2f:T4e24,inputs = `pcf: vqq glr rpx qcm qkb: ccc lxr ppx vnm: frl scx: czr zqg: lbj xkk qvs: zgv vfq pqp qbl rpt zcq sxm: rgj vrd: hbb trd fgh dbh: crj hjx bkj psx: sxc dsx: bjf zrx pld dqn: kxm lst: fzr mzv: gcq bkh mqg lzm: fdl jpf qxt xfs: zdh thc rxd cjm lqk: zth mbn: skp pxv zgv bpn kzg: mgc vnc zdt rdl: pql ptt jfm hsp zvl hhx nbj: tqk qhx rzr: cfk pdh bdm: ppx jcr tgp mhl glr: bzl snq drq prc qds: glk jvn ntx kqq: ftz blr hlr kvd fsd: hbs czr: rms sgv: kzb tvs qxx mdz: rtk txr cqr nvc: vsr kzb bkp: msz vpn fzr fbq: txq sbn xgq: dng xlh cqb qsq: vvr vqz xpv nlm dhk: bqm fvg cjm khs: dqq tfb blm: lqb rcq dmr knp vfb: tjm ltb lcd vss xvg psn: hrb hzt dhk hdg dtl: jgv tgf: rnk jlj: rhq vmq scj fsp klg nbt: khg dvg plf cng: gsf mrr: bht pbf: pxl zbf zpm: tfc jrm jfl crs hsp sfh: pmh jfl nhf vct fdl: jtj qtl: kvn glk cjv lrd pmv: mpj mmp qfv: nph klg kxm cmj vxd pqx mjn: jfk pql prc: nzf rjt qnc: kbt nth cml: gzg lpz pxs tvd lvf nxl: mgg tnt msz rqp: bkj nbg cfb: slr bmv mnf tgp bfm sff: flz nlq jtc rkz jzk: txm tnt: szr ljs jhm: sms gll tjm: vvz qsf psh: qsf ftf: rkn rcz ddg hbx jfl: rll pxp: dtc nqq cqb sjd bdg hfm: xzs krk jpj hbs fvg fvk: gnv bjh rxt: dlr sbg qhk: dqp tzz smc rxh tbf: tdl vms: sgl mps: fth kqs pnr fbq srg: ndj gdq vzk: ggd dms vdh zdt dkj: drk zmv kkb sjs hzg: drn cmp gxf mkr pqm: gmf krk vvc ldb dpb: sdj bgh plm pnq: fxt mxg mlc: brv hld mzz cxx: vrx zcx xxv crj: lxr vgl stj: tsm xxv jpj ccl zcl: fvz ntx dpd: brv sms frx snm: lnn bqx nqm kdr vdx: fbm cqr fpg pdh qjv: vhd vms xhm: lhz kkv lcq zgk: fkc vmb vjj vtg jqs ftr: crq ntc bsr rst: cxm xxm: mld qxj: nhf dns lhr: znp tfx: lgs skp fdl dsb mzr: qps kjt: kzb xbb tzs: cfk sdg xqr: lbl pdv bjf: vsz lft xnh: tfv lnz tqk: kzn tht: dld kqh cng rlc tsd: kng ndm thn: gkg xth: bns zgv fth bfg kzc fjx: kxm smx: tjq pmv nbj hdj zdt: xtp zkp hpf zcm: njk vtl fvk jbj: nrg bng jqs vgl czm: fdr zbf dkt rfk: rbm grf zqb pxn: cjv jfl zxp: dvt qvk cfv pst lrc: dpp jcr ldh bth djx: hpg dlm gvv: rlc ppn gjp mdv ddb: xgx rft qrx: ckt bdg mmh jxk: psh dbp cbn dvz bxk: mrq jzk cpv pqh vvc: nqm ngd gzm drd: tzj jgc nzf rxx cdn: jhh pxl xdc lgk zjz: ldr cfb bfm kkb: qnn dmp ctv: tfb gbh cvd: rhq rcn hcx gxb: dfn vzc jtv: jjz bqm dfb: fqz zmr pnr nlq ptr: dfv lqm dvg: clp qgz: qzq tlk jzt kqg qct: lbv gxh vdh hpg: hck dlr: jvj jgv: mmh mmp: hck krk: lqb ksr: ggd fzr dsm ncb: rxt kqs hhx mnp zcx: knr mkm zfr: gxb dsm xqg hpr: txx gpg bzf: dvm qjp: qsh qgh: sjd cpv chv pxl vnk: pxl sqs glp gkr: vtg bnj bng tdf sxq: ltl ksb plm lcl: njk zjl tsm vkq: xzj dvm brz: drl str nlk: jnc zpj: rjz psh zvt vct: frl pql tfp: zsm rsl jtc smt drx: xzk dzt hrb: kzs clp vbs: pbf zzh qlp hqc: crc pcb kml qld: hqf cxm rlc vkd zjb: mft mnc xpv kjc plv: zfr fqq fgq xkh brr: fbb mdz dpd hrb qzq: rhd zgn zgb: fft ksj jcn qgr: cmj bsr trc kdr: qns fsj rpx frx nqk: mtv zpj pbg nvh xvv kzz: blv gzm pld: pqx rcn pvm: qnd sfq: gkt nqb: mkm kzs dpl: qxf jvn fbq qxj lrn: jcr gkg: nsz gkz: rlf cbh vcr lzm ktf: hbz ncs qnd knm dmm lhl: mgc qnx xjk: mqg hlh fzv: dbk tdf gxh: dns kfh: dsb xqg: flz ztz: jfv thn kpv: hgx tqt vhq pxx nmz bbt: lgs jhh xnj: dlr mbz nzl: ggb lsx zqz: psx dlb: brz rgm jjf: bzf qfh cdf xbt pzr: nqq cqd sfk nzf: mdv kmn: fvk lbm pnb: jcn lkh: qkl gjp fkc txr fft: bmt tpn: vmk mjn qtv hbb: chn tbx: ckf rfq szr vmz fqv: mbg ncs vjj cxm dgb: qxj trf gxt nlm ntx gmf: hkd rlc hzh: scj bxz mrv xgf zmm: rcl hpt: ltt lft sjg qpl czv: vms lqm zlb fsk: nvc ztm rqp drl rqq: fxc nxk vbs ggb: fsq kcv kjb: pkd dfn: qnx gqf htg: dzv sxx krm ptt: zpp sns: rmd vgf qbq fcj: cxq tkb: ldh pgx ccl fml: rcz znp cqs flg: pst glb nfs tvs jhm vck jgk: bmt vdv mvr qxx dcv bqv: chz gfh znd zzh: ljs qsf chp: jvj hhg: cnh dgl: rdc gzm xjh lrn czf: dvz ntx ncr: bbx vhk: pvm mkm khg pls: mcd knm bmv: sbz gjp ncr cxp: kzs lrn rdx pjg vgl fkl jpr ltx scm: zbf vvr rtz: jrr gdv ndn: tgh ccc: jtr rmq: ldb dlb htj dbp: qxt kxh dmk: bbx hmj fhq: hbx jvj mfh vnv shg: btd pdl: gzm vfg: bbt jjm: kxh xbl znq: vcn cvc lgn bcm: jsz rdg rlx bdf: tqg xmc vqz: chp vfq jdl: rll xzz bkh kdl ljf: kpd pfk scx kdk cxd zqs: shg hxt vsc ctp fks: svd vgn mrq xgx: vvz xxv: lzx lbj: zbf znd: tfv npm: nxz qxx dxb jqp: czv ngd pgx txv cgf: frn rtz qgh rfk rhq: jcr cdc fhx: zpp tbx dbc nnb: ldr rpv: gxd dtd ctg sfh fth: jzt rkn qzx: pmv mtj pgl jzk xhk: qtt qml vnm fqq dlm hkx: jgl xqg nzn fpf xbh: jcr brv zcm dvg zpf: vzv mdn ksr fcj dlm nxp: bhs zlj ksb: fnx qnd zhz: hxt rjz txq msz gkx: pbp xtp lfx ptt lgp: vfg mqg qnx ctn hjh: sjs flz hjx: pvm glm: xgf pch gll pvx lpz: gxf ptt kfz fdr: qlp jtj llk ptv qff tqp: jkt sfs btx: cqp bpf kpv zkd zrh: jsv nzf qvk jjz fpg hms: xxm vzg: cdc jnj qkp: plf pbd cmr mhc vtc: gkt zjl psv: tdd fqq kvn: jkm pgv nbc: tfv rdk cqd: dpb btc jgl: rzb lll: rcl skf: xgf zpq mcd: tqg lkm kqh: bjh xbt hbz ldn: zmm tsd ksj jqq: xrv qfh: qkb txv mpt: fft hgq jjf ltl cqk: nbj lgk chz rkz rtb htj: jqs kzb jlx: tgf ddb prq: knm dzv rdc jsv sgh: njr dzv cxx khs plb: zjm jsl vfg zqg rnj: hrj dng dzb: zlb xqp qvk txf: pgl sxt: mdv qvk vbc jqm: jcr lbl qjv qcq: rst cdf msm vhd hzt dnr: sgl qgr rdp snl grb pbd hmx: bpv bjh mhc vtl xdk: qnn mgg glk fjc mft ldh: txr chl: hhj pnb pzr bpx ckf: qff kfh cvk: cfk pjg fzf mfg zln: zzh xxm ggx: pbd rqp vsr: bqx bhs rjz: nrs cxz zkd: grf gfc bbx: qbc rkp: vct vtg: qsh gzb: dct rmk xmp znq hkl lzx: pdh jzt: qds lnz mcp: ckf xlc lrd hbc jkt brl: qbc cfk xmp: czk zvg ddg: lhr sbz: gpm djv: tzx xbb kns fsp qhb: xnx kxh vsc hxz qff: cqs kmj qml hck: zvg kqd: bhs lmv: zfm mlk zrg dng: zgn xdj: pvm csq jcn xmm: qml vpn bkp gqk dns ggg: cxq mdr: qlp tcp hkl: lhr ccv mhf: vtg qvx dbk vsz bng gpg: xrv jfq mfl: psd mgg vvr gfx csj: nqf svb jtr hlh: txq bjd: mtv fdr nmg xlx fpk: pmh thn tnt dqf: ltl cbg mfg chs fzf: sjg czr bmt: krm brv: bbf fsp: jvb svb mfd: ltl pqx fvz: dtd chn: rzt bqk: hxz lcd jrm brh xkh: lql pxn mlk ltx: qkl blv mxc: ddg cjh ggd hxm: mpt tcm rxh fmn nbx: zsh jxf nxr rsd dll: xzs qdm cpq vbc rtb: qzq tqt bdg trd: zsm sfl: szh gdq rjp: tcp svd npk: bzh btc kjt hhj jrg: ltt skf hbq nbt txd: zfm rll rzt ccb sqb: str mbz: gxd brk: qdr sck dqq ptl: fzr pdq: ljs zrg clk bpf: sfs xss: tch smk fjh pnj gfl: fsn zcq jzr hxt bqn: xbz jrr hbn hxz fxd: rsq tln: rjt vxd tkg qkx pml: hrt dbk rmt vmb rqv: zgb rxh bht: xnj jfk: brh zcf: chn xkk flz jsl: dcq msz gxh vsh: mbg dqn ntc hzm lft sms: bbx xbt tpb: rgl rzm vcr sct zqj: blv zlj vmq lch: jnj mcd kzz ctm: ggg fgk sns sps: pdl mbg zcj: qpv lkm: vkf mvr: dfv vsr zrb thq: btk gbb fks bns hrt: fcs fck zgf pvr: rdk tpn qmk xlx xxq: hld mpb qmk: mpj fdh: qlb pns vmq xlc: gfc qpv qps qmz: kkc ptx cdp vgh jvn: nkr vdv: thc fbm jfj: vvz txq xnj czf ztc: vxd kqd zrx rpn sxx: ndm hsc: ggb rzt hkl hgd nmg: jqq rjp jhh: zvt gqk: rqq znp xrv rdc: zmm mxg: nqm fxt: krm htj dgr xvg: fgk fgn jzr hms pxd: pzv xnh hbb gbh: fsj pns: nrg qvd: rms tvs ksh rsm xrk: pgl rkp clk tjm zsm fnj: nkr lpr qxs jgl rnk: qps kqg: ptb fpd: gvt rst nlk mnf gzp tdf: vzg fsd flx: rgm jvr: mcl mbz rgn: rzm cdp zzh sfx dcj: zpq mcl: glk bcx qtf: rcl snh grb: nff bjh: fdq dld: cfb pvt ptc chz: thx jqq djt: rzb svd lgk hrj bbt mdb tzj: ldr nlk hqx: jvb qtd: pns pvx zks qjb plk: pls txv pgb zlq dcq: hvb xqv mst: dcq cgq mnp hlh fss: dvm lts: smt ppl nnl lhl fvc: nhf nnl ctm clk kmj pxd dcv: bsr vjj jcr jbb: rjz rnk njb rnf: qml blk: tbf sbn sqf kfh nzg rnj pzv: kqg fnn vlc: flx ltx qvk hmv xqp: xmc jhg: zps drq nxz lkc: dvm zxh dqf thc khg: gpm bzl xpv: gls nhh: lck mbc: pld rpx tkt bxp gvv bff: gvv xjm nqf btc rnb: qft vlf cdc bzf bpv: bdv mdx kbt: mdn tcm: snl tfv: sjd btc: ngf ntm: dcj mfg jdv: fsq xxm rdg pxn fkt: cbn grh zsh: sdj brx fjc: nzl shj: kzn gfh qnn jtc: jfv nsh: pzr nhh kpd xqp cvd xvf: txm gxt bxz: brx snm pcb: qxt tdd xjh: bqx rdt: kcv frn zmv dtq: qfb pkl chs nmf nqf: zbk sfq dkt: cjv qmk nqq: hbs prc rsd: klg kxm dmk llk: lvp tbf tqp rpx: svb pxs: qxs vhp mrc lxg hgn: xmc lzx rms pst: vkf lqm bxp: dxb lss: tkb lqg dhg zpv glb: vrx scc chv: zsm vcl: dtl jgv dmg nnz fdg kfm: mjp vlg fhn: hxs rdb ckb jqz lsx: zcl msm: bdv tch qfs: fgn tbf gdv hdg: mkj vkq pnb dld fvd: xhp chz tvd htd bcp: psh fcj brh qvx: qpl zpq nxr gsr: hgn gzp qvk lkl tlt mxz: fmn mql vsb krt rcz: vrg dcq kdl: rfq tvd lgt zrj: gdt kfz xcp mhx jfk nms: lnv gkr jvb hbq gns: snl vvc gzp mjp brx zks: qkl gmt: gqf dhg: dpr xvm: zzc jlq: jrm vjs: tpr cxn rdx lmh qdr bkj vhd rmq gbb: tmm dbc rxx: tlj gbh kjp: zjl dpd brl jgc: tzx pgx pdc nxk: vzc xkk vmz ktb: xbb ndj xvq dbz pzn ctn: sxc jrm lvv: rcl qbl: grh zsm cbh: gqz gsc pvt: xnb bzh cfv: rsq qfg: xlf hbn nsz fbz mlp: ggh xxq zbc dvt qgg: btd rtr mtv btd: gxd dxs: lzx ftz njk mnf lqg: ztm jxf qtv: vcr hvn: lsx jkm vvr nzd xzs: mzz fxd plm zzc: kqg fxl tlk: jdq rhd jhv pbp hld: ppx gcf: pvx szr: rdg mft pdc: dsx krk snq qqf rzm: mnc mnp: jfv xqv tdd: vvz tpr: hld czv vzq kml: nzd rhd skn: xvf tqp sss tlv: nxq cvg: ksq zls lfx rft lxh: ntv mkr jhv hgd jxr: svd czk nzn mlk htd pxx: cfm szt jhh njj: dcj kqh vzq hlr: pqx jrm: fdb sct: clk zmv pqp cnd: xlx tgh rsl: fsn fpf: zkp sbq: hmj hhz grd rgm vgs: fsj zxh rpn kfm qns: mpb cmj: jnc nbh: fsq kzc: gxh lfc tfc rsm: kcx jtv ccv: dbc bhq: fbz pmv szt shz: kkc zqs svn btd zpk: rft vfq tgf jpf: ptv tpt: lnv cfb nxp krm dfh: dpd trg vrx xjr jbm: xtf cdf zrx xsv vxj: htc bzx qsh nvk: tgf hbx dks shg gcq rjq: rhc jqm cnq bgh: pvx str ght: lcd gqg tqk rcc hhx: txf psg: gkx cqs flz hbc: jtc qnc nvx: svt rtk qnr nqb qbv: zps pgb xms: cbn zpj kdj: rtb qbq tlv vsd: mfd pvt dhg xcf: drq qqb: pqm thc jtr crq cxn: jjd svb fcm lql: svn pbf mft mdr zlx: pld cng dbh tsc scc jck: mmh sdg: xmr ppx cqp: rnf nnl cbn gtz: mxg ccl xpk qdh zcx zpp: sjd dfz: fxn cgq tdl mdn hfp hzm: ltl zrs: pgb xrm: mql dzt hbq hbx: tqp kxq: rmd rmk rgl tqg: hbz vjj: bqm lcd: dmn hvl: gxl zrg xpv gfx spt vrh: qtf zks zsd vkn rbv: kzb gsf zbk: rdc ldb: fkc vqq: gnv zmm lkm mkj: sjg dbz: gtf pnq jsp: sxg hzm zkt bpx jpj snq: rms cxm ndc: vmk znd zln rdk xkq: jkt vsc fdb tph: psg ddg czm lgn sxh: bzx pcf rmt: mql qtf ldb cqd qrk: bth hmv csq bxp rqp nph: nld pnn: znr zvt lxh tlk zmv gpt: lgs znp hlh mrq xqz: nqt clp tcm gfh: sxp jfq xpf: ctg kfh fvz dkd vzt: tcm hbq lck tzz mrq: xqv cxd: cmj xxq xxv dvt: ctv mrv: htc lcl sps sck krt crs: dfl mlf xgx xbl: frh fgq rft xzk: rbv qcp dbk: gpm cbg kfl: zlj gnv ngk: sck sqb scx zcx xvq: qkx drq lqm nlf: jnj fgn: xnx ktr: qnc hjh fxl xmh: zcx ptr fjx mtl rkk: crj lft fjx hgq zqj pzn: zpq sfl bzh mjs hxs: frn vvl: hxt hms hxs mnc mlf: frh qcm: kpp dqn bkh: qmf thx: mfh gsc zvm: xhk kmj zqb clc: njj tgd mdv dcj xmg: csj xrq xcg bnb tvq: cgq cfm rln: ggh ksh hjx brk plf lrn tkg: kpp zks vqh: xjh nqb qbv vlg bdg: fnn mdb: jqq pql vnk cdp: rcb gfx xgh: sbd jfq bpj: plf kxm rhc sms kls: jlx sqf fxc zln clk: chv nmz: dvz pgv jpr: nbt mpf: nth ccv htl scm pct: qjp fjh rqv vrh bzf xdv rfq: cmp kns: nqm pgx: tgp grb gzp: qjp nxq: vcn gzh: tzg tlv hbd: csq zpt sxg bgh fds: xrb zjb vcn gqz fbm: ppn fxd zpc: zkt zbc ncs kmn jxq: dlb rjq ccc jtr jjd: nff tsc qkz sfk str: sjg zlb: mql hqf jpj gbm: hhs vpn gzg ddb psv xvm zcj vmk: ndn jcp jlg bns hgx: qtv fgq zqz cfm dmg: vhp jtj lrd: svn nbj bng: qsh kcx: lll ndm hsp: mmh xcp: hcs bhq qhx dkq: fzv cnq npm fjh knp nmt: kdc qcm dlg: qds fqz gvn vld mnc: vnm rvt: jcn trc jsv bdf xcq: dks rsl kzn gvn zmx: lst ckf czf hfq: zmx qfs mgc sqs gcc: tqk lks rkp nnp: drl pvm mbg: drl cqb: pnr rpr: rhc hgn fck zrs ppl: njb bht tvq pnp: tsc rxd zgb szh bfg: sjs ntc: tzx dxb xpk: ccc gcf rtk rgl: sxp hjh frh sss mnp tdl: jck vkt: fxm hjx vdv hlr pls qcp tkh: kjb nqt tsc rvx hrl: rtr sfx vpq tdd jvn nmf: ztm ndj zxh: pdh xcg zjm: cpv cxz dmm: rtk mrk: xdj pdh bdf sdg rdb: zcj kxg smk: hqx mpb zbc: gjp nlf plf: dxb gll: mpb xcg dmd: ckf vnv gcd nkr nxr: mxg rvx tch: frx fbb: fsp qcz sbz