%%@@@@%%%@@@%@%%%%%%%%%%%%%%@%%%%@%%%%%@%@@@%@@@@%@%%%%@@@@@@@%@@@@@@@@@@@@@@@@@@@@@@@%@%*:..  
@@%@@%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@%%%%%@%%%%%%@@%%@%@@@%%%@%%@@@%@@@%%%%@%@@@@@@@@@@@@@@. 
%%@%%%%%%%%%%%%%%%%@%%%%%@%%%%%%%%%%%%%%%@@%%%%%@@%@@@%@@@%@%%@%%@%%%@@@@@%%@%%%%@%%%@%@@@@@@- 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@@@@@@%@%%@%%%%%%%%%@%@@@@%%%%%@@%%%@@@% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@%%%%%%%%%%%%%%%%%@%%%%%%-+:++:-@%%%@@@%%%%%%@@@%@@@%%%%%@@@@@@@@ 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%=:-:+=-:@@%%%@%@@@@@%%%%@@%%@@%%@%%@@@@@@.
%%%%%%%%%%%%%%%%%%%%@@@%%%%%%%%%%%%%@@%%@%@@%%@@%%%@@%=+--:-:%@%@@%@@@%@@@@%%@%@@@@%%@@%@@@@@@.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@%@%%%%%=--=.+*-+@@@%%@@@@%@@@@@@%%@%@%@%@@%@@@@@.
%%%%%%%%%%%%%%%%%%%%%%%%%%%@%%%%%%%%%%%%%%@%%%%%%%%@%+:::.:..:%%%@@@@@@@%@@%@@%%@@%@@@%%%@@@@@-
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@:=::-.:::-@@@%@@%@@%@@%@@%%@@@@%@@@%@@@@@+
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@%%%%%%%@%%%%%%%:...-:.=:.-*%+++@@%@@@@%@@%@@@@@@@@%%%@@@#
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@%@*+**.+%::..=-.+:...-...--%@@%@@@%@@%@%@#*#**%####
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%**.*:=:..-..:-*.:......:::..@@@@@@++*++++*%%*****##
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@%++*:*+*=-=:..:..::.... .....:.+++=+++=++=++++*+******
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@@#@%%@%%@@*-:-=+==+*-:..:..:::...--.....++++==++==+++=+*+++++++
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%@#=====+====@-::::--=++=+*=-::#:..:#**+-:.:=++:--::==+=++++++++++*
%%%%%%@%%%%%%%%%%%%%%%%%%============:.--*=:=.--=..-==+#%####--=**=#*=:==+-.-+:.===++++++++++++
%%%%%%%%%@%%%%%%%%%%====-===========.=::.=-+.=:---:=+=++##+%%%+*+*.::=+*--::..=.====++++=++++++
%%%%%%%%%%%%%%%%-=-===-=-----===-===.:. =-+=*:#**-++#.::=-*-:+##-.=:#.-=.==**+-.:+=:=+:++*+++++
%%%%%%+==-----:------=------=-=---=--.=+-+-+==**#*===++*-:-:::.:-:*+*=+*+###*%#*==.==++*-:=++**
-------------===-===:-=-.-==-:-:-=...=:++*#%**=*#*#-*-#+:*++#..+.=+##**==+-=##+++-.:=++*#**-:*+
-:=:-----=====---:------::+:====.: ..::.-+*=:+:***+=*+-=*:+==++=+*=+*+=+:+--**-:--=+++=*=**++++
--:-=--------=----=---.:=-=.-+-==+.:.-::+**-..=:-+**+:+=*=*++=***++=.+*=+=++*-=.:+=++-+*=+*+++*
==:----:---=-------=...::.-+:=+**-.:..:.-*--::*=--+**-*#+*++#*##*=++*-.-.-.*=..==:.-..+=##*.+*+
---:-:--::-------=--:+-.:..==-=+=.:-..--*:#.*+-*=+=:++*--+###++==*##*:+*+#==++:::=...:....-+++#
--:-------:---=--==..+.-.:........==+-+*+.++=++-+++*==+*#***++#**#############=-*+*+**+.:-+=.+=
----=---:-----:+----+=-.....=.. =:-=+:*+=******=#**+=**+=+*+*#***##%##*#####*****+*++*=++*###**
-----:-==---:=+=::--++-.:=:-::+=:-+*+=++=+++***######*=**###+***##++%###############*++##*+=#%%
-----====----=::==.=--.+=..=++=+--+=++*+++:++****+**#####%##############**###*##%############%%
======-=-=*---=..:---.+..+++.**=++=.+++=:-.*++=*+=+*+**#*#*****###%######%%########*#%##%%%####
=--.-=-.+:.+-===--=-.-.-++==+:+++:*.==**=:+.=*-:*++*+*+#**######***-=:.=::-:-=--:-==-.=--=%%**%
===---:.:..:.+:+=.-::=*+++*+*.-++++-+==-+*++==*=**:**.+#++*+=+*:-==#*:*#####*####*############%
--:=.:.:.*==+=*=.:::+++++-*==:***=++***+*=#*-*#****:.=:.=+%##################-+#########%#%%%%%
:+::.:-.:=.:::+**==+-++=+**+*+=*=+=%=++*++++++*+*#+*+=-*+=*####%###############%#---:==:-*:... 
:--++++:++==++**-*+++***++*#+++#++**#=*++#***:*-**#:***#**#+=.....