')))(((''''''&&&&&&''''''(((((('''''''''&&&&&&&&&((('''%%%$$$$$$%%%'''(((''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&$$$######$$$&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&''''''(((((('''''''''&&&&&&&&&%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''***(((&&&%%%&&&'''&&&&&&((('''&&&%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&%%%%%%%%%###$$$$$$$$$%%%%%%%%%&&&((('''&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$&&&''''''&&&%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$'''%%%######$$$%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$######$$$$$$%%%&&&%%%&&&&&&'''&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%$$$######$$$%%%%%%rrrhhhdddhhhfffhhhpppuuuvvvwwwyyyzzz{{{}}}zzzqqqeeeaaaddddddoooyyy{{{yyyzzz||||||wwwqqqhhh[[[MMM@@@777111444222000000111111000///,,,,,,------,,,,,,+++******,,,,,,,,,***)))***+++,,,,,,++++++***))))))((())))))(((''''''''''''((())))))))))))))))))))))))''''''&&&&&&&&&&&&''''''))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))((('''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))&&&&&&'''(((((((((((('''***)))((((((''''''(((((('''''''''''''''&&&&&&&&&'''&&&%%%$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''###$$$$$$%%%&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&%%%$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&''''''(((((('''''''''''''''&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''+++)))'''&&&&&&&&&%%%$$$&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&"""$$$&&&'''&&&&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$)))'''%%%%%%&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%&&&'''(((###############$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%yyylllddddddaaaccckkkqqqsssvvvzzzzzz{{{|||{{{qqqfffbbbeeebbbllltttwwwxxx|||}}}|||xxxuuunnndddWWWHHH:::111444222000///000111111000......//////......---,,,+++,,,---,,,***)))***++++++++++++*********)))))),,,+++******))))))******((((((((((((((((((((((((***)))(((''''''((()))***(((((((((((((((((((((((())))))))))))))))))))))))******))))))((((((''''''))))))((('''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((************************&&&&&&'''''''''(((((((((******)))((((((((((((((('''''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&'''''''''''''''((((((((())))))$$$$$$%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&''''''((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&&&&'''''''''&&&&&&&&&'''''''''''''''***((('''&&&''''''%%%$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&###%%%''''''&&&&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$'''&&&$$$%%%'''(((((('''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$$$$$$$%%%''')))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''%%%$$$###"""###%%%&&&$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$#########$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%nnnccc```\\\^^^eeelllpppuuuzzzyyyzzzzzzxxxnnndddaaaeeedddhhhlllqqqxxxzzzxxxvvvqqqjjj___PPP???555444222///...///000000///......//////......---,,,+++,,,---,,,*********+++))))))*********+++++++++,,,,,,+++***************((((((((((((((((((((((((***)))(((''''''((()))***(((((((((((((((((((((((())))))))))))))))))))))))******))))))((((((''''''))))))((('''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))&&&&&&&&&&&&&&&''''''(((******)))(((((((((((((((&&&'''''''''''''''''''''&&&&&&&&&%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&''''''((()))))))))&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%&&&''''''((('''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&'''''''''(((((('''&&&&&&&&&(((((('''&&&&&&&&&&&&''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%'''((('''&&&$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$"""!!! """%%%'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$$$$$$$%%%''')))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%###""""""######&&&%%%%%%%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%ssseee___[[[ZZZ```ggglllrrrxxxxxxxxxyyyvvvlllbbb___bbbeeeeeefffjjjttt~~~~~~yyyyyyvvvsssnnnfffXXXHHH===666333///......//////...,,,,,,------,,,,,,+++***+++------,,,+++***+++,,,((())))))***++++++,,,,,,******)))(((((((((((()))))))))))))))))))))))))))((((((''''''''''''(((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))((('''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&%%%%%%&&&&&&'''(((***)))((((((''''''((((((&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''&&&&&&&&&''''''(((((((((''''''&&&&&&&&&%%%%%%%%%((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&))))))(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&'''(((((((((&&&%%%%%%'''((()))(((&&&%%%&&&'''(((((((((''''''$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&%%%$$$%%%%%%&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&'''''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&'''((((((%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&%%%$$$######&&&&&&&&&&&&&&&'''((((((%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%nnnaaa\\\ZZZ^^^cccgggmmmrrrvvvwwwzzzxxxmmmaaa\\\]]]bbbcccccceeemmmxxx{{{yyy{{{xxxvvvsssmmmbbbSSSHHH999555111///...//////...,,,,,,------,,,,,,+++***,,,---...---+++***+++,,,******************+++++++++***))))))(((((())))))))))))))))))))))))))))))(((((())))))))))))(((((())))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))((('''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&'''((()))(((''''''&&&&&&''''''&&&&&&&&&'''''''''((((((%%%&&&&&&&&&&&&&&&&&&%%%''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&'''''''''%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&)))))))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%&&&''''''((((((''''''$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&'''(((((()))'''&&&&&&'''((((((&&&$$$$$$%%%&&&'''''''''&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&$$$$$$%%%%%%&&&''''''(((&&&&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&((('''&&&%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$"""!!! """$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&%%%$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&!!!"""$$$&&&&&&%%%$$$###&&&%%%%%%%%%%%%&&&''''''&&&%%%$$$$$$$$$&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%zzzddd^^^ZZZ\\\```ccciiinnntttwww{{{zzzpppaaaZZZZZZ^^^aaacccccchhhqqqyyy{{{}}}{{{xxxvvvrrriii[[[QQQ;;;777333000////////////......//////......---,,,,,,---...---+++***+++,,,,,,,,,++++++***)))))))))---,,,++++++***+++++++++))))))))))))))))))))))))***+++,,,------,,,+++***))))))))))))))))))))))))))))))))))))))))))))))))''''''(((((())))))******))))))((('''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&%%%$$$%%%&&&'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&***))))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%&&&''''''((((((''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&'''((()))))))))(((((((((((('''$$$""""""###%%%&&&'''&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&(((((('''''''''&&&&&&&&&$$$$$$%%%%%%&&&'''((((((&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&'''''''''(((((('''''''''&&&&&&&&&###$$$&&&'''((('''&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&###%%%&&&'''&&&&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$)))'''%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&& ###%%%%%%$$$###%%%%%%$$$$$$%%%%%%&&&'''&&&&&&%%%$$$%%%&&&((()))&&&&&&&&&&&&&&&&&&&&&&&&!!!!!!"""###$$$&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%pppggg```______```fffnnnsssttttttuuusssjjj^^^UUU\\\^^^bbbffffffgggooozzzxxx{{{}}}|||zzztttiii]]]JJJ@@@444///000222111...000000///...---,,,,,,,,,------------------------,,,,,,,,,+++++++++******++++++++++++++++++++++++************************))))))))))))(((((((((((())))))))))))))))))))))))(((((((((((())))))))))))''''''((()))))))))))))))))))))((('''''''''''''''))))))))))))))))))))))))((('''&&&&&&'''((('''&&&&&&&&&&&&''''''''''''(((''''''''''''''''''''''''))))))((((((((((((((()))))))))(((((('''''''''&&&'''''''''''''''''''''''''''&&&%%%$$$%%%%%%''''''''''''''''''''''''''''''%%%&&&'''((())))))))))))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''((((((((('''''''''''''''''''''''''''((('''&&&%%%%%%&&&'''(((((((((((((((((()))******+++***((('''%%%$$$$$$$$$''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%'''(((((('''%%%$$$((((((((((((((((((((((((''''''''''''''''''''''''%%%&&&&&&&&&'''(((((((((%%%&&&&&&&&&&&&&&&&&&%%%''''''''''''''''''''''''(((((('''''''''&&&&&&&&&((('''%%%%%%&&&&&&%%%$$$%%%&&&&&&&&&%%%$$$$$$###***)))'''&&&%%%%%%&&&'''%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$(((''''''&&&$$$######"""&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&$$$$$$$$$%%%&&&'''&&&%%%%%%$$$$$$######"""$$$$$$$$$%%%%%%%%%&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$###&&&&&&'''''''''&&&%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&''''''''''''((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$######$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&"""%%%((('''$$$###$$$'''%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''#########$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''$$$$$$######$$$$$$%%%&&&%%%%%%%%%&&&'''((())))))((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''######$$$%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&'''&&&&&&&&&&&&'''((((((|||qqqfffaaa___```fffnnnrrrrrrssstttrrrjjj^^^TTTQQQSSSYYY___aaaeeeooozzzyyy|||~~~~~~|||yyyoooeeeRRRHHH:::333222333111////////////......------,,,------------------------,,,,,,,,,+++++++++******++++++++++++++++++++++++))))))))))))))))))))))))+++++++++*********))))))))))))))))))))))))))))))(((((((((((())))))))))))(((((()))***************))))))((('''''''''''''''((((((((((((((((((((((((''''''&&&'''(((((('''&&&&&&&&&&&&''''''''''''(((((((((((((((((((((((((((((((((''''''''''''(((((()))((((((((('''''''''&&&''''''''''''''''''''''''((('''&&&%%%%%%%%%&&&'''''''''''''''''''''''''''######$$$%%%&&&&&&&&&&&&))))))))))))))))))))))))%%%&&&''''''((((((''''''''''''''''''''''''''''''((('''&&&&&&&&&&&&'''(((%%%%%%%%%%%%%%%&&&''''''))))))((('''&&&%%%%%%$$$''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&'''''''''''''''&&&&&&&&&%%%%%%$$$%%%'''(((((('''%%%$$$''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''''''''&&&&&&&&&&&&(((&&&%%%%%%&&&'''%%%$$$&&&&&&&&&&&&&&&%%%$$$$$$'''&&&%%%$$$$$$$$$%%%&&&%%%&&&&&&''''''&&&&&&%%%''''''''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&%%%%%%%%%$$$$$$%%%$$$$$$###""""""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&%%%%%%$$$###$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''((('''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&''''''&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$###$$$$$$%%%&&&%%%&&&&&&&&&'''((((((((()))(((''''''&&&&&&&&&'''(((((('''%%%$$$"""!!! %%%&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%&&&&&&'''%%%%%%%%%%%%%%%&&&''''''qqqhhhcccccchhhmmmnnnoooppprrrqqqiii^^^VVVKKKLLLQQQXXX]]]cccnnnxxxzzz~~~~~~wwwooo___SSSDDD999555444222///........................------------------------,,,,,,,,,+++++++++******++++++++++++++++++++++++((((((((((((((((((((((((++++++************))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))************++++++))))))((('''''''''''''''''''''''''''''''''''''''&&&'''((())))))((('''&&&&&&&&&&&&''''''''''''((())))))))))))))))))))))))''''''&&&&&&&&&&&&''''''((((((((('''''''''''''''''''''''''''''''''''''''(((((('''&&&%%%%%%&&&&&&''''''''''''''''''''''''&&&''''''(((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((''''''''''''''''''''''''''''''((('''&&&&&&&&&&&&'''((($$$$$$$$$$$$$$$%%%&&&&&&&&&'''((((((((('''%%%$$$''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''((((((((('''''''''''''''%%%&&&'''(((((('''&&&%%%'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%&&&((())))))(((&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&&&&&&&&&&(((&&&%%%%%%&&&'''&&&$$$&&&''''''''''''&&&%%%%%%$$$############$$$%%%%%%&&&&&&''''''''''''&&&&&&&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%$$$$$$###""""""###$$$$$$%%%&&&&&&''''''&&&&&&&&&'''''''''(((((('''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%$$$$$$###$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%&&&''''''&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&''''''''''''''''''))))))(((''''''''''''(((((('''&&&$$$""" ((((((''''''%%%$$$""""""&&&&&&&&&%%%&&&''''''(((%%%$$$$$$$$$$$$%%%&&&&&&sssmmmjjjkkkllljjjjjjlllooopppkkkbbb[[[OOOMMMOOOUUU[[[aaajjjssszzz|||vvvkkk```OOOAAA:::555222///............////////////------------------------,,,,,,,,,+++++++++******************************)))))))))))))))))))))))))))(((((((((''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))))))))******))))))((('''''''''''''''''''''''''''''''''''''''%%%''')))***)))''''''&&&&&&&&&&&&''''''''''''(((((((((((((((((((((((((((''''''&&&&&&&&&'''((((((''''''''''''''''''''''''''''''''''''''''''''''''((((((''''''&&&&&&%%%%%%''''''''''''''''''''''''((())))))))))))(((((('''%%%%%%%%%%%%%%%%%%%%%%%%''''''(((((((((((('''''''''''''''''''''''''''''''''''''''&&&&&&'''''''''''''''&&&&&&''''''((()))$$$&&&'''))))))(((&&&%%%''''''''''''''''''''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''((((((((('''&&&&&&&&&%%%%%%''')))******)))'''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%&&&'''&&&%%%&&&''''''(((''''''&&&&&&"""""""""###$$$$$$%%%&&&&&&&&&''''''''''''&&&&&&$$$$$$%%%'''((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%&&&'''''''''%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$"""$$$''''''%%%"""%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&&&&&&&&&&%%%''''''&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''%%%$$$$$$$$$$$$%%%&&&&&&'''''''''''''''&&&&&&&&&(((((('''''''''''''''((($$$$$$$$$###############((((((''''''&&&$$$###"""'''&&&&&&&&&&&&'''((((((%%%%%%%%%$$$%%%%%%&&&'''{{{wwwrrrmmmhhhhhhiiilllooommmgggbbbTTTOOOMMMRRRXXX^^^fffmmmwww~~~zzztttjjjZZZLLLAAA999333000......//////////////////------------------------,,,,,,,,,+++++++++******************************************************(((((((((''''''''''''&&&(((((((((((((((((((((((((((((((((((()))))))))))))))(((''''''''''''(((((())))))((('''''''''''''''''''''''''''''''''''''''%%%(((******(((''''''(((&&&&&&&&&''''''''''''(((''''''''''''''''''''''''((((((''''''((())))))***&&&&&&&&&'''''''''''''''''''''''''''''''''''''''(((((((((''''''&&&&&&&&&''''''''''''''''''''''''%%%%%%&&&&&&&&&%%%$$$$$$(((((((((((((((((((((((('''(((((((((((((((''''''''''''''''''''''''''''''&&&''''''''''''''''''&&&((((((((((((((())))))***$$$%%%'''))))))(((&&&%%%''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((('''&&&&&&&&&%%%&&&''')))******)))'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&'''%%%%%%%%%''''''&&&%%%&&&&&&''''''(((''''''&&&""""""###$$$%%%&&&''''''&&&''''''((((((''''''&&&%%%%%%&&&&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&"""###%%%'''(((((((((''''''''''''&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%%%%''''''%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%###!!!###%%%&&&$$$!!!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&''''''&&&%%%%%%&&&&&&%%%%%%$$$$$$######%%%&&&&&&''''''&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''&&&&&&&&&'''&&&&&&%%%&&&&&&''''''######$$$$$$%%%&&&''''''%%%&&&&&&''''''&&&&&&%%%'''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&''''''(((}}}tttkkkiiiiiikkknnnnnnkkkhhhWWWOOOJJJMMMTTTZZZ```fffooowww{{{yyyqqqeeeXXXKKK@@@777222////////////////////////------------------------,,,,,,,,,+++++++++************************************************************))))))))))))(((((())))))))))))))))))))))))(((((((((((()))))))))))))))((('''&&&%%%&&&'''((())))))((('''''''''''''''''''''''''''''''''''''''&&&)))+++)))'''&&&(((***&&&&&&&&&''''''''''''(((''''''''''''''''''''''''((((((((((((((()))***+++&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&'''((((((((((((''''''''''''''''''''''''''''''%%%&&&&&&'''''''''&&&&&&''''''''''''''''''''''''(((((()))))))))(((''''''''''''''''''''''''''''''&&&&&&'''(((((('''&&&&&&'''&&&&&&&&&&&&'''((((((%%%&&&'''((((((((('''&&&''''''''''''''''''''''''%%%%%%&&&&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''(((((('''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$%%%'''''''''&&&%%%%%%&&&''''''''''''&&&###$$$%%%&&&''''''''''''''''''((((((((((((''''''))))))((('''$$$""" %%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&''''''''''''!!!"""###%%%&&&&&&&&&&&&'''''''''&&&%%%$$$$$$###$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%((('''&&&%%%$$$%%%&&&&&&'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''(((&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$######$$$%%%%%%###"""%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&''''''&&&%%%$$$%%%$$$$$$$$$$$$$$$######%%%&&&&&&''''''&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%&&&&&&'''&&&&&&''''''''''''''''''&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&''''''(((((((((&&&&&&&&&%%%&&&''''''((('''&&&&&&&&&&&&'''((((((~~~rrrnnnkkkjjjlllmmmllljjj___UUULLLLLLQQQTTTXXX\\\cccnnnxxx}}}}}}|||wwwooocccVVVIII===666111111000000//////......------------------------,,,,,,,,,+++++++++************************************************************)))))))))((((((((())))))))))))))))))))))))(((((((((((())))))))))))***)))'''&&&&&&&&&'''((())))))((('''''''''''''''(((((((((((((((((((((((((((***+++(((%%%%%%(((---&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''&&&'''((()))******%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''%%%&&&'''((())))))((((((''''''''''''''''''''''''''''''((()))*********)))%%%%%%%%%%%%%%%%%%%%%%%%)))))))))))))))(((''''''''''''''''''''''''''''''&&&&&&'''(((((('''&&&&&&&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''&&&&&&''''''''''''''''''''''''%%%%%%&&&&&&'''(((((()))''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&'''''''''(((((((((((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''''''''''''''&&&%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%$$$%%%'''((('''&&&$$$$$$%%%&&&&&&&&&&&&&&&###$$$%%%&&&''''''&&&&&&''''''((((((((((((''''''))))))((('''&&&$$$"""!!!&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&'''''''''(((&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&&&&%%%'''&&&%%%%%%&&&'''***+++''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''((('''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&'''((('''&&&%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%'''(((((('''%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%%%%%%%&&&''''''%%%&&&&&&&&&'''(((((((((&&&&&&&&&&&&&&&'''((((((((('''''''''&&&&&&%%%%%%$$$%%%&&&'''((((((((((((%%%%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&'''(((wwwrrrmmmjjjkkkmmmllljjjjjj]]]QQQNNNPPPQQQRRRSSS[[[gggttt{{{~~~~~~}}}zzztttkkk]]]NNNAAA999222111111000///......---------------------------,,,,,,,,,+++++++++******))))))))))))))))))))))))))))))))))))))))))))))))((('''''''''&&&&&&&&&&&&))))))))))))))))))))))))(((((((((((()))))))))))),,,***((('''&&&'''((()))))))))(((''''''''''''''')))))))))))))))))))))))))))***+++((($$$$$$)))...&&&&&&&&&'''''''''(((((())))))))))))))))))))))))%%%%%%%%%&&&'''((()))***%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''$$$%%%'''(((******))))))''''''''''''''''''''''''###$$$%%%&&&''''''''''''(((((((((((((((((((((((()))))))))))))))(((''''''''''''''''''''''''''''''%%%&&&'''(((((('''&&&%%%'''&&&&&&&&&&&&'''(((((()))((('''&&&&&&&&&&&&'''''''''''''''''''''''''''%%%%%%&&&&&&'''((())))))((((((((((((((((((((((((&&&%%%%%%$$$$$$%%%%%%&&&'''((((((((())))))******((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%&&&&&&''''''(((((((((((('''%%%$$$$$$%%%'''(((''''''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%$$$%%%'''((('''&&&###$$$%%%%%%&&&&&&&&&%%%###$$$%%%&&&'''&&&%%%$$$''''''((((((((((((''''''%%%%%%&&&'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&"""######$$$&&&''''''(((&&&&&&&&&'''''''''((((((+++***(((&&&%%%%%%%%%%%%"""######$$$$$$%%%%%%&&&&&&&&&&&&'''''''''((((((%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&&&&&&&%%%$$$$$$%%%'''***---///'''''''''&&&&&&%%%%%%%%%&&&&&&&&&'''''''''(((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$'''***)))&&&%%%&&&(((%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&(((((('''&&&%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%'''(((((('''%%%$$$%%%%%%%%%&&&&&&'''''''''%%%&&&&&&''''''&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%%%%%%%&&&''''''%%%%%%&&&&&&'''((())))))'''''''''''''''((()))***&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''%%%$$$$$$$$$$$$%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''~~~ooojjjjjjjjjiiijjjmmmhhh\\\QQQNNNOOONNNIIINNNYYYhhhuuu}}}~~~~~~{{{uuuooofffYYYJJJ@@@666333///......000000000000000000///...,,,+++*********+++++++++,,,,,,,,,+++++++++************)))))))))))))))************''''''(((((())))))******))))))))))))************(((((((((((())))))))))))&&&&&&'''((()))***+++++++++*********))))))((((((&&&'''''''''(((((()))))))))((('''&&&&&&'''((()))(((''''''&&&&&&''')))***''''''''''''(((((((((((())))))))))))************''''''((((((''''''&&&%%%&&&&&&&&&&&&&&&&&&%%%%%%###%%%'''((()))((('''&&&((((((((('''&&&&&&&&&%%%((((((((((((((((((((((((%%%%%%%%%&&&&&&&&&&&&&&&(((((((((((())))))))))))))))))(((((('''''''''&&&'''''''''&&&&&&%%%%%%%%%(((((('''&&&&&&%%%$$$$$$((((((((('''&&&$$$###""""""###$$$%%%&&&&&&&&&&&&''''''(((((('''&&&%%%%%%(((((('''''''''&&&&&&&&&&&&((())))))(((''''''(((&&&&&&&&&'''''''''((((((''''''''''''''''''''''''((('''%%%$$$$$$%%%'''((((((((())))))))))))((((((***))))))((('''&&&&&&&&&(((''''''&&&&&&&&&''''''###%%%(((******(((%%%###''''''''''''''''''&&&&&&$$$$$$$$$%%%%%%'''((()))$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''''''''&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''""""""""""""###$$$%%%%%%%%%%%%%%%(((+++---...---)))((('''&&&%%%$$$######''''''''''''''''''''''''$$$%%%&&&''''''&&&%%%$$$ !!!###$$$%%%$$$$$$###&&&%%%%%%$$$$$$%%%%%%&&&)))'''%%%$$$$$$%%%''')))'''''''''&&&&&&%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&&&&''''''''''''''''''&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%&&&&&&''''''&&&&&&''''''''''''''''''''''''))))))((('''&&&&&&%%%%%%###$$$%%%&&&'''''''''''''''&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&%%%$$$$$$tttmmmiiiffffffhhhllljjjbbbXXXSSSRRROOOJJJKKKSSSaaapppzzz~~~~~~}}}}}}zzzvvvqqqjjj___QQQGGG;;;777222///////////////000000000///...---+++***+++++++++,,,,,,,,,,,,---++++++++++++************))))))))))))************)))))))))))))))((((((((())))))))))))************(((((((((((()))))))))***(((((((((((())))))))))))))))))))))))(((((('''''''''''''''((((((((()))))))))((('''&&&&&&'''((()))'''''''''''''''((())))))''''''''''''((((((((((((((((((((()))))))))******''''''((((((''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''))))))((('''&&&'''''''''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''(((((((((((()))))))))))))))((((((((('''''''''&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&'''''''''&&&&&&%%%%%%'''(((((()))))))))''''''(((((('''&&&&&&%%%(((((('''''''''&&&&&&&&&&&&&&&%%%$$$"""###%%%(((&&&&&&&&&'''''''''((((((''''''''''''''''''''''''((('''%%%$$$$$$%%%'''((('''(((((())))))(((((('''***))))))(((''''''&&&&&&'''&&&&&&&&&&&&''''''(((&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%&&&&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((%%%%%%%%%%%%$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%'''+++---------))))))((('''&&&%%%$$$$$$''''''''''''''''''''''''%%%&&&&&&&&&&&&&&&&&&%%%###$$$$$$%%%&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%''''''&&&&&&&&&%%%%%%%%%)))((('''&&&%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&''''''''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%&&&&&&''''''&&&&&&'''''''''''''''''''''''')))(((((('''&&&&&&%%%%%%$$$$$$%%%&&&'''''''''''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%}}}sssiiibbbbbbeeeiiillljjjbbb[[[WWWRRRLLLGGGMMMXXXhhhvvv}}}~~~||||||zzzwwwtttooofffZZZQQQAAA<<<666111/////////...000000000///...---,,,+++,,,,,,,,,---------......,,,+++++++++************)))))))))*********++++++++++++***))))))(((''''''))))))))))))************((((((((()))))))))************))))))((((((''''''((((((((((((''''''''''''''''''(((((((((((())))))((((((''''''''''''((((((&&&''''''(((((((((((((((''''''''''''(((((((((((('''''''''(((((((((((()))'''(((((((((((('''&&&&&&%%%%%%%%%&&&'''''''''(((&&&'''((()))((('''&&&%%%&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((()))))))))))))))(((((((((((((((((((((''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%###$$$$$$%%%&&&'''''''''%%%%%%&&&'''''''''''''''&&&'''(((((())))))))))))'''''''''(((''''''&&&%%%(((((((((''''''''''''&&&'''&&&$$$!!! """%%%)))&&&&&&&&&'''''''''''''''''''''''''''''''''''''''((('''&&&%%%%%%&&&'''((('''''''''((((((''''''''')))))))))(((''''''&&&&&&&&&&&&%%%%%%&&&'''(((((()))(((%%%######%%%((()))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''((('''&&&%%%&&&&&&''''''''''''((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&%%%((('''&&&&&&&&&&&&&&&'''&&&%%%%%%'''***,,,,,,,,,***))))))((('''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&''''''(((&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%&&&&&&%%%$$$###&&&&&&&&&&&&%%%%%%%%%%%%+++***((('''%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%&&&''''''''''''&&&''''''''''''''''''''''''((((((((('''&&&&&&%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''&&&&&&&&&zzzkkk```___bbbdddkkkooojjjbbb[[[UUUOOOFFFIIIQQQ```ppp{{{}}}||||||zzzxxxvvvrrrkkk```XXXFFFAAA999333000/////////000000000//////...,,,,,,------------.........