SSSSSSSSSSSSSSSS%%SSSSSSSSSSSSSSSSSS############################################
SSSSSSSSSSSSSSS%+-*%SSSSSSSSSSSSSSSSSSSSS#######################################
SSSSSSSSSSSSSS%%-,-%SSSSSSSSSSSSSSSSSSSSSSS#####################################
SSSSSSSSSSSSSSS%?+?%SSSSSSSSSSSSSSSSSSSSSSSS####################################
SSSSSSSSSSSSSSSS%%%%SSSS%%%SSSSSSSSSSSSSSSSSS###################################
SSSSSSSSSSSSSSSSSSSSSSS%+:=%SSSSSSSSSSSSSSSSSS##################################
SSSSSSSSSSSSSSSSSSSSSSS%=,;?%%%??%SSSSSSSSSSSSS#######S#######################S#
SSSSSSSSSSSSSSSSSSSSSSS%%*?%%%?:,*%SSSSSSSSSSSSS#####%?%####################S?SS
SSSSSSSSSSSSSSSSSSSSSSSS%%%%%%?-;*%SS%?%%%%%%%%%SSS##?**%##################S=,+S
SSSSSSSSSSSSSSSSSSSSSSSSSSSSS%%%%%%%%=+?%%%%SSSS%%%SS****S#########SSSS###SS*-?S
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS%%%%%%%%??%SSSSSS%??%%**++?#####SSSS?;=SSSSSSSSS#
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS%SS%%%%%SS##SS%??%%%**++*SSSSS**SS*:-%SSSSSSS##
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS%?%%S###SS%??%S%**++*+*%S%::?S%?%%S%=+SSSS#
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS%??%SS##SS%???%SS?*+*+:,?S%++%SS%++%+,;%SS##
%%SSSS%%%%SSSSSSSSSSSSSSSSSSSSSS##S%?%%SS###SS%??%%SS%***?=-%SSSSSSS?::?%*?SSS##
%%%%SS%%%%%%%%%%SSSSSSSSSSSSSSS##S%%%?%SS%%SS%%%%S%%SS?*?%S%SSSSSSSSS??SSSSSS###
??%%%%%%%%%%%%%%%%%%%%SSSSSSSSS##SSS%%S?+--?S%?%SSS??????%SSSSS?%SSSSSSSSSSS####
*?%%%%%%%%%%?%%%%%%%%%%SSSSSSS####SSS%+-;;;-*SS%SS#S?????%SSSS*,;%SSSSSS#S######
*??%%%%%%%????????%%?%%%SSSSS######S%+=-;;;;;+S#####%????%%%%S?-+SSSSSSS#S######
???=*????????*????**?%%%SS#S#######S*=---+++++*%#####%%%%%-:*SSSSSSSSSSSSSS#####
?%*-*?*+**********==*???SSSSS######S%+--=+++=-==?#####S%%%=;?SSSSSSSSSSSSSSS#SSS
?+??%%*-+?+;=*++*+;-**-:*SS%SS####S%**=-=+%S??=--?######S%%%SSSSSSSSSSSSSSSSSSS+
*-*%%%?-=?*-+*;;+=-=+*+=?%;,?S#####S*+=;-=+*=+=;-=S#####S%%SSSSSSSSSSSSSS**SS?-;
%?%%?%**??*+==-;---+++***?*+SS%##%?+-=-;;;--;;;;-=%#SSS%%??%SSSSSSSSSSSS%::*--:=
*=?=-?--?=:,,:-:=+++**+*??%SSS%SS+---=;;;;;;;;;;-=?%??%????+??;=+=?==+=*;;;+;-=-
%*%?*%???+--;-**?*++*++**??%SS%%%=----;;;;;;:;;--+?++?????????;=::-:;;-=;=;==+%%
##SS%%???*******??*+*****??%%%%%%+;:-*=+-;;;;;;-=++-*S%%%???%SSS%%%?%%SSSSSSSSSS
####S%????******???*++++*????%+;*?-::=-;;;;;;;--=***SS%%%%?%%SSSSSSSSSSSSSSSSSSS
#####S%???******???********??*+;:**;,;*+-;;;;;--=%SS#S%%%%%%%%SSSSSSSSSSSSSSSSSS
######S%???*****?????????*???****?*+::+S%+-;;--=+%+-%%?%%%%%%%%%SSSSS%%%%%%%%%%%
####S%%?????***?????????**????%???*%::-*=+----=+*-;;=*??%%%%??%%%%%%%%%%%%%%%%%%
SSSS%%??????????????????%%%%%%%S%-:==,:++-;--=*?*+;-+?????%%????%%%%%%%%%%%SSSSS
SS%%%%???????????????????%%?**?%%+::-::;;;--+??+**=+??????%?%??%%%%%%%%%%%SSSSS#
SS%%%%%%%???????%SSSS%??????*+==*%=,,:,:;-=?%*+++?S%?????%%%%%%%%%%%%%%SSSSSSSS#
SS%%%%SS#SS%???%SS###S???????*=-;;-::,,:+%S?*+==+*%%????%SSSSS%%%%%%%%%SS%SSSSS#
SSSS%S###S#S%??%%?%SSS%??*??*=-;;;::::,:-%?*====++??????SSSSSS%%%%%%%%SSSSSSSSSS
########%?%SS%??????%S%??**??%?+;::::::::-*+=--==*??%%%%S##SSSS%%%%%%%SSSSSSSSS%
########%??SS%??????%%?????????%*;::,,,,::===-==+*?%%%%%S###S#SSS%%%%%SS%%%SSSS%
###SS###S%%%%???%???????%?*****??*:,,,,,::;==-==+*?%%%?*?SS###SSS%%%%%%S%?%SSSS%
##%??%S#S%%?%?%?%%%??????++++**???*;,,,,,::;==+=*??%??*+=+++**?SSS%SSSSSSSSSSSSS
##?*??%SS%%%%%%%%%%?????*+==+**????*;,,,,,,:-=++*????*==========+?SSSSSSSSSS%%?%
#S***%%%%%%%%%%%%%%???%?+===++**???%*;,,,,:::-=+*????*--=====----=%SSSSS###%?**?
