*
*
*
*
+++++++++++++++++++
HH@HXX@MMMMMM#########MHX@MMM#####################
HX$%+%HM#############@$%$XX@MMMMMM################
%%$$X@##############@+;;/+$H@@@@@MMM##############
@M##################H:=;/%$XHHHHHHH%XM############
####################@;:/+%$XXXXXXX%/+XMMM#########
###M@##############MX+;//+%$$X$X$%+/%X@MM#########
##MM@##########MMMMH/;;:;;/+%%%$++//+$XMM#########
##M@@######MMMMM@@@$;::::;;;/+%+/////%X@MM########
##@HXX@M@@MMM@@@HHH%;::;;;;=;////////%X@MMM##MMM##
#X;;;;;H@@@@@@@HHHH/=---=:;;::;/+///%$$@MMM#######
H;/;/+=/@@@@HHHHHHX;...=;;;//;;/++/+$X$@MMM#######
%;:=::==H@H@HH@@HH$+:,,;;::;////++/+$X$@#MM#######
/:--=:==HHHHHHHHH@$/;::;;///;;;/%++/+%$@MMM#######
;:===:=-XHHHHHHH@HH$;://+/:::::/++%//+$MMMM#######
/====::-HHHHHHHHHHH/:+/;/:=;;=:/+%+;;%HMMMM#######
/===-::-HHHHHHHHHHX:://:;:==-:/+%%//+XMMMMMM##M###
/==-,=:,XHHHHHHHHH$=-=/;=-,,=;/+%%//$@MMMMMMMMM##M
;=,---:,XHHHHHHHHHX-,=:=. .,=:/+%$++HMMMMMMMMMMMMM
/---,,=,$HHHHH@@HHH/--.,,,,-=:/+%X$X@MM@MMMMMMMM#M
;---,,=.$HHH@@@@@HHX:=::-.==:;/+$X$X@MMMMMMMMM####
;---,,-.%@HH@@H@@@@X===:;,,::;/%$$%X@MMMMMMMMM####
;-,,..-.+@HHHHH@@H@H::;==--:;/+$$%%X@M@MMMMMMMMMMM
+;..,.,,$@HH@@@@@@HH%;/+;:;//%$$$+%$H@@@@@@HHHHHHH
/$:,-,.=H@H@@@@@@@@@X=:;//+%%$%%+/+$HHH@@@@@H@@@@@
::;,,.-$M@@@@@@@@@@@H/;/%$$%%+++//+%XH@@@@@@@@MMMM
;:+;%XHMMMM@@@@@@@@HHHXX$%$$+//;;/+%$XXHH@MMMM@@@@
:+%%MMMMM@@@@@@@@@@@@@M@X/;;::;:;/+$$$%+$XXH@@@@@@
:;%%@MMMMMMMMMMMM@@@@@X+/;-,-:;;//+%%%%+/+%XHXX@@M
++/%@MMMMMMMMMMMM@@@@@X+;/=-==;;;;/%%+%%/%$%%%$XH@
/$%%HHMMMMMMM@HH@HHHXXXX%/--=-=::;/%+/%%$$//++%%$X
%++$HX@M@@MMMX$XXX$$$%%$%/=,-==:=;/++/+$%/;;//+%%$
$%/%H$HMMMM@X%%$%%%%%%%++/:--=::=;//++%+/;;;;//++$
+$+$H%XMMM@X%%%%++%%%$X$+/:==:;;=;+/+%+///;;;;/+%$
%%%HX%$@MMX%%%+%%++%%$$$%+/;=:;:=/+/;///++/;;+%%$$
%$XMX%%HMH%++++++++%%%%%%+++:=/:=;+;;;//++/;+$$%%%
$X@#H%%$@%/+//++%%%%%+///+++/://:;/;;;//+++%X$$%%%
XXMM$%%$X+//+//+%%%++///////;:;+;;;;;;//++$XX$$%%+
XHMH$$%%%+///+++%%%%%++++++%++++///;//++%$X$$%++++
====-=::=:::::::::=:::::==:=-::::::;;;::;;;:;;;/;;/////;;;//;;/////;;;:;..;:.=::;/;;;;;;/;//;;;::==:
=====::::::::::::::;:;:;;:;:::=:;;;;;;;;;;;;;/////%;=+;////;;////+;;;;;,../;.=;;/+/////////////;::::
==::::==::::;:::::::::::::::;=-:;;;;;;;;;;;;/////+-/;-;//////++/;:////,=::;/+/:///+////+/++//;;;:;:=
=::::==::==:;::::::::::::;;:;;:;::;;;;;;;;;;////++:;/;+/////++/;;///+/=/;=-/;/;/+++++/+++++/////;;;:
=::===::::::;;::::;:::;;;;;:;;;;;;;;;;;;;;;/////+/;//;///////////+++++$+//;/;//;+++++++/+++/////;;;:
=:===::=::::;;::::::::;:;:;;;;;;;;;;;;;;;;;////////////////////++/+%%%$$$$%;///;/%%%+%%+++++//;;/;;;
===:::::;::::::::;:::;;;:::;;:;;;;;;;;;;/;;///////;///////////++/%%+%+++$%$$/;+;-/++;++++++++///;:;;
===:==:;;::::::;;;:::;;;:;;;;::;;;;;;;////;/+++//;+/+++//////++++++//%+%%%+$++/+=/++;%%+++++/////;/;
=::=:::;::;:::/;;;::;;;:;;;;;;;;;;;;;;;;////++++////+++//;///;//++///+/+%%+%%++/:+++%%++%+++/+/////;
=::==--:::::;;;::::;;;;;;;;;;;;;;;;;;;;;;///////////++////+///++////;//%$%%X%+++;/+++%+//+++++/:////
=:::::=:::::;;::;;;;;;;;;;;;;;;;;;;;;;;;;////////////////+///++///;;;;/%%%%X%++++/+++%++++/++/+;;///
::=:::::;;:;:::;;;;;;;;;;;;;;;;;;;;;////;////////////;;///;//+///;;::;+%%+%$%++++/++/%++++%+/+//////
::=::::;;;;/::;;:;;;;;;;;;;;;;;;;;;/////;/;;/////////;//;/;////+/;;;;/+%++%$%/++++++/%++++/++////+//
=:::::;//::;::;;::;;;;;/;;;;;//;;;;///////;;;;;/////////////;////;;/%%+/++$%%++/+++++++++%//+/+/++//
::;:==:;;:::::;;;;;;;;///;;;;///;///////;//;/;;/;;;;/////;;;//+/;;/%X%/;/+%%%+/++%+++/%+%++..+///+//
=:;:::::;;;:;:;;;;;;;;////;;;//;;////;;;;////;////;////;/;////+/;;/%$/;+++%%%+/++%%+/:+%+%+::///////
==:=;;;;;:::;;::;::;;///;////////////;;;;;//;/////;/+//////++++////+++++/+%%$%+%+%+++++%%%//+++++/-;
==::;;::;::::;;:;:;;;;;;//;;/////////;;;;;;;;;///////;;;///+++%+++++%+++/+%$%%++%%++++/:;++++/++++;/
:=::;;;:;;;:;;::;;;;;;;/;;;;//////////;/;;;;;;//;////;;///+%+/%+%%%%++++%%$$+$%+%%++++;,/%+//+++++%/
::;:::;;;;;;;;:::;;;;;////////////////;/;;;;;/////////;/+%%+/+%%%%+%+++%$$$%+$$+++++++/=;++/++/:%+%/
::;;;:;:;;;;;;;;:;;;;;//+/////////////;;;;;;;/////+//;;/+%/;/%$%%%%%+%%$%X$%%$%+++++++/:+%+/++++%%++
;;:;;;;:;;;;;;;;;;;;;;;;;;/;/////////;;;;;;;;;////+/;;;+$%+$@@$$$%%$%%$$%X%%%$+++++%++/;/++++++%%%++
