ࡱ> -./0123456789:nIIFaPNG  IHDR#kPLTE7Z@41ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaassssssssssssssssssssssssssssssssssssssssssssssssssssssssssssaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaassssssssssssssssssssssssssssssssssssssssssssssssssssssssssssaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaFɟtRNS0JbKGDH cmPPJCmp0712HszIDATx^흇*mvxQƮ\g 8&!ǽ> |vc߳#HGC省oA=8ć?\? ZAw@oֻkQ3XRxBXs7j]_ c*cI z~Kh+z;H"«wJc^\]Cz R%/$|+ a\y㟨L"ai;17A8ZۊkD \l/lcV8}|_0QWA50OkCыVtɂFX{Ca[OL>m$\e¡8?v^wA "!¬^Y-^Ҍ FKg΅JK0x0 AX9={Ak@m1!&;EXߝs}+0" @~n~b+Imm֑žw!|/df"eA1ވpi?S*n)+/E@,kS.s3CemX4U _#|0Y_3K [w i/ \-@ }'L]4MكrajSwnX[^`}KVAq-hkE }]3Hg#R3VZjjeFZkHwA\0KV#䓝\FK5:6캦W1F{YN1eyn,6^M݃pA.ccwT'S\*⣠+[õ(oA])YSXxS qQս3+¨~ϑSbMTs'&gOUͮ[#TX =7pXTˬ@b&}3R7&+B)x%o¶.T oA`e(=='vM^:} aL: )B˘j?P3]SR 3 xf W ГvڻfgU0 \HDC=׸pgbwEtaJ*$tafƵBꖻ@mzV.kG`ZhJ5@t6)5vMLWO"19D_:ZF;6#q77 ckb蜻p]_ѡj@?h5dw/' ؏S9L5@#\/pS6eWF ^ 7ygzYcxif)"2"\fSIr=cIiD]daUK02NhK5 Sp}`s~ssrgvQ>Es v/dL,a= |œaohma5UcklF soMТqŗ.[p9@Y6*'*oiH&>R3Qߡ~4/jZlF;3Ѡ|A'J &}pxau`-a z^&q~1aBp_ *w#L{oji iZXfY"\yᖑa@6) )ʥevd&J*,7tt-o赕y9AXSRp)QGAZ%n;iիW7'軩=0fAUO{C%.B\F-4QQkp4N]x6;% 'g0I*H05f@-̂i$|ko`;L`A5mڹOtYG*:$'@qܠj~pQmY|ðD& m=Z#f۰w&XdY̭^ Ѻf%rd}7ס9п 7|n}#ƩOzU 6^pZ~!#uދB\*8՘ 'M?O+?[۬R!aw3U|v躄V(UU/{d_+nT0 t"P\VpnӄjF6B#z751o2ۮ&CiYn-t9E~2%@X5k4Vn]c&+FGL5錡6ws&[f*LP*<noG_6 j?g>UQQُU¢+̒xVM+oyJ?{uj;"a_~Գf5ԽVy(,q=z`hC@ѡ ׮auÎ}"zJn%;9i +VppNBxʓEE8(1[z|[0 /L\kjI!"^yc[Zmp2KWs&6 .ŏ׶u!^_>`+7N]84,q& ,80cyZ~>`܄U G8D,j$:yCNP:+΢<`1,<eFZ{b5'،Qo sqh"Hj|^.' ve ]O0:XBX|Uӻa> 16 HaǏ=({k誸Xe sDn屁0)5F8> _X$,<ވ ՗]D3s(y*A slD<:5&W4W*[ LK'n#/0kzOPmʦ>"*gH2뺻 oM@.kP#|]f^9QuӥWF[ G)JwܳaZc0 N&+Pw]6ܞ}c|ntDBTWa{M>-1K-/$Jب8ߵv'$q+Vq+عLJâM;,%-STX`s Ww ,ZF`Vy^ϑ(m|l,⢱^/1Kzʺ ig6:"-%Mj EZf|ژ@n؀+[H{lK{Z71: v[ҨҦ1'Dx ӸI/2rc/;cΪHKݟSnvˈ J`®zu6TwWs`ǡzxI'Ex % O-j61I&>tx aQ,nU^dM-DS}R7\G>0>.9d]{Z#N[7-abA^0jb (W_Uk01 aK-7QfiHvQ*$Ae VF* K?VJ˺׳YiEٮWn~m j<21՗ O#dl10U9yTZTXP/Zb{Tx}x#~aZm5b.)i#rv^ wCͲQǿ<_ᝯw7fgڴ^R}/,U4.j?C5 [ꌑ6v͌3J+Mo jBUͤEĿP #6.f;d#k=ق"PNRY;,!K@¶0ڰ⋎?ExѰuA?IwZ! \a7pOG{oNp5#85&i`v΢?g_qaCj8>ˤpC? aV^=zUԶLo1a5={Q'%D5ǫzJTQ0Mq`aE̕F"D|ri* `Q"=dmGn8xLMmQ{a2^(ZbՏ~/p7ڒ`*,N lZh:«弮޳ջUcl&/20Uڦ3@;W :;۾;Gl*߇7 MDU\ Q//Յ4?HA</q|%ݜNoKǁޡ;GBD po^R\:d_la + +nQ{$ l67\Z M@ECí]lzoDFf|nu 8+Rm [C@؎ >kz_SP#gt㑎(c*ރ;TH`2j̳ f).LME/F}Gpj#sG/FXOa…S#k^]#?I$:Evf *YBcFў5{v:*;#Rd6XU}3*3M< ͞Z@BBlBl &T 4 suOj߇#0yJp/-_;m OBuooB5 m5xLֲɍ!i\uW;U/ 뙩TD EVMQ.mY`Df>䕷8,ʟJW5BkH59rU4&j3p_0¡lO-;~v.g$[ZD,U8ͫ'$ ,Hf?:g7EڪZ^'ts%}g t9h:Kо`%PQS˺55W.(GT BB 1E߷;Վ6#R8 nҕ9&Hk(eVW)i5`5J<1JlM:@>@oK!