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