+=+--;==-+*?%SSSSSSS#S?**??*?????%%%?????**+++++*+*+*%%????%%%??????%%???**??%%%
+-=;::;--+++?%%%?????S%???????????????*****+;;=+++--*%%*+*?%SSS%?????%???+:=??%%
+-;;,,,;-=--*??**???*???*?????????******????*+*++=--=?%*=+*?%SSS%????????*-+???%
=-;;,,,;;--=******?????*?????????*===+*??%%%SS?**+===*?+=+*?%SSSS%?????????????%
----;:;;;=-=******???*???????*?*+===-=+????%%SS%%*++=++=+*?%%%%SSS%?????????????
--==-;-=-==-****??***???*???***+=--==+*??*??%%%SSS%?*+++*?%??%%SSSS%???????????%
-===--===-=+?**?***???**??***+=+****???*+++*?%SSSSSSS%??%%??%%%SSSS?????????????
++*=-;+=+=-*******??**??****+=+?%%%%%?***?**%%SSSSSSSS%%%??%%%SS##S**??????**???
==?*++*+*+=+++**??***?******-=*?%SSS?*=+*?%?*%%SSSSSS##SSS%%%SS###S++**?????*???
==*+*+*?**==++*?***********=;+*?%%?**+-=+*%%??%SSSSSSSS##SSS######S%*+=-**????**
==++++*?*+==+++************;-+*?*====+=;=+?%%?%SSSSSSSS###########S%?*+-***?????
++++++*?+++++++++++*******+;=+*+----=++;-=?%%%%SSSSS##############S#S%%%%????*?%
*++==+++++++==-==++++***++===**-;---=++=-+*%%S%S#################SS##SS##S%?**-*
*+====+====--;;;;--=++++++=+=*=;;;;-+*?*=**%SSSS################SSSS###@@#%%**+*
**=-========;;;;;;--==+++++++*-::;=?%%%%?*?%SSSS###############S%%S#####S%%S???%
+-;;-=+=----;;;;;;;-====+++++?*-;+%%**??%?%%%SSS############%??*???S###S???%*%SS
+:,,,:-=;;;;;;;:;;;;----+**+***=;+%%?%S#SS%SSSSS############%??***?S###%??**%S#S
+;,,,,:-,,,,::;:;;;;;;;;--+*?%*==?%######S%%SS%SS###########S%?**?%####***+*%#SS
+;,,,,,,,,,,:::::;;;;;;;:,;*S#%*??**?%%%%??%SS%SSS##########S??%?*?S##S-+*+?%SSS
++,,,::::::,,::::;;;;;;;::=+++*??*+---=+*??%SS%%SSSSS#######S%S##S%%###%*?**?%%%
=+=-;;;--==-;:::::;;;;;;;-**==?%%*=----=*?%SSS%%SS#SSS######%%SS#######S??**???%
=*+=----=?%?=-;;-;;;;;;;;--+=*%%%*---=+*?%SS##S%SS#S%S######%%%%S###SS#S%***?%SS
-+*+++==-*%%?++;?---;;;;;----=+??*--+*?%SSS###S%SSSS%S#####S%%%%S##SSSSSS*+*%S%%
=*?%S%%SSSSS%?**?-?=---------=+**+=+*?%%SSS###S%SSS%S#####SSS%%?SSSSSSSSS**%%%%%
**%?SSS########%+?SSS%?*+=---+*??**?%%%SSSSSS#SSSSSS######SSSS??%%%SSSSSSSS%%%%%
**??*%SS%%***???%S########%*==+?S%%%%%%%%%SSS#S#SS#@#####SSSSS%?%SSS%SSS#S%%%%%%
*=+*?%%S%*--=+?%%##?++***??*++*%SS%%%%%%%%SSS#S###@@#####S%SSS?%S###SSSS%%%%%%%%
*==+*%%S%+--=?%++S#%++++++++**%SSSS%%%%%%%SS####SS######S%%SSSS%S#####S%%%%%%%%%
?++*%%%S?+--*%++*%SS*++++++++=*?%%SS%%%%%SS#####SS#####S??%SSSSSSSSS#S%%%%%%%%%%
?**?%%%%*==+-*?%SSSSS%+++++++--+?%SSSSSSS######S#S###SS%++%S%SSS??%SS%%????%%%%%
?%%SS%?**-=-+%S%*?S#S%*+++++++*%SSSSS###########SS#%%%?*-=*%SS%?*%S%%%%????%?%%%
%%%%%%%?+--=?%%?*?%SSS%++*+++*?%%%%?%S########S#S##?+=+=-++?SS%**%%%%%%%????%%%%
S%?%%%%*---+%?=?SSS#SSS?+*+++**+*****?%S######S####*;;;;=+=?%S??%%%%%%%%%%%%%%%?
