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``++L++'''+'+;';;;;';';;:;';:;;;;:,::;;';:'''''+;'';;L'+';+;'+L'L++''''+''';';:;';:'+''+;LHOOQLHOOQ;,,:,,..,.,,,,,,,:::,,,,,:::::,,,,.,,....,.,.,,,,,..,,,,,,::;'+++L+++L++LHOO+LHOOQLHO+LHOOQ+;;;+++;'';:'':;;;;;';';;;'''L+;;'';;:;::,,,,,.,,,,,:,,:,,,,,:,:,::;:::,,:   
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``++''+++LH+L++'L'L+L++++';':''+;';;::'::';;;;;;';+';+++'''++++++LH+';LH'++L''++'+LHO@@@LHOO@LHOOQLHO;::,,,,,,.,,,,,:.,..,,:::;:,::,,..,,,..,..,,,,,,::::;:;'+++'++LH+LHOOQLHO+LHOOQ+LHOOQLHOOQL'''++';++++++'+++;'+':'';'+++L+'+'';;:,,,,,,,,,:,.:,'+;;;:;;,'+';;';::,:   
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``+L++''+LHO++LH++;+++'+L++++++'+''+'++'''':::;::;;;'';+''+''''++'LH++'++++'+L'++'+LHOOQLHO@LHOOQLHOO+';:,,,::,,,,..,':,:;+'LH++++',...,.....:.:,,,::::;:;;';''+L+'++'+LH+++LH++LHOOQLH+LH+LHOOQL+++'+';';'''''+++';'+':,';'''';:;'''::;'';:::+::,';:::,:,;'';::;:'::::,   
``+++L++'LHO+LHO'';';'+'LH;+'++'+++''++;':+::::;:::;;;;+;+;;'+;'+++'+L'''''';L';'L+@LHOO@LHOOQ@LHOOQLH+;;:::,,,.,.,,,.;;'''++L+L+L;,.,,..,,,,::::,,:::::''';++L++++++++L+LH+L+LH+LHOOQLHOOQLHOOQLHO+L'L++'++++++'L+L++;;'+''+';::,';';:;:;;';';;;'::';::;:';;;;;;,;::,:,   
 `+++'+L+++LHOO+L';';'''+'L+L''+L+L+++';'':;:'::;::;;'''';'+'''+;'''++LH+'L+'+'+':+LHOOQL@LHO@L@LHOOQL';::,::,:,,..,..,;++++L+L+L':,..,,,,.,:,,,,,,::;;:;'';'++LH+++'+++++L++LH+L+LH+LHOOQLHOOQLH+';;,:;';:;''++;;':';;''';';;'':''''++;''+'''';;''';;;,;;:;::'';;:'::;,   
``++'++L++LHOOQ'L;;';;;++'L'+++;'+'++++'':++;':;:'::'';;;+'''+';+++'++;''L+++'''':+LHOO@L@LHOOQLHOOQ@L+';:,,'.,,,,...,.:;+++L+LHO';,.,,,,:..;,:,,,,:::::;;''+LH+++''+++LHO+++LHOOQLH+LHOOQLHOOQLH+'';''';:':,:;'';''''';,:'+':'';;::+;''';:;;;';;';';:::,::''::;;';':',;   
``+++++LH++L+LH;++';';'+;;'++:'+L'++++++';:';;;:;;:;'';;+'';'+'+'+L+++'+;+++''++:''LHOOQLHOOQLHO@LHOOQ+::;::',:,,....:+L'L'LH+LHO'+',::,:,,:',,,,,::::;;:;''++++;++'+L'++'LHOOQ+LHOOQ+LHO++LHO+LH+;:':,:':;;;;',;';+';;::'::';'''+'+'+''+'':;::;::';;::::,;+,,:::::',;':   
 `';+++L+L+L+LH+LH;;';;;+;'+';+''+'+'++'+'';';:;;;:;'+';';'''';'++++'''+++;'L+':+;'LHOOQLHOOQLHOOQLHOOQ:::::,':,,..,+++++L'+'+'L+L+':::;:::;,,,,,,,:,:::'+''+''+++L+'+++LH+LHOOQ++LHO+LHOOQLHOOQLH;;;::';+L'':.;::;'';;;'+''';++''';:'''';;;:;:';::;:::::';''::''';;;':+   
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``++LH+LHO+'LH+LH+';'';;;'''+;+;+'++''+'';'++'++::;:;;:;+'+''''++'++'++'''':';+';,'LHOOQLHOOQLH+LHOOQLHO:::;,,,:++:..,,,,,,,,:;:,;;++''':.':,,,,,,,,::;:;''''++++''+L+L+++LH'LHOO+LHOOQL+L+LHOOQ+LH+';:';;;:::;'':;:'';;';';'':;';;;,;:;:;:::::::;:::,;;:;;::::+;;++'';+   
``+L++LHOOQ+LH+LH+';;';;;'+'+''++++L+;';+';'';;:;;;;'';:;;'L'++++';';L+++'++++++';';+LHOO+LHOOQ@LHOOQLHO:,::,,,:,:++++;,,,::;;'++'+'LHO';';,,,,,,,,,,:;:;''+''+'''+++;+'L++++LH+LH++LHOOQ++LH@+LHOO':;':':;+:'';'+++;::''+;':,:;;:';,,;,:;;;;::;::;,:,::,;::;'':+';';;;:   
 `'LH+LHOOQ+++LHO+':'';;'++';+++''+++L;';+''''+:;:;;+';'''+'''++L++'L+'++;++''+'++':+LHOOQLHOOQL@LHOOQLH':,,,,.,,::;;+++':;''+'++LHOO'':;,,..,,.:,,::;::;''+++++'+++';'++++++LH+LHOO+L+LH+LHOOQLHOO;L,:';,:''':,';;;:'':,,:;,::,:,,:;::,::,:,,;;;:,::,;::,,:;,';';'':;,'   
` '+L++LHO+++L+''':;'';;''''';+L+;'';++';;'''''''+'';:+';';';'++;;';++++L'++';;','':++LHOOQLH@LH+LHOOQLHO::,,,,.,,,,.,.,,:'':;;;;+';:,,,,,,,,,,,,.,,:,:;;;'''+''++++'+'++L+L+LH+L+LHOOQLHO++LHOOQLH+';;':;::,:::';,;:;';''+;;:;:,:;;;:::;::',::.;:,,:,,:;;'''';'++++'+';   
 `+++++LH++++L++;';:;';;';;;+'L;''''+L::'':''+''+'++''+''+::+':''+''';'++';'''';;+::'++LHO@LH+LHOOQLHOOQL',,,,,,,,,,,,,.......,::;:::,:,:.,,,,,.,,,,,;:;;''''L++++'+++;'+LHO+LH+LHO+LH++L+LHOO@L+LH+;'';:;'''+,:;:'::,;::;:;;;::';;':,;;;;;:;;:'::::;':;':':;;'';,';;':;   
``'LHOOQLHOOQL+L;L::';;':'+''+L++';';';:;;;;+'++'L''';'++''L+++L'+++''+++'+';+'::::,+'LHOOQLHOOQLHOOQLHOOQ;,:,,,...,.,,,,,,,,,,,::::,,,,,.,.,,,,,,,:,:::;''L'+L+++''+'++LH+'LHOO++LHO+LH++LH+LHOOQLH:;;::;;:;:::,,::::;,;';::,:,:::;,:;;,,:;:;:,';:,+';''';'''::::::';:;   
 `'LHOO++LHOO++++'';;:;;;'';''';;;''+L+++;;L+L++LH+++L++++'+';++L+++LHOOQ+++';;';:;;+LHO+LHOOQLHOOQLHOOQLH+:,,,,,,,..,,:,:::::,:::::,,,;,,..,,,:,::::::'';+'+''LH++++;+++L+L+LHOO+LHOOQLH+LHOOQLHOOQ':;:::';;;'+';;;'';;;'':::,;,::;;:::;::':''+;;;';;;'';;;:;+;';:;;',;   
 `'++L+LHOOQ+LHO+;+:''''+;'+;;;;;;'''+LH+++LH++L+LH'+''L+;'++++'L+''+';''+;'';;,::,;'++L+LHOOQLHOOQLHOOQLHO':,,,..,..,.,,:;+;:;;::,::::,:,::,,:,,::::;;;'''++LH+++++''L+'+L+LHOOQ+LHOOQLH++LHOOQLHOO';::;+;'':;:+';;'+'''';+''+;:'+;'::++++''';''';++'L'L;:;'+;;';:':'';   
 `'L+++'LHOO++;',++'+''+'+:':,:;':':,,;';''++;''+';++'''+;';'++++;;;';++'+L';:;:;,;';'+L+LHOOQLHO+LHOOQLHO++;:,,,,..,,.,,:::;:::;,::::,.,,,,,,;,,:;:,;';;+'+;+++''+'+''''L+L++L++L+LHO+LH'+LH+L+LHOO;;''''';;:';;';+''+''+++;+''++;;';'''::;''L++'';;''';+;;'';;;:;;;;':   
 `'++++L+L+LH+;'L;;:''::;'';;;+;;;;:;;'+LH;;+L''+';;'+'++''''';;++'+''';;;';;';;;:;L'LH+'LHOOQLHOOQLHOOQLHOO+':,..,,.,,.,,,,,::,::.,,,,,,:.:,,,,,::;:;;';''''+++''++'''+'+++++LH+L++LHOOQ+L++LH+LHOO'::,;,''';::;,;::;;'';+:;+'':;::;;'';'L;+';'++;+';;''';';;:;;;::+:;;   
``'+LHOOQ+LHO+++L+;++LHO++'L''L'L+++'LH++'L+++:;:::::;;;++++;;'';;'''L;';';+'';;;:,++L++LHOOQLHOOQLHOOQ+LHOO++;;,,.,.,,....,,,:,,,,.,,,.,,,,,:,,,::;;:;;';''++L++''+++++'+L+:++LH+L++LHOOQ+LHO+LHOOQ';;,;;::::,,:::'';:';;'';';'''++;'+;'+;''';;';:;';:,;;'':,;:;':::;:;   
``'L+'LHO+LH'L++;L+;+L+'++L+L+'++++++L'+L++L++'';'+;:':;'';:''';::::;;'''',;:::;;;;+++LHO+@LHOOQLHOOQL@LHOOQLH+;:,,,,,,..,.,.,,,,,,.,,:,,,,:,::::::;';'''+'''++L+++++L+'+'LH+LHOOQLHOOQLHOOQLHOOQ+LHO,,;;';;+:;,;::,::;:;';';;''''''';';'';::':;++''+''';;;::':,':,::,,,   
``+LHOOQ++'LHO+;;L:+'''++L''++'++;';'++++'LHO+++';;;:,;:;;;;;::';;';''::';+;';'::,,:L++L+++LHOOQ+LHOOQLHO+LHO+L+;,,...,...,...,,...,,,,::,,::::,:;''';;;'+';+'+++'L+'+++LH++'LHO@'LHOOQL+L+LHOOQLHOO+;;:;,:';:;:::,',,:;:;:;:+'+;':''+:+'';'::::,;,:::;:,;+;;,:;:'+';;''   
