```````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
`````````````````````````````````````````````````````````````````````````````````````````````````.``````````````.`.```````.,`.```.````````.`.,.`.`````.`,..``,```.``````..`
```````..`````````````````````````````````````````.``````.``.```````````````````````.````..````````...```,.```,```...:``.`,..`,.,``.`......`,`...,.`,..,.,.,:`..:,..:.:.,,`
```.````,``````````````````````````.````````````````,`````````````.`````````.`.```.`.```````.```.`..````..`.`...`.....`,,`,``.,,`.,,........`:.,:,..,,:,.,,`:`,,:`;``.:,;.`
``````````````````````.````````````.`````````````.`````````````.`````````````````````````.``.``...,``.`..``````..``,..`,`.,..,`...`.,.,..`,..,.```:.....;:.:,`,:`,:`:``,,,`
```.`````,.`````.```````@```````````````.`````````.```````````````````.``.``.````````````````.`````.`.````..`.`,`..`.``,`..``..,,``,``.`.`,.,.,:..`.:..`..,,,,,...,,,,,,:,`
`````.``````````````````````````.````````````````.`````.`.````````.`````````.````````````.``.``.`.``...````.``,`,`..,....`.`.,`..``...,..,..`...`,`;,..,.`,.,, ,`,.:;:,,,,`
````````.`.`````````````````````.``````````````````````.,````.``.`.```````````````````.`..````..``.`..,.`...`.``.``.`...`,.`.`......,....`.,.,.`..;```:,.:.`..::.;.:.``,:,`
``.```````````````````````````````````.````````````.````````````.`````.```.````````````````.`..`..`..``..``..,`..`..,`...```.,..`,,..,....,.`,`,,,`.`:`.`,.:,,.,,,`,`,.,,,`
`````.````````````````````.``.``````````````````````.```````````````.`.````````.`.````````.`......``..```...``.....,.`.,..`,```.,,.``.,``,....,`.:...,..,:.,`...,`,.,,,:,,`
````````````````````````````````````````````````````````````````````.``````.````````````````````.```````.```..`.`,``.``.````..`....,...`,.```,.,,....,.`..,..,..,`,.:,,,,.`
```````````````````````````````````````````````.```;```````````````.`````````````````.`.,:``:,.,,,.,````````..:,,`..,`,..,.`.`..```,,,,,.`.`,.......`..,..`..,,,,,.,,.:`.,`
`````````.`````````````````````````````````````````````````+````.`````````````..,.::''+;#;@#++'@@'@@+',,:';:::,,:::```,`,`.....`...``......,:`.`.`..,...:,`,....,,,`,,.,.,`
````````````````````.````````.`````````````````````````````'```````````.````.:@@@@@##+@@+@+;'';;,':;;;++'+:#@::.`..,,..,``..........`,.`,`,...,,.`....,....,,,,,.,.,,,.,..`
``````````````.````````````````````````````.`````````````.`;`````.`.`````:`.'++;+++''#+;#;;''+'''';:'':':::;';;;:```.:.,,`.,`...,..`,....`,`:,.,..`...,.`...,`,.`,,,,,:.,,`
``````````````````````.``````````````````````.````.`,````````,```,```````+#@#+###@#''@#'#'''''''#;'+++;;;;;''''#++,;:,,`..,..`.`...`.,`,.,`,`.,,`..,,`,`...`,.,,,:`,,`.,,.`
````````````````````.`````````````````````````````````````````.`````````'@@+''#@'##''''#+'@'#'';;'';'+'#';::;;+;;;'#:,,``..:..``...`....`,..``,,.....`,`,.,.,...,.`:..::.,`
``````````.````.`````````````.```````````````.`````````.``.```````````,#@@;#'+@';@#'#+'#'@':':++##;++;@++#+#;,;:'+:;:':.:``,,,,,,.`.,`,.,`....,..`,`..,......`,:.,.,..:..,`
`````````````````````````````````````````````````.``````````````.```.`#@'+'@@:@@@@@@@@@;+'##''';'+@+++'+#';+#';;'''';'';,;,``.`.`,:`,:`,.``.`..`..,:`,`.:..,:.:.,.,,,.:.,,`
```````````````````````````````.````````````````````````````````````;:##+;###@+@@@#@@@@@@@##@@##';;+@##+@@@#+@;'''+'#'';;;.:``..,.``.`....,,..`.....:...``...```.`.,,.,.,.`
``````````````````````````.````````````````````````````````,```.`:,+@@+#';@'+@#@#@+@+@@#@@+@@#@@@#@:;''###+#+#@'';';+#'':':;...,,.....`.`..`.,``...`....:,.``,.,......,.:,`
```````````,``.```````````.```````.````````````````````````````@@;#@+++###'#+#;+@+'@#''@+#@#++####@@'';+'+##+@'++;:'''#''''''...```,.::..`,.,`,``..```....`,,.,..,.`.,.,,.`
