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