$$$$$$$$$$$$$$$$$$$$BB$BBBBBBBBBBBBBBBBBBBBBNBBBBBBBBBBBBBBBBB$BB$B$$B$$BB$$$$$$$$$$$$BB$$$B$$$$$$$$
@$$$$$@$$$$$$$$$$$$$BBBBBBBBBBBBBBNNNNNNNMMMMMMMNNNNNBBBBBBBBBB$$BBBBB$$$$$$B$B$BBB$BBBBBBBBB$$$$$$$
$$$$$$@$$$$$$$$$$BBBB$BBBBBBBBBBNMMMMNNNMMMM#MMMMMMMMMMNNBBBBBBBBBBBBBBBBB$BBBBBBBBBBBBBBB$BBBB$$$$$
$$$$$$@$$$$$$$$$$$B$BBBBBBBBBBBNNNBBBNNNMMMMMMMNNM#MMMMMNNBBBBBBBBBBBBBB$BBBBBBBBB$$BBBBBB$BB$$$$$$$
$$$$$$$$$$$$$$$$B$$$$BBBBBBBBBBB$$@$BBNMMMMMMMMMMMM#MMMMMMNBBBBBBBBBBBBBBBBBBBBBBBBBB$$$$BBBBB$$$$$$
$$$$$$@@$$$@$$$$$$$$$B$BBNNMNNNN$@@@@@$BBNMMMMMMM########MMMMNNNNBBBBBBBBBBBBBBB$BBBBBBBBBBBBB$BBB$$
@$$@@$@@$$$@$$$$$$$$$$BBBMNNNB$$BNMMMMNNNMMMMMMMMM#############MMMNBBBBBBBB$BBB$$$BBBBBBBBB$B$B$$$$$
@@@@$$@@$$$@$$$$$$$$$$$BMMMNBNNMNN$0@BNNNNMMMMMMMMMMMM#M####MM#####MNBB$BBBBBBBBBBBBBB$BB$BBBBBB$$$$
$@@@$@@@$@$@$$$$$$$$$$BNNNNNBBN$00C@@BBBNNNBBBBNNMMM############M#MMMMBBBB$$$BB$$BB$BB$B$$BBBBB$$$$$
@@@@@@@@@$@@@$$$$$$$$BNMMNBBBNNB$@0@@0CX0$BBNMMMNMMMM####M########MMMMN$$B$$$$$$$$$$$$$$$B$$$$$$$$$@
@@@@@@@@@@@@@$$$$$$$NMMNNNN$$$0@$@0%%X@BB$BB$BNMMMMMM#M######M##M###MMN$$$$$$$B$$BB$$$$$$$$$$$$$$$$@
@$$@@@@@@@@@$$$$$$$$NMMNBBB$$@@@X%X@@CCX0$BBNNNNMMMM#M#####MM##MMM###MNB$$$$$$$$$$$$$$$$$$$$$$$$$$$@
@@$@@$$@$@@@$$$$$$$BMMNNNNN$$$0CC@$C//C$B$$$$$BNMMMMMMMM#####MM#####MNBBBB$$$$B$$B$$$$$$$$$$$B$$$$$$
@@@@$$@@@@@@$$$$$$$NMMMMMNBNB@@$@0%%C0@CCCXC@$$$$@$BNMMM###MMM######MB$B$$$$$$$$$B$$B$$$B$$$B$$$$$$$
@$@@$@@@@@@@$$$$$$BMMMMMMMMB$BB@CC@@@0C%%XCX%XC@@$BNMMM##MBNM#MMMMM##NBB$B$$B$BB$$$$B$$$$BB$B$$$$$$$
$$$$$$$$$$$$$$$$$$BMMMMMMNBBNNB@@$$@0XXC0@@@@@CC0$$BNMMMB0MM#MMMM#MMMNB$BB$$$$$$$$$$$B$$$$$$BB$$$$$$
$$$@$$@$$$$$$$$$$$$NMMMMMMMMMB$$N$$@0X%%/X0CX%X%%X@BBNBC0MMM#MMMM#MM#NBBB$$$$B$B$BB$$B$$$$$BBB$$$$$$
$$$@$$$$$$$$$$$$$$$BMMMMMMMNBBNBB$$@C/+++%%++/++X000CX%$NMMMMMMMM#MMMNB$BBB$$B$$$$$$$$$$$$$BB$$$$$$$
@$$@$$@$$$$$$$$$$$$$MMMMMNNNNNMNN$@0X+^!^^!+/++%X%//XCBNMMMMMMMMM#MNBB$$$B$$$$$B$$$$$$$$$$$$$$$$$$$$