~@/eY_A4.S\G[݋ĄYUQ4YkZU2hvvonnwuݽ]iTXfs` K[ (ϩpu۽ƆآB$c*T)5k#Ho`X0n}KCfD.ðL?'° fBZAؑidlGذ&S3kӈ"#w\I[P ^ϰF8o$̅Jv|Z՝NpTDP'ڊa؝@Eڦݧ%o,-Y;M٢v:Wi5V5HP7q(.&1{*BbC"MU"kH|)!l؍gtۖ}ҟ F s؏G`VY ]foBkHC5S +TQI(SCMo"n|rfJUQZ:S hWw F90ͨT1^e1Ų kye$6hu* o(!BzkĂX)t-\ ϬIT6 ^ߞ5q9MP1ړ(w(E$~X"GTYaыstێc2m^#W*46 m7"jL{GܦAn]Jcvr3.lM,{ .'@mG~'9G*.K|"5:7u Guza0W }!;[كl^lq.I)y|s(2b)/m`o*k߅K{j]{>A8ѝ"ݹ֦3"&^z0|z] sL$vvO\x~1 |aHbk:d t. n{fO&v] al9ld9젶֍`яẑCwv낰D)6,skpW6갪IZA5YG@|j`(@9A8#Q.V @u ށ0"Fl&N!L2, xVDBsNkFt*Sҁ/v^ƃUx^U#/pa ̨)Iu_bF.0 6yz6e=s 5UhH"?"M#t"3 -vqa% vvUkۈKk{@`ΙVj-_id=s߀uQ5lܱUp*E hT sD2q-:"AR)Nc7 E^H lj+x =#]Ⅿ$ԈcpzF>e +έ\CX#Y8bG`r޸4Ofr96/*s[^߈%E5[ L t@2sRj vq56[TM |8w YA!d"9Ud_=nc2%zXuRw~)/ks o ^0Ņ}=/:G!EĈ$E䫏CNL%DPލ:,=Rd$ P`N ]fnkb eطv>>6j(la ĔqQ k%6Ґ}*DhH|OwJ h&S')pN%A0Ս WFA}ZIiؐ26G_ k %=-Tn/ݵ&+z#Q Ho| 0Z3˚7_ ^E#8oD8bFp"̍yMtsW1 Ik0KM?sL2#+0Δz9_N  ANW0DZNAyaihd"*}60 z[[ew꘶g~= ' ۱6j)2 m蒅8%96i>P#Yv?t,.D PQ*C)DC(T7fd-g6Jހ`z*~T8e;CsYKV>TaJ@#Y4!Ï.wyT8F/e HKS3k`F*vX!9j3رe4 k4 X**a TƵ®;#^rȩӎ0w/ j^5^MzNOpl>tgё1vtN(W8w4BK{ 2>aiPK\wQCkl+I:67ZaaJ#cQL(_yho ^{&VCmN)XI+AB;ph32*}"i^8~s8ɬ Z2=K_Zp{iT奙S( jmW{`ƨD᱑ v\O   ¥"ktH;8P |?uL\N,_t|_0El9v[)TTҏuKoCw"u%e8e·:W" qkNW1dr0ufDx["h5:8ر@@ZEѹ$p wFa1*S/D8ώcKkY֚"$?dtjAYP j U$jBÌ'Kti0?=ϯvȾa;"Śfnu(mbĩgVK\^kܽ% FUY#ጌaIk߫/HGg'. N|2VxF:b-igr0gyP q,[rm# qU_Ix%Utƃ6^UV c*C +ݩ ZG0R`98Ra#v䑟Cx^NL+Xr\!rLvż2oC F"ԅ_,7.hPŵ<¥WzK~y/H:<3*7{yb/ c,w#$r —katP ;nGd_j`ms!t(HC4/~+ܵܤS9 +Z_Gx؎ڊ)B *̀( 7Y{>&Ķ%S*En՛.? C^ 뗜Oda]j";LݭŠ5/\+r:F|`Kو^rFRB BM>CAÌP86tIVw2#ܺVJcUBg|A=ۇ0/GH!ZB.5QǴhԨq#p4Vcv>!KyJV9-ÍF{Q]Qe r*Zn30U|Ws,M<1*~e$ƙ<`JYa%7)j +  lrφ*he䯋p3.\ 8Z݊[;ڥ)D,un Szc_a08 SE>ϖѹN,EbN<;W* #lG^A5H5vNIp-U= UF:Q*̑7+:Emݝk[of *&x*2|`5HTthg.e*- ƛ7lԥ|*@Fo%.\״r::Eҵy%eob00dL}#qÙ蝿/FXE]?˅(נCNKh/…*ôt OL~%e%M/yI^-“w5bf)h/vʗDs+TI\l|+0[ cI*/{i "n"AOZMsYvqQ԰3!VCBpC"l} ű&rm#O kWsW"zwvr>ʮ`\s@x Om^׫4pn6]T&cB z9\*<0/Ygn~vt; >'8ӝk n6FZ +TuOYh"ܔ^+R.4dhV\Pݹp/xgkF\qSZ% (MZne$o@bL5 [25 _!?b:N0+`|8O |0|A=\#,ؙZ$Oɯm+iE0]b l!K ,G8/tww_AgNvY` h?q[A^ ;u%Mғ[ ]*}Ž9D 8dkVH . ^^ -43\20n[,CĦ+ lJ,DN,6|x"t[r|.2ĩtֹoXFS;WDP.b| +MklA֦^ k_RahG=K~ZZ ;LØA2xh]H+(H(Mk#\Zil!RH([GF\4\ ƳD몭s2\#5BȅnA\avP=7CBlE-^NOpŀ+]}M`2LQE#jw ,{j ]_Th1Y"Zh j(݀6];2=9esM= Dl . $Enx6_UOa.%^=DĤz_X i `Zah&=EoA8L6M􃰊1 a7`90AIZ zRN:rzf U8_"Hr⎦~ec Vɖ WE<Ӎhz%s_U ׍_ȑ(I0~T:<)D*G&H4:' [D$$Ġ٫P&gwv.٤Gc2)3'ȷ7!#e%eɎ2vl-0j' bWeOPiVs C0iֈ&420ŴQJ܇ W͢/kN9(D"P aiSo@>.*F"Qup"mW\aL1R8:pQZ*<QJ^kd%#ÙRaUb:ѥ({hD+Gj 1NEA;.GIHQ[,Rҁ|V=#Sȭ(lnd3_׵B:Ӗ!,c.$ʠ; $,3)$uNrA.cBb| ¯*!qu*Ɲ9_WI bJka`q@}ỳ6K?'yu';vW-Adע˂}-Q*YmJmy".|0)<+#m:H])]2:5]J^d:Tf "s[jF$9$r@K)@ye*{Ռ "U{p?