``````````````````````````.````````````````.`````````````````.'@#:@;+'@+@@'@###'@@@@#'++@+@@###@#@##@+'''';#@+##@#'';;;@@@;#:;.`.``.```..,,`...,.,.,..,..:,..`.,,.`:..`,..`
`````````````````````.``````````````````````````````.``````:@@;'@@'@@'@@#@@;@@':'#@#+@++#+'+@@#@@''@@#@+''+'+'@##@#@''+:##'#:#;:,.;`,...`....,,`,..`.``.,,`......`.,.:`,.,`
``````````````````````````.``````````.```.```````````````,'@+#;+@####+@#'#@'++#'+##+@###+@+'#####@@;@@@@@+;'';'+@#@#@';;'+###;+:`..`..,`,,,...`.`.,.:.,..`,,....``,,,`,:,.`
``````````````````````````````````````````````````,```.:@@#@'@@''#+@++#+@#@@'#@#;@+#@+#@'##+'@+##@#''''@#@@@'''+++##+@@#:+@@'''#;,.,`.,..``````.`..,`....,.`,,...:..,`,.,.`
`````````````.````````````.````````````.`````````````'#@@+;;''+'@+#'@+###+@@@+'#++##'##'@##@;;@'+#@@'##@@@@@@+'++##++@@@@'##'+;#@'.``.:.,,,..,:``,,..`,,.`..:..,``:,.,.:,,`
``````````````````````````````````````````````.`````@@@@+';++@+'@'@++@'''+#@+###+#++#+##'#++@;;@#+#@+'+###+@@#@+''+##@@#@+'#@#+''@'..,`..`,.,,``.,`...`...```.```..,.`,.,.`
`````````````````````````````````````````````.`````@@##''';'@'@##@+@++++'''@#@'+@;'+@#'#+#+;@@;'#''#@'@#@##;@@#@@@#@+#+#@@#++@@''##+`.:`,.`..``,.`,`......,`..,,.,``.`.,,.`
`````````````````.```````````````````````````.```,'@+@''';@''+:#+@'#@'++''';#+@#@#'+'+'##''''@#'#@#'+##'@@@'@+@@@@##++@@@@@#'#@##'#+:``...,.`,,`.`..:,,.:,,...,`,,,`.,...,`
````````````````````````````````````````````````.@@##';+''+#;@;@@++#'#@'@+#''';';###'+'###;'+'@@;#+#+##@'#@@'#;@@@'#'+++##@@'++@+#@+@;`.``.`..``...`.`.`,``,,```,``,.,`,.``
````````````````````````````````````````````````@#@@,;+#';@++@@,##+'@'#'''+'#'''+'##@#@#@@@+'''#@#@#+'##@+@@@@;@@@#@@'+++@@#'+'#@@@+@;``.,..,..`;........`;.....:.,...`...`
```.```.```````````````````````````.```````````@#@@;#'+;''+';;';++#+'+#''#'';+'+++@@#'+##'@@+'@#'@@#@@##'++@@+@@#@#@#@++'+#@@@+#+@@+@@@.`...,.,.,`.,.``..:.`...:.`,,,...,,`
``````````````````````````.```````````````````@'@@';'#;'#:''+@';;#'@#''+#+'++;+:+''+++#+@@'@#@'+#''##@###@@@+@#@+@#####++@#'+#+@##@#+#@@```..``.,,...,,.`,`,.,,``.....,..``
`````````````````````````````````````````````';@@;';#+;;+;'+@@'#'''#''#+@'@'#++;;';##++#'+#++@'@@@'#####@###+@@#@'@#@@#+@@@#@@@##'+##@@@;``.,,...`.,.`...`..:...,`,.....,.`
`````````````````````````````````````````````@#@#''+@::@#';+@#++;+';+;;#:#@'+#+#@#+##+##''#@###+++@#@@##@+#@###+@@#@@@@#+'##++@@#@##++@+@,:`.`.,,``..,.....`,`:..@.`,..,,``
````.````````````````````````````````````.``@#@@'::#';:@#'';';;#;;+'';;'';+#';'#@@'+++#@+++@@#+#@@#@#@++#@+###@@##+#@@@#@##+@#++#@@#'##@#':.`.,`..`..`.`,.,.,..``.`,,,.`.``
``````````````````````.`````````````````````#@#+'+#@';'#;'';'''';';';';;:;';@#'':#####+'#'##@+##@@###@##@##+######@####@@+##@##+#@@+'####@'`,.`,...,......`.`,:`,..`:`.:`.`
````````.`````````.```.````````````````````#'+#;;@''''@#+;##+#':;;';:'#'+'';;##'''#@+'##+'+@@#+#@+@''+#@#@###+##@@+@+@##@@###@#@##@+###@#+@:```.`....``,,.``..`..,..``:`.,`
`````````````````.`````````````````.```````#@#+,;@+';'@#;;';'':';':;';:++'#';#''''+@+#+#+@'@#@++@#@@#@#@@@#@@@#@@@@@####@@#@#+#@#+#@##@@#@@@``:`.,,.,,.,`.,,,,..:```..,,..`
````````.```.`````````````````````````````@'+';:#@;'#'@#:;#:::;;;,;':::;';''''+#'#'#+####++'#@+##@@#@##+#+@@@#@#@@@@@##@@@@@@#+@#++@++#@##@@,`.``````..`:.`.,,```.@`....```
````````````````.`````````````````````````#@@+,'#@:'#'##;'':::,:;,;;;;;',';''',@#;+'#@+@@''##+@@@+##@@##@@@@##@#@@@#@@++@@#@#@+#@@+@###'@@#@#,`,,.,..`..```.....`..`...,.``
``.```````````````````````````````````.``''#:;,@@':##++'';'+:::.;;,,,:,';++;;';:@@+'#'@##@####+@@#@#@##@@@@'+@@@#@#@@@@@@@#@@##+@@@#@@'##@'@@:```.,`..,`..,.`.`,.,.....`..`
