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