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