%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%+;%%%%%;;+HHH++HH%H%%%+++++++H++HHH%HH%%+++++++
%%%%%%%%HHH%%%%%%%%%%H#%%;%%%%%%%%+++;%%%%%+;+;HHXHH#HH%+++++++H%+H%%%%%;;+++H+++
%%%%%%%%;;+;%%%%%%%%+HH%%+%%%H%//;;+++H%%%%H/M#MMMX+X/X+++++++++HH+%%%H++;;;+++++
%%%%%%%%+   ;H#H%%;;/MM/H;%%;M###/HXXXH%%++%H MMM+/;;;+%+HH/MX/H+%%%%+%H+/+++++++
%%%%%%%%%;  ;X#H%%;XX###H%%%X###M;XM##X+++++%;;HX+H+++++HHX###X+%%%%%++H+/++++H++
%%%%%%%%%;    H%%%#X+##M+%% ###M;;//M###;;;++++;++++++++++;MM#M;+%%%%%%++/++++H++
%%%%%%%%%%;;;;H%%;#+/####%%####;H+++HX##/%+++++;+++++++;H%/;+##X+%++%H%HHHH+H/XHH
%%%%%%%%%%%;###HHM# ; ;%%%%+###XHHH++H/M ;;;%H++++H+//+;++++;##XH%++%+HXXXHH/+H+/
%%%%%%%%%%%X##MHX##MH%H%%%%;+###XHHHH/M###;/HHHH+HH+X++++++;M#M/H%++%%+HXXHHX+HHH
%%%%%%%%++HX##+%M###/H#%%%H%/X##M;/H#/##### ++//++H+//+HH++XX#X+++%++;;H+H+++%H%%
%%%%%%% X/H/MMHHM#M##M##%#H++X#####M ;#### +H+/M;+++++HHXH+HXM/+++H;%;%%%%%%%%HHH
%%%%;;++#;;%%%%%+XXX###%##H++M####M##X####/;++/#M +++++HH+++++++HXH%%%%%%%%%%HHXX
%%%%;;/+;;%%%%%%%M#+#X##HXM++##MX+ +M+X+X+H+%%XM#;H+H++HH%++H%++HHH%H%%%%;%%H;%HH
%%%+X /;H%%%%%%%%X##++%%HM###+ // ; ;     ; +%++#+HH%;%%%%%;%%%%%++HH%%%%HHHH%%%%
%%%+#+X#/%%%%%%%%X##M+%+HX#X+ ;/+;         ;/+%X##MH%+/+++H%%%%%%H%HH%%%%HX/X+H%%
%%%%HH##M%%%%%%%% MM#+/%;##X  ;;;;;   ; ;;;;X+++##+H%+##X+H+/;H+HHHHH%%%;XX+XXHHH
%%%%%###X%%%%%%%%;M;#XH+;##+ ;;/;;;   ; ;;;+M/+XMMHH;+M/HH+++M/+HHHH#;%%# #XM#XHX
%%%%%%+#X%%%%%%%%;#XM#HH/M#  ; ;  ;;;      XM//;/+HH;+H+H++++#M ++++H;;%%HM++#/H+
%%%%%%M#M%%%%;X%#%M##XH%HXM  ;;;; ;;      +XM/#XH++H+H# #+H+X##M+++++++%%HX;+#MHH
%####%M#/%%%%X#;H%+#XX++H/X ;;;            +MX#HH++++# # ##+X#M+;++++++%H/; +#+++
%%HXX+/;%%%%+# ;#%H#X/MXXXM+/;            ;;MX XHHH+H# ##XX+X;H++++++++%HXX;;XHHH
%X#MX;%%%%%%M#M+HXX#X;+M//X ;             /;+X#M /XX ;XM+  /###HH+++++%%++/;/H#H#
HXMH#;H%%%%%M#XHXXX+++/M+/+     ; /       ; /+## XMX;HX+; // ####++++++HHHHHHHHHH
%XMX#%%%%%%%X#H%%%%+;;;MX;/   ;;MMMX; / ;  XMMMMMXX;;;      X####H+++++++H+++H+;%
HHXMXHH%H%%%H/H%%%%+X##X#XX;M+X+#MMXX;XXMMXXMMXM#MX+H;      /    H/+++++++++H+H++