///,,,,,,+++++++++*********))))))*********+++++++++*********)))))))))((((((((()))))))))************(((((()))))))))*********))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((())))))(((((((((''''''(((((((((%%%&&&((()))))))))((('''''''''''''''((((((((((((&&&&&&&&&'''''''''((((((((((((((((((((('''&&&&&&$$$%%%%%%&&&'''(((((()))(((((())))))((('''&&&%%%%%%&&&&&&&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((())))))******))))))))))))((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%&&&&&&''''''(((((((((((('''&&&%%%$$$%%%&&&&&&'''((((((''''''&&&'''''''''''''''&&&&&&(((((((((''''''''''''''')))((('''%%%$$$%%%(((+++''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&))))))((((((''''''''''''%%%%%%%%%%%%&&&'''(((((()))'''%%%######%%%''')))%%%%%%%%%%%%%%%&&&&&&&&&%%%&&&((())))))'''%%%$$$&&&&&&&&&&&&''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((&&&&&&&&&''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%'''&&&&&&&&&&&&%%%%%%%%%)))((('''&&&&&&&&&&&&&&&&&&%%%%%%''')))++++++******))))))(((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&'''((('''&&&%%%%%%&&&'''(((&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%)))((('''&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''((((((&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%&&&&&&'''''''''''''''''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&''''''''''''}}}mmm___[[[^^^___hhhnnnlllfff```YYYSSSKKKKKKOOO[[[jjjvvv||||||~~~{{{yyywwwtttnnnddd]]]LLLEEE<<<555111000000111000000000000///...------------........./////////,,,,,,,,,++++++++++++***************++++++++++++((()))))))))*********+++((()))))))))************))))))))))))************(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))(((((('''(((((((((((((((((('''%%%&&&((()))))))))((('''''''''''''''((((((((((((&&&&&&&&&&&&''''''''''''(((((())))))(((((('''&&&%%%%%%&&&&&&'''((()))))))))))))))(((((('''&&&&&&%%%&&&&&&&&&'''(((((((((''''''''''''''''''''''''''''''(((((()))******+++***)))))))))((((((((('''&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((('''&&&%%%%%%%%%&&&''''''''''''''''''&&&&&&'''''''''''''''&&&((((((((((((((((((((((((''')))***)))((('''(((***'''''''''''''''''''''&&&((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&((((((((((((''''''''''''%%%%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&'''''''''(((%%%&&&((())))))(((&&&$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((!!!"""""""""######$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%$$$$$$$$$%%%&&&%%%%%%&&&(((***)))((()))))))))(((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&''''''&&&%%%$$$$$$%%%&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$###!!!!!!###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''''''''&&&&&&%%%%%%&&&&&&'''%%%&&&''''''((((((''''''(((((((((((((((((((((((('''''''''''''''&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%$$$%%%&&&'''''''''&&&&&&$$$$$$%%%&&&''''''''''''qqqaaaZZZZZZ]]]dddjjjiiigggddd___YYYSSSPPPQQQWWWbbboooxxx}}}~~~|||zzzyyyvvvqqqhhhaaaUUUMMMBBB999333222222222000000000000000///...------------.........//////,,,,,,,,,,,,++++++++++++*********++++++++++++,,,(((((())))))***++++++,,,))))))))))))************)))))))))*********++++++''''''(((((())))))******))))))))))))******************))))))))))))((((((''''''((((((((((((''''''&&&''''''(((((((((((((((''''''''''''((((((((((((&&&&&&&&&''''''''''''(((((())))))))))))(((''''''&&&&&&&&&'''((((((((()))))))))((((((((((((((((((&&&&&&&&&'''''''''''''''((((((((((((((((((((((((&&&&&&'''((()))***++++++******))))))((((((''''''&&&&&&&&&&&&&&&'''''''''%%%%%%%%%&&&&&&&&&&&&'''((((((((('''''''''''''''$$$%%%&&&'''((()))))))))'''(((((()))))))))((((((%%%&&&''''''(((''''''''''''(((((((((((()))))))))%%%'''))))))(((&&&'''''''''''''''''''''&&&&&&&&&(((((((((((((((((((((((('''''''''''''''''''''''''''''''''(((((('''''''''((((((((((((((((((''''''&&&&&&%%%%%%%%%%%%&&&&&&$$$%%%&&&''''''&&&%%%$$$%%%&&&&&&''''''(((((((((&&&&&&(((((()))((('''&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((###$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&'''$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%$$$$$$$$$$$$$$$$$$&&&%%%%%%&&&((()))((('''((((((((('''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$"""  """$$$$$$$$$$$$$$$%%%%%%%%%%%%""""""""""""###$$$%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&'''(((((((((((('''((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%&&&&&&'''&&&&&&&&&###$$$&&&'''(((''''''&&&%%%%%%&&&&&&'''&&&&&&&&&yyyjjj___\\\]]]aaadddeeehhhiiifff```ZZZVVVSSSTTT[[[gggsss|||~~~|||zzzzzzyyyuuummmgggaaaXXXJJJ>>>777333222222///000000000000///......,,,,,,---------.........------,,,,,,,,,+++++++++*********+++++++++,,,,,,************************))))))))))))************))))))*********+++++++++))))))))))))((((((((((((((((((((()))))))))***************)))))))))((((((&&&'''((())))))((('''&&&'''''''''''''''((())))))''''''''''''((((((((((((&&&''''''''''''((((((((()))))))))))))))(((''''''''''''''''''(((((((((((((((((((((((((((((())))))'''''''''''''''&&&&&&&&&''''''''''''''''''''''''%%%&&&&&&''')))******+++*********)))((('''''''''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''''''''(((((())))))******$$$%%%&&&((())))))******''''''((((((((((((''''''%%%&&&&&&'''(((((('''''''''((((((((())))))))))))''''''((('''%%%%%%''')))(((((('''''''''&&&&&&&&&((((((((((((((((((((((((''''''(((((((((((('''''''''(((((())))))((((((''''''(((((((((((((((((((((''''''&&&%%%$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%&&&&&&'''((((((&&&&&&''''''(((((())))))''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''((()))(((((((((((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%###$$$$$$%%%&&&'''(((((($$$$$$$$$$$$$$$$$$%%%&&&'''%%%%%%%%%'''((('''&&&'''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$######&&&%%%%%%$$$$$$%%%%%%&&&$$$###"""!!!!!!"""###$$$######$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&'''(((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''$$$$$$%%%&&&''''''''''''"""$$$&&&'''(((((('''&&&&&&&&&&&&'''&&&&&&%%%%%%rrrfffaaa]]]```aaaccchhhmmmjjjeee^^^ZZZUUURRRUUUaaappp{{{}}}|||{{{{{{{{{xxxrrrllliii___PPPBBB999444222222///000000000000//////...,,,,,,,,,---------......---------,,,,,,,,,++++++******+++++++++,,,,,,,,,,,,,,,++++++***)))))))))))))))))))))************)))************+++++++++++++++***)))((('''&&&&&&&&&'''''''''(((((())))))+++*********))))))((((((&&&'''((())))))((('''&&&(((((('''&&&&&&((()))***''''''''''''((((((((()))'''''''''(((((((((((())))))))))))))))))(((((('''((((((((((((((('''''''''(((((('''(((((()))***+++(((((((((''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''((()))******+++******)))(((''''''&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&'''''''''&&&&&&''')))***,,,------(((((((((((((((((('''&&&$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''(((((((((''''''((((((((())))))*********)))(((%%%$$$%%%))),,,(((((('''''''''&&&&&&&&&))))))))))))))))))))))))''''''((((((((((((''''''(((((())))))))))))(((((('''''''''(((((((((((((((((('''&&&%%%$$$#########%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''&&&&&&&&&&&&''')))***+++(((((('''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((((((((''''''&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((%%%%%%%%%&&&&&&'''''''''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%"""###$$$%%%'''((())))))$$$$$$$$$$$$%%%%%%&&&''''''&&&%%%%%%''''''&&&%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%''''''''''''%%%$$$%%%%%%&&&'''&&&%%%###"""&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&''''''''''''&&&%%%#########$$$$$$%%%%%%%%%'''&&&&&&%%%$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''&&&&&&%%%''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&''''''''''''&&&&&&&&&&&&''''''&&&''''''((((((((((((((())))))))))))))))))))))))&&&'''''''''''''''''''''###$$$%%%&&&''''''((('''"""###&&&((((((((('''&&&''''''''''''&&&%%%$$$$$$}}}lllddd^^^XXXWWW^^^dddggghhhjjjaaa___[[[VVVWWW___lllvvv|||zzzyyyyyyzzzxxxsssnnnmmmiii```PPP@@@555111111333222000000111111000............///////////////************************************************************************''''''(((((())))))******(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))(((((('''''''''&&&((((((((((((((((((((((((''''''''''''''''''''''''))))))))))))))))))))))))''''''''''''((((((((((((((((((((((((((((((((((((***************)))))))))''''''''''''''''''''''''''''''((((((((((((''''''(((((((((((((((((((((((()))(((((('''&&&%%%%%%$$$***))))))((((((((())))))!!!'''***)))'''$$$''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((''''''''''''((((((((((((+++***)))((((((''''''((())))))(((((('''''''''&&&+++)))'''(((+++,,,***(((%%%%%%&&&&&&'''(((((((((******))))))((((((''''''''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&'''((()))******)))((('''(((((('''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''((((((''''''''''''((((((''''''&&&%%%&&&'''((()))'''((()))(((&&&%%%%%%'''))),,,///---(((%%%%%%(((%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''(((''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''###$$$%%%%%%&&&&&&&&&&&&$$$$$$###"""###$$$&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&''''''&&&"""!!!%%%''''''&&&%%%%%%$$$######'''''''''&&&&&&%%%%%%%%%$$$%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''((()))(((&&&%%%%%%'''(((((('''''''''&&&&&&&&&&&&&&&&&&'''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''###$$$%%%&&&''''''''''''###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''wwwlll___ZZZXXX\\\aaacccgggkkkiiieee```ZZZZZZ```kkksss|||zzzxxxyyyyyyxxxtttqqqoookkkcccUUUFFF:::444333222000//////000000///---........................------------------------************************************************))))))))))))************************************)))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((''''''((((((((((((((((((((((((''''''''''''''''''''''''))))))))))))))))))))))))''''''''''''((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((''''''((((((((((((''''''((((((((((((((((((((((((,,,,,,++++++***))))))((()))((((((''''''(((((()))%%%&&&'''))))))(((&&&%%%''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((''''''''''''(((((((((((()))((((((((((((((()))))))))(((((((((''''''''''''***(((&&&''')))***)))'''((((((''''''''''''''''''))))))))))))((((((''''''''''''''''''''''''''''''&&&''''''((((((''''''&&&'''((()))******)))((('''(((((('''''''''&&&&&&&&&((((((''''''''''''((((((&&&''''''((((((''''''&&&%%%%%%&&&&&&&&&''''''''''''''''''((((((''''''''''''&&&&&&%%%&&&'''((()))'''((()))(((&&&%%%&&&''''''+++...,,,(((%%%&&&(((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''(((''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%&&&&&&&&&%%%%%%&&&&&&%%%$$$############''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%&&&&&&&&&'''%%%%%%$$$###"""###&&&((('''&&&&&&%%%%%%$$$$$$$$$''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%'''((()))(((&&&%%%&&&'''(((((('''''''''&&&&&&&&&&&&&&&&&&'''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''###$$$%%%&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''pppbbb]]]YYY[[[]]]```fffmmmpppkkkddd``````fffnnnsss{{{yyyxxxxxxyyyyyywwwvvvrrrooohhh]]]OOOBBB999444222000//////000111000/////////......------,,,,,,++++++++++++++++++++++++************************************************++++++++++++************************************))))))))))))))))))))))))))))))))))))))))))))))))***)))))))))))))))((((((((((((((((((((((((((((((''''''''''''''''''''''''))))))))))))))))))))))))''''''''''''((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))''''''((((((((((((''''''(((((((((((((((((((((((())))))(((((('''&&&&&&&&&((('''''''''''''''((((((---,,,***(((''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((''''''''''''((((((((((((''''''''''''((()))***+++((((((((((((''''''''''''((('''&&&&&&(((((('''&&&******)))(((((('''&&&&&&)))))))))(((((((((((('''''''''''''''''''''''''''&&&''''''((((((''''''&&&'''(((((())))))((((((''''''''''''''''''&&&&&&&&&((((((''''''''''''(((((('''(((((((((((((((((('''%%%&&&&&&&&&&&&'''''''''&&&'''((())))))((('''&&&'''&&&&&&&&&&&&'''(((((('''((()))(((&&&&&&&&&'''&&&)))+++***'''%%%&&&((()))(((''''''''''''((()))%%%%%%%%%&&&&&&&&&''''''(((''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%$$$$$$'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&%%%$$$%%%&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&'''((()))***+++%%%%%%%%%%%%%%%%%%%%%%%%&&&(((((((((&&&%%%&&&''''''''''''''''''&&&&&&&&&&&&&&&'''''''''(((((((((((((((((((((((((((((((((''''''''''''''''''''''''$$$%%%&&&'''''''''''''''))))))(((((('''&&&&&&%%%%%%&&&&&&&&&&&&'''''''''vvvggg```[[[ZZZ[[[___hhhqqqrrrnnnhhheeeffflllssswwwzzzyyyxxxxxxyyyzzzzzzzzzuuusssmmmeeeXXXJJJ<<<444444222000000111222222111//////...---,,,+++++++++************************************************************************+++++++++******)))))))))************************((((((((((((((((((((((((((((((((((((((((((((((((************))))))))))))((((((((((((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((('''''''''(((((((((((((((((((((((((((((((((((((((''''''((((((((((((''''''((((((((((((((((((((((((&&&%%%%%%%%%$$$$$$######'''&&&&&&&&&&&&''''''((()))(((&&&%%%%%%'''((()))''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((''''''''''''(((((((((((('''''''''''''''((()))***((((((((((((((('''''''''(((''''''''''''(((''''''******))))))((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''''''''((((((((((((''''''(((((((((((((((((((((((('''''''''''''''''''''''''''''''''&&&&&&'''''''''''''''((((((((((((''''''&&&&&&&&&&&&''''''''''''%%%&&&((())))))(((&&&%%%&&&&&&&&&&&&''''''(((((('''((()))((('''&&&'''(((%%%'''((((((&&&%%%'''((()))(((&&&%%%%%%&&&((()))%%%%%%%%%&&&&&&&&&''''''(((''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&'''''''''&&&%%%$$$$$$!!!###&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''***)))((('''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((&&&%%%&&&((('''$$$ %%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$###$$$%%%&&&'''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%&&&&&&'''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''&&&%%%&&&(((''''''''''''''''''''''''''''''''''''(((((((((((())))))))))))))))))))))))''''''''''''''''''''''''%%%%%%&&&'''''''''''''''((((((((('''''''''&&&&&&&&&&&&&&&&&&''''''''''''yyymmmddd[[[XXXYYY^^^gggpppssspppllliiiiiimmmsssvvvyyyyyyyyyyyyzzz{{{|||~~~xxxvvvqqqkkkaaaRRRAAA666555333000///000111000000//////...---,,,+++++++++------------------------*********************************************************))))))(((((('''))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))************((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((''''''''''''(((((())))))''''''''''''''''''''''''''''''((((((((((((''''''(((((((((((((((((((((((()))))))))))))))(((((((((&&&&&&&&&&&&&&&'''(((((($$$$$$%%%&&&'''(((((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((''''''''''''(((((((((((())))))(((''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((())))))******'''''''''''''''((((((((((((((((((((((((((((((((('''(((((((((((((((((('''((((((''''''''''''((((((&&&'''''''''''''''''''''))))))(((((((((((())))))%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&'''''''''(((((($$$&&&'''))))))'''&&&$$$&&&&&&&&&''''''''''''''''''((()))(((''''''((()))%%%&&&'''&&&&&&&&&'''(((((('''%%%$$$$$$%%%'''(((%%%%%%%%%&&&&&&&&&''''''(((''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&&&&%%%$$$ !!!$$$&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''***)))((('''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&%%%$$$%%%''''''###&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%'''((('''&&&&&&'''(((&&&''''''''''''''''''''''''''''''((((((((())))))))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&''''''((((((''''''%%%%%%&&&&&&''''''''''''&&&&&&&&&'''''''''((((((sssttt{{{xxxkkk]]]YYYZZZ^^^eeekkkssssssqqqlllhhhiiinnnsssxxxyyy{{{|||{{{|||}}}yyywwwssspppjjj\\\JJJ===666333000............---//////......------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,************************************************)))))))))((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))(((((()))))))))))))))***(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))''''''''''''((((((((((((((((((((((((((((((((((((%%%%%%%%%&&&''''''((((((''''''''''''''''''''''''''''''((((((((((((''''''((((((((((((((((((((((((************************&&&&&&&&&&&&'''((())))))&&&'''((())))))((('''&&&((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((''''''''''''((((((((((((***)))((('''&&&&&&&&&&&&'''''''''((((((((((((((('''((())))))''''''((()))&&&&&&'''(((((()))******&&&''''''''''''((((((((((((((((((((((((((((((((('''(((((())))))(((((('''(((''''''&&&&&&''''''(((&&&&&&&&&'''''''''''''''++++++************++++++%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&'''''''''(((((((((%%%&&&'''(((((('''&&&%%%%%%&&&''''''((((((''''''&&&((())))))((('''(((***''''''&&&&&&&&&''''''((('''&&&%%%$$$$$$%%%&&&'''%%%%%%%%%&&&&&&&&&''''''(((''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&''''''''''''''''''''''''''')))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&""""""###%%%''''''&&&%%%'''''''''&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''$$$%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%&&&&&&&&&''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&((('''&&&&&&'''(((&&&&&&&&&'''''''''''''''''''''((((((((()))))))))((((((((((((((((((((((((''''''''''''''''''''''''&&&''''''(((((((((''''''$$$%%%%%%&&&''''''((((((&&&&&&'''''''''(((((((((sssqqqssswww~~~xxxfff___```ccceeehhhnnnqqqrrrmmmfffeeekkkrrrwwwzzz}}}~~~}}}|||}}}xxxuuuttttttrrrgggUUUGGG;;;777333000/////////...........................))))))))))))))))))))))))************************************************))))))))))))))))))******))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))''''''((((((((()))))))))(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))''''''''''''((((((((((((((((((((((((((((((((((((%%%%%%&&&''''''((())))))''''''''''''''''''''''''''''''((((((((((((''''''((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''((()))***+++(((((())))))(((((('''&&&((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((''''''''''''(((((((((((((((''''''&&&&&&&&&''''''''''''''''''((((((((()))&&&''')))(((&&&%%%''')))''''''''''''''''''((((((&&&&&&&&&'''''''''(((((((((((((((((((((((((((((((((((())))))))))))((((((((('''&&&&&&&&&&&&'''(((&&&&&&&&&'''''''''((((((***))))))))))))))))))***&&&&&&''''''''''''&&&&&&''''''''''''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''((((((((('''&&&&&&((())))))(((((()))***)))(((&&&&&&&&&'''((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''(((''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&''''''''''''''''''((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''(((''''''&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$!!!###%%%&&&&&&&&&''')))((((((''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%((()))***((('''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&'''((())))))&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''%%%&&&''''''&&&&&&''')))&&&&&&&&&'''''''''(((((('''((((((((())))))))))))''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((''''''''''''''''''''''''((((((''''''''''''((((((((((((uuussssssqqqpppzzzoooggghhhiiihhhhhhgggmmmqqqmmmeeedddllluuuvvvzzz~~~~~~}}}}}}~~~vvvttttttvvvwwwnnn]]]OOO@@@<<<777444333222222111.........///////////////,,,,,,,,,,,,,,,,,,,,,,,,************************************************))))))******+++++++++,,,************************))))))))))))))))))))))))))))))))))))))))))))))))&&&'''''''''(((((())))))(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))''''''''''''((((((((()))((((((((((((((((((((((((((((((((()))***++++++,,,))))))))))))))))))))))))''''''((((((((((((''''''(((((((((((((((((((((((('''''''''''''''''''''''''''''''''((((((***++++++'''&&&%%%%%%&&&'''((()))))))))))))))))))))))))))''''''''''''((((((((()))((((((((((((((((((((((((''''''''''''((((((((()))&&&&&&&&&&&&&&&'''((()))&&&'''''''''(((((())))))$$$&&&((('''%%%$$$%%%(((((((((((('''&&&&&&%%%%%%&&&&&&&&&'''''''''(((((())))))))))))))))))))))))(((((())))))))))))((((((((('''&&&%%%%%%&&&'''(((&&&&&&&&&'''''''''((((((&&&&&&%%%%%%%%%%%%&&&&&&''''''((((((((((((''''''''''''''''''((((((((()))'''&&&&&&%%%%%%&&&&&&'''%%%%%%'''((((((((('''&&&&&&((())))))(((((()))++++++)))'''&&&'''(((((('''''''''((())))))(((''''''%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&'''((((((((('''&&&%%%%%%$$$%%%&&&((()))%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''((((((((((((((((((((((((''''''&&&&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%(((***(((%%%$$$&&&((())))))((('''&&&%%%%%%%%%%%%%%%%%%&&&&&&'''''''''###&&&)))++++++***'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''###$$$%%%&&&''')))******'''''''''&&&&&&%%%%%%%%%%%%&&&&&&'''((()))******''''''''''''''''''''''''%%%&&&''''''&&&&&&((()))&&&&&&&&&'''''''''(((((((((((((((((())))))))))))'''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((''''''******))))))((((((''''''''''''''''''((((((((()))xxxqqqqqqpppsss~~~kkkfffhhhgggccceeeiiimmmmmmjjjhhhjjjlllssswww{{{}}}|||{{{{{{{{{{{{}}}}}}{{{yyytttgggZZZHHH@@@666111111111000...000000000000///...,,,+++,,,---------,,,,,,+++***++++++++++++++++++++++++(((((((((((((((((((((((())))))))))))(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))******))))))((((((''''''******++++++++++++******$$$$$$&&&((()))*********))))))(((((((((((())))))'''&&&%%%$$$$$$%%%&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&'''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''((()))++++++)))((('''&&&&&&&&&&&&&&&(((''''''''''''&&&&&&&&&&&&&&&''')))******(((%%%''''''&&&%%%$$$######"""((((((''''''''''''(((((()))((()))+++------+++))))))))))))))))))))))))))))))(((((((((''''''''''''''''''''''''''''''''''''(((***+++***)))((()))***))))))(((((('''''''''&&&''''''''''''((((((((()))))))))************))))))))))))))))))))))))))))))+++***)))((((((((((((((()))))))))(((''''''&&&&&&''''''&&&&&&'''(((***+++&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%''')))+++---)))))))))(((''''''&&&&&&(((''''''((())))))(((&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$&&&(((((('''&&&'''(((((((((''''''''''''((((((((('''&&&%%%%%%&&&'''(((%%%&&&'''((()))((('''&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&((((((((((((((((((((((((''''''&&&''''''((()))***''''''''''''''''''''''''$$$$$$%%%%%%&&&'''(((((())))))((('''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$***)))((('''&&&%%%$$$$$$(((''''''&&&&&&''''''(((%%%&&&'''(((((('''&&&%%%&&&'''''''''((()))))))))$$$%%%'''))))))((('''&&&((((((((((((((((((((((((%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&''''''''''''&&&%%%%%%%%%%%%&&&'''))))))))))))************+++*********))))))((((((''''''''''''''''''''''''***))))))((('''&&&&&&&&&((('''%%%$$$######$$$%%%''''''''''''''''''''''''wwwvvvsssqqq{{{rrrgggfffggggggeeeiiimmmnnnmmmkkkjjjjjjqqquuuyyy{{{|||{{{{{{|||{{{}}}|||{{{zzzwwwlllaaaPPPGGG;;;444222222111////////////...---------,,,,,,,,,---------,,,,,,+++++++++++++++++++++++++++))))))))))))))))))))))))***)))))))))(((((((((((()))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((''''''''''''''''''((((((((((((''''''%%%%%%'''((())))))******))))))(((((((((((())))))+++***)))''''''''''''(((((((((((('''''''''&&&&&&&&&''''''((((((''''''&&&&&&&&&'''''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((()))***+++,,,(((''''''''''''''''''((())))))((((((((('''''''''&&&&&&''')))******(((&&&((((((((('''&&&&&&%%%%%%((((((''''''''''''((((((((((((((()))++++++)))'''))))))))))))))))))))))))))))))((((((((('''''''''))))))))))))))))))))))))((()))******)))((()))***)))))))))((((((((('''''''''''''''((((((((())))))))))))************))))))))))))))))))))))))))))))((('''&&&%%%%%%%%%%%%%%%''''''((((((((((((((((((***)))(((''''''(((((()))((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''')))***+++''''''((((((((()))))))))((('''''''''))))))'''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&(((((('''&&&'''(((&&&&&&%%%%%%%%%%%%&&&&&&((('''&&&&&&&&&&&&'''(((%%%%%%&&&'''''''''''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&&&&'''''''''''''''''''''''')))((('''''''''''''''(((''''''''''''''''''''''''$$$$$$%%%%%%&&&''''''((()))(((((('''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&%%%%%%%%%$$$''''''''''''''''''''''''%%%$$$$$$######$$$$$$%%%&&&&&&''''''''''''&&&&&&''''''''''''''''''(((((($$$%%%'''((()))((('''&&&((((((((((((((((((((((((&&&&&&&&&'''''''''(((((((((''''''''''''''''''&&&''''''%%%%%%%%%%%%''''''''''''''''''((((((((((((************)))))))))(((''''''''''''''''''''''''&&&&&&''''''((()))))))))'''&&&&&&&&&'''((())))))((((((((((((((((((((((((}}}yyyuuuvvv}}}~~~mmmfffhhhmmmjjjkkknnnoooooommmjjjiiinnnrrrvvvyyyzzz{{{|||}}}|||~~~}}}||||||{{{tttkkk\\\RRRCCC888333222111111///...---,,,,,,---...///+++,,,,,,---------,,,,,,++++++++++++++++++++++++******************************)))))))))((((((((())))))))))))))))))))))))))))))))))))))))))))))))((((((''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&'''(((((()))))))))((())))))(((((((((((())))))+++***)))(((((((((((())))))))))))(((((((((((((((&&&''''''((((((''''''&&&''''''((((((((()))))))))(((((((((((((((((((((((())))))))))))))))))))))))''''''''''''''''''''''''))))))))))))***+++,,,,,,''''''''''''((((((((((((***)))))))))((((((((((((&&&&&&'''(((******(((&&&))))))))))))))))))(((((()))((((((''''''(((((())))))((('''((())))))'''&&&)))))))))))))))))))))))))))))))))(((((((((''''''************************((()))******(((((()))******)))))))))))))))((((((''''''((((((((()))))))))))))))************))))))((((((((((((((((((((((((***)))((((((((((((((((((&&&&&&'''(((((()))******+++***)))(((''''''''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((((((((((((((($$$$$$%%%&&&'''((()))***((('''&&&'''))))))'''&&&$$$%%%%%%&&&&&&'''''''''$$$&&&(((((('''&&&'''(((&&&&&&%%%%%%%%%%%%&&&&&&((('''&&&&&&&&&&&&'''(((&&&%%%%%%%%%%%%&&&'''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%$$$$$$&&&&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''***)))((('''&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%%%%&&&&&&'''''''''((((((((('''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&$$$%%%%%%&&&'''((())))))''''''&&&&&&&&&&&&'''''''''''''''&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&$$$%%%'''((((((((('''&&&(((((((((((((((((((((((('''''''''((((((((())))))***))))))(((''''''&&&&&&((('''&&&%%%%%%&&&'''(((''''''''''''((((((((((((************))))))))))))''''''''''''''''''''''''&&&&&&'''(((((()))******''''''(((((((((((((((((())))))))))))))))))))))))|||yyyzzz{{{xxxkkkjjjppptttsssrrrqqqooommmkkkiiillloootttwwwyyy{{{}}}}}}}}}~~~yyyssshhh]]]LLL===555222111111000...