rrssssr2###M###@@#Mi;rrrrrrrrrrrrrHMM#M#######MHAAAGX3&AHMM#####M&h3339hAM#MM#MMBAisrrrrrrrrrrrrrrrrrrrrrrrr
r:;;;;:S@#BHBM#@#M@@5::;;;;;;;;;:r@##MM###MHA&9&BA&3rs2AMM######@H#@@@@@@##BM##BM@X:;;;;;;;;;;;;;;;;;;;;;;;;
r;rrrr:h@#BHB##@@B#@@#s;rrrrrrrr;&@#M##@#MA&&H#@@#B3SXH#####@@@@@5A@@@@@#@MM##@##@@X;;rrrrrrrrrrrrrrrrrrrrs;
r;rrrr:A@#BHBM##@BH#@@@9;;rrrrsri@@####MAAHM#@@@@#Bh5GM######@@3:.S#@@@@###B##@@##@@5:;r;rrrrrrrrrrrrrrrrrr;
r;rrr;:A@#HAHM##@#AHM#@@#s;rrrrrB@###M####@@@##@@#HXi2&AAHABAi,  ,;M@##@#MBA###@##@@@2;;;rrrrrrrrrrrrrrrrrs;
r;rrr;:H@#BAHBM#@@AAAH#@@@G;:::s@########@@@#######HGXSiSSs;.  ,::,i@@@@@MAhH@@@##@@@@h;:;r;;;;;;;;;;rrrrrr;
;;r;r;,B@#BHHB##@@MHHHB#@@@@s..2#GHM#####@@#@###@@@#MGSr;,   ,::::,r#@@@@#AX&#@@#@@@@@#9r;;:,,,...,,,:;;;;;:
:.,,,,.H@#BHB###@@@M#MMM#@@@@X.r&5GB##MM#@@#@##@@@#2r:.   .,,,,,;r;i@@#@@#H2G#@@#H@#@@@HXSsr;;;:::,..,;;;;;:
, .... A@#MMM####@@@@@###@@@@@G;55hAB##B@@@HB@@BXiir.  .,,:::r5GAG2A@@#@#MB3&#@@@h9##@@@933X5issrrrr;::;;;;,
, ,... 9@####@##@#H#@@@@@@@@@@@Gi5HBBHBB#@#h55rrGh&#@#X;:;;X@@@@@#ASA@@@3MAGB@@#@#9B@@@@@Ghh95isrrrrr;;:;:;:
, ,,,, 5@@###@@@@#AA##MBBBB##@@@@@MMMMAAM@#@X   2@@BiBX,.,;2G2MGA@#:S@@MXBHB#@@#####@@@@@hX332irrrrr;;;;;:::
,.:;::.r@@@#@@@@###MAh3XX22X9A###BM#@@#BH#@@@5.  ;rss;... ;;..::s;,.9@@BXHH#@@###B###B#@@HGG3XSsrr;;;;r;;;;:
:::,,,  #@@@###BHHAG9XXXX339G&AB####AGA#@B&AMG:.       ., :r.     .;@@@MAMB#@@MMM#@MHhB@BHAAAG95r;:::;::::;:
:.;,,,. 2@###MHAA&hh939GG&AAAAB@Bs:.   .s@#2;,;;,.  ..,:: :5;..,,;r#@@@@#MB#@@MHM@@@G3G@H&AHAAA9Sr;,,,,,,,,,
;,;::::.S@##BBHAA&GhhhG&AAAAABMi.    .,,.:@@: :rr:::::::: .i9::;riH@@@@###M#@@###@##AGB#Mh2GhX33XSr:,,,,,,,.
;:;;:,: r@#BAA&&AAGG&&G&AAAABB: ... ..,::,:@#.,;r;;;;,,:;;3@A:;s59@@@@##@@###@##@####B#@#A2XX222225s;;::;:;,
:,;;;;;:5@#MHA&hhGGG&&AAAAAH#s ....  .,:;:,2@5.:;;;;;;;::rSi;XiiX@@@M#@@@@#BM@#########@#M9XX22222X5s;;::;:,
, ...,:,2@##MBAAGhGG&AAAAAH##:.,,.. ..,:;;;:@@.:;;;;:;r:::.,5XsXM@@@&H##@@#hX############AXXX2X2SS5rrr;;:::,
. .....,;@@##HAAAAAAAAAAAHM@#,,:,,...,,::;r;9@;:r;;;;::;;;;S5r9##@@@HAi.i@#S2#@#########A2XXX2X2isr;:;:;:,,,
,.:,,:,, G@#MBAAAAHHHHHMBB#@@:,:::,,,,,::;rrS@B,rr;;;;:,,:;:;XMAH@@@Mr   :XHHH@###HM####h3hh9X25s;:::,,,:::.
