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