---,,,---...000222+++,,,------------------***+++++++++++++++,,,,,,++++++++++++++++++++++++*********)))))))))(((((())))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((('''((())))))******))))))((((((((()))))))))(((((('''))))))(((((((((((())))))''''''''''''(((((())))))((((((((((((((((((((((((''''''((((((((((((''''''(((((((((((())))))))))))((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''))))))(((((()))******+++(((((((((((((((((('''''')))))))))((((((((('''''''''&&&&&&((()))***((('''((((((((())))))*********))))))(((((((((((())))))***)))(((((())))))'''%%%(((((((((((((((((((((((()))))))))(((((((((((('''((((((((((((((((((((((((((()))***)))((('''(((***************))))))))))))'''(((((((((((()))))))))))))))************))))))((((((((((((((((((((((((+++******))))))*********''''''(((((()))))))))))))))(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&'''((((((((('''&&&%%%"""######$$$%%%&&&'''((('''&&&&&&'''(((((('''%%%$$$$$$%%%%%%&&&'''(((((($$$&&&(((((('''&&&'''(((((((((''''''''''''(((((('''''''''&&&&&&'''''''''&&&%%%$$$$$$$$$%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%$$$$$$######&&&&&&%%%%%%%%%&&&'''''''''''''''''''''''''''''')))((('''&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%%%%&&&'''((())))))((((((''''''''''''((((((((('''&&&%%%%%%&&&'''((('''''''''&&&%%%%%%%%%$$$%%%&&&''''''((((((''''''((((((((((((((((((((((((&&&'''''''''((((((((((((((((((((('''''''''''''''((('''&&&%%%%%%&&&'''((())))))))))))*********************)))))))))))))))''''''''''''''''''''''''))))))))))))((((((''''''(((((()))((('''%%%###!!!))))))))))))))))))))))))}}}zzzyyyyyy}}}uuuooorrr}}}xxxsssnnnllllllllljjjmmmrrrvvvxxx{{{~~~~~~|||wwwqqqfffUUUDDD999333111111111000///...///000333444,,,------......---------*********++++++,,,,,,,,,++++++++++++++++++++++++************)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))******++++++******)))))))))))))))))))))((('''))))))(((((((((((())))))(((((((((((((((''''''''''''''''''''''''''''''''''''(((((((((((((((((('''(((((((((((())))))))))))))))))))))))))))))))))))((((((((((((((((((((((((''''''''''''''''''''''''(((''''''''''''((())))))))))))))))))((('''%%%$$$((((((((('''''''''&&&&&&'''&&&&&&'''))))))(((''''''''''''(((((()))******))))))(((((((((((()))))),,,***(((((())))))((('''((((((((((((((((((((((((***)))))))))((((((((((((((((((((((((((((((((((((''')))***)))((('''((()))))))))))))))************(((((((((((()))))))))***))))))************))))))(((((((((((((((((((((((('''''''''&&&&&&'''((((((******))))))((((((((((((%%%%%%&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&'''((((((((('''%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&'''(((((('''%%%$$$$$$%%%%%%&&&'''(((((($$$&&&(((((('''&&&'''(((((((((''''''''''''((((((&&&''''''''''''''''''&&&'''&&&%%%$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%$$$$$$######%%%%%%%%%%%%%%%&&&'''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&'''((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&'''''''''''''''''''''%%%%%%$$$$$$$$$$$$%%%%%%((('''&&&%%%%%%&&&'''((('''''''''&&&%%%%%%%%%$$$%%%&&&&&&'''''''''''''''((((((((((((((((((((((((%%%%%%&&&&&&&&&'''''''''$$$$$$%%%&&&''''''((((((((('''&&&&&&&&&&&&'''((())))))))))))************))))))))))))))))))******(((((((((((((((((((((((()))))))))))))))(((((((((((()))))))))(((&&&$$$###((((((((((((((((((((((((}}}zzzvvvtttwwwxxxwww~~~vvvnnnjjjkkknnnjjjmmmqqquuuxxx{{{~~~}}}yyyvvvmmm]]]MMM???666222111222111000000111222333444...............---,,,,,,*********++++++,,,,,,---++++++++++++++++++++++++++++++*********)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************++++++(((((())))))))))))(((((()))))))))******)))(((((())))))(((((((((((()))))),,,,,,++++++)))'''&&&%%%&&&&&&''''''''''''(((((('''(((((())))))(((((('''''''''((((((((()))))))))))))))))))))))))))))))))))))))))))))))))))))))))'''''''''''''''''''''''''''''''''&&&&&&''''''((('''((((((((((((&&&%%%###''''''''''''&&&&&&&&&&&&((('''&&&'''((())))))(((&&&&&&''''''(((((())))))***))))))(((((())))))***+++***(((((()))***)))((())))))))))))))))))))))))******)))))))))(((((((((************************'''((())))))''''''((()))(((((()))))))))))))))***((((((((()))))))))******))))))************))))))(((((((((((((((((((((((()))(((((((((((())))))***++++++***))))))(((''''''$$$$$$%%%''''''(((((('''))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&'''''''''&&&&&&%%%,,,,,,+++***))))))(((((('''&&&%%%&&&((((((&&&%%%$$$%%%%%%&&&&&&'''''''''$$$&&&(((((('''&&&'''(((&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''(((((('''&&&&&&'''&&&&&&&&&&&&'''((((((%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''((()))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((('''&&&&&&&&&%%%&&&&&&%%%%%%%%%%%%&&&&&&'''''''''&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((((((((((((((((((((%%%%%%%%%&&&&&&&&&&&&'''"""###$$$%%%&&&((()))))))))((('''&&&&&&'''((()))''''''''''''(((((((((((())))))))))))************((((((((((((((((((((((((&&&&&&'''(((***+++,,,,,,'''((()))***++++++++++++((((((((((((((((((((((((~~~yyyuuutttxxx}}}}}}zzzoooiiijjjnnnkkknnnrrruuuxxx{{{~~~{{{yyyrrreeeUUUFFF;;;555222111111111111111111222222////////////...,,,+++***)))******+++,,,,,,------+++++++++++++++++++++++++++++++++*********))))))))))))))))))))))))))))))))))))))))))))))))))))))((()))))))))************''''''((((((((((((''''''((())))))*********))))))))))))(((((((((((())))))(((((()))))))))(((''''''''''''((((((((()))))))))(((((())))))))))))((((((&&&&&&'''''''''((((((((((((((((((((((((((((((((())))))))))))))))))))))))((((((((((((((((((((((((((((((''''''''''''((((((###$$$&&&'''((('''&&&%%%((((((((((((''''''''''''((('''&&&&&&((())))))((('''''''''(((((((((((((((******))))))))))))*********(((&&&&&&((()))))))))))))))))))))))))))))))))*********)))))))))(((((())))))))))))))))))))))))'''((()))(((''''''((()))''''''((((((((()))))))))(((((()))))))))*********))))))************))))))))))))))))))))))))))))))++++++******++++++,,,---******))))))))))))))))))&&&'''((()))))))))((('''))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&&&&%%%%%%&&&'''''',,,,,,+++******)))((((((&&&&&&%%%&&&''''''&&&$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&(((((('''&&&'''(((&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''(((((('''&&&&&&&&&'''(((((())))))((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%&&&&&&&&&&&&(((((('''''''''&&&&&&&&&(((((((((''''''(((((((((&&&&&&''''''''''''&&&&&&''''''''''''''''''((((((&&&&&&&&&&&&&&&'''((((((((((((((((((((((((((((((&&&&&&&&&&&&''''''''''''$$$%%%%%%&&&'''(((((())))))((('''&&&&&&'''((()))''''''''''''((((((((((((((()))))))))************((((((((((((((((((((((((&&&&&&''')))***+++,,,---'''(((((()))***,,,---...)))))))))))))))))))))))){{{wwwuuu~~~vvv}}}}}}qqqiiiiiimmmkkknnnrrruuuxxx{{{}}}|||{{{uuujjj[[[KKK>>>777333000000111111111111000///111000000///...,,,+++***))))))***+++,,,,,,------************************+++++++++************)))))))))))))))))))))))))))))))))))))))))))))))))))'''((((((((())))))******(((((())))))))))))(((((((((((()))***************))))))(((((((((((()))))) ###&&&(((*********(((((())))))*********+++(((((())))))))))))((((((&&&&&&&&&&&&'''''''''((((((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))***)))(((((((((((())))))!!!###&&&((((((((('''))))))))))))(((((((((((()))'''&&&&&&((())))))((()))))))))(((((((((((((((******))))))))))))******(((&&&$$$$$$&&&((()))((())))))))))))))))))))))))************))))))))))))'''''''''''''''''''''''''''((()))((('''&&&''')))&&&'''''''''(((((())))))))))))))))))************))))))************))))))************************((((((''''''((()))******((((((((()))******++++++******+++++++++)))((('''((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&%%%$$$%%%&&&'''((()))(((((((((''''''''''''&&&%%%%%%&&&''''''&&&$$$&&&&&&&&&&&&&&&&&&%%%%%%$$$&&&(((((('''&&&'''((((((((((((''''''(((((((((%%%&&&'''(((((('''&&&%%%&&&''')))*********)))(((%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''$$$$$$$$$%%%&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&'''(((((('''&&&%%%&&&'''''''''((()))))))))'''&&&&&&&&&&&&'''((((((((((((((((((((((((((((((''''''''''''((((((((()))'''''''''((((((((((((((()))((('''&&&&&&'''((()))))))))))))))************(((((())))))*********+++)))))))))))))))))))))))))))))))))))))))*********)))((('''''''''(((***+++************************zzzyyy{{{wwwxxx{{{ssseeedddlllnnnpppooommmrrr{{{}}}zzz|||~~~}}}zzzvvvrrrkkkZZZEEE888777222000//////000000///---/////////...---------,,,............------,,,+++++++++++++++++++++++++++************))))))))))))))))))))))))))))))))))))************))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))************))))))((((((((((((((((((((((((''''''''''''((((((((()))))))))))))))))))))))))))))))))************))))))))))))))))))))))))))))))))))))))))))))))))))))))******))))))((((((''''''+++***)))'''''')))***+++))))))(((((('''''''''&&&((((((((((((((((((((((((******))))))((((((''''''(((((())))))))))))((((((&&&''''''((()))******+++******++++++++++++******))))))))))))((((((((((((''''''''''''((((((((()))++++++***)))((('''&&&&&&************************))))))))))))))))))))))))(((((((((((())))))))))))+++*********))))))((((((******+++++++++******)))))))))************))))))))))))))))))))))))))))))'''''''''''''''((())))))))))))(((((((((((())))))((((((((((((((((((((((((''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&'''((())))))(((((((((((((((((('''&&&%%%$$$%%%%%%%%%&&&&&&'''''''''%%%&&&''''''((((((''''''&&&&&&''''''(((((())))))(((((((((((((((((((((((('''&&&%%%%%%%%%%%%&&&'''((((((((((((((((((((((((''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&(((''''''''''''((())))))'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%&&&&&&&&&''''''%%%$$$$$$###$$$%%%&&&'''%%%&&&&&&&&&'''(((((((((***)))'''&&&&&&''')))***&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&*********)))))))))))))))((('''''''''((()))+++,,,++++++***)))((('''&&&&&&%%%&&&&&&'''((())))))***''''''''''''((((((((((((******))))))((((((''''''((((((((((((((())))))*********++++++++++++******,,,,,,+++******+++,,,,,,+++*********))))))((((((}}}yyyzzzvvvxxxrrrhhheeeiiiiiimmmooonnnqqqyyy|||{{{|||~~~}}}{{{vvvrrrlll^^^JJJ<<<888222000//////000000///..................------------------------,,,++++++++++++++++++++++++++++++************))))))))))))))))))))))))))))))))))))************))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))************))))))(((((((((((((((((((((((('''''''''((((((((())))))))))))))))))))))))))))))))))))************))))))(((((((((((((((((((((((())))))))))))))))))))))))***)))))))))((((((((('''***)))(((''''''((()))***))))))((((((((('''''''''))))))))))))))))))))))))***)))))))))((((((((('''(((((())))))))))))(((((('''''''''((()))*********)))******++++++******))))))))))))))))))))))))((('''''''''((((((((()))))))))))))))))))))(((((((((************************))))))))))))))))))))))))(((((((((((()))))))))***************)))))))))(((******+++++++++******)))))))))************))))))((((((((((((((((((((((((((((((''''''(((((()))***))))))(((((((((((())))))((((((((((((((((((((((((''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&'''(((((((((((((((''''''(((((()))(((((((((&&&&&&&&&''''''(((((((((&&&&&&&&&''''''''''''((('''''''''((((((((((((((('''''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&'''''''''''''''''''''''''''''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%$$$######$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&''''''''''''''''''&&&&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''(((((((((((((((((((((((('''&&&&&&&&&'''(((******))))))))))))((((((((((((''''''(((((()))*********((((((((()))))))))******++++++*********)))))))))+++***)))(((((((((((((((******++++++++++++******))))))))))))))))))))))))+++*********))))))))))))~~~}}}wwwtttqqqjjjeeeeeeccciiinnnoooqqqvvvzzz{{{|||}}}~~~~~~}}}xxxsssoooeeeTTTCCC:::222000......///000///...---------...............,,,,,,,,,,,,,,,++++++***++++++++++++++++++++++++************))))))))))))))))))))))))))))))))))))************))))))))))))))))))))))))))))))))))))******))))))((((((''''''))))))************))))))((((((((((((((((((((((((''''''((((((((()))))))))))))))))))))))))))))))))((())))))******))))))(((''''''''''''''''''''''''))))))))))))))))))))))))))))))))))))(((((((((((()))((('''&&&&&&'''((()))))))))((((((((((((''''''************************))))))))))))(((((((((((((((((())))))))))))((((((''''''(((((())))))******)))******++++++******)))))))))))))))))))))))))))(((((((((((())))))))))))((((((((())))))*********************************))))))))))))))))))))))))((((((((()))))))))******************)))))))))))))))******+++++++++******))))))************))))))'''''''''''''''''''''''')))(((((((((((()))******))))))(((((((((((())))))((((((((((((((((((((((((''''''''''''''''''''''''(((((((((''''''''''''&&&&&&''''''(((((((((((((((&&&'''((()))************'''''''''(((((((((((((((''''''&&&%%%&&&'''((()))(((((((((((((((''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&$$$$$$%%%&&&&&&&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%&&&'''''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%$$$$$$((('''&&&%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((''''''&&&&&&((('''''''''&&&&&&%%%%%%''''''&&&&&&&&&&&&''''''&&&'''((())))))((('''&&&&&&&&&''''''''''''&&&&&&)))))))))(((((('''''''''''''''''''''((((((((((((&&&&&&%%%%%%&&&'''((()))''''''(((((())))))******))))))))))))************)))))))))*********+++++++++++++++++++++*********,,,,,,***)))((('''''''''******++++++++++++******((()))***++++++***)))(((***************))))))))){{{qqqnnnjjjeeebbb^^^eeemmmpppppprrrwwwzzz{{{{{{|||}}}~~~~~~yyytttrrrlll^^^LLL???333111///...///000///...,,,---------.../////////+++++++++,,,,,,++++++***++++++++++++++++++++++++************)))))))))((())))))))))))))))))))))))************)))))))))(((((((((((((((((((((((((((******))))))((((((''''''))))))************))))))(((((((((((((((((((((((('''(((((((((((()))))))))))))))))))))))))))))))))(((((())))))))))))((((((''''''''''''''''''''''''(((((((((((((((((((((((())))))))))))(((((((((((()))((((((''''''(((((()))))))))(((((((((((((((((())))))))))))))))))))))))))))))))))))(((((((((((((((((())))))))))))(((((('''((((((((()))))))))***))))))************)))))))))))))))))))))*********(((((()))))))))*********(((((()))))))))*********************************))))))))))))))))))))))))(((((()))))))))******************)))))))))))))))))))))***+++++++++******))))))************))))))(((((((((((((((((((((((()))))))))))))))******+++))))))(((((((((((())))))((((((((((((((((((((((((''''''''''''''''''''''''((((((((('''''''''''''''''''''((((((((((((((('''&&&'''((()))))))))))))))''''''''''''''''''((((((((('''%%%$$$%%%&&&(((***))))))((((((''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&###$$$%%%&&&'''&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%$$$$$$$$$'''&&&&&&&&&%%%%%%$$$$$$)))(((''''''''''''((()))&&&&&&&&&&&&&&&&&&&&&&&&)))((((((''''''&&&&&&%%%((((((''''''&&&&&&%%%%%%''''''&&&&&&&&&&&&''''''&&&'''((())))))((('''&&&&&&&&&''''''''''''&&&&&&))))))(((((('''&&&&&&&&&''''''((((((((((((((()))&&&&&&&&&''''''((((((((((((((((((((())))))))))))***))))))))))))))))))))))))))))))*********++++++++++++++++++++++++******,,,+++***)))((((((((((((******++++++++++++******)))***,,,------,,,***)))************************~~~nnnkkkjjjgggccc]]]ccckkkpppoooooosssxxxzzzzzz|||}}}~~~{{{wwwtttqqqfffTTTFFF666444111//////000///...,,,---------.../////////***++++++,,,,,,+++++++++++++++++++++++++++++++++************)))))))))((())))))))))))))))))))))))************)))))))))(((((((((((((((((((((((((((***)))))))))((((((((('''))))))************))))))))))))))))))))))))))))))(((((((((((()))))))))***))))))))))))))))))))))))(((((())))))))))))((((((''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))))))))))))))(((((())))))))))))))))))(((((((((((((((((((((((((((((((((((())))))))))))(((((())))))))))))(((((((((((((((((()))))))))))))))))))))******)))))))))((()))))))))*********+++)))))))))************+++************))))))))))))************************))))))))))))))))))))))))))))))))))))************))))))))))))))))))******((()))***+++++++++++++++))))))************)))))))))))))))))))))))))))))))))))))))))))))******+++))))))(((((((((((())))))))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((('''((((((((((((((('''''''''(((((((((''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%$$$%%%&&&(((***))))))((((((''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&%%%%%%&&&''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&'''''''''&&&%%%$$$###$$$&&&'''((((((''''''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''&&&&&&&&&%%%(((((((((''''''&&&&&&&&&''''''&&&&&&&&&&&&''''''%%%&&&''''''''''''&&&%%%&&&&&&''''''''''''&&&&&&'''''''''&&&&&&&&&%%%%%%((((((((())))))*********'''((((((((())))))))))))))))))))))))((((((((((((((((((((((((((((((''''''((((((((()))))))))************************************))))))))))))************++++++++++++******)))***,,,------,,,***)))***************+++++++++zzz|||sssmmmllljjjgggaaadddiiioooooommmppptttxxxyyy|||~~~}}}yyyvvvssskkk\\\MMM:::777333111000000///...---------...............***++++++,,,,,,,,,,,,,,,++++++++++++++++++++++++************))))))))))))))))))))))))))))))))))))************))))))))))))))))))))))))))))))))))))((((((((()))))))))))))))))))))************))))))))))))))))))))))))))))))((((((((()))))))))******))))))))))))))))))))))))'''(((((())))))(((((('''''''''''''''''''''''''''))))))))))))))))))))))))(((((((((((())))))))))))))))))************))))))(((((())))))))))))******''''''''''''''''''''''''(((((((((((())))))))))))(((((())))))))))))(((((((((((((((((())))))))))))((())))))******))))))(((((())))))******+++++++++)))*********+++++++++++++++++++++******)))))))))************************)))))))))))))))))))))))))))))))))*********++++++))))))))))))************((()))***+++++++++++++++))))))************))))))************************)))(((((((((((()))******))))))(((((((((((())))))))))))))))))))))))))))))(((((((((((((((((((((((('''(((((((((((()))))))))(((((((((((((((((('''&&&(((((((((((('''&&&%%%$$$&&&&&&&&&&&&&&&%%%%%%%%%''''''&&&%%%&&&'''((()))((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&%%%&&&''''''((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((('''&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&%%%&&&'''((()))''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((())))))******++++++(((((()))))))))))))))(((******))))))((((((''''''''''''''''''((((((((((((((((((((()))))))))******)))))))))***************)))))))))))))))***+++,,,******++++++++++++******((()))***++++++***)))(((*********+++++++++++++++yyyvvv}}}vvvpppkkkfffgggeeehhhmmmooolllmmmqqqwwwyyy|||~~~~~~|||wwwsssnnnaaaTTT>>>;;;666222111000///..................---------++++++,,,---------------++++++++++++++++++++++++************))))))))))))))))))))))))))))))))))))************))))))))))))))))))))))))))))))))))))''''''(((((())))))******))))))************))))))))))))))))))))))))))))))(((((()))))))))*********))))))))))))))))))))))))''''''((((((((((((''''''(((((((((((((((((((((((())))))))))))))))))))))))'''((((((((()))))))))***((())))))))))))))))))((((((((()))))))))*********(((((((((((((((((((((((('''((((((((()))))))))***(((((())))))))))))(((((())))))))))))(((((((((((((((((())))))))))))((((((((())))))******+++,,,,,,*********+++++++++,,,,,,)))***************++++++************************))))))))))))))))))))))))))))))*********+++++++++((()))))))))************(((((()))++++++,,,,,,+++))))))************))))))))))))))))))))))))))))))((((((''''''(((((()))***))))))(((((((((((())))))))))))))))))))))))))))))(((((((((((((((((((((((('''((((((((())))))))))))((((((((((((((('''&&&&&&''''''(((((((((''''''&&&((('''''''''&&&&&&&&&&&&&&&&&&&&&''''''''''''((('''''''''(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&'''&&&$$$######%%%''')))'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))((('''&&&%%%%%%%%%&&&&&&&&&''''''!!!"""$$$'''((('''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&''''''(((&&&&&&''''''(((((())))))''''''&&&&&&&&&&&&''''''((('''&&&%%%%%%&&&'''(((&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&''''''((((((''''''(((((()))******+++''''''((())))))(((''''''(((((((((((())))))))))))'''''''''((())))))******)))))))))*********++++++*********+++++++++,,,,,,++++++******)))***************++++++++++++******))))))))))))))))))))))))*********++++++,,,,,,,,,~~~xxxzzztttjjjdddkkkfffgggmmmooolllkkknnnvvvyyy}}}}}}}}}wwwsssooodddYYYAAA===777333111000///.../////////......------,,,+++,,,------............++++++++++++++++++++++++************))))))))))))))))))))))))))))))))))))************))))))))))))))))))))))))))))))))))))&&&&&&'''((()))***++++++))))))************))))))))))))))))))))))))))))))))))))))))))************))))))))))))))))))))))))''''''((((((((((((''''''))))))))))))))))))))))))))))))))))))))))))))))))'''((((((((())))))******''''''((((((((((((''''''(((((())))))*********+++))))))))))))))))))))))))'''((((((((())))))******(((((())))))))))))(((((())))))))))))(((((((((((((((((())))))))))))((((((((())))))***++++++,,,,,,******+++++++++,,,,,,,,,'''((()))***+++,,,------************************)))))))))))))))))))))))))))************+++++++++(((((())))))*********+++(((((()))++++++,,,,,,,,,))))))************))))))(((((((((((((((((((((((('''''''''''''''((())))))))))))(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))'''((((((((())))))******(((((())))))((('''&&&&&&&&&'''((()))************))))))(((((('''''''''&&&%%%&&&''''''((((((''''''&&&'''''''''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%((((((((((((((((((((((((''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&'''%%%""" !!!###&&&)))'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))((('''&&&%%%%%%%%%&&&&&&&&&''''''"""&&&'''%%%"""$$$$$$$$$%%%%%%&&&&&&&&&###$$$$$$%%%%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%&&&'''((((((%%%%%%&&&'''((()))******'''''''''&&&&&&'''''''''+++)))&&&%%%%%%&&&)))+++&&&''''''''''''''''''&&&%%%&&&&&&'''((()))******&&&&&&&&&'''((())))))***&&&&&&((((((((('''&&&%%%&&&&&&'''((()))***++++++'''(((((()))***++++++,,,******+++++++++,,,,,,,,,+++++++++,,,,,,---------------+++***))))))((((((******++++++++++++******,,,,,,+++******+++,,,,,,*********++++++,,,,,,,,,}}}xxxzzzsssoooggghhhhhhfffgggiiiiiihhhqqqwww~~~}}}|||xxxtttsssrrrkkkbbbHHHBBB:::444000//////000//////.........---------------,,,,,,,,,+++++++++//////.........---------************************,,,,,,,,,++++++************+++,,,---,,,***(((&&&************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))&&&''')))*********)))(((''''''(((((())))))******))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((***)))((('''((()))+++---******))))))))))))******&&&''''''((()))******+++))))))))))))))))))))))))******))))))((((((''''''''''''''''''(((((((((((())))))))))))))))))))))))''''''''''''''''''''''''************************+++,,,,,,------,,,,,,+++---,,,++++++*********+++,,,+++++++++******))))))++++++******************))))))))))))))))))))))))***+++...000000000///...,,,++++++******++++++,,,************************(((((())))))************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************''''''((())))))***))))))&&&'''''''''(((((()))))))))(((&&&'''((()))((((((&&&&&&&&&''''''''''''(((%%%%%%&&&&&&'''((((((((()))((('''((()))******((((((((((((''''''&&&&&&&&&((((((((('''&&&&&&&&&%%%(((((('''''''''&&&&&&&&&(((((((((((('''&&&%%%%%%''''''&&&%%%%%%%%%&&&&&&((('''&&&%%%%%%&&&'''(((%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$$$$%%%%%%%%%&&&&&&&&&((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''((((((((((((&&&&&&''''''''''''&&&&&&&&&&&&&&&''''''''''''(((%%%&&&&&&''''''&&&&&&%%%((((((((((((((((((((((((******))))))((((((''''''))))))((('''''''''''''''))))))))))))))))))))))))&&&(((***,,,,,,+++)))(((******))))))((((((''''''---+++***(((((()))+++,,,+++***)))(((((()))******))))))***+++,,,,,,---------,,,+++***))))))))))))******++++++++++++************))))))******+++,,,------------------------zzzwww}}}qqqgggfffdddcccdddfffgggfffkkkqqqyyy~~~zzzuuutttsssllldddOOOGGG<<<444111111111000//////.........---------000000/////////.........---------,,,,,,,,,++++++************************+++++++++******)))))))))'''(((***+++,,,,,,++++++************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))'''(((((()))))))))))))))'''((((((((()))))))))***))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((()))((('''&&&&&&((()))+++******))))))))))))******'''''''''((()))*********))))))))))))))))))))))))******))))))((((((((((((************++++++++++++)))))))))))))))))))))))),,,,,,,,,,,,,,,,,,,,,,,,************************++++++,,,,,,,,,,,,++++++,,,,,,,,,+++++++++******+++++++++*********))))))+++++++++++++++*********************************'''(((***,,,---,,,++++++,,,++++++++++++++++++,,,++++++++++++++++++++++++************************************************))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''''''''''''''''''''''''''((((((((((((++++++***)))'''&&&$$$###'''''''''((((((((()))))))))(((&&&&&&'''((((((((('''''''''((((((((())))))''''''''''''''''''&&&&&&'''&&&%%%&&&'''((((((&&&&&&&&&&&&%%%%%%$$$$$$$$$'''''''''''''''&&&&&&&&&(((((('''''''''&&&&&&&&&&&&''''''''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&&&&&&&&&&'''(((%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''(((((((((((((((&&&&&&''''''''''''&&&&&&&&&&&&&&&''''''''''''(((%%%&&&&&&''''''&&&&&&%%%((((((((((((((((((((((((***)))))))))((((((((('''))))))((('''''''''''''''))))))))))))))))))))))))'''((()))*********))))))((((((((())))))))))))))),,,+++***))))))***+++++++++***))))))((()))***++++++++++++,,,,,,---------......