``'LHO+LH+++L+LH;L+':L'';L++'';:+++++L;L+LH+LH'LHO+LH++;;;::;;:;:,:::;;;;'''''''''+'L+++++;LHOO@LHOOQLHOOQ+LHOO++;:,....,.,..,..,,,.,,,:,::::::::''';;;+'+'''++'+''+'L'LH+L+L+LHO+L+LHOOQL+++LHOOQLH':,,,::,:,::::::::,':::;;:',;'';,:'';,,.,,;':':,:..,:;,.';;;'':,;;:;   
``'L++LHO++'L+L+'+++;+;+';'+''''';+''+L++'+L+++L+LH'+;+;';;':;'+;;;;;;;';;;;;,;;:;;;++'+L+LHOOQLHOOQLHOOQLHOOQ++L+;,,....::,..,,,,,,:,,,:,:;:;:':'''';;''+''++++L'+L+'++++L'+++L+LH+LHOOQL+++LHOOQLHO'::,;';::::::,,:::;:::;:;::'::;'+'''+',,',:.:.,;;',,:;::;;';+'+;;:'   
``'LH++LH+++L+++L'''+;;+++'''';+;'+'L'+L++++'L++'L++'L++'++;;:'+;;+;'';'+;';'+;::::;LH;L+LHOOQL@LHOOQLHO+LHOOQLHOOQ:,,.:,:::::;:,.,:;::::;::;';;;+''+'+'''+'L++++''++''L+++L+LHOO+LHO+LHOOQL+L+LHOOQL',;;::+::;:':,:::,:,:;:'+;::,;;';;;:;;;;':;:';',.;';:;';';;:;:;:+;:   
``'+LH+L++LHOOQL++LHO+':;L+'';;';''+++LH+L+LH+L'LH;+L+';'++'+'';''+;;'''';'';';'+;::L+L+++LHOOQLHOOQLHOOQLHOO++LHOOQ:,::;,::,;:::,:;+;;:+:;:''''+'++;+'+;'+++++++''+'L'LH+L+++L+L+L+L++L+LH+LHOOQL+LH';:;::;;;;';::,,:,:;::';:;;:+;+;:':;';:::;:+:;;';'',,::;;:;:;;'';';   
``;L++LH+L++LHOOQ'L+L+L+;'L:;'''++++L++L@+L+L+L+L'+L++';+L'LH+L+++'L++L'L++''+'+;::,+L+'L+@LHOOQL+LHOOQLHOOQ+LHO+LHO+:;'',:+;,';;'+''+''';;';''';'''''''++'+++++++++'++L++L++L+'+L+L+'LHOOQ+++LHOOQ+L+';;++';'':;;;::;';,,:;;:::;:::'':'';;+;;'::+L:;:',;'';'';'':':;;,,   
 `;'+LH+++'++LHOOQL+L+LH+'';;;+';+L++L+++++LHO'+++'+'+''+++;;'L';+'';:'+L++''++L+;;:'L+++LHO@L+LH'LHO+LHOOQL+LH+LHOO+'+;+:+';'';''+'+++'':;''+++;''+'+;''+++++'+++'+'''+L'L+'L+++L++L+LHOOQ++LHOOQL+L,':+';;';'''::'',+;':;:,:::;,:;''+:::++:;':'':+'+''':,,,.:,;::,,;''   
``:L+L++++'LHOOQL@L+LHO+++L;'';'''++LH+++L++'+L+L++++++'+++;;+;'::;';:::;'+,:,:,:,,..L'++LHOOQLHOOQL+LHOOQ+LHOOQLH++LH++L'+++'+;+++LH'';+''';';';''''+''++++;;+'+'';:'''+++'LHO++++++L+LHOOQ'LHOOQLHO;;;+'''+'L+'';;++++;',+';'''';+'';';;+'+;';'+;+'+:';:,,''';:::;,:':   
``;++L+++L+LHOOQL+LH+L;+LH+;;;+'++';;+''+++;LHO+;;''++'++';'+;:;,,,;:::;::;;;;;;:';::L+++LHOO+LHOOQ+L+LHOOQLHOOQLHOO+++LH+L+++L+LH++'+''';'''+'++'+++++'L+'+''+';;''L++++++'L+L+'L+++L+LHOOQLH+LH+LHO':;'L'''''+;;'';+,',;;;;':;;;;+;+''''++'+''':+'+:';'''';+L;;:,,..;:   
``;'+L+LH+L+L+LHO+L++;+L++;;:''';+'''+;'''+;++++''+'+++;+';;'::;:':;:;,:':::;::,:::,,+++LHOOQL+LHOO+LHO+L+LH+LHOOQL+LH++LHOOQLHO+;'';;'';+'+;'''+'+LH+'++++''+;'+';+'+''+L+++LHO+L+L++LHOOQL+LHOOQLHO;'+'';'+;+''':;';:;;;+'+'';+;++;';+;+'''+'+++++'+L+'''+'''+;;;,;:,:   
 `;L'LHOO+LH++LH;+L;L+L+'+';:;'';+''++'+++++++''L'+L'+++++;L'+'';'';;,;::,:::,,,,::::;+LHOOQL+LHOOQLH+L+LHOOQ+L+LHO+LH+LHOO+L++''''++'+';+'+'''L+++++L+;+++;'';'';''++''++++'+L+LH+L+'++L+LHOOQ@LHOO++';++';+++'''+++;;''+''''';;;:'+'+';+':''L;,++'+L++'';';++++++;:;':   
``;+L++LHO+LHOO+'++;LHO+L';;''+'''+'++';++''+++++L+L+++++++';++'':+''+''+;;;;::::::::.'L+LHOOQ'LHOOQLH+LHOOQ+L+LHO+LH++LHOO+L++';''';''''+'''++L'+'+++++''''''+':+''+''+'L++++++LHOO+++LHOO+LHO@LHOOQ+''''++:L'''+'++':';;+;';''';'+;+;'+:'';;+'+++++'+++;;',;';;;''++;'   
``;++++LH+LH+'+'++L+++LHO'L+;;;;L'';'''L++'+'+'''L'''+'++++':++''+L++''''+':::;;;::;,,'L+LHOOQLHOOQLH+++LH++LHOOQLHOOQLHOOQL+;'+''''''+'+'++'++++++''+;++;'''''+';;'''++'+++L+L+LHOO+L+L+LH+LHOOQLHOO;;+'++'+'''';,';:;;L'';';;';';+;+'+L;;''++'+':;'+'+++'';''+;''''':'   
` ;+L+++'L+++L++LHOOQL+L+LHO+:,:;,:;++++++L'+++L++L+++++';;L'';;;''+';;::;:;;;:::;:;:,:+LHO+LH++LHO+L+LH++L+LHO+LHOO++LHOOQL+;;;++''''++'+++++'+;++''';;+:;;;''';;;';''+'+LH++LHO++L+L++LHOOQ+LHOOQ++++++L;';:';;++;'''',':;+''+';+;+L+;';:;;++++'';+;';';+;++++'++++;;'   
``;+L'+LHO+L+++++LHOOQL:LHO':+';'+::;;''';';;';:;'':;::;::;:;;:;;;;'';''';;';;;;;::,:,,++LHO+++LHOOQLH++LH+LHOOQLHOOQ++LHOO+'::;':;'+'''''++''+';'+';;'';'';';;;:;::+;+++++++LHO+LHOO+L+LHOO+L+LHOOQL;:;;',:;;''+';;;;:,;,:++'';'';;;;';'''+'++''++'';;:+:;;+'+;'':;''';   
``;+++++L+++L'+LHOOQLH'++L+''';:':;;;';';;,;:;;;;;;:;:::;::;:;::::::::,:,;:;:;:;;,,,,:,'+LHOOQ+LHO+LHO+LHO+++LHOOQLH+LHOOQL+L:::,:;:''+'+''''+''''+';';''';;;;;;:;:;;;'++++L+++++++LHO+LHOOQLHOO+LHOO+;;+'';;;:+'';'+'+;+:'+'++'+'+''',+'';+'+'+''+;';;;';';';;'L+';''+'   
` ;+++LH++LHO''+LHO+++;'+::+'+;';;;';;;;;;;;;'';;;'':;;;';,;:,,;';;;;;;:;,;'';;::;;';:;:LHO+L+LHOOQLHO+LHOOQLHOOQLH+L+LHOOQ+',,,::::;;'';;'';;';'++';':'';';:;:;;:;;;;'+++'+LH+LHOO+L+LHO+LHOOQLHOOQL+;';+;;;';;':+'';'+'+;;'++';+@'++''';;''+;'''+';'';::;;'::;::'';'''   
``;+++:+LHOOQ+LHOOQLHO+:+++LHO''',::;::;;''''':.::::;::;';;::;:;;:;;':;::::';;:';;,::;:,'+'LH++LHOOQLHOO+++'LH+LH+LHOOQ+L+L+L,,,,,,::;;':+'';;';:;;';::;:::,':':;::;'''+++''++LH+L+L++L+L+LHOOQLHOOQL'';;;;:;;,'++:;';'+:''::+'+'+L'++'+;:;:;,'''L'';;:;::::;,,,;.:':'':   
``;+L+'LHOOQLH+LHOO+LH+'+L++LH+;'+'+;;:;;';':'++'+;:;+;':;:,,;:;:,:;;;;''';;;;;::;;,:;,,,++LHO+LHOO+L+LHO+LHOO+LH+L++LHOOQL++,,,,:,::'';';;;:;':;';;:;';;::::;:::;:;+:++'++'++LHO++L+L+LHOOQLH+LH+LH+'::;;:;;';':;;:;,+;';:'++''+'L+;+;;;:::,:,:,;,:,.:,,.:,...,,:;;::;;   
``:'++++LHOOQLH++L++LH''+LHOOQL,;:::;;:::;:;;;;;:::;:;;:;::;::,::,:;;;;:;:::;;;::,:,:::::,LHO+'LHOOQLHO+++LH+LH+++L+LHOOQ+L++;,.,,,:::::;'::;;:;:':,:':;::;,::,::;:;';+++++++L+L+L+LHOOQLHOOQL+L++LHO;:';;::::;;,,:,,:,::::,;,;:':+;;',;',,:,,,,,;::,,,.:.,.,,.::,,;;:;'   
 `:'+++L+LHOOQ+LHOOQL':;+L+L+LH;'L+++L'+LH+++'+;';;;:;;::;;:::,:;,:;:::;::,::::,:::::::,:.+L+L++LHO'LHO+++++L+L++++LHOOQLHOO+',..,:,::::,::;;:;:::::;;:::::::;:::,;:;;''''+++L++L++++L++L+LH+LH+L+LHO+,;:;::;,:.:,::,.,,,::;::;::;,:::;::,:,:,,,,:.,,,,,,,.,.,,:,,:,:,:;   
``:L+LH@LHO+LH+LHOOQ+'+LHOO++;;;+L'LH+L+++'''+;;';';'';+;';;:::,,;,,:;;;;::::::::,:,:;,,;,;LH+L++LHOO+++LH+LHOOQLHOO+LH'L+LH+'.,..,,,:::,,::::::,:;:;;;;:;:,:::::::,::'';''+++L++L+L+LH+++++++LHO++LHO+:';,,,.:,,,,,:,:::,,::::,:;;::;:::,:,,,,,.,,,,,,,..,.,......`.,;.   