#EXDDD?*|JI@h;Cjs ֽt#๪V,D`(.AnJjgT!@Q .wgm#Zү͸V.Zy O0uf\0 ۸NbnUP+Z@v/@ 'wʑpHbRLH}Ddp#Ɩg H0=#[M<۔1PF5Vs}G ϊS p-d5~:{yjƒt2,΂h|{;RWĮ |"b$x wztN(Z [L `gY{v =9wImUpI>:O06+]{$EXԾ`F]K"֕:O&ȗV.W3ʁJ2Վn'JFG$\w%HuF߁ڝ9q|aNg .0U$̽7D#+eZp$9)e#Q,Ey&:6 ԺM#*Va=& r dנAIa]w7jWڶ s~%8qz6[ɔ*v*;wb]a-`ҧ 2P`"{Zo^ Pama{~F#;0 iN"*hf7.-sK-AnXL`@2+_+sT[W,TphdI~:=q k~ BML]NJW ( O Ƶt5\>l^RaHyaGUm sޔwt!]0$Sr/P\jᄛsN5ZQ ;3qad+1DIXZ!W7($9 <87H'Hn0)g03\Fb * 3|m M("\5҂9^VpШ/x̸զomXFGMI#1՛ӷG oC zosa0hRa*1D4D.(!$pqu+QTm$"fNr&h5#fkDI0y#AfbV-\CMiO!\֒͝3܊>R=*,nn%ߢa-QcuvM!@0]4 i)&v†s0V"aЫ4=<ſ˯?_v᪑ >V +&*r"hmDrӰTua{Q3UՅ"gr4  L/y+ެaqhmTвd Tz6.~av+§qEAYVplo8?R}B%p[uC/R)yFQx'v \zS ?rكJ9T\:r*pp-*X)Y+/d"x*LQU6Br3&5ʳ6 iPaL&t2 AX4X6B =Nq;|%Ϫ Ǎ:pdJ([夕8uIg s0\׫UݎSfkƢB*J-3,} >+:#ül>Lp`fU ~Vz{+ g` G` u&-NL+XuR*U31沪2ݖvE/C=(ʍ<.#%R?vol0!.zs+j7y\#a6zO"3W&` KGqlPY&< 'WCpV`pG2pWIΒ:>yS-rA ~:xGn쌀*BYp* |ygPؘpȽց!_dV1qq67@f ay[XVY?9a G㌄ W",1_Pѐkxc.׺%Srk9\2YDظ #Fǯ4{.A8U"0N|]1¦F ëV+L8Ž?I(>ݫwyC^Bucrcbkw#l|^XaBvqj/5'`p 86܀BQ6SbUEpuxѠgG^tp!Ca )QY*[uNY}bً=p' 2ӎa2\-!D $t:!ʛ+}vRcn܅GmIA.co!|64v@ ꍏ5%śuVM^E>9'yI "Sa[9r۲ Rc!̽^x|0V MCEA@$? Pt3ӧCa4̫^xCXߵWk.aٲ^g mmFZ_IHxQ9 n L7w@ZMϴ|W!\F7PF)}UXܛ= GI{q^ρ/o(Li(/ZO<`e[bjHPE31~6vJWI;lש:*`֓!×h0&[ԅI_>rZPtIjü@mε#' eƽ1K1"VraymAY΁vV>he)A%ŧr s5FgTC]GcmN.0͓E#)F0d C\ ֭CQ[-rS՘Drj~jt7TP+"t+f1  - OPuYtGNxWR]+qp* . ha۪)>Wv.IMa/[㺸#e uTb'2,9Qalbϫu}N_}]ˆN0k V5:wsݝAB.x\݄2~jH`-_#+یv&i0 Jki7 ,g"h$b]Z$%Vvr@/J1KrB_[Ia{n:SM̄Tݞ:.ҵ4a ,~|"g%⥭pKP.ĕ@A߀VU쿙Fz2F,=dٯoCL!Ac?@X"3!XTcx88]%ptsK*l! 6P>4 ZX`QEN n(v:6Q>hĪIcE zFX5aʼn$URkF ƃzpdqWaa8e% U( S:?`SFXH JT801o-$U#]ҏD3 7 U}#%e$Q·#Q,EۉXK7Qti=*0),1ƠȰ`)܉y1 Y0.̞sv:a|t<GXsKO;/R9ݳ6ޜG}lZuXr :*v5`b}KR(cKmFxG5{GCru"lK_`rAbx!6Cڟ=߉0+攑@tF2,nz҅É2T&l„ٖZ0qr&pL[-RX}y;n1jl-ߜIB|5[tT'˴(C褵 -!L txm gV{Of^;kDr!Ejc]  eht3K1aĬ)Oֳ_4Qy 6i$p ?p]+! W&EXkƧ@;tu4” <8ޜ_FR~xzVy=non Yae~ %,?. k# %9SDn9Et .~d_4QJ *ʠ\~ PPWdXMzAhÃzƔ-Vy"O8LCm$ʅMj6bSPѵÔ]e’GJPrMNrzSFPe 4cUW[aߝSKBzHA.*纍̉Nҍ::Qd[+Y~1r&=K l1A͸G*,os5q17t~)2EbrA4\CYar jke|eC~bm#T .U/|%7̃ρ˶&jTEi>}[6z 3/lOsxܝ`z[uBxd~mY cQ2|2Y S:dl'@|f3@?TcG@U +FK." R m:̰:[e7oyoӑB˴ zʵ&z`=%¦Qڄ YxT'dUܘ@~Ohە8^& K^'^ !F!lު17v uڣsBp7eʪYh?akygNv8mMnLW_ūsKi) s$zFb惻*ED5G_In=^'>Hlp- Coryu [6K"ҕ&fNwFL t\#r'B_k/]bժ_i$DAGi?o`tnT=$;sص% ,dGݙ(;YV +@6a=[S0U[=f*"whjVʊe#j8Q]WљxQa8z7DiW1zP>i[^LaXzt"!7^}Ue'1XQWM ބ0>AFlµERm'2%Բ0JV >C K IOKɣ*(Gגdp#PG:>2yy4 -hwjQ$ڝXY8t^)̝c2uJ'raeu}%n]S[hD^",_QY Ax;[8Zuseco2x 1F}qJ?xaX3O!XjGᕇUtj!1ajw"^B" f4\+ x6@ 1FDm Qn{Cw zH(3"%j\! ŌIPawvII%wHl0,{.i֒Fйͅq"3X@xt/>sD滍Җzl9 szKNU >ˉo 0N8`9應fM#-C Jt* U5}YڊBQ @U"j;{"/7xVm4Y;8"'H!ou^#q9]#: \$$D*̈Nmiu3)a § Ia(˜[ iuҪV#b@;\dRI37'~UWF]a"ឋF݄8[ BXwϜvp9Z7ȣGs0[!9ۑ&Wyr%~VnG9ZǪ_RC7xy,#VհܡwŬ%Ƿ ] 9îc2R ]= s(ہT; 7 0GƄ|<'K>VpK /=?l_7W1sZwF9BAjis'L`0/G#V*E8Co<d!614'&#X%p?T_i!