S%%%??????******+++++++=++**?S###@@@@@@@@@@###S%%%S#######?---=--=--------------
S%%%??????******+++++++=++*?SS###@@@@@#######S%%%%SS######?---==---------=------
%%%%???*******++++++++++***?SS#########SSS%SSS%SSS%S######%---==---------=----;;
????%%********+++++=+++**+*%S##@@###SSS%?****??%SSS%%S####S=-===---------=-----;
%%%%?%*******+++++====+**+?%S###@#S%??**++++++*??%%??%S####?=-==----------------
SS###%********+++====+*+**?%SS#@#S?*==-----===+**?%%?%S####S===-----------------
####%**********++===+*+*+*?%SS##S?+=-;;;;;---==+*?%%SS######?==------------=-==-
##S%?*********+++==++++*+*?%%#@#%*=-;;::;;;---=+*?%SS#######S+=-------;---====--
SS%??********+++==+++++?+*?%%#@S?+-;;:::;;;;--==+*?%S########*--------;----===--
%%??*******+++++==+*++*?++?%%##S?+-;;::::;;;---=++*?%S#######%=------------=-=--
%???*******+++++==++++??++??%##%*=-;:::::;;;;---=++**%S######S?=----------=----=
???****+++++++++=++++*??++*?%##%+=;::::::;;;;;---==+*?%#######S?=--------==--===
??*****+++++++++=+++*?%?*+*?%#S?+-;::::;;;;;---=*?%%??%S#######S%+==----===--==-
??*****++++++++==+++*?%??+*?%###S?*+=-;;;;;-+?S#######%S########S%?=----=-------
?*****+++++++====+++?%%%?+??%#######S%*----*S###S%**?%%%S@@#@###SS%?=-------==--
?*****+++++++====+++?S%S?+?%%#S???%SSS?=--=*SSSSSSSSSS%%S#@@@@##S%%%+------===--
?*****+++++++====+=*%SSS?+?%%####SSSS%?=--=?SSS%%##@##S%%#@@@@#@#%%%?=--=--==---
?*****+++++++====++*SS#%**?%%#@@##S#S%*=;;=?%%???%%#@S??%#@######%%??+===-==----
******++++++======+*SSS%**?%%S#@S*%?+*=-::-?**=-*?%##?**%#@@#####%???*===--==---
*****++++==+======+%S#S%*??%SS###S%?*-;;::-*+--+*%%%*++*%#@@#####%?*?*====-====-
*****++++==+======*S#S%%??%%SSS%??*+-;;;::-++-;--===-=+*%#@@##SS#S?*?*=========-
***+*++++==+=====*%#SS%???%%SSS?+=-;;:;;::-++=;;;;;--=*?S##@#SSSSS???*==========
***+*++++=======+?SSSS%???%%#S%?+-;;::;;;:-+*+-;;;;-=+?%#S###SSSSS??**+========-
**++*+++========?SSSS%%%?%%%#S%?+-;::;-;::;=?*-;;;-=+*%%#####SS%SS??*+++=======-
**++++++=======*SSSS%%%??%%S##S?+=;;:;-;::-*%?=-;--+*?%S@@@##S%%%%?**+++===+====
**++++++======+%SSSS%%%??S%#@@S%*=-;;:-+++?SS%+---=+?%SS@@@##S%%%%?**+++=+=+====
**+++++=======*S%SSS%S%?%SS#@@S%*=-;::;?%?S##S+--=+*%SSS@@##SS%%%%?***+++++++===
**+++++======+%%%SS%S%??S%##@@#%?+-;:::;;=+**+====*?%S%#@@##S%%%%%?*****++++++++
**++++=======*??%%SS%%%%%S##@@#S?+-;;::::;:-=====+*%%%S@@##SS%%%%%?*********+*+=
**++++=======*+?%SSS%%%%S###@@@S?*=-;;-===+****++*?%%%S@##SS%%%%%%????******+*++
**++++======+***SSS%%%SS#####@@#%*=-=?%%%SSSSS#S???%%S@@##S%%%%SS%?????******+++
*+++++====-=++*?%SS%%SS###S#S#@@#?+=-*??SS*+=+??*?%%S#@#SS%%%%SSS%%%?????******+
*+++++====-=++?%%S%%SSS###SSS##@@S*=+??%#=;-+?S%?%SS@@@##%%%%%#SS%%%%%?????****+