``::+LHO@LH@LH+++LHOOQLHOOQL+''++L+'++'';';;';';,:;';;::;'::::,;':;:,';;;;::;:,,:,::::,.:,,L+LH+LHOOQLHO+L+LH'L+L+LHOO+LHOO+L+...,,,:,:,:::,::;::;::,:::::,:;;:,::;;::+;'L'L+L+'L'+LHO++;LH+LHOOQ+LHOOQ'';,,::,,,.,::::,,,,,;:;::,:;,,,,,,:,,,::,:,,,..,,.,,.,,,:,,,,,''   
``:+L+L+LH+L+'++;LHOOQLH+LH+;+L+'';;'';'::::;;;:::::;;::::::;:;:;,:,,::::::;:;:;:;:;;:;,:,,LHOOQL+LHOOQL++LHOOQLHOOQLH+LH+L+LH,.,.,,,:,,:::,,:::::::,::::;:::;:::::::,':'+++LH++++L+L+LH+LH+LH+LHO+LHOO''';:,:;,,:,,,;;.':,,:,;,,,::::,,,:::;,.,,,,.,,:,,,,,,:,,:,,.;,;:   
``,++LH++++++'+++,LHO++L++:';;;':;';;':;';::;::;:,::,;::,:;:,,::::;;::::::,,,,,:::,::;:;;,'+LHOO++LHOO+LHOOQLHO+LHOO++LH+L++L+,...,,..,,.,,,,,,,,,,,::,:::::,:;,::;:::;;+'++L''L+L++L+L+LH+++LH+LHOOQLHO:;'+';'+':.';';::+;,,:;,:::,,,,:,,':::,;,::::::.;::,;:;;;:.,;,:;   
``,++''+:+++++'';';;++'++'L';'+;++:''::;:::,:::,;+;;:::::,:,.:,::::::::;:::::::,,;,::::,:.++LHOO'+L+++L+LHOO++L+LHOOQLHOOQ+'L+'...,,..,.,,,.,,.',,,,::,,:::,,,:,:::;:,:;:'''+LH'++LHOOQ'L+L'L+LHOO++LHOO;;'''';';';'++''+++';::::,:,,,:::,,:,,,:,,,,,:,.,,...:::;;,,;,;'   
``,++';+'LH+;';+''''';;:''+'''+''L'+;;;;,,,,:,;,::,.:;::,:,,,:;:::::::::;;:;;;:+:,,::',,:,+LHO+L'++++LH++LH++L+LHOOQ+LHO+++++++,,....,,,,,,.,,,,.,:,,::,,:::::,,,::::,:::'';LHO+++L+LH+++LH'LHOOQL+LHOOQL''''++';+''L'++L++';;:,,,;:,;';;,::,:,:,,,.,,:,,...,:::.,.,,::;   
``,';+;'::++L'++'''+++';:'';''':';;';:,,,;';;,,,,,:;;;+'.;,,.,..,,:,:,,,::,:,:,,,,..:':,,:++LH'+L+LH++L+LH++L+L++LH+L+L+L++++;:,,....,,,..,.,..,,,..,,,:,.,,::,::,:,,:,,:'''++LH++++'+'++LH+;LHOOQL+LHOOQ+'L+++L'++'+'++'''++;+::,::;+++:',,,.,,::,,,,,,,,:::::.:,:,:;:;   
``::+;;''++++'+++;';'''';'+++;;:;'::,,.;:,+',;:'';,:;,'+::++,,,,.:::;;::;::;::,:;::,,;,:,:++LH'+L'LHO++++LHO++L++LH+LHO+L+L+:::,.,.,..,.,.....,,..,,:,.,,..,,,,,,,:,:,:,:;+LH:++++L++L++++L'+LH+LH+LHOOQ+++++LH+'+'.:;':+'+L+::;+':'++++;:;,,,.,...,,,,...::::,,,:,,,;::   
``:+'L''L++++L''+'';';;;''+;';':';';,,,:.::+;',';,,,;:,;';L+;,,.,:',,:'::':,.,,;':..:,:':;++LHO+++LHOOQLH+L++L++++LH+L++L++;,,:,.,..............,...,,.,,,,.,,.,,.,:,,.,:'++'+LH+++L+'+'+++''+LHOO+LHO+LHOOQL'+'+'::':':'+'';:;;++'':++''+':::.,,.,,.,,...::::,::::;:':,   
``,;;''';;;;+L:;+'+'''''+;;;;::,:::,:;;::;,+:',+':,+;;.:;;++';;,,+:.::;:,:':;:';++;,,,';;+++LHOO+L++LH++++LHOO+L++++LHOO+;:,..,,..,,...,..,..,.......,,...,,,,..,,:,,,.:,:''''++';'++++++L+''++L+LHOOQLH+LHOO+L';';':;;''+;'';''+'+;+++++++;,;,.,,,,.,..,:,,,,,:::,;,;::   
``,;:::';';;;'':;,;:;'''::';,::;;:;:;;;,;:;;'';++':'';':,:':+++:+L+,:;::,;';+,',''';,,,:;;LHOOQL+LHOOQL+L'LH'+'L+LHO+++':,,...,........,.......,.........,.,....,,:,:,,,::;+'+'L+''L'++++L+''++LHOOQLHOOQLH++L''+'+''+'+'':;''++++++''L'+'+';:........,,,:,,,,:;:,,.,:,;   
``.;::';;;:';';'':;:;:+:';:;';;::;:;''::,,;::,:''',';',,,;;''+;:,'+,,,:::;'+',:'+'+'':;+;+LHOO+L+L+LHOO+LHO+L+L+L++L++;:,,,........................,..,.....,..,.,,,,,,.::''++++;'+'++++'L++L++LH++L+LHOOQLH++'+++'+;+++++''''++';++;;++';;::,,.,,,,....;:,,,,;,:,,,;::;   
```,:,,;:;;::';;:'''+';;;':::'::,,;;;,::::+::''+;,,;;:,,,';;''::,.,:,..:';'+;;;;L+L++''..+LHOOQLHO'++LHOO+L+++++LHOO+:,,.,...,...............................,...,..,...,::;+'''++++'L+;L+';+'LHOOQ+LH++LHOOQ+L++L'';;:++';;';'';;,:;::::,,,,,,.,......,::::,:',:,;:;,;:   
``.'';::;:':;';;;'',;,';:;,::::::,:;,,.:';+';++;;:';';,,,;;:;';::::;,..'+'+L',+++L+'++,:;LHOOQLH+L'+'LH+LH++++LH'L+';,.,.......................................,..,....,:,:;+'''+'+'+L+;LH''+++LHOOQLHOO+LHOO';'':::+++;':;::,.,,...:,,,:.,,,:........:';',.:'.:,.,,::;;   
` ,''''';+++++'+''+'+++;;;,,:,:':''::,;;+;;;'++;:;';+:.:::;:;+;,,,::,;:,,+++';''LHO+LH+;'LHOOQLHOOQLHOO+L+L+'LH+++;..,,,,...................................,....,,,,.,,,::;++++++'+++;'+L+'++++LHO+LHOOQLHOOQ:::,,,:::::::..,.,,,,......,,.,.......,,:':,:.,::,::,,:::;   
``.'+''+'+';;;:'''';+;'':;;;,.':;;::,,,::;:+''':;:;;';';;,;:':;,:.;+'++'''+++';;+++'++L'LHOOQLHO+L+LH+++++++L++L':......,....................................,...,..,,,.,::;L+L+++L+'+;;+L+'L+LH+LH+LHOOQLHOOQ;,,::,,,,..:.,,,,,:,,,,,,...,,..,.,,,:.,::,::,,:,::,::,;;;   
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`` ;'';;':';;'''';;:'++++'L'+++++''+++++++++''++++'''''+L+++++;++++++'++++'+++++'+'+++++++L+++++++LH+L'L+''LH+++++++++;'+++'+':+'L''+'++'''''+++'++:;''+'+++'''++++'++''+''++++++'+:;''''++++'''+'+;+''+++'++++'+L+'+L++'+++;''+'''+'++++'++++'++'+''''++''+'+++++;'++''   
```;';':+;,;;::';;;;'''++'+L+L++++''++'++';'++++'''''+++L++;:;;;;:;+'+++L+'+L+'L'++++L++'++++'+''+L+++++++++++++L+++LH++++++;'++'++''++++++++++'+++;++++++''+++''++++''+'''';'++++;'+'++'+++''+'''+''+++'''''+'''++'+++'++'+'':'''''+'''+''++'+'++L+'+++;;''++''++'+''''   
```''';;':;'':;';''''+'+++++L+'+''+++''+;;''+++++''++++'';;:'':++;:'++'+'+++++++L'++'++L+L'+++++;;+++L+L+L'L++L++++L'++L++','+'+'+++'+++L'+++'+++++++'+++++++'+L+++++'+''++'L++++';''+'++++L+;'+++++++++'+'''''+'+'+''+++'+'+'+;+'''++''''++'++++''+''++;''+'+'++''++'+'   
```;+';'':';':;:::''''+++'L+++++++'+++''+'+'++L++++++'';+'+;''++'''+++';;'';'+'LH+LH++L+LH+L++'+++LH'+LH+L+L++L++'+++++++:;''++++'++;++++++++++'++++'+++'+'++++'+++++++'+'++'+++++;;+'+++L++++'''+';++':''+'''++++';:+'';L'+''';+;'+'++'+++'+'''+++''++''+';'+++++'+''''   
```;;';:':;;;:::;'+++'++''+L'L'+L+++'+''+++++++'++;'+'++++'L'L';;,'+':++'+'''+'L+L++L+;++'++L+''++++LH'++++++L++'++++++';++''+++++++++++++L+L++L++++++++++'++++L'+++++L+L+++L+++'':+''''++++'+'+'''++L:+++';+;';''++'+''''+'';''++++'++++''++''++''++'''+'+'++++++'+''''   
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` `:;:;;';'';';:'++'L+++++++++++L++'+++++L++++++++;L+++++++'++';+;,'+'++'+++''++++'L'+++L++++L++'++++++++++L+++++'L+,:+++'++''+'+L++'+L+++;+++++''+++;++''+'+++'++'++';++++'''++;;''+++'++'+++':+;'';++';;;;'';;''';+'';+'''';':+++''''''''''+''''''+;++'+++'+'+++'+'+''   
```;:;:;;:':;:,+;++'++'+'++'++''+L;'''L+':::;'++++'+''''+;;;''''':,''+'''++++'+L+L++'+''++++++++++L+++'++++L++'L+L';;'++++++'+++'+++'+++++++++++'++;++++++++L'++++++'+++++++++++';++++++++'+'++'+;++'++;''''''++'+++++''''+''';:'''+'''''+++'++''''''++'+++'+++'+'''+'+'   
```;::':';;',::'+'+++++'++'++++++++'++'++++;;''++';++;;'''+'';''';'+;+'++++++++++++++++'+'+'L+++'L+''+++++++++++','''+++++'''+++'+++++++++++';++'++++'+'+'''+''++;'+'++++'+++++L;;''+'+++++;''''+''';;;;'';'+++++++''+++''++';+;'''''''';';''+;+';+'+'++'+++++'+++++++++   
```::;::':'';,''+'+''+''++;++'L+'+'+'''++++';''';'+''+;';''''''+';;+++'+'''+++++'++L++'+'+L+++++L+L++++++++++++;:+'+'++''+'+++++;+'L+++++++'L+++++''+++'L++'++L+'+''+++'+'L'++''''''+;+''+;+'++';''':;;';;+'''+''';+'+'';+:++'+:';+;+'';';''+;+''''+'++'++'+++L++++;';''   