tsm hmj ztm: cdf vbc drx bpn: rcb rdb ckf dpp: qcz trc vtc gdt: qml ggb vmb: xjh dzt lvv lqg bbf nsb: svt zxh ngf jfm: ptm nrm rmk jdm: lhr bpg mbh chn mtv gcd: bqr lgz jhv: drn tqt srd: kqg rzm fxc trc: txr str sgr: khs scc dkq kng gqg: hrj djr dks slr: qjb sgv tkg ddv: smc ntm cpq xqz bmx: lck gcf qpl zrg: rnk rdm: bfg fnn ctk vfq hzt: qcz vkn lfc: grx nfs: jpr vmb fjh: ntm zpr: hrn cnq mlc rhq hrn: pkl vgl msj: qdr nsb qnr hxc jxf njz dmr: pkl kzb njr: dfv pnq bjk: lvv dbz hrt rjt qqm: vkf ggh glb nff nzg: vpq zls gxf: cgq bpx: jcs bbx dtm: fds htd flz xbz mld: fsq pbd: jjz ptm: vrg sbn jdq kjc jqz: dkt sdf bcm sfx jvr fbz: ssl xlh vkb: vpn hkl qtt vpq khb: mrr vcn tdj gxb drn: bns jjv: jtc ptb gxt shj qxs: rcb qvl: txf ckt nkr htl vqz pcp: rgj lgt frn jbr jcp: hpm fxn nlq trf: vpt dms: kfz fdb jzb: pgv cnh pgb: scx qxx rdx: bmt dgr xsv: xqr srg pct pbh: vdx scj sfk rdc dct: kns pmh jck klf: gfx glp: dsg qxj xcq nld: rxd shc: qmk zpq: tqg qhm: smc xqp cxd rsq sfq ctk: rzb cqs jfv lhz: lmv ptv dcs: gzh qgg gpg fpf lxg bkh ptv: ptb gzg: mdr sbg: ccv jgv tvd: dvz qdh: thc chs fgb: dmk rvr qfh tzs vrx: ptc fxn: ptl fxl ksj: pdv gtf lcq: jgv sxm zgv njz: mhl gcf jtv crc: nbh mqg nff: tzx kxg: ndq dkj llk hbn: qgh nhf gxt: mdn qbb: fqz zcj fvz dmn bsp: lzm rnf cfm pkd: hhj xzj bjh qmb: kdl shc cvv fgn kmq: nmt hft bqm qcz xkf: nxq fjc qpm ckt zcq: jlq mcl hzj: zjm qpc crc nzl lnv: vkn kpd: htj xnb zcz: fsd bqm nbg tln lmh: pkl ntv: kjc hbx jgl szt: kcv bcx znd rdg zrt: tsd hlr nlk nnp nph cnq: tkt bgm: kpp mdv fsp bfm: rms mhc: bzx zxg: qpm xvm zvg nlm bpg: xgh mdr cqr: jsv bqm hfp: jfq sxm gfc: sxp vss: mld tlv nzd mlf nlm fml lzv: xlh vct ltb kch: fxn rjz dkd lvp pxv cmr: jnj dqp hcx srg ktc: ths rsq kjb zpt hhk: dbp dsg tzg njb trg: vbc jtr xzj hcs: zth cnd nnz: hck dmp bpf djx scc: lck lvc: zzc blk psv mhx xbz: qtv lzv bqq: tqg qkz kdc ngd: hqx grd: fkc vhk hgq jcs: zrs qft vxj sbd: hpg qjb: crq kfl szh: hkd frn: zkd hsp dbc gvn: zzh sxp mjs: fdq lnv xxz: cgq mgg jpg shc rfq mkm: ggx jqr: sjm fsn hms zqz vrg jpg: mlf ksq: ktr ssl blk lpm gls xrb: nzl tcp mzr xtp: mrc hhk qft: xjm frx cfk: dzt bbf lbn: vkb gbb htq: ggg bpg kzg nzg vhq: sxc bsz: rcn pdl glm grd qjq: kxq nvk tmm jfj ftd: kkv gcd mdr mjz rbg: pql hvb zkp jgl phj: fxd gmf qdh ldn rjh: fft sxt kdr nbg drk: cnh xhp: bsp qct zhj xlf: lhz nmg dbf: gpm vtc nzf hqf snh: drl cjm fxm xmc lsp: qnn ppn: zlj xcf xcd: dmn xbc vhq sqs czm lbm: gkt pkl qbt: sbd jtj vzc cst: hxs fgh jxr lbn llz: lbj psd zfm xqg fbq nvh: dns tfv txx zjn: rdx ldh bkj qkz nvc pnj: nlf vdv lch zvq: rgm msm tlj sps pfk: tcm rsm pls fnv: fxl xlx tfv qdb: rnb vbx flx qjv nln: jvr dng txb ksv vvh: vzg hzm zrx ptr rmd: lvf chv jvn pbg: dfn gfc gdv vbb: vlf ptc qnr bmg fpg hbs: gsf lxr qjp tsm: qbc txb: jbb dtl hhg qbq mvd: rqv mjp vvh bqx xzz: zkp trd jxb: pns ksq hhj jqm sck snl tlj: nlf zpv mhm: vfg tzg qpc gxd xbr: txx mrq tqp ksq zpt: fbm pjg mkj nmt fsd ksz: nbh jvj drk vrd zhj: mdn mjn pnr hjp: bhs dqn rxh qbv drx qdm: kqq nhh vzt ssk: xzz xms lvf lsz fxc: cnh cpq: mjs kcx lgz: gcq pbp xkk: mmh kdc: zbk lll dkg: dtc xvv fqz: srd lgz grx jjm rjt: vkf mtj: mmp pmh btd xmr: qqf bxp czr lvf: fxn rzt: vzc tfc: qhx lqk hpm: lgk rtb vvr zmv: rkz gdl: jrr gcq gcc bmg: nqm rbv klg: dmm shs: chs xjr qsd rsm jsz: ckf czk tqt htl jvd: qsf zhz vll: rjp gvn jfq cjv vhp: gkg dks znr: ptl mzv mbz tdj: lhr fcj xvm xqv bzh: ksb fbg: dmr ccc qfb: gnv zbc xqr xbb: kzs ckn: ggg mcl sjs qbt gdl sck: hjx tsc: sfq qpc: lvp lfd: sgb xnx xms jpg bcp lgt: bbt vbs txf mrc: sxm lsp dsg: nxl jlg mlk fsn dkd: lsx ptb qpl: fck jrr: dsb pzt: lbm tkt jjd qbc bnj: hbz bng sxg: sqb sfq fpg: lxr tzz: qkl qdr xrq: scc kdk mhl fvg bth: fdq dpr fsn: trf kkc fxx: xpv lxg smt mkr: lqk tnt rpt: kxh gqf kbt mpj: lbj qtt: zth mdr zvz: bff dqq cnq csq qkx: pnb hgn fcm htd: zgn ldf: lll bpv bsr knr vlf pzg: kkb ggb rnf vld: psx frl nzn: tdd thx fhm: kns xxq fsj txv