```````````````````.```.````````````````,;;#::;##;;#+'';,':,;,,,:,,,:::;';'';+::.#@+#;+##@##@##++####@#@@@@@@##@#@@#@@@@@###@@@@##@##@@+@###@@``,,`.:..`....,....``,....,.`
```````````````````````````````````..```':@#`''##;;'++';;;.,:;,,,,:,;;';'::;+#;;','##@'+''#+@@@@#@+@+####@@@@#+@@@@@@@@@@##@@@@@+@#@#@@##+@##@`'`..`............`.....,...`
``````.`.``````````````````````````.````@;'+,';#'++;#'++:,:...,,:.;,::,;;:;#'###@:;;''##++##@'+@#@'@##@@+@@@@#@##@@@@@@@@@@@@@@@@@@@@#@'+@@@'@'`.,...`.,.,.`..`....`,,``.``
```````````````````````````````````.```:'+':.++@;'':@'+;;..,,,.::,+,;,:;;+',+';+'#,,+#@'@#@@+@@@@@#+@@@+@##@@@###+@@@@@@@@@@@@@@@@@@@@@@#+@@@@@.``..,.,..`...`,`.``.`..:.,`
``````````````.``````````````,`````````@;#.,;'''':',+;+',,.,,..;:....:,;:,;,;#;:####;+'@;@@@@#@+#@@@####@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@#+@@@@;``..,,`...``.,`.,.,..,...``
```````````````````````````````````````@;:,;:'#'':+;#'':.:.:..`.;;,:.,.;';;;,+;:;''''';@+#+#@#@#@@##+@@#@#@@#@@@@@@@#@@@@@@@@@@@@@@@@@@@@@#'@@@@`.,,,,.,.,,,,.,,`.`..::...`
`````````.``````````````````````.`````:+',:,;##'+;#:'+':,:,`,...:,,.,:`'::`''::'','''''+@@####+@@########@@#@@@@@##@@@@@@@@@@@@@@@@@@@@@@@@+#@@#`..:`.`.```......:,...`,:.`
``````````````````````````````````````@',:::#+'+#;#;''::.,,.,.,.,.,.::,.,:,:;:;;,'';;++#;@+#+@@#@@@@@##@@@#@@#@@@@@@@@@@@@@@@@@@@@@@@@@@@@@##@@#:`...`.,,,.`,..,..`.,...,.`
`````````````````````````````.````````@',:,,'@'+#,'+;',,.......,..:,,,,,,,,;:;:;:;';;''+''+#@###@@##@#@@@##@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@#@@@##@@.`..,,:.,......,..`,...`.`
`````````````````````````.```````````,#::',:'#''@,+#:':,,......,.:`.,,.:,`,,.';';;;'::'++##+###@####@@@@+@@#@#@@@@@@#@@@@@@@@@@@@@@@@@@@@#@##+@#@,`.......`.`......`...,..`
`````.`````````````````.`````````````@;;::;;#@'++:;;;:,..,,..`..`.,,.,.:,,,:,,,;';;;;:';''@#+##@@@+#####@#+#'@#@@@@@@@@@@@@@@@@@@@@@@@@@@@@@##@#@@``,..,..,.`........:..,.`
````````````````````````````````,````',::,';@'+'':;'::...,........,...`.,,.:,,.::':';''::;'###+@@;##@##+@#@'+'#+#@#@#@@@@@@@#@@@@@@@@@@@@@@@@#@#@@``.,..,,`.`.,`,,...`....`
````````.```````````````````````````#,,':;:'@#;##,'';:.,`...,`:.,`....,..,..:,,`:;::''';#;:;'+@'@+###@#'+++;'':;'''@++++@#@#@@#@@@@@@@@@@@@@#++@@@:`.`..`...`..,....`..,..`
`````````.``````````````````````````@:,':';;+#'##::;'``.......,,....,.:..`:.::.,:,;:'+':;;:,:;'#@+'#'++@@''';::':''''':'+'++'#+@@@@@@@@@@@@#+##@#@+`.,`...,,..,....`.,,...`
`````````````````````````.``````````',+':''++'#'+;:;;`,.,,.,.`,........,...,,::,,,.,:.':::::.,;;+@'+.;'+;;;:';;;:::;';''+''''+'+'@@@@@@@@@@@@@+@@#@``,,.:.......,`,......,`
````````````````````````````.``````';.':;;;,@+@#::,:,`......`.`,`........,,..:;:,:,::,,,,,:::,::'#+;;'+;;'::::';:''';';;'';'+'';#@@@@#@@@@@#@##@#@@:``,,:`.`,`..:.`..``.,.`
```````````````.````````````.``````@;,':';@,@#'#;:,+.`..``.....,.......,,.,,.`:,,:.,,`:::..::,,,,:+';:::;;;::;;;;;;;;;;';'''''+'++#@@@@@@@@@#@#'##@@...`.`,.,,,``.,```,..``
``````.``````````````.``````.``````@:,;,+;#::@;;+:.+...........,``...`,..,......,::,,.,:,,.,:;:,::,:;:;;:';::::;:;;;;'';;''';'''+;#@##@@@@@@@@#@##@@.`::...:,.`..`.,..,...`
``````.`````````````````````.`````,'::',+:',:@:;#..;...............,,.......,...,..,,:,,:,,,;::,,,,,:';;:;:;;:;;;;';;';';;';';;;;++@@@@@@@@@@@#+'@#@@,`,``.`..,,`.,.```.,.`
``````.```````.```````````````````.',;'`#+;,`@;'+,::`.....`..``...........,....,`,:,.,..:::.:,:.:,:,;:::,:::::;;;:;;;';;'+';:'';+'+#@@@@@@@@@@#@+#@@@;..:...`,,`@@,,.;``,,`
```````.`````````````````````.````;:,':':':,'+;''`'...`..,..,...`...`...`,,,.......:.,,:,.,,:::;,::,;:,:::;;:::;:;;;;;;';;;';;''''''@@##@@@@@@@#+'@@@@,,.`.`...``:``,.`,.``