;;::;;/;;;;;;;;;;;//;;//:;///////////;;;;;;;;;;/;//;;;;$$+XM#MX$$$$%%%$%$X+%$$++++/+++///++++++%%%++
:;::/;/;::;/;;;;:;//;;/////;///////;;;;;;;;;;;;////;;;;X/+M#M#HX$$$%%$$%$$+%$%++++++++///++/++++%%%+
::;;//;://;/;;;;/;/////////////////;;;;;:;;;;;/////;;;$$%@MM#M$$$$%+%$$$%$%%$%++++++++/+//+++++++++/
:;;;;//;;;;/;;;;;;/+////////////////;;;;::::;;/////;/;$XXH@@M@$X$$%+%X$%%%%+$%%+++++++//%++//+%%+++;
:;::;///;;;/;;;;;;/////////////;/++/;;;::;;;;;///+;;//$X$XHMMH$%%%%+%XX%$$++%%++++++++//+%%++%+++++/
::::;;;;;//+/;//////////;////+/;;//;;;;::;;;;;///+;///$$$$H@@@$%%%$%%XX$$$+%+%++++//++//+%%+%%%+++%/
:;;;/;;////+/;/////;;/;;///++////;;;;;;:::;;;;///+;;/%$%%$HH@H$%%%$$$XXX$$++%+/+++/+++/+%%%+%%%%++%+
;;;///;/;//+/;;;:;;;;;;;///////+//;;;;;;;;;;;;////;;/$$+/%XH@H$%%+%$XX$$XX$/%+//+//+++/+++%%%%++++%/
;;;//;;/;;;+///;;;////////////////;;;;;;;;;;;;/+//;;%X+//+$HH@XX%++$XX$%HX$+%++////+++/++++%%%+++%%/
;;;//;;;;;;+///;//;;//;/////++//;//;;;;;;;;;;;///;;/HX;///$XXHHX%++$XX$%X$$$+%+;/++//+++++%%%%%+++%/
//;//;:;;;//+;;/;;;/;/;///+/+=;///;;;;;;:;;;;;/+/;;+;;///+%%XHHH$$%%HX%$$H%X$%+//++//+++%%%+%%+%%++/
;;;;;::;;;//:;;:;/;/////+///+/+///;;;;;:::;;;/++/;;$==+//++%$XXHX%%XHX%XXX%$X$%//++//+++%%%%%%%%%++/
;;;;;;:;;;;;://;;//////////+++/////;;;;:;;;;;///;:/H::+//++++%XX$$XH$$XXX$%%X$%++++/++++++%%%%%%++++
;;:;;;;;/;;;/;;/;///////+++++/+////;;;;;:;;;/+//;;+$////+++++%$XXXHX%$HXX$%%X$%++%+/++++++%%%%%%++++
;;;;;/;;//;;+;;///+//////++/+%+/;//;;;;;:;;//+/;;/%+//;+/++++%$XHX$$%%XXX%%%X$+++%++++++%+%%%%%%++++
;/;;/;;;;;;/;//;//+////+/+///+////;;;;;;////////;;$/;/;////+++%$XHX%%%XHX$%$$%+++%++++++%++%+%%+++%+
;/;;/;;;;///:;;;/;/;///+//++++/+//;;;;;;;;//++++++%;;//////+++%$$HX%%%XX$$$$$%+++%+++++%++++%+++%%%+
;;;;;/;;;//;/;;+/;+/++/+//+/+++///;;;;;:;;/++////++//;;;;;///+%$XX%%%$XX$X%%%%+/+%+++++++%%+%%+%%%%+
/;///;////;;//;;/;%/;//++/+++++////;;;;;;;///;/;+++;;;;;;;;;;/+%$$X$%$H%X%$$++++%%%+++%++%%%++%%%++%
////;;//////;;;;//++;//++++++/////;/;;;;///+//;;+%+;;;;;;;;;;;+%$XH$%$X%$%$%++++$%+++++++%%%+%%%%%%+
;;//;;/+//;////////+/+/+++++///////////;//++//:/%%////;;;;;;;/+$$HX$$XX%$X$+/+/+$%+++++%+%%%%%%%%%%/
;////;;/+//////;///+++++++++//++///////;//+//;;+$%////;;;;;;//+$$H$%XH$+%X$//++%%+++%++%+%%%%%%%$%++
////;;/////////;///++++/++++////////;//;;/+//;/%$%//////;/////+%XH%$XX%+%X%///+$++++%%+++%%%%%%%%+++
////////;///////;///+++/+++++++/////;;;////;/;+%%+//;/;;;///++%$XX$$X$+%$X%////%%+++++%++%%%%%%%+%++
///////////////;////+++++++++++//////;;//+/;;;++%+//;;;;;;//++%XXX$$X%%$$$+//+%%%%%%++%%%%%%%%%%/+/;
;////////;;////++////+/%+++++++//////;;/++;/;/%+%++//;;:;;;/++%$HX$$X%%$$%+//+%%%%%%%+++%%%%%%%+/%+/
;///////;///;////////++;/++++//;///;//;/+///;+++%+//;;;;;;///+%$H$%XX$$%%%/+/+%$%%%++++++%++%+%/;+%+
////+/+////;/+//;////++/++++///;/;///////////++%%+//;;;:;;///+%XX$%X$%$$$%///+%$$%%%++++%+++%%%+/++/
//////////;://///////++++++%///;;;;/;///////+//$%+//;;;;;;;//+$XX%%X%%$$$%///+%%$%%%%+++++%%%%//+++/
///////+///////;///++++++//+//;/;;;;;///////+/+$%+/////;;;;//+$HX%$$%%%$%+///%%+%%%+++++%+%+++;+////
//////++///+/////;/++//+++/+//;/;/;;//////////+$%+/////////++%$H$%$%+%$%%+//+%%+%%%++++++%%%%+/+////
/////++/++;///;+/;/+//////////:/;/;;+////;////%%%++////////+%$XX$%X%++%%%+//+$$%%%%%+++++%%$%++////;
////+++//+//++//+/+///////////:/;/;/+//////+/+$%%+++//////++%$X$$$$+++%%+////$$%%%%%%+++%%%%%+%+///;
/+////++//+///////+/;///+/++//;////++/+//+/++%$%%+++//////++%XX$$%%+%%%%/////$%%%%+%%++%%%$%%+%+;//;
/++////+////////+/++;/+//+++////+;/+/////+++%%%%++++//;////+$$X$%++++%%%///++%%%%%%+++++%%%%++++///;
//+++////////++/+++//+/+++//////+++/+//;/++++%%%++////;///+%$X$$%+/+%%$%++//+$%%+++++++%%%%%%%%%/;/;
//++++///////+++++//++/+/////////%+/++;//++++%%%/++/;;;/;/+$$X$$%+++%%%++///%%%++%%%%%%%%%%++%%%+/+/
/++++++++/++///++//+++//////////+$/+/;-:/+%++%%+/++/;;;;/+%%$$$%+++++%%+////$+%+%%%%%%%%%+++++++/++/
/+///++++//++///+//+//+/////////+%/%//:++%%++%+//;;:;;;;/+%$$$$%+++++%%+///+$%%++%%%%%%%%+++++++//+;
/++///+++++//+//++/++/++///////++++//;;/+%+++%+//;;:;:;;/+%$$$%%+++++%%////$$%+++%%%%%%%%+++++++/++;
/++//+++/+++/+++++//+/++///+/++%+++/;;/+++++%%+////;;:;/++%$$%+%+//+%$%////X$%%+%%%%%%%+%++++//++++/
/++/++++++++++++/+/+//+/////++%%++//;;/%++++%%+//+;;:;;/++%$X%%%+//+%$+;/;%XX+%%+%%%%%%+%++++//++/+/
