''''`.`'..'`'..''`....'.`.'...'.`''.``
'...''`'.`'..'`.. ...'''``.
...```..``.`.'..' TTTTTTTTTT WW WW IIIIIIIIII NN NN PPPPPPPP OOOOOO RRRRRRRR TTTTTTTTTT SSSSSSSS ''`'.`'.'`''
..`.``.'.'.``'`'. TTTTTTTTTT WW WW IIIIIIIIII NN NN PPPPPPPP OOOOOO RRRRRRRR TTTTTTTTTT SSSSSSSS .`'.`'`'`'.
```.`..''``'...`. TT WW WW II NNNN NN PP PP OO OO RR RR TT SS ..``'.
.`.'`..`''''``'`` TT WW WW II NNNN NN PP PP OO OO RR RR TT SS
....'.''`.'.`.''. TT WW WW II NN NN NN PP PP OO OO RR RR TT SS
.'`'````...`'`'`. TT WW WW II NN NN NN PP PP OO OO RR RR TT SS
.``..'.`'`'.``.`' TT WW WW WW II NN NNNN PPPPPPPP OO OO RRRRRRRR TT SSSSSS
.```.`.``'``'`''` TT WW WW WW II NN NNNN PPPPPPPP OO OO RRRRRRRR TT SSSSSS
`'.`''``.'``````` TT WW WW WW II NN NN PP OO OO RR RR TT SS
`.'.''`````'..`.. TT WW WW WW II NN NN PP OO OO RR RR TT SS
....''``'```'''`` TT WW WW WW II NN NN PP OO OO RR RR TT SS
'``'.`'.'```.``.` TT WW WW WW II NN NN PP OO OO RR RR TT SS
.'````'.```'''''` TT WW WW IIIIIIIIII NN NN PP OOOOOO RR RR TT SSSSSSSS
'.`..''``'.''..`. TT WW WW IIIIIIIIII NN NN PP OOOOOO RR RR TT SSSSSSSS
`'.`...'...'''''
'`'`.''.``.``'' tt ii
...`.''```.'`'` tt ii
.'`'``.``.''`.` tt `
'`..`.`'.''``'' tt `` `.'..`''..`
''``'`....`..`''... ssssssss tttttttttt oooooo rr rrrr iiii eeeeee ssssssss `.`'.''.-::-:-:-,
..`''''.'```'.``..`` ssssssss tttttttttt oooooo rr rrrr iiii eeeeee ssssssss -,::,,,,,,,,,:-:-
.'`.`'..'.'``..` ss tt oo oo rrrr rr ii ee ee ss -:::-,,,,-::--:-'
...``'`'...```. ss tt oo oo rrrr rr ii ee ee ss ::--:-,:,--,,`'`
``'.`'`.`'`` ssssss tt oo oo rr ii eeeeeeeeee ssssss --,-:-:,-..`.
`'`..'`. ssssss tt oo oo rr ii eeeeeeeeee ssssss :-,,:,,:`...`'.
''..''`.`'..`''```.`.'.. ss tt tt oo oo rr ii ee ss ,---,---``..'.'.`
`.'.'. .`'..```.'.''...''''.'`' ss tt tt oo oo rr ii ee ss ,::,:,-,''.`..'`'
''`.`. `'.`'.`.``..`.'`''`.'`..` '... ssssssss tt oooooo rr iiiiii eeeeeeee ssssssss .'`'`.''`'.`..`'`
:'``''`''`''`''`.`''`''`.''.'`` '. `.'..'` ssssssss tt oooooo rr iiiiii eeeeeeee ssssssss ''`'.....
''`..``''````.```'`'.`..'''```' ..'''`. .'`.'`'`.'
''`.`''''..`'.'.'`.''''..',-'.' . `.'.``.`'-,.'..``.''.'`.' .``.. ``'''`..'''`.``.'... `.'``.`''.'.
