/*
	:.;.. . . . . .  .:,,..........:r..,.                                                 ..::r;r;r;r;r;r;;;;:;:;:;;:   . ... . .   ,:;:;:;:;:::;:;:;:;::,
	                               .,,.:,                                            ,,:::::,:,:,:,:,,.,.,...........                ....................
	      .   . .   ,zIZ999IL,,..           . . ...                        .rzJLzzIJJzzLcLLrr;r;r;;;;:;:::;:;::::,::::  . . . . ..,.,;;::::::::,:,:,:,::;.
	         . .    jILcLr;;;LLLrr;;,,.                  .,.             zB$BkFFJJzcrLrrrr;;;;;;;;:;;;;;;r::,:::,:,,,:,  .   . ..,,;,;::::,:::,:,:,,::,::.
	,     . . . .   SL;:;:;;;;;;;;r;rrL;r;;:,..     ..,;cJjL.         . .rr,,.::;rccJJzccrr;;;;;;:;:;:;:;;;,:,:,:,,,,,z.        .,:,,::,:,:,:,:::,:,:,:,:.
	c;cr   .        FI:;;;;;;;:;:;;;:;;;;;rzczcL;rrLzjr;;r;rcjZZc:                   ,,rLzICFIzJzIJjFZIIL:,:::,:::,,,,c,   . . . ..,,;::,:::::,:,:,:,:,:,,
	r,cc,           ;B;:;;;;;;r;;:;::::,;;:.. .;zrJObJeZZZeIJr:.:;L         .             :J6B#BH66S6eSeeL:::::,:::::,L.    . .      .;::,:::,:,:,:,:::::.
	;,rc.            H6;:r;r;;:;;rrL;Lzjzcr;::,;;ZJerzjjzr,,;Jcr.            ..  ,:,          ,Jb9ZFccLIFZ;::;:;::::,,c.       .     :::,::::::::;:;::::,.
	;.LL:   .        .$e::r;rLJzJzzcCKbSZJzzjS9crFF;zzJcLzCJ;..:Fbkc,             .:c;.          ,zIFzL;LIj;;;;:;:;::,JC            .:;,::;:;:;;;,:,,,,,,.
	;,:Lc,            ,$C;::,ZJzzIC969KzrIZkOd .JL6ILFLKz.,rzZJ;..redkc;.            ,Lc,          .;FjzrLLL;;;;;;:;::L#I           :r;;::,,,,.......,.,,.
	;,rcz.             r$ZLcJzIIK69ZZZIJSeekS  cc:9ecK;:SF,:,.rJIr,.:J6jcJL            .LCJ           ;FC;..;;;;;;;;;:;:Sz         .:,...      ...,,,,,,,.
	c;rL;.   .....      I#eZICZKCKjZeZCeCZKO   Z:r9S;ZC.r9c,;;.,:Lr:..,KbrLS;             JB:           ;Fc;,::::;;;;;:;,;.                . ..,,,,,,,,:,,
	.     . .......     ,bIIZCZzKOeSZJCjZIG;  :J,LGk;zB:.ZZ:,LL,:,:,::,.F0J.jJ  .          ,$F            IHbIzrr::,::::r:          . ....,.,.,,,,:,,,,,,
	   . . ... ...    .IZFIjCIzbDZkKzzZZJjK   Lz.JOS;.dC.rZ;;,cr::,::;;: r#9,LF, z,          Bk            :H#dd69KZFzLL;c,      ....,.,.,.,.,.,.........
	. . . .......    LbZjIFCzck#zFKJLCCJJzJ.  c;,ZkcL ZB,.J;L;,rr,.:;::;r.;Gd;;z: ZJ          HH    .        I8KSKOHDB#88OBL .....,...,.,........ .....,:.
	  .. . . ..    :ZKIFJIZzcKkLCKFLJFcJzLL,  zL.GL::,r$Z,,;,F, ;r:::;::;L:L6Or;cz.Ck:     .   $H   Lz        ;6Fz;,.,,rLLcc.....,.,.... . . ....,,,,:,,.
	. ,.. ...     JKjzJIJFZLe;;K9zjcI;Lcc;c:  e;r9,,:,.k#c.,,zz .:Jr,:::::rLJS9c;rFzjkF     .   @S   #z        :SLL;:.              ....,...,,,,,,,.,..
	. ,.   .     ZZJcJFFzbc;.LZGzcCrL:cL;:rr .k:Jj.:,:.ZeG,..Le  ;:Zr,:;:;,rcZK9c;;Z6zK6.   .,  :@;.,c@L    .   JbczzIJJc;,              ..,,,,,.,.,..
	. .         eFcLIzJIec  bG9I;zC:::c::,;L .6,k,,,:,.cSJK..,O  ;,,eL,,::;,;zee6;r:zkJjd;   J;  H@.k:HG,   ,d   KSzJzJzJJFJJL;,.             ..,.,..
	   . .     ZzLLZJJFz  ,Z#9Z.,Sj,,;;:,:;r ,CLJ.;,,,.;e,Jk, K; L,,,Zc,,,,;,;IbeZ;z.,ZCFOz  Fd, ;@jJ;Fd6    $H   8FczzJzJzzcJczzzLL::,.           ... .
	. . ...   FzrLbJJz, .JcF$e..J8L.,:;,,;J; .6Z, z:,,.,Z.,rk:Jz :,,.,Zz;:,,;,;eO9cLF  ISC6c,8Z#  $BZrL6HI   9$S  cdrrL;r;LrLLLrLrLrLrLrL;;::..         .
	     . . zz;r9Jc,  ;Se.99  FdS,,,::,.rj:  dc..cc.,,,z,,.,IbZ ,,,,..jJc:,:;;L90ZrJZ  rSjbZjJHj k$jFI9KG,  GS0L ,OBdSCFz;;:;;LrL;r;;;;;;:;;;;;::,:,,..
	        ,J;rdj,  :;:ZZ;J .6HbF,,:,,,.;e., I.,.cZ. ;L;.,,,.IC :,.,,,.JJJ::;;rIBbrzIZ  ;KJZzzIB.LDZJFZKbZ  kCZd:Cr$BBBBHHSjL;:;;r;r;;;;:;:;::,:,,,:,:,:.
	        crLZc  ;zL..KD: reJrkC.,,,,,.;Z,..L,..;e, .SFLLzL;zJ K;..,,..LJZrrL;cd9cLJZC  ZCIzcJZF:8ZJJZZZO  SIFZKZ:60H8G88BBB6Zc;:;;r;r;;:;:;:;,:,:,:,,,.
	       LzLL,,;czF: .Kc.ZKc..GZ..,,,,.:e,..r:. LJJ..F9,:,,.c; LIJ: ..,.rJKrLLrSdLccJZ; CFFzczICIZSzJCeJd..ZFIICC,FH0H8d8OGOHH8CjL:,;rLr;;;:;:::;::.,,,.
	     .;z;JJ,r;:cj,.L;c,OJr ,6z.:,.,. .C, ,,L. rJJ: :I..,,,c,.:.;cJ:..,.:ceccLekcrzzIj rjJJcJJjJjezzZFIS;LjFFJJz.L6ZGb9kO996dOH8BbJ;  ,;;;;;;:::::,.:r;
	  ,,rrr,:k: ;,rLSzz;C# IZ  rcL.:: .. ,Kz  ::, ;;cJ. c,,,,.c.;.. .,rr:...,;Fzze6rrczzj:;IJcccJJccKzJCFCjJJcjJzJz rZ:JHkkKSS6b96dOBBBC;,::;;;;;:;:;:;Jr
	:....::.cJ ,..zZdz. :0.c. cz:F,cc....ZJj:  ;L.,:,Jz .;...;L,         ,..  ,rcCeL;LLzcc;JczLczZLcZzJZFezFrJJz;JL.LC,,c8dkKSeSKbk9bdOD8OJr,::;;;;;:LJ,