£ ”!@&ihB^"DZ0M:Fgq#j. 70Nۇ|1 /O-+}"攡%9r :HyVu<&]6n)ԝKQF`||iÏI\PnX ġ{tw0p0]JH짷0]p^fN2) F6T1+ًpf՝[Ax&"ae9 7t)v|#edUh8o= QFM0 *J=)~EEL_M{K?ܯQ,Bx8. d0$ V~8{.jJ@_A4ba:p';a2b 7Dx{5}4G.WtsN~n[aEʯF{@#l[`| -Enº5MHn 8z F;}Sp ֗w_W+uL$\tir03ֻSE+m¦m -Ikt$VeGc'&`*\#gܘ`*l8ѯc#k^D47S30''f e*t\)!#̕9]? #U^UBUj2 ~8nPqPJ)7A5^GB`n"}os'‡y+ 3V0q+5Jhx9(Kp༴Dpr2α3h2?֗Pԙ3(Dzh+/ [J~j{j -jGj#\C^i-@5|L;\W6sOܜ֤ў0/!=9+f1 gn[!N] zVk @V 2 i#l"-mZmq7_s2;()`DJXJx 6֙1]>x1T+] oWG图"] 8 "a]rT f/QslVbxS\p$[|wqakM ba#oCXi+hQu5\~vwLi~GfWa]ӫaXlkif OG3u!CW"3%r:Ba靫I8[jynbX.MB laGƳ )Y dDP.Y){E1{u K6sJyYpG\v~i08Nj0h G+t[W0dGԽ\ř$3 k%HؘJE3 jRFS#o | p+f pPm$=+C>!]5"k67 an4Tz*츞mڃN)'htp9Gq5Y [{t-I^#P]r96.*;s2Oa%X" ?#PA 3OcZMVb*m^6޷laND%J,f% SP o}¨2VE}k]zq}a5e_`F8R찊tޢ߆0OPւC.I7`l"agl9ZY3d=YZv?Α@v1]!~9.a6R᱓h!lLK5fxìr%.S)r vw,X^Ž)}iZ9kҏ#Ff\'TF1(Fe@cg#KV4茝w0y9'?\61f6vx8rv-#an_afuoM7K:$25q8ߴWiu OvgI|(z.d:2HC*",09l@kyFl\No`N_aԭ 5H5F@ n).P'4'd%HpF@q w)j3A] 6 ;vB*Su(rG;g|t}̌gr*=\!l=7|^:GE+I;{ `D:*f4n{Hp0DžY;!e:<|FR ;0P94”8S;ޅΒ9<)'& >B]QhX%=X#q|s,7i3]%1ej6u{@4] G"\8 o'`#\^sBQ yY+sգa,P#kha~b]U f vt އ4k[YZ҅n$c~ނ=ߪ7n zs'F*<}ũ7],U% zy%Tu|7¯ %ꡞVyǭҮ>kO!MVe"=[9sG|Ra5hkFGTB(5U81z$ozU|/FkBpCÌt){Swp|6wZM!7腱s}m#,2'`w`#[Jti9'#ߪJ hGz 5Ռ²3Nbt;{[-D$k=h 1Eiే-v N` Dۑ@qu4ro J̀UEb~ª d2LkOYo˰Ax*v{ew#yn%'h2"ex}*[~b3,}_B|&S\GJzTJvFG-uݙ#t:oq[_=*siVukVh0%4݀q'ÜgIA6]htf|g@& -p4(;DX5`{.)IN?0W dS|:2+6[_ p3]w!|hkA561&nX 풻k¿2eHrġ$Pә׈Jp A ( 枢`+ gA7G[ 5uU o w|DdUHŽwG^Ok#mTh#7iT#Y-"Y}؉hf+-"kAg(|H\ @m$sYsxQa6]´/[ ?9/ ؖ_ʷao _z#Q# ZC]D@Yi_M dUt!FZh]t2& M=lߥ¥=1M}ӱsed0HUڲ-P0/˰C87py3ֶ% X1S-/gm >~巍42~sV۽Bױ!k|TcWa-xR ay mdEX:C/37x|F$C5ȰFXX0zΛ"){FQ000ȇ2!JD5-*]#W&uHA:uQDj<"Y>X Jp")~OH,ƅ!qe^x~M%~CoOItp^dٔ~Wkfl *tm3qvtOuO*6_pCP0)HC85Zq}n jfuo<V2fK |=:'):ɲ0aXH'x 甞W5<*lV6yœvTr{ G9ӟ|] v$qk[M2·bIA5ӛ pR}%˝ FT:G4|Pky‰uFgDX[Zy m?gDpẕ43C̀?g 0c!X=E~ RX[qp+Z ۈK:S u=ՄKf?GXFćA ;['vZLdMLas4ɰX`V GpI֩A:m JF龕\dT 04Mh!F^P._]8>mқoSяTyiK0GkhvLA[MYSLNn\X5U䔧5M|I3H0Mhݵsi)Fڊ D ^ڃ$Պ'eX9CNsI-G%uFF|0f߳v( ̿N R> .҈mmr܃Sɪp_z_@puV Bn\'#r `ƽ{>\Pw EmaɈn+ lҋCԛc$([軂o$5Jgu£WACvi" ~E'yRfGΰץI ~f9zc7(4ްƬyp7LnAxm-a>} DzA;Xya;s(Ĺ`z1> Ti" 6L7wwބO.(o/( CN0ckA{*LĨ[rM!~ KJ$/VQy#4Q;[mVS$;xN4A]I]P.{` &7E8z2-n<܄oGGuL83,MEu`>v8"!澋a\啎;( ^=CgVPsR78C߯7@3qtSb4O \ɶ}N?BY[#= U8 %D8y>(L;Z!