114514

/*
XqQRREXJ7ii:..::::iiiiiirirrv7vvvvsuIXDQBBBDPJ7i:...::r2vrrr7rrr7rvJLuqPXdd22Yrii:.:.  .::......... ..........:.....:...:.:.:...:...:...:.:.:...:.:.:.
r:irrLuIIqX52u7i::.......::::::::i:i:::rrvsSKZEgEP2uri.i::.:...::..i::.::r77vUJ1r: .                                                 .   .     .   .
i:i:i:i:rrvLSPdZQDEqKjY7i:::::::i:i:iii:iiiiir7YIbMMRgSL7irriijPDKqqKUI15XZPXSEMBQD5uIJ::.    ... . ....................................:.......:.:...
:.:::::i:::::iiirvLjIPDgEDPXUu7r::::.::::i:iiiii:::r7UdPKggMDRQBBBBBQBBBBBBBBBBBBBQBBBBM57::       ...................................................
vii::...::::::::::::::iirvj2PdZdDddSuvri::..:::.:r1dRQBBBBBBBBBBBBBQBQBBBQBQBQBBBQBBBBBBBBQgXr.         ..............................................
gDDZPKuv7r::::.:.::::::::i:::iir7sjISbPEK2Yvr7YPMBQBBBQBBBBBBBBBBBBBQBBBBBQBQBQQQQRBQBQBBBBBBBdvi:         ...........................................
::vLuUqbZEgEb5jvvii:::::::::::::::::iivs5PQQBBBQBBBQQQBQQQBQBQBQBBBQBQBQBBBQBQQQQQBQBBBQBQQQBBBBBMXYv7i.    . ........................................
:::::::::r7YY5qZgQDPI5uvrr::.:::::.::7sIbQBBBBBBQBQBQBQBQBBBQBBBBBQBQBQBQBQQQQQBQBQQBBQBQBQQRBQBBBBBBBgIr:.    .......................................
:.::::::::::::i:ii7vu2XPggMPP51vr::ivJSEQQBQBQBQBQBQBBBQBQBQBQBQBQBBBBBQBBBQQQBQBQBQBBBQBQBQBQBQBQBQBQBBBggX7.  .....................................
7i::.....::::::::::::::iir7YuSXqXXqdZMQBBBQBQBQQQBBBBBBBQBQBQBBBQBQBQBBBQBQBQBQBQBQBQBQBQBQBBBQBQBQQQBQBQBRBBPi. .....................................
ZqgDESIJvrr::.:::.::::::::::::::ivdRBBBQBBBQBQQQBQBQBQBQBQBQBQBQBQBQBQBQBQBQBQBQBQBQBQBQBQBBBQBQBQQQQQQQQRMPKPP7. ...................................
i:i7vU5KSbZZPdSjv7i:.:...:.:::.i7PQBBBQBBBBBQBQBBBQBQBQBQBQBQBBBQBQBQBQBQQQQRQQBQQQQQQQQQBQBBBQBQQQQRQRQRQQBgggI:.....................................
i.::::::::rrvs12PPPbgdXJsri:::vKRBBBBQBQBBBBBQBBBQBQBQBQBQBQBQBQQQQQQRBQBQQRQMQQBQQQQQBQBQBQBQBQBQQRQRBQBQQQBQQdv.....................................
..:::::::::::::::ii77YUqqdbZXEQBQBQBBBQBQBBBBBBBQBQQQBQBQBQBQBQBRQQQMQQBQQQBQQRBQQQQQQMQQQQBQQQBQQRQMQRQMQRQRQBQdr ...................................
si7i::..:.:.::::::::::i:i::i5QBQBQBQBQBQBQBQBBBQBQBQQQBQQQBQQQQQQQQQQQBQBBBBBQBQQQQMMgRgQQBQQQBQQQQMRgQMQRQRQRBQQPi .................................
qPZZddS2jvri::.....::::::::7ZBBBQBQBQBQBQBQBBBQBQBQBBBBBQQRQQQQQQQRQRQRQgMZDDgZgZgEZEZEggMRBQBRQQQMQMQRQMQRQgRRBMqv  .................................