	    .c,,Z,.   KzH.  ,d6 ,ekLIZzLz . rCFzZ, .jLr,..cz,LL:;;,.rce669BH8OSzr.  ,JZ;r;LLcLLcLLcrJerLZcjZeJcrrJzr;c;,zL,,,,k8OSbKSekKKebSOdBGkJr,::;:Lc
	    c; Lc. ..LJr9,  .jc;Oj,..;;JL  ,zcz,rZ, ,;rJ:..C8Kc:;K@@@@@@$$9SSH@@@@$KLJj;;:;LrLLrLcLrjS:zjJeKCLr;LLL;:r::;:,,,,.L8HbbSkeKZeZKekS9O8dkz;,;c
	   :L .L;  ..JzJ9,  Z9ez.; ...rJZ  :,:z:.,IL.,.;cr:,.,LB@@@Ze$$$KcKzFZj6$@@@zzJ,;,rrrrr;crL;bC:zKeeCI:;;LJL,;::,:,,,,,j, eB9kSkeSKSZKZKZKK69GOKF:;.
	. ,,. .c,. ..SFZe:.jLSLc;r,....:J. , .,zr..;Lr;,:,,,,:$@$c  B@@@@@@@@@G ZF$..I:::,;r;;,rrL;LHc:F;:,,;z:;IC::::,:,,:,,;,GJ ;8dbSkeSZKZeZeCZCZZk6GH$.
	. . : .J,.  :89ISJ.  JI.Lrr   ..rr,L:...rc;.,:r;;;...Z@S    $@8dIB@8,..O@;, rJ,L,,;:,,L;r;:C6,zCJFJJ:LLJS:;::::,,,J,,:, @G  OHkKKZSeKZejZCZFZFZ6$,
	.  ., .j.   ;#eCcK   LJ. :;:  ...::;c; ..,:;;r;;.;:,.;r  .. ,@;   .:   ez  :F:r;.::,.Fr;;,L9z:6IcFJJz.ke:;:;::,:,,I,..; ;$$: eH6KKZeZZZZZZZZCeOd.  .
	    , ,L:   cBZ;;O;  ;J.  ;O$$$9OOHZ:   ....,,rLr:;;,....... :6c;,:LjL6c..,J:;z.,,.,6C,:,;eZ;FkFZzzc:,ezc:;::,,,,.e,..;, ,SG: Z8bKKeKZeCZZZCSHF     .
	   ., r;;   cBJ.Jde  :z  $@@@$jD$6jd@@b,.........,.,,,.,,,,:,..6$DGB9F:,.,zr;I....,Ob,.,:FZc;;FKZFJF;zjJ:::;:,,;.,S;..,r  zcI. KdOSSeeCeCZZ6G;     ..
	. ..: z.r   ;K:c9;br  I 8@@L,  @@BG9SS@L:...........,.,,::;:;::.,,. ..,,:LcLJ.  .cGZ:.:;JFI;:.jLzzczz9C,:,r::,:L.,O,..,:. IFLz  FjSSSZZCZZGK.   ..,.,
	. ..,,c,.;   ZZ6. CH. L8@@     @@B$$; OZ ..........,...:,         ,;,::rcrcz. .LS6c:,;;zFj;:,;eIJZJr6Z,:,Lr:,,:; LG,  .:.  Fcrr :rrJZbKK6Hc  ..,.,...
	  . .;z;.c,  Fe. JKeO;cCD@L.   ,6,     Z......,...,.,.,,,         ;;::;::rr..;Cbz,;:;:r;;,,c;;9rcLr$K,:,;Z:,:.r: Jd.. ,..   F;r,,Lr;rIHHF.  ..... . .
	     ;Lc,:c. ,. IeCSde.,Lrr. .   ,JZKbc;...,,,.,...,.,.,,,       :;:,,,;L;.,:Jz:.:,:,:,,,,,I.F,.c,G8,::,6z.:F.::.Kz   ,.    .J,;,rLJJc:.   .     . ..
	.   ..LzL.,c, rjZC9Z: Lr;LKc. ,:,.;Fz:,.,.,,  .,,.,.,...,,:.    .:,,,.::,...Lr,,::;:;::::.JL,ZzZ,j#;,,,c@:,.Z;,,re,  .,      rc;Lzz;.       . .......
	.  .r:,Lz,rL::.ZK9r..r::FjceS;.::;,,,:,:,,,,  .:,,........,:,. .,,.,.... .:LcL,;:;:;:;::.zO cB8r;GK,,:,BOc .Jk LJI  .: .  .. .r:..   . . ...........
	  ,.. ..zbL ,LzIF.:r,.;CFJJcC6L.;:;,:,,,,,,rL.,,............,,,,,...,....;rrz,;;;;;::,,.zD:,OZZ.ZSe.,.z8cF. L8,cZ.  L. .  ,....   ...............
	  ..:;;:;r,..zZ:,Ck, :ZCJJzJcJ9c ,,,,,.,.,.,,,...    . . . ........,....r;cF,::;:;::,..FGr ezrI.ZeI...kC:CL .JJL;  :,.   ,.,,,.,........ . .         .
	..rr;::r;  ,:;:LOZ..,JJLzczLLJCdL ..,.,...,...  .:;;r;LrL;;:, ....,....r;zZ,::;:;::..,eb; jr.;Z,JrF  .9r..C: LJr..:.,   :,:,,...... .             .;JL
	L::::::L  :;:zZSj..,;L;cccLccJzbB; ,.,...,.,...b#Scr;r;;;r;LJ,.,......;rzI;,:;::,, .LSZ; F.. Jjrr.L  ;Z:  ,crr..,..,,  :,,..     .            .,;JIz:
	;,;::,L,,;;,zZJz, ,,;:LLLrJL:LZc;Z: ....,.,.. I@J.::;:;:;;;;J...,....rrLzL,::,:,. LbSJ,.Z: . J.,C ,. .L.  . ,:...  .: ...       . .          . cC;,.,.
	,,:;::r;.,,,Jz;r ;.,,;LrrJr,;c::ccIr  ...,.,...JLr;;:;;;:;;c,.......:z:,cr,:::,..deFz,,IL ,. : .c; . ,,.   : .. ..                          :, .;,,:.
	r,;:;::. ..:c:L.;r...:rrJr,,;:;zzLzZJ,   ...... .:;,,,,,,.,...,.,...c; ,J,,,:,.,kdrrrLzr  ; .....,    ..,  .;  .;.. . .     .   . .        :,z. ,..
	r,:;:::, ..L;;r.I:..,;,,...;rzzc;rrJ9OFL,    . ... ............,.. ,L,;IC:,,..rKLZczFL;, ..             .:,.  ,;,.       .     . . .      .,;IL  .   ,
	;,;;r;r,  ,L;;r:F. .:,. ,:L,:,;;L,cJz;LzeSF:,       ......,.,.... .LkJIrI:,,.;$CcSjrcL;  ,....,,,,;JJ r.  . .:;,;.            .          ,.;J,LL  .,Jc
	r:rLrLLz. :JrzrLJ. ,;z,,.rc;: .;,LL;::,rCICIFFLr:,..   ....... ,;Ijjz;,.rL..,0e,.cKIj;:  Jc:,r;;rbD$$ODO;.  ....                        ,.:F;. 9: ,Ic,
	r,r;;:;;:.:::,;::. .;:.    :kz.:. .:;:;J;:z;;;,,cLcr;;:,,,,.,rJjjcr,,.,.:J,.CB; ,.dC, ,:,L;;;;;LCKj;;;;;.     . ... . . . . .   .   .  ..,jr: ,J  JL;
	              ,, . ,:        .:: . ,:;J, :Cc,,. ,,,. ;,::,rc::e;rL,..,,,.cL:zb:,;J;,.:FI;rrr;;JJ;:.....,,.       ....... . . . . .... ...Cr;. c; rcr,
	. . . . . . . .,  ,:: . . .   ;;  .:;;,. .Z,:;r.,,,.  .:;,;::rHF;.,,,,,,,.Je;;rcj::.:CjrcLLLcZeLr.,.,,:...,..        .... . . . . .   , jL;,.,Z  c;,.
	. ................ :,......,.  .;,.:r.  .,L .z:.,rr;,LcCz;,;FzJG.,,:,:,:,:,Jc;jJ::::ZerLLcLcFOLc....,,.....,,,..       ,,,.,.,...... , zzr;, zz ,c,. .
	,                                .;.,     .     .,:....   zZL;Lb. ..........Lc,.,,.cZ:::;:;rC,,   ...,.                             . :L,.: .J  ,...,.
	 