------,,,---------************************------,,,,,,------....../////////.........------xxx{{{vvvfffbbb___^^^___bbbdddeeefffllluuu{{{~~~~~~}}}}}}|||wwwvvvuuuooogggZZZNNN@@@666222222222000/////////.........------------------,,,,,,,,,,,,++++++++++++************++++++++++++++++++++++++*********)))))))))))))))((())))))***++++++,,,,,,************************)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((()))******(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((()))((('''''''''(((************))))))))))))******''''''(((((())))))******))))))))))))))))))))))))***))))))))))))((((((((((((((((((((())))))))))))))))))))))))))))))))))))************************++++++++++++++++++++++++***++++++,,,,,,++++++***+++,,,,,,------,,,*********************)))))))))++++++++++++++++++++++++++++++++++++++++++++++++&&&''')))***++++++***))),,,,,,++++++++++++,,,,,,++++++++++++++++++++++++,,,+++++++++++++++++++++************************))))))))))))))))))))))))((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''((((((((((((,,,+++***)))'''$$$"""!!!''''''(((((((((((()))))))))((('''&&&&&&'''((()))(((((((((((()))))))))***)))(((((('''&&&&&&%%%%%%'''&&&%%%&&&'''((((((&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%&&&&&&'''&&&&&&&&&$$$%%%&&&'''(((((('''&&&(((''''''&&&&&&''''''(((&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((((((''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&''''''''''''(((&&&&&&''''''''''''&&&&&&(((((((((((((((((((((((())))))))))))(((((((((((())))))((('''''''''((((((((((((((((((((((((((((((((((((''''''(((((())))))''''''((())))))***++++++************************+++******))))))***++++++,,,,,,,,,,,,------------,,,+++++++++,,,,,,---...,,,,,,++++++++++++,,,,,,---......///000111111222333222222222111111000000|||zzz~~~}}}eee^^^XXXXXX[[[^^^bbbfffdddiiiqqqyyy}}}~~~~~~}}}|||}}}{{{wwwvvvwwwsssmmmdddVVVEEE888444333222000////////////............,,,,,,,,,++++++++++++***++++++++++++************++++++++++++++++++++++++******************))))))---,,,+++***))))))))))))************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))***)))((((((((()))+++,,,(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((++++++************+++,,,******))))))))))))******'''((((((((()))))))))***))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))++++++++++++++++++++++++***++++++++++++++++++******+++---......---+++)))************************+++++++++,,,,,,,,,,,,,,,++++++++++++++++++++++++)))***+++,,,,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,---------************************))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))************((((((((((((((((((''''''(((((((((((((((((())))))))))))((('''&&&&&&((()))''''''((((((((()))))))))(((((('''''''''&&&&&&&&&)))((('''((()))******(((((((((((((((((('''''''''%%%&&&&&&&&&'''(((((((((''''''''''''''''''''''''$$$$$$%%%&&&''''''&&&&&&"""$$$&&&((())))))((('''((((((''''''''''''(((((('''''''''&&&&&&%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&''''''''''''(((&&&&&&''''''''''''&&&&&&(((((((((((((((((((((((())))))))))))(((((((((((())))))((((((((((((((()))(((((((((((((((((((((((()))(((&&&%%%&&&''')))***(((((()))))))))*********))))))***+++++++++******************+++++++++,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------.........---------...000111,,,---///111444555777777::::::::::::::::::::::::zzzzzz|||ggg\\\SSSTTTXXX\\\aaagggbbbfffmmmuuuzzz}}}}}}|||xxxzzzyyyvvvvvvyyywwwssskkk^^^LLL>>>777444111///000000/////////.........////////////............,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++---,,,+++***))))))))))))************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))***)))((((((((()))+++,,,))))))))))))(((((((((((())))))))))))))))))))))))************************))))))))))))))))))))))))++++++************************))))))))))))******(((((((((((())))))))))))************************))))))))))))******************+++++++++,,,,,,,,,))))))))))))))))))))))))+++++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,+++++++++***+++---......---+++***************++++++++++++++++++,,,,,,------------------------------------,,,,,,------------------+++,,,------------,,,+++,,,,,,,,,,,,,,,,,,,,,,,,))))))***,,,---...///000************************))))))))))))))))))))))))))))))))))))))))))))))))************************))))))))))))************&&&'''((()))***+++++++++))))))))))))))))))(((((()))***+++***''''''((()))&&&&&&'''''''''(((((((((&&&&&&&&&'''''''''(((((()))((('''((()))******(((((((((((((((((((((((((((%%%&&&&&&&&&'''(((((((((&&&'''''''''''''''''''''$$$%%%%%%&&&''''''''''''###$$$''')))))))))((('''(((((((((((((((((((((((('''''''''&&&&&&%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%$$$$$$&&&&&&''''''''''''&&&&&&&&&&&&&&&''''''''''''(((&&&''''''((((((''''''&&&(((((((((((((((((((((((((((((((((((())))))))))))))))))((((((((())))))***(((((((((((((((((((((((()))(((&&&%%%%%%''')))++++++*********)))))))))(((((()))***+++++++++++++++******++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++000//////......//////000/////////000111333444555111333666:::>>>@@@BBBCCCGGGGGGHHHIIIJJJKKKKKKLLLyyyuuuvvvnnn___SSSRRRVVVYYY___fffbbbdddiiiooovvvzzz{{{zzzvvvyyyyyywwwwwwzzzzzzxxxnnndddUUUGGG<<<555222000000000000/////////...............------------,,,...---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++,,,,,,,,,((())))))***++++++,,,,,,************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))***))))))))))))***++++++))))))))))))(((((((((((())))))))))))))))))))))))************************))))))))))))))))))))))))((((((((((((''''''''''''******))))))))))))******(((((((((((())))))))))))************************)))))))))************+++)))************+++++++++))))))))))))))))))))))))************************,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,------,,,,,,+++++++++---......------,,,+++++++++,,,,,,,,,,,,,,,+++,,,,,,------......///------------------------,,,,,,,,,,,,,,,,,,,,,,,,+++,,,---......---,,,+++------------------------))))))***+++---...//////++++++++++++++++++++++++))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((''''''''''''(((((((((((()))******++++++******)))******))))))))))))(((((((((,,,......***(((((()))&&&&&&&&&&&&''''''''''''%%%%%%&&&&&&'''(((((()))'''&&&%%%&&&'''((((((&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&'''''''''''''''&&&&&&&&&'''''''''''''''&&&&&&''''''((('''''''''%%%%%%'''((())))))(((''''''(((((())))))(((((('''&&&&&&&&&&&&&&&&&&%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&''''''''''''(((''''''((((((((((((''''''(((((((((((((((((((((((((((((((((((())))))))))))))))))((((((((()))******(((((((((((((((((((((((()))((('''&&&&&&(((***+++,,,++++++***))))))(((((()))))))))***++++++,,,,,,******,,,---------------,,,,,,,,,,,,,,,------------------------...///000222333555888:::<<<<<<===@@@BBBEEEIIIMMMOOOQQQQQQUUUUUUVVVWWWXXXYYYYYYZZZ}}}uuurrr{{{yyyeeeUUUSSSUUUVVV[[[ccceeeeeegggmmmtttyyy{{{{{{yyy||||||yyyxxxzzz{{{yyypppjjj___PPPBBB888333333000000000000/////////...,,,,,,+++++++++*********------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,)))*********++++++++++++'''(((***+++,,,,,,++++++************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))***++++++++++++******)))))))))((((((((('''))))))))))))))))))))))))************************))))))))))))))))))))))))'''''''''''''''&&&%%%%%%******))))))))))))******))))))))))))((((((((((((************************))))))*********+++++++++''''''((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))),,,,,,,,,,,,,,,,,,,,,,,,,,,------......------,,,,,,,,,,,,---------......,,,,,,,,,------.........,,,,,,,,,---.../////////........................------,,,,,,,,,,,,,,,---+++,,,---//////---,,,+++------------------------++++++++++++,,,,,,,,,,,,++++++++++++++++++++++++))))))))))))))))))))))))++++++++++++++++++++++++((((((((((((((((((((((((''''''''''''((((((((((((***************)))((((((*********)))))))))(((((((((---222222---)))((()))''''''''''''((((((((((((&&&&&&'''''''''''''''''''''&&&%%%&&&'''((((((&&&%%%&&&&&&&&&'''''''''((('''''''''''''''&&&&&&&&&&&&&&&&&&'''''''''((((((((((((((()))((((((''''''''''''''''''(((((((((((('''((()))******)))((('''%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''((((((((((((&&&&&&''''''''''''&&&&&&&&&&&&&&&''''''''''''(((''''''((((((((((((''''''(((((((((((((((((((((((('''((((((((()))))))))***))))))(((((()))******+++))))))))))))))))))))))))))))))((((((((()))***+++***************************))))))))))))+++,,,---***+++,,,---.........---------......//////000000+++,,,---...000222444555:::===AAAFFFIIIJJJKKKJJJPPPRRRUUUXXXZZZ[[[[[[[[[\\\\\\\\\\\\\\\\\\\\\\\\xxxoooqqqkkkXXXTTTUUUTTTXXX```iiihhhiiinnnuuu{{{~~~~~~|||{{{yyy{{{{{{zzzqqqnnnfffWWWFFF:::555555000000000000//////////////////.........------------------,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,(((((())))))*********+++***+++,,,---,,,***(((&&&************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((()))***,,,,,,+++************))))))((((((((('''))))))))))))))))))))))))************************))))))))))))))))))))))))(((((())))))((('''&&&&&&******))))))))))))******))))))))))))((((((((((((************************))))))******++++++++++++***+++++++++,,,,,,,,,,,,))))))))))))))))))))))))------------------------,,,,,,,,,,,,,,,,,,,,,,,,---......//////......------,,,,,,,,,,,,---...///---------....../////////,,,,,,------...///000000//////////////////////////////...------.........+++,,,...//////...,,,+++........................------,,,++++++***))))))++++++++++++++++++++++++))))))))))))))))))))))))++++++++++++++++++++++++************************))))))))))))************'''((()))))))))))))))(((+++*********))))))(((((('''---444444000***))))))(((((((((((())))))))))))((((((((('''&&&&&&%%%%%%)))((('''(((*********((('''((((((((())))))******(((((((((''''''&&&&&&%%%&&&&&&&&&'''''''''(((((())))))******)))((('''''')))(((((('''''''''(((((('''((()))******)))((('''%%%%%%%%%&&&&&&'''''''''(((((((((((((((((((((((())))))))))))))))))))))))&&&&&&&&&'''''''''((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((()))************&&&''''''''''''''''''&&&&&&&&&&&&'''''''''((((((''''''((((((((((((''''''(((((((((((((((((((((((('''((((((((())))))******))))))((())))))***++++++************************)))))))))))))))******+++)))))))))***++++++,,,,,,***)))(((((()))+++---...)))+++,,,...//////.........//////000111222222333111222444666:::===@@@BBBCCCGGGMMMRRRVVVXXXWWWWWWZZZ[[[^^^```aaa```______]]]]]]\\\[[[ZZZXXXXXXWWW{{{sssvvv|||yyy^^^SSSSSSTTTUUUWWWbbbeeekkkrrrwww{{{}}}}}}~~~|||{{{yyyxxxxxxxxxwwwsssiii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pppqqquuulll]]]XXXTTTTTTVVV^^^bbbiiiqqqwww{{{|||}}}~~~}}}}}}|||zzzyyyxxxxxxuuurrrkkk```RRREEE;;;666222222111///......000111///...------,,,,,,,,,---......---,,,,,,,,,,,,---+++++++++******+++++++++,,,,,,,,,+++++++++******++++++,,,,,,,,,,,,++++++++++++************+++++++++++++++*********))))))))))))))))))))))))))))))))))))))))))))))))))))))************************************)))))))))((())))))))))))))))))******************))))))))))))))))))))))))))))))))))))))))))))))))************************************)))************+++++++++******++++++++++++******************++++++++++++***************************++++++++++++,,,,,,,,,***+++------,,,+++,,,---,,,++++++,,,...///,,,)))...///000///......///111//////000000000000000//////111333333333333555777666444444555888999777555888777555555555666666666666555444444333333333333000111111222222111000000/////////////////////...---------,,,,,,+++++++++...---+++*********+++,,,,,,,,,,,,++++++++++++***++++++++++++*********)))******************************************************************************))))))))))))******))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((''''''''')))))))))(((((('''''''''%%%&&&''''''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&'''((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((()))***++++++,,,''''''''''''''''''&&&&&&&&&&&&&&&''''''''''''((((((((('''&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&(((((((((''''''&&&&&&&&&))))))))))))))))))))))))(((''''''&&&&&&''''''((('''''''''''''''''''''''''''''''''''''''((())))))))))))))))))((((((((((((((((((((((((((((((((((((&&&&&&'''(((((((((''''''++++++******))))))(((((()))))))))))))))(((((((((************++++++++++++++++++++++++*********)))+++++++++,,,---......///+++---///000///...///000000111222444666:::<<<>>>DDDFFFJJJNNNRRRUUUWWWXXXWWWYYY[[[]]]]]]ZZZXXXVVVSSSSSSSSSQQQPPPNNNMMMLLLJJJHHHFFFEEEEEEEEECCCBBBrrrooonnnzzzvvvbbbVVVPPPPPPSSSYYY^^^fffooovvvzzz||||||{{{|||}}}}}}}}}{{{yyywwwsssrrrnnnfffZZZMMM@@@999333222111000///////////////...------,,,---------......---,,,,,,,,,,,,---++++++************++++++,,,,,,,,,+++++++++******++++++************++++++++++++************+++++++++++++++***************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************))))))))))))''''''(((((()))))))))***---,,,+++***)))((('''&&&)))))))))))))))))))))))))))))))))*********++++++++++++++++++++++++++++++)))************+++++++++******++++++++++++******************+++++++++,,,++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,)))+++------,,,,,,...///...---,,,,,,......---,,,...///111111000000111222222333555666888888999999888:::===>>>???AAACCCEEEEEEEEEEEEGGGJJJKKKJJJIIIGGGGGGFFFEEEDDDDDDEEEEEEAAA@@@>>>===;;;::::::999555666777888777666444222222111111111111000000000000///...---,,,+++++++++.........------,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++************++++++++++++++++++++++++++++++++++++++++++++++++******************************))))))))))))******)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((('''''''''''''''''''''&&&&&&''''''((()))''''''''''''''''''((((((&&&&&&&&&&&&'''((())))))&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((((((((((())))))*********))))))(((''''''&&&&&&%%%&&&&&&&&&''''''''''''(((''''''&&&%%%%%%%%%%%%&&&&&&&&&'''''''''''''''&&&((((((((((((((('''''''''))))))))))))))))))))))))(((''''''&&&&&&''''''((('''''''''''''''''''''''''''''''''''''''((())))))''''''(((((())))))******((((((((((((((((((((((((''''''((())))))(((&&&%%%,,,,,,+++***)))(((''''''(((((())))))))))))))))))************+++++++++,,,++++++++++++************++++++,,,,,,---...///000,,,///222333222111111222222444888===BBBFFFIIIKKKOOOQQQTTTXXX[[[\\\\\\\\\YYYZZZZZZZZZWWWSSSOOOLLLHHHHHHGGGFFFEEECCCBBBBBBAAA@@@??????@@@AAA@@@???}}}uuuooouuugggVVVNNNPPPTTTTTTZZZcccllltttyyyzzz{{{yyy{{{}}}~~~|||zzzxxxssssssqqqlllbbbTTTEEE;;;555444222111000///...---......------------............---,,,,,,,,,,,,---+++******))))))******+++,,,,,,,,,+++++++++******,,,+++***))))))***+++,,,++++++************++++++************************))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))*********)))))))))))))))''''''(((((()))*********,,,,,,+++***)))(((''''''))))))))))))))))))))))))))))))*********+++++++++++++++++++++++++++++++++))))))*********+++++++++******++++++++++++***************+++++++++,,,,,,+++++++++++++++++++++++++++++++++,,,,,,,,,------+++,,,---,,,,,,,,,---//////...------...///000000000222444666666777999;;;>>>@@@BBBDDDGGGHHHIIIJJJJJJLLLOOOQQQSSSUUUXXXZZZ\\\\\\]]]^^^```aaa``````\\\\\\\\\[[[ZZZYYYYYYZZZUUUTTTRRROOOMMMLLLKKKJJJCCCDDDEEEEEECCCAAA===;;;999999888777555444333333222111000...------.........//////000//////......------,,,,,,,,,+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++******************************))))))))))))******((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''&&&&&&((('''&&&&&&&&&''')))***&&&&&&''''''(((((())))))'''''''''''''''((())))))((((((((((((((((((((((((((((((((((((((((((((((((((((((((()))))))))))))))((((((((((((''''''''''''&&&&&&&&&''''''''''''(((''''''&&&&&&%%%&&&&&&'''%%%&&&''''''((('''''''''((((((''''''''''''''''''''''''''''''''''''''''''((((((''''''''''''(((((('''''''''''''''''''''''''''''''''''''''((())))))(((((((((((())))))))))))((((((((((((((((((((((((((()))***+++***)))'''&&&+++*********))))))((((((((((((((())))))******+++*********+++++++++,,,,,,++++++++++++++++++++++++,,,++++++++++++,,,---......000222333333555777999999===BBBIIINNNRRRUUUVVVXXXZZZ\\\^^^]]]\\\YYYXXXUUUUUUTTTSSSOOOKKKGGGDDD???????????????@@@@@@AAAAAA@@@@@@BBBDDDEEEEEECCCtttsssttt___UUUUUUWWWSSSXXXaaajjjqqqvvvyyyyyywwwzzz}}}~~~{{{yyyvvvuuutttppphhhZZZJJJ@@@999666333111111000...,,,......---------......///......---,,,,,,,,,,,,---++++++************++++++,,,,,,,,,+++++++++******,,,+++***))))))***+++,,,++++++************++++++************************))))))))))))))))))))))))))))))))))))))))))))))))''''''(((((())))))))))))))))))))))))))))))******)))))))))******+++++++++))))))))))))))))))))))))************************************++++++++++++++++++++++++++++++++++++))))))*********+++++++++******++++++++++++*********++++++++++++,,,,,,,,,++++++++++++++++++++++++++++++,,,,,,,,,------------......---++++++---///...///000111222333555777777:::>>>AAACCCEEEHHHJJJQQQSSSUUUXXX[[[]]]^^^___```bbbdddffffffhhhjjjlllkkklllnnnnnnoooooooooooommmnnnoooooolllkkklllmmmlllkkkiiigggeeecccbbbbbbYYYYYYYYYWWWUUUQQQNNNKKKKKKJJJHHHFFFCCCAAA???>>>:::888666444111000///...---....../////////......---------,,,,,,,,,+++++++++++++++++++++++++++,,,++++++++++++++++++++++++******************************************************))))))))))))******((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&''''''''''''''''''(((((('''&&&&&&((()))***&&&''''''(((((()))))))))(((((('''''''''((())))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((()))))))))&&&&&&''''''((()))******&&&&&&&&&''''''''''''(((((('''''''''''''''((((((%%%&&&&&&'''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((((((''''''((((((((((((((((((((((((((((((((('''''''''''''''((())))))))))))))))))(((((((((((())))))))))))))))))))))))***+++,,,,,,+++***)))((((((((())))))*********+++(((((())))))******++++++***++++++++++++,,,,,,,,,+++++++++++++++++++++,,,---,,,*********+++,,,---111222333555777;;;AAAFFFIIILLLQQQVVVZZZ\\\]]]]]]``````aaa```]]]YYYTTTRRRNNNNNNNNNMMMJJJGGGDDDBBBAAAAAA@@@@@@@@@AAABBBCCCEEEEEEFFFHHHKKKLLLKKKJJJ|||uuuyyynnn```YYYUUUTTTYYY```hhhnnntttvvvxxxwwwyyy||||||{{{yyyxxxvvvtttnnnbbbSSSHHH>>>999444111111111///---.........---......///000......---,,,,,,,,,,,,---,,,++++++++++++++++++,,,,,,,,,,,,+++++++++******++++++************++++++++++++************++++++***************+++++++++))))))))))))))))))))))))))))))))))))))))))))))))'''(((((())))))******+++))))))))))))************+++++++++***************'''(((((()))***+++++++++*********************************++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,)))************+++++++++******++++++++++++******++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------///000000...---...000222222555888:::<<>>555111111333222000...............///000000......---,,,,,,,,,,,,---...------,,,,,,------...,,,,,,,,,+++++++++******+++,,,---......---,,,+++++++++************++++++))))))******++++++++++++))))))))))))))))))))))))))))))))))))))))))))))))((())))))***+++,,,,,,,,,(((((())))))*********+++++++++***)))((('''&&&&&&((()))))))))******************************************+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,)))************+++++++++******++++++++++++******++++++,,,,,,,,,---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------......000111222333555888<<<@@@HHHNNNVVV\\\___cccgggjjjiiilllqqqtttvvvvvvxxxyyywwwxxxyyy{{{|||}}}}}}}}}vvvvvvtttpppkkkgggeeeeee[[[___dddgggiiikkkooosssvvvzzz|||{{{}}}~~~~~~~~~}}}|||zzz{{{|||~~~wwwwwwvvvuuutttsssrrrrrrmmmmmmkkkgggaaaYYYRRRMMMFFFCCC???999555333111111......---------,,,,,,,,,+++++++++,,,,,,---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++******))))))))))))******))))))))))))))))))))))))))))))))))))))))))))))))'''((((((((())))))******'''((((((((())))))******&&&''')))*********)))(((******))))))((((((''''''***)))(((((((((((())))))((((((((((((((((((((((((((((((((((((((((((((((((%%%%%%&&&'''((()))***+++(((((((((((())))))))))))&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%&&&'''((($$$%%%&&&'''((((((((((((&&&'''''''''(((((())))))''''''''''''''''''''''''))))))(((((((((((())))))))))))))))))))))))))))))'''''''''''''''((())))))&&&&&&'''((()))***++++++)))))))))))))))))))))))))))(((&&&$$$%%%'''***,,,************)))))))))))),,,+++++++++***)))))))))++++++,,,,,,,,,---------+++++++++,,,,,,---------//////000333777===BBBFFFGGGLLLSSSXXX[[[]]]^^^___[[[[[[ZZZXXXVVVTTTSSSRRRTTTTTTUUUWWWYYYZZZ\\\]]]^^^^^^```aaacccdddddddddaaa```______```bbbdddeeeccccccccceeefffeeeccc```lllgggbbbaaafffkkknnnrrrwwwxxxyyyzzz|||}}}||||||{{{{{{xxxwwwwwwssskkkeeeUUUFFF888555333///,,,---................................................+++,,,------++++++,,,------------,,,,,,+++++++++******+++++++++,,,,,,,,,,,,++++++******++++++,,,******++++++++++++******))))))))))))))))))))))))***************************)))((((((((()))+++,,,************************************************(((((()))***++++++,,,,,,,,,,,,,,,++++++*********++++++++++++++++++++++++******++++++++++++******&&&''')))***+++++++++***)))+++---,,,+++***+++,,,//////...---,,,,,,,,,,,,,,,------......------,,,...//////...---///333555444888===AAADDDHHHMMMQQQZZZ^^^dddjjjnnnqqqsssuuuppprrrvvvyyy|||}}}}}}}}}~~~~~~}}}}}}xxxtttmmmgggbbb]]]YYYVVVTTTSSSRRRSSSWWW^^^eeeiiiqqqtttwwwwwwwwwxxx|||~~~|||{{{{{{|||||||||{{{{{{~~~}}}||||||}}}|||zzzxxxxxxyyyzzz{{{}}}}}}{{{wwwrrrmmmlllkkk```[[[TTTPPPMMMGGG>>>888444222000000111111000///111...,,,,,,,,,------,,,---------------,,,++++++---,,,++++++******++++++*********)))))))))))))))************************(((((((((((((((((((((((())))))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))))))))(((((((((((())))))******))))))((((((''''''(((''''''&&&'''((()))*********))))))((((((''''''''''''((((((((((((''''''((((((((((((((((((((((((******))))))((((((''''''''''''((((((((((((''''''''''''''''''''''''''''''((('''&&&%%%%%%%%%%%%%%%(((((((((((())))))))))))'''''''''''''''&&&&&&&&&+++***)))'''''''''((()))(((((((((((())))))))))))************************)))))))))))))))))))))))))))************+++++++++++++++,,,,,,,,,---------,,,++++++,,,---,,,+++))),,,+++++++++,,,---...///444666:::@@@FFFKKKOOORRRUUUWWWYYY[[[]]]]]]\\\[[[RRRPPPLLLIIIGGGJJJPPPTTTUUUVVVXXX[[[___bbbdddfffdddcccbbbdddfffhhhiiihhhjjjjjjjjjjjjjjjiiihhhgggmmmjjjhhhhhhkkklllkkkiiinnngggcccffflllnnnqqqtttwwwxxxzzz{{{|||||||||{{{|||zzzyyyzzzwwwpppjjjYYYJJJ<<<777555111...///................................................+++,,,------++++++,,,---,,,,,,,,,+++++++++******+++++++++++++++++++++,,,,,,++++++******++++++,,,******++++++++++++*********************************************************)))((((((((()))++++++************************************************((())))))***++++++,,,,,,,,,,,,,,,+++++++++******++++++++++++++++++++++++******++++++++++++******((())))))***++++++++++++***+++------+++***+++,,,...------,,,,,,,,,------------,,,,,,,,,,,,,,,,,,,,,...//////000333777:::>>>CCCIIINNNRRRVVV[[[___eeehhhmmmppprrrtttvvvwwwwwwyyy{{{~~~uuuqqqkkkfffbbb^^^ZZZWWWRRRPPPNNNNNNPPPTTTYYY]]]dddgggjjjlllmmmooossswwwvvvtttqqqqqqsssttttttssstttvvvyyyzzz{{{}}}}}}}}}}}}}}}}}}||||||||||||yyyvvvuuuvvvrrrllleee```[[[TTTKKKDDDAAA<<<666222111111111000---,,,,,,---......,,,*********+++++++++******)))---,,,++++++***+++++++++))))))))))))************************************)))))))))))))))))))))))))))))))))***************((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''))))))(((((((((((())))))(((((((((((('''''''''&&&&&&'''(((((())))))((((((***)))))))))((((((((('''''''''((((((((((((''''''((((((((((((((((((((((((((((((((((((''''''''''''''''''((((((((((((''''''''''''''''''''''''''''''******)))((((((((((((((('''''''''((((((((())))))((('''''''''''''''''''''+++***)))(((''''''((()))(((((((((((()))))))))***************************************************************++++++++++++++++++,,,,,,,,,------------------...//////......000///......000333666888<<<>>>BBBGGGLLLPPPSSSUUUWWWXXXXXXWWWVVVSSSPPPOOOCCCCCCBBBBBBCCCHHHPPPUUU[[[\\\^^^```bbbddddddeeedddcccdddeeegggjjjkkklllmmmmmmnnnooopppqqqqqqqqqqqqnnnllllllmmmnnnllljjj~~~rrrhhhggglllnnnppprrruuuvvvxxxzzz{{{|||{{{{{{~~~|||zzzzzz{{{xxxsssnnn^^^PPPAAA999666333111111................................................+++---...---,,,+++,,,---------,,,,,,,,,,,,++++++++++++++++++++++++++++++,,,++++++******++++++,,,******++++++++++++******************************************************)))))))))((()))******+++************************************************)))))))))***++++++,,,,,,,,,,,,,,,++++++++++++***++++++++++++++++++++++++******++++++++++++******+++++++++******+++,,,,,,***+++------+++++++++,,,,,,,,,,,,,,,,,,------.........---,,,,,,---...///---///333666999===BBBEEEMMMRRRXXX^^^bbbfffiiikkknnnpppsssuuuuuuvvvwwwyyy|||}}}~~~{{{xxxsssooollljjjgggeee___]]]ZZZXXXWWWYYY\\\^^^]]]___aaabbbbbbbbbdddfffgggeeebbbaaaccceeeeeeeeefffhhhjjjmmmooosssxxx|||yyy{{{}}}~~~~~~}}}|||vvvrrrmmmggg___YYYTTTMMMCCC;;;666444444333,,,,,,---///111000---***************++++++++++++------,,,+++++++++++++++((()))))))))***+++++++++************************************************))))))******++++++,,,,,,((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''))))))(((((((((((())))))''''''''''''&&&&&&&&&&&&$$$&&&(((******)))'''&&&))))))))))))((((((((((((''''''((((((((((((''''''((((((((((((((((((((((((&&&&&&&&&&&&''''''''''''''''''((((((((((((''''''''''''''''''''''''''''''((('''&&&&&&&&&&&&&&&&&&'''''''''((((((((())))))((((((((((((((()))))))))***))))))(((((((((((()))((((((((()))))))))******************************************************************+++++++++,,,,,,,,,,,,,,,------------++++++,,,------.........333222222222555:::???BBBFFFHHHKKKNNNQQQSSSTTTTTTRRRRRRQQQOOOKKKGGGDDDBBB888999;;;<<<@@@FFFMMMSSSVVVXXX[[[^^^```aaaaaaaaabbbbbbcccdddfffhhhkkklllnnnnnnnnnnnnpppqqqrrrssssssqqqpppooopppooonnnlllrrrjjjkkkmmmoooqqqtttuuuwwwyyy{{{||||||{{{zzzyyyxxxxxxyyywwwtttpppcccWWWGGG<<<777444222222................................................,,,---...