```````.``````````````.````.``````@,,'`+;';,@;#+,,:,`.`..`,.`.....``.,..`.`,,,,..,`.,.:.,,.,,,::,:;;;;,:;::::;::;;,;;;;:;+;''''';;''+#@@#@@@@@@@##@@@','`;.`.....`.,.`,,..`
```````````````````````````````.``@,:;.;:+;,+'#'';,.`,...,`.``......,...`,......,.,,.,,,,,,,:,,::;:::;:::,:::;::;;;;:;:;+;;';;;'''++;###@#@@@@@@###@@@'':``:.,..,;.,`,:..,`
``````````````````````````````````@,;,.:,@#;@+',;,`.....,.............,.`,,.`..,,,,.:.,:,:,::.::::,::;;;;:;;;:;:;::;:;;';;':;;;'''''':#@#@+@@@@#'@##@@',:,,,:`,..`:...,`,.`
`````````````````.````````````````',',..'#+:.@;.:,`.`...`..`,..,,..`.,,.`,:.,,,,:,,.,,,.:,:,:,::;:;;;::::::;,;:';::';:;;''+;;';#;''+;';#@#@#@@@@;@@#@@@.`..`,;:,``.`.,..`.`
`````````````````````.```.````````;:+,;:##;,#@;.:``..`......,...,,......:.,,,,:,,,:,,,:,,,::::::;:;;:;:;;;;';;';,;:''+''''';:'''''''+''+@#@+#@@#;@#@@#+:..,;:.`...`.,,`,.,`
`````````````.````````````````````';'.;`@#';@::,:..```..`,.,..,..:,::,;,,:,:.:,,,:,,,,,,::,:,;:;,';;:';#'#+'+##++;+'@#+++'+'';;;'+++#'';@#@##@@+'@@#@@',..,,...,,,.,,.,.```
``````````````````````````````````#:':.:#+'#@':.......`.:,,`,:::,:::::':,,,:,:,:;,,.,,,:,,,,::::;:::;';';;''++##@@#+++@#''@#'';;;+''''+:@@@#@@##'@##@@;`;,....,,.:`.`.,..``
`````````````````````````````,````@;:,.+#+:@+@.,`....`.:.,;::;;;;+:;'::';::,:,;:,::.,.,:,,,,::;;;:;;+:';';;'+'''@++####++#+@##'';;;''++;@@###@@@'@@@@@',.:,,..:,..,,`,.`..`
```````.````````.`````````````````#::`.++@:@@#.,`..`..,;::;;''';#'::'':,;':::,::,::,:,.,:::::::;';;';'''+'#'+#+#''+#''+##+@#@###';';''';+@@@@@'@'@@@@@;,:,;:.:;`,,:,`,`..``
``````````.```````````````````````@,'.:@:''@@#,,,.```.;::;:::'+'++'';';;;;;,::;::,:::.,,,:,::::':'';''+'+#+'@;+';';';+''+'##'####+:'''+;'@@##@#+'@#@@@:,,:.;:.;.`,.,,..,```
``````````````.``.`.``````.```````#`:..@;,;@@',.``.`,;;;;;:::;;;:';:;';;:,:'::;,.,:,,,,,.,:,:,';;;';'++''''''+;';;';'';;;+';+'+#'#+'+;';'@@#@@+##@#@@@..,,,,,..,;.,`....,,`
``````````````````````````````````@.;;;#;.:@@'...``,+::';':;',,.:::,,.;:,::::,:,,:,,,,,,,:.:::;;;''+#+'''';++';;''';';+'++;#@'+++#'''+'+;@@@@@++@@##@@,,;:::,,:,.;.:.`....`
``````````````````````````````````@,,:'#',;@@'``..,';:;;;::.,,,.,,,,,,,::,:,,::,::,,,,,,,,:;;:'';'++';'''+'+'''';''++'';'+'''+'''#@+''+';@@@@@+#@@@@@+;.,:,.,,::;:.:.:`.,``
````.``.``````````````````````````,:;:;;:,@:@;`,``.;,,,.`..,`:::,,:,::,::,,::,:,,:,.:,,,::;:;;:;#''''''+'';'+':;:::;:;';'+''+'''''#@'''';@@@@@@@@@@@@;.'::;::.,,,,;:,.;`.,`
``````````````````````.```````.````:.,::,,@;@;``.`::.,,,,``,,,...,.,.,,::,;:::,.:..,..:,,::::;:;';;;+#+#'+';''';;''++;';'''''+'+++@#;''';@@@@@@@@@@@#+,;::,.:,,,:::,:,`..,`
`````````````.``````.````````.`````;;'',.'@@@:```.;,,.,`,..`.`.,,;;;###;::,,';,,:,,,,`,.::::,;;;'''#;'''';+'+'';';;+'''+++''+'+'''+##'';;;@@@@@@@@@@@@:,;,,:::::.,`,:.,,,.`
``````````````.`````.````````.````.'.@`:,::@@#``..:,`...``..,:,,;;;';;''+#;;,;,,...,`.`,`:,;':;+;''+@##+#+'#'':::;;;;''@#+@@+;''''''++'+':@@@@@@@@@@@@@.:,,:::;:::,::,,,,.`
````````````````````````````.``````#`#`,:``#''```,,`..`..`.,.,;;:;:.,:;,+#@+;::,......`;.,;:;';'''+##+#@'';';;''@@+#+;;;'+@@#++''+'''''+';@@@@@@@@@#@+',',:,,,:,:,,,,,,,',`
```````````````````````````````````@`@:`+:`@:#```.,``.``.:,::,:,,.:,,;::';'##;,,,..``.`.`,,::;#:#++##++#';+++@@@@@@@@@'@'''##@#+#''+++'+';@@@@@@@@@@@@:,:::,,:,.:,,:.;.,,:`
````````````````````````````````.``@.::`#'`@.@```.,``....';,..,.;;:;''#:;;::#@+,,,......,,,;;,;';+'@+'+''#++@@@@@@@@@@@@'#'++#++#''+'';';;@@@@@@@@@@@@+',,,:::,,,:..,,.:.:`
```````````````````````````````````@;:'`';`@`#`..``.`,..'',..`;:@@@@'@@@@#'':;;::::.,`...,:,:;:'''##+@';##@:@@@@@@@@@@+@@#'+'+''#'+''''+':@@@@@@@@@@@@@@;;;,,:,::,;:,:,:,,`
```````````````````````````````````+:;':'..@@'``;`.`.,`,,```::@@@@@@@@@@@@'#':;;.:.`.`:.:.::;;:+'+##+;'#@#:`@@@@@@@@@@:#@@#@+#''''+''';+''@@@@@@@@@@@@#@@+;:,:.,,:,;,,:.:.`