'`'`.`...`'''.`...''.`.`.'.'.'.`'H. ..'``.NNMW#HMWHM#MMMMWHMM##H#HHMW###MMM###M#H#WMMHWN`.'''.`.``` `'`.`.`...'`
`....'..''`..`'..'````'.````.'#M:#,'MWWHWHMMHHMW#MMMM#MN:MMMH,"MN-#WMM#HM@#H#MMHMHWMW##M#M#WH#M#HMMMW'.` .''...`' ...'```.:---,
``'.'''``.````.,,,::,-:,,,:::,##MHMMW#MWH#MW#WWHHHHHM,#MMMHMMH=WHH#WW#WNMWWMHM#WHMMMMMHMWHWMM#WHH###MWMWMWMWH-,-H::'`.. `'''``..`.:-:-,
,::-,-.`.'..,::,,=~~=;=~~~~#;MMHH#N#HMWM#HHMWMWWH~==NWM#MMW:"@#MMM#W,,@WMWMWW-@M#WMMWM`HHHMW#M#WWMMHM#HMWWWWWMMW#,.''' ..`'.'.':,-,
:,:--:-:-,-:::-,;;~~;=~=H~~##W#MM#WMM#M#HW##MWMW#M=~#MM#M##N;;H#MWW#H:,HMMM###`@HWNM#W.'#M@@WW`WMWMWMWHMM#NHHHW#MWW .`.`''.``'``-
";==:...`-,----";=~"~"~;WW#MM#H##W#MWMH#HWH#HWM#HW###MWHWM#MWH#HWMWHMMMH#MWW###W@MMMHMMMHHMWW##@MWMMHMMMWMM@HMMMHMW# .''`''..::,'''
=~~~,-,-:-,::::"""=;"=;=#WMMM#MMM#####H#####M#HW#MMMMMW#WM#MMHH#MHMHM#MMMMM#WMMWMH#H#MWMWMWHHMH#MHWMMMHW#H#HMM##WWW#MM#'' ``````'-,,,::,
";~==;"~="=~=,-,-:-:--,WMWMMWMMMMHHM"###N##N#@#M@NMMH#HHHHMH##HWHHHMMHW#HMH#MM#HW##WHHWHMMHHMMHHMM#WMWMWWMM#MHMMM#WMHMH.``' ..``.`--,:,:-:
~;;==~~=~"::,,,`...''`:MMMWW#W#HM##----'```.'`''::,--:-,:--:-::'...'.```'`''`-::,-:,,`'..'.`'-:,:MH##MWHMMM#MHMWWWWM###.`'..'`'''.```'..``.'.`..'..'`.
:,--::..'.'`.`'`'```,:-MM#MNHH##MMW,,,--::,,---,-::,,-,:,,::-::,::-.`.''`.',-,--:,:-,:-,,,:,:,--:,-MMN@MMM--#M#NHM##W#MW`.''``''...`....'.`''`''.''`''
-:,-,-'``.`'..`'.,-,--~MWMMMW###-#H:-----,:,:-::'`--:-::..'.-,,-:-,,--::::,,:,:,--,,,,;~~=";"==-,:-MW:MWM#'@W##,MMMHHHMH,-`..'`.``'``'...'..`'``'`'`''
=~=---:,`.,:--:,:~"=""HMHWHMHNMW@MW-````'`.`'''`'```'`..'`'`:--,::---,:,:-,,--,-,::--:~";"~=~;=,:-:#W@HWHH:HMW-MMH#MM#:M:,,`''''.''``'```:-,:,:,-,,:--
~=;";;"::-::,:::,~=;~~HHMH#HM#HWWH##`'``'.....'.`'.....'''..`'`'-:,--::--,::.''::,,---::-,,:-,::--:#MWH##WHMM#MW@W#MWMMMM,-`'`.''..`.''`:,,---,,-,,-,,
~=~-:,-:;""=;"="==;":-WN@HW,.,M#`HMW,,-,-::--'...'`'`.'''.``.``'.`'':#,,--:::::,:-,:--:,:,,:-,::::-:HM#M#WHHMH,::#MMM:-WM:``'`.`'...''``'.`...'.`'`.``
-,-,"~=~"==,,,:-,,:-'#WH#HW#MW##M=WW===;~;-::,,`'`'''N,-:''`.''-,::,@H,:::--:::-::-,-:-:-::-:,,-,'',HWWMMM#HWWM::WHWH,WMM-````'```'`''.`..`''.'.'`''.`
~=;"";=";~"~~,:,,-,''WMMWMWMHMMM:=WM,-:---:::,-,-:-,:H:------,:-,:,:MN-:::-,,-::::-:::-::,-,-:,-`..'#WMM:MMWHW@#H#WMMMMWWW'..'...``..`.`..''`'`'`'.`''
;,-,-:-,-:-M#--::-,::MH#MWWMMNMHN;MH,-,,:::,:--:,-:,:W.''':--,--,,:,#M::--,:::,-,-,-----,H,-,,,-'.'.MWWHNW#WH#@M#WMHM@MW:H'`.'`.`'.`''.``'.```''.'`.'.
;=;;";~="~=@M;-,---,MWMH##M-WMWHHHMW::,-,:-,:::-,,:-,H:,:,,,,-,-::-,W"-,:-:,-:,:,----,-:WMM--:,-,::,WWHWHWMMMMM:,#WMHH#@#M,`.'...''``'```...```..```..
;~~=~"~"=";#"N"""=;~MMMM#WHWMWMMMM##:-::-:,-,,::-::-##::,:::---::::,W::-,,MM@---,,,:::,:WWM#---:-:::MWWMMHMH#MMWHHWWHHWMMMH'`.``'.'...'`'..`.'.``'`..'
---:,WN~,,,WMW-~~,:-WHMMWH@MMMWMH#M#-,-,::,::,--:,,,NM,::,,:,,::,-,:#:--::##M::-,,---,,-;MM-,:,---::HWMWNM##HMH:-#HW#H#MMW#`'```.'''.'..`'`.`'.`.`..''