:.ri77j5PqEddKP51v7ii::...:1BBBQBQBBBQBBBQBQQQQQBQBQQQBQQRQMBQBRQQQMRggPK555X5SXPPKSPbZZggRMQQQRQQQRQMQMQMQgQMQQQbu. ................................
:.:i:i:::::rrvs22SPEdbqbIvrdBBQQBBBBQBBBQBQBQBQBQBQBQQQBQQgQRQZdMgDgdbSSUIU2u1JUjUssuXPPPZZZKqgRDMRQQQQQRQRQgQMQQBg7 ................................
:.::::::::i:::::::iir7vs11PQBBBQQQBQBQBQBQBQBBBBBQBQQQQMgZggQEX5ZbEdPSSI5IUJuYJj1j1j5XPXqqqI2uPZDEgDRRQQQMQgQgQRQBBd: ...............................
17rr::.:...::::::::::::::isRQBQBQQQBQBQBQBQBQBQBQQQQQQQQdddZdES5IPqqI5U1JusJYYvJ1I5X5SIIu1LvvYY2IqqPbDDggQRMgMgQQQBBv  ...............................
K2DDEPPXSJYvr::.:.:.::::i2QBBQBQBQBBBBBQBQBQBQQQBQRgQMQgEqXSKKXJsvsYJsJ77r77vvLvvLJLJsjv77777777YYU2qPEEZDRgRgMgQQQBR: ..............................
:.:ii7LjuXPDPbbP51Jsri::.YQBBBQBBBQBQBQBQBQBBBQBQRgRMgPPKqSIUIUuLJsjYYv77v7v7v7v777777irirr77777r7rYsU5ddDDRMQRRgRQBBI. ..............................
i.i:::::::::ii7vj2SSbERbXqBBBQBQBBBQBQBQBQBBBQBRQRQRQdqXKSKI2uusJLYvv7vrrirrrr77777r7rrrrirr777r7r77Ys15bbEERgRgRMQRBgi .............................
...:::::::::::::::::iri7vLbBQBQBQBQBQBQBQBQBBBQQQQRQgdXX55I52UsJsY7777r7rririrr7r7r7rrv7rrrrrrrrrrr77vL1IqqbEZbRgQMQQBY...............................
Uvsri:::....:.::::::i:::irZQBQBQBQBQBQBQBQBQBQQQQRQQRPPPq555X1uLJLv77r7rrrrr7r7rrrrr7rvrrirrrrrrrr77v7sLjJU5EZEDQQBQQB5..............................
U1KEdDZP55svrri:::.:.::::UgBBBQQQBBBQBQBQBQBRQQBQBQRDgPPKK5SS2uuss7v77r777r7r7r7r7r7r7ri:iiiiiiri7r7vYYjJuLJ2bqbgBQQQBs. .............................
i.i:iir7sUSSEEdqdPKJv7rruRBQBQBQBQBBBBBQBQBQQQQQBQQggZEPbqS22U2uUYv7777r7r7rrr7r7r7r7rrrriiiiirr7777LvJs1jusjuU1dQBQQBj..............................
:.:::::::::::ii77ss2SPqPDQQBQBBBQBQBQBQQQBQQRQRQQQMMZDEDdb5512121s7v777777rrr7r7r7r7rr77rrirr777r7r77L7LLJs1u1YsXQQQQBu..............................
:.::::::::i::::::::::::iYKQQBQBQBQBQQRQMQQQMQRQMQRMDMggPPXXII2511vsYsLYLYvv7777rrr7777777r7r7rrrrirr7r77vvLYuuuY5RQMBBv ..............................
PuYvrri:::...::::::i:i::i1RBBBQQQBQQQQQQQQRRMRgQQBQQgEKS2IU5IS5SuJu5U21uuuvv77rrrrrrr7rrr7r7r7r7rrrrirr77v7vvjssuRQQQBL. .............................
1LqqddEEd5I1j7ri::...::::YMBBQQQQQQQQQQQQRRMQggRQQgPXU2U5I5IXSX5SIKXPPKuvrriiii:iiiii:iirr77777iii:::irr7r7r7vY7uZQRBQ2..............................
