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