	 */









	//  MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMHBYYYWMMMM#BYYTTTYWMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMB9O1==?????zzCC111>>;;;;;;;;;;;<?TMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMMMMMMMMMMM9Olll=l======??????????>>>>>>;;;;;;;;;:;?TMMMMMMMMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMMMMMMMM9ttlllllllll=l=======?????????>>>>>>;;;;;;;;;;?TMMMMMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMMMMMBOttOtttttltlllllllll=======??????????>>>>>>>;;;;;;?TMMMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMMMBttwOtttttttttttttlllllllll========?????????>>>>>>;;;;;<TMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMBrwZrttttttttttttttttttlllllllllll======???????????>>>>>>;;?HMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMSw0trtrrtrtrttrtttttttttttttlllOllllll========????<<zz??>>>>>>ZMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMX0ttrtrOOttrttrttOOttttttttttttltwllllllllll========??wy?????>>>vZMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMM0ttrI+wV1rtttttttwZtttttttltttOwylOXOllllllllllll=l====1dkz???????vZdMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMSrrwrtwZCjttttttttwSttOlllltllllwtXOlZkOlllllllllllllll==z+dk===?????X2JMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMBrtwwtrw0<jttttttttOXllOttltllttllOZwHOtXkyltlllllllllllllll<+XZ======?dk?JMMMMMMMMMMMM
	//  MMMMMMMMMMMMStwdZtwXC<+ttttttOOOd6ltZlltllllttllStWWOOHWytttttltltOllltllz:zHllll===zX=?dMMMMMMMMMMM
	//  MMMMMMMMMMBrwdKOtwW3;;zrttttwZwXRlldOllltltlltttwlXvktdXWytltttttttOttlttl<<dklllllllZ===dMMMMMMMMMM
	//  MMMMMMMMM8tQM#ttwW3;;;1trttwSwfUOlORltllltlllllldtX>dktDOWOtlttltttOOttltO<;+WOllllllXlllzMMMMMMMMMM
	//  MMMMMMMM9OdM#Ottd$;;;;;<?1z0OKjRltd0llltOllllllldZX>?WOw_WWOtttttttttOttI<;;<dkttttllllllldMMMMMMMMM
	//  MMMMMMM9wMMMSttwS<;;;;>;;;J<j>(I<?U111zltllllllld0X>~dkwl(WkttlttlOOwWk<;;:;;zHttttttwOllllMMMMMMMMM
	//  MMMMMMBdMMM8tttdI+zttttttdSXt~dlzXwlllzzOzzzzzlldkW<~?kOk~?sx++++jdHmH6+++<;;jdZtttttdkOtlldMMMMMMMM
	//  MMMMM#dMMM#tttw0+tttttttdKdf((RsdfRllllldZllltlldWK~~_W0w_~OWOlOdgg9ZtOWOtttz+wktttttdpktttwMMMMMMMM
	//  MMMMMWMMMMSlttdIttttttOdWHH>~(IzWDRll=llzRlllzlldk$>++dkd<~_XkdgH9tttttdktttt+OkrttrtdfpkttOMMMMMMMM
	//  MMMMNWMMM#Zttlk=tttttOXWWd$_.(IdW1R=llll=SlllzOldK<_._(kd6+-(MM9lltttttrWktttztWZttrwXppWttrMMMMMMMM
	//  MMMMNMMMM#lltwDzttllOXyW0X:..(OXk<Rl=ll=lwOlllOld3<``.(Rd>~?CdklllltttttXdXttzOWktrwwWpfpkrtMMMMMMMM
	//  MMMMMMMMM@ltldIzlttOXyW$w$```(OyD(Rl==llldZ=llIlw;~```-Xd:~~~~UkylltttAyHdgSrzObRtOXwpfppWrrMMMMMMMM
	//  MMMMMMMMM@llldtlllldVyW+d>```.wZ$ wl==lI=wRl=ll=w<```` dd_..~~(RZXOQdggHH9ZwrzwHWrdXXppfppkrMMMMMMMM
	//  MMMMMMMMM#llldlltlwyyyD(S-...,Wk] zI=l=llzWzl=l=P~```` jZ``...~zQkH@MBUtrZtrtldHRdSdpfpffpkwMMMMMMMM
	//  MMMMNMMMMNZllXtllldVyW3(Mf=<ONMHP~(k===l=zdk=lld3```...(C````..(M96lttttrrtrrtdHWHXpfpppfpRwMMMMMMMM
	//  MMMMMMMMMMNzzWZllzyyyy(W@`  =~MWK6 jz=lzlzvRz=lZ`.I+JgkWm&-. `..(ZltlttttrtttrWWHppfppfpppSdMMMMMMMM
	//  MMMMMMMMMMMkAWRllzVyyS_(b    .MNHU-(Uz=lI={XkzO>.dVT7<TMHMNHHx-.(kwZyltttrtrrdHHpfppfpffpp0dMMMMMMMM
	//  MMMMMMMMMMMMKyWzOzyyyk.`<!  hdWMH]``(S==t=l(kX2 ?_`    WMMHH#HH+.XwkwOttttrwrZ~(HfpfpppfpWwXMMMMMMMM
	//  MMMMMMMMMMMMMHWROOyyyW;` `. (WVM#b```(0=zzz wX!```  a.dM#NM@N(4WhXkXkWtttttwd3O_(HpffpfpfWwSMMMMMMMM
	//  MMMMMMMMMMMMNZvWzXXyyXP```-_ ?o+?!````.4=Z=`(:````  HpbNNMHHH (C=XXyWZWttrdwf:(>.dfppffppSXSMMMMMMMM
	//  MMMMMMMMMMMMMRzuHzXyZXH.``````````````` ?zz ``````` ZKvTHHbWt `` XZyyHZWOdSZ<::~`(fpfpfffXp0WMMMMMMM
	//  MMMMMMMMMMMMMKzyyHvyZZW____.`````````````.I_```````` ?nJzX7^````.WXWyyHyWKZ<:::_`Jffpfpfpfp0WMMMMMMM
