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