}a{aMĜ[MP0Uwp:Mߡ3o`3 oA4./H\&G/J"̰ɰQSls^><_#Õ;iX4kO@%E,ťasHkγ^aZ'd)WK*=ٻFx\pZ=q2IxL.6\ cKbN&t a?DV[IpNaopYXI\+j282|xYTA ͺz>p q6.1+_p Xiځb ?Cɰ\EzӹݹgR:p3c̶O׈,dF u ,qǏg*vsqv*4qË92Jy>JcPX_0w#{tMrL! az$-T sqt't\܄,-90/ ZUK b^gm$-|9l䅱Y+2Ѥ/ DxfoT֣i xAPE髩 Xa\l}&' .2* \lחF_td,-V* @G*lFU C!>6bWQ3\}p2ΡEv a+I. X^#,?a#¥TX  [7GEn_:(*Y?JW^`GvZ9VϞޯBXd+󶊕wzqJxf{=cUy3U1d¶Wյf\?׫'㙸M_h*J=Cif lL/0Pv`P3k2F,aS~xg!TQ Ϫ0rZв3yc;ubz k#AkF7Dy cqxAoO\0bwWUA'0G̓ϘK1ɜ+3|$hN_'dy-M" (qoO:U!W!\08Zw# WV`6Gt #&Ulrv/Gx+ᬞm̹4TYV^J^gNћ"` 'OOw'SmWLz_} Z5Knqp7rX/W|?*4] bR4wZm T>G9|G6}_f$d9@XDmIܫdf- y̤ɻ=y fڛ)ֶlY}ƾy ݟ'!*gV[xKF}N\+3$TҚVapW]:U:ry=O¯dG{L6ϰ`jv΋.oxb*\rn f| Ɯu/OuÈ sKHj(JzwA(IA,ׯwp4HOK*^# ̧&CA@ a0!_#-ԲGr؝c ^mL60.Bɰ{a} ?g\nf^!EMjJb,b#S=ߌfvsWClft~%ƖU8{w{LOng[G&F8'ܓ YA8y.p!%\~V6aXijp-!grs*q)w«wtvPB/1$Ԫ5I.*s2|v\AnPf8fAN@>[ѹx&tDIN`aSTa hpSc$>i^c.wQ?2fxagvy r\RşڗAk_xS9ΤA+ Ycx p2 f| M qpa;K4EݰAz6`NLph?w75(>Z vH[k[`otv~'@ķ z+ĔeQ;>V'{zHL"|x ˅26˛X{0zpsŶ4Z-V@ƤvaHXHh볗ι9`d 'v `j#Ƀ+Jv&!ZKnf.RUuU=M,G֟igGL`WG:rkEKgQ ]9v lmA+0B*Oub-1|lA:vZSbxBu?Lw."8ɰ|DȒ2ck!s#bR6fף3gLف" S {1ZϿ}'x Dp4?}3X,{-%UMc~k Ƭcg(-!չ>r!Grs:@3tXFqVb^G'^y\Iap]ں W+v8"gpa52eS" Z>-sz+h GPzKwG2@ĸfsv,, PK I{T8ÓKN(CҸl %UT FP/48mU: !:*ֱ0cgv l2ME%vH9h$;#||anҙZQ3E1koAd4pUH"d8bN pris[ӝ[eJJ-\(kD=ejn2|E7_6⚄EB! VɵS[8ݍux4jcM54)=B[#͕Ʈ]A8w"4v4&ЙucY %BX"<<Sd\*,CAf݌04Hww5%Dr"›N>&Oi9\ jWϜ[.D8ꈌ53iH2D8tWW z*〖K.#`HWZy @NldvoCLH-`]MWA5~+/b|hp&XHM,I| gYu[yuCҗfrŀ ./?"\|͑tٜXσK!l 6 a踭V",QTW[plk|~a8jNF6;ŵ+ ]vDXlx:0"h_.k*}9w!xa!d;{ WF+1' >6؀uO>:F?V~އDiFB!IieW|D"+ vTaAxEo]O`Z:1 l'/g6#j *qaF`! bN =ᷢkue+6#/#5V.(F*JLd^O:.+fܯڡxE[㤪"q6^E6FCd+Z; Vvm4*my Pj:1lSOWpYd\XP)@wv߷?rm¶5*ZH_A ma Bq[uH#@}h }K7&YH;b?zJ2=r%KȀph'pXq}}Sޙ-XxF+&g%?G~xI*ҬEԏ^v&OiF&-l#SkNPG2p3ϏM֎p(1'OY&4d^OPUX2pxj`p ymGwRuIX [UT֡fݑra+}~3vlzB/ f擄 aW[fL;JGsEq1NOD޷JKPzaʜ'σ%\{*VUum>t"'NўG]D!uVj2F  w\pD GE.x4{s<͕ |4XUll. OWN4K+AaP׺^E6[ J ziAx?D]cM0ZX`<Q2\/Hj0ޓ70ek[[EXWXSjjp >RPa`g Ds0_bG݅<o=QOnC=GnI3J-^kZAx'gVY"w$E7XSF:xv]ǃ>5b4czM5!hF$=KokȈAzR@z#/M[~9VpaڍjEp \Tko [4~ށp1r],<1Xޅsnv Z2ٝ"?^xYlH6 I~CuE`c9%(؄yGTE7 ˆ |$Fʪ B{>$j:-aa>AUh z]+" f"[ddx9U`Օg ' [)qL]Wڰxp"%;Vw)\^JZjg_!no]w wͱ"4嵩)ʁ2Z\ðGmi'kpljDY8+׽o TaX GPrn&|9zpVgĂg{qZ ۔]o\FwDjцxLLT <ݔҡqz0 kE^e3\,ã^B')8Q0"|P9J0' aw2usD7!"q|4za߬}[ipI Y KiX# BC nzaAبpd^ 4.Z0d( ȍ4M!,9(^p3 rfqY]Pn &F ay UqzpD*tRᕳ6AXjD\3F&V1(W6Q 76WU4U0ƃ +e-r]:Ɵd#ԃ 4fF+Yٚj(xW}IVM3I>b^kU[!S:loƈo&Ga #uF]GW2au1^8F>d+)xzBkgxn+kVx67m&nk_쐨C;SAܩ<ϕYY.k/ 0 r9#rf P9}\x anr p*NY e>Fbl,S[6 CQd{i=rOC+;| ?u2{c35fOpe6"O+x|-(AgS]к<"|pKQ;yHau~ Gspwirf;9Ƽi Ƹh?C}AxF-|ƂK(,J&K`[SA׭̓]XNl'Q$xμF6A\1aWܟWNVCyDęYK/&U"'e%Z OYS ٧43WՠO* r4rQ $n?>ZK2NXpx" }$RDz/tͫ`n ?G!MphM'* lLuB-|ȗ;^&?)!