#S***???%SS%%%%%%%?%%%%?+====++**??%%*;:::,:::-+???%%*=-====------+SS#######S%**
%%**+*?*?SSS%SS%%%%SS%%*==-===+***??%%*;,::::::+??%%S?+=====---;--=%S#########?*
*?****??%SS%SSS%%%%SSSS*=---==+++**??%%*;::,,,:=?%%SSS?+===----;--=%SSSS######?*
??****??SSS%%%S%%%SS#S%+=----=+++++**???=;;;:,:-?%SSSS%*==----;---=SS%%?%%S###S*
%??***%%SSSS%%SSSSSSSS%+=----=+===+++*??*=;;::::?SSSSSS%+==---;---+SS%?????%###?
?%??**?%S##S%SSSSSSSSS?+=----++=====++***=::::::=%SSSS%??*=---;--=*SS%%????%S###
?%%%%??%S##S%SSSS%%%SS?+-----++==--==++**=;:::::;*%SS%??%?=---;--=?SSSS%%???%S#%
???%####SS??%SSSSS%SS#?=-----++==---==++*+-:;:::;-+%%%?%S%=--;;--=%####S%%??%SS%
??%S###SSS%%%SSSSSSS##?=-----++=-----==+++-:;:::;;-=%S%%S?=--;;--=%#####S%??%##S
%%SS###%SSSSS%SSS#S%?+--;;;--+=---;---==++-;;:::;;--*SSSS*=--;--=+SS#####S%%S###
?%%%####S%SSSSS##S*==-;;;;;;-=--;;::;--=+*=-::;:;;-**?%S%+--;;--=*S#####SS%#####
S#S%S####SSSSSS##?====-;--------;;::::;=+*=-::;:;;;*?**+-;;:;;;-=?#S####SS######
S##SS####SS#####%+-==------;-==*?*=::::-++=-;;;:;;;???+--;;;;;;;-?SS####SS##@###
S#SS##S%SS%#####*+=====--;;;=+%SSS%*;:;;===-;;;;;;:-=+=--;;;;;;;;;+S#######@@###
######S%##SS###S??*++==----++%SSS%??*---=+*=-;;;;:;-??+-;;;;;;;;;;:-?#####@@####
######SS####S%S#S%?++==--==+?SSSS%?*+--=+*%=-;;;;:;;?SS=;;;;;;;;;;;;;*#######@##
###S####S#S%%%S##S?++=-==--*SS#S%?=:;-==+%S+--;;;;;;=SS*-;;;;;;;;;;;;-S#####@@@#
S##S####SS%?%%%###%*++=----*SS#SS?*=;;-==*#*--;;;;;;;%%++;;;:;;;;;;;;;S##@@@@@##
##S####SS%??%%S###S%?+=----*%S#SS?*=;-==-*#%=--;;;;;;-?===;;;;;;;;;;;-S#########
########%??%%##@#@##?+=----+%S##S%??**%S?%#S=----;;;;-*====-;;;;-;;;-+###@@@@###
#######%??%%##@@@###?+=----+%S###SSSSSSSSS##+=---;;;;;==--===------=?SSS###@@@@@
######%??%S####@@@@#*+==---=SS##############*==---;;;;-----=++=--==%###SSS###@@@
#%S##%??S#@@@##@@@@#*+==--==S#S#############%==----;;-;-----=*?+=+?###SSSSSS###@
#%##%?%S##@@@@#@@@@#*+==--==S###############S+==-------;;--==*S%??##SS%%####SS##