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