:.:::irr7sUKSPPDEPIS2uvr:rIQQBQQQBQQQQQQRQMQRMgQREX2u21I55IXXKSqPPPdbEPXUusuvv77rriiii::...:::.... ..::ir777vUjsvPQRBZi...............................
i.i:i:i:::::i:iirrj2IUXXPUPQBQQQQQBQQRQMQRQMRMQRd5212UI2I5XXqqPdRgMgRMQQBQBQBQDKPuJJLriii....  ...ir7L25PPdXXXdX5XQBB7  .............................
:.:::::::i:i:::::::::::::72QBBQBBBQQQQMMQQRRDQQQqIUIUIU5ISXPqddEKSj1sYY5XPbEPEPPPqS2svr7r7rrii:irvs5SEMBQBQBQMdEPEMBDi ...............................
512vvrii:.::::::::i:i:i:::uBBBBBBQBQQMRgQRRMRRQbX25IX2I255X5X5X1s7ririrr77vvLvYLsYjYL77r7rrrrr7rLYU5XIXqPPDZDEZgQMRBP:...............................
LL15XbddqqSSujYvii::::::::rDQDbDQBBBRQMQRQMQQQMb55ISIS25252UujsYvLY7r7r7rriiir7v7v7Lvvr7rrr7r777vYYjLYvv77r7r7v12EQBv  ...............................
i.::::ii77LJ5KdPPqbPKu1J7iv2qKSuUqBBBQQRQRQQBRgPX25I5I512u2j1JsLYvL7rii:::::::irv7v777777rrrrrv7vvs77rriiiir7vY77JBBi ...............................
:.::::::::::::::i7r7vJ1UJSqEEdKquvLdQBBBQQRQQMdP55IS252511suYJvv777LssLjjUujYr:i7Yvvrrri:iirrvYJsJvr::...::irYYY7sBM. ................................
:.:.:.::::::i:::::i::::::YdEq221I1v71XdRBQQQBDZXS5SIIISIIJjsJs1u25bgBBBBBBBKgQZY7vuvrrr:::i:7vYs1vriYXEPSIULrr77vsB7  ...............................
b5U1jvii::::.:.::::::i::iUqKIXUYvjUJ7v1PZBQBMgqX5X5SI52S11LYvYjXPdEdPQBBBBq..7QB2r7vrrrririrrLLJ7vqBQBBBRsKBQbY77sgi .................................
L7U5PqPEMEbS51uv7ri::.:.rSP2UXjiirs2jYUUKRBMgbK5K5X5X252IJJv7777YLvvYvvJKUv7jjSbXirr7rv77rrrY1jiiSRBBBBBP.:1QBDj7vQL.................................
:.:::::rirrJJ22KPZPPqEKUUqK12XvrrsvS51USIMRdKPKKSX5S5SIXUUJYvLvv77777rrrrrrv77rii7rv7vvL7777vSqLrYY1XEPPIU1UU2I2LLbi .................................
:.i:::::::::::::iiir7vsY1XPU5YYuIKgMb5PSKDQdbXX5X5XISUI1Ussvvvsvv77777v777L777rirr7vv7YLvvL77YSJ7irrrr7rr777rrvvsY5: .................................
:..:...::::::i:i:::::::::1SIYJ1KPEX7jqXKKMMZKX5S5SISI2u2jJYY777v777v77r7r777rrrrrrrv7LYLLYvLvssY77r7rrr77v77777v7Yui .................................
bUqUsvLri::::::...:::::::rI2Yjq52Yriuj1UKgQbK5K5SIIUIuUU1ss77r77v7v7v777777r7r7rrr77vYJYJLLLsLY7v77rrirrrrrr7777vvJr.................................
7rLJuqbPSKqPIU1UsLrrii::..r2sIKXvrrsYvuSqMgdIS55I51U111UssLLrrirr77777777777r7r7rrrvvJuuJYvsvsLYvv7777r7r777777v7vLJ: ................................
:.::::::iirr77u2K5XXPPPSq55SSsSqvivLJvjSbEdKSIXS5II1Uj1jjLsv7rrrrrrr7r77vr7r7rriiivs1uU1UYvvYvsYJvv777v77777777777LJr................................