	//  MMMMMMMMMMMMM@zZyZWwWyXo-_~(~ ```````````` `````````````` _`````.WXkyyVWmWc::<~ .HffppfffffkXMMMMMMM
	//  MMMMMMMMMMMMMKzZZZZXkUXr~....```````....```````````` ...  ````..JXWWyyW83vXx~..WfffVfWVffffkdMMMMMMM
	//  MMMMMMMMMMMMMRzZZZZZZZZb````````````<````````````./<~._<_.____`(WfdyW3<:~~(XWkVVVVVVVHVVVVV0dMMMMMMM
	//  MMMMMMMMMMMMMSzZZZZZZZWX-```````````````````````````.......~~._j9jX=_~~_(XZyVHHkyyyyWHyyykykOMMMMMMM
	//  MMMMMMMMMMMMMSzuuuuuZXWZW,```````````````````````````````.``..(3<! ...JWyyXWyyyWHkyyWHyyyHyklMMMMMMM
	//  MMMMMMMMMMMMNXzuuuXXuXSuuXh,```````` .... ```````````````````_~ .JWyyyyZyy0HyyZyyZyZXWZZZWHZIdMMMMMM
	//  MMMMMMMMMMMMNwtuuuXkuXXuuuuXh,``````(:::~<?71(,``````````````.(UMNUkZZZZZZZHZZ0ZZZZZWWZZZWNXIdMMMMMM
	//  MMMMMMMMMMMMNKOzuzXkuXuuuuuXuXW, ```` _~~~:~~(}```````````.(YC;::<kCfZZZZXO#ZZVZZZZZMZZuuMMNXzMMMMMM
	//  MMMMMMMMMMMMHKOzzuXkzdzzzzuXXzuuU&.``````````````````` .JY>::::;;J=:dZuZuZd#uuruuuud#uuuXMMMNXdMMMMM
	//  MMMMMMMMMMMMMNOvzzXkvMRzzzzXKzuzzzXh, `````````````..JC<;:;;:;;+7<:~(HHuXIdNuuzuuuXMSuuuWMMMMROMMMMM
	//  MMMMMMMMMMMMMNvvvrdkvM#vzzzzHzzzzzuzzUG. ``` ...JdY<:;:;:::;;+v<~~~:(HpHmzMNXZzuzzd#zzzdMMMMMMRdMMMM
	//  MMMMMMMMMMMMMNwrrvdRrMNwvvvvdRvvvzwkzzzzXWWHY=~~O+::::::::<+<~~~~~~~dppppWMMkZzzzwM#zzdMMMMMMMMNMMMM
	//  MMMMMMMMMMMMMM#rrrwRrMMbOrrOZNkrvvvXwvvvvvwX;.~._W_:::::(?!~~~~~~~~(HpppppppHWdvwM#XwdMMMMMMMMMMNMMM
	//  MMMMMMMMMMMMMMNyrrrRrWMMmzOrzdNyrrrZNvrwQWWfb....(r~~_J>_.....~.~~-dpfpffpfpppWHHMNdMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMNrtrStdMMMNxzrzMNmrrrdNWfVfffP._-.(~_J!............JpfpffpfpfffpppWNppppHMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMNOtXtdMMMMMNxzZMMNmgHyVVVVVW%..?/(.,(x-..........(HfffpffpffpffWHHffpffppfVyyWMMMMMM





	#include<bits/stdc++.h>
	#include <ctime>
	using namespace std;
	typedef unsigned long long ll;
	typedef unsigned long long ull;
	typedef long double ld;
	#define endl "\n"
	#define pb push_back
	#define mp make_pair
	#define mod 1000000007 
	#define MxN 100000
	#define pi acos(-1.0)

	//safe hash function
	/*
	struct custom_hash {
	    static uint64_t splitmix64(uint64_t x) {
	        // http://xorshift.di.unimi.it/splitmix64.c
	        x += 0x9e3779b97f4a7c15;
	        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
	        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
	        return x ^ (x >> 31);
	    }

	    size_t operator()(uint64_t x) const {
	        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
	        return splitmix64(x + FIXED_RANDOM);
	    }
	};
	*/

	//unordered_map template
	//unordered_map<long long, int, custom_hash> safe_map;

	ll gcd(ll a, ll b)
	{ 
	    if (a == 0) 
	        return b;  
	    return gcd(b % a, a);
	}  

	ll findLcm(ll a, ll b)  
	 {  
	    return (a*b)/gcd(a, b);  
	 }  

	int gcd(int a, int b)
	{ 
	    if (a == 0) 
	        return b;  
	    return gcd(b % a, a);
	}  

	int findLcm(int a, int b)  
	 {  
	    return (a*b)/gcd(a, b);  
	 }  

	// operator() for set sorting according to data structure
	 /*
	struct cmp
	{
		bool operator()(const pair<int,int> &a,const pair<int,int> &b)
		const {
			int len1 = a.second-a.first;
			int len2 = b.second-b.first;

			if(len1==len2) return(a.first<b.first);
			return(len1>len2);
		}	
	};
	*/


	// check hack function of unordered_map
	/*
	void insert_numbers(long long x) {
		int N = 2e5;
	    clock_t begin = clock();
	    unordered_map<long long, int, custom_hash> numbers;

	    for (int i = 1; i <= N; i++)
	        numbers[i * x] = i;

	    long long sum = 0;

	    for (auto &entry : numbers)
	        sum += (entry.first / x) * entry.second;