% ;/+%%%%;%%%;X;/;;++++;X#+X#MX +;XMM### +  /  M##+;;;       H#HH+/;+%+++++++++++
%%H##%+/%%%%+###+++;/HH;+##M#X;  +XM####M    ;  ##XH;;;;     +HHHH/;+++++++%+++++
%HH%%%;;%%%%+###;%%;;+//X###     ;+MM#M;/    ; X +H; ;       ++;HHX/+++++++;+++++
HHHH%%%%%;;%/####;++;//MM###M    ;;XXM+   ;  ; +M+H; ;       /H+HHX/+++++++++%+%%
H///#%%H/++ /######;;;/MMM#M+        ++      ;/ XX/;;;      M#HH%++;%++++++;+%+%%
H//H#%#H/#M;H;M#####/HX+MMMM/   ;//  +;     ;;///XM+;;;     ##XH++%+%++++++;+++++
%%%H##H+H/+%%%;+X###;;/;MMX;;;; ;/            ;XXX#+;;     ;##XH++++%++++++;+++++
%%%HXHH%HHH%%%%%;+##M/+/XX+;; ;  ;    ;   ;   ;XX;X+;;    ;##XHH+++++++++++%+++++
%%H+H++%%%%%%%;%%;##X;+;/;;;            ;;;    ;++/ ;     +#X/+++++;;++++%%++;+++
%%%/+HH+%%%%%H+H#;###M////;;            ;;;   ;/H%+ /    ;++++H+HH+++%+++;%++++++
%%H%+H+++%%H#%+XH++####++;;;;         ;;;      ;%%%         +XH;H+++++%;;;;++++++
%%%%%HH++%%##%HXXHH/M####MX;/       ;; ;; ;  ;/;+%% ;      ;M/H%%%+++++++;+++++++
%%%%%+HH%;%%%%%++;%%/##M#XMXX;;;XX;   ;     ;;;;%++;;;     X X++%%%++++++;+++++++
%HH%;X/H; %%%%+++;+;H/XXMMXXMXXM##M+;;; ;  ;+;; +/+;+;     X #H++%%++++++++++++++
H+++/MX;+X##HH+/+;  ;+; +X++XXXXMXMMXXX+/;;;;/MMX+#;;;     ;H%%%%%%%;%+%%%%%+++++
HHH++//;/MXHHHHMM    ;+;;M+;X//+X+XXXXXX+XXXMXMM##M+;   / ;;%%%;+%%%+++++%%%+;++%
 XXH#+H;/XX/HHXMX    ;H/MMX+;/+/;;    ;+++XX//+;/X/;   ;X;;%%HH /%%;+++%;%%%%;+++
### #HH+H/HHH/XMM   X+ M##M//+%X;     ;++;XXH##%H/H; X # #%%%+XX+%%%%%%%++%;%;+++
M++#M/#XH+H+/+HXM;/M####MXMX/+%HX ;   ;++;;+H%H#X##X ## #%%%%;  %%%%%;%%;++;+++%+
X++M#XXXXH++/#X#H;X ## XMMXX/+%HH; ;  +XX;/+HHH##      ##%%%%%%%%%%%%%%%%%%;%;+++
++++X;H+H++++ XH###+#;#+;;;;/;H#H/;++;XMM;H+H#H##HXHH##%#%%%%%%%;%%%%%%%;%%;;%%%%
 +++++++H++++++HHH#HH%HH/+++++H#H/XXXM#X/HH+%HHH#XX#H%%%%%%%%%%%%%%%%%;;;+%%%%+%%
 ;++X+;/;++HH+HXXMXH#%;++;%+;+H#HHMMXM#;H%+;%++;/XM;%%%%%%%%%%%%;%%%%;;;;%%+++;;;
 +++X++//HHHX++++##/H%+HH+%+;+HHHHM#/; +%%%%++/;M#M;%%%%%%%%%%%%%%%%%%%++%%+++%%%
;+X+X+;/H+%+;;;;HMM+H+H+H+++/;%HHH+++++H+%;;;; X##M+%%%%%;%%%%%%%%%%%%%++%%%%+%%+
++X++XMMXHHHH%%HHHH+++H+H%%+++%H+H#HHHHHH%+;%%XX#XXH%%%%%;%%%%%%%%%%%++++++++%%++