S%%%%%%?=-=**;*SSSSSSSSS*************++?SS###SSS###S=:;;+++??S%???%????????%%%?*
?%%%%%?*=-=+;*S######SSS%************++*?SS##SSSS###S-:;+++++%?*???????????%%?**
?%%SSS?+*+--+%########SS%?************=+*%SSSSSSSSSSS*:;=---*?**?**????????%%?**
%%SSSS%%??**%S########SS%%?**********+=+*?SSSSSSSSSSSS*;=-;=*******???????%%%???
?%SSS##SS%%?%#########S%%%***********+=+*?%%SSSSSSSSSSSS?%***++**???**????%%%%%%
%%S#####S%%?%S#########S%%??????****+=+**?%%%%SSSSSSSSSSSSS?*+**????***???%%%%SS
#SS#####S%SSSSS########SS%???????*+=--=*?%%%SSSSSSSSSSSSSSSS%?????????????%%%%?%
####S#######S**S#######S*?%?**???*=---=+*%%SS%SSSSSSSSS%%%%%SS%?????????%%%%%%??
##SSS#SSSSS?+-*%%######**%%?**?*=+*+++=++?%SS%SS%SS%SSSS%%%%%%%????%%??%%%%%%S?+
###S##S%SS%???%S?%S####+*?%?*??*--====+*+?%%%?%%%%%%%%%%%%%?**??????%SS%%%%%SS*?
S#####%+%SS**?%%???S##S+*?%????*----==+**??%?*???????%%%%%?*****????%SSS%%%S%S%%
#####S??%S%?+=?%*%SSSSS+*????%?*=---==++*?*??*????%%%%%%%%?*++++****?%SS#SSS%%*?
####S+;+%SS%*=??=SS%##%+*??%%%?*+=======+**???????%%%%%%%?*++=+++++**?%S#SSS%?%%
S####?+?%SS%??%?+*+S##%+*?%%%%??*+=====++*****????????????*++=====+**?%S#SSS???%
SS###%%%%%???*%*--?##S?**%%%%???*+++==++******????????????**++====++*?%S#S%%S??%
%SS##%??*???%?%--+##S#**?%SS%???***++++**??**?????????????**+++===++*?%S##%%S%%%
SSSSS%%%%%%SS??;=S#%S#**?SS#S%??*********??****????????????**++===++*?%S##%%SS%%
S#%SSS%%%%%%%*?-%#??#S*?%SS##S??*******???*?**********??????**++==+**%SS##S%S%%%
**?*???%%%%%?***S?+#S#*?%SS#@#%?******????************????????*+==+*?%SS#S%%S???
?****+*%SSSS+==??=S%##??SSS#@@#%*****???%%?**********?????%%%%*++++*?%SS#S%%%???
??*+==+SSSSS?==*=?S%#S?%SS##@@#%?***??%%%%?*++++*****??%%%%%SS*++++*?%S##%%%+==+
=-----=?SSS%?+*++#?S##%SSS###SS%?????%%%S%?*+++++***??%%SSSSSS*++++*?%S##%%+-===
;;;;---====--=+*S%?###%SS##@@#%%%%%%%%%SSS%*+++++***?%%SSS###S*++++*?%S##%*+++++
;;;;;;;------+*%S*S###SS###@##SS%%SSSSSSSS%?+++++*???%%%SS####*+=++*?%S##???????
-----;;;;;;--*?%%%####S####@##S#SSSSSSSSSSS?++++*???%SSS######*++++*%SS#S??????%
;;;;;::;;;;;-?%%%##########@@#SS##SSSSSSS#S?+++*??%S%%SS######?+++*?%S###SSSSSSS
;;;;;:;-;=--+%%%S##########@@#SSSS##S%S###S%**???SS%###S######?+++*?%S###SSSSSSS
*=-;;-++=***?%SSS###########@@#S%SSSSSS####%**?S%%SS%?%S######?+++*?%S###SSSSSSS
**-;;-=+*+*?%SSS##########S#@@##S%%SSSSS##S??S?=*%S%%%%#####@#?+++*?%S###SSSS%SS
**+;;;+*++**SSSS#########S%#@@##SSSSS#SSS#??S%**%%???S%#####@#*++**?%S###SSSSSSS
***-:;+**++*SS###########%%#@@@##S%SS##S%%?SS%%?*+**?SS#####@#*++*??SS###SSSSSSS
***=:;=*?+=*S########@###%?S@@@@########%SS%?*******?%S#####@S*++*?%SS###SSSSSSS
+**=::-*?*+*#######@@####%??#@@@@@@@@@#####S?***?%??%S######@%*++*?%SS##SSSSSSSS