pxg: svt vms dmm lmh qlb: pch zsh fkl qnd nlm: nzd hgq: hbs nbg: bzx sjm: dkg nvk xnx fcm: knr htc hqf qlz: kmn nqt zlb sgl nrm: jlq ptx fkt hdj: mft xlh rsl vzv: gqz mnc zhz pzg vlg: zpq jqs vfq: jdq vkd: krt qkb hbs bpv jzr: qpc dvz vgn: txm jlx hvb mcl zqb: cpv ptx tzg sgb: qbl txf ndn qfj: rst qsh bfm fss nfs lzp: rtr gdt fgh vhs mjz: lfx htl fpf klq: tbf fqq ndn xgq nzb: ndq hhx gcc svd zpj xzj: tfb pch: nxz qvx fzf xdv: kjp rnb qxx zlq: nrg zbk nnb rvr: sxx hss ccl cpk: dkg djx fxx cmp: skn nth bmn: hkd tvs xcf pdl gzm: cdc qbq: jsl mdg: zvt rdk mbh psd: drn hhh: vnk jjm fhx ptv xcp jzb dtm ztz tgh gxl: sqf kzn pbc: fgk qsf sjs vvz fdx: jcs dpr xcf dzl: nbc dfb dtd ljs xrb cxq: glk brh lft: mbg bnn: rdt vld qzx jqq dfl: hsp frl nxz: czr ggd: jfq fgq krt: zbc scj: rgm lnn knm: pdv ksv: vnv xvf tvq vhs: bns fxl sbd fvg: dzv cjm: khg ctv gdd: sfs txm jnv gff: xgx lst hhg xlx hfp gvt: vsd hcx zgx xdc: cnd tcp ccv lgs: zgn gkg snn: lhl qxs mfh nbc ckb: mzr pdq mpj zmr: fkt xrv mrr hhj: ngd hxz: tfv mmr: mtj pzv tgh vrg qpm: rhd hbc vqm gvk ckt: njb dfl mhx: gvk mld ctg fzr hjm: fbg ndm mfd jsv sdf: gxf lsp tfv rkn: jzk zcl brh lbl: pkl lhv: qbc fjx jcr vkf tsp: xlf vhq spt pdq nbh zls: jfv qvv: qbv bdv plm mfg zpv: csq qxx qsd: nph hld bdf fgt: xzk qpl xzj zgx qxf: zvm fpk fdl jtj: nsz kpj: ncr njk cfk smp: bfg scm dms ctk gxl sbg fdg: kmj xbz rzb tmb: kzz nld ksj zjl pks: fzv sxq ngf dpp lgn: shc kkc vpt: txm rtr dqp: lck bzx qbh: lfc gzh pcb kjr: bpf chp jlg xnh xbc: hdj vcr xdc kng: brz tfb pbp: qhx xjm: str ckp: pdv bqq cng xrm sgl: nnb vql: jvd psx xcq qnx fnn: kbt cvc: bcx xvv ctn rjp zpk mbh: skp dlr ccb: pzv dsb shg vgf: gsc ddb zkp hpm ptl jpp: rcz lnz chp hgd: czf zzc rkp lks: grx dtl xnj klv: vnv kdj qrx nxq flz gkv: htc kqd xgf jnv: xkq bht mgc kcv: vqm txs: vvr rnj pxv jvd hkd: gkt btk: vct zqz spt rvn: xhm kvn tcp rll qcp: fkl qnx: nsz vck: ndj nnb nzf knr dtc: zfm drk vpt bnb: sfq bxz gvv rsp: nhh htg lmh kpj fdh jnc lqb sfx: gdd ktr ctp: zqz pgl sbn cvv: vnm gsc znp mjp: vlf jrp: jgv grh qps tfc tvs: kpp fcs: dzb kfl gtf xtf gqz: mqg zgv: lsp jpf ktm: sbz mkj dpb mnf xjm lkl: vzg sxh vhk lbv: bcx tdl skp zrb: dpr jhm jxf: gtf blv: dgr hcx: kzz zsd: bdv dbh fss hmv: xbt gpm cxz: jhh dfv: cfk xxv gdq: nxp ptc vtd: kfz zcf kbt dmp: gmt flp: hvb kml thn dqq: vkq fnx dqn ltt: mcd dgr bpd: dfl hpr ggb xnh rcc: jpp sfs lxg xkh hpf: mpj jrr gcd mgc hbb fnx: kpp rlf: pbf zzc zls tlt: qxx qkz tzs sqs: xjk vmf: rnk frh rtr pxv: jlg znp: vqm crh: bpg rxt nrs smt xch: qjb qqf prc mtl: bnj rcq xch kcz: sxx jnc brl kns kvd: qqf vxd rzr xjr: kjt ths: dvg hrn hmj rfh: fdx nqt qnr fbg tmm: vqm jfk sxc pgl knp: rgm gpm txx: lst pqh: gzg xbl sqf vzc: lfx kkv: jtc plb gpf: sxg sfq rcn ftz: bzl jtr kdk: bqm njr hrj: jdq ngf: bjf rmk: fnn zcf tdc: qzx czk grh hqc lcq lbn mxc vbx: jhg zrs vsz ggh gvk: glk sss lqk rgj tlv vmz: gdv dmn xkk cjv: ctg vtd vld zqb zps: sgv rcq zdh: kjt kdk lvv rlx: lfc nbj rzm bqr: gqf qxj jlq grf qcs: zqg btk grf mmp tgd: lqm gsf kjb hss: rzr gtf mdz qlp: zvg zgf: zrb sfk sfl dvm bgm bsr: kng sdj hmj: qns dsm: cxz gcq rcr: ldn xjr zkt skf ldr: fmn lkm mdx tkt: nph vsb: mnf ftr dhc ggx dzs: bbf jjz nmf bjf mzz: nqm nnp dtd: jck gls mdx: hqx rqp ssl: sjd lfc nmz lgb: pcf vtc mhc hld fxm: nld fck xxv qkt: xmp smt ndn hrj ltb: vpt klf rdp: tzj sxh ncs dbz xgf: knr rdk: nlq vzp: fnx gpf nbg jpr pqp: zkp mzr xzf: hpr lsz rtz cpk kjc nnl psd rdg brx: pjg kqs: qgh trd xnb: jcn qcp skp: dms nrs: trf xvv smc: jsv rvx: plm vhd gnv djr: msz dms qxt rbm: lhz grx chp lsz: dmp ltc cjh: hpg bqv rdg qmf: zgn pnr lvp xgj: zjz nlf szh hfm hkd cbg: fkl kqh xtf: krm ncr jkt: jfv mhl: qvx bmg vkn rll: fdb qpv: kbt xkk tjq: nlm vgh dmg ndq: pgv hxc: clp tzx jvb hhs: ztz klq jpf dhc: lqb kqd crq jbr: ksz qmf mtj zgx: rxx jjz sqb vzq: rhc sdj svb: gzm fgk: gcd lnz stq: flp cqb fnv hhg vdh: xjk rcb klf vnc: rgj vsc gmt ckh: nth nsz jxk sss jzb vtl: kfm