---,,,+++,,,..................---------,,,,,,,,,++++++++++++***,,,++++++******++++++,,,******++++++++++++******************************************************)))))))))))))))******+++************************************************))))))*********+++++++++++++++++++++++++++++++++++++++++++++++++++++++++***++++++,,,,,,++++++***...---,,,+++***+++,,,---***,,,------,,,++++++,,,------,,,,,,,,,,,,------000///...---...000333444444777===BBBGGGMMMRRRVVV]]]```eeeiiikkklllllllllkkkmmmppprrrsssuuuxxx{{{}}}}}}}}}}}}~~~~~~{{{zzzyyyxxxwwwuuusssooolllkkkkkkllllllhhhgggeeeccc___\\\ZZZYYYZZZWWWTTTSSSSSSUUUVVVVVVVVVYYY\\\___bbbfffjjjmmmrrrsssuuuwwwzzz|||~~~~~~~~~|||zzzwwwrrrnnnggg```UUUKKKDDD???<<<:::222111111111222111///---------------------......------,,,++++++++++++,,,(((((()))***++++++,,,,,,************************************************(((((()))******+++,,,,,,(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))))))))(((((((((((())))))''''''''''''''''''''''''&&&&&&'''((()))((((((((())))))))))))((((((((((((''''''((((((((((((''''''((((((((((((((((((((((((&&&&&&&&&''''''(((((((((''''''((((((((((((''''''''''''''''''''''''''''''&&&&&&%%%%%%$$$%%%%%%&&&((((((((()))))))))******)))))))))))))))*********)))))))))(((((((((((()))(((((()))))))))******************************************************************+++++++++,,,,,,,,,,,,,,,------------...,,,---------------///000222333666:::>>>CCCGGGIIILLLMMMOOOPPPPPPOOOMMMLLLEEEEEEEEECCCAAA???===;;;777999;;;===@@@DDDJJJNNNNNNQQQVVV[[[___```aaa```dddeeeeeeeeeeeegggjjjllloooooonnnmmmmmmmmmnnnoooqqqqqqqqqqqqqqqqqqpppoooooojjjkkknnnrrrssstttwwwyyy{{{|||||||||zzzyyyyyyyyyxxxwwwtttsssfff\\\MMM@@@888555333111////////////////////////........................,,,---......,,,,,,---...,,,,,,,,,,,,,,,---------++++++++++++++++++++++++,,,++++++******++++++,,,******++++++++++++******************************************************((()))))))))***************************************************************************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,++++++...---,,,+++++++++,,,---***,,,...---,,,+++,,,---///...------,,,,,,,,,---/////////000222666999;;;AAAFFFLLLSSSXXX]]]bbbeeeiiiiiijjjkkkjjjhhhdddaaa___bbbeeeiiimmmrrrxxx|||}}}}}}}}}~~~~~~{{{zzzyyyyyyzzzxxxvvvrrrnnnhhhccc^^^ZZZVVVSSSOOOMMMMMMMMMMMMLLLMMMQQQWWW\\\___bbbeeefffjjjjjjkkkmmmqqqwww}}}~~~}}}uuuppphhh```YYYRRRLLLHHH???;;;777444333222222111//////...---......///000...---,,,,,,++++++,,,,,,((())))))***+++,,,,,,---************************************************''''''(((((()))***++++++))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))))))))(((((((((((())))))(((((((((((((((((((((((()))(((&&&%%%&&&''')))+++(((((((((((())))))))))))''''''((((((((((((''''''(((((((((((((((((((((((('''''''''(((((())))))***''''''((((((((((((''''''(((((((((((((((((((((((()))((((((((((((((())))))))))))*********+++++++++))))))))))))******++++++((((((((())))))))))))((())))))))))))***************************************************************++++++++++++,,,,,,,,,,,,,,,---------.........///000111111000000333555555888???EEEJJJLLLLLLLLLKKKKKKKKKIIIGGGDDDBBB@@@;;;;;;;;;;;;:::999999888888;;;>>>@@@BBBFFFIIILLLOOORRRWWW]]]aaabbbcccccchhhhhhhhhfffeeefffiiimmmoooooooooooooooooopppppppppqqqssstttuuuuuuuuuvvvwwwllljjjnnnsssrrrtttwwwzzz|||}}}~~~~~~}}}}}}|||{{{yyywwwuuutttiiibbbTTTDDD;;;777444000////////////////////////........................,,,...///...---,,,---...))))))************++++++******+++++++++,,,,,,,,,,,,++++++******++++++,,,******++++++++++++******++++++++++++++++++++++++************************(((((()))************)))***************************************************************************++++++++++++,,,,,,,,,++++++++++++++++++++++++++++++,,,,,,,,,,,,++++++,,,,,,,,,++++++,,,------+++,,,......,,,,,,,,,---//////...............///111222444777<<>>BBBIIIOOOQQQPPPMMMJJJEEEDDDBBB@@@===;;;999888888888888888888888888888999<<>>DDDIIILLLOOOQQQOOOKKKFFFBBB===<<<:::888777777777888888888888999:::;;;<<<===???CCCIIINNNQQQSSSUUUWWWXXXZZZ]]]```bbbeeefffgggjjjlllmmmkkkiiikkkqqqwww|||~~~uuulllmmmrrrsssuuuxxx{{{~~~}}}}}}{{{xxxtttqqqpppooonnnkkk___MMMAAA===777000000000000000000000000000........................---...///...------...///---------....../////////(((((()))***,,,---...///,,,++++++++++++++++++,,,******++++++++++++******++++++++++++++++++++++++************************'''((()))++++++******)))************************************************++++++***************************++++++,,,,,,,,,+++++++++++++++++++++++++++,,,,,,------,,,,,,+++''')))***,,,------,,,,,,+++---......---,,,,,,---++++++---///111444666777AAADDDKKKRRRZZZ```eeehhhiiikkklllkkkgggaaa]]][[[QQQNNNIIIFFFEEECCC???;;;:::<<<@@@DDDJJJRRR[[[aaaiiilllqqqwww{{{~~~~~~|||xxxsssmmmfffaaa\\\^^^___```bbbdddhhhkkkqqqrrrtttvvvyyy|||}}}{{{tttooohhh```XXXPPPIIIEEE999777444222111000111222......---,,,,,,,,,,,,---,,,,,,++++++++++++++++++************************((((((((((((((((((((((((+++++++++***************))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))))))))(((((((((((())))))&&&&&&&&&'''''''''((((((''''''''''''((((((((()))'''((((((((())))))******''''''((((((((((((''''''(((((((((((((((((((((((((((((((((''''''&&&&&&%%%''''''((((((((((((''''''))))))))))))))))))))))))'''''''''''''''((()))***&&&&&&&&&&&&'''''''''(((&&&''''''((()))*********&&&'''(((*********)))((()))************+++++++++************************++++++++++++++++++++++++++++++,,,,,,,,,------------------........./////////444999<<<>>>CCCLLLSSSPPPPPPPPPNNNJJJCCC===:::888777555444444666999;;;666777888;;;===@@@CCCDDDHHHLLLRRRVVVXXXYYYZZZ[[[^^^___bbbfffjjjnnnqqqssswwwyyy{{{zzzyyy{{{{{{mmmkkknnnqqqtttwwwyyyzzzzzz{{{||||||zzzyyyxxxxxxwwwtttrrrrrrnnncccTTTEEE:::666555///000000000000000///...000/////////..................------------......,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---...,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++******))))))+++++++++*********))))))))))))))))))))))))))))))************************((()))***+++,,,+++******,,,++++++******++++++,,,)))************+++++++++,,,,,,,,,+++++++++******++++++******++++++,,,---000000///.........//////---.../////////...---,,,,,,---...---,,,---///222///000222444666:::@@@DDDRRRUUUZZZ```fffkkknnnpppqqqmmmhhhccc^^^WWWOOOHHHGGGCCC???===============;;;<<<===>>>???DDDLLLRRRZZZ^^^cccgggjjjooovvv{{{zzzuuussslllfffaaa```]]]YYY]]]eeennnpppuuu{{{}}}yyytttoookkkfff___ZZZKKKEEE<<<666333333444444000...,,,+++,,,------,,,...---,,,,,,++++++,,,,,,************************************************)))))))))))))))))))))))))))))))))))))))(((''''''''')))***)))((('''(((***---+++)))'''&&&&&&'''((((((((((((((('''''''''''''''&&&&&&&&&&&&'''((((((((((((((((((((('''&&&&&&)))(((((('''''''''(((((())))))(((''''''&&&'''''')))))))))))))))(((''''''(((((('''''''''&&&&&&&&&))))))))))))(((((((((((()))))))))))))))(((''''''******))))))((((((''''''&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''(((((()))))))))))))))))))))))))))))))))************+++++++++))))))))))))************,,,,,,,,,+++++++++******++++++,,,,,,,,,++++++***...---,,,+++************+++,,,------...000333666777999>>>CCCIIINNNRRRTTTSSSOOOIIIBBB<<<888777666666666555666888999999888<<<>>>AAAEEEHHHJJJKKKKKKRRRTTTVVVVVVWWW[[[aaafffeeehhhmmmqqquuu|||pppjjjkkkppprrrvvvxxxyyyzzz{{{|||zzzxxxwwwwwwxxxwwwuuusssrrrnnneeeXXXIII>>>888666000000000000000000/////////............---------------,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---...,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++*********)))+++++++++*********))))))************************************************((()))***+++,,,++++++***,,,++++++******++++++,,,************++++++++++++,,,,,,,,,++++++++++++***+++++++++***++++++,,,---,,,,,,+++++++++++++++,,,------...//////...---,,,+++---......---,,,---...111444888===AAAGGGMMMRRR[[[]]]aaaeeeiiimmmoooqqqrrrooojjjgggccc]]]UUUPPPHHHEEEAAA??????@@@AAAAAA>>>??????>>>>>>@@@EEEJJJNNNQQQUUUXXX\\\aaaiiinnnvvvzzz~~~zzztttnnnjjjddd]]]]]]bbbgggjjjooovvv}}}{{{xxxuuuqqqlllhhh[[[TTTJJJAAA:::666333111111000///000111111///......------,,,+++,,,,,,,,,************************************************)))))))))))))))))))))))))))))))))))))))((('''''')))***+++***)))((()))+++,,,+++)))'''&&&'''((()))(((((((((((((((((((((((('''&&&&&&&&&''''''((((((+++++++++++++++***))))))'''''''''''''''((()))***,,,,,,+++***************)))))))))))))))(((''''''))))))((((((((('''''''''))))))))))))(((((((((((()))))))))))))))(((''''''***)))))))))((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((((((((()))))))))))))))))))))))))))************+++++++++))))))))))))************,,,,,,+++++++++*********++++++,,,,,,,,,++++++***,,,,,,,,,,,,,,,,,,------,,,---...///000222666999@@@EEELLLRRRVVVWWWVVVTTTMMMJJJDDD???:::777666555666555444555777:::===>>>CCCDDDGGGJJJMMMPPPQQQRRROOORRRVVVYYY\\\aaahhhmmmqqquuu{{{tttjjjhhhlllppptttvvvxxxyyy{{{}}}xxxwwwvvvwwwxxxxxxvvvtttqqqooohhh]]]PPPCCC;;;666111111111111000000//////.........---------,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---...++++++++++++++++++++++++++++++++++++************+++++++++***************************************++++++++++++++++++++++++))))))***++++++++++++***,,,++++++******++++++,,,************+++++++++,,,,,,,,,,,,,,,+++++++++++++++++++++++++++,,,------******)))))))))***++++++,,,------.........------,,,...000000/////////000777<<>>777333222222111000000000000//////.........---------------,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---...************************++++++++++++++++++++++++************************************************++++++++++++++++++++++++))))))******++++++++++++,,,++++++******++++++,,,*********+++++++++,,,,,,------,,,,,,,,,+++++++++,,,++++++++++++,,,------,,,+++++++++,,,------...,,,---------...............///111222222444777:::BBBHHHPPPWWW^^^ccchhhkkkmmmnnnppprrrssstttuuuuuuuuuuuuuuutttssspppllljjjaaa___]]]]]]^^^```aaaaaa]]]\\\[[[XXXUUURRRQQQPPPKKKJJJGGGFFFHHHMMMSSSWWWYYY\\\bbbhhhnnnuuu|||yyywwwttttttvvvyyy{{{|||~~~xxxrrroooooodddcccaaabbbgggqqq{{{~~~~~~yyypppeeeZZZNNNDDD===999666222000///000///...///......---------------++++++++++++++++++++++++************************))))))))))))))))))))))))))))))*********))))))((()))***++++++))))))***+++((((((''''''((()))***+++))))))))))))************&&&''''''(((((((((((((((''''''((((((''''''&&&%%%'''''''''''''''((()))***(((''''''&&&&&&&&&'''''')))))))))))))))(((''''''(((((((((((((((((((((((((((((((((((())))))))))))(((((())))))))))))(((((())))))))))))((((((((((((%%%%%%&&&'''((()))))))))***)))))))))((((((''''''))))))))))))))))))))))))))))))*********+++++++++))))))*********+++++++++************************++++++,,,,,,---,,,,,,,,,***+++---...////////////---000333666:::@@@FFFKKKNNNPPPTTTVVVSSSNNNGGGBBBAAA@@@>>><<<;;;;;;<<<<<>>FFFKKKSSSXXX^^^ccceeefffggghhhmmmppprrrsssssssssuuuvvvxxxwwwwwwyyy}}}}}}{{{yyyxxxxxxzzzwwwuuuvvvzzz|||{{{{{{~~~|||{{{yyyyyyzzz|||}}}}}}~~~}}}|||{{{{{{|||~~~}}}}}}~~~{{{zzzuuutttqqqmmmhhh___UUUOOOKKKIIIJJJOOOTTTZZZdddnnn~~~yyylll]]]TTTQQQQQQUUU]]]ccchhhpppxxx{{{}}}yyytttjjj]]]TTTEEE???888333111111000///+++---///...+++))))))***,,,,,,,,,+++++++++******++++++++++++++++++++++++)))***++++++)))(((((()))***************************)))((((((((()))***+++)))))))))))))))))))))))))))))))))))))))***+++,,,))))))(((((((((((())))))))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&&&&%%%''')))***+++***)))(((''''''((())))))(((''''''(((((((((((())))))))))))((((((((((((((((((((((((************)))))))))(((((())))))***************,,,,,,+++++++++,,,---...------------------------+++,,,---///000000//////555666999===BBBGGGKKKMMMNNNOOOOOOMMMJJJHHHIIIJJJOOOSSSYYY___cccdddcccbbb^^^]]]\\\\\\]]]```ccceeefffnnnwww|||}}}~~~~~~|||xxxsssnnnjjjgggaaa`````````aaabbbcccdddbbbcccccceeehhhlllppprrrwwwzzznnnccc[[[XXXVVVYYY```hhhooossszzz|||~~~}}}{{{{{{{{{xxxyyywwwuuutttpppdddXXXFFF===555333333000000111222000//////000000///---,,,------.........------,,,------------............,,,++++++---......---.........------,,,,,,+++,,,,,,,,,,,,++++++++++++)))***++++++++++++++++++******+++++++++,,,,,,,,,,,,,,,++++++++++++,,,,,,++++++++++++,,,,,,,,,,,,---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,+++,,,---,,,++++++,,,---......------------......//////.........///000000333555:::>>>CCCJJJQQQUUU^^^aaaeeeggghhhiiikkklllqqqsssuuuvvvvvvvvvwwwyyyxxxwwwxxxzzz~~~}}}}}}}}}~~~~~~}}}}}}xxxtttsssvvvwwwuuusssuuusssrrrpppppppppqqqssstttyyyyyyyyyyyyxxxwwwuuuttttttuuuuuuuuuvvvvvvvvvvvvwwwxxxzzz|||}}}~~~~~~~~~|||wwwsssqqqqqqpppooollleee\\\VVVPPPMMMMMMOOOQQQTTTZZZbbbrrryyywwwjjjaaaZZZXXXYYY\\\___aaagggnnnuuuzzzyyyooohhhZZZOOOAAA888666555222...---...///...+++******+++,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++)))***,,,+++***((()))))))))***+++,,,,,,+++***)))******)))(((''''''(((((())))))))))))))))))))))))&&&&&&((()))***+++++++++(((((())))))))))))(((((())))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))(((((((((((((((((((((((())))))))))))((((((((((((((()))))))))))))))))))))'''(((((())))))(((((('''(((((((((((())))))))))))((((((((((((((((((((((((************))))))))))))((()))******++++++******,,,,,,+++++++++,,,---...------,,,++++++,,,------***,,,...000222222222111888;;;@@@EEEIIILLLNNNNNNOOOMMMKKKHHHFFFHHHLLLPPPUUUYYY^^^cccffffffdddbbb___``````^^^]]]```fffkkkuuu|||{{{yyyqqqooojjjeeeaaa^^^\\\[[[YYYZZZ]]]```eeeiiimmmooonnnppptttxxx~~~|||kkk[[[UUURRRUUU[[[bbbhhhmmmvvvzzz~~~|||{{{zzzyyyzzzxxxuuutttrrriii___III???555333333222111222333111000///000///...,,,,,,,,,---......///......------------...............---++++++---......---......---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,)))******+++,,,,,,,,,,,,******+++++++++,,,,,,,,,,,,,,,++++++++++++,,,,,,+++++++++,,,,,,,,,,,,,,,---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,+++,,,------,,,+++---.........------------......///............///000111888<<>>999333///000000///...------......,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++)))+++,,,,,,***))))))***((()))+++,,,,,,+++)))(((******))))))(((((((((((())))))))))))))))))))))))%%%&&&((()))******))))))'''((()))******)))((('''(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))((((((((((((((((((((((((******))))))))))))))))))+++***)))((((((((()))***((((((((())))))((((((((((((((((((((())))))))))))))))))))))))))))))))))))*********)))))))))))))))))))))***++++++++++++***+++++++++,,,,,,,,,------,,,,,,------------,,,,,,+++,,,---///111444555666999===BBBHHHKKKLLLLLLKKKLLLKKKJJJHHHIIIMMMSSSXXXZZZ\\\___aaacccdddccccccbbbcccccc```^^^aaaiiiqqqtttkkkfff```___\\\[[[[[[]]]___aaafffhhhlllqqqvvv{{{sss___VVVPPPTTT[[[___ccciiiqqqvvv{{{}}}{{{zzzyyyzzzxxxuuutttrrrkkkcccLLL@@@555222333333222333333111000///000///...,,,,,,,,,---...////////////---------........./////////---,,,,,,---...---,,,---------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,)))***+++,,,,,,,,,,,,,,,******+++++++++,,,,,,,,,,,,++++++******++++++,,,++++++,,,,,,,,,------------,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,+++---......------...000///......------......///............000333555777AAAFFFMMMSSSXXX[[[___aaabbbdddggghhhiiikkknnnqqqooorrruuuxxxyyy{{{}}}zzzyyyxxxyyy{{{}}}}}}}}}|||{{{zzzyyyyyyzzz{{{||||||~~~~~~|||zzzyyyzzz{{{wwwwwwxxxxxxyyyyyyyyyyyy{{{{{{uuuuuuvvvvvvuuuwwwxxxxxxwwwvvvtttvvvzzz~~~~~~xxxqqqmmmmmmnnnllllllmmmnnnpppsssuuuvvvuuutttsssrrrrrrrrrssssssxxxxxxyyyyyyyyyyyyxxxxxxwwwwwwxxxyyyyyywwwrrrnnngggdddbbbaaa]]]XXXXXX\\\aaammm{{{yyytttnnnkkkfffaaaccchhhvvvzzz||||||zzzzzz}}}{{{wwwuuupppgggZZZLLL@@@888444111000...------...///000,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++***+++,,,,,,***))))))***((()))+++,,,,,,+++)))((())))))*********+++++++++))))))))))))))))))))))))'''((()))******)))(((''''''((()))******)))((('''(((((((((((((((((((((((())))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))))))))******************,,,+++)))(((((()))***+++)))))))))(((((()))))))))(((((((((((())))))))))))************************))))))))))))))))))******))))))***+++++++++++++++++++++,,,,,,,,,---------+++,,,...000000...,,,+++...------///222777;;;>>>AAACCCFFFHHHIIIHHHFFFDDDFFFHHHJJJMMMPPPTTTYYY]]]`````````aaacccfffhhhiiidddeeefffdddccchhhqqqzzzwwwmmmbbbYYYTTTVVVVVVXXX[[[```gggmmmqqq{{{}}}{{{eeeYYYSSSXXX^^^^^^aaaffflllqqqxxx}}}~~~}}}{{{{{{yyy{{{zzzvvvtttrrrllleeeQQQCCC666222333333222222222000//////000000///---------.../////////......------.........////////////---,,,,,,---------,,,------------------------++++++++++++,,,,,,,,,,,,***+++,,,,,,,,,,,,,,,,,,******+++++++++,,,,,,,,,++++++************++++++++++++,,,,,,------......---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,+++---............///111//////............//////......///222666:::???BBBLLLPPPWWW\\\___aaacccddddddgggiiikkkmmmooorrrtttppprrrvvvxxxzzz{{{}}}{{{yyywwwwwwxxxyyyxxxwwwxxxwwwvvvuuuvvvvvvxxxxxxvvvwwwwwwuuussstttxxx|||zzzzzz{{{{{{|||}}}}}}}}}|||{{{~~~yyyuuuuuuwwwuuuuuuuuuvvvxxxzzz}}}~~~|||yyyvvvtttttttttuuuvvvvvvuuusssrrrqqqppppppssssssuuuyyy|||}}}|||{{{yyyvvvtttrrrllldddaaaccccccmmmyyy{{{wwwqqqlllmmmqqq|||~~~xxxuuuwww{{{||||||xxxnnn___QQQFFFAAA555222...,,,,,,.........,,,,,,,,,,,,------------++++++++++++++++++++++++***+++---,,,+++))))))***)))***+++,,,,,,+++***)))((()))***+++++++++++++++)))))))))))))))))))))))))))*********))))))((('''(((((())))))))))))(((((())))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))************+++***)))((())))))+++,,,***))))))(((((())))))***(((((((((((())))))))))))++++++++++++++++++++++++))))))))))))************)))***++++++,,,+++++++++***+++,,,---------,,,,,,,,,---///000000///---,,,000000111333777===BBBEEELLLJJJHHHFFFDDDCCCBBBBBBDDDHHHNNNTTTXXX[[[^^^```aaaaaabbbdddgggkkknnnqqqiiiiiiiiiiiijjjoooxxx|||wwwooofff^^^XXXTTTSSSYYY\\\aaahhhpppyyykkk^^^WWW]]]bbb``````dddhhhmmmtttzzz||||||||||||yyy||||||xxxvvvsssnnngggYYYIII999444444333111000111000...///000111///......////////////......---............////////////000...,,,,,,---------+++------------------------*********+++++++++,,,,,,,,,,,,,,,---,,,,,,++++++******+++++++++,,,,,,,,,++++++************++++++++++++,,,,,,---......///---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,***,,,------------...000//////............/////////000222666===DDDJJJNNNTTTYYY___ccceeefffhhhiiigggjjjmmmooopppqqqsssuuutttvvvyyyzzzzzz{{{|||~~~zzzxxxvvvvvvvvvwwwvvvuuuuuutttrrrqqqpppqqqqqqrrrppprrrsssrrrqqquuu|||~~~}}}~~~~~~zzzyyyxxxwwwtttpppmmmkkkoooooopppsssxxx|||~~~~~~zzzsssppprrrooouuu~~~}}}yyyzzz~~~}}}wwwuuuwwwzzz}}}{{{rrrfffYYYQQQ???:::444000//////......,,,,,,,,,---------......++++++++++++++++++++++++***,,,---,,,+++*********************************)))******++++++***)))((())))))))))))))))))))))))******)))))))))******+++))))))(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((()))))))))******))))))))))))***+++,,,,,,******)))(((((()))******(((((((((((())))))))))))************************((()))))))))************)))***++++++,,,,,,++++++***+++,,,---------,,,,,,111000///......///000111222444777<<<@@@EEEHHHJJJKKKHHHCCC???>>>AAAEEEHHHLLLQQQWWW]]]```bbbdddeeecccfffjjjnnnssswwwyyyzzzsssqqqmmmkkkkkknnnrrruuummmhhhaaa\\\ZZZ]]]```bbbiiimmmvvvoooaaa[[[aaaeeebbb```dddfffkkkrrrxxx{{{|||}}}}}}zzz~~~~~~{{{wwwtttnnnhhh___NNN===666555333000...000///...///000111000//////000000000///...------............/////////000000...,,,,,,------,,,+++------------------------)))))))))******+++++++++------------,,,,,,+++*********+++++++++,,,,,,,,,++++++************++++++++++++,,,,,,---...//////---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,)))+++,,,,,,,,,,,,.../////////............//////000111444:::BBBJJJRRRWWWYYY]]]cccgggiiijjjkkklllhhhkkknnnpppqqqqqqrrrsssxxxyyy{{{|||{{{zzz{{{|||yyywwwuuuuuuvvvwwwvvvuuusssrrrpppnnnllllllllllllnnnppprrrrrrrrryyyzzz}}}~~~|||{{{~~~zzztttqqqooommmmmmooossswwwyyyzzz{{{{{{}}}~~~yyywwwzzz{{{~~~zzzuuuuuuppptttzzz~~~uuuhhh]]]IIICCC:::555333222000...,,,,,,,,,------.........++++++++++++++++++++++++***,,,------+++******+++++++++***))))))***++++++******+++***)))'''&&&$$$))))))))))))))))))))))))))))))(((((()))+++---...***)))(((''''''((()))***))))))))))))))))))))))))))))))))))))))))))))))))************************))))))))))))))))))))))))''''''(((((()))))))))***(((((()))***+++,,,,,,,,,+++***)))(((((()))***+++(((((((((((())))))))))))))))))))))))))))))))))))(((((())))))*********+++******+++,,,,,,,,,,,,+++***+++,,,---...---,,,,,,555222///,,,,,,///222555222666<<>>EEEHHHKKKMMMJJJBBB>>><<<:::;;;AAAIIIPPPTTT^^^bbbfffiiijjjlllpppsssxxx~~~tttiiiccc```\\\ZZZ[[[ZZZ\\\aaafffoooyyy~~~~~~iiiaaaeeeffflllooojjjhhhhhhmmmvvvzzzxxxxxxzzzyyyzzz{{{zzzyyyvvvrrrpppgggXXXFFF999666666444111000000000000///////////////............---------,,,---......//////......------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,------,,,,,,+++***++++++++++++,,,,,,,,,++++++,,,,,,,,,,,,------***++++++++++++,,,,,,,,,------,,,,,,,,,,,,---------------............///........................///000111111111111444666;;;@@@HHHOOOUUUZZZ___cccggghhhiiiiiihhhiiilllnnnrrrrrrssstttuuuvvvwwwwwwxxxyyyzzzzzzxxxvvvuuutttuuussspppllljjjiiiiiiiiihhhkkknnnooonnnooossswwwyyyyyyzzzzzz|||}}}}}}{{{zzz|||~~~{{{xxxtttsssrrrqqqsssvvvyyy{{{}}}~~~~~~|||rrrkkkhhhnnnvvv}}}}}}tttiiiYYYJJJ@@@:::555333//////000///...---......///---,,,---///000---+++...---,,,++++++************************************************************))))))(((((())))))************))))))))))))))))))))))))))))))))))))))))))))))))*********++++++((((((((((((((((((((((((************************************)))))))))((()))************))))))((('''((())))))(((((()))+++))))))))))))*********+++************************++++++++++++++++++++++++---,,,,,,++++++,,,,,,---,,,,,,++++++++++++,,,,,,...------------...//////...------...000333777999===EEEKKKLLLLLLKKKEEE======<<<<<<@@@FFFNNNUUUYYYaaadddiiilllpppvvv|||vvvlllbbb]]]YYYVVVXXX[[[eeeiiipppyyy}}}zzzxxxvvvzzzwwwllllllkkkrrrxxxtttkkkggghhhooouuuvvvvvvwwwyyyzzz{{{{{{zzzxxxuuutttlll^^^LLL>>>888666444222000000000000///////////////............---------,,,---......//////......------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,------,,,,,,+++++++++++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,------++++++++++++,,,,,,,,,,,,......------------......---------............///////////////////////////000111222222333555999<<>><<<<<<======CCCLLLTTTZZZ___dddggggggiiinnnvvvzzzqqqnnndddcccffflllrrr{{{~~~yyyrrrzzz}}}mmmlllnnnfffaaaZZZWWW\\\dddjjjpppvvvzzzzzz{{{{{{{{{{{{zzzzzzssslll___OOO@@@666222111000000000000///////////////............---------,,,---......//////......------------------------------------------------,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,------,,,,,,+++,,,,,,,,,,,,------------++++++,,,,,,,,,,,,------,,,,,,,,,,,,------------------,,,,,,,,,,,,---------------............///---------......//////000111444777<<<@@@GGGNNNSSSUUUXXX]]]```ccceeegggiiilllnnnooooooooooooqqqsssttttttssssssrrrqqqqqqppplllmmmrrryyy{{{uuutttsssssstttuuuxxxyyy~~~}}}zzzvvvvvvtttsssrrrqqqnnnkkkhhhhhhggglllxxx|||zzztttwww{{{~~~~~~xxxoooiiifffdddccceeejjjnnnnnnmmmkkkkkkllloootttwwwxxxxxxnnnoooqqqrrrrrrrrrsssssszzz}}}wwwsssooonnnqqqwww|||}}}ssskkkggggggggghhhiiijjjmmmttt|||zzzooofffdddhhhtttzzz~~~}}}ttteeeYYYDDD>>>666111000111000...---///000///...,,,,,,---+++,,,---......---,,,+++,,,,,,,,,,,,,,,,,,,,,,,,************************)))******************)))))))))))))))************))))))))))))))))))))))))((((((((()))))))))******))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))************((())))))************)))((()))+++***))))))***,,,+++++++++++++++*********************************++++++++++++++++++++++++++++++++++++,,,---......------,,,,,,,,,,,,------,,,,,,------...///000111///222888???FFFLLLPPPRRRKKKEEE???===<<<<<>>999777555333///111222000---******,,,)))***,,,------,,,***))),,,,,,,,,,,,,,,,,,,,,,,,***************************)))(((''''''((()))***++++++******))))))(((((())))))))))))))))))))))))************++++++++++++))))))))))))))))))))))))************************(((((())))))*********+++***************)))((('''(((***++++++******+++,,,,,,,,,,,,++++++*********************************++++++++++++++++++++++++++++++++++++,,,---...///...------,,,,,,------...000000000111222444555666===AAAHHHNNNPPPMMMIIIEEEAAA<<<<<>>BBBHHHMMMRRRVVV[[[^^^aaabbbeeehhhkkklllmmmmmmlllnnnpppooollliiihhhhhhjjjgggeeeggglllssszzz}}}yyy{{{uuupppjjjfffdddaaa]]]]]]```^^^aaaccc```\\\ZZZ\\\```ddd```\\\[[[]]]______^^^ccceeehhhlllnnnooonnnnnniiinnnnnniiidddddddddcccdddcccbbbbbbddddddcccbbbeeegggmmmsssyyy{{{{{{zzz{{{~~~vvvooolllmmmrrrtttuuuuuusssrrrrrrssswwwyyy{{{|||||||||~~~~~~}}}~~~yyyvvvtttvvvyyyyyyyyy{{{wwwoooggg```\\\cccpppyyyyyyuuuwwwvvvvvvzzz|||xxxlllbbb[[[\\\dddqqq|||{{{yyynnn]]]MMMAAA:::666555...//////...------...///---------,,,,,,,,,++++++************************,,,+++***((((((***+++,,,))))))))))))))))))))))))++++++************************))))))))))))************))))))))))))******''''''(((((())))))******))))))))))))))))))))))))++++++************++++++))))))***++++++++++++***(((((()))***************)))************+++++++++*********)))******+++,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,---------......---,,,,,,---------...//////......222999>>>CCCIIIPPPQQQKKKEEEBBBBBB???AAACCCGGGKKKPPPSSSTTTXXX___gggjjjjjjiiikkkmmmqqqvvv}}}{{{uuupppiiikkkooouuu}}}{{{xxxzzzrrrbbbXXXSSSPPPQQQVVV]]]cccllltttxxxzzz||||||zzzyyyxxxyyyvvvqqqllldddTTTAAA888777222222222222111111111111000000/////////.................................------------------------,,,,,,,,,,,,,,,,,,,,,,,,------------------------------------------------------------------------,,,,,,,,,,,,,,,,,,,,,,,,------------------------//////.........---------------............//////111111000111333666999;;;CCCFFFLLLQQQUUUZZZ^^^aaadddeeegggjjjkkklllmmmmmmooooooooommmkkkjjjiiiiiihhhggghhhmmmuuu}}}}}}sssnnnfffaaa^^^^^^\\\YYYZZZ]]]ZZZ]]]```^^^[[[[[[```eeegggfffddddddfffiiilllnnnmmmooorrruuuwwwxxxwwwwwwwwwzzz{{{wwwuuuwwwwwwuuutttrrrqqqqqqrrrsssrrrpppuuuxxx|||zzztttooommmuuuuuuvvvvvvuuutttttttttuuuwwwxxxwwwvvvvvvxxxyyy|||xxxxxx|||~~~{{{wwwzzz||||||zzzyyyzzz||||||wwwrrrkkkeeegggooovvvvvvsssmmmkkkkkkooorrrppphhh```UUUVVV\\\hhhssszzzyyylll]]]OOOCCC999333000000000...