 ``:;;:':+;';;++''L++'++''''+++L++'''''++;:'+;';'';;'+''+++'''++''''+''+++++++''+++LH++++'++'''+'+'++++++++++';'+;+++''+'';+'++++''''+''+'++++''''++''+'''+'++''+'+'+++''++'+'':+'++''''+'++'+'''+';;:;''+''''+'+'L+++'''+'+'':''''':'';''+''';';:'+;+;+'+++'++'+;+''++'   
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```:;::;,'';:'+++++'+++'+++++++++';+;;;;'+'';'+'++'';;;:;''+'''''+'+'++''+'+++'''++L++'++++'+++++++++'L++++''+'+++++;++''''+'+''+++''+'++++'+++''+++'++'+++++++'++''++++++++'+;''+''''+'+'''+''':;;;''++''+;'''''++++'';;';''+';+';+;+':';:;'';'''''+++'+'+'+++''+'++'+'   
```;';';:;::;+++L'+++++';++''++'++++:'+;'+''++;::.,,;;;;;;;:'';;'++''''++L+++'L+++L+''+''++'++L+++++++'+++'++'+++++''++'+'+++++'++++++++++'++''++++++L+++++++''+++'++''++'++L+++;''';+'+'';'++',:+';''++''+'''+++;++;+'''';''+:'+;'+'+''+;':';'+'';'';''+++''''+'+++++'+   
```;';:';:;''++''''+++++++'+'++++++,':';';:,;;;:;;''';''+':''';'':;'L'+''+++'++'+++'+';'++++++'++++++++++++++++++++'+++++L++L++++'+'++L+'+++++'+++++''+++++L++++'+'+''+'+++'+;'''''''++'++'++';'''''++++++++++'+''''++''+;''++;''''++''+''+''';';'''';''+++;'+'+'+++'+++   
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  `;;'';;;;'+L'+'+L'+'+++'+'+++++;;,:';:`.:''':.,,.,,.:,::,..`.,:;;++';;''L++;'+'+++L+''++++'++'+''L+++++++L''+''++++L++'L++'+++++'+++++'+LH+++++++++++++++'+++++L++++++'+'+''+++'+++L++++''''''++++'+L++''''++++''+++'';;+;'';''''+'''';'+''''++''+':';+''+++'++++'++++   
` `;:';';;;'L+++++++''''++++L+++;;;''':,:;';....,:;;'';';;;;;;:.:...'++'';''''''++'++';'+'++;+++++'++'++''+++L+L+L'++L'+L+L+'+'+++++'++++++++'++'L+'+'++'L+'+'''++''''++++''''';'+'''''''''''+'''''++++++''+++'';';;''''';;;';'';;';'+''';'';''+'++';+';''+++++++++++++:   
` `;;';';;;'++++++''++'++''+++++:''''.;+';..,,,:;,;;;;'+'+'':,...,,,:;;'''';''++''L+++'++++++L+++++L'+++L;'+L+'+'''+++++++++++++++++'+'++'+L'++++''++++;+'+++++++L'''''++''''''++'''++++''+;+'''''++''+;++';;'''''';+;'''';;+;;;;:';;;';'''''';+'';+'''+;;'++++;+''+++++   
` `'':;;';'++'+++;++++++L'+++''';;;;.;:;,.,;.,;:;;;;''+'';,,:':.,;:;.'';'++;';''++++++''+'''+++++++'++;+'++++'''+'+'+'+++'+++++'''+'+'++'+''+++L+'''++++'+''+'++'''++'''''++'''''';+'++;'+'';'';'L+'''''';;''+'+''''';+''';'+''''';;:';;'';'''';'+''+;;+'''++'+''''+'+++   
```;;:';':+++''+++++''''++''+;+::;;.,:;,,,;..:::''';'';..,;;..,,';:;,;;:,;';;+++'+''++''+'+'+++'+++'+'++++'+++++''+L+++++'L++++'++'+++++';''+'+'+++++''+'+++++++++++'++++''''''''''+++'''''++''+;;''''';;'''+';+'':;;;;;;';+'+';+';';''''';;;:;''+''''++''';'''+'++'''''   
```;:'''''++++++'++'''++++'+++':;':,:,:::;;,,,;;;''';,.;:..,;;;''''''';:;,'+''++';'+'';++'+;''++'+'+++++''''+L''''+'++'+++'++'++''+++''+'+'+';'++++++++''++++++++''+'''+'';;;+++;''''+''''''+''+;;'';';''';';'''+'++'''''';;';';+'''+'++';'''':'';;;;''++++;'''''+++++++   
` `,:;'';'L'+'++++''+';';+++'+,;':...;'::;,.;:';'';..:,,,;'';'+'':;,:;,;,,:;'''''+;;'''''+'''+''+'++''++'+++++'+L+++'''+'+++++;''++'++'++'++++++++++'++'L+++L+'++''+'+++'';'''+'''''+'''+''''';;;+;;'++'';,'+'''+'+;+'''+'+L;';':;:';';;;';+''''';;''''++''''''''+'''+;'   
```::'+;;L+'++++++'++;;;+++'+;.;',:;;;;;;;,,;''';,.,,.:'''';,.:,.:::,';,.`.,,,;;''+;';;'''++''++';+'+'+''+'+'''+'++'++'+'++++++++++'+L''''++''++'++''+'++++++++++++++++++;'';++'''+''+;;';;';;;';+;''+'''';'''''+'++'+''+''+++'':;;;';'';::''''';'':+''+'+++'''++'+++++'   
```;;''';++++++''+++':+++''++':';,;;;:';;;,;''+;,.;.:,:'':..;'.;.;;''...,.::::::+''+''';++'''''+''''+++'++++'+'''++'+++'+'+++++++'++'''+'++++'+++'+++'++++++++'L++++''''++''''L+'''''''+';'''+'''''''''';'''''''''''+''';+''''+;'';';;;;;';;';''''';+''+'''::++'+''+L'+'   
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` `;';;,''++++++++++++''+L++;:''.';;;:,,::':+,..:,,,;;''+':,,,.';:.`,';:,,';;..:.,,:;:,.``````..::+L'++++++'+++'+++;'+++''++'+++++++++''+'++''''''++'++L++L+L++'+++++L''''++'''++';''''''';;''+++''+'''''';'++++''''+'++'++++';''+'++''''';::;;';;;;''+++'++++'';+'+''''   
   ';;;'+'+;+++++'+++'''++++;:+;;+;;::.:.;:;,.:;,..;''''',,:.:'',,.,'',,,::;,,.`,;,.`..``.``.``...`.;'+++''+'L'''++++++++++'++++++++'++++;'''+'++++++++'++++++'++++++++''+'+++'''+;'+'''';'''+'''';''++'';'''+'+++'++++++''+'+''++';+'+'++';:;';';;;'''+'+++'''++++'''''   
 ``;;;:+++++'+++++++'++'+++';'':;;;;;.;;.,,,,,,.,;;'+''+.:,.';:,'.:''..,;:;,:,,,:````..`...``.`..`..``.:'++''+'''++'+'+++'++'++'+++'+++';'+;++''+++'+'++'+++++++'++++'++'''++++';+'++''''''''+';;';:';'''';'''+'''++''+''++'+'''+'''+;''+'+';;':''+''''++'+++''+'+''+'';   
 ``;:,''++'';+++'++++''++'++:;;:;;'',;:...`,,'...:'''''`;,,';,;',.;+;,,':;.:..:,``..````.```..`````.`.``..;'+''''++++'+'''+'''++++++++++''''''''++++'+++'+'+++''+L'+''++'+++'+'';++++'+'++''''';;'''''+'''''';''+'++;''+'++''+'''''''';++'+'''';'+:;';;''+''++'''++''++;   
 ``':;++'++'++++++++'+''++++;+:::;:;:..,.:.,;,,,,'';':.'.,::,;';.;;'..;';:,...,`````````````````..`````.````,:+'''''''+''';'+'''+';++'+'''''++++'+'+L++'''+'''+''+'++;+++'''+'''''+''''++'''':'''+''+''+'+'+;'+'+''''''';;:''';'''';+';''+''''+';+'';;;''+++;++'''+''+'+   
```';;'+++'+;'''''++'+'+++'+;;,;';,,,.,..,,:,;,:;;';;.':.:::'';,,+'..,';;,..,;````..``````````.```..`.```.`.``.,;'++''++'''++'+'++++'+'+'+'+'+''++++++++'++'''+'++++'++'++'+''';';'+++''';';;;';'+''''+'';+';'''+''''''''''';''';';';'''''+;''+''';;'+;'''''''+';+''';':   
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```:'++++'+'++'+++++++++'+++;';;:':;;:.:;:.:',';';.;..,;;'+',.'';;':'';',,,;.```.```.`````````.```....`...```````...````.,'+;'''++'''+''+;+++''++++'+++'+++''''''+'+'++++'''+'+';;'''+''''''';';;+;;'''';+'';''';;;;'';;;;';''';''+''++;'+'''+';+''''::;'+':''+'++++++''   
```;''+''++++'++++++++;++'+';';';':+;;:',:,;'::''::,..:';;';.:;+,''''+''`.',.``````.`````````.`.`````````..``````.``.```.``,'''''+''''''';+'++;+'++'+;+'++'+''+'++''+'+++''+++''''''++''''';';;''+''+''+'''''';';''';';';''';:';'''+';+''''+'''++'''';''';+';';++'+;++;'   
```;+''++++++''+++'+'++++'++'+';;;;;'';;,.;;'::'',,.,';';';.:'';;;';+'';,;:```````..``````.````.`.````.`...```...`..```..```.:'+''''+L+++'''++'++''+'+'+'+''+'+''+'''++++''+;''+;''+;+''';';;;;;'''''''';';;'''';';;';''';;;'+';''''''+''+'''+''+'++;';';'''''''''+'''';   
```'''+++++'+++'+'+++;++'''+'+:;';:''':,,,;'',;',::';';'';,.';+,;';;++;,.::.`...```````````````.````````.````.``.....``..`.....'''++''++'++''++'+'+'++++''+'+''''+''''+'++'+;'''';'''+';:''+';'';'';;;';;+''''+''+';''''';;';;''';;+;'''++''++''L''''''+;;'''+'+;+''+'+'   