:,:::::, :@@#BHAAABBBMM##M#@@;,:;::,,,,::;rrs@@:;srrrs25sii2AHAG&@@@2.,:.  ,;A@@#@####@@&&&Gh35ir;,,..,,::;,
::;;;::::.i@@MHHHMMMMM######@r::;::,,,:::;rsr@@i:iii5Xh99B##BHA&3#@@,,::,,,,:A@###BB##@BhG93X5srr;,......,:.
:,::;;;;:, s@@###MMMM##MMMM@A:::;;:::::::;r2r#@i,s552XSr;rs3MMH&X#@H.,,:::::;M@BMAAHB#A9AG2irr;;;:....    . 
:.,,,:::,.  ,9@@@#MM###MMMM@i:;:;;;:::::::;2SM@s,r22is;:;:,,;232i@@5.:::::;;r@@BAHAHHA&AAAX25s;;:... .. .., 
,.::,,,,...   ,X@@@@@@##MM#@;;S,:;;::::::;;rA@@:,rSXir::;;;:,,::r@9.,::::::;i@@@###MAh22h&Ah5r;, .......... 
, ,,,,,,,,..     ;9AGB#@@@@@;:A::;;;::::;;;;A@s.;ri32srrrrr;;::;S@s.:,,,,:;;S@@@@##HAA9Ss5S;:,............. 
,.,,::,:::::,,.        ,rXA@A,Xi,::;:::::;;;s@::rs5h3Ssrrr;;;;;;5@X,::,,::;;S@@@@@@@@@#Br...,.,:,....,..... 
:,::::::::::,.,,...         95;X:,::::::::;;rMA;rs2h&5;;;;;;;;;;r&h::::,::::2@@##@#H#@@@@3  ..,::,,,,,,..,, 
,.:,....,. .,........        ;sr;::::::::::;;9@i:ri2@2:;;;;::::::r9::::,::;:2@@@MGr.:2X2@B, .. .,,,::,,..,:.
. ....,,,,. .,..  ....        :sr;:::::::::;;i@&,;;s@9:;;::,,,:::;G;::::::;:2@#M2:,:  ..2;..,....     ..... 
.   ...,,,.....,,,..     ..    :Sr;:::,:,:::;r#@:,:;9&,::,,,,,,:;;&r,:,:::::5ASr,  ,..  ...,,::,,,...     . 
. ....   ...............,,..    ,rr;::::,:::;;h@s.:;iG::::::,::;;:Ar,:::::;:5MX;    .,.,,:,,..,::::::,::,,:.
, ,,,,,...........,,........,.....rr;::::::::;5@3.:;iA:;;;;;:;;::;@;,,::::;;SBh; ,,... .,,,,....,,,,:,:,.,:.
,.,,.,,,,,...... ............,,,,,.rr;::::::;ri#B::;i@s:;;;;;;;;rM@,,,,::::;iHs,::,,,,.....,,,,,,,,,,,,.,,:.
, ,,.......,..........,...,,....:;,,sr;::::;;;sA@r:rA@hsrrrrrsiXA5:::::;;;;;iG:.::,::::::,,:::::,.,::,,..,:.
, ...........,,...... . ......  .:;.:s;;::::;;rSBHSir  ,:,:;;rr:. :;;;;;;;;;i5,.,:,,:::,:;:::;:,:::,,,,,. ..
,.,,::,,,.,,,,,,,,,. .   ......  .,::rr;:::::;;rS#9.             .;;;;;:,,,,:i;,:::,,,,.,:,,:;:......,,,,...
..::;::,:::,,,,,.,:,,,,,.......     .:sr;:::;;rrr5s  .....  ..,,::rr;;,.:sXG&G5.,,,::,,:::,:::::,,,,::::,...
.   ................. . .             .;::,:::;;;rr;,......  ...,,::::iA#@@@@@#X:,,,... .......,,,,.....,..