:.:::::::::::::::::iirrYJJv2P2YuuUKX12Y5PEPP5XXX5S1Ujuj1ssLYvv7rirr777r7r7riii::iL5K55U2jL7v777sJjriirirr7r7777v77vJr.................................
i.:.......::::i:i:::i::::::rKdK2UuUIKX22bKPSKXK5XIIuUj1jjsjLYL7iiirr7rriiii:i::72SXu1ujv7:.::..rsJr:i:iir7777r77v7LY7.................................
DqPq21svrri::....:.:::::::::rqKXIU77vJJXqqXqXqSX5S2I11J1JuJusY77rr:.:iirii:iirLKX1svriirr7iir::irLY7iiii:ir7777v7vvjr.................................
risY1IKPgMMPPPP2UJj7rii::....i5II1j7v7JUPPPqqSK5S5X2UJUu21Uj1Lv7vri.::rrr:iirLPXXjs77sPKXUYrrr7LsvLJvir:::irr777v7Lur................................
:.:::::::iirrYLu1SPbPdEgZP5IsvL5SUsuvvrv5bKqPqXXISI5U2UUuUjujL7L7rii:irriiiriY1UXP5KDBBBggbPSKRBBIJSLirrr::rir7v7LYs:.................................
:.::::::::::::::::::iiri77JjIUjuKPPSUYvYbdbPPXK5S5SIS2Uu1suJ1LY77rr:ir7rr:iiiiir7vIX2YYuI2PPXuPDZ52Lrirrriii7777vv1r.................................
:..:.......:.::::::::::::::::::::7jKPZERQQbbKK5S2II52IU2uuJjJYvL77riiririririiiri77s7vvUI7irirvY77rriiirii:rr77v7Js: .................................
DKEX2JJYYrri:::.:...:::::::::::::::.7gBgd2PdPKXIS252S2IUIuuJ1sLvvrrii:irrirrrr7rvYJYYYs7r77r77UusvL7riiiiiirr777LJr ..................................
ri7LLUUXXqPDEbI52UJYrrri::::::::::.:.IDSYs5EPPXXSSU5UI12UUuUJJLY77rriii7rrrr7v7L7YvYsusLvYvLvvJU1UJuvvirirr7r77LYY. ...................:..............
i.i:::::iii:rr7vJjIIIXdPqSqqP2Jvs77i:7DSUsIbDdPSS25UUU2UUu1JuJJ7vrrri:rrrrv7vr7777v777vrrr77vi7vsYjJ1Y7irrr7v7vv1r ...............:::::::::::.:::....
...::::::i:i:i:::::::::ii7rvvLs2Sq552XEP221dDZPXIIII1U1Uj1JjJ1Jv7rrriiirrLYv77rri7rrr77YsJYjLLvLvLvsLs7777r77v7JY:.:...:.::::::::::i:::::::::::::::::.
Jrrrr::::::::.::::::::i:i:i:i:i:::iiiijdKIIKZEdqK25U212U2UUuuYJvvrriririrv1u1JsjKqbEMRRgRDgZDDgEPU177LYLL77777Yu7.::::::::::::::::iiiiiiriiiiii:::i::.
SXZRgDPEbZq5uuLvrri:::.:.::::::::::i::7dqX2qdEbPqXI5UU1Uj2u1J1ss7777irr7sPZMgMgRDDddqX2I1IU21XPggDgDX2LLvv7777uI:::i:i:iiiii:iiiiiirr77v7v77r7rrrrii::
i.iiiir7YLu1XPDDRZDdRDEKX221J77rii:::.:uESS5dEDbPXK221U1UjUuIuJLv7L7rrvjX1JJUUX5K5XUJrrrririii7vuIPPZbKsvvv7vvSviirr7rrrrrrr7r7777v7LvYvLvLvvvL7v77rr:
:.:::::::::::::::iir7LL12XPZdDgRgRgZPbSDdPSKKEZEPPqK5S252I12uUJ1Y7r777vjv77v7LYjJ111Jvr7r7rrrr7Ys1Lssuus777vvIJri7r7777v7v7v7vvLvvvv7v7vvvvY7v7vvLvL7r
:.::::::::::::::::::i:i::::::iiir7LYU2UIgPPSXPZEZbdbPKXIS25UUu21uv7r7r7777v7vvsLYvYsUu2u1j1suYujuLsvv7L77777j2virr7r7r77v7v7v7vvLvv7v7v7vvvvL7YvLvLLY7
riii::.:.:::.::::::::::::::::i:iii:::i:iPDKXSXqZEdddqPKK5SI52I1IUjvvrrr7r77vvYvYLYvLvJJU1I1UjuYjLLLY7v777v7L1virr77777777v7v7v7v7v7v7v7v7v7vvLvYvLvLvv
ZqZPPKqqKu1Lv7rii:::....::::i:i:iiiii:::SZq5KSPPDEZPPqqKKS5ISIIUI11v7rrr77LYJLsYsLsvv77r77L7v777vLYvY7v7vvuuYirr7777v7v777v7v7v7v7v7vvv7LvLvvvLvv7LvY7
i:irrvsJY2IPdgZZPbEdIUJ1uj77rr:i::::::::JDXKXKSPbDgDbEPPKq5S55U51I1uv7r77v7LYJYJvYLsvv7v7v7v7vvYvYsJYY7vvjULirr77777777v7v7v7v7v7v7v7v7vvvvL7LvvvvvYv7
i.i:::::i:::::i:rrvLJj5XPKPPdbdqPS5IIUYrIZPKXIX5SKZEDEEddPbXq5SUI1IU1v7rrrrrvLsvYvsLsvLvv7Y777YYsYJYLvYLUUsrrr7r7r777777v77777v7v7v7v7vvLvvvvvvvYvLvL7
:.:i:i:i:i:::::::::::::::::iirr7rvJ22KXPPDPKSX5XI5KDDgZDdEPPPPX5U1jU1uv7irirrv777LLLvYvLvLvvrvvJLJvsvvYU2Yrrr7r7r7777777777v777v7v7vvv7Lvvvv7L7vvLvLv7
7:r:::::::::::::::::::::iii:::i:i:i:::i:7dEKX5X5X5X5bEMggdZPbPP5522uU1Uvv77rrrrrr7YvLL1U1vvY1JujjLLvLvJuvrrrrr7r7r7r777777v7v7v7v7v7vvvvLvLvLvL7L7vLY7
X5ZMgdSSI521sL77rri::::::::::::i:i:i:i::rdPqSK5SISI52IXggRggbPPPSK5SI522u1YL7777rvsuJUU5UUjSSIJ1ujvLvjuLirr7r7r7r7r777r77v7v7v7v7v7vvYvLvLvLvLvv7L7YL7
i.iirr77J121IIPPgDbKPqPXIsYvLv77rii::::.rPbXXIS25252S1U1qZQMREEPPPPPbqqXPS2sJvLvJj2UIISI52S5XU1JuYJsI5srrrrr7r7r77v77777v7v7v7v7v7vvvvvvvvLvvvvvvvLvs7
:.:::::::::::::::ir7vJsuuuuPPPXPqPZgPq1YugbPKKSXIS55I51UjU5PZQQRDDPdPdPqKP55U2uUjjsU15XqIX5qSPS1J1USXJrrr7r7r777r77v777v7v7v7v7v7v7v7vvLLvvv7L7L7v7YL7
:.::i:::::::i:::::::::::i:::::iirr77vYus5DdKPXKSqSSI5UI1UuuJ15EMBQQgZbbPbPdPbqKIIjuu12K5XSqSPPqISXdKLirr7r7r7r77v7v7v7v7v7v7v7v7v7vvL7LvY7vvLvYvLvLvY7
rirr:::::::::::::::::::::iii:iii:i:i:i::rEPPXKSKXS5522u2UIuujUuI5ZRBBQgZPddEPdPPSKSK5XSSISSXXPPPPbqJirrrr7r7r7777777777v7v7v7v7v7vvvvLvLLvvLvvvYvYvYvv