---,,,---...---------,,,,,,,,,++++++************************))))))************))))))******************************************************))))))))))))************))))))))))))******)))))))))))))))((((((((())))))))))))))))))))))))))))))(((((((((((())))))))))))***++++++++++++***((())))))***************)))************+++++++++***************++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------///......---------.........///000000111666===CCCHHHLLLOOOMMMHHHCCCAAABBBDDDFFFJJJMMMOOORRRUUUVVV^^^ccciiillllllmmmqqqtttuuuxxx|||}}}zzztttmmmiiiiiioooyyy|||xxxqqqqqq}}}kkk___WWWRRRPPPTTTZZZ```jjjsssyyy{{{}}}}}}{{{zzzyyyzzzvvvsssooohhhZZZHHH<<<888333222222222111111111111000000000/////////......////////////////////////------------------------,,,,,,,,,,,,,,,,,,,,,,,,------------------------------------------------------------------------,,,,,,,,,,,,,,,,,,,,,,,,------------------------...............------------........./////////000111111111333777<<>>:::555222222222111000.........---------,,,,,,++++++++++++++++++++++++,,,+++***))))))***+++,,,************************))))))*********+++++++++++++++************++++++******))))))))))))******((()))))))))*********+++))))))))))))))))))))))))++++++************++++++))))))***++++++++++++***))))))***+++++++++++++++))))))*********++++++++++++++++++***+++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,.........------,,,,,,,,,------,,,------...//////222333666<<>>EEENNNTTTXXXZZZZZZ```cccfffiiikkkllloooqqqmmmllljjjhhhffffffffffffppp}}}|||zzzyyywwwvvv|||yyyqqqmmmllljjjhhhhhhhhhgggjjjuuu{{{zzzyyyvvvsssrrrtttxxxxxxkkk___WWWVVVXXX[[[```^^^\\\ZZZTTTQQQUUU]]]hhhsss|||wwwsssjjj]]]LLL???999666444222//////.........---------,,,,,,,,,,,,,,,,,,,,,,,,***+++---......---+++***++++++++++++++++++++++++((())))))***++++++,,,,,,,,,++++++******++++++,,,******))))))))))))******,,,,,,++++++***)))))))))))))))))))))))))))))))))++++++************++++++))))))***++++++++++++*********+++,,,,,,,,,,,,+++)))************+++++++++,,,,,,++++++,,,,,,---...,,,,,,,,,,,,,,,,,,,,,,,,,,,---------.../////////111111111111222333444555666999???FFFKKKJJJEEE???>>>???BBBGGGMMMRRRTTTUUU\\\___jjj{{{uuujjjdddbbbbbbcccjjjsss|||rrrjjjggghhhuuuvvvggg\\\VVVTTTYYYaaajjjnnnsssvvvxxxxxxyyyzzzzzzzzzxxxsssnnnfffVVVGGG;;;777222111333444333111111111111111111111111111//////000000000000/////////...---,,,,,,---...///------......---,,,++++++***+++---...///...------,,,------......------,,,---------------------------------.........//////////////////////////////...///000111111000///...////////////111444777999???DDDKKKRRRWWWZZZ]]]___aaadddhhhkkkkkkkkkkkkkkklllkkkhhheeeeeeiiipppvvv|||{{{pppmmmnnnmmmiiikkkpppuuuzzz~~~wwwvvvyyyooopppoooiiidddfffpppzzz~~~~~~wwwooonnnmmmpppxxx~~~xxxqqqiiiaaa\\\XXX___ffflllkkkccc[[[YYYZZZbbblllyyy~~~{{{zzzzzzpppkkk___NNN===333222555000000111111111000///...,,,***)))+++...///...,,,************))))))((((((++++++++++++++++++++++++***+++,,,,,,,,,,,,+++***++++++++++++++++++++++++))))))(((((((((((())))))************************))))))))))))************++++++************++++++))))))))))))))))))))))))((((((((()))******++++++************************,,,,,,,,,++++++*********,,,---......//////...............///////////////---...---------///444777;;;@@@EEEHHHGGGCCC???===>>>CCCIIIMMMOOORRRVVVYYYbbbpppvvvjjjeeedddeeellluuu}}}wwwlllfffdddlllmmm```YYYVVVYYY^^^ggglllrrrvvvxxxxxxyyyyyyzzzzzzwwwrrrooogggYYYKKK;;;777333111333444333111111111111111111111111111//////000000000000/////////...------------...///...............---,,,,,,+++,,,---.........---,,,+++,,,,,,------,,,,,,+++------------------------------------............//////////////////////////////000111111000///...000000000111444777;;;>>>CCCHHHOOOUUUYYY]]]```bbbdddfffiiijjjjjjkkkmmmoooooopppqqqsssuuuzzz{{{xxxqqqjjjjjjmmmnnnjjjpppssswww{{{}}}{{{|||xxxxxxvvvpppkkkkkkqqqxxx~~~}}}yyytttmmmlllnnnsss{{{{{{tttllleeeaaabbbiiiqqqtttqqqkkkgggfffgggooo{{{~~~|||{{{uuuqqqiii[[[MMMAAA:::777000000///.........---,,,///,,,***+++---...,,,++++++++++++******)))))))))++++++++++++++++++++++++***+++,,,,,,,,,,,,+++***++++++++++++++++++++++++***))))))(((((())))))***************************))))))))))))************++++++************++++++************************(((((())))))******++++++************************,,,,,,,,,+++++++++******+++,,,------......------.........///////////////.../////////000222666:::===@@@DDDEEECCC@@@>>>===AAAFFFLLLPPPRRRWWW^^^dddrrruuummmhhhjjjnnnsss}}}{{{ooogggaaaeeeyyyvvveee\\\XXXXXXZZZdddiiipppvvvxxxyyyyyyyyyzzzyyyvvvrrrooojjj]]]QQQ===888333222333444333111000000000000000000000000//////000000000000/////////......------......////////////............---------.........---,,,,,,++++++,,,,,,,,,,,,++++++------------------------,,,,,,,,,---------......//////////////////////////////000111111000000///222222222444777<<>>???CCCFFFPPPVVV]]]```bbbiiivvv{{{pppqqqvvvxxxooogggdddooo~~~lllccc^^^\\\[[[ccciiiqqqxxx{{{|||{{{{{{~~~|||wwwrrroookkk```TTTAAA<<<555222333444333222//////////////////////////////000000000000////////////////////////////////////............///000.........---,,,,,,,,,,,,......////////////......------------------------,,,,,,,,,---------......000000000000000000000000000000000000000111222222333444777;;;@@@FFFKKKNNNTTTWWW\\\```cccfffiiikkkeeefffhhhmmmuuuyyyrrrnnnmmmnnnuuu{{{~~~zzz}}}|||xxx{{{}}}xxxvvvwww{{{{{{{{{|||{{{vvvqqqrrrxxx}}}~~~}}}}}}zzzyyyuuujjjZZZNNN>>>888111...000222111000------,,,,,,,,,---...000,,,,,,,,,,,,,,,,,,,,,---++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,++++++++++++,,,,,,************************************++++++++++++++++++************++++++************************)))))))))***++++++,,,,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,------...///////////////......//////000111111222000333666888999;;;===???DDDBBB@@@>>>===AAAGGGLLLSSS[[[eeekkkqqqyyy{{{yyy~~~tttiiibbbhhhssspppeee```______dddjjjrrrxxx{{{|||||||||}}}|||wwwrrroookkk```UUUCCC===666333333444333222000000000000000000000000//////000000000000//////...//////000000//////...///...---------...///000......---,,,,,,,,,------///000000000000000000///---------------------------------.........//////000000000000000000000000000000000000000111333333555777<<>>@@@????????????AAAFFFNNNSSSYYYaaannnyyy{{{zzz{{{nnndddfffpppttthhhbbbaaabbbfffjjjqqqvvvyyyzzz{{{|||yyyyyyvvvrrrppplllbbbVVVEEE???777333333444333222111111111111111111111111//////000000000000//////...///000111111000///......---,,,+++,,,---///000------,,,,,,,,,---.../////////000000000000//////------------------------........./////////000000000000000000000000000000000000000000000222333444888;;;AAAHHHNNNRRRTTTUUU]]]___ccceeegggjjjmmmooorrrvvv~~~}}}zzzuuuqqqppprrrvvvxxx}}}{{{{{{zzzzzz|||~~~}}}pppfffccciiirrrxxxzzzzzz{{{}}}}}}yyyqqqkkkXXXMMM???777555444111...***---000000...------...***+++++++++,,,,,,,,,,,,++++++++++++++++++++++++,,,,,,+++******+++,,,,,,++++++++++++++++++++++++++++++************++++++*********************************+++++++++,,,,,,++++++************++++++++++++++++++++++++++++++)))******++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------......---......///000/////////---...///000111222333333555888===???@@@???@@@@@@???@@@CCCFFFJJJQQQYYY___fffnnn{{{{{{xxxyyytttjjjkkkssswwwiiibbbbbbdddfffjjjppptttwwwxxxzzz{{{vvvvvvtttrrrqqqnnncccXXXFFF???777333333444333222111111111111111111111111//////000000000000//////...///000111111000///......---+++++++++---///000---,,,,,,+++,,,---///000......////////////......------------------------////////////000000000000000000000000000000000000111000000///000222444555:::>>>FFFMMMSSSVVVWWWXXX```bbbeeegggiiikkknnnqqq|||vvvuuutttuuuwww{{{~~~~~~{{{vvvttttttwww|||sssddd]]]bbbmmmuuutttvvvyyy|||}}}zzztttpppfffYYYIII>>>:::888444000+++...222222///,,,++++++*********++++++,,,,,,,,,++++++++++++++++++++++++---,,,+++******+++,,,---+++++++++++++++++++++++++++******************+++******************************+++++++++,,,,,,,,,++++++************++++++++++++++++++++++++++++++)))******++++++,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------.........,,,---......//////......---...///000111222333333888;;;???BBBBBBAAAAAAAAAAAADDDIIINNNTTT\\\dddiiiuuu{{{~~~xxxuuuyyyzzzrrroooooo}}}mmmeeedddfffcccfffkkkrrrxxxzzzzzzxxxwwwuuurrrqqqppplllgggbbbRRRGGG:::333333555333111000000000000000000000000000000000000000000000000111111000000//////......000000///...------,,,,,,//////.........---------///////////////.....................///////////////////////////.........111111111000000000000000222111000000111444888:::BBBFFFKKKPPPTTTXXX[[[^^^eeedddccceeekkkttt~~~}}}yyyvvvyyy}}}}}}uuuooonnnsssxxx|||qqqbbbXXX\\\fffooovvv{{{{{{|||~~~yyyrrrnnndddUUUGGG===777333111000111000///------...///------,,,,,,,,,++++++++++++,,,,,,------,,,,,,+++******+++++++++,,,,,,,,,+++++++++++++++++++++++++++++++++++++++++++++++++++++++++******)))))))))************************++++++******************)))************+++++++++,,,,,,,,,+++++++++************+++,,,...///000000---,,,,,,,,,,,,---......///000111000...------...000000000111222444555666===???AAABBBAAA@@@@@@AAAAAAGGGPPPXXX^^^fffnnnttt~~~sssrrrsss{{{xxxssssss}}}pppddd```___bbbdddiiipppvvvyyyyyyxxxwwwuuusssrrrpppmmmhhhcccTTTIII;;;444333444333111000000000000000000000000000000000000000000000000000000000000////////////000//////......---,,,,,,...---------,,,,,,,,,+++/////////////////////...............////////////////////////////////////111111111111000000000000333222111111333777;;;>>>FFFJJJOOOTTTVVVXXX[[[]]]dddeeehhhnnnvvv}}}zzztttqqqqqqrrrxxxzzzvvvgggZZZXXX]]]eeemmmuuuxxx|||~~~zzzsssqqqkkkaaaSSSEEE;;;666555000111000///---,,,,,,,,,------------,,,,,,,,,,,,+++,,,,,,------,,,,,,+++***++++++++++++,,,,,,,,,++++++++++++++++++++++++************************,,,,,,+++++++++*********************************++++++++++++++++++++++++************++++++++++++*********++++++,,,,,,,,,,,,,,,,,,------.........------,,,,,,------...//////000111000...---...///000000000111333666888999@@@AAABBBBBBAAAAAABBBDDDHHHPPPZZZeeennnvvv~~~wwwrrrtttzzz~~~yyyyyy~~~uuueee^^^\\\aaacccggglllssswwwxxxwwwvvvuuusssrrrqqqnnniiifffYYYMMM???666333444444333000000000000000000000000000000000000000000000000////////////000000000000000//////......---------............------------......//////////////////............////////////////////////////////////111111111111111111111111333333222333666<<>>EEEKKKNNNPPPSSSXXX[[[^^^```ccceeeiiivvvwwwdddTTTJJJNNNWWWfffttt{{{|||{{{}}}zzzwwwssskkk]]]KKK>>>777555222111222222111000000000/////////.........+++,,,,,,------,,,,,,+++++++++,,,,,,,,,---------++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,)))*********+++++++++,,,***++++++++++++,,,,,,,,,++++++++++++++++++++++++******+++,,,---...///000...------------...//////...000111000//////000111111222333555999>>>BBBEEECCCBBBAAA@@@AAAFFFNNNSSSaaafffppp}}}nnnhhhiiiiiigggdddeeehhhkkknnnoooppprrrtttssspppnnnlllllleee\\\NNNBBB:::666444333000000000000000000000000111111111111111111111111////////////000000000000////////////////////////............////////////------......///000000000............////////////...//////000000111111222000000111111222333333333333555999???EEEJJJOOORRRUUUWWWYYYZZZ\\\___bbbeeeuuu~~~|||}}}jjjZZZOOOLLLPPP]]]llluuuzzz}}}~~~zzzvvvuuussshhhWWWIII<<<777111///000111000...000/////////............+++,,,,,,------,,,,,,+++,,,,,,,,,,,,------------++++++++++++++++++++++++------------------------++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,)))))))))******++++++,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,+++++++++******)))***+++,,,...///000111......------......///000...000111111//////000222222333555888;;;???BBBCCCAAA@@@@@@AAAEEELLLUUU[[[eeelllwwwwwwooopppnnnjjjfffdddeeehhhjjjkkknnnpppsssrrrooommmllllllggg___SSSFFF===666333222000000000000000000000000111111111111111111111111000000000000/////////////////////////////////000---------....../////////------......///000000111............////////////...//////000111111222222000000111222222333444444555888>>>EEEKKKPPPSSSUUUYYYZZZ\\\^^^aaafffmmmqqq{{{{{{~~~ttteeeUUUMMMJJJTTTbbbmmmvvv}}}~~~{{{yyyyyywwwpppdddZZZFFF???666000000000///---/////////.........------+++,,,,,,------,,,,,,+++,,,,,,,,,------------...++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,*********+++++++++,,,,,,************************))))))***++++++,,,------+++++++++,,,,,,,,,------++++++++++++++++++,,,,,,++++++,,,,,,---...//////...............//////000...000111111000000111222333444777:::===???@@@@@@>>>???AAADDDIIIRRR\\\ccckkkrrrwwwvvvqqqmmmgggddddddfffhhhiiilllooorrrrrrooollllllmmmhhhaaaUUUIII>>>777333111000000000000000000000000111111111111111111111111111111000000//////......////////////000000000000.../////////000000111111---------...///000000111............/////////000...//////000111222222222000000111222333333444444777;;;BBBJJJPPPTTTVVVWWWZZZ\\\^^^bbbhhhqqq{{{}}}{{{|||}}}}}}qqqZZZNNNGGGOOO\\\hhhsss||||||}}}}}}|||yyyssslllgggQQQGGG<<<444222222000...///.........------------+++,,,,,,------,,,,,,+++,,,,,,,,,---------......++++++++++++++++++++++++++++++++++++++++++++++++)))))))))******+++++++++((((((((((((((((((((((((******+++,,,,,,---......++++++,,,,,,,,,---------))))))***+++,,,------...------------------------...............///000000...000111111000000111333333555999<<<>>>???>>>>>>>>>???BBBFFFMMMWWWaaahhhttt}}}{{{{{{yyymmmcccaaafffgggdddiiijjjlllmmmmmmmmmmmmlllgggeee]]]PPPAAA777444555444333222222111111222222111111111111111111111111000000000000000000000000111111111111000000000000000000000000000000000000////////////////////////////////////000000000000111111111000000000000000333444333222222333666999:::@@@HHHPPPTTTVVVXXXYYY]]]]]]^^^eeeppp~~~~~~~~~wwwsssxxxzzz~~~}}}fffWWWHHHEEENNN^^^ppp}}}{{{}}}}}}|||{{{zzztttlllaaaRRR@@@666555555333///000000///...............,,,------......------,,,++++++++++++,,,------...+++,,,---,,,***)))***+++++++++*********+++---...,,,++++++******++++++,,,......---,,,***)))((((((++++++******++++++,,,---++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,..............................///000000000000000///000000000111111111111333555999===;;;777888<<>><<<888999>>>@@@@@@GGGTTT```lll|||vvvmmmjjjmmmyyyyyyjjjcccfffhhhgggiiijjjlllmmmnnnnnnmmmmmmllljjjcccWWWIII===888777444333222222111111222222111111111111111111111111000000000000000000000000222222111000000///......000000000000000000000000/////////////////////////////////000000000111111111111111111111111111111222333333333333666:::===CCCHHHOOOTTTVVVYYY]]]``````eeennnyyy~~~wwwxxxzzz{{{}}}{{{iiiUUUJJJIIIQQQ```mmmxxx|||~~~{{{zzzzzzwwwqqqkkkaaaRRRDDD:::555333222111000//////....../////////...---,,,,,,---...///...---,,,,,,,,,,,,,,,,,,+++,,,---,,,+++***+++,,,---,,,,,,++++++++++++,,,,,,++++++******++++++,,,***++++++,,,---...//////+++++++++++++++,,,------)))******+++,,,------...,,,,,,,,,,,,,,,,,,------..............................///000000000000000000000///000111333555777:::;;;===???===999;;;@@@CCCFFFPPP___ooo}}}~~~uuukkkggghhhssspppgggfffgggfffiiijjjlllmmmnnnnnnnnnnnnmmmkkkdddYYYLLLAAA999777444333222222111111222222111111111111111111111111////////////////////////222222111000///......---//////////////////////////////////////////////////////000000000111111111000111111111111111222222111222444444666999===AAAGGGMMMSSSVVVWWW[[[aaafffkkkpppyyy||||||}}}||||||~~~ttt___QQQJJJMMMXXXdddsssyyy}}}{{{zzzzzzxxxuuuqqqiii\\\MMM@@@777333333111000000///.../////////000...---++++++---...000///...---,,,,,,,,,,,,,,,+++,,,------+++***+++---------,,,,,,++++++++++++,,,++++++******++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++,,,------+++++++++,,,,,,,,,,,,,,,***+++++++++++++++,,,,,,..............................///000000000000000000000000000222555888:::;;;:::<<<>>><<<999===CCCKKKQQQ^^^ooouuuiiiddddddnnnzzzwwwmmmjjjiiihhhiiijjjlllnnnooooooooonnnllljjjddd[[[OOOCCC:::666444333222222111111222222111111111111111111111111////////////////////////111111000000///......---////////////////////////000000000000000000000000000000000000111111111111000000111111222222222333111333555666888<<>>777444333222222111111222222111111111111111111111111000000000000000000000000.........///////////////000000000000000000000000000000000000000000000000000000111111111222222222000000111222222333444444333555888;;;???DDDJJJOOOPPPUUU[[[]]]___hhhxxxyyywww{{{~~~vvvcccRRRLLLOOOYYYiiixxx|||{{{{{{}}}}}}yyywwwrrrjjj^^^PPPCCC:::222111000000//////000000///..................///...------------......///+++,,,------,,,,,,---///+++,,,---.........---,,,,,,++++++******++++++,,,))))))*********+++++++++---,,,,,,,,,,,,---......,,,,,,,,,,,,------......------......///000000111..............................///000000000000000111333555888999:::999999777666999>>>BBBHHHSSS^^^ooopppfff___[[[```jjjxxxrrreeeaaadddfffiiijjjlllnnnpppppppppppphhhgggddd___WWWLLL@@@999444333222222111111222222111111111111111111111111000000000000000000000000------......///000000000000000000000000000000000000000000000000000000000000111111111111222222222000000111222333333444444333666999<<<@@@FFFLLLQQQQQQWWW]]]___bbbmmm~~~{{{zzz}}}yyyzzzzzz}}}~~~iiiTTTJJJJJJSSSeeewww|||{{{{{{}}}~~~{{{yyyuuuoooeeeWWWHHH===222111111000000000000000......////////////......---------------...///000+++,,,------,,,,,,...///***+++---...///...------,,,++++++++++++++++++,,,......---,,,+++))))))(((---,,,,,,,,,,,,---......)))***+++,,,...///000111******++++++,,,---.................................//////000000000000000111333777:::;;;:::999888888888;;;AAAFFFNNN[[[gggqqqddd]]]\\\___dddzzz{{{pppjjjfffccccccfffgggjjjnnnqqqrrrqqqnnnllllllfffbbbccc]]]NNNAAA;;;888666333222222222222111222222222222222222222222000000000000000000000000222222111111000000//////111111000000000000111111111000///......///000111111111111000000000000000111111111111222333444444888999;;;@@@GGGNNNRRRTTTZZZ[[[]]]aaakkkyyy|||yyyzzzyyy|||qqq\\\PPPMMMQQQ[[[jjjvvv~~~~~~}}}|||xxxuuupppdddQQQCCC777777666333///...///000//////.........---------000000/////////.........------,,,++++++*********,,,++++++******++++++,,,,,,---...---,,,+++---///******,,,---------------++++++++++++++++++++++++---------............///,,,,,,,,,---------......---------......000111111///000111000///000222333333555999:::999888888888999:::???FFFLLLWWWmmmrrrddd]]][[[^^^cccvvvzzzmmmfffbbb___```cccgggiiimmmpppqqqpppnnnlllmmmgggdddddd^^^QQQDDD>>>888666333222222222222111222222222222222222222222000000000000000000000000111111111000000000000000000000////////////000000111111000//////000111111111111111111000000000000222222222222333444666666999;;;@@@FFFLLLRRRUUUVVVZZZ___gggnnnxxx}}}zzzzzz}}}{{{|||vvvbbbSSSNNNMMMVVVcccpppyyy||||||||||||yyywwwsssiiiZZZNNN;;;999777444222000000/////////.........---------......---------,,,,,,,,,++++++++++++++++++,,,,,,,,,,,,++++++++++++,,,,,,,,,---...---++++++---...+++,,,,,,,,,,,,,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,---------............///---------.........//////...------......000111111///000111000000000222444666999;;;======<<<======<<<>>>EEEQQQ\\\jjjssseee]]]ZZZ\\\aaappp~~~yyyjjjaaa]]][[[\\\```fffhhhllloooqqqooommmkkknnniiifffeee```TTTHHHBBB999666333222333333222111222222222222222222222222000000000000000000000000000000000000111111111111/////////....../////////222111111000000111111222111111111111111111111111333222222333444666888999<<>>888444333333111////////////.........---------------------,,,,,,,,,*********+++,,,---------,,,,,,++++++++++++,,,,,,,,,---------++++++---......---,,,+++++++++,,,------------------------------------............///........./////////000000............///000111111///000111111000111333555555777999::::::;;;<<<>>>@@@DDDNNN^^^ooouuufff^^^YYY[[[^^^iiivvvyyyggg^^^ZZZYYY[[[___dddgggkkknnnooonnnkkkiiillliiifffeee```WWWLLLEEE999777444333333444333222222222222222222222222222000000000000000000000000//////000000111111222222000000////////////000000222222222222222222222222000111111111111111222222222222222333444777:::;;;@@@CCCHHHNNNTTTZZZ```ccciiiuuu{{{xxx||||||uuuuuuzzz~~~ooo[[[MMMEEEIIIRRR^^^jjjtttzzz||||||yyyxxxwwwssskkkeeeOOOFFF:::333222333222000////////////............////////////////////////+++++++++,,,,,,,,,------,,,,,,,,,++++++,,,,,,,,,,,,------,,,++++++,,,...///...,,,*********,,,---........................---------............///---.........//////////////////......///000111111///000111111111222444666777888999888888:::<<>>DDDGGGKKKPPPVVV___iiiqqqyyy}}}zzz{{{{{{sssssszzzwwwcccSSSFFFHHHMMMWWWeeeqqqzzz~~~~~~{{{xxxvvvuuurrrnnnjjj[[[OOO>>>444111222222111000000/////////............/////////////////////---------,,,,,,,,,++++++---,,,,,,,,,,,,,,,,,,---+++,,,---,,,******,,,---///...,,,*********,,,---........................---------............///,,,,,,---------.........000////////////000000111///111222222222333555777<<<======<<<<<>>CCCFFFKKKPPPWWW___hhhtttxxxwwwxxxxxx~~~pppaaaNNNJJJHHHOOO]]]mmmyyy~~~~~~}}}|||zzzxxxvvvtttrrrjjjaaaTTTFFF;;;444222111000000000000/////////...,,,,,,,,,---------......------------------,,,,,,------,,,,,,,,,,,,------+++,,,,,,+++******+++---+++,,,,,,,,,,,,,,,,,,------------------------------------............///------------............111111000000000000000111000111222333333444777999::::::;;;>>>CCCKKKUUU\\\lll}}}~~~nnnccc[[[YYY[[[[[[```mmm|||rrrkkkeeeaaa``````cccgggjjjkkkjjjgggeeefffhhhfffaaa______WWWMMM;;;999666555555666555444222222222222222222222222111111111111111111111111222222111111000000//////111111000000000000111111000111222333333222111000000000111222333333444444777777666888;;;@@@FFFIIIMMMTTT^^^gggqqq}}}xxxtttrrryyy|||pppbbbPPPKKKHHHMMM[[[kkkxxx~~~~~~~~~}}}|||zzzxxxwwwlllggg\\\OOOAAA777111000000000000000////////////........./////////000000+++,,,,,,------......///...------,,,,,,------...+++,,,,,,+++******+++---***+++,,,------------------------------------------------.........//////............/////////000111111000000000000000111000111333333333555777999<<<===???CCCJJJVVVbbbjjj{{{uuufff]]]ZZZYYYZZZ\\\fffuuuvvviiidddddddddccceeehhhjjjjjjhhhfffdddeeecccbbbcccccc```YYYTTTEEE???777333444555666555333333333333333333333333111111111111111111111111111111111111111111111111222000///------///000222111111222222222333333333222222222222222222333333555222333999>>>CCCJJJQQQTTT[[[fffsss~~~~~~vvvqqqsssxxxuuummmVVVLLLFFFLLLWWWeeeqqq{{{~~~}}}|||zzzwwwtttrrrooogggXXXGGG:::666666///000000///...---...000........................111...,,,,,,...///...,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++,,,,,,++++++,,,,,,,,,---------..................---------.........//////000000//////000000///...------///////////////000111111///000222444666999===AAA===???CCCIIISSSccctttxxxiii___[[[ZZZYYYZZZcccppp|||~~~nnnhhhfffeeebbbdddgggiiijjjhhhfffdddeeecccbbbcccccc```YYYTTTFFF@@@888444555666666555333333333333333333333333111111111111111111111111111111111111111111111111333111000//////000111333111111222222222333333333333333333333444444444444777555666<<>>EEESSScccuuupppddd___]]]ZZZWWWZZZaaaiiiwwwxxxjjjdddbbb___aaacccfffgggggggggfffdddcccbbbccccccaaaZZZUUUJJJDDD===999888888666444333333333333333333333333111111111111111111111111111111111111111111111111333222111111111111222333111111222222222333333333444444444555555666666666999888<<>><<<:::777444333333333333333333333333111111111111111111111111111111111111111111111111111111111111111111111111111111222222222333333333222333333444555666777777777;;;DDDOOOXXXbbbqqquuuppppppssswww}}}wwwoooggg^^^[[[bbbmmmvvvvvvrrrmmmhhhhhhmmmrrrrrrqqqpppqqqnnneeeWWWLLL;;;777111///111222111///////////////////////////...//////...,,,,,,---///------------------------,,,,,,,,,++++++*********,,,---------............,,,,,,------.../////////------------------------//////000111111111000000000000000000000111222222666777888:::===CCCJJJOOOZZZccctttwwwnnnjjjccc```bbbdddcccfffvvvoooddd___ZZZ[[[^^^aaadddfffhhhhhhgggfffeeeggghhheee```ZZZQQQKKKDDD???===;;;777444333333333333333333333333111111111111111111111111111111111111111111111111111222222222222222222111111111222222222333333333333444444555777888888999:::@@@LLLYYYbbblll{{{wwwrrrrrruuu{{{yyywwwrrriiicccgggpppxxxyyyuuukkk___\\\bbbjjjppppppqqqsssqqqjjj```XXXCCC<<<555222222333111...////////////////////////...///000...,,,+++---///........................,,,,,,,,,,,,,,,,,,,,,+++------------............,,,,,,------...//////000//////////////////////////////000111111111111111000000000111222333444555777888:::>>>DDDOOOZZZaaapppwww|||sssnnneeeccceeegggeeeeeesssmmmaaa\\\YYYZZZ]]]```dddfffhhhiiihhhgggfffhhhiiifffaaa\\\RRRLLLEEE@@@>>>;;;777444333333333333333333333333111111111111111111111111111111111111111111111111222333333444444333333222111111222222222333333333444555666777888999::::::===DDDQQQ___iiissswwwuuuwwwxxxzzz|||yyypppiiillltttzzz|||xxxjjjYYYSSSZZZdddoooqqqssstttrrrmmmfff```IIIAAA999444444333000---000000000000000000000000---///000///,,,+++---///........................,,,------------------------------.........//////,,,,,,------...///000000------...000111333444444//////000111111111111111000000111222333555666777666888<<>>@@@GGGRRR```ooozzzqqquuuzzz||||||zzzyyyzzz}}}zzzrrraaaQQQLLLPPP```hhhnnnppprrrrrrmmmeee\\\QQQCCC:::777666444222000000000000///////////////////////////.........---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,---................................................000000000000////////////000000000000111111111111111222333333222333555777888<<>>:::888555222444444444444444444444444222222222222222222222222222222222222222222222222222222222222222222222222222222333444444444444333555555666666888<<>>AAAHHHQQQ___rrr}}}yyyyyy|||wwwrrrbbb___^^^^^^___aaadddgggdddddddddffffffddd```]]]XXXSSSJJJBBB;;;777555333444444444444444444444444222222222222222222222222222222222222222222222222222222222222222222222222333333333444444444555555777999:::999:::???IIIPPPbbbqqqxxxwww|||}}}qqqbbbTTTJJJDDDLLLXXXeeemmmoooooopppjjjbbbUUUFFF:::333222333000000000000////////////............//////000000...------,,,,,,------............------,,,,,,,,,........................