+++/+///++/+++++++++++/////++%$%%+//;//+%+/+%%/++//;;;/++%%X$+$+++/+%$+;//$H$$+%+/++%%+%%++%//+++++/
/+++/+///++++++%+++++++//++/+$$$++///+++++++++//+//;;//++%%X%%%++++++%+//+XX$$%%%++%%%+%%++++++++/+/
/+++/+/;+++//++%%%+%++/++++/%$%%///;/+%++++%%++///////+++%$$$$%++++/%%%//+XX$$$++%+%+%%%%++++++++///
/++++/+/%%+//+++%%%%++/++/+%X$++//;;+++++++%%/++////+++++%$%X$%++++/%$%;++XX$$$%+%+%+%%%++%+++++////
+++++++++++++++++++%+++++/+XX%+//;//%++++++%%/++//+++++++%$%XX%+++++%%+;%+$HX$$%%%+%+%$%++%++++////;
/+++/++++++++++%++++++++++%X$/+///+%%+/++/+%+/+++/+++++/+$$$$X%+++++%%%/++$H$%%%%+++%$$%+%%+/+++//+;
/+++///++++++++%+++++++++$$$+////+%%////++%%+/+++/++++//%$$X$$%%++++%%%+/+XH$%%$%+%%%%%%%%++/++////;
;/+%+;/%%++%%%+++++/+++++XX+/+//+%%+;/+//+%%/+/++/++++//%$$$$+$%++/+%%+/++XXXX$$%+$$%+%$%%+++%/;+//;
///++%+;+++%+%%+++++++%%XX$+///+%+/////+/%$%/+/+/+++++//%X$$$%%%++/+%%%/:+HXX$X$%%%$%%$$++++$+/+++/;
///+%+%+%++%++%++++++%%$XX++++%+%+///++++%%%/+++++++++++%$XX$$%%%++++%+/;/HH%%$$%$%$$%$%%+%+%+/+///;
+++/%+/%%%%%+++%++++%$$$X%//++%%+//////+/%%++++++++++++%$$$$$$%%%%+//++++/XX+$$%%$$%%$$%++%%++++///;
/+%$/+$%+%%%+++%++++%$$X$//++%+%/////////+%/+/+++/++++%%$%$$$$%%+++//+++//XH%$$%%$$%%$$$%+%%%++/////
//+++%/%+%$%++++++++%XXX+//%%%$%/////////%%/+//++/++/+%$$%$$$$%%++++++++/;$X$$$%%$$%$$$$$%%+%+/+++//
%%%%$$$+%%%%%%%++++%XHX%//+%%$%+/++//////%++/+/++++++%%%$%$$$$%++++++++++/%XX$$$%$$$$%%%%%++$++++///
/%X+%$%$%++++%%%+%$XHX%/+/$$%$+//++//////%++/++/+//++%%$$$$%%$%%++++++++//%X$$X$%$$X$%%++%+%%+++++//
+%$$+%$%%+%$%%$$%$H@$+/+++%$%++++///////+++///+////+%%%$%$$+%X%%++++//+++;/X$%$%%$$X$%%+$%%+%+%/++//
+$%%$$$%+$$$%$%$$H%%$/+/++%%///+/////////%+//++/+///%%%$%$$%%$+++%%////++/;%$%%%$$$XX%$$$$%%+/%+/+++
+%%%$$$$$%%%$$X$X#$+;+%+++%///+/;///////+%+///+++//++$$$$$%%$%//+%%++///++/+$%$%$$$XXX%%$$$$%/+%+//+
%+%%$$$X$%$$X$X$H#%+;+;/+%%++//;;////////%+//++++//++$$$$%%%$%//+++++//+/+//%X%%%$XX$$$%%%%+%%++++++
%%$X$X$$$$$%$$XX@M$%+;=/+%+//////////////%+//++++/;+%$$$$%%%$%+++++++///++//%$%$X%XHX$$%$%%%%%++/+++
%%$$%$%$$$$+$$XHMM$++;/+++//////+//;/////%+//+++///+$$$$%%%%%%+++++++/;;/++/X$$$%XX%$X$%$%%$++%+/++/
%%%%$$$X$$X+XXH@#X+//+%+%++///;;////;////%%+++++/++%%%$$%%%++$%+++/+++//;//+XXX$$XXX$%+%++/+/+%/++++
++%%$%%%%$X$$XH@M%++///%%;/:;///////;////%%+++///++%/+$$$%%++$%+++//++++/;;/$X$X%%H@HHX%%++%+//++///
$X%$$$$$%$XX+H@@#%+/+/:%%:+;//////;;/////%+////+++/$;+$$$%%++%%+/++/++/+/=/+X$%X$$@XXX$%++$/%+/++++/
$X$%%%%%$$XXX%M@@++/;:+++/++///;;;/;/////+%+;;%/+/+%$X%$%$+%+%+++++/++++///%XXX$XHH$XX$%%+%%+%%/+++/
%$$%+%%%$$$$H$HM@+/+++%/;/++///;/////;//++%++++++/+%$$%%%%+%%%%+//+++++++,-$X$XXXHHXXX$++++++%%+/+++
%$$$$$$$%%%$HHX@M$+/++++;+%+//;//////;;//%+++++++/++$$%%%%+%%%%++/%+++%++//$$X$$H@HX$XX$+%%+%+++++++
%$$$$$$$%+$$H@HHMX%+%/;+++%+//;;;;;/;;;//++++%+++++%%$$%%%%%%%%++//+%%%//%//$$$X$H$$$$$%%%++%/++++++
%$X$$%%$$%$%H@@@M$+++//+++++///;;/;/;///+/+++;++/++$$$%%++%%%%%+++;%:++%%+/+%+XX$@H$$$%$%+/+/;+++++/
+%%%%%++%%%%HH@@@%$$%+++++%%////;///;///+++%/ ++/++%$%%+++++%%%%+/++-=%%%%$%%$H+/@@XX$++%%/%//++%+++
%$$$$$%++%%$H@H@#XX$++%+++%%///////;/;//+%/%/.++/++%$+%++++++%%%+;+++;%;;:;;%HX+%@M$$$%%+++++%+++++%
%$X$$%%%%+%$$@@@M@$%%%;;+%%+/////;;;/;//+/+++++//++$$%%%++/++%+++%//%++++::;+H%$H@MXX$++%%+;+++/%%++
%%%%%%%%+%+$H@@M#X$$$+;/+$+++/;;;//;;////+//++/+//+%$X%%%++//%++++%;:$%%+/+/+$XX$X$$%%%%%++%%++++%%+
++%%%%%%$%/$H@@M#H%%%%%++/:+//+:;/;////////++=:+//++X$%%+%+/:+/%;%++///:+%++%$XXHH@H$%%%++++++++%%%+
+%$%++%%//+$HH@@MM%$$%%;++/+/;//////////;+/;/++//+++$$%%%%++;//+++++++++;+;%$$HHH@HXX$%%%+///+++++++
+%%%++%%$%%%XH@@@MXXX%+:/;%++///++///////;;//////+/+%X%%%++/++//+/%/++;+//;$X$HXHX%%+++:++++%++++++/
%+++%%%%/+%+X@@@@MX%$++;;;+/%+++//;;;////;///////+/++X$%+++/++/+//+/+;/%+/+XXXHXXH$%$$$$%%%%%%++++++
%%+%%++/+%%%XHHM@MH+%%++;%+/%++%;/;;;;/;;;;;//////+++%X$%++%++;////;/:++%+XX$HHHXXXX%+%+%%+%%%$$$%%+
%%%%%++/////$HH@MM#X$$%+;++%%%%///;;;;;;;///////////++$$%%+%+%;/+++///++%%HXXHXXXX$%%%/++%%%%%++%%++
+%%%++//////+XH@@@#@+++++%%++++%+/;;;;;/;;;;//////////%X%+%+++++$%+;:/%$+%X$HH$XX%$%%%/+%%%%%%%%++%%
%%%++++/////+$H@@MM#$%++++/++%%%%=;+;/+//;;;/////;///+%%X%%+%%+%+++%$XXX%+XXHX$$X+/+++%+++%%+%++%+++
%%+++++++///+$XH@@M#HXX$%+%%+%%%%///////;;;;;//;/;///+%+%$$%$%/%//+$$%$$$%X@HX$XH%++++++/+%+%+/++%%%