`````````````````````.``````````.``@;';;,`'@#@``;`.....::`::+@@+.@@@@@@@@@;#@@:..,,,,`...,:.;;';#''#';#@@@;,@@@#@@@@@@'@@#@@@#'#;+'';;++';@@@@@@@@@##@@@+';::,,,,.,,:::,,:`
```````.```````````````````````````@''@;,.@`@@`````....,`;@@@@,,`,@@#@@@@#;#@#@`,.,``....,:,;:++'#'++':+;':':@#@@@#@@#'++#@####+';';'+;';;#@@@@@@@@@+@;'';',,:,::,,,.:`,:,`
`````.`````````````````````````.```'':@:,,#`@@````..`.,.@##;##+;@,'@@@@@@';+';;,.,:,...,.::.:;+;#;#+;+';';;;::#+###+@#+#+'#+@;'##'';''''''##@@@@@@@@#@,::`::,,;,::,;,.::,,`
``````````````````````.````````.```'#'#:.:',@@`````..`,:;;.::;#;#@#++'','''#,:;:.,,..,.,,.:;:;:';'##;'';'':;;::;:::;;';;;''+'+''+'+''''+;:@#@@@@@@#@@@;:.;;:,,,,;;::.;,;';`
````````````````````````````````````#'',;.#+:@````...;,,,.`.``:;,:;,:;;:::':;'''.,.,,.:.`.::;+':;';+;++'''':'';::';+;++';;;+'+'';'';';''';@@@@@@@@#@#@'::,::::;:.:,.,::...`
```````````````````````````.````````@;+.;::#'@````..,.,.`....`.,.,,.''';';;''':,,:,.,...,.,:;;''+';'';+''#'#';'';+';;;++';+''+';'':';'+'':@##@@@@@@@#@;;,;:,:::,:;:,;,:,:.`
````````````````````````````````````::@;;:+#@@``..`,`,.`,...`..`.,`,::;;;';#;;;,..:,....,,;:';';''';''''@'+;+#+;#''#''';+'+;'+'';';';'+';;@#@@#@@@@@;',,;:,,:,,,,,:,.,,,,:`
``````````````````````````.``````````@'':::;@@```.`,`..,.,....,.,.,,;;';'';:;,.,.,,,...,,,::';'';;;'';;';;;+'+'##'+@''++'+;'#;;;'';;+'''''@@##@##@#:.',,,,::,,.:;:,::,,:..`
```````````````````````.``.``````````@+':'`;@@``.`..```,`,,.:,:,,';:;;';+;::,;,:..:.,,,,:,,;:;'+#''';;';';;::;;;#+'###+;'';;:::;;'''''+'';@###@@+@+:;;;::;::,;::,::;,,,:;:`
``````````````````````````````````````#+##.@'@`.`..`..`,,.,.,.:,;::;':'';,::.,,,.,,.,,..,,:,;,:;''''':';':::;;;;:;:::;:;,':;;;':;'';'+''';@#@+@'@:';.;::;:,:.:;:,.,,,::::,`
``````````````````````````````````.```;@#+:,.@``````.``..:,,:;:::;;:;:;,,.;.,,.:.,.,,.:,,:,;;;';''+';;;';;::::;;::;:::;;;:;;';;+;'+;;;;''#@#@'@'@`,.:,:,:::::,,,:..,::::,.`
````````````.````````.```,```````.````.:++#..'`````.`.,.,..,:,:::,;:,,:,,::,,,,:,...,.,,,,;,::;';'+;'';;:;:::::';;;:;;;::;::;;;:;'+'#''''@###'@#@,::;:,,:.,:,,,:.::,:,,,,,`
`````````````````````````````..````.````@##'.;```..``.`.,,.,..:;:,,:,::,.:,:,,:..,,.,.:;,,::;;;;'''':';';;;:::::;:;::;;;;:;::';+;;;';'';;#@##''#::;;;::,,::,,,,::,:::.,,,.`
``````````.`````````````````````````````;;'':,#````.`...`..,,.,.:::::,,:,,,,:,,,.,,,,:::,:::;;:;;#'+;'''::;;:,;;;;:;;:;,:::;;::';;''+'++;@++#+#',:::;:;;,::,,;:::::.::,,:,`
````````````````````````````,```.`.```.``:##.,#``.````.`....,.,,,,,,::.,,.,,,:....,.,,::,:;;';;'+#+;';;:;;;::;:,,::::::;:::;':'';;';+';''@@@+#@:'::;:,,;',,:::,,,:::..,,,,`
````````````````````````.````````,`````.``,@`::`..```..,`.....,,,:::,.:::,:.,`..,,.:,,,::;,:;;;';+#'#+;;;'',:;::::;::;,::::;;;;;;;''+;'''#@';+,:,;::;;;,,;:,,:;,,:,.;:;,,,`
``````````.```````.```````.````````````.``.``;'``````.`.`.....,,:,::::,,:,,,....:..,,,,,,::;:,;';'+++'+:::;;:::::,;;;;;:,;::;':;;';;++++'#+';@`;;:;':;,,'.::,:,,::,:,::,,.`
`````````````````````````````````.````.```.`,,#,`..`````..`.`,,..:,,.,,,,..,..,;,:.,,:`,:,,::::;''+';+;;;;:::,:::;.,:::;,;;;':;''''';++''#+#;@.;::,':,,,:,:,,::,,;:.;,,.::`
`````````````````````````````````````.``````.:',`.````............,,,,,,.,.,..,::,`.:,,,:,:,::,;;;'+;;';':::::,::,:::;:.;;::;;:''';''#'+'##''',;;;:,,,,:,,,:,:,.,.:,,,::,,`
``````````````````````.``.```````````````.``..;+``....``,.,....,,.,,,,,,,,,,,.,,:,...,..,::,,;;';''';''+;;;:;;;:,:;:::::,:;;;:;:'';'''''#@#'#:,;::;:;;,,:,::,,:,,;,,.:.:,;`
``````````````````````.`````````````````.````.:+```.```..`.,.`,..,,,.,,,,,,,.,,,,...`.,.:,:;::''+'+';''#':;,::,,:,,::;:;;:::';;';+'+'+'###''#`:,',,::'::;::,:,.:,,,,:,::,,`