////////////////////////.../////////000000000111111111111111222222222222222222333333333666:::===>>>DDDLLLWWWfffxxx~~~~~~tttwwwpppggg___]]]___```cccfffccccccccceeeeeeddd```]]]WWWSSSKKKCCC<<<888666555444444444444444444444444222222222222222222222222222222222222222222222222333333333333333333333333444444444333444555555666777:::<<<<<<>>>EEEQQQ[[[mmm{{{}}}vvvxxx~~~}}}sssgggVVVIIICCCEEENNN\\\gggkkkmmmoooiiiddd[[[MMM>>>555333333000000000000////////////------......///000000111......------------......//////......---,,,,,,+++........................////////////////////////......//////000000111111111111111222222222222333333444444444555888===AAA???GGGTTTccctttxxxtttzzzuuueee```aaabbbcccfffccccccdddeeefffdddaaa^^^UUURRRLLLDDD===999777777444444444444444444444444222222222222222222222222222222222222222222222222333333333333333333333333555444444333444555666777666:::===???CCCMMM\\\gggwwwyyyvvvyyy~~~~~~wwwmmm\\\MMMFFFBBBEEETTTbbbhhhkkkmmmeeeeee___SSSDDD888333333000000000000////////////.........///////////////......------------.....................---------........................////////////////////////.........///000111111111111111111222222222333333555555555555666:::???CCCDDDNNN]]]ooo}}}uuuxxxkkkeeeeeeeeefffgggddddddeeefffgggfffbbb___TTTRRRLLLEEE>>>999888888444444444444444444444444222222222222222222222222222222222222222222222222333333333333333333333333555555444333444555666777555999>>>BBBGGGSSSdddqqq~~~|||wwwwww{{{}}}|||ssscccRRRHHH@@@@@@NNN^^^fffiiilllhhhiiiggg\\\LLL???999888000000000000////////////000000000///......------......------------......,,,,,,------.../////////........................000000000000000000000000---......///000111111222111111222222222333333333666666666666777;;;AAAEEEIIITTTdddvvvzzz{{{yyyiiieeedddeeeggggggfffeeeeeeeeedddaaa___YYYUUUNNNFFF???999666444555555666666555555444333444444444333333222222222555444222111111222444555333333333444444444555555111333666777666666888999999<<<@@@FFFQQQaaatttvvvlllqqq|||~~~wwwgggWWWHHHAAA???FFFRRR]]]hhhpppkkkiiihhhcccTTTAAA777888111000......000000000///222000---...000000...+++////////////////////////---------...///000000111000///.........///111222333333222111111000111111////////////////////////444666777777555444333333555222222666999<<>>999666555555666666555555444333444444444444555555555555444444444444444444444444444444555555555666666666666777888777777888;;;>>>CCCQQQggg~~~~~~{{{yyyfffXXXKKKLLLUUU\\\aaacccgggiiijjjiiihhhaaaSSSEEE:::666222//////000000000111222222111///......///..............................//////////////////......///000000000000000000000//////000000111111111111111111111111111111444555555444333333555777;;;;;;???DDDGGGLLLYYYeeewwwxxxfffccccccbbbfffeeedddddddddbbb___\\\XXXUUUQQQKKKEEE???:::777555555666666555555444333444444444444555555555666444444555555555555444444555555555555666666666666777777888888888:::>>>AAAJJJ[[[ttt}}}{{{~~~{{{|||ooo^^^OOONNNVVV]]]bbbeeedddiiikkkiiigggcccWWWKKK<<<888444111000111111111000222333222///---...000......................../////////////////////...---...///000111000000/////////111222222222111111333333333333333333333333222333333333222333666888:::<<>>:::555222111222222222000222444222///---...111///////////////////////////////////////.........---...000111111111000///...///222333444333111000444444444444444444444444111222333333444666999<<<:::===DDDLLLRRR\\\lll||||||jjjdddaaa______eeejjjiiigggeeeaaa\\\ZZZWWWRRRMMMHHHBBB<<<888777666666666555555555555444444444444444444444444444444444555555555666666666666666666666555555555888666666999;;;===FFFOOO___qqq}}}vvvvvv{{{~~~uuummm\\\NNNOOO[[[eeegggdddhhhiiigggfffeee___XXXIII===444333333///...000000000000000000000000000///.........------------+++,,,,,,,,,------......000000000000////////////////////////000000000000444444333333222333333333222333555555555666888;;;;;;@@@GGGMMMVVVggg|||{{{ggg___\\\ZZZ^^^eeejjjiiifffeeeaaa\\\[[[WWWQQQLLLGGGBBB<<<999777777666666666555555555444444444444444444444444333333333444444444555555666666666666666666666666666666888<<<===@@@IIITTTkkk{{{~~~}}}vvvuuuyyy~~~~~~}}}xxxqqqbbbSSSPPPZZZdddhhhggghhhhhhfffffffff```YYYLLLAAA666444333111000222////////////////////////////////////.........---....../////////000000000000000000000////////////////////////000000000111222111111111111111222222222444555555666777:::<<>>???CCCQQQ^^^xxx~~~|||zzzzzz{{{}}}~~~vvvsssuuuyyy|||}}}}}}wwwkkk[[[SSSWWW```fffiiihhhfffccceeegggbbbZZZPPPFFF;;;666444222222444000000000000000000000000000000000000//////////////////000000000000111111////////////000000000000/////////000000000111111111111000111111222333444333444555666777999<<>><<<777777777666666666666555555555555555555555555555333333333444444444555555666666666666666777777777777888:::>>>@@@III\\\mmm|||{{{zzzyyyyyy{{{~~~wwwooonnnsssyyy~~~|||rrrbbbVVVTTT[[[bbbiiigggcccaaadddgggccc[[[SSSJJJ???777333222333444222222222222222222222222111111111000000000000///.........///////////////////////////000000000000//////000000000111111111222222222333444555666777444555666777888;;;???BBBIIIKKKRRRbbbxxx|||wwwrrrooollljjjhhheeeddddddccccccjjj___\\\[[[\\\cccgggfffeeeeeeccc___[[[VVVOOOJJJFFFCCC@@@>>>888777777777666666666666555555555555555555555555555555555555666666666666666666666666777777888888:::999:::>>>EEESSSjjj~~~zzzyyyyyyyyyzzz|||~~~{{{oooiiimmmvvv~~~}}}vvviiiZZZRRRUUU\\\dddccc```^^^aaaeeeccc]]]UUUNNNDDD999333222222222222222222222222222222222222111111111000000000000///////////////............/////////000000000111000000000000111111111111333333333333444555666777444666777888999===BBBFFFKKKOOOZZZmmm{{{wwwsssooollliiifffdddbbbaaa```___^^^___```aaa}}}}}}iii___[[[YYY\\\bbbfffeeedddeeedddaaaZZZVVVQQQLLLHHHEEEAAA???888888777777777666666666555555555555555555555555555666666666666777777777555666666777777888888999<<<:::;;;CCCOOObbbyyy~~~xxxxxxxxxyyyzzz|||~~~~~~~~~~~~sssjjjkkkssszzz}}}|||xxxooo```SSSQQQUUU\\\^^^^^^\\\^^^bbbbbb^^^VVVRRRIII===555333222000000000000000000000000000111111111111000000000000111111000000000000//////......//////000000111111000000000111111111222222222222111222222333444555555666777999;;;???EEEIIINNNVVVeee{{{|||wwwkkkhhheeebbbaaaaaa___^^^[[[\\\\\\[[[ZZZ[[[^^^```|||||||||jjjaaa[[[WWW[[[aaaeeedddccceeedddaaaYYYVVVRRRNNNKKKGGGCCC@@@888888888777777777666666555555555555555555555555555555555666666666666777555666666777888888999999===;;;>>>LLL^^^rrr~~~zzzzzzzzz{{{|||~~~}}}||||||}}}|||oookkknnnttt|||zzzyyytttfffWWWPPPQQQSSSYYY\\\[[[[[[^^^```___WWWVVVNNNAAA888666333///////////////////////////111111000000000/////////000000000/////////...............///000111111111000000111111111222222222333333222222222333333444666777888999<<>>FFFNNNTTTbbbsss{{{tttkkkfffeeedddaaa^^^[[[\\\]]]\\\ZZZZZZ[[[]]]___^^^]]]\\\\\\^^^```aaauuuxxxzzzppphhhaaa^^^```ccceeeeeedddcccbbb\\\YYYVVVRRRNNNIIIBBB===:::888666666666777666555555555555555555555555555555555555666666666777777888555444777999888888;;;BBBFFFUUUlll~~~}}}yyyxxxvvvvvvxxx{{{}}}~~~vvvnnnmmmoootttyyyyyyqqqeeeXXXQQQMMMWWW\\\YYYVVVYYY]]]_________[[[QQQDDD999444333000000000000111111111111...........................///000111111000///...000000////////////000000222222222222222333444444333444555444333333555666888999:::<<>>:::888666666777777666555555555555555555555555555555555666666666777777777777444555999:::999;;;>>>DDDPPPfff}}}}}}~~~{{{wwwwwwxxxxxxyyy{{{||||||tttnnnkkkpppwwwyyytttjjj]]]TTTNNNUUUYYYVVVSSSUUUXXXZZZ^^^___\\\TTTHHH<<<555333222111111111111000000000------------------------//////000000000000//////111000000//////000000111222222111111111222222333333444555444333333555777666999===@@@FFFRRRbbbnnnwwwnnnhhhhhhccc^^^]]]___aaa```___bbbbbbaaa___]]]]]]```bbbcccbbbaaaaaaaaacccfffggg|||xxxjjjccc``````aaacccdddcccaaa___\\\ZZZWWWSSSPPPJJJDDD???;;;999777666777777666555555555555555555555555555555666666666666777777777888666888;;;<<<;;;===AAACCCWWWttt~~~||||||}}}yyyuuuvvvvvvvvvvvvxxx{{{}}}}}}rrriiimmmsssxxxwwwooobbbYYYNNNRRRTTTRRRPPPQQQTTTWWW\\\^^^]]]XXXMMMAAA888333333333222111111000//////000000000000000000000000111111111222222111111111111000000000000000000111222111111000111111222222333444555444444444666888666:::@@@EEENNN___sss{{{sssmmmiiigggeeebbb___^^^```ccccccccceeeeeecccaaa___```ccceeeeeedddcccccceeegggjjjlll}}}}}}mmmgggbbbbbbccceeegggeee```\\\\\\ZZZWWWTTTPPPKKKEEE@@@;;;999777777777777777555666666666666666666666666666666666666777777777888999777888;;;:::999===CCCHHHaaa~~~{{{{{{}}}~~~|||}}}}}}xxxtttttttttrrrrrrvvv{{{xxxjjjlllpppuuuxxxrrrggg^^^NNNNNNOOONNNMMMMMMQQQUUU[[[]]]^^^ZZZRRRFFF<<<666444444333222111000//////111111111111111111111111222111111111111111111222111111000000000000111111111111111000111111222222333444555555444555777999777<<>>FFFSSSggg~~~xxxpppjjjgggfffffffffggggggfffeeedddeeeffffffggghhhiiiiiihhhhhhjjjlllkkkkkkkkklllooorrrvvvxxx}}}yyyqqqlllgggeeeffffffccc___\\\ZZZXXXUUURRRMMMGGGBBB<<<:::888777888888777666666666666666666666666666666666777777777888888888888777777999999<<>>333333333222222111111111////////////////////////111000///......///000111222111111000000111111222000000000111333444666666222444555555555666888:::===@@@HHHYYYrrrvvvrrrmmmiiihhhhhhhhhhhhiiiiiiiiihhhhhhhhhiiijjjhhhjjjmmmnnnnnnnnnoooqqqppppppqqqrrruuuyyy}}}~~~xxxqqqhhhcccdddeeeeeeccc]]][[[XXXUUURRRMMMGGGCCC<<<:::888777888888777666777777777777777777777777777777777777888888888888:::888999;;;<<>>:::555222333333000///111222222111000//////000000000111111111111222222222000000000111111222222333222333333333333333333444555666666666777999<<<@@@@@@EEEPPPbbbyyy|||wwwtttrrrooooooppprrrssstttrrrrrrrrrrrrrrrrrrrrrrrrrrruuuyyy}}}}}}{{{yyy}}}|||{{{}}}wwwiiieeeeeedddddddddaaa^^^[[[WWWTTTPPPLLLHHH@@@===999777777888888777888888888888888888888888999999888888888888999999:::===@@@@@@CCCQQQgggxxx|||vvvqqqnnnkkkiiihhhiiiiiiiiijjjiiiiiiiiirrruuuyyy|||||||||||||||zzzxxxuuuttttttvvvxxxzzz~~~yyynnnkkkooosssrrrooo^^^TTTNNNNNNJJJAAA???EEEKKKUUU[[[YYYYYYYYYOOOBBB;;;555222333333111111333222222111000000000000000000111111111111222222222111111111222222222222222222222333333333333444444555666666666666888<<>>:::888888888888777777777777777777777777777999999888888888888999999:::<<<===???GGGZZZttt|||xxxrrrmmmjjjhhhfffdddcccdddeeefffgggiiiiiijjjppptttyyy|||}}}|||{{{{{{xxxvvvsssqqqrrrwww|||zzztttsssttttttsssdddZZZTTTSSSNNNDDD@@@BBBEEEQQQ[[[[[[ZZZYYYQQQHHH>>>777222222222000222555222111000000000000000000000111111111111222222222333333333333222222222222222222222333333444444444555666666666666888;;;>>>EEEJJJUUUeeezzz}}}{{{~~~~~~~~~~~~mmmfffeeeccccccdddaaa___[[[XXXUUUQQQLLLIIIBBB???;;;999888999888777666666666666666666666666999999888888888999::::::::::::;;;@@@MMMdddyyyrrrnnnjjjhhhgggfffeeeccc```aaabbbdddgggiiikkkmmmooosssyyy||||||{{{zzzzzzyyyvvvsssrrruuu{{{}}}zzzxxxxxxjjjaaaZZZWWWRRRIIICCCBBBAAANNNYYY\\\ZZZYYYTTTNNNCCC;;;444222111///111444111111000000000000000111000000111111111222222222444444444333333222222222222222222333333444444444555666666666666888;;;>>>HHHOOO\\\mmmooohhhfffdddcccdddbbb___\\\XXXUUUQQQMMMIIICCC@@@<<<999999999888888666666666666666666666666999999888888999::::::;;;<<<===AAAIIIYYYqqq~~~uuuoooiiigggeeedddeeeeeeeeeddd```aaabbbeeehhhkkknnnpppooosssxxx{{{{{{zzzzzzzzzxxxvvvtttuuuyyy}}}{{{ppphhh```[[[WWWOOOGGGCCC@@@KKKVVVZZZZZZXXXUUUQQQHHH???777333000...///222111000000000000000111111000000111111111222222222444444444333333222222222111111222333333444555555555666666666777999===@@@IIIRRRbbbvvvqqqjjjhhheeeddddddbbb```\\\YYYVVVRRRMMMJJJDDDAAA===::::::999999888777777777777777777777777999999888999999:::;;;<<<;;;>>>FFFTTThhh~~~|||tttmmmhhhbbbaaa```aaacccddddddcccccccccdddfffiiilllppprrrpppssswwwyyyyyyyyyzzz{{{xxxxxxxxx{{{}}}uuummmddd^^^ZZZUUUMMMHHHBBBIIIQQQWWWYYYWWWTTTRRRJJJAAA999555222......111000000000000000111111222000111111111111222222222333333333333222222222222111111222333333444555555555666777777888;;;???CCCIIITTThhhsssllljjjgggddddddbbb```\\\YYYVVVRRRMMMJJJEEEAAA===;;;::::::999888888888888888888888888888999999999999:::;;;<<<<<<999???MMMaaaxxx|||vvvqqqkkkeeebbb```______```ccceeeeeedddeeeeeeeeefffiiillloooqqqqqqsssuuuwwwwwwxxxzzz||||||~~~}}}xxxpppfff___\\\YYYSSSLLLFFFHHHMMMSSSWWWVVVSSSQQQHHH@@@999666333000000333000000000000000111222222000111111111111222222222111111111222222222222222000111111222444555555666444555777888:::===BBBFFFMMMZZZpppsssmmmkkkhhheeedddccc```\\\YYYVVVRRRMMMJJJEEEBBB>>>;;;::::::999888888888888888888888888888999999999999:::;;;<<<===<<>>;;;:::999999888777888888888888999999999:::::::::;;;<<<===;;;:::AAAIII[[[uuu{{{vvvrrrmmmfffbbbbbbbbbaaa```___aaacccfffggghhhhhhhhhjjjjjjjjjjjjjjjlllpppsssrrrsssuuuvvvwwwzzz~~~uuuwwwrrrggg^^^___ccc```XXXNNNIIIIIIQQQXXXXXXSSSPPPKKKEEE<<<666444444333222333333333222222222111111111111111111111111111111222222111111111111111111444444444555555555555555888555555888:::<<>>;;;:::999999888888888888888999999999999:::999:::;;;<<<<<<<<<;;;BBBMMMccc~~~zzzqqqlllgggccc___]]]___aaabbbaaa___```cccfffhhhiiijjjjjjjjjkkklllmmmmmmooorrruuuuuuvvvwwwxxxzzz}}}{{{rrrsssoooggg^^^^^^bbbaaa[[[SSSMMMLLLSSSYYYXXXTTTRRRNNNGGG>>>888555444333222333333333222222222111111111111111111111111111111333333333222222222222222444444444555555555555666777555666999;;;???GGGQQQ___tttqqqeeeccceeeffffffeeebbb]]]YYYVVVSSSOOOMMMGGGCCC>>>;;;::::::999999888888888888999999999:::999999999:::;;;<<<======BBBRRRlllwwwnnngggccc___]]][[[[[[^^^aaabbbccc___```ccceeehhhiiijjjkkkjjjllloooqqqrrrtttvvvxxxxxxyyyzzz{{{}}}xxxpppooonnniiibbb___bbbcccbbbYYYSSSQQQVVVZZZYYYUUUTTTRRRKKKBBB:::666444444444333333333222222222111111111111111111111111111111333333333444444444444444444444555555555666666666777555777:::===BBBLLLWWWjjj~~~qqqfffdddeeefffhhheeebbb]]]YYYVVVSSSOOOLLLGGGCCC>>>;;;::::::999999888888888999999999::::::888999999999:::<<>>CCCOOO\\\qqqooofffdddcccdddfffcccaaa]]]YYYVVVRRRNNNKKKGGGDDD???<<<;;;::::::999888999999999999:::::::::888999:::::::::<<>>DDDSSSaaawwwlllfffddd``````dddccc```]]]ZZZVVVRRRNNNJJJHHHDDD???<<<;;;;;;::::::999999999999::::::::::::999:::;;;::::::===DDDJJJYYYpppwwwsssmmmfffaaa___^^^___]]]```ccceeefffgggiiikkkeeefffggghhhkkkmmmpppqqqsssvvvyyyzzzzzzyyyxxxyyyxxxyyyzzz||||||uuuqqqkkkiiihhhfffbbb___bbbhhhhhhcccaaabbbaaa\\\YYYYYYTTTQQQLLLDDD<<<666555555333333333222222222111111111111111111111111111111111111222222333333444444444444555666777777888999999999;;;>>>@@@HHHYYYhhhnnnjjjgggbbb```dddcccaaa^^^[[[XXXTTTNNNKKKHHHDDD???<<<;;;;;;::::::999999999:::::::::;;;;;;:::;;;<<<;;;;;;???GGGMMMddd{{{~~~yyykkkhhhdddaaa^^^^^^___```aaaeeehhhiiiiiihhhiiijjjfffgggiiilllpppuuuyyy{{{zzz|||~~~}}}{{{yyyyyyyyy{{{{{{|||~~~zzzwwwoookkkhhhhhheeeaaaaaafffhhheeedddfffddd]]]YYYYYYRRRQQQMMMFFF>>>777555444333333333222222222111111111111111111111111111111222222222333444555555555444444555666777888999999888999===AAADDDNNNaaasssqqqooollleeecccgggdddbbb___\\\YYYUUUPPPLLLHHHDDD@@@<<<;;;;;;;;;:::999999:::::::::;;;;;;;;;:::<<<===<<<;;;???HHHPPPiii~~~qqqllleeecccaaa___^^^```aaaccciiilllooonnnkkkhhhggghhhfffgggjjjooouuu{{{|||zzzzzzzzz}}}~~~}}}uuunnnkkkllliiiddddddhhhhhhffffffhhheee^^^YYYYYYPPPPPPNNNHHH???888444444333333333222222222111111111111111111111111111111333333444444555666777777444444555666777888999999777999===BBBGGGRRRgggzzzwwwrrrpppjjjgggjjjdddcccaaa]]]XXXSSSOOOLLLGGGEEEBBB>>><<<;;;;;;;;;888888777777888888999:::<<<;;;;;;<<<===@@@LLLXXXxxxxxxkkkccc___``````aaadddgggjjjkkkllloooppppppmmmjjjhhhgggjjjlllqqqwww}}}~~~||||||}}}~~~}}}rrrjjjllllllccc___bbbdddeeeffffffccc___[[[XXXWWWSSSMMMHHHCCC===777444222222222222222222222222333333333333333333333333222222333333333444444444555555666666777777888888666<<>><<<;;;;;;;;;999999999999999::::::;;;;;;;;;<<<===>>>CCCRRRbbbxxxmmmddd```______aaacccgggjjjnnnpppppprrrrrrqqqooommmmmmmmmqqqsssxxx~~~}}}{{{{{{|||~~~vvvlllmmmkkkccc^^^```dddeeeffffffdddaaa\\\ZZZXXXUUUOOOIIIDDD>>>888444111111111111111111111111333333333333333333333333222222333333333444444444555555666666777888888888666<<>><<<;;;;;;;;;:::::::::::::::;;;<<<<<<:::;;;>>>??????GGG[[[ooo|||qqqhhhbbb```___]]]___aaaeeejjjooosssvvvuuuuuutttrrrqqqqqqsssvvvzzz}}}|||yyyzzz|||~~~{{{pppnnnkkkbbb]]]^^^cccdddffffffeeebbb^^^\\\ZZZWWWQQQLLLFFF@@@999555222222222222222222222222333333333333333333333333333333333333444444444444555555666777777888888999777<<>><<<;;;;;;;;;:::::::::::::::;;;;;;<<<:::<<>><<<;;;;;;;;;999999999999999:::;;;;;;;;;===???@@@AAAMMMhhhwwwnnn}}}qqqnnniiiccc___]]]\\\\\\\\\^^^ccciiiooouuuyyy{{{vvvvvvuuutttuuuxxx~~~~~~vvvooojjjfffaaa```]]]___aaacccccc```^^^\\\[[[XXXTTTPPPJJJDDD===888555555555555555555555555333333333333333333333333333333444444444555555555666666777777888999999999:::===DDDNNN___wwwoooiiihhhfffdddfffeeebbb___ZZZTTTPPPMMMGGGEEEBBB>>><<<;;;;;;;;;999999999999999::::::;;;<<<<<<>>>AAAEEETTToooyyymmmiiizzzxxxrrrdddcccbbb___]]]\\\ZZZZZZ___bbbfffkkkqqquuuyyyzzzuuuwwwxxxyyy{{{~~~zzzooojjjgggccc```\\\^^^```bbbbbb___]]][[[ZZZXXXTTTPPPLLLFFF???:::333333333333333333333333333333333333333333333333333444444444555555555555666666777888888999999:::;;;@@@IIIWWWjjjpppjjjiiigggccceeedddaaa^^^YYYTTTOOOMMMGGGEEEBBB>>><<<;;;;;;;;;:::::::::::::::;;;<<<<<<<<<;;;===BBBKKK\\\wwwnnnfffggg{{{{{{tttmmmhhh______``````aaaaaa``````dddfffjjjooosssvvvxxxyyyvvvzzz~~~}}}pppjjjgggbbb^^^]]]^^^aaabbbbbb```\\\ZZZXXXVVVSSSQQQMMMGGG@@@<<<222222222222222222222222333333333333333333333333444444444444555555555555666777777888888999::::::===CCCOOObbbxxxsssmmmmmmjjjddddddcccaaa]]]XXXSSSOOOLLLGGGEEEBBB???<<<;;;;;;;;;<<<;;;;;;;;;;;;<<<======;;;:::<<>>EEETTTiiiwwwllliiifffaaadddcccbbb___ZZZUUUPPPMMMFFFEEECCCAAA>>>===<<<<<<999999::::::<<<===???@@@===;;;>>>IIIYYYllliii\\\```kkk~~~~~~uuukkkdddbbbbbbcccbbbcccfffhhhkkkmmmoooooosssrrrqqqrrruuuxxxyyyzzz}}}~~~zzznnneee___\\\ZZZ___cccdddaaa^^^\\\\\\YYYWWWSSSPPPMMMHHHCCC???666666555333111000111333333333333444444444555555666666666666666555555555555777999999999:::;;;===AAAFFFXXXttt}}}oookkkiiieeeccccccaaa^^^ZZZTTTPPPMMMFFFEEECCCAAA???===<<<<<<:::::::::;;;<<<===>>>???>>><<>>CCCJJJ]]]yyyssslllkkkjjjcccbbbaaa^^^YYYTTTOOOLLLGGGFFFDDDAAA???>>>===<<<<<<;;;;;;;;;<<<======>>>???===BBBRRRfffyyy{{{cccXXX___ooozzzuuupppmmmhhhdddaaaaaacccdddooopppsssvvvxxxxxxxxxwwwwwwwwwwwwxxx{{{|||yyy{{{{{{nnnccc]]]ZZZ]]]aaacccaaa^^^\\\[[[XXXVVVSSSPPPMMMIIIDDD@@@:::999777555444444444444333333333444444444555555555555666666666666666666666777999999999;;;===???EEEOOOfff|||uuullljjjkkkcccbbb```]]]YYYTTTOOOLLLGGGFFFDDDBBB@@@>>>=========<<<<<<<<<<<<<<<======??????GGGZZZooosss```XXXaaarrryyyqqqlllggggggffffffgggjjjlllnnnwwwyyy{{{||||||{{{yyywwwxxxzzz|||~~~|||{{{}}}ssseee]]]ZZZ]]]```cccbbb___\\\[[[WWWUUUSSSPPPNNNJJJEEEAAA;;;999666555444444444333333333333444444444555555555555555555666666666666666777999999:::<<>>>>>======<<<<<<<<<======>>>???BBBNNNcccxxxnnn___ZZZbbbttt{{{rrrllliiibbbdddhhhlllppptttwwwxxx~~~}}}{{{xxxvvvzzz~~~wwwggg^^^[[[]]]```ccccccaaa^^^[[[WWWUUUSSSQQQOOOKKKGGGCCC<<<999555444444444333222333333333444444444555555444555555555666666777777666777999999:::===@@@CCCKKK^^^zzzzzzqqqkkkhhhdddcccbbb___ZZZUUUPPPMMMIIIHHHFFFCCCAAA@@@???>>>===<<<<<<<<<===>>>>>>???AAAHHHYYYooolllaaa\\\cccssszzzsssmmmkkkiiieeehhhnnnuuuzzz~~~~~~|||zzzyyyzzzkkkaaa]]]^^^```ccceeeccc___\\\XXXVVVTTTRRRPPPMMMIIIFFF===999555444555555333111333333333444444444555555444444555555666777777777666777999999:::>>>BBBFFFRRRggg|||{{{zzzpppjjjeeedddccc```[[[VVVQQQNNNIIIHHHFFFDDDBBB@@@??????<<<<<<<<<<<<===>>>@@@@@@DDDOOOddd{{{lllddd]]]cccooozzzsssooommmmmmnnnooossszzz}}}ooofff^^^___aaadddgggfffaaa]]]YYYWWWUUUTTTRRROOOKKKHHH???;;;666555666777444111333333333444444444555555444444555555666777777888777777888999;;;>>>CCCGGG[[[rrrxxxvvv{{{vvvmmmfffeeeccc```\\\WWWRRROOOIIIHHHFFFDDDBBB@@@@@@???;;;;;;;;;<<<===???@@@AAAFFFTTTllllllfff]]]bbblll}}}wwwqqqoooooorrrtttzzz~~~rrrjjj______aaaeeehhhgggbbb^^^YYYXXXVVVUUUSSSPPPLLLIIIAAA<<<777666888888666222333333333444444444555555444444444555666777777888777888888999;;;???DDDHHHbbbyyyppprrrzzzyyyrrriiifffccc___\\\XXXSSSPPPLLLKKKIIIFFFCCC@@@>>>===>>>===:::999<<>>======<<<;;;;;;>>>BBBDDDDDDUUUrrrxxxiiibbbdddlll}}}zzzqqqhhhhhhhhhhhhhhhfffdddbbb[[[YYYVVVSSSQQQNNNJJJGGGBBB>>>888555444444444444444333333333444444555666777777666666666666777777888:::777888>>>>>>HHH]]]tttvvvnnnrrr{{{vvvllliiieeebbb^^^ZZZUUUQQQKKKJJJHHHFFFCCCAAA???>>><<<;;;<<<>>>@@@CCCGGGIII```qqqjjjjjjrrrwwwlllkkkjjjjjjiiigggcccaaa]]]ZZZWWWSSSQQQNNNJJJGGGCCC???999555444444444444444444444333444444555666777777666666666666777777777999666999@@@BBBNNNeee|||ooommmrrr{{{sssmmmjjjfffbbb^^^YYYTTTPPPKKKJJJHHHFFFCCCAAA???>>><<<;;;===???AAABBBGGGMMMhhhzzzzzz}}}ssspppmmmlllkkkhhhddd```___[[[WWWSSSPPPMMMIIIGGGDDD@@@:::666555555555444555555444444444444555555777666666666666777777888777999777999@@@DDDRRRlllvvvkkkkkkqqq{{{~~~rrrmmmjjjeeeaaa]]]XXXRRRNNNJJJIIIHHHFFFCCCAAA@@@???>>><<<>>>@@@@@@@@@HHHRRRppp~~~yyyrrrooommmjjjeeeaaa___\\\WWWSSSPPPMMMJJJHHHEEEAAA;;;777555555555555666555555444444444555555666666666666666777888888888;;;888:::@@@EEEVVVrrrrrrkkklllrrr{{{tttnnnkkkfffaaa]]]WWWQQQMMMJJJIIIHHHFFFCCCAAA@@@??????===???AAA@@@@@@KKK[[[{{{xxxrrrooolllgggccc```\\\WWWSSSPPPNNNKKKIIIFFFBBB<<<888666666555555777666555555444555555555666555555666666777888999999<<<:::;;;BBBHHH\\\zzzyyyooolllnnnsss|||wwwppplllgggbbb]]]XXXRRRNNNJJJIIIGGGFFFCCCBBB@@@???@@@===???CCCAAABBBRRRfff~~~tttqqqnnniiieee___[[[VVVSSSPPPOOOMMMKKKGGGBBB===888666666555555777777666555555555555555555555555555666777888999999===;;;===EEEMMMdddqqqllllllpppuuu}}}wwwqqqnnniiiddd___YYYSSSOOOIIIIIIGGGFFFDDDBBB@@@@@@@@@===???CCCCCCEEEXXXooovvvrrroookkkfff___[[[VVVRRRPPPOOONNNLLLGGGCCC===999777666666555777777666555555555555555555555555555666777999999999===<<>>@@@HHH]]]zzz|||nnniiijjjkkkrrrxxx}}}wwwoooggg```YYYSSSPPPLLLJJJHHHFFFDDDCCCBBBAAAAAA@@@AAAEEELLL]]]www~~~yyysssooojjjfff```\\\WWWTTTRRRPPPMMMKKKHHHFFFAAA===999777666666555555555555666666666666555555555555666777888888888;;;???DDDOOOeeevvviiifffiiillluuuzzzzzzpppggg```YYYSSSPPPLLLKKKIIIFFFDDDCCCBBBBBBAAA@@@AAAEEEQQQggg}}}sssppplllgggaaa]]]YYYUUURRRPPPMMMKKKIIIFFFBBB>>>:::777555555555555555555666666666666666666666666777888999:::888;;;???FFFTTTkkkpppfffdddhhhnnnxxx|||zzzqqqhhh```YYYSSSPPPLLLKKKIIIGGGEEECCCBBBBBBBBBAAAAAAFFFUUUnnnvvvsssoooiiiccc___ZZZVVVSSSPPPMMMKKKIIIGGGCCC???;;;888666555555555555555666666666666666666666666777888999:::999:::???HHHYYYppp~~~mmmfffdddjjjqqqyyy}}}zzzrrriiibbbZZZTTTPPPMMMKKKIIIGGGEEEDDDCCCBBBBBBBBBCCCHHHZZZuuu{{{vvvrrrkkkddd```[[[VVVSSSPPPMMMKKKHHHFFFCCC???<<<999666555555555555555666666666666555555555555666777888888:::;;;@@@LLL___wwwxxxlllgggfffjjjrrryyy}}}{{{tttllleee]]]VVVQQQMMMLLLJJJGGGEEEDDDCCCBBBAAACCCDDDJJJ___}}}zzzuuummmeeeaaa\\\WWWSSSPPPMMMJJJFFFEEECCC@@@<<<:::777666555555555555666666666666666666666666666777999999;;;<<>>EEEUUUmmmoookkkjjjgggjjjqqqwww{{{zzzpppeee]]]XXXVVVRRRNNNJJJGGGFFFEEEDDDCCCCCCEEEHHHQQQhhh~~~~~~~~~sssooolllfff^^^XXXUUURRRMMMJJJFFFEEECCC@@@===:::888777666666666666777777777777555555555555666888999:::999;;;FFF[[[sss}}}kkkddddddfffjjjmmmwwwzzz~~~tttiii```ZZZVVVQQQNNNIIIFFFEEEEEECCCBBBCCCEEEJJJUUUlll}}}uuupppkkkeee]]]XXXTTTQQQMMMIIIFFFEEECCC@@@===:::888777666666666666777777777777666666666777888999:::;;;<<<>>>III]]]tttwwwhhhccceeehhhlllpppwwwzzz}}}wwwlllbbbZZZUUUPPPMMMHHHFFFEEEDDDCCCBBBBBBFFFMMM[[[rrr||||||~~~uuuooojjjddd\\\WWWSSSPPPLLLHHHGGGEEECCC@@@===:::888777666666666666777777777777777777777888999:::;;;<<<>>>AAAMMMaaawww|||ooocccaaaeeejjjoootttwwwzzz}}}wwwlllbbbYYYSSSOOOLLLHHHEEEDDDDDDCCCBBBAAAFFFQQQccczzzvvv|||~~~rrrkkkhhhbbb[[[VVVSSSPPPKKKHHHGGGFFFCCCAAA>>>;;;888777666666666666777777777777777777777777999:::;;;<<>>;;;999888666666666666777777777777666666666777888999:::;;;???EEESSShhh|||nnnfff```bbbeeehhhmmmqqqxxxzzz}}}{{{qqqggg^^^YYYPPPLLLIIIFFFFFFFFFEEEDDDDDDLLL___www|||ttt{{{}}}yyylllggggggaaaZZZUUUSSSPPPLLLIIIHHHFFFDDDAAA>>>;;;999888666666666666777777777777666666666777888999:::;;;AAAGGGVVVjjj~~~kkkeeebbbcccfffgggjjjnnnvvvxxx{{{~~~~~~rrrggg___ZZZPPPMMMIIIGGGGGGGGGGGGFFFHHHQQQggg{{{zzz~~~{{{}}}yyyoookkkgggbbb[[[VVVSSSQQQMMMJJJHHHGGGDDDBBB>>><<<999888666666666666777777777777777777777888999:::;;;<<>>;;;888777777777777777777777777888999999999888888;;;===DDDQQQaaaoookkkcccbbbaaabbbdddgggkkkmmmpppqqquuuwwwwwwzzzrrrjjjcccWWWUUUNNNIIIHHHHHHGGGHHHLLLUUUkkk~~~yyyyyyzzzzzz|||~~~~~~~~~}}}wwwpppjjjbbb[[[UUUPPPLLLIIIHHHFFFCCCAAA@@@>>>;;;999777777777777777777777777777888999999888999;;;===FFFSSSbbbppp{{{fff```______```bbbeeehhhjjjmmmoootttwwwwwwzzztttjjjcccWWWUUUOOOJJJIIIIIIGGGJJJNNNZZZrrr~~~xxxwwwxxxwwwyyy}}}{{{|||{{{zzzzzz||||||sssmmmddd\\\VVVPPPLLLIIIIIIFFFDDDBBB@@@>>>;;;999777777777777777777777777777888:::::::::;;;===???IIIVVVeeessstttbbb^^^^^^^^^___aaadddfffhhhkkkmmmrrrvvvwwwzzzuuujjjbbbWWWTTTOOOKKKJJJIIIHHHLLLRRRccc}}}}}}xxxxxxxxxvvvxxx{{{zzzzzzzzzzzzyyy{{{~~~uuuooofff^^^WWWQQQLLLIIIIIIGGGDDDBBB@@@>>><<<999777777777777777777777777888:::<<<======>>>@@@BBBIIIVVVffftttnnn```]]]]]]^^^___aaadddfffgggiiikkkpppuuuvvv{{{wwwkkkcccXXXSSSNNNKKKJJJIIIIIIOOOVVVjjj}}}zzz{{{{{{yyyyyy{{{zzz{{{||||||||||||~~~~~~wwwqqqhhh___XXXRRRNNNKKKIIIGGGDDDBBBAAA???<<<:::777777777777777777777777888:::===??????@@@BBBCCCHHHVVVggguuuiii___\\\]]]^^^___aaadddfffggggggiiinnnsssvvv|||yyylllcccYYYQQQNNNKKKKKKJJJKKKRRRZZZrrr~~~~~~|||}}}{{{}}}}}}wwwqqqhhh```YYYTTTOOOLLLJJJGGGDDDBBBAAA???<<<:::777777777777777777777777666999===???@@@AAABBBDDDJJJYYYjjjyyywwwddd]]][[[\\\]]]___aaacccdddeeeggghhhlllqqquuu~~~zzzmmmdddZZZPPPMMMKKKKKKJJJKKKSSS\\\{{{||||||wwwrrriii```ZZZTTTPPPMMMJJJHHHEEECCCAAA???<<<:::777777777777777777777777555888<<<>>>???@@@BBBCCCNNN]]]ooo~~~sssaaa\\\ZZZZZZ\\\^^^```bbbcccdddfffhhhkkkpppuuuyyyqqqfffXXXSSSMMMJJJLLLKKKLLLVVVddd}}}}}}}}}}}}||||||~~~xxxuuuqqqkkkddd[[[TTTNNNKKKHHHGGGFFFCCCAAA>>><<<;;;999999888888888888999999;;;<<<===<<<:::<<>>===999999888888888888999999888:::;;;::::::<<>>999999888888888888999999777999;;;:::999<<>>999999888888888888999999777999:::::::::===CCCHHHUUU```qqqvvveee^^^\\\^^^^^^___```aaabbbbbbccceeegggjjjpppyyy}}}{{{uuurrrkkk]]]RRRMMMKKKLLLOOOYYYrrr~~~~~~|||}}}~~~~~~~~~yyy{{{}}}}}}{{{yyyoooooonnnooopppsssvvvxxxxxxzzz||||||xxxrrrnnnllljjjjjjjjjjjjkkklllmmmmmmkkkmmmppprrrtttuuuuuutttpppppprrruuuyyy~~~xxxvvvqqqjjjaaaXXXPPPKKKGGGFFFEEECCCAAA???>>>===999999888888888888999999777999;;;;;;;;;>>>DDDJJJVVVaaarrrsssccc]]][[[\\\]]]^^^```bbbbbbccccccdddfffiiioooxxx~~~}}}xxxtttlll^^^SSSOOOMMMOOORRR\\\vvv|||~~~~~~~~~zzz{{{}}}}}}{{{zzzqqqpppooonnnnnnppprrrssstttvvvxxxxxxtttpppmmmkkkggggggffffffffffffggggggbbbccceeeggghhhhhhgggfffeeefffhhhlllppptttwwwyyy{{{}}}}}}zzztttkkkaaaXXXQQQMMMHHHGGGEEECCCAAA???