%%%%+////;/;;/XM@@MMH$$$%+%%%%%%%++///;/;;;;;;;;/;///+%%+%$$X$%+++%%+++%$$X@X$$%%%$%%+++%+%+/+++%+++
++++/////;////%$H@MMMX$%%$$%$++%++////+/;;;;;;;;///;;/%$%++%$X$%++%$+++%%XHX$$$++%%++++%+++++++%%+++
+/;;///;/////+++$HMMMM@XXX$%$+%+/+/++++/;;;;;;;;;;//;;/+$%%%+$H$%%%$%%%%%HX$$$$%+%++%%+++%++++++++++
+////;:=-=;;//++%$HH@M#MH%/++/%;;%++%+/+/;;;;;;;;;;;;;;/+$$%$%%XX$$%%%%%$XX%$%%%%%+++++%%+%%++%+++//
+//;;;;;:===:/+++%%X@MMMMH%%%%%;/%++%+/+/;;;;;;;;;:;;;;//%%$$%%%$$$$$%%%XXX$%+++%++%$$+//+++%%%%%+//
////////;///;/+%%%%%$XH@@MHX$$+$%+++++%//;;;;;;;;;;;;;;;/++%$$$$$$$%%%%%HX$$+++++%%%++++%%%%++%+/+++
+++++//;/+++/++%%+++/+$$X%X@@HXX$$%%X%++//;;;;:;;;;;;;;;///++%%$$$$++/%@X$$$%%+++%%+++++++%%%+%+/++/
%+++;//;+%/+%+%%++///++%++++$XXHM$+$X$/+//;;;;:::::::;;;;////+++%++;;+XH$$%%%%++%%%%%%%%++%%%%++++++
;/++%%////++$%++++//++/++//++%$X@H+%$X+///;;;;;;:::::;;;;;///////+;;+XHXX$%/+++%%++++++%$%+%%%+++//+
/+/;+$+%+;+/%$%+++++++///;/+/+%$%H@$%$%++//;;;;;:::::;;;;;/////;//;%XX$$$%%+%++%%%%%%%%%+///+++++++/
++$+/%%%%+//+$X++/+++///;;;//++%%$@HX%$X%+/;;;;:::::::::;;;;///;;/%HX$X$%+%%%%%%/+%%%+/;+/+++/+++++/
+%XXXX%+%+///%$$%//+///;;;/;/+++++%X@H$%$/;;;;::::::::::::;;;;;;+%$X$$$$$$$$%%%%+%$+//+%%%++++++++++
%X$$$X%+%%%//++$$%++++//;:/;;/+/+++++$HHX/;;;::::::::::::::;;;/%H@H$XX$%%%%%%++/++/+%$%++/;//+++////
+%$X$XX+$H+;;;//$X$+++//+//;/;;//+++;/$@@+:;;:::::::::::::::;;+HXXXXX$$%+%%%%%%%$%%%+++%++%+++++%+/;
+%X$$XX$%XX%/;;//+XX%++/++++//;;;/+;++$H@;:;::::::::::::::;:;;$$XXX$$$$$$%%$%$%+%%$$$$%++++%%++++++/
+$%X$%$HXXXH%/////+%$X$%%%%%+++%+/;:++$XH;:::::=::::::::=::;;/$$$$X$$$$$%%%%%$%%%%%%%$$%%++++////+%+
$X$$%++XH%X$X%%++//+%$$XX$%%%%+++++++%HH$:::::========:::;:;:+X%$$$$$$$X%%%+%%+%%%%%%++%++++++++++%/
%$X%$$$X$$$$XX%++%%$XXXXXXX$$++++/+++$H@%=;:::========:::;:;;+H$%$$$%$$X%%%%$%%%%%%%%+++++++///++/++
%XX%$X@$%XXXXX$%+$XX$%$X%%$$XXX$%+%++XHH%=;:::=========:::::;;X$%$$X$X$XX$XXX$X$%$%++/+++%%++%%$%++/
$HH$+$H@HXHHXXHX$$%++%%%++$$%$XXXXX%+H@#$=::::==========::::::+%$$$XXXXHH$XHX$XX%$%+%%%%%%%+++++%++/
X$$$$HXH@XX@XX$%%++%%$$$HX$X$$X$$H@@M###@:::=:=:==========:;;;+$X$$%%%%$$%%X$%$$X$%%$X%+%%%%%++///+/
$XH@@$%$$XHX@H$%++%$XXX$X%%X$XXXH@HX@MM##:=:=:=:========:::::;/$%%$+%$$$$X$$$%++++++%++%+++++++%+++/
$$XX$$$%XHXXXXX$$XXX$XX$$HHHHHHH@XHH@@M##;=:::=::========:::::/$%X%$XX$+$$$$%$%%%%++%%%+%%%++///////
XX$+%$XXHX$HHXHHHHX$$$$$X$XHHMM@HH@H@#MM#;::::=:::=======:=:;;+$%$%$%%XHX$$$+%X$%%++++++%++/++////++
@MHXXXXH@HX@@@@@X$%%$X$$HHHHH@@@@@@$$@###:::=:==:========::::;++%$$$%+$$XX$%$%%++++%%++++++++++////+
X@@H@@@MM@MM@HHH@H$%XXXXXM@HH@@@@@M@HMM#M:::=::===========:;:;%$%%++%$X$%%XX$%%+///+%%+++++///++++//
%$$$$HHHXXXX$XXXXHHHHHXXHM@X@MMMM@H@M#M#@=::::============:::;%XX$%++++/$%%X$$%%$%++/////+//////////
%%%%%$$++//++%$$$XXXH@M@@HXXX@MMMM@@##M#$=::::=:========:==:::/+$$$$$%+++$%%+%+%++++++++/////;//////
%%%%%%%%++%%++%$$$$$XX$%%%$XXH@@MMMM####/::::============:::;;///++%%%%%%%$%%XX+++++///+++//;;/%++//
%$$X$%/%%++++%%%$$%/:----===:;/+/+X####M::::::===========:==:;;;///++%%X%%%$X$%++/+%%++%+//+++///+++
%$$XXXXXXX$X$$$X$+=,-=---===:===::+MM##+:::::=============:::;;;;;//++%%%%+%XX$$XXXX%%$%%+///$%%++%/
%$$$$$$$X$%%%%%%/.,==,-=:;;;:;+%$//%M#$=:::::=============::::;;;;;///++$$$%$$XXXHHHX$$$%%%%++++%$+/
%$$$$$$$+%%%+/++/-=,--==:::;:/$%%+%$MH:;:::::============:::::;;:;;;;///%$XXX$$XXX$$$$XXXXX$%+/++$%%
+%%%%%%%+%%++///;:=----;;;;:::++%++$M%:;;:::::==========::::::;;::;;;;//;/+%$$$XX$%%%%++%%$$$XXX$$++
;////////;::/;///:,---==:;//+;;:/+/%@/;/;::::::=========:::::::;:;;;;;////;+%%%$%%$$$%%$$$X%$$$%$$$$
=:::::==:=-;///+++:,-,-,,-=/++//:/;/X/;;;;::::::======:::::::::::;;;;;;;;/;/++++%%%++//%%%XH@HXX$$$%
=::::::::=:+%//+;++;:,-:==-=-=:;/++/+/;/;;::::::==::::::::::::::;;;;;;;;;;;;+%++//////;//;++%%XHXXX$
:;;;::::::=//++++;+%+//;;;/++//:==:/;+//;;;::::::::::::::::::::;;;;;;;;;;;:;++///++/+/;++/+%+/;;%X$X
:::=:::;::::://++%//++++%/%%$$%XX%;::;;;;;;::::::::::;::::::;:;;::;;;;;::;:==:::;;;///+/++/;;:=:;/+$
+==:::;::==-=//+/////+++++//+++/%$XHHX%%+/;:::;:::;;:::;::;;;:;;;;;///++%%+/=--==--:;;;;;/:====:::;+
$+=://;:==::////+////++/++////;/+%$$$$XX$++/;/:;;:::::::::::::;;//%%%$X$X$$X$+;::=-----=-===:===:=-,
%$/;:;+%/+++++//+///+%+++//+/+;+++++////:=:///%$%%%////+;///+%%$X$$X$$$$$$$%%$$$%+/:--===--==:;/:=-.
