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