	    printf("x = %lld: %.3lf seconds, sum = %lld\n", x, (double) (clock() - begin) / CLOCKS_PER_SEC, sum);
	}*/
	 /*
	int xrr[]={-1,1,0,0};
	int yrr[]={0,0,-1,1};
	const int size=30;

	void dfs(int arr[size][size], int visited[size][size],map<int,pair<int,int>> &ma,int dist,int x,int y,int n,int m)
	{
		visited[x][y]=1;
		if(ma.find(dist)==ma.end())
		{
			pair<int,int> p;
			if(arr[x][y]==1)
			{
				p.first=0;
				p.second=1;
			}
			else
			{
				p.first=1;
				p.second=0;
			}
			ma[dist]=p;
		}
		else
		{
			pair<int,int> p=ma[dist];
			if(arr[x][y]==1)
			{
				p.second++;
			}
			else
			{
				p.first++;
			}
			ma[dist]=p;
		}

		
		int i = x+1;
		int j = y;
		if(i>=0 && i<=n && j>=0 && j<=m && visited[i][j]==0)
		{
			dfs(arr,visited,ma,dist+1,i,j,n,m);
		}

		i = x;
		j = y+1;
		if(i>=0 && i<=n && j>=0 && j<=m && visited[i][j]==0)
		{
			dfs(arr,visited,ma,dist+1,i,j,n,m);
		}
		visited[x][y]=0;
	}
*/

	int main()
	{
		ios_base::sync_with_stdio(false);
	    cin.tie(NULL);
	#ifndef ONLINE_JUDGE
		freopen("input.txt","r",stdin);
		freopen("output.txt","w",stdout);
	#endif
		//Hackaing unordered_map or set
	    //insert_numbers(126271);// for GCC 6 or earlier
		//insert_numbers(107897);// for GCC 7 or later
		
		/*ll t;
		cin>>t;
		int testcase=1;
		while(t--)
		{
		}*/
		int a,b;
		cin>>a>>b;
		string ans="No";
		for(int i=0;i<=a;i++)
		{
			int val = i*4;
			int val1 = (a-i)*2;
			if(val1+val==b)
			{
				ans = "Yes";
				break;
			}
		}
		cout<<ans<<endl;

		
	    return(0);	
	}












	//  MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMHBYYYWMMMM#BYYTTTYWMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMB9O1==?????zzCC111>>;;;;;;;;;;;<?TMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMMMMMMMMMMM9Olll=l======??????????>>>>>>;;;;;;;;;:;?TMMMMMMMMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMMMMMMMM9ttlllllllll=l=======?????????>>>>>>;;;;;;;;;;?TMMMMMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMMMMMBOttOtttttltlllllllll=======??????????>>>>>>>;;;;;;?TMMMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMMMBttwOtttttttttttttlllllllll========?????????>>>>>>;;;;;<TMMMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMMBrwZrttttttttttttttttttlllllllllll======???????????>>>>>>;;?HMMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMMSw0trtrrtrtrttrtttttttttttttlllOllllll========????<<zz??>>>>>>ZMMMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMMMX0ttrtrOOttrttrttOOttttttttttttltwllllllllll========??wy?????>>>vZMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMM0ttrI+wV1rtttttttwZtttttttltttOwylOXOllllllllllll=l====1dkz???????vZdMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMSrrwrtwZCjttttttttwSttOlllltllllwtXOlZkOlllllllllllllll==z+dk===?????X2JMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMBrtwwtrw0<jttttttttOXllOttltllttllOZwHOtXkyltlllllllllllllll<+XZ======?dk?JMMMMMMMMMMMM
	//  MMMMMMMMMMMMStwdZtwXC<+ttttttOOOd6ltZlltllllttllStWWOOHWytttttltltOllltllz:zHllll===zX=?dMMMMMMMMMMM
	//  MMMMMMMMMMBrwdKOtwW3;;zrttttwZwXRlldOllltltlltttwlXvktdXWytltttttttOttlttl<<dklllllllZ===dMMMMMMMMMM
	//  MMMMMMMMM8tQM#ttwW3;;;1trttwSwfUOlORltllltlllllldtX>dktDOWOtlttltttOOttltO<;+WOllllllXlllzMMMMMMMMMM
	//  MMMMMMMM9OdM#Ottd$;;;;;<?1z0OKjRltd0llltOllllllldZX>?WOw_WWOtttttttttOttI<;;<dkttttllllllldMMMMMMMMM
	//  MMMMMMM9wMMMSttwS<;;;;>;;;J<j>(I<?U111zltllllllld0X>~dkwl(WkttlttlOOwWk<;;:;;zHttttttwOllllMMMMMMMMM