/++;-,:;+%++++++/++/+/::;+;%++%++/::::==/://://%$$X$%++%$X$$$$$$$$X$%$%/%$$$%+%$$X$$/;:==:;/%$XXX$+:
:/;;/:==-==::/;;;;;-==:+/+;+;:===--:////;///;+%%%%+/+%//;/+/%%%%%+%%++%$$%+%+/;/%%/+/++%+++%$$%%$$X%
,,........... ...  ...,....,-,..,,-,,,.,,,--=,,-,,==:;:,.. .  ,......,......,......   .......    ...
,,,................,..,,...,,,.,,.,..-:+$$%+X%$XX$XX$$%%X+%;.,..,...........,,................   ...
,,,......  .. ....,,..,,,,,,,,,.,-==/XHHXXXX$%$$$$$$X$%%XX@X+%;-,..,,,,.....,,,,,..,...  ...... ...,
,,...,..   .. .,,,,,,,,,,--,..-==+X$$XXXXXH@X$%%%$$XX$%$%%+XXXX%+;-...,,...,,,,,,........,,,....,...
.,. . ..   .......,.. .,.,-,=;;+HX%%$XXXXX$%%$+$XHH$$$$$++/+%%++X$%/-.,..,,.,.,,. .  ......,,..., .,
,,... ... .  .  .-..,.  -/%%$$+XX$%XX$XX%XH%XH%$H$%%$$$$%%$+%X$%H%$H%/-, . .-,. ,, ....   .,..... ..
,,. ..... .  ....,. .,:$$$XHX$$X$$$$$$XX$XX$$+%$::++$%+%X%%%%$%;+/+%$X$%=,...,-..,.,...   .....  ...
..  .....  ...,,. .=+%++%$XH$$XX$X$+$X$$H$%$%X+-:X@%+HX%%+%%$$++$$$+//%X+//:-..-, -.  . .......  .  
,,..,...... .,. .-;/+%+XXXXHXXHX$$X$$$$XXX$$+/+$@$:%H/=/$XXXX$%$$$HXX%+$+$X+;=..,,,,  ......... .. .
,,,,,,..... ...,:+%$X$+$XH$$$XXX%$$$$$XX$X$+/+X%$%%%/=+X$$$$$$%$$XH%$XHH%%%%++/=..,,.... ...,,..,.,,
....,..    .  -/%%%$$X%X$XXHHX%%XH$$HH$%X%/%X%XXX%/=/X$;/+$XXX%+;;+%%/+%/+%%X%+%;. ,. .. ...,,... ,,
   ....... .,=X$$X%X$XHXXH@HXXH$X$$X$%XX%%%$%$X$;;%X$$+/X@XH%$+/$+/$$$$XXHH$$H%/%/..,. .. . ........
    .. -, .,+$$+$$%$%XXXX@@HHXXXX$$X$%$$$H$%XX%:$XXX/%$+$%+%//;;/::/+%%%HH$HHX$$$%;  ..  .      ... 
......   ,,:$$%$X%$X%$$XX$%$HX%$$$$XX$X$%%%$X%,+@+%$/$X;=-:-=+$%+/%@$$XXXXXX$$$$$$H:. .....  ..     
        ==-+%+%X$%XX$XXX$XXXX$%XX$X@HHH$/;;+; /%=:/+$X%/+%:/$=-/%$XX%$%XX$XHH%%$%+$$;, ......... .. 
    ., .+-/$+$X$+X$$$XXHX@MX/+$$%%%X$%%//$%/-==:=:HH/+%/;$;/;-:/++/++$X+XH$XX%$X$+/%X+, ..  .... ...
 ..... /-%H%/$$$+X$X$H$$$X$%%$X$%+$XX%$%%$+/;$+$H%/%+%+/+;=;:;=.-,-%$+//$X$HX$XXXXX$%X+......,,,..,,
,. .. =X:H:++%XX$$H$$X+%H%/$;$/$%X$XH%$$%XHXHXX+;==:++%X%+:;/%X$$%++/+/%$%XHX$$$XXH$$$$/, .,.... .,,
.. ,. +XX+-;+$%/HX$%%%/$%++;.=/+;$$%X%%XXH@X$%/=--==::/%::%$%XX+:;:==%%+%+++XX$XXHHXX%%%=  .  . .,,,
.  ,.-/;$X+;%H++H%%$$/++-+%//-;+X$$H%+XX%$HHXXX+;==%X%/=-=/+/$+;-:=+/+;/X$%X@X$$XHHXX%%$+- .. . ....
.  . ;/+/X=/%$;H+,$$+++==+--:;=+HX$+/+X$%HX$%$HXX%$H+---:=.-;+-:/%%HX$:%X$HXHX%$XXX$$$$%$:..... ....
.... ;/+:/;:%+;X:-+%=$:,==/,.:-$%X$=/+$HHHXXHX$%XXXX%%X%++/X%;=%HX%+;+;;+%HH@HXHX$$%%XX%%;. .   ....
,..,-/;+/+/-+/+/:/$H/X:=/;$ ,:;%%++/=+HH$HX@XXXX@@HXHX$X$$$$//X@X%$@XH@$$XXX@@@@HXX%+$$%%+- . ......
,  ---/$=%=:+/X:/;%$$/;//+-,/%-:-/H%-%H$X#HXXXXXHHH%%$$H%%;=;XX$$XHH%$+%++$/+$$XXH@H$$%//$:.,...,,,,
. .,--:;-/==$/H-:$X+++;++/;::%--:%H;,$HXHHHHHXXHHXX$$H@X$%XHHXXXX$X$;=/%XHX@@H$%$$$H@H$X$%/,,,  ..,.
   .--,%//:+%+H;:$X$;+/+$/%+:/--/M%--$@HXHHXX$X@MHXH@H$X@HXM@++%+%%:=++++;=;+XH@H@@H@@@H%+$:... ....