$@@@@@@$$$$$$$$$$$$$BMMCX$NNNNNNB@C%+:':!!^+^+//+/X00BNMMMMMMMMMMMMMBBB$$BB$$BB$BBB$$$$$$$$$$$$$$$$$
@@@@$$$$$$$$$$$$$$$$$$C//:%$BNNB$0%^''::!!!^^^/%X@@0$BMMMMMMMMM#M#MMBB$$$$$$$$B$$$$$$$$$$$$$$$$$$$$@
@@$@$@@$$$$$$$$$$$$$$$/%::^/0NNN@%^!!^!^+++/XC0@@$BNNMMMMMMMMM####MNB$B$$$$$B$$$$$$$$$$$$$$$$$$$$$$$
$$@@$$$$$$$$$$$$$$$$$$0^'%X/+0NB0/!:!^/%XXXC0$B$NMMMMMMMMMMMMM#M###M$$B$$BB$$$$$$BB$$B$BB$$BB$$$$$$$
$@$$$$$$$$$$$$$$B$B$$$$^'+^.':BN0^'.'.'!^%0C%0C$$BMM$CXCC@NMMMMM#MMM$$$$$$$$$$$$$$$B$$B$$$$$$$$$$$$$
$$$$$$$$$$$$$$$$B$$$$$B0''..:+0N@+'....'':::^+/0@BMNX^^^^^CNMMMMM#MN$B$B$BBB$$$$$BBB$$$$B$$$$$$$$$$@
$$$$$$$$$$$$$$$$B$$$$$$$0:..:^%00/!''.....':!!+X@$0/!::'..^0MMMMMMMB$BB$$$$$$$$$B$$$$$$$$$$$$$$$$$$@
$$$$$$$$$$$$$$$$$B$B$$$BBNC^^^/@@C%!''''''::!^+%/^^^:'.. .:XMMMMMMN$$$$BBB$$$B$$B$B$B$$B$$$$$$$$$$$$
$$$$$$$$$$$$$$$$B$$$$$$BNMMMMM%C/++!:''::!!!^^!!:!+%!..  .:/$MMMMMB$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$$$$$$$$$$$$$$$$$$B$$$$NMMMMMM%:':!:::::!!^^!:::!+%/:. ...:%0NMMMM$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$@
$$$$$$$$$$$$$$$$$$$$$$BMMMMMMMX:''!!:'::!^^!!:':!+^'':!^^++0BMMMMB$$$$$$$$$$$$$$$$$B$$$$$$$$$$$$$$$$
$$$@$$@$$$$$$$$$$$$$$$BMMMM#MMC:'':^!:::!^!!!::::''':!^++$0@M#MMN$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
@@@@$@@@$$$$$$$$$$$$$BNM#MMMMM$:'':!+^!:!!!!::''':!/%%%%%0CBMMMMMB$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
@@@@@@@@@$@@$$$$$$BBBNMMMMMMM##%'::!^/+^!!!!!:''^X0CX%XC@X^@MMMMM#N$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$@
@@@@@$@@@@@@@$$BBNNNNNMMMMMMMMMMX::!!^/%/^!!!!!!++^!!!+/%X+.^BMMMMMMB$$$$$$$$$$$$$$$$$$$$$$$$$$$$@$@
@@@@@@@@@@$$BNNMNMMNNNMMMMMMMMMMMNX!!^^+%X%^!!!!!^+^^+X$BNM0'.XMMMXBMN$@@$$$$$$$@$$$$$@$$$$$$$$$$$$@
@@@@@@@@$BNNMMMMMMMMMNMMMMMMMMMMMMMN0/++/%XX%+!!!!!!!+XXX0$NB+ !$M+0MMM$$@$$$$$$$$@$$$$$$$@$$$$$@@$@