ZKPSKbdPP11uJYL7r:i:::::::::::i:i:i:ii::UDdXPKKSqIX5IU212j1u2UUJu1UXDRBQBMMDZEZbZdEPdKKSXXKXbZDdb55vrrrr7r7r7r7777v7v7v7v7v7v7v7v7v7v7Lvv7LvL7LvLvYvL7
i:iri77vLssU2PXX5KPEPP5SI5I5jv77rriiii:iPgPPqPKqKKSS2I1Uu1uU12122I1UjUKMBBBBBQRRggDgDggMgMZgdZKXI5Ijirr7r7r7r777777v7v7v7v7v7v7vvLvvvLvL7v7LvLvLvYvYLv
i.i:i:::::::::::iirrrr77suSIXISXPXqSSI25DdbPqKKXPSSI5UU12uUu22I2S2S2S1uY1IERBBBBBBBQBQRdPS52I25252SJrr7r7r7777v777v7v7v7v7v7vvvvv7LvL7vvLvLvvvLvYvYLY7
:.:i:iii:i:i:::i:::::i:i:i:i:iiii::rir5MdEPbKKXXXq5SU5221IU2121IUI2X5SIX5515KERBQBQQEPIU1IU52S2S22S2rrr7r7r777777v7v7v7v7v7v7LvLvv7v7v7L7L7LvLvYLYvYvv
siririiii::::::::::::iiiiiiiiii.::i..YgZbbbPPqqXK5X5X5X222IU52S2IISSqXPqbdEPPXSIS552S2SKPqPKKXX5SIKU7i7r7777v777v7v7v7v7vvvvLvv7LvvvvvL7L7vvLvLvLvLLY7
SIPdddXXXKSX21Ysv777irii:i::::.rIMBd2DbZPdPPqPXKSX5X5IuUjuYjJuJjsusuu1jUJjYJYJJJJ1122IU52I252I2SU5I57rr77777777v777v7vvvvvvYvvvL7L7L7LvL7Lvvvv7LvLvLL7
i.iiiirr77LvJjIIqqdPPXPKP1sLv75QBBBBQgZPPqPKqXK5SU212uuJjvYvL7vvv7vr7r7777vvYvsLjJ1sJsuu1ssYJsjj11I2sirr7r777777v777L7v7LvLvLvvvvvLvvvLvL7vvYvLvLvYvs7
i::i:::i:::i:i:::::i:iiri7ZQgBBQgRMQQQRRgMDdqK52jjsJLujussLYvv7v7v7v7v7v7vvLLYLsvsYssJYuJJsuJujuJUUS17irr7777v777v7v7L7LvvvLvYvLvvvv7LvLvLvvvYvYvYvYLL
i.::::::i:i:i:::i:i::....vBBBBQMRggDggQQBQBQQgMDDPX2jvvr7777vvv7v7v7v7v7v7v7vvLvv7LLYLJjusuJujuJ11215usriirrr77777vvv7v7vvLvv7vvL7vvv7vvL7v7vvYvYvLvL7
Yrrrrrii::::::::.:.::rsKPQRQQQQQQQMQgMZgDRgQQBQBQBBBQREdS2v7rrr77vvvvY7v7v7vvLvvvv7v7vvLvvvsvuJ1uU2IUSQBZKvriirrr77vvv7LvLvvvYvYvL7v7LvvvLvL7vvLLYvLv7
KIqSSXbqS1Jvv7777vuKRQBQBRgZMDMgRQBQBBBQBQBRQRRgQMQMQBBQBBBMgq2s7r7r7vLvvvLvv777v77777v7v7vvssjJ11UU2uqBBBQZPUuv7rr7v7vvY7LvLvYvLvLvv7LvLvvvvvYvYvYvY7
...:.ii7vIKgMRQBQBQQRMZgDMDgDgDgZgDggRMQRQQQQBQQQQRQMMgggMMBBBBBgPI1v7r7vsvLvv77r7rv7v7v7LvJYjjujUu2UUsPQBBBBQgRP1rrrrr7777v7v7v7LvLvLvvvYLYvYvLLYvsLv
v71UqbEZggggRgMggZgZDdZdZEggggMggggDggMgggMgRMRMQMQQQQBRRgRgRRQQBBBQMq5Yv7vvYvv77r7r77vvvvYYssjsuj1u2U2YSQBQQEZgQgES2sv77rrrrr777vvvLvYvLvsvYvsvsLsYY7
BRQQMgEEPdPbPEPdPZdEdDDgEZZgEDDggMgMgggMggDgZgDMgRggggDMgMgRgMggZMgRQBBQEKuYvv77iriiirrrrrr7r77v7vvYLsYLvIIPPddZbDgQgMDgDZPPS5jJvL7v7777r7r7r7r7r7r77r
*/