 . .=-,+-,:X//X%/X$X:;+/%;+H$%:+$H:+X$$$$$XX$HH$$H@@@HXXHHHHHHHXX+;%%:+HX$H+-;%$%%%$X$$X$$X+-.  ....
 . ,=,/H/+:H%%$$+HXH$/X%$%$X/+%$$$:$/+XHH$$@XX$XHMHXXH@@H@@$$@HX%+$%%XXX%::H@H++%XXXHX$XHXX%/, ...,,
  .,=:%$+%-+$$$$$X%XX/X$XX$X%+%$$X+%%%%$$$X@XHXX$XXH@HHHHH$XH$$+%XX$%+/+/==/:+@H++%$@H%%%$$%%= ...,,
  ,===/$%:=/XX$$HX%HX$$$X$$HX$%X$+/++%H$/$@%XX$%%XHHX$XHHXHHXXHHH$/%$/H$+;::,-/X@@XX@HXHXXX%%;. ..,,
...-://X%+%;/HXXH$X@%XXX$$X%%$$X$/+%$HX+%H$;+;/+HHX$$X@@$XHX%X@HX$X+/$///:::;/;=::$XXXXXHHX$%/,.,,,,
.  ,:/;%%+X$;$HH$HHHXHHHX$X$$$$%//$$$%++$X$H+/%%$%+/$++%$$%$XMH$H$//+$:;/:+//%$$XX//X@X$XH$$%/,.,,,,
.. ,=;/;X%%X%%H@H@HHH@XH$%XXX$$$%%HX$+XXX%XMXX@@X%++@X+%H$XHH@HHH++XX%//;=-,-=-:+@+$XHHHHHX$/;-.,,..
...,=;$;%$+/$XX@H$@H@H%X$%$XX$$X$%+;%%%%+%+;++$$++$+%$%%$XXX%XH%;;$%;+/;==-===-:;/+$$XH@XXXX++:.,...
.. .==+%/;$/:+$XX@HX@H$HHXXX$%$H$%%+$$%%/%$++/+%+XMX$%%%$$%%$H$/++%%+%+;:===;+/;$///%H@HHX$X%$;. ...
 . .-.;XX:+H+$X$%HH$@HX@HXHX%+$$+/$%%///;;///+/++XH$@$%%%%XX%$%%%:;$$;/:=,,.;%%+XX%X++X@HHXX$$: ....
 . .==:=X/;$+$$HHXX$HX$X%%$%/+$$%+%/+///+/;;;/:/++XX@%$@HX$%$HH$%/%+;+:::-=-;=+X%%$+%%$XH@XX$$= ,,. 
 ...-:-=++;%XH$HMHHH$HX$%XX++$%%$%+++///;+/;;/:;//%HX$HHXHXXXXX$%+$X%$X%::==+;::H+XHX$%$H@XX$H:.....
 .  ,,---:%//$++%+$X$$%;:+%%$$++%++%+//;;//;//;;;;;$X%$XXH$$XX%%H$+XH%%%%+:,.=H%%/$$$$%%XXX%X$;,....
.....,===:;=;%//++$$+%++/+++%%/+++%%+++/;;;:;/;//;;XHXHH@H$$$$+XH$@H%X%::=-:%;%XH+%$$$$$$XH$@%;-....
.....-====.=++//++$+/++%+++++%++++%%//;;;;;;;;;+/;/XHH@H@@XH$XXXX$XX%+/+X%;;++X$$XHHXXHH$HXHH%:,....
. ....-::=:;/;;+%%%+++;;/%%%%+/+/++//;::;;:://;///+%HH@@XHXX$XHH@X$XHXX$$//$%+;/$XXX%%$X$X%@X$/,....
,.,,.,,:=,=+$///++%++%/+///%$$%+/+%+++/:;;:;+/;/;+$/H@HMXH$XXXHX%+$HX@%%H%$+==,-::%$$%$XH@XHH%$-.,,,
,.,,,, -:=;+//+++%/++++$%+/+%%+++%%++/;;/;;;/////%%%@@HMX$%XXXXHHHXX$$$+/;%$$/:$;-HX$$%X@@HXXXX-..,,
. .,...=::;%;+++///+%++$$%%%%%%++++/;/////+/+%%//%%XHH$X%$XHXXXHHHHHX$H@X%X/===%$%%$XH$X@@X$$HX= ..,
  ....,=,=+%+$++//+%%%%$%+%%%$$%++++/+///;///++//%%$$@HM@$HHH@XHX$XHH%+/%%+/=/$XH@HHM@HXXH@HXX$=  .,
  ....--,=/;+%+++/++%$$$$%%%%%%%%+%++/;//;;;;///+%$%+HXHHH@HXMXHHXXHX%%--=-,,/X$+%X@H$HHXHHHXXX;   ,
  .,. -:=:::%%/+++%%%$$$$$$$%%%%+%%%//;;//+++++/++$+%XXHM@MHXM@@@@@HXXX$++$++$XM@HXX@H@XHHXHXXX/  .,
. .,...-=;++H%%%+%$$$$$$%%%$XXX$%%$$%%+//:;////+++$%+$%H@XXHX@MM@@@@H@HHH+;$@@H@@@M@M#@XXH@HX$$:...,
...,..,:::;+H/+%+%%$$$$$$$$XXXXX%%$$%%//+;;/+/++%%%%/%/$HHHHXXH@HX@HHHHHXX@X$XH@@X%+:+$H@HHHX$X;..,,
.,,,...-;;;%$/%$+$$%%$$XH$XH$$$%/+%%++//;;//+///+%%++%//$$X@MH@HHXHHH@HH@XHH$@M@$+//:-=;HXHXH%X;.,,.
 ......,=:+XX%%$%$%$H@X$$+%X%+%/++++%+///;/;///;/+++%$++%;;+$HX$@@HH@HHHH$HMMMX++$XH%%:-=/HXHX$, .  
  ... ,--=/%$$$HXHXXHH$$%/+/:;//++++%+///;/;:;////;;+++%$+%%HM@%%%XHMMHH@@@@HH%/H#####X/-=XHX@X,    
  .,,.--=:/;+%$X$$$$$%%$%++/:/+/////+/+++/+;//;;;/;/%//+/+%+/%HHX%XHH@M@HH@MH$%%@M@@X$M#%./H$X$-   .
  .,,.-.-:++%$$$++HHX$%%/;//;/;:;/++%$HHX%%;::;//;;/%++/;;%%//$$+;%$H@H@X@@HH$$M###MM$X@@==XX$%,   .
.... .=-=;/%$%$$+$X$%+%%+;;;;/;+$HHX@@MMXXH$+;;+%/+++%%%//;/;;+$H%::++X@X@H%%%%MMHHHHH$$M$,+XX$.   .
... .-;:::;;+;+%%%$X++$$%;;;/%X@MMM@#@@M@@#M@X++%+%%;;/;:/;++///%XHM@$HX$X$+H+H##@M@HH@XH@,=H$+ .  .
. , ..=:///:;=;+$/%X%+++/;%%HMM@@M###MMMM###@HXXX/+X%///+;;//;//;;+%+X@XH@H$M%###H@H@HM$XM;=@X:... .
. ,..+/:;;;/;:;$%/%$XX%$%%@@M#@@@@@X$++$@#MHMMM##HXH%/+/+;;;;;//;;+/+M@HHMXXX%#MMHXXHHMX@M+-%@,.....
. ,.=HXX$+:::;:X$/+%%XXH@H@#@@M#@X$+;+$%%$HMXMMMMMM@%+%+//;;;;//;:/%+$MM@@%HXX#####@@HH$HM/-/#=.....