*++++======-++*SS%SSSSSS#SSSS###@@#?*?S#@%?%S#%??%S#@@@#S%%S%S#SSS%%%%%%????***+
*++++=====-==+?SSSSSSSSSSSSSSS###@#**%#?#S*+++*?%###@@@#SSSSS##SSSSSS%%%%????**+
*++++=====---=?%%%SSSSSSSS%%SS##@#*+%#?=%?+==+?S####@@##SS?***???%SSSS%%%???****
**+++=====---=+??%SSSSSSSS%%SS###*+?#S???%???%S#####@#*--;;;;;;;;-?#SSS%%????***
*****++++======+??%SSSSSSS%SS###?+*S#???%%%SS########@%====++=---;-?#SS%%????***
?******+++++++++?%SSSS%%SS%SS##?+*S#S??????%SSSS##########%?***%=;;-%#SS%%???***
%????****+++++*?%SSSS%%SSS%S##?+*%##%?**????%%SSSSSS####@#+=-;;-=--;=%SS%%???***
?????????**?%%SS%SSS%%%%S%%S#?+*%###S??***??%%%%SSSSS####S-;:;;;;;-==+%S%%???***
??????????SSSSSSSS%%%SSSS%S#%++%####S%?***?????%%%%%SS##*;::-;;---;;-==*%%???**+
?????????%SSSSSS%%%%SSSSSSS%++?##S##S??****??**%%??%SS#?::;-;::;;;-------*???***
?******??SSSSSSSS##SSSSSSSS++?##SS##S?**+***++*??*??SS%-;=-:;--;--;;-===--???***
*******?%S##SSSSSSSSSSSSSS*=?S#%S###%*++++++==+*****S%-;=-:;;;;;;;;------+???***
*******??S%SSSSS%%SSSSSSS?+?S#%%S###%*+==++=--=+++**S?-+*;--;;-=-;;;--===*%??***
*******?%#S??%%SSSSSSSS#*+?S#S%SS###?*++++==--==++*?SS%S+-===*%#?=-;;;--+%%??***
*****+**%##S?**%SSS%%S#S-;+#S##@####%+++++==--===++%SS%*-=+*%S#SS%+-;;;-+S%??***
+++**??%S#####S??%S##@@@%++S###@###SS*++====----==*SSS%++==?%SS%??+-;;-=*##???**
??%%S%%#########%?S#@###@S%##S#@###SS?+====-----==?SSSS##**?S%?*+*+-;-=+%@@S???*
#SS%##SS##S###@##S%?%%SSSS#S%%@@###SS%*+==-------+%SS%S@@@S*?+====;;-=+?S@@#%??*
%SS%?*?%#SS####@#####S##@#%%*S@###SSSS?+===-----=?SS%S#@@@#+=---=-;;-=*?#@@#S??*
*??%%S%%S#SS####@###@##@@?*+*@#S##SSSS%*+==-----=%SS%%S#@@@*---=-;;;-+*%@@@@#???
%%??**?%S##SS#######@@#@S+++?@#S#SS%%SS?+==-----?SSS%%%S@@@S=---;;;-=+?S@@@@#%??
??%%S%SSSS#######@##@@@@*+++#@##SS%%%SS%*+=-----%SS%%S%%S@@@*=--;;--+*%#@@@@#???
SSS%#S%S#SS#######@##@@S+++?@###S%%%%%SS?+=----+%%%S%%%%S#@@S=-----=*?S@@@@@#%??
????**?%###S#######@#?S%*?*??%S%%%%%%%SS?*=----?%%%SS%S##S#@#+---=+*?%S@@@@@#%%?
??%%%??%###########@S??%%?*?***%%%%%%%SS%?+=--+%%%%%S#@#S%S@#+=--=+*?%#@@@@@#%%%
??****?%S###########S??%%?????%S%%%%%%%SS%*=--?%%%%S#@@S%%%##*=====+*%#@@@@@#S%%
%%%%SSS#SS########@#S??%??%S?*+%%S??%%%SS%?+=+%%%%S@@@@S%%?##++=====+?#@@@@@#%%%
SSS%S%?%S#########@#S?%?*?+*-+?%%S%?%%%%SS%*=?%%%##SSSSS%%%S%+=--===+*%@@@@@#S%%
???***?SS#######@##@S?S?=+=+?*SS%S?%%%%%SS%?*%%S#SS%%SS%%%SSS+=----==+?#@@@@#SS%
?%%%%%%########@#@##S?%+S%?+==#S%S%%%%%%%#S??%S#S%%%%SS%%%%SS+------=+?#@@@@#SSS
?****?S###########@@S?%SS==?%SS%%%%%%%%%%S#%%S@S%?%SSS%%%%%S%=------=+%@@@@@#SSS
%%%S%SSSSSSSSSSS#####??%S?SSS%%?%%%%%%%%%S#%S@#%?%%SS%%%%%%S%=-;;--=+?#@@@@@#SSS
SSSSS%%%%???%%%%%SS##???%S%????%%%%%%%%%%S#S##S%%%%S%%%S%%%S?-;;;--=+%#@@@@@##SS