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