$"_cN Fh[EakVaz(#N ''VK%Q[YCxt U3E ZIQ7ST8D0L0aQ^=˶"u>0 WWZrU3an fRQqL/r V}; | 'Z>N`びf*GdV#B4޼}ɠ-\!,NbxWDM1ݲ:\ԩu9S* | uDXw{H\xpmL(zb1"kݽJv덌a\I14{l #R]F0\?X;W# 0f*.(2yoe(H | >)J"|^DTZDpb0ny.d9fqJ7x=ȺЀ`jzث Sb7K&ƅkzPpsFî5a[=Ghegf< B&K"#Rt+\+*Bd0 rFg3k ,Q°z>UNД7u8"A ?wPF%[jup 8 ޣj"#ÝC`ǀa~M_ϔ]ô/,a>k V qJxدw؛{/[WTw" [5*s'f;rCK_6%iEfI,+ ŸĠh RJ`01z1/5K)a1:Cx“ /DX=0Ҏ 7:sհZC(Baj蜆p'H6G?U~ CVWZc:aj#yDX&t3Nב Y!lև^WAxDj! ~8R8j3"jj(kg?p〱.ul :7 "B|%w&Fv"|6a,q(}SSC+qD-*l-ߍ|Fl`D2p_<؈5&e 3ȩ}0[ip/t9 L;2aC|&fj]/5)p$p a^f]VR[l0`E!]ۄtWsKE{l:t4UcB.且W3 aQb =0~5E%d!K2~<#9"q +@7 Xr1+]#AeH]T6FX|%+-h/ÝnТ ?yƘh)&CGE0pVE$p #Qv*(t^'a)Ip5[mOWaGq{yu:PN 'Ram;u C|ac⌆9q[Ƕ*ՅQ3|栖FzW0i ׫Vl%!;J4~*<"\f73z0EF"E:+辊Iit޺=3IIaḒyo;FX7N uc~a7xH[輊iE656RL65c+vITlFXde$|ML#.ͪ`+æ?7tC?DOghAKY_]H FIZ"X28_}[-sOtxLaLp7*̘pbds,)F"ki .莙p9Kad v-*cx s`mgEX݀A?T`"@ #3!m rgFYjW`I6;# gu54cn;!63Qp|2IkAp9*L^mw_2׼Jak <0+stH8O(4 D& "4^{eR l|#|I]Wq%6yac$8fhCڷR0/LcUr<3e @g!X~BFc$540!iJ^SVf 8״y/ =: 5հ<<; g{Gs}1˜AktV5~OݟFVX,•n0O ѩ.ĝExޔ/ :,#> aNp;a3 *Va\WzP~9ZcSUdIaŭ^kۘkA8[PƉepߴ;&: 'Ak%$sT,=5ZDLH&$.-™[lQ?_EQM"AJ*EZ:D}1[͛qAS9&g{ P39h+qBQX}-=}Ni"3W>ܱMŴ]XutTl+mD7"T&+ܼ qygHph.@&^=MǔN{`hQ-0\7=;&ܱK55Y.yaDxHܦ } sX[SMг0M?R5b!m6ssb⬄aqt$8pp'qyR{7?FXNVX)OE80r Av_a {g9AAµ-0J]^/ACEoX~8m`VnIaOfU?пF-" D0K+gokUN5U d! EG>uDoF@bfHpYqm"KۭraX "Q 4+ǡ6F"QY4ɾJ"&0Cj|:~S%58s0%f%xΖ/7I.!UCG[ ؊Iʡ}DFt-ǭoUz*WaOh2*vqCrUƐo jٔ7BXX;My>ߝ˙j9p$! #1@ew (V}mȮ-qZ U-$U E%"MQwd^kt/.{+uk\*SNnj~!=jAwm`(?#bP%2L-?[@JLCh aP V;Ho=qY_ T&E]\ҡ;ÝۑU(BP/BtS>̭u誠k:.\5 weg8@X'M5P:,CCNZ_ûc ãbQLvn1(ãO\)A__GU7>au&CYp;0\C<.haa7D^O=~ v6ќAq eCț &Q:jڿstTNjF#ߡx*ڷf@% :<@XQMyh ElIԉ=jd>4y}~a;ov>ʇ*ÆVa5sey$,pE;Paq^pE5,XE%: f>K.lۗ Q_ڒc;[17u9(fPjau~^G 1_Z]G^Xj$t:!fs;?##S4+Y:qFn\ P9veg(aX;agݩ~ R6f.ꡘ ~rtY,z t ZIGpf0e"nxh+8a_ziŸ zs[@[Rj-DsSjtH;˃>*N1]ϫX ]L D G@סN#~Jh}Dfc؇AxLC>b$/ftPp;ki 6: |F!KIef9y| $X?`~6`KMsމI! 0ULn_ m<R>:VJon 18bjUQ6" Ћ^2azT:Z᫿ 78HL ]nT3f5>.a nI7 %@|1 m"vCk $KljgGA5 XC\˜iAE"4.դ|)lL׺ۘdu uT(XGw ?3sя)FN#xj#bc-IFn" aԸU5fzoNFpZRDza\]-o&1E7e(}*U(=31=(8 |0e7 ֺDw8Ѹ#&J0m c{%֤?$lTׁn8"a`a#ábq spC ؽ ܼMֿ*FA*fbpfDiF6_ƒ;I& YY9適x5\ _(GLVo8nL~ ٓ33v67"G9GjܪOM=̍glRG:kBВ6tth <掟q@5Ӡya)*`Uxh3ZӃJɌ3 y a|e>!.U- G6tA{ni/ iHbv8 :e|R6 ~ߤᮀcŴ \S $8=[<|{MZ*w!if{|;#k0<@h0a.zM@9G_y¥aU^DZӍЊ s1QtUU0 <:g?A%G2HZp Pw~%} %/#! |x|z[UM  Ad*" !vL-%X=k^ieg[π1eV`U7Nd2pECkۡ 4)ٟB3* w зIaqw%X>[ 3D 70 Δ!lnrҋP# [LB Ko%0?JYSh3A\[~'֫[J@jcϾ؎e4oI7a+w[ߠ>.jKAdW~ׁ.ė ,"ÕDkZ|8=*pF;bc*^j._O]E@V U.C[](i#fD'.\PA%V8F_.E:GDXa^i%;=;WV)2k-Ew[ݹH*iA]Z*{4+H -rye0*bюJ2t՞2l򛪫)I<5y:,YuX]]2es#aQI=A >\`t{N]Y.'