``````````````.```````.`.``````.``.`````.`````.;#```..```...`,,.,..:.,,.;:.,.,,...`.....;:,';+'''';:;''+#;;;;:,:,;:::;:;::;;;:;;'';+;+;@+@;+#.:;,,::,,,,,,:,::,:;;:,,,:,:;`
``````````````````````````````````.`````.``.`.``@``````.,.,..,.,,,,.,.;,:,,::`````.`..`,:.;:;''+;;:::;;++;;;:;,:,,,:,;::;::;;+;;;''''''@#;;+@.:;::,,::,,:;,,,:,,,:.:,,:,:,`
```````````````````````````````````````.`````.``'````...```......,.::;:;,:,.,```,,````...,';';@++#;,:'+++;;;,;.:,,:,;::;;;'::';;'''+;+'';;:@'::::,:,::::;,;:::,,,,,::,,,,;`
```````.`````````````````````````````.```..``.``,`````..`......,,.,,:::;,..,.`.;;#;'.``,,:;:;'#@#@+..;'##';;;;:,:,,:,::;:::;'';#''+'''#;;'++,::::::,::,;,,:;::,:,,:::,::.,`
```````````````````````````````````````.```.``.```````````.....,,..,:::',..:;``:'@@@#``,.:';;'#@@@;`,;'##;+;::',,:::,:,;;;''''#+'#;'''++'';@`:;,;:;;::,,::,,,;::::,.;.:,:,`
`````````````````````.````.```.`````````.````.`````.`.````.`.,..,,,:;;;,.,.::,..:::;';`:.:;;#+'+'+:,;+++;'''+,';':,:::;;;';'':';+'+'+;#';;+',::,,,:,:,::.::,:::::,,::::,:,`
```.```````````````,````````.````.````````.``.```.```.``.`..``.:.:,::+:.,`,`..,...:,,.:`.,;'#''''';:,++';;;'''+':;:,,::;';'';'''''+;'+';;'#`;:;:,;::,,;;,,:;:,,:::::,:,,,,`
````````````````````````````.``````````````````.```.`.``..`..`,.:;,;:;.,...`..,,..`.,..`,,:+#++''+#++++'#;';'+;;;,:,:;,;;;';'''''+'++++';'@.;::,::;,:::,,:,,,::,::,,:,,::.`
``````````````````.````````````````````````````,`.````.`.....,,:,,:;::;...............,..:;'+;;;+++#'';+'':;;;'';:;:::'::;;;;;'''''+;++#+'@.:,:,,,:,;:,,,,,,.;,;:::,,::,,;`
````````````````.````````,``````````````````.``.`,```.```.`...,,;:',:,.``.......,...`..,;.;'#';;#'''#'+'++'+;;+++';::;:;;;;';+'#+++++##''#`::;::,:;:,:,,::::;,,:,,,:,,,;,.`
````````````````````````````````.``````````````...``````,`..,.,:::';,,,`...`.`,.....`..;'.:,';''#''+'#''';;''++'';';:;:;;''+''';++'';@''#+:::;,::::,:;;;:,,::,::,::,;,,,,,`
`````````````````````````````````````..`,```````,.`.`.``......,,;';:;.`...`........,`,:;#,.,;;'+++'++'';'+'''';''+;@,,;';:''''''#'#;'@#;``:::::;::::::,,:::,,,:,,::,::;:,,`
`````````````````````````````````,`.`````````````.````..```,.:,:';,,.,,`....,`.,,,,,.::'+,`:,:'';;'';';'''';;;;;''''#,::;'';+';++'+'':;;,:,::;,:;'.;:,:,.::::,,:,,,,:,:,,,`
```````````````````````.`````````,`````````````````.`.````...`:;++,.:.....,...,,,...,,;';;`::'';';;;#++'':';;:';;';#@::;+;;'++#+++#''.,:::,:,::;:,::,:;;:::::::::::,:;,,,.`
```````````````````````,`````````.``````````````````````.`.`,:,'#:,..,........,,...,.::;',..:'';#;';'';'''+'''';''#'@,::''+'#++''+'#.,;:::::::::,;::,;:,:.,,.:,,,,::,,,,::`
```````````````````````````````````.`````:```````````````.``,,:;@....`...`...,.:....`'::;,,::;::';+';''''';'';;'+''+#,:;;''#''+'###@,:;.;;:;:::::,:;,:,::::,,,:,,:,::,,:.,`
``````````````````````````,`````.```.`````````.```````````.``.,##`..``,```..`,`.`,..,:,:;::,:';;;;'''';+''''@+'+'++'+,,;+':+''+'###',;:;:;:::;,::::,,:,,::,::;:,:,,,:::,::`
``````````````````````````,`````.`.`````.`````.```````````....:;+`..:.````.``.`,.,,.,::,,,,:#'';;'#;;#';'':'''+'';#'#,,;;+';++;''#+,,:;,:::::;',::,`::;::;,::::::::,,::,:,`
``````````````````````````,```````.`````````````````.`````..`,:;+,,,,,''..`....,,,.:',::,;';;#;;'#'#'''+#+##+@#++'++:,::;'''+'+'##@,:;';:;:'::,::;,@`:;::,,:,;,,,:.,,.:,:,`
``````````````````````````````````.``````````````````````.```..';;:.,,:'#+;,::;,;,,,,,;,::';;'::+''#####@#@#@##+''++:,,,;'+;'''#'#':;::::::,:;;,,,,,,:;:::,,,,,,,:';::;:;,`
``````````````````````.``````````````.````.`````````.`````..`,.;';',.,``.##''#'+';';;:::'#'+#;############@@+;''''+';::;;'''''#''#.::,;;::;':;',,:;:,::,,:::::::;;,,,:,,,:`
