``````````````,==?=?>++))**!!!!!!!!!!!))!!*!!***)))+++>>>???=%%&%*``````````````
```````````',:+==??>+))**!!!!!!;;!!!))*;;!*****))))++>>>>???=%%&%*``````````````
````````'~!>==?>++))*!!;;::::;!!!!!!)))))+))+:--!++++>>>???==%%%%!``````````````
``````~*?=??>++)***!!;:--~^~~-:;;!*)))))))+)>+++>>?>>>>???==%%%%%*'`````````````
``````-;*)++++)*!!;;:--~^^~~-:::;;!**)))))>+>+++>>?>>>????==%%%%%%:`````````````
``````````'':^:=?+*;:~~^^~~--::;;;!!!!***)))+++>>>?>>?==%===%==%%=:`````````````
```````````.,`!&&&&&=>);----::;;;;;!!!!!***)))++>>>>>?=%=%&%%%%&%=:`````````````
```````````-`.=$&$&&&$=!>%?>)*!!;;;!!!!!***))+>??====&>+>??==%%%%%?!^```````````
``````````';`:=&&$&&&&);!%&&&&&%?+)*!*)))+===&&$&&&&&&>)))++++>%=====+,`````````
``````````.;~+*%&$&&&%!*+=%=&&&&&&&%=>=%!;+%+%&$&&&&&&?++)>=?>?=>???>+^`````````
``````````.':>*=&&&&&?%#%$$?&&&&&&%%%*?>!;;*+?&&&&&&&&?++?&&$$);''''````````````
``````````.`-+:?%%%%%&&*+%$=>&%%%%%%>!=$$$#=**=%???==%$%&&&&$&-,````````````````
``````````.`:;!>?=?=%$+:%%&&!>?===?=+)>*>%##$+)=)))+>?&=?%%$$%~'```'...`````````
``````````.`!.!+>?+?=?!->>?=^^*>)++))*-+?=&$$$++)))++>%===%&$+.'~;*)>??!````````
``````````.`;`.!>?>+>+~'*!)+..,~!~--:-,?=%&?&?$))++++>*>%&&&$*!?>+++)))^````````
```````````,!`'-+??+>>,'~^--'....,...'^))>>+?)&=+++++>-^=&$$$=??======-`````````
```````````.)'`-;>=>>>~^.^,..........'.:-!!:*:*)+>++++~,)%&$%???%&>:^-:~^```````
````````````^-',-!?=?>-^^,.......'....'^^~^~^.~+>>+>>)^,*%&==%%%&&=%).`';!.`````
`````````````-.`.;>??=)~^,...,..........^,,,.,!>?>>>>*^^)&%?%&&&%&&%%>,`.*).````
``````````'``.!;:+%===-^^,............,,,,,,,;>?>+>>):~^=%??>=???>>>==+:-)~!````
``````````~'``'->=>+?=-,,.......'.....,,^^^~*>>>+>>!-~^)%>)=>??>>++>>?>?+~`).```
``````````^-~,;*?>*+>=*.......''''.....,,,^~~^)+>>-::-+>=)-)?>>>>>+)>?==!``)^```
```````````~'!;:%+)+>==,.........''..........^+++)-*+??>)*-:=>=?>>>*++>=?'.+.```
``````````'.~,`*=))++=%).........''..........:+))%&==%?+)):-+%&=>>>?>>?%=-;)````
``````````.,``.>?+++>=&%*.....*^'''.........^)+)>&&=%%%=%>;~*%%%>>?=???==>>:,```
``````````,^``^>>??>>=&%%),...^,.'.........^;+++?=&)=&&&&?!~;?%&???=??%==+^`,```
``````````-~``,~?=?>>?%%%%=-.............,-;!+>+=>=~>&&&&=):;+%%=??%=?%%=)``~```
``````````,;`.-~%%=>==%%%%%%!.........,~:;;;*++>=+?!)&&&&&%%=%%%===%%=%==?,''```
```````````,-^!%%%=?=?%%%%&%%+,...,~-:;;;;;;)++??+%?%&&&%%&&&%%%%%%%%====?!'````
````````````.'*%%%%=?=%&%&%%%?*;*+*!;;;;;;;;)>>>??%%%&%&%%&&%%%%&%%%===??+))~.^,
`````````````,=&%%&%%%%%&%%%%+**)**;;;;;;;;;)>>?=%%%%&%%&%&%%%%%&%====??;)',,.'`
`````````````!%%%%%%%%%&&%%%=)***!*!;;;;;;;!*?>?%%%%%&%%%%%%%%%&%=??==?),!``````
````````````'+=%%%%%%%%%%%%%?****!!!;;;;;!!!!>??%%%%%%%%%===%%&&=?????).^-``````
````````````~+?%%%%%%%&%%%%%+****!!!;;!!!!!!!+=?%%%%%%%==%%%%%&%?????)'':.``````
````````````!+??==%%%%%%%%%%)*****!!!!!;;!!!**?=====%%%%%=%%&%%??????:^~^```````
```````````.>+?>>>=%%&%%%===****))*!!;;;;;;!!!==>>>+>===>>>??%=?????=>+!~^``````
``````````.+>>?>+++>?%=====>***)>)**;;;;;;!!!+==)>+*+++))+++>>?%??=?????;'``````
`````````,)?>+?+)+++>++>?=%)**+>>>??;:::::;!*==>))**++****)))+??==?======+;^'```
````````.)))>+>+++))=))))+?~:)*;;::;^''''''^?=?)****>)******)+))+?===???????>!~.
