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