``````````````````````````````````````````````.``.``.````..`.``,,;+,`.```,:'++####'###+++########+######+#'+#'++;''::;;;'+''''#'#@.:;;,::;,:,:,,,::,:,:;,;:::,,;:,,:,,,,,:`
`````````````````````````````````.```````.````````````````````.,;;#,``..``,..,,:,'';'+'#####++####'+'''++++''''';;'::;;;+''+';#+#.:;:::,;,;:::;;::::;,;,.;:::,,',;,:;',.::`
`````````````````````````````````,````.```````````````.`..```.,:.;;..``..`....:.,:::,:;++,:',;;;+#'#'+'##'+;+;';'';;;;;+'#++''+##;::;:::;::;::::;:::.,::;::,,:::,.::,,;;::`
```````````````````````.`.```.```````````````````.``.`.```````,,:;#,.`...`....::..,::;,:::,;::;,++'++''+'#''';;+':;::,';#''+'+'#:,::;;;::;,;.,:::;:::;::,:;::,,::::;:,;,:,`
````````````````````````````````.`````````````.``:`````.```.```.;:;..```..`.`..,:,..;::;;:;;;;:;##''+++#''+'+'';;';';+;+';++++++`:::::;:::,;.::::;::::,,:,,,::;::::,:::,;:`
````````````````````````````.``````````````.``.```..``.````..`..;':.```..`.`.`......:.:;+:;;:;;;#;'''+';';'';+;+':';;;;#';++'#@.::;::::,:,;::,;:::,;:::;::::::,::;,::.:';,`
````````````.```````````````.````.``````,``.```.``...```.``````..,:.``.``..```.``.,:::;::::;:+';';;++''+'++;+;'';;;'::+;''+'##;.::::::;::;:::;,;;::,:::::;:,,::;::;,;,,:,,`
``````````:````````````.`````````````.``.``````.``````.``.```.``.,,.......`.`.....,..,:,,:::,#:;,''+;;';''+';';+''';;''''++##@.,:;:;:,::::::;:;,::::,:,:::,:,:,;,:,::;:,:,`
``````````.```````````````````..```````````````.``..`.``````````...,..`...`,.`,...:.:,:,.:,;,::;#';';'';++;'#';''';'';'+'++++;,:::,;:;:::;:,:,,':::;::,,::,,::;;::,:,,:,::`
`````````````````````````````````````````.````````.``````.```...`,...````...`....`....,:.::::::;;''+;';;';'';;;+;'''++'++''+#.:,::;:::;;;;::;:,;:,:::,:;::,,::,::::;;',;,:`
```````````````````````````.`````````````````````.````````,```````...```..``,.`,..,.,,::,,:,:::;;;;;;';'+''';'''+'';';''+''#;;::;:;::;::::;::,;;::,::,::':,:::,::,:,::,;;:`
``````````````.`````````````.```````````````.````.``..````,.`..```.``..`..`.`..,....,,:::,;:;;'';;;'''''''+;';'+'+++';#'''+@,,:;;::,;::;;:;:::,;:;;,,;,:,:;::::,::;:::::,,`
```````````````````````````.`````.`.```.``.````````````````..`.......````.`.``..`,.,,,,.:,:;:,:';';;':;;;'''';;+'##'''+''#+@.;:;:;:::;:::,,::,::;::,::,:::,.,,::;,:::,,';,`
`````````````````````````````````.```````````````````````.`,.``..`,``..``..``.`,..,,,,,:,:;,,:;;::';;;';''+;''++''#+''+';'+@.::::;;:;,:,:,:,:;:::,;::::::::,::::::;::::::;`
``````````````````````````````````.``````.`````.`.``.`.`.``,..`.``...``````....`..,,.,,,.:;:,;;:;;:;'''';;;;'@##'''+#'+'++#@,;:;;;;:::::::::::;,::':,;;:':;::::::;,;;,;;::`
```````````````````````````.````````````````,```.````````.`,`.``..`.`.````.``....,`.,.,.,:::;::;;:;;;'''';;''+'+#+'''++#+''@:;;;;::::,:::;:;:.',;:,::::,:,;:::::;::;;:;;:;`
``````````````.`````.,```````.````.`````,```.````````````.`,.,`.`...`,.``````..,.....,,.,,:,;:;:;;:'';'+'''''+'''++'+'+#++#'::::::,;;:::::,:;:,;,;,':;:::;:::::;';,:;,::;;`
`````````````````````````````.``````````.`````.````````.`.`,...``......`.``..`........,,,::::::;;;';;;;;;;#++'#+++++#+#+''@,:::;:;',;;,::;;::::;:::::,,,:::;::::,::'':;;;:`
````,```````````````.``````````````````````````,``..`.``.``..`.``.....`.```.`.......,.,.:'::::;:;'';;;'''+'+''+++####'+'++@`:;:;;,;;::;:;,;:::,:,::::;'::;:,,::,':;,:;;:::`
````,``````````````````````.```````````````.````.````.``,``..``.``..,.,...``.````.`..,.:,.,,,::;;;'';';#'''++'#+'++#+++'++@`::;:;:;::;';'.:;:;,;:;::,;;:,;;:;:,::,:::::';;`
``````````````````````.`.```````,````````````,``.```,``..``:..`...``..`,````.``........:,::;;:;,+;'''';++'+;+++'++#''#'+'+@`::;;;;:,;:':::::::::,:;;,:,;;:,::;:::::'':;:::`
```````````````````````````````````````````.`````````.`.```.,`..``````,..:``.``..```.,.,:,;:;;:;'';'+;'''++###+++;''+++#'+@.;:;:;;:;:;::;::;:,;:;,,;,::::::;;:.::'::::;;;;`
