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