	//  MMMMMMBdMMM8tttdI+zttttttdSXt~dlzXwlllzzOzzzzzlldkW<~?kOk~?sx++++jdHmH6+++<;;jdZtttttdkOtlldMMMMMMMM
	//  MMMMM#dMMM#tttw0+tttttttdKdf((RsdfRllllldZllltlldWK~~_W0w_~OWOlOdgg9ZtOWOtttz+wktttttdpktttwMMMMMMMM
	//  MMMMMWMMMMSlttdIttttttOdWHH>~(IzWDRll=llzRlllzlldk$>++dkd<~_XkdgH9tttttdktttt+OkrttrtdfpkttOMMMMMMMM
	//  MMMMNWMMM#Zttlk=tttttOXWWd$_.(IdW1R=llll=SlllzOldK<_._(kd6+-(MM9lltttttrWktttztWZttrwXppWttrMMMMMMMM
	//  MMMMNMMMM#lltwDzttllOXyW0X:..(OXk<Rl=ll=lwOlllOld3<``.(Rd>~?CdklllltttttXdXttzOWktrwwWpfpkrtMMMMMMMM
	//  MMMMMMMMM@ltldIzlttOXyW$w$```(OyD(Rl==llldZ=llIlw;~```-Xd:~~~~UkylltttAyHdgSrzObRtOXwpfppWrrMMMMMMMM
	//  MMMMMMMMM@llldtlllldVyW+d>```.wZ$ wl==lI=wRl=ll=w<```` dd_..~~(RZXOQdggHH9ZwrzwHWrdXXppfppkrMMMMMMMM
	//  MMMMMMMMM#llldlltlwyyyD(S-...,Wk] zI=l=llzWzl=l=P~```` jZ``...~zQkH@MBUtrZtrtldHRdSdpfpffpkwMMMMMMMM
	//  MMMMNMMMMNZllXtllldVyW3(Mf=<ONMHP~(k===l=zdk=lld3```...(C````..(M96lttttrrtrrtdHWHXpfpppfpRwMMMMMMMM
	//  MMMMMMMMMMNzzWZllzyyyy(W@`  =~MWK6 jz=lzlzvRz=lZ`.I+JgkWm&-. `..(ZltlttttrtttrWWHppfppfpppSdMMMMMMMM
	//  MMMMMMMMMMMkAWRllzVyyS_(b    .MNHU-(Uz=lI={XkzO>.dVT7<TMHMNHHx-.(kwZyltttrtrrdHHpfppfpffpp0dMMMMMMMM
	//  MMMMMMMMMMMMKyWzOzyyyk.`<!  hdWMH]``(S==t=l(kX2 ?_`    WMMHH#HH+.XwkwOttttrwrZ~(HfpfpppfpWwXMMMMMMMM
	//  MMMMMMMMMMMMMHWROOyyyW;` `. (WVM#b```(0=zzz wX!```  a.dM#NM@N(4WhXkXkWtttttwd3O_(HpffpfpfWwSMMMMMMMM
	//  MMMMMMMMMMMMNZvWzXXyyXP```-_ ?o+?!````.4=Z=`(:````  HpbNNMHHH (C=XXyWZWttrdwf:(>.dfppffppSXSMMMMMMMM
	//  MMMMMMMMMMMMMRzuHzXyZXH.``````````````` ?zz ``````` ZKvTHHbWt `` XZyyHZWOdSZ<::~`(fpfpfffXp0WMMMMMMM
	//  MMMMMMMMMMMMMKzyyHvyZZW____.`````````````.I_```````` ?nJzX7^````.WXWyyHyWKZ<:::_`Jffpfpfpfp0WMMMMMMM
	//  MMMMMMMMMMMMM@zZyZWwWyXo-_~(~ ```````````` `````````````` _`````.WXkyyVWmWc::<~ .HffppfffffkXMMMMMMM
	//  MMMMMMMMMMMMMKzZZZZXkUXr~....```````....```````````` ...  ````..JXWWyyW83vXx~..WfffVfWVffffkdMMMMMMM
	//  MMMMMMMMMMMMMRzZZZZZZZZb````````````<````````````./<~._<_.____`(WfdyW3<:~~(XWkVVVVVVVHVVVVV0dMMMMMMM
	//  MMMMMMMMMMMMMSzZZZZZZZWX-```````````````````````````.......~~._j9jX=_~~_(XZyVHHkyyyyWHyyykykOMMMMMMM
	//  MMMMMMMMMMMMMSzuuuuuZXWZW,```````````````````````````````.``..(3<! ...JWyyXWyyyWHkyyWHyyyHyklMMMMMMM
	//  MMMMMMMMMMMMNXzuuuXXuXSuuXh,```````` .... ```````````````````_~ .JWyyyyZyy0HyyZyyZyZXWZZZWHZIdMMMMMM
	//  MMMMMMMMMMMMNwtuuuXkuXXuuuuXh,``````(:::~<?71(,``````````````.(UMNUkZZZZZZZHZZ0ZZZZZWWZZZWNXIdMMMMMM
	//  MMMMMMMMMMMMNKOzuzXkuXuuuuuXuXW, ```` _~~~:~~(}```````````.(YC;::<kCfZZZZXO#ZZVZZZZZMZZuuMMNXzMMMMMM
	//  MMMMMMMMMMMMHKOzzuXkzdzzzzuXXzuuU&.``````````````````` .JY>::::;;J=:dZuZuZd#uuruuuud#uuuXMMMNXdMMMMM
	//  MMMMMMMMMMMMMNOvzzXkvMRzzzzXKzuzzzXh, `````````````..JC<;:;;:;;+7<:~(HHuXIdNuuzuuuXMSuuuWMMMMROMMMMM
	//  MMMMMMMMMMMMMNvvvrdkvM#vzzzzHzzzzzuzzUG. ``` ...JdY<:;:;:::;;+v<~~~:(HpHmzMNXZzuzzd#zzzdMMMMMMRdMMMM
	//  MMMMMMMMMMMMMNwrrvdRrMNwvvvvdRvvvzwkzzzzXWWHY=~~O+::::::::<+<~~~~~~~dppppWMMkZzzzwM#zzdMMMMMMMMNMMMM
	//  MMMMMMMMMMMMMM#rrrwRrMMbOrrOZNkrvvvXwvvvvvwX;.~._W_:::::(?!~~~~~~~~(HpppppppHWdvwM#XwdMMMMMMMMMMNMMM
	//  MMMMMMMMMMMMMMNyrrrRrWMMmzOrzdNyrrrZNvrwQWWfb....(r~~_J>_.....~.~~-dpfpffpfpppWHHMNdMMMMMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMNrtrStdMMMNxzrzMNmrrrdNWfVfffP._-.(~_J!............JpfpffpfpfffpppWNppppHMMMMMMMMMMMM
	//  MMMMMMMMMMMMMMMMNOtXtdMMMMMNxzZMMNmgHyVVVVVW%..?/(.,(x-..........(HfffpffpffpffWHHffpffppfVyyWMMMMMM







