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