######################################################################
######################################################################
######################################################################
######################################################################
WWWWWWWWWWWW##WW################W###WWW######W##WWW###################
DDEEKKEEKWWWWWWWWWWWWW#WWWWWWWWWKKKKKKKKWWWWWWWWWWWWWWWWW#######W#W###
DDDDDEDEEEEKKKKKKKWKKKEEDDDDDEEEEEDEEEEEEEEEEEEEEEEKW##WWW#WWWW#WWWWWW
LLLfLLLLLGGGDGGGGGGDDDDDDDEDDDDDDDDDDDEEEDDDDDEDDEEEEEKWWWWKKKKWWWWWKK
fLLLLfLLfLGGGLGLGGGGGGGDDGDDDDDGDDGDDGDDDDDDDDDGDDDDDDEEEKKEEEEDDEDDDD
jLLLLLffffLLGGGGGGDGDDGGGGGDGLGGGGGGGLLGGGGGGDGGDDDDDKEEEEEDDDGGGGGLLL
jGLfffffffLLDDDDGLLGDGLGLLGLLLLLLLLLLLLLLLGLGGGGGDGDDGDKEDGLGGLLLLLLfL
jjfffffffffLfGEDKDGGGLGDLDGLffLLLLLLfGDLfGDLLLLLLGGGGGGGGGGGGGLLLfLffL
jfGffffLffLLLLGGLLLLDGGLLLfLjfjfLfffffffffffLffGGGGEGGLLLGEDGLLLLfffff
jjfLLGffffLLffDfLfLLDLLGLffffLfffffjffjjfLffLfLDEEKKGLLGGLGGWLLDDLLLLL
tjjjjjffffjjjfffLjLLLffjfjfjjffDLLGLffGLffLffLLLGEDDfGDEEELGLLGfLfLLLG
ttjtjjjfttfffLLffLjjffjfjLfGGfGGLGGLjfGLDGffGDGGKEEEfGDDLDDDLLLLfffGLf
jjjittjfjjfjjjftfjjLfLLGGGLLGGDDDDDGffjjjjjjLGGGDfLGfDffLLLfLLffffffff
;;;it,:i.;jjGf:,jt:LLGGDjGjGLGDGDDDGLDGDGGGGGGGjLjDDEGGEDGGLGLLffLLLff
:,,;t;;j;::tiijL::,;LLjfLfjLGGDLGEELGDEDGGGGEEDLLtttjjGDDKKKDGDDDLGLGD
,,,;,j,tt,:jiiLt,::,LGjiGDGGtjGLDGDLLGLGfLLGGGEGEittjjjjjLDWKKKEDGDGEE
:::t;ti,;;,;jiff,t;,LLL;tLLffLtfjfGLGGGDGGGDDDDDDGLt;ttttjfGEDGEKKGEGD
.;iitt;it;ttj;Lti,,,tjLfGGLLftjjfGDDDGGDDDDDGGGGGDLLjGiiittftjjffjfGfj
.::;ttjtj;:tj:Ljt:;ijjDGGffLjjfLLGDGGGDGDDDDGDDLGGGLGLjL,iiiititttfLLG
.,::;it;fi;;itfffjftLLLijftttjjffGGLDGGDDDDDDGGGGLLGLLLfD,,:;;;iiiiitt
.,,,,,i;tLLtLLLGftjLffLj.ifj:;tfffLfLDGGDDDDGGGGGLLLLLLGLft:::,tti;;;i
.,;iitttj;ii,,ijjLffffGLt;ti.;t;ijLLGLLGDEDGGGLGGGLLLLLLGGff:::,;;itti
i;i;,,,;;iittttLjffffijLi.;; ..:....:::,LGLffLEGDLjjfLLGff,:.::,::;
;,;i;;;iit;;jffLffffff.,f: . .....:.::.,,j,.,tjjjLLGLGtj ..;;;t
,;;;;;;iti;tLfLLfjjfjjffffi;:. ... . .:tjijjtjjjLGfGLfj...,;i
,,,;;;;,;ijjffffjjjjtjjjjjjjjjtfjjjtjffffjjtLjfLfjjttttttjLfjfGjij..:,
:,,i;,:itjjLffjjttjfjjtjjLtjjtffjjjtjffjtjjjfjffjjfjjtttttjfjfjjtit,.:
,;:,;;ttjfffjfjtttjjjttjLjjjjfttjtjijjfjjjjjjjffLfjjtjtttjtffjjjjjf,t.