,:::WM#WHWWMWMWWM,:~HHMM=;HM##HMN:MH--,,,,,,,,----,-#M::,-::,::,,-,-W:--::MMW,--,:,:-,-:M##M,-:,--:,#WWMWWHW##,M#MHMNMMWWMW:'`'`'`'MHHMH#-@::,:--N:--N
=#M:H#M##HWWHHMHW~~HWHHMMMMNMMWM-,WHN-,::,,,,-:-:#MHWMN--,--:,,,,,--#,--:-HMM--@M:H,-,,@W##W,:,:,--,MM#WMWMM#M:,WWHW~HH#M:M#-M-``.WWMMMHH##MHWMWMMHHHM
WHMMHMH##MMM#HWMM#HHM#MH#@MHWMMM@MMW#----,WMW@#HWMHWM#HW#,,-,---:MMWWM#W#HM#MHW#MHMWMW,M@#MMN-,M::WMW#MMHMMWMMMW,HMMMW##MMMHHMMMW#HMM#HMMMMH#HMMMM#WMH
MMH#WWW#HHMHMHMMMMM#MMMMHMH#M##M#MMMW:#-:,M#WHMMMM#W#HHHWW##W#HH#MHMWH#WHMMM#WHWMMHMWWWH#HMM#WMWWM#MMM#HM#HHWWWMMHMH#WHM#MWWMHMMW#HM#MHWW##W#MMH#M#WMM
W#MWHWHWM#Heaoc#HHWMM##MHMMWW###W##HMHHM#MWMHHH#HM##MWMW#HHHMMH#HMWMHWMMMMMW#WHWWHM#M#WH#HMMWMWM#WHWMM##HHH##M#MWW#WM#MMHMH#H#MWW#MMWWMMM#M#HMWHMHMWWW
#MMWHMHHaoaeMWocaMM####WMMW#MMMMMMHMHMMMMHHM#WHWMHM#MMHMM#HMM#M#HMMH#WWWHM##HWWWH#H####MWMWHMHMMWWWWH#WWMMHMWM#H#@MN_-,,@M#N,--.-.-.,.-,..@_``..N_.`_.
#MMMMW#eeeooacecacaHMWMMMWMWM#WMMM#HMHH#H##MWMMHMMWMH#MMMHMH#MMM@@MMHW_HM#WWM#HWMW~-MNWWM~_NN#--@W,WMWW...N.W,-..#,-.--,-N-M.-.--.W,,-,.,.W_._.__`._..
WHMMWMoo00@@O0O#aecHHHM#M###MMMWWMWHWW#MH#M#WHM#WWHWMH#WM#W@@WM####N@M@o#@NN.,#MM#WM#,@M,N@WNW@#NHNN##M@W,NNM,-,N-#.-.,-,,.#,-..-,.-,@-.--.-_W_.```__.
WMMMHMoHQW@@H@M0#oWcMM##H@@##He#HM#MHWHWMM,@MMMMMWWWM@###NM@##WHWWN@MWN-N-#M@#HW#M##-..-,M,MM@#W@,,,.N@WWHM@MM-M@N.--N,W@M@-WM-,.M-@-@###_..`W__`#_._.
MMM#MWecMQQ@@@O0cc##HWaWHWMMHcMMHMWMMWHMMMNMWW-NMWMWH@MMNHN#M#W,NW#HW#W-#M#MWWMo.-MHHWWNN@W@#@N#WN.-@@@,M#oM-,@--,o.@WW@.@@@--@N,.,NN--..N.WMW@N--W.``
MW#MHWMccHQQ0OOoeHWHMM###@W#WMH#W#HMWNWM-WM#MM@-@MM@MMMWMHM##_NNN@MMW..M,W-.WN#NMM,,W.##W-#@MWWM@#@.WM@,,-.-@,@-W,,,#MN,,-.-,.,#@No#,##,#@...N--,NW`_.
MWHMM#MMHaaeoeeWMMWHWMM@H#MWMWHWMHM#M###HWM~_N_#HWHMMW#HM#M#MMHH,.,-NM@M#..@W-..W@@-@W--M-M.-.N#N-@W,-W-M#M,.W@WN.NM#M@,#a,.M@.,W..#-o,,WMM-...NN_...`
HM##HWHWM#WWMMMMMHWMMHM#MMHMMWHMMMWWNM@@@NMMMMH#NMW.-M#@H#NWH@#MM,-,MM@@M@N#.-,...NMNM#MW#-@..@NH#-..WN..,.M,-,c@-#aM,W@N,oc,WN.-@.-,M@.,-,@,MoMW.@_.`
#WH##M#MWMHM#NMHHWM@M#M#WHMMHHHM#MWWWM#W#WHM#M#WM##NHMMHNMWWNWHMNH#WNM.,WNH.@M,#NW-@@#.@W@N#-.-M-M-#.WMWMW-W@###MNMM--N-NM##o..o,-.#,,MN#,oW,M#N-.#M-,
MMMH#M#WWW#MW#MW#MMWHW@@MM#H#WWHMM#WMW#MNWMHW#MWMMW#HM_---W@@M#H.##HN-,WM,-MW#W-W--#HM@M@,WW-W#-#.#,,M#MMMW@#,.#M#NN,NW.-,##@.-MN,....WN,-WMMHM#M#-W.`