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