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