;tt;;;jjffffjfjttttttttLLttjjjjtjtjfjjjfjtjjjffLfjjjjtjttttjffjjjjjti;
,,;,itfffjjfjtttjjjjtttfLitjjtttjjjtjjjfjtjtjjjjLfjtjjtfttjtjffjfjjfjj
,;;ijfjjjjfjjtjtjtjtttfffLijtttjjjjfjfjjDfjtjjjffjjtjtjjjtijtjjjtLjjft
,;;tfjjjfjfjtjijtfitfjjfLGtttttjjjtjjjjjLjjjfjftjjtjjtjttji;ittjjtftfj
,::jjffjfjjtjjtiitttjjtttiitjttjtLtitjjjLjfjtjfjjjtjtjttjjtiiittjjjjjj
. jfjftjjitjttitttLttftiitfjtjLfftitjtjfjjtjjjfjjjtjjjtttjtt;ittjjjtt
. .tjiiitjtjiitjjijti,jittttjtjtjitjjfjttjLLtjjjttjttjtttti,iittttt
.:.tiiiiitjitittitjt;ijiittttjjtfttjjjtjjtjfitjjjttttjtjiit;:,ittti
..;;iitfttitttiifjiiittttijftjjtjjjjttjijtjjjjttttttjjtijii.iiiit
. .,;;iititjti;;tt;;ttjttttjtttjjtjjjttjjjtjtjjjtttttttjifti;,iii;
. :i;iiiiiji;;ijttitittitttiitfjitff;itfjjtttttttitttjjtjft;i,it;
...,,i;iiiti;titjt,;iitttttiiitffjjjjttijjttjtttttiiittjjtjtt,i;it
. .,,;;;iii;;;ifitiiit;itttititjttjjfititLtjjitttttiiiiLttjftt;,;i
. . .;;;;iii;;;itj;ftt;tittitjiittt;tttjiitttttjttttiiiiitttjfjt;,,i
: : .;;iijii;;i;tt;titiiitiiitttttifttjttittjttttjjtiiiiiitttjjf;;:,
. .;,i;;;;;;;if;;;tttiiii;iitttiifttttiiiiitttijttti;iiitittjtj;,.
. . .:,;;i;;;;;it;;;;tii,;tiiiittiiittttttiiiitiitjtti;iiiitiittji;,
.. .:,:t;;,i,;ij:,;;ii;i;it;iiiitiitiitttiiiiittitjtti;;i;iiiititi;,
.. :,:,,,;;;;ii;,;,ifti;;itiitiiiitiiitiiii;iiittjtii;;;;iiiiitit,;
. ...:.;,,:;;;;fj;;,jji;;i;;iitiiiiiiiittiiii;iiijitti;;;;,;;iiiiitt;
. .::,:,,;,;i;:;f;i;i,i,itt;tiiiiiij;itiiii;i;ijiiti;i;;,;;iiiiiiti
. ..:.::,,,,,tii;i;,,;;;i,t;;iiii;iiti;itiiii;i;tiitiii;;,,;;iiiiitt
. ...::.,.:,;;;;,i;i;fi,;t,i,,;ii;ii;ij;iii;;;;i;ttiiti,i,::,,iiiiitt
.....::.,.:,;,,.,.i;iff;,;;;;:ii;i;jifL;i;;;;i;,,;t;tii;;,,:;,;;ii;ii
. .......:::,;,::;:,;iit,iiit;,,;;,;t;,jti:ii;i;;,;i;iii;,,,,,:;;,;iii
..:... ..,:,;,.:;,:;i;;GLL;;t;;,;ii;ti;;;i,;i;,;;,;i;;ii;;,,,,,,:,,iii
.:.....:::,i::,ii,,:;fitii;j;j,;i;;t,,;,;jii;,;;,;i;;ii;,,:,,;,,;;;ii