.,../MH@H@H+;:,%X++%+X@MM###M#MHX+/;/%$$XXX$$@###MH@X%/;;;;:;;;;//;+++X@@H+$$@#MMM#MHHHX@#:-;M;.....
.,,./@X#@MHHH$++$$XHXH@#MM#MMMX$$/;:////+%%+%$XM#MMMX$X+;;;:;;;://;/+%%H@@$$XM#M@H@#M#H%HM===@: ....
..-.:@$@XMMMM@#HXHXH@MXM#H##M#MMM@@X@HH@X++%$X$%$@@@X%%+///;;/;//;/+:;$$$$$%$M##MH@@##X+HM;/=H-. ...
..-,,@/==:+M@MMM$;/XXMH$$+:/@#@#H%%XXH@MM##HHX$%@H@HH$;/;/;;;;;;/:++/$%$$+%+$H##H$M@#M@+X@%:%X......
.,-,.;X+;;;:X#@#M+:X@H%+/+;;XM@MMM##MM@@@####HM@X$HX%$$$;;;;;;::;;/+;++%X$X%$%X##@@M@#HX@X+:/X,,....
.,,,.-++/+H$HMMMMM;$MHXXX%;:/X@M###MMMHXH@@@#MM@MM@H$X$+//;;;;:;;//+/++/%$X$X+%XMMMHM#+$@H%:+$ .   .
..,,,,-$@XH+$XHMM@X+@$X$X+/+$HM#HHM#M@$%$+/%X@@@@X@#@X+/+//;:::;:;;/++//++++X%XHMM#M#M$HX@+=X$ ,. ..
..,,,-.;X@XXX@##MMH%MHH%$X%/XMX@@@X%$$//++$@@$%%;;++$HX%/;;:===:=::;+//+$+++X$XH##MM#@X@H#+:@/ ..  .
 ....-,:XMM#HM@+@M%$@HXX%+/+XM#@MM$;;/;/%$@##M@#X%H%%%+$+//;:=::=:;:/;/+%+$%$$XH###HHM$HMM+;H-,..  .
 .,,.,-;#MMMM#@$@@%H@X%H%/+HX%H@@MMHX%$HHHHHX%+%HHX$$%/%;//;:;;:::;;/;/+++$$%X@@##H;=;/@@$/;X.,.....
..,,.,-,X@@#@%:+@H+H$%;/;;+%+;/+H#MM####H@@@H%%+XX%HX$$$;:::=::=:::;///%%+%%$XX@MH+:;:+M$$/XH ,,...,
,...,,--=H+@%:=/#=$MH$++;++;/+//X@MM#MMMH@MHH@$XX$%$%$%%/;;::::=::::;;/+++%%$+%@@XX+;:/@X$=@$ - ....
... .,-=,$;%:;%XH/$H+/+%+%%;+%+%X@@H@XXH@M@$$@$XX$$$+%/;;:::::::::::;;;///+%X%%@@H@H+/+H$::MX.,.....
.... ..--++XH@H#//@H%++%%//+%%%%$@M@MMM@H@H$X@X$%%X$+%/::::::======;/////+++$$X@MH$$%%$%:,$HX, .  ..
..,,,-,,-:+XHX$#;+@HX$%+%//%%%$XXHM@#MM@@@HHXXHX%XX$+%//;:::=--=:===::++%%+%$$%$@@HX$//:;X#$HX;,.  .
,..,-.,,-:+%%/XH=%$+%X%$$//+%%%X$X@HMM@HXXH@H%@X%X%+//;;:;=::=::;:::;;:;+%%%$$%HM@XH@/+:+M$@HH$/;,..
,,,..,.,-+/X%+H$;HH$H++$+;/+%X$X$HH$@#@$$$H@HXX+X@+$%/;;:==:::;:==:;;;;+;/++/$HX@@@@X+++X+/%HH%%+/,.
-,.. ...,/:%%%XX/XXX$/$%:=;%%XHXHHH%@MHHX%%$%X@+%X/%+//;:::========;:;/+/%%+%$%H#@@M$+$$+;+%$@X%/+;-
,..  ..,-/::;+$%%X%+%++/;:/$+/+HM@MHX$%XX%%$+%X%$X+%/;;;;;:==::::==;:;;;/%++$$%M#@@H$%$+;:/+%M$;;;//
...  ...,/:::+%:$$%/%+;;:=;;//=+#@XXX%+%%%%$$%%%$++%;:::;====::::=:;;;;;;+/+++$M#MMMH$+::;;/$M/::=:/
...  ....;:;;%+:H$$$+;;:===-/$;=HMH@X$%/+++++$X%++/+;;;::====::====;:;+/;///%%$@#MH@%//::+/;$H;/::==
.....,.,,:-==+=$X%%+:;;;=-=;%$%%+###H$$%%%++/%%%+++/:;;=:===:::=:==;::/+;///%$%@H%X%///=:++;$$=;:==:
   .....,:-=:;-X$+%=-/:=/%H@XH@M$H@HMH%+$%++X%%%++%+;::=:===:::::::;;;;/;;/;%++H$/H%%$/=;+;/$/=-=-=;
  .,,.,.-;::+::$$%X;:/;;$XXX$X$@@%M@HMH$X%++++%++/+/;;//;;:::=:;::::;//;;///%++HX+%+++;/%%:%H;/=--==
...,...,-::=/-+%+%$$%;%$X%;:;//@MX@#MMH@@X$%+%%%+%$+/+++/;;;::;;::::;;/;/++%+%$$$$%%+/;/%%/%H;;:====
 ... ..,,=/-;.;/+%$$%;$$//%/;%XXMH$H#M@#MHHX$$++/$$+///;;/;;;;;;;;;;//;;;/+++%$++%$$%%++++/+$::=--==
 .,,...,.,/;+--/+/$%%;%$HM####MMM@X%@@M#MHHHXX$$%$$+/++++;/;;;;;:;;;;////++++%$$%+$%///%$$+++;:=----
...   .. ,:;//-$$$$$X$H###M@HHHM$$%+%$X@MM#MXXHHX$$+//;;/;/;;;;:::;;;;;;/++++%$X$+$$+//+%%+%//::====
     .,.,-,:;X:XX@H@XM#@@HHHX$%+%X+XX$+XMM#MMHHXHXX%/;;;/;;;:;:::;;;;;:;/+%%%$%++%$$%$$%+//X++;;====
........,,,//+$X$@@#H@@HXX@M@%XX+HXX#HXM@HMH#HXXH+$%++/://;;::;;::;;;/;;+%%%%$$%%++++%$%/%:H;+/;;:=:
........,,-./X$@HM####@HMM@HM@MMXM@XM@MM@@@@MHH$H$X$+++/++/;;;;:::;;;///+%%%+%%+%+%+%%+///:X;///;;:;
..  .....,,,:%$@M##@#MM@HH@H@@HM@M#H@@@H@M@#HH#XHH$%+//;//;;;;;:::;;//;+++%X%%%+++%%$$++%;%$////:::;
..  .......=,:X%MMMMMX@$@@XX@M$HXHMM@@@H@MHMHXMX@X%$%+%+/;;;;;/:::::/++%%+%$%%%+%+++%+/+%;X%++///;:;
..  .......,.;$;@X@MHXH;%%X@$H@@$XHM@XHHM#M#@$H%HX+%%+%+////;;;;::=:;//%+/%%%$$%%///+//%+;X;;+;;//::