@@@@@@@BNMMMMMMNNMMMNMMMMMMMMMM#MMMMMMB0XXCCC@@X/^^^^^+%C$NMMM@'.@00MM#MNB$$$$$$$$$$$$$$$$$$$$$$$@@@
@@@@$$BBBNNNNNNNMMMMMMMMMMM#MM#MMMMMM#MMMNBNNMMMMB@@00@$NMMMMMMNC/NNMM#MMMMN$$$$$$$$$$$$$$@$$$$@$@@@
@$BBBBBNNNMMMNMNNNMMMMM#MMMMMMMMM##MMMMMM##M##########M##M#M##MMMMM####M####MMB$@$$$$$$$$$@@@@@@@@@@
@$BBBNNNNBBNMMMMMMMNMMMMMMMMMMMMM###MMMM#M##########M#######M##MM#MBN###M#####MM$$$$$$$$$@$@$$@@@@@@
$$BBBBBBBNNNMMMMMMMMMMMMMMMMMM##MM###MM#M######M#####MM########B%X0C$MMMMMM#####M$$$$$@@$@@@@@@@@@@@
$$$BBBBNNMMMMMMMMMMMMMMMMMMMMMM###M#################MM#######MM!:+'::$NMM#######MN$$$@$@@@@$@@@@@@@@
BBBNBNNMMMMMMMMMMMMMMMMMMMMMMM#MM####MM##M####MM#M#M#M#M###MMM0.'''':XNMMM####MM##N$$$$$$@$$@$$@@@@@
BBBBNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#M##MMMMM####M#######MMN@C!'':::^+CNMMM########MM$$@@$@@$$$@@@@@@
B$$NMNMMMMMMMMMMMMMMMMMMMM#M#MMM#MMMMMM#M#MMM#####MM##M$X^::::!^+%0$NMMMM##M####M##MMB$$$$$$$@@@@@@@
$BNNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM###M#MMMMMMMMMMM0!'':!+%XC@$B$@@@$BNM#########MMMB$$$$$$$$@@@@@
BNNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNN#MMMMMM#MMMMMMB+...'!+//%X/+^%XC@BNMM############M$$$@$$$@@$@@@
NNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNMMM#MMMM#MMMM0'....''''':^X@BNNMMMMM#############M$$$@@@@@@@@@@
NMMMMMMMMMMMMMMMMNMMMMMMMMMMMMMMMMMMBM#MMMMMMMMMM/'.........'+@NMMMMMMMMMM#############B@$@$$@@@@@@@
MMMMMMMMMMMMMMMMMMMMM#M#MM#MMMMMMMMMMMMMMMMMMMMN^'........''!@MMMMNNNMMMMMM#M#######M#MN@@@@@@@@@@@@
NMMMMMMMMMMMMMMMMMNMMMMMMMM#MMMMMMMNMMMMMMMM#M$!''......'^^!C@CX/%$MMMMMM#MM##########MN@@$@@@@@@@@@
MMMMMMMMMMMMMMMMMMNNMMMMMMMMMMMMMMMMMMMMMMMMM0:''......!++!!!:::+BMMMMMMMMM##M######M##M$@@@@@@@@@@@
MMMMMMMMMMMMMMMMMMMNMMMMMMMMMMMMMMMMMMMMMMN0C:''''''':++!::!^/++@MMMMMMMMMMM########MMMMB@@@@@@@@@@@
MMMMMMMMMMMMMMMMMMMNMMMMMMMMMMMMMMMMMMMMMMB/'''''''''++!::!^%C%@NNNMMMMMMMM#M####M##M#M#B@@@@@@@@@@@