	/*
	:.;.. . . . . .  .:,,..........:r..,.                                                 ..::r;r;r;r;r;r;;;;:;:;:;;:   . ... . .   ,:;:;:;:;:::;:;:;:;::,
	                               .,,.:,                                            ,,:::::,:,:,:,:,,.,.,...........                ....................
	      .   . .   ,zIZ999IL,,..           . . ...                        .rzJLzzIJJzzLcLLrr;r;r;;;;:;:::;:;::::,::::  . . . . ..,.,;;::::::::,:,:,:,::;.
	         . .    jILcLr;;;LLLrr;;,,.                  .,.             zB$BkFFJJzcrLrrrr;;;;;;;;:;;;;;;r::,:::,:,,,:,  .   . ..,,;,;::::,:::,:,:,,::,::.
	,     . . . .   SL;:;:;;;;;;;;r;rrL;r;;:,..     ..,;cJjL.         . .rr,,.::;rccJJzccrr;;;;;;:;:;:;:;;;,:,:,:,,,,,z.        .,:,,::,:,:,:,:::,:,:,:,:.
	c;cr   .        FI:;;;;;;;:;:;;;:;;;;;rzczcL;rrLzjr;;r;rcjZZc:                   ,,rLzICFIzJzIJjFZIIL:,:::,:::,,,,c,   . . . ..,,;::,:::::,:,:,:,:,:,,
	r,cc,           ;B;:;;;;;;r;;:;::::,;;:.. .;zrJObJeZZZeIJr:.:;L         .             :J6B#BH66S6eSeeL:::::,:::::,L.    . .      .;::,:::,:,:,:,:::::.
	;,rc.            H6;:r;r;;:;;rrL;Lzjzcr;::,;;ZJerzjjzr,,;Jcr.            ..  ,:,          ,Jb9ZFccLIFZ;::;:;::::,,c.       .     :::,::::::::;:;::::,.
	;.LL:   .        .$e::r;rLJzJzzcCKbSZJzzjS9crFF;zzJcLzCJ;..:Fbkc,             .:c;.          ,zIFzL;LIj;;;;:;:;::,JC            .:;,::;:;:;;;,:,,,,,,.
	;,:Lc,            ,$C;::,ZJzzIC969KzrIZkOd .JL6ILFLKz.,rzZJ;..redkc;.            ,Lc,          .;FjzrLLL;;;;;;:;::L#I           :r;;::,,,,.......,.,,.
	;,rcz.             r$ZLcJzIIK69ZZZIJSeekS  cc:9ecK;:SF,:,.rJIr,.:J6jcJL            .LCJ           ;FC;..;;;;;;;;;:;:Sz         .:,...      ...,,,,,,,.
	c;rL;.   .....      I#eZICZKCKjZeZCeCZKO   Z:r9S;ZC.r9c,;;.,:Lr:..,KbrLS;             JB:           ;Fc;,::::;;;;;:;,;.                . ..,,,,,,,,:,,
	.     . .......     ,bIIZCZzKOeSZJCjZIG;  :J,LGk;zB:.ZZ:,LL,:,:,::,.F0J.jJ  .          ,$F            IHbIzrr::,::::r:          . ....,.,.,,,,:,,,,,,
	   . . ... ...    .IZFIjCIzbDZkKzzZZJjK   Lz.JOS;.dC.rZ;;,cr::,::;;: r#9,LF, z,          Bk            :H#dd69KZFzLL;c,      ....,.,.,.,.,.,.........
	. . . .......    LbZjIFCzck#zFKJLCCJJzJ.  c;,ZkcL ZB,.J;L;,rr,.:;::;r.;Gd;;z: ZJ          HH    .        I8KSKOHDB#88OBL .....,...,.,........ .....,:.
	  .. . . ..    :ZKIFJIZzcKkLCKFLJFcJzLL,  zL.GL::,r$Z,,;,F, ;r:::;::;L:L6Or;cz.Ck:     .   $H   Lz        ;6Fz;,.,,rLLcc.....,.,.... . . ....,,,,:,,.
	. ,.. ...     JKjzJIJFZLe;;K9zjcI;Lcc;c:  e;r9,,:,.k#c.,,zz .:Jr,:::::rLJS9c;rFzjkF     .   @S   #z        :SLL;:.              ....,...,,,,,,,.,..
	. ,.   .     ZZJcJFFzbc;.LZGzcCrL:cL;:rr .k:Jj.:,:.ZeG,..Le  ;:Zr,:;:;,rcZK9c;;Z6zK6.   .,  :@;.,c@L    .   JbczzIJJc;,              ..,,,,,.,.,..
	. .         eFcLIzJIec  bG9I;zC:::c::,;L .6,k,,,:,.cSJK..,O  ;,,eL,,::;,;zee6;r:zkJjd;   J;  H@.k:HG,   ,d   KSzJzJzJJFJJL;,.             ..,.,..
	   . .     ZzLLZJJFz  ,Z#9Z.,Sj,,;;:,:;r ,CLJ.;,,,.;e,Jk, K; L,,,Zc,,,,;,;IbeZ;z.,ZCFOz  Fd, ;@jJ;Fd6    $H   8FczzJzJzzcJczzzLL::,.           ... .
	. . ...   FzrLbJJz, .JcF$e..J8L.,:;,,;J; .6Z, z:,,.,Z.,rk:Jz :,,.,Zz;:,,;,;eO9cLF  ISC6c,8Z#  $BZrL6HI   9$S  cdrrL;r;LrLLLrLrLrLrLrL;;::..         .
	     . . zz;r9Jc,  ;Se.99  FdS,,,::,.rj:  dc..cc.,,,z,,.,IbZ ,,,,..jJc:,:;;L90ZrJZ  rSjbZjJHj k$jFI9KG,  GS0L ,OBdSCFz;;:;;LrL;r;;;;;;:;;;;;::,:,,..
	        ,J;rdj,  :;:ZZ;J .6HbF,,:,,,.;e., I.,.cZ. ;L;.,,,.IC :,.,,,.JJJ::;;rIBbrzIZ  ;KJZzzIB.LDZJFZKbZ  kCZd:Cr$BBBBHHSjL;:;;r;r;;;;:;:;::,:,,,:,:,:.
	        crLZc  ;zL..KD: reJrkC.,,,,,.;Z,..L,..;e, .SFLLzL;zJ K;..,,..LJZrrL;cd9cLJZC  ZCIzcJZF:8ZJJZZZO  SIFZKZ:60H8G88BBB6Zc;:;;r;r;;:;:;:;,:,:,:,,,.
	       LzLL,,;czF: .Kc.ZKc..GZ..,,,,.:e,..r:. LJJ..F9,:,,.c; LIJ: ..,.rJKrLLrSdLccJZ; CFFzczICIZSzJCeJd..ZFIICC,FH0H8d8OGOHH8CjL:,;rLr;;;:;:::;::.,,,.
	     .;z;JJ,r;:cj,.L;c,OJr ,6z.:,.,. .C, ,,L. rJJ: :I..,,,c,.:.;cJ:..,.:ceccLekcrzzIj rjJJcJJjJjezzZFIS;LjFFJJz.L6ZGb9kO996dOH8BbJ;  ,;;;;;;:::::,.:r;
	  ,,rrr,:k: ;,rLSzz;C# IZ  rcL.:: .. ,Kz  ::, ;;cJ. c,,,,.c.;.. .,rr:...,;Fzze6rrczzj:;IJcccJJccKzJCFCjJJcjJzJz rZ:JHkkKSS6b96dOBBBC;,::;;;;;:;:;:;Jr
	:....::.cJ ,..zZdz. :0.c. cz:F,cc....ZJj:  ;L.,:,Jz .;...;L,         ,..  ,rcCeL;LLzcc;JczLczZLcZzJZFezFrJJz;JL.LC,,c8dkKSeSKbk9bdOD8OJr,::;;;;;:LJ,
	    .c,,Z,.   KzH.  ,d6 ,ekLIZzLz . rCFzZ, .jLr,..cz,LL:;;,.rce669BH8OSzr.  ,JZ;r;LLcLLcLLcrJerLZcjZeJcrrJzr;c;,zL,,,,k8OSbKSekKKebSOdBGkJr,::;:Lc
