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