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