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