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