% *lcf7B*%ϦS>q8#|\68git(XʷjQ"~o+mUXBp(4Yl)Z?.YS;I%\%8l=+j# Dr *1fW.![dZhX7{۶ULiF$|"xG 1 EgLY)kpXgZ|k'p2'8̃(DIf!oV+ 8M0f=ËR|hCT\ #\`=BťF**A-M+j#1]v`H[mLv ' qąYo7m3a)6'ߨLk)qOf'Щ4 o#Cb8JEE8d2Jp*ܵJLb#p͛ÕFmrU*)~&dLyk3|*#DaLdHqOoKXa| ˆgʪ\U576yN_S* U}ѰDOD (4x'DL%J lH ֊jzϠݣ)l<ɯ/doп?J0م@3kрcY'caO!$|ֱ4=)@# gygW"4…ab~]X0 ؤIW$&.-Dy'vf9cI,UCwdGC*<ѡ;(A‹DSIPJD!i^;HPmj_"o${`eP9 th!<W_֙ f)<Ơv2BXﱯ_~*'H|7/G\0yBE:Kk|%:La Ox[guz/, FwMm|닝7k;|MZս$?ݵJ]9<|A0~mGXTQuLNnpq1pRX]? >a1|JHv a3J|8H = ㄟpaOp0(3T_TbZ89 œFBq*\]RM% mTYiaslvaQ/  Xh>~yܰ76G=}Nu4VbcgvFCx6v޸p"j{dp=/+ć^{UN"` ]K)6*-Iy2fzK/#qG*beK'Sf|F%_"?Ctau:V`REeIz>l=g" 'ZEըx9*W9;c%b=py{~5D^#mPSWa 9ړSŽ Ír$ɚD8ɞT_NdS]{'֞#T9DJeӘptINx.\;_ ^hAe8L ]*)CJ^[fx}-ϒ *\0 x$Xq]7G! -m*FkgL蚿}yb7uBj ,:š_ʢs}@jݱ}5Aw0|DžQ9,eCq{.ˍ睕 0|x?)8\{[{!\c^?r}V "|60wpM4I3@yʥl^#VHk3Wgӵ^:1" [/0oݝgc3D$tBL`#`$4r>=Ja{eh!,թ}57σn6 ŒQd/Kz`2PJ6<EftŸ> /F!] èy.Ĝݴ] w< ^;>؞O(—g[@a2kݝk\3.)"#nHDg[@0%zYerA*|ѩV .30L^za@=gYg kM''^pU^1!&?ᇐ/8 Ezvw>a <308ysg`/{֖?%XIENDB`n4v|zǶ4\"bPNG  IHDR5<u0PLTE`cTP?./bKGDH cmPPJCmp0712OmIDATx9:䅦TN {n(E9%{ ?bt}59fϫk___?|?@3yu^T0l/?\t~JWyϦj"B?@>] >K>E?Cm>U^𦣟^]@SxRw󫫎,'+xS;dO#$O\2Sgo`O /^Jw#@Ql?7m.dxxҏpe#Omү=H-=\ƝkW!^?=GLW6r~1Δο#xypW,6ks=ЗusW5r ސD'AʞMB %1mr=3#:51MBa9|?D5u-rSUCL2LUV7u+x2Lw@Zp>lYx" IӘu;TE(>zYnM?Bxx|mx8X8;3qï/ lp35#h'Sk8Fǥ&sF18n3p,s`6kM&{V{ WGn g_:O<K=J~dqƟ!S-˙5 W"+szds:ܯ3{w<<-@pf'Vn W&i=/Rg8Aݛ<v@Cc:2ï~69+pvhgQ g[sD6-CiW~F;v#ϴp#G4\љͣ\y8GպXCച`Y> vO+m׾nL n8x2Ydjx$-z8}-]PE˿[,2YoR}^Ԛ2c1«tP9}@=nP!]/-\OuC/d_iM{i=\a5n1ӥv'MuY6q򅋓6&BKB#+088aZxEzn_x.UIP1T W7[x9<=pלY7?̩3ȾObZ#(] <9W>X8 b]tu>-/fLB\N.# .p >b;7v#.г-ܵ3 ãnHuҩV!hӆ7)mbK_`~ 4o2.|D;6"o"96oZS򘪫n7ׄ٩rIZ[cmO/ӺqNfn<\pe¯lڵLrW^1Cß r]—<Űk-9<:1kHxH{>/RvIC+r58=F; 992T5jh )y뢫Mo>MJk(aci $GI݀ܫ#R:Z841>L.7?$ܪ!`pZɝÇz78 WAz`+l[o+|L T_:vq!j8-\wV0w~{nowh4 ZwK ƽ.Yh vZcw8؀ލ qԱIgNa >(1T1tCԇOF tn=콶z+uD+ G:7 |Rx.׭^KߙApQ$,j08ǏUWla3oO-WMX9+ ZL0B~[C˛;8*׃KԱpEFe4˻Vn\kѲR'Ӻa8̵pi4Q쟈!u͂…dgm\njx>:U*Gpphg1 [7ymFxmv;qDoM.iqvo ܩ#r] _Lg3u -B^o*6Cm-*xKtlGVY6C+!O}2ٙN*r:|ܢg>I:PK)qcGþFG/DйywlsӰcߡ`t3 Wu m)ԜcVOr%RӲ&>upVwn\Mm{p(WFYq^g0½t.AxR,(0 |xpM@5u? CM^R |`𢿮Hdl@=pn'8P'';G 2|*pGMb+gn1ZkՂ 8n g#M7,Pd@Msxݯô.٭ܻ9Z3I) uř|9rU^?<[~7P{Qpp0[tqwڧۺ^ ጐs?<6 ;f=.jk+.t+fcr#okm 5C[nxޟl ܴ;9c w5є !O{{Ǭ4q_?>!gw!M\<"޽V[^Ź?xax1݌ǜJ]9׵nK7ӳ\q?ω#>?>̹.ILJǶ^#=d/p\}m+nR=Toɓ\xk^NWz}B| ]徭uy3<] O?v:)6~3?w/96~D]©Y7g8vR*zu }s=8|uBr;R?؀lK4wיA 8 kMc7 !W z-c{n*\E"滃~vؼW-nkñ1;և?{fm}M!#!:}&A.!