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