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