````````;-..,^~-*+)>>+***)*':*:~^^^~:`''`'':+)*****)+*******+**))+>==+++++>>>???
```````'!,.^,...,*)?++))*);-^::~^^^~!,''`'^)*!!**!!+****!**+*****))>??+))++++>>>
```````,....,^~-~-;)+))**)~..::~^^-!):'`'.)**!!!*!*+******)*!******)>?=)*))))++>
``````.^.......,--:!))****''.:-~~:**~-.'';)**!!!!*+)*****)+!!**!***)+>==*****)>>
`````,;,.......,,:+))**!*;''.::-;)*^.^^'-)***!!**)+*****)>*!**!!!*))+>=%*****+)?
````.*~,......,-:;+)**!**-''^)))+),.'.~~)*!!)**)+>+*)**)+)*!**!!***)+?==+***))>&
```.)!,,....,,,^*+)*****)^''*!;!!!'''.^!)!!!*++))+**!!))>******)***)>?==>+*)++%&
``,)+~....,,.,-)=+******).'^)-^^~-.''',*!!*!*)*:^,...,!>)*****)****+?==%>>)>+=&%
`,)+),..,^-:-^!=?+*******'.-:~^,^-.''.-***!!*))~,,,...,-****)+)***)+?==%=>>>>%&=
*>>>!^^^-;;+&%==>+*****)!'--~^^^^-''',********;,.......,-)))>+)*)))>?==%=??>=%%?
%?>>;:::;!*%&%=>++)****+;^-^~^^^^:''.;**;::!**-,........,!+>>))))))>===%==??=%=?
=?>>;;;!)!*&&%>+++)))))>;-~~^^^,^:''-***!!;!**:,,,.......^>?+)))+)+>===%==??%&&?
=?>>!;;)!!+&&%>>++)))))+!-~~^^,,^:',)****!+*))-....'......!?>))++)+====%=%=?%&%?
=?>?*!****?$&%>>+>+)))++*-~^^^^^~;.!***)+>))*++~~^........^?>+++++>====%=%==%&%?
=???+*)**+%&&%??>>+++++)!:~^^~^^:!:)****)*+++=!............)?++++>?====%=%==&$&?
==??>))))?%%&%=?>?>+++>+;;-~~~~~:*))))**!*+?=+)~^..........-?>++>>???%?%%%%=&&&=
==???))+)%%%$%%=???>>+>+!!:-~~--;>)!~-:;;->>))>?);^.........)+>>>>??=??%%%%%&&&=
=%==?+++>%%%$&%====?>>?+!!;-~-::*+);```,**+:,,~)=&*~........-!?>>???>>=%%%=%&&%=
%%===>+)=%%&$&%=%=%??>?+**!:--:!>+):,-~..^~~.'`:%&%!~,......,:>???>>>=%%%%=%&%%=
=%%%=?++%%%%&&%%%%%=???>)**!;;;++++;^:-,,;+>)-^-=%%%)-~,...,.*+??>>>?%%&%%=&&&&=
%%%&&=+=%%%%%&%%%%%==??>))***!)>+++;^--,->>>>*^:?%%=&?!:~,,,,))+?>?=%==&%%=&&&&&
%%%&&%=%%%%%=$%%%%%%=?=?))))))?>>>>!....;>+>?>~:?=&%&+*);:^'!)++??==%==%%%%&&&&%
;?%%%%&%%%==)=&%%%%&====+)++)>??>>>!...'-:.->+~:?=&&&*!*!~.-++++?======%&%%&&&&%
`'+%%%&%%%+-`)&%%%=%%===+++++=???>>*^-^.-!.^?+^;=%&&%!!*-^~)++++??%====%&%%&%%%=
``'+%%%=?-```:&%%%=%%==%>+++?==???=)^~^,-+!;?)~!=%&%%***-:)+++++??=%==%%%&%&%===
```';!!-.````^&%%%%=%%==?++>=====%%=>)*;::-:!!~*%%%%%=*)!*>>>++>??=%%==%%&&&%===
`````````````.%&%%%%%%%%=+>=====%&========??>+)?%%&%%%?)>>>>>>>>====?====%&&%===