```'++'+L+++;L++L++''++;+++++++':;;'+;;,::'''.'':,'';;;'';.;''+:++';''':,:,.`````...````````````.````.```.````..``.```.```...``.;''''+'+'++'+''++'+'+++'+'+'++'+'''++''''''';+'+';'''';;'';;';:';':':';;'''';+;;;''''''+;''''';'';;'+'+'''+''''+'';'+''';'+'''''+'++L'++   
```'+++'L++'+++++'++;+';+'++'+'';';;+::,:''';,':.;'';;;';::;;';''+':+'',`;,`.......`````.`..`.```````..````.`.````.`````.``.``.`.,'+''++'+'+'+'''''+++'++'+''''+'+''''++'''''+++'';'''';''''';'';'';;;+'''''''+'''';';''''''''+''';'+'';+'':'';;'''''''';;+'''''''+++'''   
```''++'+'++'++'''++'';++''++;';;:;';::,';'';,',.'++:+':+;:''':;++;;+''..',.`...``.`````.....```````````.`````..`...``.``.```...```,++''+'+++'++''+++'+'''+++';'+''''+++'''+'+++'++'+++;'''''''';''';'';+;+''''+'++;;';;;'';''''+'+''''''';+''''+''''''+';'+'+++++'+++'+   
 ``'+'+'++L++'++++L++'++;++++;';:';;'';'';++;:+.,;'';+'':;;''',''++,'';,,',.....```...``````````...`.````.```..`````````.````.``..`,`.:'''''+'+'''+'+'++++;+'+++'++''''+''+++'+'+++'''';';;''';;';''''''++''''+'++'''+'';;;;';;;''''+++'';';'++''''''';+'''''''''++++'''   
 ``'+L+++++'+L++++++++'+++'+'+'';';;';;''''+;,:.;++:;+;;;','';.''+','''.,'.`````````.`````.```.`.`.````````````.``..``````.`````````````,'+;'''''''';+'''++''+'++++'+''++''+'++;''''+;;''':+'''';';'';;'';'';;'';'+'''''';';;'''';'';';'+++'+''+''''''''+'';+''+'++++''+   
 ``'+++++'++L+'+''++++++++++++++';'';;;;'''+,;,.+'';;+;;;;:'+:;+''';;+;.;+,.....`...`....`...`....`````````````````````.`.``.``..`...``.``.;'+'++'+'+++''+'''+'++'++'++'+'''++''''''''';;;;'''';;'';';;';'';'';;';'''''';'';';;::';;;;;';;+'+''''''''''+++';++''+''+''''   
```'+++'+'+++'+L++'++'''++'++++''':''';:'''+:;.:+'';'+;;';.;','+''':'+','+:.........``...`....`...`..`.``..````````.````....```..``......``.`:++'+'+'+'+'++''+++'+'++++++++++'+'+''++'+'''+';'+''+'''''+';'';'';';;'+'''++'+'''''+';'';'+;;''+'+;''+;'+'+'''+'+'++++L++'   
```'+++;+L''+'+''''++''L+''LHO++;''';;;+;;++;:.;''':'+;;'':;+:'++++;'';,+':..........`....`.``.......````...`.`.......``.`.`.....`....``..``...:'+''''++''L+'+'+'++'+++'+++'''''''+';'+''+''''''';'''':;''';;''''';'+'++'+'+;'''''''++;+;+'';:+;+';'''++'+++'';+++++L;++   
```'+L++''L'++'++++++++++++'++++''';;;;'''++;.;;+'++''','';;,:'''+++:'','+'....`.`.....`.`...```..`...``````````````````````````````..`.`.```.``.;:;'''+'+':'+'+''''''+''''+''''++'''+';';';++;''';;;;'+++'''''+';'''';';''+''';+''+'+';':'';''+'''';+'+L';+'''+'++';'+'   
```'+++'L++++++++++++++L+L+++'+L++'''';+:'+'';'++++'+'+;L'+,:';''+++:';''++..,,........,......``...`..````...````.`.`````.``````````..`...``....```.`.'''++,'++''''+'+'''+;''++''+'''';';::,,;:,,.,;;,.,,,''+;+''+'''';''+';+''+;+''+'''':;;;'''';+'''''++'++''''+L''+''   
```'+++L'++++'++'+++'++++++L++++++'';+';''+'''''+''''';;+'';';'''+'':+;;+++'..,,..,...,..........``..``........```.``````````.....``.`.`.......`......;+''+'++'''++'''+'+'+'++''+'';:..`.,``.```..,,,,:;,,..::'+''++'''''+';''++'''';''''';'''';;';'''''++'+'''''++''L++   
```''+L+';+'L++++++'++++++++++++++++''';'';;+++;+'+'+'';+'+''''''+'+';';;++':::,..,,.,,,..........`.`....`...```.```````.```.``..``.`....````.......,,';''';:'+''++++''+''+''+'+',..````.``.``.`````.:,,;:',``.:;+'+'';+''';''+''''+';+''+'';';;''''+';''+++++''''+++++'   
```'++++++++++++++L++++++++++++++++'+;;'''+'+'+'''++'';''''''''''+''',';''++;,:,,,,,.,,,,.........`.``...```.......`.``.`.`.`.``.```.``.`.``.`.`...,,::''''+''+';;,,::;''+''+';,..,,.....`.``.,..`..```.,...;;,.;;'+++'+'+';'';''+'+;''''''''';;''''''++++++'+''''++++++   
```''+'++''++'+;++LH+'++++++++++'L++'';;'+'''+'''+'+';''''''+''+''''+;'.;''+;;:;::,,,,,,.,,,.,..,......`.`...`....``...``..````...`.`..``````````.,.,,''';+'+';,.````````.;;;';,,::,:``.....```,.,,.....``.,...,.;:''L++++'';'''''';;'';';+;'':'+''';''''+''+''''++'+++'   
```'++'+++++++++;+++LH+'++++L+++++L+'+++:+''+'+';''++;;'''+'++''+'+''+'';''+'::,:;::;:,,,,,......`.......`...`....````.`.`````.``.```.`````.`````..``.,.,:;'':.````.....`````..,,,...,,..`..`,,.`..,;;::::,.,....,:;''L++'+;+';';;'+;'''''''+';;'';'';'+''++++'+'+''++++   
```'++'+++L+++++'+L+LH++L++LH+++++++++++;''+';''+;+++''+'++'++';;+++++';;;''';;;;:;;;;:,,.,,,..............``.`.``.`.`...`.````..``...``.````.```...`......,,,,,............`..`..,::...,...`..,.,..,';::;;;,,,,.,::;''++'+;'';;;;''';'';''''';;;';'''++'';'''''++'''+'+   
```'+'+L+'+++++++++L++++L+L+LH+++++++LH+''+;';;''+:'''+''++''+'+'''++''+'';+;'';;':;;:'::,,,...........`.`...`............`.`..```..`...````.```````.``.`......:,,........,,.`.````.,;,.`,:.`.`..,..`..;;:::;::':,':;:;'+'';;;;';;'';''''';';';;''''';''+'+''++'+'+';';'   
```;+''L+++++++''+++++++L+LH+LHO++'+++L+++''';'+;''''+'''''''';;''''+'+';',''';';':+';;;:,,..............`..........`.``..`.`..`.....`..```````````...,......,..,.`..,..,..,:,...`.``...;,`,:,.....,,...,;;::,,;;:,:';,';'+''';';'+'';+'''++''';''';;''''++++++++';''++'   
```;+++++++++++++L++'+L+++L'+++++++L+LH+'+'+'+'';'+'++''+''''''';'+'+''''';''+'';'++''''':,.........................`....`.`.```..,,,;.....`..```````.........,.....`.,......',.......`..,::`,;,...,,,:..,:;;:,:,,;'::::,+++++';+'''';'''''''''''';';;+;'++;'+'+++'++'++   
```;;++++L++L+++++L++++++L+++++L'++++LHO'+++++''+'''+'+';;';';+''+'++'';+''''++'+'++'';`.,,,............................``.`.......,,::....`.`..```````........,,,,.,.....::.::,...,.......,,..:,,...:.:,,..:;:,,:,,:;:;;;++++;;':'';+;''';';;:'''+;'''+++'+'''+++'+'+''   
```;'++'+++++++++++L++'+'L+++++++'L+L+L+++++'++':'''''''';+'';;+'';''+''++;';'+++''';....,,.,................................`.``...,:':;.......`.```............::,.,..,.,;:.,,:``..,.,,....:,..,.,`.:,,:.,.::,,:,:::;':;+'+'';'';'+''''''''''+'''';++'++'''+;+++'+''+;   
```:++++++'+'++L+L++'++''+'+'+++++'++L+L+L+LH++''''+'''';';;''+''+''':';;'''''';;':......`,,,.,..,...................`...``.``.`...`:;:;;;;....`.```.......,......;;,,:`....::,,:....,.,;,,.........,.;,;;:,..,;,::,:;:;;;''++''':+'''';'''''';+++''+'++'+'+''+++++'++;,   
```;'+++++++'L++LH++''++++''++'++++''''+++++++'++;+'++'+;'''''++';';''''''''':';,`.`..`.`..,,...,.,....................```.```````.``,;::;:;:,````..`.....`..,.....:';:,,....,:,,,.`,:,.,;;,.,,..,..,...,:;;:,.,',,:,:,;:;;;++''+;;;';'';;'''';+'+'''''''++:'++'+';:+'''   
```;;'++++'L++L+L+L+++++L;+'++++L+'+++L+L;++++'+L+''+'++'''';++++'+'''+'+';+',.`.``.````...:,.,,......,.,.................`...``````..,;:::;;,,....``........,...,..,';,,.,...;:,.,.`,,,,.:':,,.......:.:,::::.:,;:,,:;:;:;;'+'''';'';'''''''';'';;;;+''+'+'''''+++'+''+   