===<<<999999888888888888999999777999;;;<<<<<<@@@FFFKKKVVVaaassspppaaa[[[XXXYYYZZZ]]]___aaacccccccccaaadddhhhnnnyyyzzzuuulll^^^TTTPPPOOORRRTTT^^^yyy~~~{{{}}}}}}}}}|||~~~|||zzz|||~~~~~~|||zzzrrrqqqooonnnmmmnnnpppqqqrrrtttvvvuuurrrooolllkkkeeeeeedddccccccccccccccc^^^___```aaaaaaaaa```___]]]___bbbfffjjjmmmppprrrtttuuuyyy||||||uuulllaaaXXXQQQMMMHHHGGGFFFCCCAAA>>><<<;;;999999888888888888999999777:::<<<<<<===AAAGGGMMMVVVaaatttnnn```YYYVVVWWWYYY\\\___aaaccccccccc```cccgggnnnzzz{{{|||xxxmmmaaaVVVRRRNNNNNNVVViiixxx}}}{{{zzz~~~}}}~~~~~~~~~}}}{{{wwwsssooommmmmmnnnnnnnnnqqqppppppqqqqqqnnnjjjgggeeebbb___^^^___`````````\\\[[[[[[ZZZZZZZZZZZZZZZ]]]]]]]]]^^^```bbbcccdddjjjkkkmmmqqqtttyyy|||~~~~~~{{{tttoooggg\\\RRROOOHHHFFFBBBAAA@@@@@@???>>>999999999888999999::::::888999::::::;;;AAAIIIPPPXXXaaarrrhhh[[[YYYXXXWWWZZZ___aaabbbaaaaaaaaaaaacccggglllvvv}}}~~~zzzmmmbbbWWWSSSPPPQQQ[[[ssszzz{{{}}}}}}}}}{{{wwwrrrooonnnnnnmmmmmmpppoooppppppqqqnnnkkkgggcccaaa^^^\\\]]]^^^^^^]]]ZZZYYYXXXXXXWWWWWWXXXXXXXXXYYYYYYZZZ\\\]]]___```dddeeegggjjjmmmppprrrssstttuuuvvvxxx{{{}}}uuuppphhh\\\RRROOOIIIFFFCCCAAAAAA@@@???>>>:::999999888999999::::::888:::;;;;;;<<<@@@HHHNNNWWWbbbttt~~~fff[[[XXXXXXWWWZZZ^^^aaaaaaaaaaaaaaaaaadddhhhnnnxxx|||nnnbbbXXXUUUQQQSSSbbb}}}}}}|||~~~{{{vvvrrrpppooommmlllnnnnnnnnnoooooonnnkkkhhhbbb___\\\[[[[[[[[[ZZZZZZWWWVVVUUUUUUTTTTTTUUUUUUSSSTTTUUUVVVWWWXXXYYYZZZ\\\^^^```cccdddeeeeeeeeeggghhhjjjkkknnnttt{{{wwwqqqhhh\\\SSSOOOIIIFFFCCCAAAAAA@@@???>>>::::::999999888999999:::888:::<<<<<<===@@@GGGLLLVVVbbbwwwzzzcccYYYXXXXXXWWWZZZ^^^`````````aaaaaaccceeejjjpppzzzpppbbbYYYVVVRRRTTTggg}}}{{{||||||xxxtttrrrpppnnnllllllllllllmmmmmmmmmjjjhhhaaa^^^[[[ZZZZZZYYYXXXWWWUUUUUUTTTSSSSSSSSSSSSSSSQQQQQQSSSTTTUUUVVVVVVWWWYYYZZZ\\\^^^___^^^]]]\\\^^^___```bbbeeekkkrrrwww{{{rrriii]]]SSSOOOJJJGGGDDDBBBAAA@@@???>>>::::::999999888888999999888:::======>>>@@@FFFJJJTTTbbbyyyuuu```XXXWWWXXXVVVYYY]]]_________```aaacccfffjjjqqq}}}rrrcccYYYVVVRRRUUUkkk|||{{{||||||xxxuuusssqqqooommmjjjiiiiiijjjjjjjjjhhhfff___]]][[[ZZZYYYYYYWWWUUUUUUTTTSSSSSSRRRRRRSSSSSSQQQRRRSSSTTTUUUVVVVVVUUUUUUWWWXXXZZZZZZYYYWWWVVVXXXYYYZZZ[[[^^^cccjjjoooxxxuuukkk___UUUPPPKKKHHHDDDBBBAAA@@@???>>>;;;:::999999888888888999888:::======>>>@@@FFFJJJSSSccczzzqqq]]]VVVVVVWWWVVVYYY\\\]]]^^^^^^```aaadddeeejjjqqq~~~sssdddXXXWWWSSSWWWooo||||||~~~~~~~~~}}}zzzwwwtttrrrooommmiiihhhffffffggggggeeeccc]]][[[YYYYYYYYYXXXVVVTTTTTTSSSSSSRRRRRRRRRRRRRRRPPPRRRSSSUUUVVVVVVUUUTTTRRRSSSTTTUUUUUUTTTSSSSSSTTTUUUVVVVVVXXX]]]ccchhhsssxxxnnnaaaVVVQQQKKKIIIEEEBBBAAAAAA???>>>;;;;;;:::999888888888888888:::<<<<<<===@@@GGGLLLUUUeee|||nnnZZZUUUVVVVVVVVVXXX[[[\\\]]]]]]___aaaddddddhhhppp~~~tttdddVVVWWWVVV[[[ttt}}}~~~~~~}}}~~~}}}yyyvvvsssooolllhhhfffdddddddddcccaaa___YYYWWWVVVVVVWWWVVVTTTSSSSSSRRRQQQQQQPPPPPPQQQQQQOOOPPPRRRTTTTTTTTTSSSRRRQQQQQQRRRRRRSSSSSSTTTTTTUUUUUUVVVVVVWWW[[[aaaeeeqqq}}}zzzpppcccXXXRRRLLLIIIEEECCCBBBAAA???>>><<<;;;:::999888888888888888:::;;;;;;<<<@@@HHHNNNYYYiiilllYYYTTTUUUUUUVVVXXXZZZ\\\\\\]]]___aaacccccceeennn}}}uuudddUUUXXXXXX^^^yyy~~~~~~}}}|||}}}|||xxxsssnnnkkkgggeeecccbbbbbbaaa___]]]VVVUUUTTTUUUUUUUUUSSSQQQRRRQQQPPPPPPOOOOOOPPPPPPMMMNNNPPPRRRRRRRRRPPPPPPRRRRRRRRRSSSTTTUUUWWWXXXXXXXXXXXXXXXYYY\\\aaafffqqq}}}|||qqqeeeYYYSSSLLLIIIFFFCCCBBBAAA???>>><<<;;;:::999888888888888888999::::::;;;AAAIIIPPP]]]kkkkkkXXXSSSUUUUUUVVVXXXZZZ[[[[[[]]]___aaacccbbbccclll}}}uuuhhhVVVVVVXXXeee|||}}}~~~|||}}}~~~xxxqqqkkkgggeeeaaa___^^^]]]\\\[[[XXXUUURRRRRRSSSUUUUUUUUURRRQQQPPPOOOOOOOOOPPPQQQRRRQQQPPPOOOOOOPPPQQQQQQTTTTTTSSSSSSTTTTTTUUUUUUVVVVVVWWWYYY[[[^^^bbbdddqqqyyy{{{pppggg[[[SSSKKKHHHEEECCCCCCBBB@@@>>>;;;:::999999999:::;;;<<<<<<::::::===???AAAGGGNNN^^^llllllZZZVVVWWWWWWZZZ[[[]]]^^^______^^^^^^___^^^```jjjzzzvvvhhhYYYXXXYYYfffzzz{{{}}}~~~~~~zzzsssmmmgggddd```^^^]]]\\\[[[YYYWWWUUURRRQQQRRRTTTTTTTTTRRRRRRQQQPPPPPPPPPQQQRRRQQQPPPNNNNNNMMMNNNOOOOOOSSSRRRRRRRRRRRRTTTUUUVVVYYYZZZ[[[\\\]]]```ccceeennnwww{{{qqqggg[[[SSSKKKHHHEEECCCCCCBBB@@@>>>;;;:::999999999:::;;;;;;;;;999:::===???@@@FFFMMM^^^mmmhhhVVVSSSUUUVVVZZZ[[[\\\^^^^^^^^^^^^]]]______cccmmm~~~xxxiii\\\YYYZZZggg|||xxxyyy{{{}}}uuuooofffccc___]]]\\\[[[YYYWWWVVVSSSQQQPPPQQQRRRRRRRRRRRRRRRQQQQQQQQQQQQRRRSSSQQQPPPOOONNNMMMNNNOOOOOORRRRRRQQQQQQRRRUUUWWWYYY^^^___`````````aaadddfffkkkttt}}}ssshhh\\\SSSKKKHHHEEEDDDCCCBBB@@@>>>;;;;;;:::999999999:::;;;;;;888999<<<>>>???EEELLL]]]llleeeTTTSSSVVVVVVYYYZZZ\\\]]]^^^^^^]]]]]]```aaafffrrryyyiii^^^ZZZZZZhhh}}}{{{wwwxxxyyy~~~~~~vvvpppfffccc___\\\ZZZYYYWWWUUUTTTRRRPPPPPPQQQQQQQQQPPPQQQQQQQQQQQQQQQRRRRRRRRRSSSRRRQQQOOOOOOOOOPPPQQQSSSRRRQQQRRRTTTWWW[[[]]]aaaccceeedddcccbbbdddgggkkkuuuwwwjjj^^^UUUKKKIIIFFFDDDCCCBBB@@@???<<<;;;:::999999999:::;;;:::888888<<<===???EEELLLYYYjjjdddUUUUUUXXXYYYYYYZZZ[[[]]]]]]]]]]]]\\\aaacccjjjvvvzzzjjj___ZZZ[[[jjjxxx|||xxxyyyyyy}}}~~~vvvpppfffccc___[[[YYYXXXUUUTTTRRRPPPOOOOOOQQQQQQQQQPPPPPPPPPQQQQQQRRRRRRRRRRRRRRRQQQPPPOOOOOOPPPQQQRRRRRRRRRRRRSSSUUUYYY\\\^^^dddgggiiihhheeeccceeehhhooo{{{{{{lll```XXXLLLIIIFFFDDDDDDCCCAAA???<<<;;;:::999888999:::::::::888888<<<===???EEELLLVVVgggcccUUUVVVYYYYYYYYYZZZ\\\]]]^^^^^^]]]]]]bbbeeelllyyy}}}mmmaaa[[[]]]ooottt|||yyyzzzzzz~~~vvvqqqgggddd___[[[YYYWWWUUUSSSOOOOOONNNOOOQQQRRRRRRQQQPPPQQQRRRSSSTTTTTTTTTSSSPPPPPPOOOOOOPPPQQQSSSTTTSSSSSSUUUWWWYYY\\\^^^___fffjjjmmmlllgggeeegggjjjvvvmmm```ZZZLLLIIIFFFEEEDDDCCCAAA???===<<<:::999888999999:::;;;888999<<<>>>???EEELLLUUUggg|||aaaUUUVVVXXXVVVZZZ[[[]]]^^^______^^^^^^bbbeeelllzzzqqqbbb]]]aaauuu{{{ssszzzyyy{{{|||~~~wwwrrrhhheee```\\\YYYWWWTTTRRRNNNMMMNNNPPPRRRTTTTTTSSSRRRSSSTTTVVVVVVVVVVVVVVVRRRRRRRRRRRRTTTVVVXXXYYYYYYZZZ]]]___bbbcccddddddhhhmmmqqqpppkkkhhhjjjnnn|||mmm___YYYLLLJJJGGGEEEDDDCCCAAA@@@===<<<;;;999888888999999;;;999:::===???@@@FFFMMMXXXjjj|||bbbWWWXXXXXXVVV[[[\\\^^^___``````______bbbeeelllyyytttddd^^^dddyyywwwuuu}}}yyyxxx{{{}}}~~~xxxsssiiieee```\\\ZZZWWWTTTRRRMMMLLLMMMPPPSSSUUUUUUTTTTTTUUUVVVXXXYYYYYYXXXXXXVVVVVVVVVWWWYYY[[[]]]___```bbbeeehhhjjjkkkkkkjjjjjjoootttsssmmmjjjmmmpppkkk^^^YYYLLLJJJGGGEEEDDDCCCAAA@@@===<<<;;;999888888999999<<<::::::===???AAAGGGNNN\\\nnn~~~eeeZZZ[[[[[[XXX\\\]]]^^^```aaa``````___bbbdddkkkxxxzzzfff```gggzzzwwwzzzzzzyyywww|||~~~yyyvvvnnniiiccc\\\XXXUUUSSSRRRQQQQQQRRRSSSTTTUUUUUUVVVYYYXXXXXXYYYZZZ\\\^^^___bbb___[[[ZZZ\\\___bbbccckkklllnnnqqqttttttsssrrrqqqpppqqqrrrpppmmmpppvvvkkk^^^YYYOOOKKKFFFCCCDDDDDDBBB???===<<<:::999888888999:::;;;:::;;;======>>>EEENNNWWWmmmzzzbbbZZZ[[[ZZZVVV[[[\\\]]]___```aaabbbbbbbbbdddkkkwww{{{iiiccckkkyyy{{{yyyyyyxxxwww}}}{{{yyypppllleee___ZZZWWWTTTRRRRRRSSSTTTUUUVVVWWWXXXXXX[[[[[[[[[[[[]]]___aaabbbdddbbb```___bbbgggkkkmmmuuuuuuvvvyyy|||}}}zzzwwwyyyxxxyyyzzzyyyvvvyyymmm```\\\OOOKKKFFFCCCDDDDDDBBB???>>>===<<<:::999::::::;;;;;;:::;;;======>>>FFFNNNZZZpppxxxaaaZZZ[[[ZZZVVVYYYZZZ\\\]]]______``````bbbdddkkkxxx|||kkkgggqqq~~~wwwxxxxxxxxxwwwwww~~~}}}{{{ssspppkkkddd^^^YYYVVVTTTTTTUUUVVVWWWYYYZZZ[[[\\\]]]^^^^^^```bbbdddfffggghhhgggfffgggkkkqqqwwwzzz~~~~~~mmmbbb]]]OOOKKKFFFCCCDDDDDDBBB??????>>><<<;;;::::::;;;;;;;;;999:::======???FFFOOO^^^sssuuu```YYYZZZYYYWWWWWWXXXZZZ\\\]]]^^^^^^^^^aaadddkkkxxx|||kkkjjjvvvwwwtttvvvxxxwwwvvvwww}}}|||{{{vvvtttqqqkkkddd]]]YYYWWWVVVVVVWWWYYY[[[\\\]]]^^^___```bbbdddgggjjjlllnnnmmmmmmnnnooorrrxxx|||lll```[[[OOOKKKFFFCCCDDDDDDBBB???>>>===<<<:::::::::;;;;;;:::999:::===>>>@@@GGGPPPaaavvvppp^^^XXXXXXXXXXXXWWWXXXZZZ[[[]]]^^^^^^^^^___bbbjjjvvv~~~kkkmmmzzzvvvppppppwwwwwwvvvuuuxxx~~~~~~}}}zzzyyyyyyxxxyyywwwrrrjjjbbb]]][[[WWWXXXYYYZZZ\\\]]]^^^___```aaaeeeiiimmmqqqtttuuutttuuuuuuvvvwww|||xxxjjj___YYYOOOKKKFFFCCCDDDDDDBBB???===<<<;;;999999999999:::999999:::===>>>AAAIIIRRRaaavvvlll\\\WWWVVVWWWZZZXXXYYY[[[]]]^^^_________^^^```gggrrrnnnqqqqqqkkkllluuuxxxvvvvvvzzz}}}{{{zzz|||~~~~~~yyyvvvwwwxxxzzz|||}}}xxxooogggaaa___ZZZ[[[[[[\\\]]]^^^______aaaccchhhnnntttyyy|||~~~|||}}}}}}}}}}}}vvvkkk```ZZZOOOKKKFFFCCCDDDDDDBBB???===<<<:::999888888999999999888:::===???AAAJJJSSSbbbvvvgggZZZVVVUUUWWW[[[ZZZZZZ\\\^^^___`````````]]]___dddooorrrwwwooohhhiiirrryyywwwvvv{{{~~~|||zzzxxxvvvuuuyyy|||zzzwwwuuuwwwyyyzzz~~~}}}tttjjjeeeccc^^^^^^______````````````cccffflllsss{{{wwwnnneee___OOOKKKFFFCCCDDDDDDBBB???>>>===;;;:::999999::::::999888:::===???BBBJJJTTTbbbwwwdddXXXVVVTTTVVV\\\YYYZZZ\\\^^^___`````````^^^___dddnnn~~~vvv|||nnnggghhhvvvyyywwwwww|||~~~|||{{{zzzxxxvvvssspppuuuyyyxxxvvvuuuxxx{{{{{{vvvmmmgggfffaaaaaaaaaaaaaaaaaaaaaaaadddhhhooowwwyyyrrrjjjcccOOOKKKFFFCCCDDDDDDBBB??????>>><<<;;;::::::;;;;;;888888:::===???BBBKKKTTTcccxxxbbbWWWUUUSSSVVV\\\YYYZZZ[[[]]]^^^___````````````dddnnn~~~xxx{{{mmmeeelll~~~yyyvvvtttzzz~~~}}}}}}|||||||||yyyxxxwwwvvvuuuuuuuuuuuusssuuuwwwxxxxxxwwwxxxyyy}}}uuunnnkkkkkkeeeffffffeeeddddddgggiiijjjqqqxxx|||vvviii___VVVLLLDDDDDDEEEDDDCCCCCC@@@>>><<<:::999:::;;;;;;:::999:::===>>>@@@HHHQQQcccwww~~~```UUUTTTSSSTTTWWWWWWXXXYYY[[[]]]^^^^^^^^^___```dddlllzzz{{{lllfffmmmyyyvvvtttzzz|||zzzxxxxxxxxxxxxvvvvvvuuuttttttttttttuuusssuuuwwwyyyzzz|||wwwppplllkkkggghhhhhhgggeeefffhhhjjjnnnvvv|||{{{mmmbbbWWWMMMEEEDDDFFFDDDCCCCCC@@@???<<<:::999:::;;;;;;:::999:::===>>>@@@GGGPPPaaauuu|||___TTTSSSSSSTTTWWWXXXYYYZZZ\\\]]]^^^______^^^___dddmmm{{{jjjgggooozzzwwwtttyyy~~~yyyuuurrrrrrrrrssssssrrrrrrqqqrrrssstttuuutttvvvxxx{{{}}}{{{rrrnnnmmmjjjkkkkkkiiihhhhhhjjjlllsss{{{rrrfffWWWMMMEEEEEEFFFEEECCCCCCAAA???===;;;::::::;;;;;;;;;999:::======???FFFOOO^^^rrrzzz]]]SSSSSSSSSTTTWWWXXXYYYZZZ\\\]]]^^^______\\\___eeeooo}}}{{{hhhiiitttzzzvvvtttyyy|||vvvqqqnnnnnnoooqqqpppoooooooooppprrrtttuuuvvvxxxzzz}}}uuupppnnnnnnnnnnnnllljjjjjjlllnnnuuu}}}tttgggXXXNNNFFFEEEGGGEEECCCCCCBBB@@@===;;;::::::;;;;;;;;;:::;;;======???FFFOOO]]]qqqyyy^^^TTTTTTTTTTTTXXXWWWXXXYYY[[[\\\\\\]]]]]]ZZZ^^^eeeppp~~~uuufffkkkxxxxxxuuutttyyy}}}yyysssnnnkkklllnnnpppmmmlllkkkkkkmmmooorrrtttwwwyyy{{{~~~xxxrrrqqqqqqrrrqqqooollllllmmmooosss{{{yyyuuussstttuuu~~~tttfffZZZPPPGGGFFFGGGEEECCCCCCBBBAAA>>><<<:::::::::;;;;;;:::;;;>>>>>>@@@GGGPPP___rrrzzz___VVVVVVUUUUUUXXXUUUVVVWWWYYYYYYZZZZZZZZZYYY^^^fffqqq~~~pppeeelll{{{~~~vvvtttssszzz|||xxxrrrmmmjjjjjjlllnnniiihhhgggggghhhkkknnnppptttvvvzzz~~~}}}wwwuuuttttttsssqqqnnnmmmnnnppppppxxxxxxpppjjjiiijjjkkkuuu|||uuuggg[[[QQQHHHGGGHHHFFFDDDDDDCCCAAA???<<<:::::::::;;;;;;:::<<<>>>@@@BBBJJJSSScccuuu{{{```WWWWWWUUUUUUWWWTTTUUUVVVWWWXXXXXXXXXXXXZZZ^^^fffqqq}}}mmmcccmmm||||||sssrrrssszzz{{{wwwrrrlllhhhgggggghhheeecccbbbaaabbbeeeiiikkknnnqqqwww}}}|||{{{vvvuuutttrrrooonnnooopppnnnvvv~~~}}}zzz|||~~~uuulllfffdddeeeggglllsss}}}wwwiii\\\QQQIIIGGGHHHFFFDDDDDDDDDBBB???<<<;;;::::::;;;;;;:::<<<@@@AAADDDLLLUUUhhhyyy{{{```WWWVVVTTTSSSUUUUUUUUUVVVWWWXXXXXXXXXXXXZZZ^^^eeeppp|||~~~lllccclll|||{{{rrrqqqrrrzzz{{{xxxrrrkkkgggdddccccccbbb```^^^]]]___aaaeeegggiiimmmttt}}}vvvvvvuuurrrooonnnooopppnnnuuu|||wwwsssvvv}}}wwwmmmgggeeefffgggeeemmmwwwyyylll\\\RRRIIIHHHHHHFFFDDDDDDDDDBBB???<<<;;;::::::;;;;;;:::<<<@@@BBBEEENNNWWWlll|||{{{```VVVUUUSSSQQQSSSVVVVVVWWWXXXYYYYYYYYYYYY[[[^^^eeeooo{{{}}}lllfffnnnzzzxxxsssrrrssszzzyyypppjjjgggeeeccc```]]]\\\[[[ZZZZZZ\\\^^^___gggmmmttt|||zzzxxxuuurrrpppoooooooooooouuuxxxyyy{{{rrrmmmmmmpppsss}}}wwwlllfffeeefffkkkqqqxxx|||{{{kkk___UUULLLIIIHHHFFFEEEGGGEEECCC???<<<:::::::::;;;<<<:::;;;>>>@@@CCCMMMWWWnnn~~~cccVVVUUUVVVTTTSSSRRRSSSUUUWWWYYYYYYYYYYYY[[[]]]dddrrr}}}iiidddnnn|||yyyrrrrrruuu}}}zzzqqqkkkhhhfffdddaaa___^^^\\\[[[\\\]]]___```fffkkkssszzz}}}{{{wwwtttrrrqqqqqqrrrqqqvvvyyyyyy{{{qqqkkkjjjlllmmmtttxxxvvvnnnkkkkkkmmmsssyyy|||kkk^^^TTTLLLIIIHHHFFFFFFHHHFFFDDDAAA===;;;;;;<<<<<<<<<;;;;;;>>>@@@CCCMMMWWWjjj~~~dddWWWVVVVVVUUUTTTQQQSSSUUUWWWYYYZZZZZZZZZ\\\]]]dddqqq{{{fffbbbppp{{{rrrrrrvvv{{{sssmmmjjjhhheeebbb```___]]]]]]]]]^^^```bbbfffkkkrrryyy}}}zzzwwwuuuuuuuuuuuutttwwwxxxyyy~~~|||qqqjjjfffeeeeeeggglllttt~~~yyysssqqqqqqvvv}}}~~~lll]]]SSSKKKIIIHHHGGGGGGIIIHHHEEEBBB>>><<<<<<<<<===<<<;;;<<<>>>@@@DDDMMMWWWhhh|||fffXXXVVVVVVUUUUUUQQQSSSUUUWWWYYYZZZZZZZZZ]]]^^^cccnnn}}}yyyeeedddwww|||tttsssuuu|||tttnnnllliiifffccc```___^^^]]]]]]___aaabbbggglllrrryyy|||zzzxxxwwwxxxxxxvvvwwwxxxzzz~~~~~~sssjjjddd```___]]]bbbkkkuuuzzzwwwwww{{{mmm]]]SSSKKKIIIIIIGGGHHHJJJHHHFFFBBB>>><<<;;;<<<<<<===;;;<<>><<<===@@@AAAEEENNNXXXhhhhhhUUUQQQQQQQQQRRRVVVVVVWWWXXXXXXWWWVVVVVVWWWXXX\\\bbblllyyy~~~}}}sssrrr|||pppqqqyyy~~~{{{xxxsssooohhhgggeeeeeeeeefffhhhjjjkkkpppwww~~~zzzwwwyyyyyywww{{{~~~yyyqqqhhh```\\\SSSUUUWWW[[[cccsssuuuddd[[[QQQNNNMMMKKKKKKLLLKKKHHHDDD@@@===<<<<<<<<<>>><<<===@@@BBBEEENNNXXXllliiiVVVRRRRRRRRRSSSWWWWWWXXXXXXXXXWWWUUUTTTUUUWWW[[[aaakkkwww}}}wwwuuutttssssssxxxuuuvvv{{{xxxrrrllljjjhhheeeeeefffgggiiinnnttt{{{}}}yyyvvvuuuuuuuuuttt|||}}}}}}zzzsssjjjccc___ZZZVVVUUUXXX^^^iiiyyyxxxfff[[[RRROOONNNMMMNNNQQQOOOKKKEEE???<<<;;;<<<>>>===<<<===???@@@EEERRR___yyymmmVVVOOOQQQSSSSSSTTTUUUVVVVVVUUUTTTUUUWWWUUUXXX\\\aaagggrrryyysssrrrrrrrrrvvvuuu}}}vvvtttvvv|||{{{vvvooommmjjjhhhggghhhiiikkkrrrwww}}}|||wwwtttsssrrrqqqqqqyyyzzz|||zzztttmmmfffbbb^^^YYYVVVWWWZZZ```lllxxx{{{eee[[[QQQMMMLLLKKKLLLOOOPPPLLLFFF@@@<<<;;;<<<>>>===<<<===???@@@EEERRR___xxxoooWWWOOOPPPRRRRRRQQQRRRTTTSSSSSSRRRTTTUUUUUUXXX\\\```eeeppp|||uuullljjjlllmmmuuuuuu{{{uuusssuuu~~~{{{sssqqqnnnkkkiiijjjlllmmmuuuzzz|||wwwssspppooommmlllsssuuuxxxxxxvvvpppiiieeeaaa\\\XXXXXXWWWYYYaaajjj|||}}}}}}~~~hhh]]]RRRNNNMMMLLLMMMPPPQQQMMMGGG@@@<<<<<<===>>>===<<<===???AAAFFFRRR___wwwqqqXXXOOOOOOQQQQQQOOOQQQRRRSSSRRRSSSTTTVVVVVVXXX[[[^^^dddmmmyyypppddd```cccfffrrrooo|||{{{uuurrruuu}}}}}}~~~xxxvvvqqqmmmllllllnnnooowww{{{}}}wwwssspppmmmjjjhhhmmmooorrruuuuuuqqqlllhhhbbb]]]YYYZZZYYYYYY^^^dddlllttt{{{}}}~~~|||wwwtttvvv}}}mmmbbbVVVRRRPPPOOOPPPSSSSSSOOOHHHBBB===<<<===>>>>>>======@@@AAAFFFSSS```vvvtttZZZOOONNNOOOOOOPPPQQQSSSTTTTTTTTTVVVXXXWWWYYY\\\^^^ccckkkvvvqqqaaa[[[^^^bbbnnnkkkxxx{{{vvvrrruuuwwwrrrppppppqqquuu}}}~~~zzzuuuqqqnnnnnnppprrrvvvzzz{{{vvvrrroookkkiiihhhiiilllpppsssrrrnnnjjjccc^^^[[[[[[[[[YYY[[[___```fffkkkkkkkkknnnnnnkkkllljjjmmmwwwooocccXXXSSSQQQPPPRRRUUUUUUQQQJJJCCC>>><<<===>>>>>>===>>>@@@AAAFFFSSS```vvvwww\\\OOOMMMNNNOOOOOOQQQSSSSSSSSSTTTVVVWWWYYY[[[]]]___bbbjjjuuu}}}xxxhhhaaabbbfffmmmjjjwww|||wwwsssvvv|||rrrlllhhhggghhhkkksss~~~zzzuuurrrrrrtttuuuvvvzzz|||xxxtttpppmmmhhhhhhiiimmmqqqrrrooolllhhhbbb]]]]]][[[XXXWWWYYYZZZ```cccbbbaaaddddddbbbcccbbbfffqqq}}}nnncccWWWRRRPPPPPPRRRVVVWWWSSSKKKDDD???======>>>>>>===>>>@@@BBBGGGSSS```vvvyyy^^^PPPMMMNNNOOOMMMOOOPPPQQQPPPQQQRRRTTTYYY[[[]]]^^^bbbjjjttt|||vvvpppoooqqq{{{llliiivvv{{{wwwtttwwwvvvppphhhfffeeefffllluuu~~~yyyvvvvvvxxxyyyxxx{{{~~~zzzvvvrrrkkkiiihhhkkkpppsssrrrooonnnfffaaa```___[[[YYYZZZZZZ___bbb``````cccdddbbbbbbaaadddooo{{{ooocccWWWRRRRRRRRRUUUYYYYYYTTTLLLEEE???======>>>???>>>>>>@@@BBBGGGTTTaaavvvzzz___QQQMMMNNNPPPNNNOOOQQQPPPPPPOOOQQQRRRWWWYYY[[[]]]```hhhsss{{{uuuiiihhhttt{{{wwwuuuwww}}}vvvkkkhhhfffeeeiiipppyyy~~~}}}yyyyyy{{{|||zzz}}}|||~~~yyyvvvnnnkkkhhhkkkppptttsssqqqqqqiiicccccccccaaa```aaaZZZ```cccbbbcccfffgggffffffdddgggppp{{{qqqeeeYYYUUUTTTUUUXXX]]]YYYUUUMMMEEE@@@======>>>???>>>???AAABBBGGGTTTaaawwwzzz```QQQMMMOOOPPPPPPRRRSSSRRRQQQQQQRRRSSSVVVWWWZZZ[[[___gggrrrzzz~~~~~~nnnhhhcccooo~~~yyyxxxyyyvvvqqqkkkgggiiinnnsssvvv}}}~~~~~~~~~~~~|||{{{zzz{{{|||wwwpppmmmjjjjjjnnnrrruuuwwwooojjjffffffddd```___```dddfffiiilllmmmlllkkkjjjkkkggggggooo{{{uuugggYYYTTTUUUWWW[[[___ccc[[[NNNDDD>>>===>>>>>>???>>>???AAABBBGGGSSS```xxx~~~bbbSSSQQQPPPMMMOOOOOOOOOOOOPPPRRRTTTUUUUUUWWWYYY[[[^^^eeeooovvv~~~|||lllhhheeesssxxxxxxzzz}}}xxxrrrnnnnnnpppssstttwwwzzz}}}~~~}}}zzzyyyyyyzzz|||rrrnnnjjjiiilllpppsssuuutttnnnkkkkkkjjjfffeeegggkkkmmmppptttuuuuuutttssspppkkkjjjpppzzzvvvhhhZZZUUUVVVYYY\\\```ddd[[[OOODDD???===>>>>>>???>>>???AAABBBGGGTTT```xxxcccTTTQQQPPPNNNPPPPPPPPPPPPQQQSSSUUUVVVUUUWWWZZZ[[[^^^eeeooovvv|||~~~xxxjjjiiihhhxxxwwwyyy{{{~~~yyyvvvtttsssqqqqqqsssuuuxxx}}}{{{xxxwwwwwwxxx~~~vvvqqqkkkhhhiiilllppprrrvvvrrrqqqrrrqqqlllkkkmmmrrrtttyyy}}}~~~wwwqqqmmmqqqyyyxxxjjj\\\WWWXXXZZZ^^^bbbeee]]]PPPEEE???===>>>>>>???>>>>>>AAABBBGGGTTTaaaxxxeeeTTTQQQQQQPPPQQQQQQQQQQQQRRRTTTUUUVVVUUUWWWZZZ[[[^^^dddmmmtttyyy{{{}}}wwwjjjjjjkkk|||xxx{{{}}}~~~xxxsssooommmnnnooorrruuu|||yyyuuuuuuuuuvvv{{{}}}vvvnnniiihhhjjjmmmnnnssssssvvvzzzyyyrrrooopppuuuyyy~~~}}}vvvpppsssyyyzzzlll___ZZZ[[[]]]aaadddggg^^^RRRFFF@@@>>>>>>>>>>>>===>>>@@@BBBGGGTTTaaaxxxgggTTTOOOPPPPPPQQQQQQQQQRRRRRRSSSTTTTTTUUUWWWZZZ[[[]]]ccckkkrrrwwwyyy{{{~~~zzzlllkkklll}}}|||tttoookkkkkkllllllooouuu|||}}}wwwssssssttttttxxx}}}}}}tttllliiiiiikkklllpppsss{{{xxxssssssxxx|||yyytttuuuzzz}}}oooaaa]]]^^^```cccgggiii```SSSHHHAAA>>>>>>>>>>>>===>>>@@@BBBHHHUUUbbbyyykkkUUUNNNOOOPPPOOOPPPPPPQQQRRRRRRRRRRRRSSSVVVYYYZZZ\\\aaaiiiooovvvxxxzzz}}}}}}nnnllllll}}}vvvpppiiiiiihhhggghhhmmmtttyyy{{{tttppppppqqqrrrtttxxx}}}{{{rrrmmmkkkjjjjjjnnnsss|||zzzvvvwww|||}}}xxxyyy|||rrrddd___```bbbfffjjjkkkbbbUUUIIIBBB???>>>>>>===<<<>>>@@@BBBHHHUUUbbb{{{pppXXXOOONNNPPPOOOOOOPPPQQQRRRQQQQQQQQQQQQTTTWWWYYYZZZ^^^fffkkktttvvvyyy|||nnnkkkkkk~~~wwwqqqfffeeecccaaaaaaeeekkkpppxxxxxxqqqkkklllnnnnnnooorrrwww~~~xxxqqqmmmkkkiiikkkooovvv{{{zzzuuuuuuyyy}}}}}}}}}~~~tttfffaaabbbdddhhhlllmmmcccVVVJJJBBB?????????===<<<===@@@BBBHHHUUUccc}}}vvv]]]QQQPPPPPPPPPPPPRRRRRRSSSRRRRRRQQQPPPSSSVVVWWWXXX\\\ccchhhqqqsssvvvyyy}}}oookkkkkk~~~xxxsssdddccc```]]]\\\___eeejjjsss{{{~~~~~~uuunnnhhhiiikkkkkkllloooqqqwww|||uuuoookkkiiihhhjjjooorrrpppnnnrrrxxx|||}}}uuugggbbbccceeeiiimmmmmmdddVVVJJJCCC?????????===<<<===@@@BBBHHHVVVccc~~~zzz```SSSQQQQQQQQQRRRSSSTTTTTTSSSRRRRRROOORRRUUUVVVWWW[[[aaafffoooqqqtttxxx|||llljjjnnnvvvmmmiiiccc]]]\\\\\\]]]bbbhhhqqqwww~~~}}}~~~}}}rrrlllhhhiiiiiiffffffhhhooosssyyy|||xxxrrrmmmllljjjhhhiiikkknnnooopppuuuzzz|||zzzzzz|||}}}|||qqqiiihhheeejjjqqqooorrrhhhYYYKKKAAA======>>>???>>>???BBBEEEKKKYYYggg{{{dddTTTOOOOOOSSSSSSTTTUUUUUUTTTRRRQQQRRRRRRSSSUUUXXX[[[^^^```jjjooovvvzzz|||nnnlllnnnxxxpppiiiddd____________ccciiiooovvv~~~~~~~~~~~~{{{rrrlllhhhhhhhhheeedddffffffiiiooouuu}}}}}}wwwqqqnnnkkkhhhggggggiiijjjjjjooossszzz~~~yyyuuurrrrrrsssuuuuuuzzz}}}}}}|||vvvtttvvv{{{qqqjjjjjjfffkkksssqqqsssiiiYYYKKKAAA===>>>??????>>>???BBBEEEKKKYYYgggzzzfffSSSOOOQQQSSSTTTUUUUUUTTTSSSRRRQQQSSSSSSTTTUUUXXX[[[^^^___gggmmmtttwwwyyy}}}rrrmmmooo{{{tttkkkfffcccddddddcccfffkkkmmmsss{{{}}}zzzrrrlllhhhhhhgggdddcccddddddfffjjjnnnuuu~~~|||tttpppjjjfffeeeeeeeeeeeeiiimmmsssyyy~~~|||xxxrrrllliiiiiijjjlllnnnsssvvvvvvxxxzzzyyyuuuooommmmmmrrrwww|||rrrkkkllliiinnnuuutttuuujjjYYYJJJAAA>>>>>>???@@@???@@@BBBDDDKKKYYYfffyyyjjjSSSOOOSSSTTTUUUUUUUUUTTTSSSQQQPPPSSSTTTTTTUUUXXX[[[]]]___ggglllsssvvvxxx|||~~~~~~uuuoooooo~~~xxxnnnjjjhhhiiiiiiggghhhllllllqqqyyy}}}yyysssmmmhhhhhhfffcccaaacccfffgggiiikkkpppxxx|||wwwpppjjjgggeeedddccceeehhhmmmtttyyy|||}}}|||vvvrrrlllfffcccccceeeggghhhmmmqqqqqqtttwwwvvvsssnnnkkkkkkooosssxxxsssmmmnnnlllrrryyyxxxyyylllYYYIIIAAA>>>>>>???@@@???@@@BBBDDDJJJXXXfffyyypppUUUOOOUUUUUUUUUUUUUUUTTTSSSQQQPPPTTTTTTTTTUUUWWWZZZ\\\^^^hhhnnntttxxxyyy}}}|||vvvuuu{{{vvvooonnn||||||~~~vvvrrrooopppnnnkkkkkknnnmmmqqqxxx~~~{{{vvvooojjjiiigggcccaaabbbdddddddddeeeiiiooowww}}}~~~vvvoookkkhhheeecccbbbcccgggmmmtttwwwwwwvvvooolllfffaaa______aaacccccchhhlllnnnqqquuuuuurrrnnnjjjiiilllooottt}}}tttoooqqqpppvvv}}}||||||nnnYYYIIIAAA?????????@@@???@@@BBBDDDJJJXXXeeeyyyxxxZZZQQQVVVTTTUUUUUUUUUTTTSSSQQQPPPTTTTTTTTTTTTVVVXXXZZZ\\\ffflllrrrvvvxxx}}}}}}yyysssnnnmmmttt~~~tttooommmyyyvvvttt}}}yyyxxxtttpppooorrrpppsssyyy~~~yyyrrrmmmkkkiiidddbbbccccccdddddddddeeejjjpppuuuwwwqqqkkkfffccc______bbbhhhooorrrrrrpppiiigggccc___\\\\\\]]]^^^^^^dddiiilllpppuuuvvvsssrrrnnnmmmnnnqqquuu~~~uuuqqqttttttzzzoooYYYHHHAAA?????????AAA@@@@@@BBBDDDJJJXXXeeezzz```SSSVVVSSSSSSTTTUUUUUUTTTRRRQQQSSSSSSSSSSSSTTTVVVXXXYYY___eeemmmqqqtttyyy}}}zzzxxxooonnnjjjffffffmmmyyyrrrmmmlllvvvppplllwww{{{uuutttvvvsssuuuzzz|||vvvpppnnnkkkfffdddeeedddeeeeeedddeeehhhlllpppzzz{{{rrrjjjeee```___aaafffmmmqqqpppmmmjjjhhheeeaaa^^^\\\[[[[[[^^^dddjjjnnnssszzz{{{yyyxxxtttqqqrrrtttxxxuuurrrvvvvvv}}}pppYYYHHHAAA@@@@@@???AAA@@@AAABBBDDDJJJWWWeee{{{fffUUUUUUQQQRRRTTTUUUUUUTTTSSSSSSRRRRRRRRRRRRSSSTTTVVVWWWYYY```ggglllpppvvv~~~}}}yyywwwuuurrroooffffffeeeccccccjjjvvvppplllkkktttooohhhoooxxxwwwyyyvvvwww{{{}}}|||}}}~~~~~~xxxrrrpppmmmgggeeefffaaabbbbbbbbbbbbcccgggiiioooyyyyyyoooiiidddbbbccchhhooorrrqqqnnnnnnllliiieeebbb^^^\\\[[[aaagggnnnrrrxxxxxxtttqqqqqqssswwwvvvssswwwxxx~~~qqqYYYGGGAAA@@@@@@???BBB@@@AAACCCDDDJJJWWWddd{{{jjjVVVTTTPPPQQQSSSTTTUUUUUUTTTTTTRRRQQQQQQQQQRRRSSSUUUVVVWWW]]]fffkkkooouuu~~~~~~xxxsssqqqooollliiibbbcccdddbbbcccjjjvvvpppnnnooo}}}|||iiieeepppyyy{{{vvvvvvyyywwwwww}}}sssmmmnnnkkklllqqqzzzyyysssnnnjjjgggdddcccdddeeecccaaa```cccfffoooqqqzzzyyyppplllfffdddhhhmmmqqqwww}}}}}}yyytttnnnjjjgggffffffjjjkkknnnttt{{{|||xxxuuusssvvvyyyxxx}}}oooTTTFFFBBBAAA@@@@@@>>>>>>>>>@@@AAAGGGWWWgggxxxsss[[[SSSTTTTTTSSSSSSSSSSSSSSSTTTSSSSSSSSSSSSSSSTTTTTTUUUXXX\\\cccjjjqqqxxxxxxllljjjllllllllllllaaa]]]ZZZ\\\___dddoooyyy~~~llllllqqq~~~yyyhhhaaajjjrrrzzzyyyyyyxxxyyy~~~uuulllgggccc``````eeemmmyyyzzztttppplllhhhfffeeefffgggeeecccbbbdddggghhhiiirrrxxxnnniiifffkkkrrryyy~~~xxxsssooonnnmmmrrrrrruuuzzz~~~{{{xxx{{{yyyyyyoooTTTFFFBBBAAA@@@@@@@@@???@@@AAAAAAGGGVVVfffzzzuuu]]]TTTUUUUUUTTTTTTTTTTTTUUUUUURRRRRRRRRRRRRRRSSSSSSTTTWWW[[[bbbiiipppwww}}}xxxllliiijjjiiihhhiiiaaa]]]ZZZ[[[]]]bbblllvvvvvvgggkkksssyyywwwkkk```fffkkk~~~|||zzzzzz{{{~~~uuullleeeaaa[[[XXXWWWZZZaaalll}}}wwwsssooojjjgggfffggghhhgggeeeddddddeeeccccccjjjxxxwwwqqqmmmqqqyyy}}}{{{{{{~~~{{{{{{oooTTTFFFBBBAAA@@@@@@AAAAAAAAABBBBBBGGGVVVeee|||yyy___UUUVVVVVVVVVVVVVVVVVVVVVVVVRRRQQQQQQQQQQQQRRRSSSSSSVVVZZZ```gggmmmtttzzz~~~vvvkkkggggggeeeeeeeeeaaa]]]YYYZZZ[[[^^^gggpppqqqdddiiitttyyyyyyrrrdddfffhhh{{{|||}}}~~~wwwmmmeee```^^^[[[WWWUUUWWW\\\gggxxxzzzvvvqqqllliiieeeffffffeeedddcccbbbbbbcccbbbfffqqq~~~~~~wwwyyy}}}~~~nnnSSSEEEBBBAAA@@@@@@@@@@@@AAACCCCCCIIIXXXggg~~~}}}bbbUUUUUUUUUUUUVVVVVVVVVVVVVVVRRRRRRRRRRRRRRRSSSTTTTTTTTTXXX___eeejjjqqqwww{{{tttiiieeedddbbbbbbdddaaa\\\XXXXXXXXXZZZaaajjjpppccciiittt}}}|||{{{jjjgggfff~~~}}}~~~{{{ooofff```]]]\\\\\\XXXVVVWWW[[[cccsss~~~zzzuuuoookkkeeedddcccbbbaaa```___^^^cccaaadddlllxxxmmmRRREEEBBBAAA@@@@@@>>>>>>AAACCCDDDJJJYYYhhheeeUUUSSSSSSTTTUUUVVVVVVUUUUUUTTTTTTSSSSSSTTTTTTUUUVVVTTTXXX]]]ccchhhnnnssswww}}}|||rrrhhhdddbbb```aaadddaaa[[[XXXVVVUUUVVV]]]dddqqqccciiittt~~~ooogggccczzz}}}{{{|||~~~uuujjjbbb]]]\\\\\\\\\XXXVVVXXXZZZ```mmmyyyzzztttooohhheeebbb`````````___^^^```___bbbjjjuuulllRRRDDDAAAAAA@@@@@@===>>>@@@CCCDDDIIIXXXfffhhhWWWRRRSSSTTTVVVVVVVVVUUUUUUUUUTTTTTTTTTTTTUUUVVVVVVTTTWWW]]]bbbggglllqqqttt|||~~~}}}sssjjjeeeaaa___```ccc```[[[WWWVVVTTTTTTZZZaaaqqqdddiiittt|||}}}vvvjjjbbbxxx~~~}}}~~~~~~~~~tttjjjccc______```^^^\\\[[[\\\]]]aaalllvvvyyytttmmmiiicccaaaaaabbbbbbaaa``````cccjjjrrr}}}lllQQQDDDAAAAAA@@@@@@??????BBBCCCCCCGGGTTTbbbmmmYYYRRRSSSUUUWWWXXXWWWWWWVVVTTTTTTTTTSSSTTTUUUUUUVVVTTTXXX]]]aaafffjjjooosss{{{}}}wwwmmmfffaaa]]]]]]aaa___ZZZVVVUUUSSSSSSXXX___qqqccciiittt}}}yyy{{{|||mmmcccwww}}}}}}zzz{{{|||}}}vvvmmmfffcccdddeeecccaaaaaabbbcccfffoooyyy}}}xxxrrrlllfffbbbcccdddeeedddccccccfffkkkpppxxxlllQQQDDDAAAAAA@@@@@@AAAAAACCCCCCBBBEEEQQQ^^^ppp[[[SSSTTTWWWYYYYYYYYYXXXWWWSSSSSSSSSSSSSSSTTTTTTUUUUUUXXX]]]aaaeeejjjooorrr{{{}}}{{{ppphhhaaa[[[[[[^^^___ZZZVVVUUUSSSSSSWWW^^^vvvfffhhhuuuwwwxxxgggiiitttxxxzzzxxxxxxyyy{{{||||||{{{~~~~~~uuunnniiifffeeeeeeccccccfffhhhjjjqqqxxx}}}yyyuuupppkkkhhhgggggghhhjjjiiihhhiiinnnyyycccLLLFFFAAA@@@AAA<<>>???CCCAAABBBAAABBBCCCCCCEEEMMMWWWqqq{{{]]]XXXVVVYYY\\\[[[YYYXXXVVVUUUUUUUUUUUUUUUTTTTTTPPPQQQRRRUUUZZZaaagggkkkpppvvv}}}yyynnnddd```aaa^^^]]][[[XXXUUUUUUWWWYYYnnneeelllzzz|||}}}uuupppuuu~~~|||xxxvvvwww~~~{{{xxx}}}~~~wwwZZZHHHCCC>>>???DDDBBBBBB@@@@@@CCCCCCEEELLLUUUjjjhhh]]]WWWYYY\\\ZZZWWWWWWVVVVVVVVVVVVUUUUUUTTTTTTRRRQQQRRRTTTYYY___eeeiiimmmssszzz}}}uuujjjdddccc``````]]]ZZZWWWWWWYYY\\\kkkcccjjjxxx~~~uuunnnsss~~~|||{{{~~~qqqWWWGGGDDD??????DDDBBBBBB@@@???BBBDDDEEEKKKSSSbbb}}}vvvfffZZZ[[[^^^ZZZWWWWWWWWWWWWWWWVVVUUUUUUTTTTTTSSSRRRQQQRRRVVV\\\bbbfffjjjooovvv{{{~~~~~~ssskkkgggdddcccaaa^^^[[[ZZZ]]]___{{{hhhaaahhhuuutttmmmppp|||lllTTTGGGEEE@@@@@@CCCBBBBBB??????BBBDDDEEEJJJQQQ[[[wwwooo^^^^^^```[[[XXXYYYXXXWWWWWWVVVUUUUUUTTTTTTSSSRRRPPPPPPSSSYYY^^^bbbffflllsssyyy}}}uuuoookkkjjjhhhdddaaaaaacccfffyyyggg```fffsssssslllppp{{{jjjRRRGGGFFFAAA@@@CCCAAABBB???>>>BBBDDDEEEJJJPPPVVVsssvvvbbb```bbb]]]YYYZZZXXXXXXWWWVVVVVVUUUTTTTTTSSSQQQOOONNNQQQVVV\\\___dddjjjrrrxxx|||wwwqqqqqqnnnkkkhhhhhhjjjmmmxxxiii___dddsssyyyxxxnnnfffuuu~~~yyyfffRRRBBBBBBDDD@@@???CCCBBBBBBBBBBBBBBBDDDIIILLLVVViiifff\\\^^^^^^[[[XXXWWWXXXXXXYYYXXXWWWUUUTTTRRRQQQPPPOOOPPPSSSYYY]]]ccciiirrryyy}}}{{{tttooonnnnnnooopppzzzjjj^^^bbbooo{{{yyynnngggwww~~~xxx~~~bbbPPPAAAAAABBB???>>>AAABBBBBBBBBBBBBBBEEEIIILLLTTTeeemmm``````___[[[YYYZZZZZZZZZYYYXXXWWWVVVUUURRRRRRQQQOOOPPPSSSXXX\\\bbbhhhpppwww|||zzzxxxwwwvvvvvvoooaaaaaakkkzzzpppiiiyyy~~~www|||^^^NNNAAA@@@AAA???>>>AAAAAABBBCCCCCCCCCEEEIIIMMMRRR```xxxwwwfffbbb```]]][[[]]]\\\[[[YYYXXXWWWWWWWWWSSSSSSRRRPPPPPPRRRWWW[[[```eeemmmtttyyy}}}|||{{{|||{{{~~~ttteeebbbjjj}}}zzzvvvlllyyywww}}}~~~~~~~~~|||ZZZMMMBBB@@@AAA@@@???AAAAAABBBCCCCCCDDDFFFJJJMMMRRR\\\qqqkkkbbb```^^^]]]^^^\\\ZZZXXXWWWWWWWWWWWWTTTTTTSSSQQQPPPRRRUUUXXX^^^ccckkkrrrwww|||~~~{{{yyyxxxxxxyyy~~~wwwgggccciii{{{zzz~~~oooxxxzzz}}}{{{{{{}}}~~~}}}{{{zzz{{{}}}~~~{{{vvvtttuuuuuuxxxwwwUUULLLCCCAAABBBBBBBBBBBB@@@BBBCCCDDDEEEGGGJJJMMMRRR[[[mmmpppccc```___^^^]]][[[YYYWWWVVVVVVVVVWWWVVVUUUTTTRRRPPPQQQSSSVVV]]]aaahhhooouuu{{{xxxwwwxxx{{{~~~yyyiiicccgggwww~~~rrrxxx|||}}}xxxtttrrrrrrqqqqqqtttvvvxxxyyyxxxxxxxxxyyyyyyzzz~~~~~~wwwwwwwwwyyy~~~{{{rrrmmmkkkkkkkkklllttt~~~oooQQQKKKDDDAAABBBCCCCCCCCC???AAADDDEEEFFFHHHKKKMMMRRRZZZkkktttccc___^^^\\\ZZZZZZYYYXXXWWWWWWWWWWWWWWWWWWUUUSSSPPPPPPRRRTTTZZZ^^^eeelllrrryyy~~~|||zzz||||||~~~nnnggghhhuuutttyyy~~~}}}{{{tttpppnnnmmmlllmmmpppsssuuuttttttuuuwwwzzz}}}~~~yyyzzz~~~uuutttsssuuuzzz|||{{{{{{~~~sssjjjeeebbbaaa```aaaiiirrryyyfffMMMIIICCC@@@@@@CCCCCCBBB???AAADDDEEEGGGHHHKKKNNNQQQZZZiii}}}yyyddd]]][[[XXXYYYYYYYYYZZZZZZYYYYYYXXXXXXXXXVVVSSSPPPOOOPPPRRRVVVZZZaaagggnnnvvv~~~ssskkkjjjvvvuuuzzz|||~~~xxxssspppnnnmmmjjjnnnrrrtttssssssuuuwwwvvvyyy{{{~~~~~~}}}|||{{{yyyzzz~~~tttrrrqqqsssxxxwwwvvvwww|||zzzooofff___\\\ZZZYYYYYYaaajjjpppuuu___JJJGGGBBB??????BBBCCCAAA???AAADDDFFFGGGIIIKKKNNNQQQZZZhhhzzz}}}eee\\\YYYUUUXXXYYY[[[\\\\\\[[[ZZZZZZXXXXXXWWWTTTQQQOOOPPPQQQTTTXXX^^^dddkkkttt|||~~~