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