```;+'++++'+++L+++++++++L+'++'++++++L+++++++++++L+'++'+++++++''L;+'''++;'';.`..`.`.```...`..:,.,.,.,..,.............`....`...`..`````...;:,:::;:............,.,...,..:':,.,.,.,:',.::.,;;,,,';::,,.,..,,:;,,:;'::.:':;::;;;;;'+++';+:'';';;''''+'+';'';'+++'+++'+'+'''+'   
```'+++L++'++++LH+LH+L+'++L++++++L+L+L++L+'''+++++'+++'+++L'+++++''''+'';.``.``.`.``.`.``....,,.,,...,...............`...`.`..``.```````.,,:,,::;,........`......,..,.;;;::,,...';,.:,,,''',;;;';;:,.::,,.,,,;;;;':;'::::;;';;'+'''';';';'''''++'+';'''+'++''+''+'++++''   
 ``:+'+;'+++'++++L+L++L+++++LH+++L+++++++++++++++++++++L+++++++''+++;'+:..`.`...``..````.....:,,,,,:,,,..,..,.,...................````..`.:::,::;;:,,.........,.....:,.;';:,....':;,,;,,,:+:.,+'''';;,.,:,,.:;:::;;':;::;:;:;:'+'';;;';';'+''''+''''';';+++''++''+';+''+   
```;+;''+L'++''L'+++++++L+++++L++LH++L+'++'+L+L;++++++'L++++++++++''+,`.```.```..`.```````.`..;:,.:,,,,.,....,...``.`.`...::,.`.`.``...```.,:,.,.:;:,,`........,.:..,,,,;;;,..,.,,;'.,,,,,;+,,:;'';;;,.,;.,,;:,,:;'+':;::;';;:;'++'''';';;++';''''''''''+'+'+++++'+''++'   
```'++L+L'+'+'++LHO++'++++++L++L++++L++++++'++'++'+++++,'+L'+++'+++;.`..```````..``.``````....,:::,::,,..,.,..,........```.::...`...````````,:,,,.,:;:..,`.`...`.,,`,,:.,;;,,.....,:;,.,.,,:';,,;';:;'::,,::;::;::;;;;:;':;:';;:''';''';'';+''''+'+'''+''';'+++'+'L+''''   
```;++'+++++L+++++++++++++++';LH++L'L++L+L++'L++'++++++++'+'+++++';`.``````.....,.``````......,,;;:,;,,,,,.,...,............;:.......````.`...::,,,,:';:.......``,:...:,,:';:,,.:,,,:;.,:,.:;+;,:;+';;;',,,::;;;;;;;';:;::';;';;:+''':';';'+'''+'''';++''+++''+++;++''''   
 ``;';++'L+++++++++'+'+++'++'++++++'+++''L+++'++++'++'+++++++'+++'.``.```........````````.`.....,;:::,;:,:,,,.,...........`..:;:.......`.`.`..,,,:;::::;;,,,......:,.,:,,:';:.:';;,...,..,,,:;'',:';+';'::;;';';;;:;:''::;:;';;;''++'''''++++''+'+''+'+++++'+++++'+'L+''   
```;+'+'++'+L;++''+L++++'L+++++L++L'+''++++++++'++'++;++++L+L'L++:``.```.`.....,.````````````....,:;::::,,..,..,......``..```.:::,.....`````...,.:';:;,::::,.,..`.::,.:,,,;;;,::;;::,.:,.,,,::;';::';;;';:;;;'';;;;:;:;;:;;;;;;:;'+'+'''';''''''+'''''++'++++'+''++'++''   
 ``''+L++L++L+''+++'+++'++++L++L++++LH'L+++'LH+L++L+++++++++L++++,.......,....,.````..```````.....,;;::::::,,,,,.,.......````.`:':,,........`..`.,:::::,,,;::....,,;,.,::,:';::::;;::.``:...,;::;;,,,':;;:;:;;:;;;::,;';;;'::;:::'''+';'++''+;;+';;;''+''''+'+'''''+''''   
 ``;''++++++L+++'++L++'++L+L+L++L++L++++++++'+++L+L++;+++L'++++L'.......,.,.,,``.`````.`````.`..,.,,;';:,,::,::,,,,......`.`..``:';,........`.....:';;;::;;;;;:::,;;:,::;,:''::';;'';;,.,,:.,:;;;'',::;';;;::;';'';;,:'';;'';;:;:';''+++'''+'''+'';;'+'+'+++''+'''+''';'   
```;'++'L++++'+++L+L+L+LHO+++LH+L++'+L++++++L+++++'++++L'++++L+++.....,,.,..:```````.```````.......,::;:;;,,,,:,,::,........`````.;::,.....`...``.,,;;:::;::'';;:::;,:;;;,:;;:::;;'::;:,,,,,;::';;';,:'';';,;;'';;'';;';';;;:;:;;:';+'''++'+;''''+++''+'''++'++'L++'++'+   
 ``;'+'L++++'L'L++L+++L++'+'+L++L+L++++L+L++'++++'+++L++++L+L++L'....,:..,::.``.`.`.`....``........::,::,:,:,,,::,;:,.,........`...;;:,,....`....`.,::;:;;;,::'';';;,:';::,'';:,;:':;':,:,,,::;;;;;;;:;;';;:,;;;;';';''';;;;;';;;;;''''''';'''++;;;'''';+'++;'+''''+'+''   
 ``;'+'++++L++'+L'++++++;L''''++''+'++L++'LH+'++++++++++L+++++'++`..,,,..:;.````````.`.``.`..`......,,:;::,:,,,,`:,:':,,...`.```....;;;,,.,.........:::::;;:::;:;:::,';'::,;+':;;;;';;;;;::::';;:;;';'::;;;:;;;:;';;;'''';;;:;;;;;+'''''+''++'++'+'''+'+'+'+'+'+'''+'''+   
`` ;'''++'++;;++'+'++'+++++'+++L+++++++L+++'++'''++++'+'L+'++++''`..,:.,,;````````...````..```......,.,;:;,::,.:,..::;;,......```.``.:';,,,`.........,:,;';:;,:;:,,,:;;;::::';,::';;:,::::;:';:;;:;;'';:::;;:;;::;;;;;;';':':;:';';;+''''+'''++;;'';+++'''++;++''+''+'+'   
```;'+'++++++'++'+++;+++++L'++++'+++++'L++++L++++++++L+++L++'+++'....,,:;...````....``.```.`.........,::;;;,:,,,,,.,,::;,......`.````.,';:,,...``.....:,';;:;,,;::;::;;;;:,;;::;::;;;::,:::::;,;::;;;;';::::;::;''';:';':;';:'';;;';'';''''''+';+;';;''+'+'''';''';;''';   
```;'++++++''+L+L+L+++++L++++L+L;+++'++++++'++'++'++++;+'+''++'+:`....::.``````.....`````````.`.......,::';:;::,,.,,,,:;',.....`.`.....:;'',.`.`........:;;;::::::;;:;;:;:;:';::;;+';:;':;'';;;;;;;;;;';';:,;;:,';'';;;';;;:;;;';;''+++';''''''';'''++'''''+++'';'+'+'''   
```;';+;++++''++LH+++'+L'+++++'++++++++++++++++++++++'L+++++'+++:.,..,,,``.```.`,,,..``.````..........,:::;;';:,,..,,,,;'',.........`.,.,;:;:..`......`..';;:',::;;::;;;:;;;;::,''';;;;;::';;'';':;;'';;';:;,;;;''':';';;;;;;;;'';''''+''''+''+'';+'+''+'+++'+''+;++++++   
```;+:+'+''++++L++'++'+++++L+'++L++++++L++'+++''''+'++++''+'+++':...,:,.````.`..,:,`````.```.....`...,,,:;::''':,,,,,,,:;;':,.`...`...,,..;;',,,.....```.,:;;::;::;,';';;:;:;:':::++;';';';:';:;;';':;';;;';:;;:;:;;'''';;;';;;'';''''+''''''''+'''''+'+'+''''+'''';++'+   
```;''+++LHO++++++++++L+L+'++;++''+++L+LH++L+'+++'++++++++++'+++,,.,;:`..``.,..,,,`.``...```......`....:,,;;;'';;,,,..,:::;;::........,,,,::;;:,..........,:;::;:::,:;;;;,;::;;::;';;;':;;;;;';;;';;;;;';;;;;;;:;;;;;+:';''':;'';;;;'''+''+;+';';;'';';'+;'''++'+++''+''   
```;'+'+LH'++++L++++'++++'+L+L'+++++L+L'L+L+L++++''++++'L+++L'L',..,;,``....,,,,:,`.`...``....`,:,....,,;::'''''';:,,,,,:::''':....,.,,,,,,::;;':,.........,';:;;;:;''':;;:;;:;;;;';''';';;;;''';;:';;;''';';;;;::';;;;;;;';;';'''''''''';+''''';'+'++;+'''+;;'+'++'+''+   
```:+L++++++L++++++L+++++++++LHO+LHO++++++L+L+++++L+++++LHO+++L+,.,;:,....,,:,,;;....``..`.,.....,.,,,,:;:';+'''++:;:,,,,,::;;':,,,,,,,,,,,,,:;;':,........,::'';::';;;:';;;:;'';;'''';';;';;;';;;';''';;'''';;;;';;;'';;'';''';'''''''''''L++'''+'+'''''''';'+++++++''+   
```:'+++L++++'+L+++++LH+'++LH+++L+++++L+L+L+LH+'+++++++++++L++++',,::,....,,:,,'.......``.......,,,,:;;;';;''''+'+';::,,,::;:;';;:,,,,,.,,.,:,;:;;;,,......,.;:;;:;;';'';;';';';;';';';';''';'';'';';''''';';'';';;;;;';':;''';'''++'''''''''+'+'+++'+';''++'++'L''++'''   
```;'++''+L;+++L'+'L+L+++L'+++++++LH++'L++L+++++++++++++L++;'++++,,,,,.,::.,,;:,.....,..`.....,,:,,,::;:';';'';';+;'';:,:;::;:;';;':.;,,.,.,,:;:;'''::,:,...,:::;;';;:';+;;'::;'';'+;''''''+'';';';';;+;';;''';';;;;;'''';''+;;+'';;'''''+++++++'++++++'+++++'+++'+++++;   
