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