vms nrg dxp: mdg xgh mfh spt pjc: vmf gkx hcs xjk lpm: dlm ptx mrr jpg vgh: cbh jfv ndq hhz: btc vlf xzj lbl svt: mpb mmh: gls jkm: vpq nbh dvj: fjc svn qbh jlx rpn: jsv rcq grb ltc: mdg zpp gxh hrq: flx xcg zkt ldn qqf: clp bzl rxd: fdq fgh: sjd rkz zth tgp: kqd vmq: gbh vsz dvt lnv pmc: cfv gkv chs fmn hft: dhg zcx dvt ksh: bqm smk vqh bmx blr: scc cfv qdr rcq: tch lnn: qns fss zvl: xmp dbp hfp lpr: dms gmt klf`30:T59e,function* removeThreeWires(wires) { let valid = []; for (let k = 0; k < wires.length - 2; k++) { for (let l = k + 1; l < wires.length - 1; l++) { for (let m = l + 1; m < wires.length; m++) { let groups = []; for (let n = 0; n < wires.length; n++) { if (n != k && n != l && n != m) { let found1 = -1; let found2 = -1; for ( let g = 0; g < groups.length && (found1 < 0 || found2 < 0); g++ ) { if (groups[g].has(wires[n][0])) { found1 = g; } if (groups[g].has(wires[n][1])) { found2 = g; } } if (found1 > -1 && found2 > -1 && found1 != found2) { groups[found1] = new Set([...groups[found1], ...groups[found2]]); groups.splice(found2, 1); } else if (found1 > -1) { //groups[found1].add(wires[n][0]); groups[found1].add(wires[n][1]); } else if (found2 > -1) { groups[found2].add(wires[n][0]); //groups[found2].add(wires[n][1]); } else { groups.push(new Set(wires[n])); } } } if (groups.length == 2) { valid.push([k, l, m, groups]); } yield [k, l, m, groups, valid]; } } } yield [valid]; }31:T40e,function* partition(nodes, edges) { let partitions = []; function evalGraphs(set1, set2) { return ( edges.filter( (w) => (set1.includes(w[0]) && set2.includes(w[1])) || (set1.includes(w[1]) && set2.includes(w[0])) ).length == 3 ); } function partitionNodes(fromSet, toSet, cnt, nextN) { if (cnt == 0) { if (evalGraphs(fromSet, toSet)) { partitions.push([cnt, fromSet.slice(), toSet.slice()]); } } else { let newFromSet = fromSet.slice(); let newToSet = toSet.slice(); for (let n = nextN; n < fromSet.length; n++) { let moveNode = newFromSet.splice(n, 1); newToSet.push(moveNode[0]); partitionNodes(newFromSet, newToSet, cnt - 1, n); moveNode = newToSet.pop(); newFromSet.splice(n, 0, moveNode); } } } for (let cnt = 1; cnt < 2 /*Math.ceil(nodes.length / 2)*/; cnt++) { partitionNodes(nodes, [], cnt, 0); yield [cnt, partitions]; } yield [nodes.length, partitions]; }32:Ta80,function* kernighamLin(nodes, edges, maxLoops) { let partition = nodes.map((n) => (Math.random() < 0.5 ? 1 : 2)); let weightedNodes = weightNodes(nodes, edges, partition); let results = [ { loop: 0, d: weightedNodes.reduce((sum, n) => sum + n.d, 0), nodes: weightedNodes.map((n) => Object.assign({}, n)), partition: partition.slice() } ]; let swapped = []; let loop = 0; let finished = false; while (!finished && swapped.length < nodes.length && loop < maxLoops) { loop++; let gains = []; for (let a = 0; a < weightedNodes.length; a++) { yield results; for (let b = a + 1; b < weightedNodes.length; b++) { if ( weightedNodes[a].set != weightedNodes[b].set && !swapped.includes(a) && !swapped.includes(b) ) { gains.push({ a: a, b: b, nodeA: weightedNodes[a].id, nodeB: weightedNodes[b].id, gain: weightedNodes[a].d + weightedNodes[b].d - 2 * edges.filter( (e) => (e[0] == weightedNodes[a].id && e[1] == weightedNodes[b].id) || (e[1] == weightedNodes[a].id && e[0] == weightedNodes[b].id) ).length }); } } } gains.sort((a, b) => b.gain - a.gain); if (gains.length > 0 /*gains[0].gain > 0*/) { swapped.push(gains[0].a); swapped.push(gains[0].b); [weightedNodes[gains[0].a].set, weightedNodes[gains[0].b].set] = [ weightedNodes[gains[0].b].set, weightedNodes[gains[0].a].set ]; [partition[gains[0].a], partition[gains[0].b]] = [ partition[gains[0].b], partition[gains[0].a] ]; weightedNodes.forEach((n) => { if ( n.id != gains[0].nodeA && n.id != gains[0].nodeB && edges.filter((e) => e[0] == n.id || e[1] == n.id).length > 0 ) { n = weightNode(n.id, nodes, edges, partition); } }); weightedNodes = weightNodes( weightedNodes.map((node) => node.id), edges, partition ); results.push({ loop: loop, d: weightedNodes.reduce((sum, n) => sum + n.d, 0), nodes: weightedNodes.map((n) => Object.assign({}, n)), partition: partition.slice(), gain: gains[0].gain, a: gains[0].a, b: gains[0].b, nodeA: gains[0].nodeA, nodeB: gains[0].nodeB, gains: gains.slice() }); yield results; } else { finished = true; } } yield results; }33:[] 2d:{"title":"Day 25","cells":[{"id":0,"value":"# Day 25 ","pinned":false,"hidden":false,"mode":"md"},{"id":5,"value":"inputs0 = `jqt: rhn xhk nvd\nrsh: frs pzl lsr\nxhk: hfx\ncmg: qnr nvd lhk bvb\nrhn: xhk bvb hfx\nbvb: xhk hfx\npzl: lsr hfx nvd\nqnr: nvd\nntq: jqt hfx bvb xhk\nnvd: lhk\nlsr: lhk\nrzs: qnr cmg lsr rsh\nfrs: qnr lhk lsr`","pinned":false,"hidden":false,"mode":"ojs"},{"id":8,"value":"$2f","pinned":false,"hidden":false,"mode":"ojs"},{"id":15,"value":"wires = inputs0.split(\"\\n\").map((line) => ({\n from: line.split(\": \")[0],\n to: line.split(\": \")[1].split(\" \")\n}))","pinned":true,"hidden":false,"mode":"ojs"},{"id":662,"value":"wires1 = inputs.split(\"\\n\").map((line) => ({\n from: line.split(\": \")[0],\n to: line.split(\": \")[1].split(\" \")\n}))","pinned":true,"hidden":false,"mode":"ojs"},{"id":20,"value":"edges = wires.reduce(\n (edges, wire) =>\n edges.concat(Array.from(wire.to).map((to) => [wire.from, to])),\n []\n)","pinned":true,"hidden":false,"mode":"ojs"},{"id":666,"value":"edges1 = wires1.reduce(\n (edges, wire) =>\n edges.concat(Array.from(wire.to).map((to) => [wire.from, to])),\n []\n)","pinned":true,"hidden":false,"mode":"ojs"},{"id":575,"value":"(3421 * 3421 * 40) / 3600 / 24 / 365","pinned":true,"hidden":false,"mode":"ojs"},{"id":27,"value":"plotGraph = (edges) => mermaid`graph LR\n${edges.map((wire) => wire.join(\" --- \")).join(\"\\n\")}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":124,"value":"nodes = Array.from(new Set([...edges.flat()]))","pinned":true,"hidden":false,"mode":"ojs"},{"id":669,"value":"nodes1 = Array.from(new Set([...edges1.flat()]))","pinned":true,"hidden":false,"mode":"ojs"},{"id":221,"value":"//plotGraph(edges)","pinned":true,"hidden":false,"mode":"ojs"},{"id":10,"value":"## Part 1","pinned":false,"hidden":false,"mode":"md"},{"id":43,"value":"$30","pinned":true,"hidden":false,"mode":"ojs"},{"id":46,"value":"//removed = removeThreeWires(edges)","pinned":true,"hidden":false,"mode":"ojs"},{"id":106,"value":"result1 = removed[4][0][3].reduce((prod, el) => prod * el.size, 1)","pinned":true,"hidden":false,"mode":"ojs"},{"id":55,"value":"[2, 10, 17]","pinned":true,"hidden":false,"mode":"ojs"},{"id":181,"value":"set1 = [3, 4, 5, 6, 7, 9, 10, 11, 14].map((i) => nodes[i])","pinned":true,"hidden":false,"mode":"ojs"},{"id":183,"value":"set2 = [0, 1, 2, 8, 12, 13].map((i) => nodes[i])","pinned":true,"hidden":false,"mode":"ojs"},{"id":205,"value":"function evalGraphs(set1, set2) {\n return (\n edges.filter(\n (w) =>\n (set1.includes(w[0]) && set2.includes(w[1])) ||\n (set1.includes(w[1]) && set2.includes(w[0]))\n ).length == 3\n );\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":207,"value":"//evalGraphs(set1, set2)","pinned":true,"hidden":false,"mode":"ojs"},{"id":131,"value":"$31","pinned":true,"hidden":false,"mode":"ojs"},{"id":147,"value":"//partition(nodes.slice(0, 300), edges)","pinned":true,"hidden":false,"mode":"ojs"},{"id":236,"value":"edgeCount = nodes.map((n) => edges.filter((e) => e[0] == n || e[1] == n).length)","pinned":true,"hidden":false,"mode":"ojs"},{"id":238,"value":"Plot.plot({\n marks: [Plot.barY(edgeCount, {}), Plot.ruleY([0])]\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":254,"value":"weightNodes = (nodes, edges, partition) =>\n nodes.map((n) => weightNode(n, nodes, edges, partition))","pinned":true,"hidden":false,"mode":"ojs"},{"id":471,"value":"weightNode = (n, nodes, edges, partition) => {\n let localEdges = edges.filter((e) => e[0] == n || e[1] == n);\n let int = localEdges.filter(\n (e) => partition[nodes.indexOf(e[0])] == partition[nodes.indexOf(e[1])]\n ).length;\n let ext = localEdges.filter(\n (e) => partition[nodes.indexOf(e[0])] != partition[nodes.indexOf(e[1])]\n ).length;\n\n return {\n id: n,\n set: partition[nodes.indexOf(n)],\n int: int,\n ext: ext,\n d: ext - int\n };\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":258,"value":"$32","pinned":true,"hidden":false,"mode":"ojs"},{"id":291,"value":"plotPartition = (nodes, edges, highlight) => {\n return mermaid`graph LR\nsubgraph A \n${nodes\n .filter((node) => node.set == 1)\n .map((node) =>\n highlight.includes(node.id) ? node.id + \"[[\" + node.id + \"]]\" : node.id\n )\n .join(\"\\n\")} \nend \nsubgraph B \n${nodes\n .filter((node) => node.set == 2)\n .map((node) =>\n highlight.includes(node.id) ? node.id + \"[[\" + node.id + \"]]\" : node.id\n )\n .join(\"\\n\")} \nend \n${edges.map((wire) => wire.join(\" --- \")).join(\"\\n\")}\n`;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":355,"value":"/*{\n let id = 2;\n return plotPartition(kernighamLin[id].nodes, edges, [\n kernighamLin[id].nodeA,\n kernighamLin[id].nodeB\n ]);\n}*/","pinned":true,"hidden":false,"mode":"ojs"},{"id":508,"value":"//partitioned = kernighamLin(nodes, edges, 100)","pinned":true,"hidden":false,"mode":"ojs"},{"id":459,"value":"partitioned.map(\n (kl) =>\n edges.filter(\n (e) =>\n kl.partition[nodes.indexOf(e[0])] != kl.partition[nodes.indexOf(e[1])]\n ).length\n)","pinned":true,"hidden":false,"mode":"ojs"},{"id":534,"value":"function* tryit() {\n let results = [];\n while (results.length == 0 || results[results.length - 1].crosses > 1000) {\n let partition = nodes.map((n) => (Math.random() < 0.5 ? 1 : 2));\n results.push({\n partition: partition,\n crosses: edges.filter(\n (e) => partition[nodes.indexOf(e[0])] != partition[nodes.indexOf(e[1])]\n ).length\n });\n yield results;\n }\n yield results;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":582,"value":"adj = nodes.map((_, i) =>\n new Array(nodes.length)\n .fill(0)\n .map((_, j) =>\n edges.filter(\n (e) =>\n (e[0] == nodes[i] && e[1] == nodes[j]) ||\n (e[0] == nodes[j] && e[1] == nodes[i])\n ).length > 0\n ? 1\n : 0\n )\n)","pinned":true,"hidden":false,"mode":"ojs"},{"id":593,"value":"deg = nodes.map((_, i) =>\n new Array(nodes.length)\n .fill(0)\n .map((_, j) =>\n i == j\n ? edges.filter((e) => e[0] == nodes[i] || e[0] == nodes[j]).length\n : 0\n )\n)","pinned":true,"hidden":false,"mode":"ojs"},{"id":603,"value":"lap = adj.map((row, y) => row.map((el, x) => el - deg[y][x]))","pinned":true,"hidden":false,"mode":"ojs"},{"id":599,"value":"matrixEig = import(\"https://esm.sh/matrix-eig@1\")","pinned":true,"hidden":false,"mode":"ojs"},{"id":601,"value":"eiglarge = matrixEig.eig(lap)","pinned":true,"hidden":false,"mode":"ojs"},{"id":634,"value":"nodes.map((_, i) =>\n Array.from(eiglarge.eigenvectors.left.slice(i * 15, (i + 1) * 15)).reduce(\n (sum, el) => sum + el,\n 0\n )\n)","pinned":true,"hidden":false,"mode":"ojs"},{"id":652,"value":"nodes.map((_, i) =>\n Array.from(eigen.V.data[i]).reduce((sum, el) => sum + el, 0)\n)","pinned":true,"hidden":false,"mode":"ojs"},{"id":649,"value":"mlMatrix = require(\"ml-matrix@^6.8\")","pinned":true,"hidden":false,"mode":"ojs"},{"id":647,"value":"eigen = new mlMatrix.EigenvalueDecomposition(lap)","pinned":true,"hidden":false,"mode":"ojs"},{"id":605,"value":"sorted = Array.from(\n eigen.V.data[1] /*eiglarge.eigenvectors.right.slice(7 * 15, 8 * 15)*/\n)\n .map((el, i) => {\n return {\n val: el,\n node: nodes[i]\n };\n })\n .sort((a, b) => a.val - b.val)\n .map((el) => el.node)","pinned":true,"hidden":false,"mode":"ojs"},{"id":622,"value":"sorted.map((_, i) => evalGraphs(sorted.slice(0, i), sorted.slice(i)))","pinned":true,"hidden":false,"mode":"ojs"},{"id":626,"value":"plotGraph(edges)","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W33","stdlib":"1","titling":"auto"}