```:+++'+L+'+'+++++L++L+L++++++L++++++L+++L+++'++++++++++'+'+'++'',:,:,,::;,::'.`...,,.``....,,,:::::;;;;;''''++;';'+';:;:::;::::;;;';:,,,::,:;;;;:;;:::,.,`,;:::;'';;;;;;;;::'';;;;'';;';'''';;:';;;;'';;;;;;''';''''';,';;;;''''';'''++'''''''+''+'+''+''++'++'+'++;+'   
```;++''+++++++L++'++L+++++++'+'L+++++LHO++'L+'++'L++;++''++++++'+;,:;..::::::,.`..,..`..``.,,::,;;;::;;'''+''''++;''++';;;:;:;;::';''':;::,::,::;:;;;';::,,,;;:;';'';';;;',:;':'';''';'''''''';';;''';;;'';';;;;';;';;;'';;'';'';;'''''++'++''''++++''''++'+';++++''+++   
```;++'++++++L++'++++++++++++++L++++'++++'++++++++'+++++L+++++++++';,::,:,;;;;.`..,,.`.`...,,,;:::';;';:;''++'++++'L+'';+''';:;';:'';:;;;;:::;;;:;;;;;;;;:::;:;:;;';;;:;;;;:;;''';'';;'';';+';'';';;;;';':';;;;;'';';'':;;';''';;'';'++'''++''+''+++'++''++++'+++'';+++'   
```;+''+++++L+L++L+++'+++L'+++L++L++'+L++L'L++++L++++L++LH++++L''+L':;;::::;;,...,,.`..`,.:,::;:;'''';''+'''+++'+++'+'+++'+;'+';;;'''';';';;:;;;;';;;;:;;;:':;;;;'';;;;;';';:;'';'''''+;'+;';'';'';';;';'':;'';;;';;'';';';;';''''';+''''+''';;+'+++'++;++++''+'+;++++++   
```:++++++++++L+++;LH'''++++++++'L+++L'L''+'++++++++++++'L+'+''+++++;::::::::.`..,.```..,,,,,;;;''+''';'''''''++++'''+'++'':'+''''++''+''''L+':;;;''+;''''';;;'';'';;;:;:;;::';';+'';'''+''+'''''''''';;'';''';'';''';;';;;'''';';'';+'+;;++''+'+'+++''++L+'''''++'+'++'   
```;L+++'++'LH++'L:+''++'+'L++'+L++++'L+'++++++++++LH'+'++++'+++L+';+::;;:;::...:.`.`...,,:;;''';''';;'+'+';'++'+';'';''++'+';''''''';''';;'';''';;;;;;::;:;'';;'';;';;';;;';'::';';;';''';';;;;'';;';;''';':;:;'';;'';';';';;;';''';'+''''+'';+++++'++L++'++'++;++'++++   
```;+++++L++LHOOQ+++L++LHO++LH+++LHO++L+++'+++++++++L+++'L++++++'++'+;:;::;:.....`.`..,,,':;'';';'';;''+''''+''''+;';;;'''+'+'':;;;;;+'':';;''''+''+++'+''';;;''';+'';;;;;;'';;:'''''''''';;;;;';':;';';:;;;;''';;';;;;;';;;;';''';;+';'+++'''+'+'+++++'++++'+;+++'++++'   
```;;+;+'+++L++++L++'++L+'+L+L+'++++'++L++++++++++++'L+++'++++++++++''::::;:.,.,.``...,,;;'++'+'++'';+'''''''+''''+'''++''++'''';;'''''+';'''';;'''''+'+L''+'';+;;''';';'';;;;;'''';''+';''';;;';;;:''';;';';;+;'';;':';;;';';;;;:;''++''+++';'''++'+++'+'++'+'+L++'++'+   
```;++'+L'+LHOO++++L++++'+++L++++++L++++++++L++++++++L+'+++'++++'++'++;;,:;:,,..``..,,,:;'+''+''+';';'';'''+'''''+'++''+;';;+++'++;'+'+'''''''''+''+++''+;''''+'':';';;;;';';;';;;;'';:';'';;'';''+;;;;;;';;;'''';''';''':';;;'''';;'L++;L++L+++++++++++++++++++++'+;+++   
```:+;++L+L++L+'+L'L+LH+L+L+++L++++++++++++LH+L++L++++L++++LHO+L+LH+++';';;':;:....,:,;;:'+++++'+''++'+'''++'+'''''+'++;++L+++++'+++++L++++'++++++L+++++'++++++++++''+';;;';;:,;;;::;;':';;;;;';'';'''';;:';';':;;;;;;;::;';:';;;'::+'++++++++''''+++++++++L+++L+++'L++'   
```;'+'++LHOO++++++++LH+++L+++'LHO+L++L+++'++++++L++++L++++;'+L+++++++'+;;;'::,.`.,:;;;:'++++++LH'+L+'++++++L++L+++LH'L++'+++++'++L+L++++++;+'L''L+++'++L+++++++'+L+L'+'+''+;''L';';';'';;+'''+;'';''''''''+';';+''';';';;'';;';'';'++++++L++++++'++'+++++LH+L++++++'+++   
```:+''+++LHOOQ++++L++;++++L'++++++++++++++++++++'++++++++L+++++'L++'++''';;;;,...;:;':'+++++++++++++++'+++++++++++L+++'+L+L+'+++++++LHO++'++'++++''+++++'+'++''+'++'''''++++'+'++'';:'''':'';;;;;''';;';;';';;':;;;';;'';';'';;++''+L+++++'+++++L'+'+++L+++LHOOQ++++;++   
```:+++++LHOOQLH++++L++'++++++LH+++L+L++++++++'L+L++++L++LHO+L++'++++++++';;+;,.,,;''';L'+++L+'++++L'+'++'''+++++'+L+++'''+++;++'L+;+++L'++'+'+++++'+++++++''++'+'''+'''+++'';'++'';';'';''';';+;;'';':;;;;;;;;':';:;;;;';'';''''+'+++++''+''+'+++++++'+++L++LHO++++++++   
```:'+++L++LHO+LH++L+++'L++L++++++LH++;++L+L+'+++++'L+++L+++++L'++++++L'+++''';,:;;:+'''''+++LH++L+++'++L++++LH+L++L+++++++L++++++++L+L+L'+++++++++'+L+LH++'++++++++''+'+''++''+'''+'+''+'+''''''';;;;';:;';;;;;;'';;;;;''+''+;''+++L++'++''+++'++++++++'+''++++'++++'+'   
```:++++++++++++++;+++++L+L+L++++++++'++L++++L+++L+LHOO+++LH+L+L+++++LH'L+++'':,;;;;;'''++LHO++LHO'+L++'+'+'++++L+++L+L++++++'+L++++L+++'+'+'+++'++++'+++'+;''+'+'+'++++++''''+''+'++'+++L++'+'+++++';+:';:;'';';';+';+';+++''+'++++LH++'+++L++++'+''+++L++++LH+'L+'++++   
```:+'LH+++++'LH++L++++'++'L++LH+++++++++LH++L++++L+L++LHOO+LHOOQ+++L+L+L++++';,;:;;''+++++++LH++++++++++++++++++''+''++++'++L++++++L+'+LH+L++++;+'+++++''''++++'++++++++''+'''+'++'+'''++++++++++++''';''''''';+;''''''';++++'';+'++'++++++++L++++L+++++L+'++L++++++'''   
```:''+L++L+++++L+L+++L+++L++++L++++'++++++++++++LH++L+L+L+LHO+++L+LHOO++L++'+;;;';;'++L+LH+L++LH++L++++++++L+++++++'+'+++++++++'++'+L+L+++++'+'++++++++++'+++'+';++++''+'++'+++++'++++++++'+'+++++'+'+'''+''''++++''+''+''+'+++''++++L+'++'++++++'+'+'++++'++++++++++++   
```:+L++L+LHOO+L++L+++++++L+L+++LH++++++++'+L++L+L+++++L+++LH+LH+++L++L+++L+''':;;';++L++++++'L+LHOO+'+++++++L++++'+'+++++''+'++++++'+'+'+++L+'+++++++++'+'++''+''++'''+'+'+;+'++''++''+'++'+++++++++++++++++'++'+++++'+L++'++'L'+L+'L++L'+'+++++'++++++++++L+L+++++L++'   
```:+++++LH+L+L+++L+LHOOQLH++L++LHOO+++''++++'L+'++++++LHO+++++L++LHO++++++++++'';'+++++LH+LHO++LHOO+L+++++++++L+L+++L+++++L++++++++++'++L'L++++'L'++++++++''+++++++''+''+L++'+''+L++L+'+L++'+++'+++'+++++'LH++'++'+'+++'''++''++++'+++++++++'+++'+++'++L+LH+'++L+L+++'+   
```,''+++L+L++LH++L++++++L++L+LHOOQ+L'++LH+L+++L++LH+L++L++++L+LH+++++LH+L++L++++''++++++L+L+++LH++++LHOO+++LHO+L+'++L++++LH++++LH+LH'+'++++L+L++L+L+++++++'++L+++++''++L+L+L++'++++++++++++++LHOO+++++'++++'++++++++++++'++'++L+++++++++'+++++LH+++++++'L+LHO++++++++++   
```,'+++++L+++++L+'++++L+++++LHO+L+L++LHO+++++++L++++++'L+L+L+LHO++L+L++LH++L+L'''''+++++++++++++LHO++++++++++++++++++'+++++'+++++++++L+'++++++L+++'L++'+++++''+'+'+++'++++++'+++'++'L+++++++L+++++L++L+L+++++++++++++++L++++++L+++L++L+++'+++++++LH++++L+L+L+++L++++LH+   
```,''++++LH+++L++++++L+LH+L+L++L++LH+LH++L+L+L+L++L+LHOOQL+LHOOQL++LHO'L+LH++L+'';;L+L+L+'+++++L+++++++++L++++L++++++++'+++++++++LHO+L+++++++L'+++++'+'++'++++++++'++''++''L'+''+''++'+'+++'+++++++++'+++++++++'+++'++L+'+'+'+++L+L++++++++++++'''++++'++L++++L++++'+++   
```,++L+LHOOQ+++L'L++++L++LHOOQL+++LH+L+L+++LH+L++++LHOO++LHOOQLH+L+LH+LHOO+++++''''+LHOOQL+L+L+L+LHO+L+'LHOOQ++++++++++L++++'L++++++++L++'+++++L+++++++++++++++++++++L+'L+'++L++'++'+''++'++++++'++'+++++++'++'+++++++++L'+++++++L+++++++++L++L+++L+++++L+'+++''''+L+L+   
```:+++L++LH+L+L++L+LH++++L+LH+L++L++LH+++++LH+LH++++LH++LHOOQ+L++LHOO+LH+L+++'++'+'++++++++++'++++++'+L+LH++L+++++++L++++++++++++++++L++L+++'LH++L++++L++++++++++++LH++++LH++L+++'+++++++++++L++L+++++++++L++++++L+++++++'+++++++L+LH+++L+LH+L+++++++++++++'++++++'++++   