M##XXXX;HHHH#%H%%%%%+;H%%%%H+%%H++HHH%%++%%;%++HHHH%%%%%%%%%%%%%%%%;;%%++++++%%%+
####X//HHHHH#H#%%%%HH;%%%%%+H+%HH+H%%+++H%%%%++%%%H%%%%%%%%%%%%%%;+%;%%%++%++%+%+
####XHH+H++;# ###%%HX+%%%%%+++++/;+%+;;+++%%+++%%%%%%%%%%%%%%%;;;%%%%%%%%%+++%+++
XX/H##+//  / M H#HHH#H%%%%%;++//X;%%;;%HH+%%+++%%%%%%;%%%%%%%%%;%%%%+++%%%+++++++
X/HH#XM+     //+X;+%H%%%%%%%+///H;H%+;+%H++%+++%%%%%%%%%%%%%%;;;%%%%+%;%%%%%+++++
X//X  #X      /;XM;+%%%%%%%%+X/X//#+H;%%%++%%%%%%%%%%%%%%%%%%;;;%%+%%++;++%++++++
%/+XXXX         ;X;;H%H%%%%%%/;++X###%+;;;+;%%%%%%%%%%%%%%%%%%%%%%%%%%%;%%%+++%;%
%+XXH/X         ;X+/H+/H%%%%+;+X+X# #H+++HH+%%%%%%%%%%%%%%%%%%;%%%+++%%%%+++++%;+
HHHHXX+         ;X+///+%H%%%+;+X+;/##%++H#X+%%%%%%%%%%+%%%%%%;;%%%+++%%%%+%++%%;+
HHHHXMX         +X;;/;+%HHH%+;+XXXX//;+HHHH##%;;;%%%%%+%%%%%%;+%%%;+++%%%%%%%++%+
%+H# M + /;;; ++XX+;;;+HH%+H+/XMMXX/  ++%#HX#H;;;;%%%%+%%%%%%;%%%%+%++++++%%%+;%+
HH##  #X;////;+X#HX;++/##HH/H/+XXMM//;+HHHHH#H+;;;%%%%+;%%%%%;%%+%+%+%+++%%%%;;;%
XHHHXMM;   ;/ ;HH+; ++/X#/;+++/XXX/;;%%%%%HHH%%%;;%%%%%;%%%%;;+++++%+++++;%;;;;;;
X+HXX X+++;++;+XX;+/H+/##X;+H++HH#H%%%%%HHHXX+H%%%%%%%%%%%%;%%+++++++++;+;%+++%;+
+H%+XXM;;;;;XXX;; ;++++H#HHHHHX++%H%%%%+;/HHXHH;%%%%%%%%%%%;;%%++++%%++;+;+%+%%;;
H+HHHM#+;%+HH+/;//++++%+HHHHX+H+H%%%%%%/++/H#HH%%%%%%%%%%%%;+%+++++%;++%+;%++++;;
HH%HX#X ;+/+H/+++HHH++%%;;;H+++/H+%++%+;+;/HH+%%%%%%%%%%%%%+;;%%+++;;++++++++++;+
MHH###X;+/;MMMM/HHXH+++%%+++/+++++%++H++X;/HH%%%%%+%%%%%%%%%%%%++++;+++++++++++++
M+%H/MX;++XXMM/XXXXH/++++++H//+/X+H++%+XM;+XH+%%%%%%%%%%%%+%%;%;;;%++++%%;+++++++
M+HHH//+HH/HX+HHXXHH/+++++HHHHXXX+H%H%#  HHXX+%%%%%%%%%;%%+%+%%%%;+++++++;;%+++++
/+++H+HHHH;;+;++//H+++++H+++X++/HHHH+H%X#+%H/+%%%%%%%%%;%%%%;;;;;;+%%%%;;;++%%%%%
++++++HHXHHXHHH+X/+HH+H/H%+;++++HHH++%+/H%H#H%%%+++%%%%%%%%%+;+%%%;;+++++;%%%%%%+
+++++//+HHH/XXX/H+++H++/X%+;;;++HXXH+++/H%%%%%%%%++%%%%%%%%%%%%%%;%%;;+++;%%%%+%%
++++//HHHX#HH/#XH++HH++HH%++%%%+HXXHH++XH%%%%%%%%+++%%%%%%%%%%%%+%%%%%%++++%+++%%
++++/XXXX/XH+/#M//+;/+++H%%%%%++HXX++++++++%;;;;%%%+%%%%%%%%%++%%%%%%+%%+%+++%%%;
++++HXX#XXXH++#M/X+++/++H%H%%;+HHXXH++++++++%;;;%%++%%%;;%%%+++%%%;%++%++%+++;%%;