```````````````````````````````.`````````````.```.``:````,`,`..````.....,,,.`..```...::,;;,::,,:;+;+''+;+''+++#+#+''++++##@.::';:::::,;:::;:;:':::,:::,;,:;;::;;:::'::;:;:`
``````````````````.```````````````````.``````.````.````````,.``.``````..,....``...`.`::::;;;,,;;:+''+'+''+'#+++#+''@+#+#'+@:::,;:;,;,;;::;:;::,;:;.::::::,:,;:;:;:;,:;;;':`
```..```````````.``````.````.```````````.````.`.`.```.````.,.`.,.```````....,``.`....:,;;;';:;:;':'+;#'''###++#+'#+++#++'+@,;:;;;;;:;;:::::,;:;;:::,;;;;:;:;',:;':':::;;:'`
````````````````````````````````.``.````````````````,`,.```,`...`.```..````,,,,......::;::,::::;;;;#'+;;#++++++++''+'##'#'@.;;::;:;,,,;:',::,;,,';;:;::,,:,,';;:;:,;;:::,;`
```````.``````````````````.`````````````````.``.`.``.````.`.`...`.....`.`...`...,...,,:,;:;::::,::::';'''+#++@#+'+++;+#+#+@,,:;;;.:''::;,;:;':',;:,,::::';;:,';;;,;:;;;';:`
````````.`````````````.```.```````````````,``````.``.``.```,..`````..```..``....,:,.,,,,:;:;,,.:::';+'#+###''+#+++#++++'++@.,;;;;::::;:;;:;;;;;;;;::;;:;:;::::;';;::;;;'::`
``````````````````````.``.````.`````.`````.`.`````````.```....`.`,....`..,..```..,,,,,::;:,:,;;;':@+####++#+'+#'+''+++'+##@.':;':::';;:';:;:;,;:,.:;,::;,:::;::;;';;;:;,';`
`````````````````````.````.`````````.`````````````````.```,...`.`.`.`````........`,:;,;;:'';;'#''@++#+++#+'++#''+'''##+++##.::'':;:;:;;':::;':;:''':;;;::;:::;;:':;';:;;':`
```````````````````````````````.`````````.`````.`,```.````,,,``....``..``..`.,....`.,:;::;;;;'''++++''++;+'+'''++'+++++'+'+@;:,,:':;'::#:;;;,;;:;;;::;;::;;:;:;;,;';:'';;'`
````````````:``````````````````````.```````.`.``..``````#,.....`...``.......`...`,,.:`,':::;':';;';++'+;'#++++''##+#'+++++++@@;,:,;::;:::;::::;';;;;;';;';:;::;':;;:,:':;:`
`````````````````````.```````.```````````````.``.```;#@@`,,.``.`..`....``.`.....`.:.:,,:,.;;:':+;+''''+'#'+'++'''#++'++'##+#+@@:';:::;,'';'::;:::+;;;;:;;;;,';;':;:'+;;;;'`
```````.```````````.``````````````````````.`````.`:##@+`..,..`.`...`.........`.`.``,,:,:,,;;;;;''#++++''++###'+'#'+'++###'+'+@@;;;:;;';,,;;;;:':;;::,;;,:;';:::,:;';,';;;,`
``````````````````````.```````````,````.````.`````##@``,,.,.`.,`,.............,...,.:,:.,::;:;''''''++#++#++''+''#'++'+''#+#''@':'@:,:;;;;':'::'':;''';;;;;';;:#;':;':';''`
````````````````.``````````````````````````.```.``@@`,.,.,....,,..,.,.......`..,.,,.,,,,:,,::''''+'+''++'+'''###++#@'#+#+#'+'+#@.;'++,;:;;;::';;';;';'':'';;;+;;;;';:'::;;`
``,````````.```````.``````````````````````````:,``@;.:....,,.........`,.,..`,.,..,,.,.;:,;;;:+;';'''++''+;'+'@'#+#'#+++##'##+++@;';'+#;;::;;':':'':':::;:++';:;,;''';;':;:`
`````````````.`````````````.````````````````:`:```;;.,.,,,...,.,,..,,........,,.,...,,::::;;';;'+'#'++#++'+''+++'+###++'+'+'###@:';''++;;;''';:;::;';'#;+@:;;'+,'+;'':;;;'`
`````````````````,````.`````````.```.`.```;.+`,````#....,.,,......,,....,,...`:.`,,,,,,::::;.;;;;'++'+''''+'''#+####'+#+'+@''+#@;;'';+#:':::';;;;':';'::;;+:;+;';+';;''';'`
````````````````..`````````````.````.`.``:;`'.`````@,..,..,.,.,...`.,,,..`..,,,....,,,,,::::''+'''+'''#+#'++'''+'##''##@+'++++@';';''#+;'+;';''';';'';';;'';;;;:;;;;':+'';`
```````.`````````````````````.``.````.``..``#``````@;,,,,,..,.,..,:,..,..,.,.,,,,,,,,::,,;;:;';''''+'+##''+#'+#+##@+#+##+#+#''@,+'';;;'''+#;';;;;:';;;;;''';;:+;'';;;';';'`
``````````````,```````.`.`````````````,.,```'..````:',`.....,....`.,,:,,.,,.,.....,.,,.,:::';:';+'+;'''++'##+++'#'#'#++@++#+'#@;'''''@;+;++';;;;'':;;;;;;;'+:++';+';';;,;:`
````````````````````````````````````````````````````:````````````````````````````````````````....,,:;:::::::::;:;::'';;;';;;;#`..,.,.;.`..,,..`.```.```````````````````````