	    c; Lc. ..LJr9,  .jc;Oj,..;;JL  ,zcz,rZ, ,;rJ:..C8Kc:;K@@@@@@$$9SSH@@@@$KLJj;;:;LrLLrLcLrjS:zjJeKCLr;LLL;:r::;:,,,,.L8HbbSkeKZeZKekS9O8dkz;,;c
	   :L .L;  ..JzJ9,  Z9ez.; ...rJZ  :,:z:.,IL.,.;cr:,.,LB@@@Ze$$$KcKzFZj6$@@@zzJ,;,rrrrr;crL;bC:zKeeCI:;;LJL,;::,:,,,,,j, eB9kSkeSKSZKZKZKK69GOKF:;.
	. ,,. .c,. ..SFZe:.jLSLc;r,....:J. , .,zr..;Lr;,:,,,,:$@$c  B@@@@@@@@@G ZF$..I:::,;r;;,rrL;LHc:F;:,,;z:;IC::::,:,,:,,;,GJ ;8dbSkeSZKZeZeCZCZZk6GH$.
	. . : .J,.  :89ISJ.  JI.Lrr   ..rr,L:...rc;.,:r;;;...Z@S    $@8dIB@8,..O@;, rJ,L,,;:,,L;r;:C6,zCJFJJ:LLJS:;::::,,,J,,:, @G  OHkKKZSeKZejZCZFZFZ6$,
	.  ., .j.   ;#eCcK   LJ. :;:  ...::;c; ..,:;;r;;.;:,.;r  .. ,@;   .:   ez  :F:r;.::,.Fr;;,L9z:6IcFJJz.ke:;:;::,:,,I,..; ;$$: eH6KKZeZZZZZZZZCeOd.  .
	    , ,L:   cBZ;;O;  ;J.  ;O$$$9OOHZ:   ....,,rLr:;;,....... :6c;,:LjL6c..,J:;z.,,.,6C,:,;eZ;FkFZzzc:,ezc:;::,,,,.e,..;, ,SG: Z8bKKeKZeCZZZCSHF     .
	   ., r;;   cBJ.Jde  :z  $@@@$jD$6jd@@b,.........,.,,,.,,,,:,..6$DGB9F:,.,zr;I....,Ob,.,:FZc;;FKZFJF;zjJ:::;:,,;.,S;..,r  zcI. KdOSSeeCeCZZ6G;     ..
	. ..: z.r   ;K:c9;br  I 8@@L,  @@BG9SS@L:...........,.,,::;:;::.,,. ..,,:LcLJ.  .cGZ:.:;JFI;:.jLzzczz9C,:,r::,:L.,O,..,:. IFLz  FjSSSZZCZZGK.   ..,.,
	. ..,,c,.;   ZZ6. CH. L8@@     @@B$$; OZ ..........,...:,         ,;,::rcrcz. .LS6c:,;;zFj;:,;eIJZJr6Z,:,Lr:,,:; LG,  .:.  Fcrr :rrJZbKK6Hc  ..,.,...
	  . .;z;.c,  Fe. JKeO;cCD@L.   ,6,     Z......,...,.,.,,,         ;;::;::rr..;Cbz,;:;:r;;,,c;;9rcLr$K,:,;Z:,:.r: Jd.. ,..   F;r,,Lr;rIHHF.  ..... . .
	     ;Lc,:c. ,. IeCSde.,Lrr. .   ,JZKbc;...,,,.,...,.,.,,,       :;:,,,;L;.,:Jz:.:,:,:,,,,,I.F,.c,G8,::,6z.:F.::.Kz   ,.    .J,;,rLJJc:.   .     . ..
	.   ..LzL.,c, rjZC9Z: Lr;LKc. ,:,.;Fz:,.,.,,  .,,.,.,...,,:.    .:,,,.::,...Lr,,::;:;::::.JL,ZzZ,j#;,,,c@:,.Z;,,re,  .,      rc;Lzz;.       . .......
	.  .r:,Lz,rL::.ZK9r..r::FjceS;.::;,,,:,:,,,,  .:,,........,:,. .,,.,.... .:LcL,;:;:;:;::.zO cB8r;GK,,:,BOc .Jk LJI  .: .  .. .r:..   . . ...........
	  ,.. ..zbL ,LzIF.:r,.;CFJJcC6L.;:;,:,,,,,,rL.,,............,,,,,...,....;rrz,;;;;;::,,.zD:,OZZ.ZSe.,.z8cF. L8,cZ.  L. .  ,....   ...............
	  ..:;;:;r,..zZ:,Ck, :ZCJJzJcJ9c ,,,,,.,.,.,,,...    . . . ........,....r;cF,::;:;::,..FGr ezrI.ZeI...kC:CL .JJL;  :,.   ,.,,,.,........ . .         .
	..rr;::r;  ,:;:LOZ..,JJLzczLLJCdL ..,.,...,...  .:;;r;LrL;;:, ....,....r;zZ,::;:;::..,eb; jr.;Z,JrF  .9r..C: LJr..:.,   :,:,,...... .             .;JL
	L::::::L  :;:zZSj..,;L;cccLccJzbB; ,.,...,.,...b#Scr;r;;;r;LJ,.,......;rzI;,:;::,, .LSZ; F.. Jjrr.L  ;Z:  ,crr..,..,,  :,,..     .            .,;JIz:
	;,;::,L,,;;,zZJz, ,,;:LLLrJL:LZc;Z: ....,.,.. I@J.::;:;:;;;;J...,....rrLzL,::,:,. LbSJ,.Z: . J.,C ,. .L.  . ,:...  .: ...       . .          . cC;,.,.
	,,:;::r;.,,,Jz;r ;.,,;LrrJr,;c::ccIr  ...,.,...JLr;;:;;;:;;c,.......:z:,cr,:::,..deFz,,IL ,. : .c; . ,,.   : .. ..                          :, .;,,:.
	r,;:;::. ..:c:L.;r...:rrJr,,;:;zzLzZJ,   ...... .:;,,,,,,.,...,.,...c; ,J,,,:,.,kdrrrLzr  ; .....,    ..,  .;  .;.. . .     .   . .        :,z. ,..
	r,:;:::, ..L;;r.I:..,;,,...;rzzc;rrJ9OFL,    . ... ............,.. ,L,;IC:,,..rKLZczFL;, ..             .:,.  ,;,.       .     . . .      .,;IL  .   ,
	;,;;r;r,  ,L;;r:F. .:,. ,:L,:,;;L,cJz;LzeSF:,       ......,.,.... .LkJIrI:,,.;$CcSjrcL;  ,....,,,,;JJ r.  . .:;,;.            .          ,.;J,LL  .,Jc
	r:rLrLLz. :JrzrLJ. ,;z,,.rc;: .;,LL;::,rCICIFFLr:,..   ....... ,;Ijjz;,.rL..,0e,.cKIj;:  Jc:,r;;rbD$$ODO;.  ....                        ,.:F;. 9: ,Ic,
	r,r;;:;;:.:::,;::. .;:.    :kz.:. .:;:;J;:z;;;,,cLcr;;:,,,,.,rJjjcr,,.,.:J,.CB; ,.dC, ,:,L;;;;;LCKj;;;;;.     . ... . . . . .   .   .  ..,jr: ,J  JL;
	              ,, . ,:        .:: . ,:;J, :Cc,,. ,,,. ;,::,rc::e;rL,..,,,.cL:zb:,;J;,.:FI;rrr;;JJ;:.....,,.       ....... . . . . .... ...Cr;. c; rcr,
	. . . . . . . .,  ,:: . . .   ;;  .:;;,. .Z,:;r.,,,.  .:;,;::rHF;.,,,,,,,.Je;;rcj::.:CjrcLLLcZeLr.,.,,:...,..        .... . . . . .   , jL;,.,Z  c;,.
	. ................ :,......,.  .;,.:r.  .,L .z:.,rr;,LcCz;,;FzJG.,,:,:,:,:,Jc;jJ::::ZerLLcLcFOLc....,,.....,,,..       ,,,.,.,...... , zzr;, zz ,c,. .
	,                                .;.,     .     .,:....   zZL;Lb. ..........Lc,.,,.cZ:::;:;rC,,   ...,.                             . :L,.: .J  ,...,.
	 
	 */

Measured memory_bytes: 3656