..  .  .....-=+/H%H@+X$;%;$#/%XH%X+H@XHM@@M@M@@HMH$X$/%+////;;;:;;;/+//++%XX$XX%%+++%+/+;+X+/%/+;/;;
..... ...,,,-.=%;%H$;HX+M%/@$+%X$%:$@X$HHXM#@@@@@$$HX;///;;;;/;::;;/+%+%+%X$%$%++//+$+/+:+%+/+;;//;/
.,...,,,,,,,..,X;/H/+@@%$%$HM%$+X+/$H@@HHXXM#MM@@X$$X+%+%///;+;;;:::/+$$$XXX$$$+%%+/+;:+:$+%+++;+/;/
.,............-;H:H/X@@XXX@@M$XH@XXX%XHX@@HH#MM@@HX+++$/++%+;/;/;;/++/+%$XHXX$+++++%/++;$%/%//;;//;/
.,.........,-,-;@%@%HM@M@@M@MHHM@H@MMM@X@M@HM@MMM@HX%+%//+++/+++;;+%%+%%%$XXHX%%+///++X-H/+%//////;/
... ........,,/MH$H@H#HM#@MH@@MM@@H@#####M@@M@M##@@MH%%$%+++/%+////+++$XHHXXX$$$%+%/++//%+++//+/++//
..  ....... ,:+@$@X@@M@M#MMMMM#MMMM@M@@M#MMM###MMH@#H%+%++++/%++++++%%+$HHHX%%$%%++/%+=H;%++/++//+/+
 . ........,-;+HH@H@MHM#M@@#M@@#M##MMMMM@@@MMMMXH@@@$$++%/%%++++/+%$XX$XX$XHX$%+%%;/%:$X+/+%+%+/;///
.....,.....,:+$XH@@MH@++X%+@XH@#@M@MM@@MM@@MMMMM@X$X$$%%%+%%/%%/++%%%$$HXXXXX$$%+%//;,X;%%%$+++/%+++
........... -/%$XXX#XH%;=;/;%#HM@#MMM@X$HHHMM@HHHH%$%%%%$+$%+$%+X$%$XXXHXHHX%%$%%+:+:+H++%%$%%//+++%
.........,,.....,.-%$%/%$+H@@M@MMMHHX@X%XX%XX$$$$H%$%$$%+%$$%$%/%$$@H$HHXHH$%%/;+///;@$%+$%%XX%%++/+
............,. ,--,-%;=X#$MH@MMM@HXXX$$$$$%+%$$%%%+$$HHX$%$%%%%$X$XH$XHHXHX$$$+%+:%:$H/%+$+$%%%%%+/+
..................-,:::/$$H+X@H@@@HH$+$H$$$+%$$$$$$X%$XXXXX$XXXMHXHH$HHHHH$$X%+$+:%:@$++%XX@$%%+++%%
...   ....,  ..,,.,,,/==+@HM@HHH@@XX+%X$$$%%%$$$$XXH$XX$$$X%H$XHXH@@XH@XXH$$H%///+/%$/%/$%+$X$+++++%
          .  .  .,,. ;-,/@HXH@M@MHXH$%%++++%$$$$%+%XXHHHHXX$HXH@@HXXXH@XXXX$X%%+//:@+/X%@+;/X@$%$+++
        ..    ....,-:/%.:%$%HHXHH%%%+/++///%$%$X$$XX$XH@H$XXXXHHHHXXXHH@HXHH$++/%:H%;/$$@%H%=+H$%XX%
      ...  ..  ,-=/+XH$=:++%%//+X%%%+++;;++%+%$$%$HX$HM@XXHMM@@@@@HHH@HHHHHHX+/%%:H;%+%X+$#M+=+X/$%+
.     .,,,,,,,=/$XH$X$X+=/;:::/;++%%+%%//+++%XXXXHX$H@@@@HH@@@@@HHHHHH@HMMX$%+$@;$/;%+X@+MM@#X:+X$%$
.....,,,,..,:+$HHXHHXXM$=/=-//:;//+%+++++++%%$$XHHXXH@#M@@@@@@M@HHHHXXHH@H$%/+@+/$;//;$%+M#MH@%-+XX+
.,,,,-,..=;+$XXX@HHHXX@@=:;:;;:++/%%+%$%+++$XXX@#MHHM@HHM@MMM@@@@HHHHHHX$%%%X$M//X/%++H/X#M###M+-%H+
.,,..,-:+%$$X$+XHHHXXXX@/==;+;;/+%$%%$X%%$HMHHH@#@@M@MMMM@MMMMMM@HH@HHHHX$$$$X+:H://%$H;@#H+;$M#+.%X
-,-==++$X$;;:=++%%%H@@%X$,/=;++%%+X$$HH%%XHX@HHM@@@@MMMMM@@@@@@@H@HXXXHX$X%%XX;X+/+;/H+/#@=-=,:M#:=%
,-;+$$XH/;+/+XHMMM#@;+X$X=/;:+%XX$HX$X$$HM@@@@@#MMMMMM@@@MMMM@M@H@@H@HHX$@$%#=;%%$;%XH/X#/:#H%-/@M+=
+HH$%X+$+XHX$++#/;@;;H/+#/=%$X%XHXHH$HXXM@HM##M#MMMMMM@@MM@MM@@@H@@HHX%X$$+X%;M+;/%$H%+##//@ :-:X#@:
$%$HXX:$@@+;:=%+/$/=M$$MH$+H$@XXXXHHHHHHHH@M@M@MMM###MMMMMMM###M@@HXX%X@@%$M=X+/%%/%$/HMM+%@.-/-$H#$
X$XHH#@M@;/X=:%,X::XXHH%X@@X%@H@@@H@MH@M@M#M@M@MM##M#M@@@H@@@M@@HHXXH$$$X%H%/$/+/++@$%M@#$$@H%X=X##$
X@$XM/#X%:/+:-++=/#M@HH@@@@@M#MM@#@MMMMM#M@MM#MMM@MMMM@@@M#MMM@HHHXX@X%$$$H=H%//+%+X+XM@M@@$@%:-H#%%
HHXH@%M%+;%%+@+;HMMHHX$$$+X$XM#@M#MM##@@@@@MHM@M@@@@MMMMMMM@M@XHHXXHHXXHXX++%/+/%$%$/@M#@##MHX%@MM;@
H+XMHH$XXHH%+/%@#HX/+@$+$$@X;+MH@MM@##MMM@#M#M@MM@MM@MM@M#MH#@HM@@@HXXX$#;=H/;;/+$$$+M@@H######@M@/M
XMHH#$+X%HXXHM#M$/$/X+/H%$+=:X##@M#MM##MMH$;%X#M@##MM##MM@MHH@@HMMHH@XX@+-H+:+:+%%H/M#@M@MMMM@HH#;/H
$@$@$M##MMM#MHX%/+$:$/+:==:$@@@@HHMM@@HMMM$/@+M#MMMM@M###@M@@@HH@HHM@$M@,$X++%/X$$$+##MM#M@@MHHM@=$$
@$XHX#MH%%H$//++/+/;:--=;HMHHMM$$HMM@HHX@HM@X$M#M@HMHH@MM#@M#HH@HXHHH@H.%X+/%/+$$H+@#@#M#M@@@H@#$/@%
X$@$#M#XMX%%%%$%//=-,/+HMM@#MH$HX@MMH@$M@@@H%##@#@@#M@@@@M#@%@H$XHHH@#=;H/+;//%+XXX#MM#MM@MM@@M#=+$+
H@XMHMX/+%%%+%/;==:/XXMMMM@HX$$X$XMM@@H@#M@@#M@##M@@#M@M@X@#HXHXHXX@X=-X%/;/;%$+@:@#@#MM#@M@@M#@:X++
XMXM/XXX++%+;=,=/$$@#MM@HX@H$+%$%X@MM@M$#@@@@M#MM#HHMH#H#@X%#HX$@XHX-/X%////%%$%H/##M##MM#@@@M#%%H/X