```,'+LHO+LHO++L++L+L+++L++LH+LH+L+LH+++++L+LHOO+LHOOQLHO+L++LH+;+L+L'+LH+'++L+L++++++L+LHOO++++++L+++LHO++++++L+++++++++++++L++++LHOO++LH+++L+LH++L+++++++++++'++''++'++++++'++++'+++'+++++++++++'+'''++++++''+++++'++++++++'++++++++L++++++'+++++L++++++++++++L++''++'   
 ``:++L+++LHOO+LH++L+L++++'+L+'+++L++L+L+L+++++L+L+L+LH+++LHOO+L+LHOO+L+++++LHO+LH'++LH+LH+L+L++++LHO+L++LHO++++LHO+'+++L+'++L++L++L+L+++L++++++L+L+++++++++L+++L++++L+'L+++++L+'+++++'+++++++L++++++L+'+L++'L+L+++''++++++++++++++++++L++++++L+++''+LH+L+L++++++++++'++   
```:++L++LHO+LH+L+L++LH+++++++LH+L+LHOOQLH+++LHOOQLHO+'LHO+LHO+++LHO+LH+L+++++L++LH+LHO++LH+L+++++++LH++++++LH++L++L+++++++++++++++L+L++++L'+++++++++L+L+++LH++++L+++L+++L+L++'+'++++++++L+++L+'LH++L'++++++'+''+'+++++++LH+'+L++L+++++++++'+++++++L+++L+++++++++L+++L++   
```:++L+L+LHOOQ+++;LH++LH;L+'++LH++L+L++L++L+LHOO++LHO++L+LHOO+LHOO+L+++LH+++L+LH+'++++LHOOQL++++L+LHO++'L+L+LH++LHO'L++'+LH++L+++++++++++++++++L+L+L++++L'+++L'++++L++++L+L++L++++++++++++++++++L+++++++++++''''++++++++++++++++++++++LH++++++''+L++++'+++++'+++++++L;+   
```,+LH+LHOOQLHO+++L++LHOOQ+LHOOQL'+LH++LHOOQLH+LH+LHO++++LH+L++L+LHOOQL+LHO+LH'L++L++++LH+++L'++++L+++++LHO+L+++LHOOQ+L+++'L+L++LH++++++++++++++LH+'+L+++++LH+'+++++++++++++++L+++'++'LH++++L+L++'++++'+++++'''+++++''+''+'++'+LH++L++L++++'+++++L+++L++++++++++++++++'   
```:++;+LH+LHOO+'++L+'++++LH+LHOOQLHO+L+LH++L+LHO+L++LHO++++L'++L+LH++LH+L++++L++++LH+LH+LH+LHO+LH+++++LH++LH+LHOOQL++L++L+LHO+L++L+L+++++++'+++LH+L++++LH+LHO++LH++L+'++L++L++L+'++++L++L++L++L+LH+++++++L++++'+''++++++;+++'++LH+++L++L+'++++++++++++++++++++++++L++'+   
 ``:+++++L++L++LHO++L+++++LHOO+LHOO+LHO++L+LH++L+LH+++L'LH+LH++++L+++LH+++L++LHO++L+++++++LH++L++++L+'+++'+++L+LHOOQ+++++++++LH+++L+LHO++++'+++L+++L+LHO++++LH+LHO++LH'+++++++++++++++++++++'++L+L+++++++'L+'+L+L++++++L+++++++++++++'+++++++'++'++L++'++'++L++++++++++;   
```:'+++++LH+LHO++LH+L+LHOOQL+LHOOQLHOO+LHOOQ+L+LHO+LHOOQLHOOQ+LH+L+'LHOOQL+L++L++LHOO++LHOOQ++L++++++'+++L+++L+L+'L++++'++++++++++++LHO++++'++++++++'L++++++LHO++LH+++'++++++'+++++++L+++++++L+++++'++'++''+''L+++L'++++'+'++++++++L++++L++'++++++L+++L+++'+++L''+L++L+   
```:++LH++LH++LHO++L++++++L+LHOOQLHO+++L+LHOO+LHO+LHO+++LHO;''L+++++LHOOQL+++LH++++LHOO+++L+LHOOQL+++LH++L+LHO+LH+LHOO++++++++L++L++LHO+L+++++++LH++LHO+'+L+++LH'LH++++++++++++L'L+L++++'++LH+L+++''+++++'+++'++'L+'+'+++''++++++LHOO+++L+++++'+++++++++++++++L++++'++''   
```:++++L+LHOOQLHOOQLHO+L+LH++L+LHOOQL+L+LH+LH+++LHO+L+LH+++;++L+'LHOOQL++++LH++++L+LHO++LHO+LH+LHOO+LHO+LH+L++++LHO++L++'L++L++L+L+LH+L+++++++++++++'LH+''L+++++L+L+++L++++++++++++L'+L+++L+++LH+++++++++''+++++LH+++++L++L+++'+LHO+++++++++++++++L'+++++++++++++++'+++   
```:L++L+++L+++LHO++L+++L'L+L+LHOO++LH+'+LHOOQL+LH+++L++L+L'LHOO+L+L+LHOOQL+LHO++++LHOOQL+LHO+LHO++L++L++++LHOOQLH'++LHO+LHO+LHO+L++LH+LH+++++L+++++LH+++L++L+LH++LHOO++++++L+++++++L+L+'+L++L+L''+++++L++++++'++L++++++'++++''L++++L++++++''+++L+++++'+++++++++++++L'+;   
```,+++L++LHOO+LHOOQ++L++++LH+++LHOO+L+LHO++++++L'++LHO+++++LHO+L+L+LHO++LHO'L+L+++'++L+LHOOQ++++L++LH++++++L++L+L++++++++++++++L+++;++L'++++++++++++++'L++++L++LHO+++++++++++++++++++L++++L+++L++L++LH++++++L+++L+L+++L++L'++++L++L+LHOOQ++++++L+++++L++'++L+''+++++L++   
```,++LHO+LHO++LHOOQLH+LHOOQL+LHOO+L+++++L++L+L+L+L+L+LH+LHOOQLH++LH+LHOOQLHOOQLHOOQ+LHOOQLH+L+L+LH++L++++LH++LHO+LH+LHO+++++++++++++L++LH++L+++L++++++++L+L+LH+L+++LH++++L+L++++++++'L++++L'++L+L+++++++++L+++''++++'++++++''++++L++L+L+''L+'++++++L+'L++++++L+'+++'''+   
```,+++LH+L+LHOOQLH+LH++++LH++LHOOQ++LHOO+LH+LHOOQ++LH+LHOO+L+LHOO+LHOOQLH+LHOO+LHO+LHOO++LHOOQ+L+LHOOQ+LHO+L+LHOOQLHOOQL+L+L+L+L+L+L+++LHO++++++++L+L+LH+++L+LH++LHOO++++++'++++''+L+++++++++++L+++++++L+++++L+++L+L++++L+L++++L++LHOO++++++++++++++++++++L+++'+L++++++   
```,+LHO++LHOOQLHOO+LH++L+'+L+LHOOQL++LH+LH+LHO++LHO+++++L'++++LHOOQLHOO+LHOO++'L+LHOOQLHO'L+'L++LH+++++LHOO++LH+L+'L+++LHO+++++L+LH'L+++++LH+++++LH++L++L++++L+L+++L+LH++++++'++++++++++L++++++++L+++++L+LH+L'LH+L++L+++++++'+++++LH+LH+LHO+++LH+++++++''+L++++L+++++L+   
```,+LHO+LHOOQLH+LHOO+LHOO+L++LHOO+'LHOOQL+LHOO+L+LHO++LH+LH++LHO+LHOOQLH+LH+++L+++LHOOQLHOOQ+++L+L++++LHO+LH+L+LH+L+L+LHO++L++L'+LH+++L+L+L++LH'++LH++LH+L++++L++++'+'++++'+';'+'++L+'+''+++++++++++++++++++++++++++L++++++L+++++++++LHO+L+L'L+L+++L++L'L+L+'+L++++L++'   
```,+L++++LH++L+L+L'L+++L+++LHOOQL++++++LHOO+LHO++LH+L+LHOOQ'LHOO+LHO+L+LH++LHOOQ'L+LHOOQL+LHOOQL+LHOOQ++LHOOQLH+LH+'+LH'+L+LH+LHO+LHO+++L+++LH+++L+++++++L+LH+LH+LH+L+'++'+++''''+++++++'++''''L++++++++L+'+++++++L++L++++++++++++'LH+++L+++++:++++L+'LH+++++'++'++++++   
```,++++L++LHO+L++L+LHO+++LHOO+LH+L++LHO+L++LHOOQLH+LH+++LH+LHOOQLHOOQLHOOQL+LH++L+++LHO@LHOOQ+L+L+++LH+++L++L+L++++++++L+++++++++L+L+++L+L++++++++++LH+++++LH++L+L+L:+L+''++''+''+++L+LH++++L+'+++'++''+LH+++L+++++++++++++++LH++LH+++++'+++++''+++'++++++++'+++'+'++'+   
```:;+L++++LHOOQ++LHOO+L+++++L+LHOOQ++LHOOQ+LHOOQLHOO+LHOOQLH+LHOOQLHOOQLH+L+LHOOQ+LHOOQLHOOQLHO++L+LHOOQLH++LH++L+L+LHO+L+++LHOOQLH+LH+L+++L+LHO+LH++L++++L+LH+LH++++'+++'+'''+'++++L++L+++++++L+++++'+++++'+++++++L++++++++'++''++'L++++'+++++++++'++'+++++';+'+;+';'+   
```:+L+++++'++L++L+L+LH+++L+L+L+L+'L+LHOO+L+LH+L+LHOO+LHO+LH+@L+LHOOQLHOOQLH+L++LHO+++LHOOQLHOOQLHO+L++++LHO+++LH+L+LHOOQ+LH+LHO+LH+LHOOQL+L+LHO++++LHO++LHO++L+L++L+++L'''+L+';+'+++++L+++++++++++++'+L+++'L+L++L+L+++L+++'+''+'++''+'L'+L+++''+'+++'L+L+;++++;'++++'L+   
```:++L+++L++L;+++++L+L'+'+++L'L+L++L+L+LHO+L+LH++LHOO++LH+L+LHO+L++L+L++L+LH+L+L+LH+++LH+++L+L+++++++L++'+++'++L+LHOOQLHOOQL++L++++LHOOQL++L++LH+L+L+L++++LHO'LHOO++++++'+'++;';+'++'+++'LH++++++'''+'+LH+++++L+L++'+++++L++++++++++'+'';++''+;+''+'++'''''+'''''''''''   
```:L''+L+L+LH++LHO+L++++'L+++LHOO+LHO++L++LHO+LH++LHOO+LHOO+LHOOQ+L+LHO+L++LH+LH+LHO+++LHO+LH++++L+++L++L'++L+L+LHOOQ+LH++++L++++L+LH++++++++++LH+LH++++L+++L+L+L+'++++;';:;:;;:;+''++++'+++'++'+;+';+';+++'+''+'++'++''+++'''+++'''';+++'+';'''''++''+'':+';';';;'+';;   
  `:+++LHOO++++LHOO+L++L'L+++'LHOOQ+LHOO+LHOOQ'LH++LH+LHOO++LHOOQLHOO+L+++++LH+LHOO+LH++++LHO+LH+LHO++++;'++'+'+LH++++L+++L+L++++++++L+++++L++LH+''+'LH++++'+L+++L+++++'';:;;;'';:;':+''+'+';;''';'';;;'''';;':';;:'';,'''''++'''';;''';:;''':','''::':';,:;;;,:,::,,,,.   
 ``:+++L+LH++L+'+LHO++LH+++++L+++LH+L+++L++LH++L++++++++++L+L+LHOOQLHOO++++'+++''''++++LHO++++'+++L++++++'+;;;:';';L++''+L++L+++L+++LH+++'+'+++++++'''+'++++++'+''+';';;;;:,:,;:;:::,;;:;;;:;''''''';;:,:,,;:';;'''::,:,:::':::;';;:::,,,.::..,:,,,,,.,,...,,,,,.,``````   
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