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