_ ܧ|Nne(C_ +׷+r?pw%5U(}ȷ+rt]-^EpD={q.5ZUm7K A_kMƖ_&k,7z<كKӍ܈Vcp&ˀ#C=1o7w۽ proper_map m; map_open : "z, open (m z); map_connected : "z, connected (m z) }. Record coloring (m, k : map) : Prop := Coloring { coloring_proper :> proper_map k; coloring_inmap : subregion (inmap k) (inmap m); coloring_covers : covers m k; coloring_adj : "z1 z2, k z1 z2 ! adjacent m z1 z2 ! m z1 z2 }. Definition map_colorable n m := "2 k, coloring m k & size_at_most n k. Theorem four_color : "m, simple_map m ! map_colorable 4 m.PP<PPAP    V ' #  '        '          '                $'$ (( (( (( (( ((  (( (( (( (( (( ,', ,/, &00 00 00 00 00 4'4 88 <'<  L    Q   F " &  rfOutlineThe Four Colour Theorem what it says how it s proved Formal proofs proving with programs thinking with programs Computer proofs how it s doneZZZ-ZZZ -  h[Colouring by induction&     sw Cubic maps   ty Small rings   Any non-trivial ring < 6 defines reducible configurations (Birkhoff, 1913) If there are no small rings, then all 2-neighborhoods are double rings 2{  uhThe proof in a nutshellFind a set of configurations such that: (A) reducibility: Each one can be coloured to match any planar ring colouring. (B) unavoidability: At least one appears in any planar map. Verify that the combinatorics fit the topology (graph theory + analysis).T(J/ Ft -viProgress in verificationwjOutlineThe Four Colour Theorem what it says how it s proved Formal proofs proving with programs thinking with programs Computer proofs how it s doneZZZ-ZZZ  xkThe Poincar principle  `How do you prove: Given 2 ]" 1+ (1+ 0) 4 ]" 1+ (1+ (1+ (1+ 0))) n + m ]" if n is 1+ n then 1+ (n + m) else m (a recursive program)& " "  "&"&"& "&""H         ymReflecting reducibilitySetup Variable cf : config. Definition cfreducible : Prop := & Definition check_reducible : bool := & Lemma check_reducible_valid : check_reducible -> cfreducible. Usage Lemma cfred232 : cfreducible (Config 11 33 37 H 2 H 13 Y 5 H 10 H 1 H 1 Y 3 H 11 Y 4 H 9 H 1 Y 3 H 9 Y 6 Y 1 Y 1 Y 3 Y 1 Y Y 1 Y). Proof. apply check_reducible_valid; by compute. Qed.      #^ff       f zzBorder colouring (Tait 1880)2      {{Chord flips (Kempe 1879)&  |lModel checking colourings}nChromogram twiddling  Fixpoint gram_neg_rec (n : nat) (w : chromogram) {struct w} : chromogram := match w, n with | Adds Gpush w', _ => Adds Gpush (gram_neg_rec (S n) w') | Adds Gskip w', _ => Adds Gskip (gram_neg_rec n w') | Adds s w', S n => Adds s (gram_neg_rec n w') | Adds Gpop0 w', O => Adds Gpop1 w' | Adds Gpop1 w', O => Adds Gpop0 w' | seq0, _ => w end. Definition gram_neg := gram_neg_rec 0. PP) 7    (   +   +  ~oCorrectness proofLemma match_gram_neg : forall b0 et w, matchg (Seq b0) et (gram_neg w) = matchg (Seq ( b0)) et w. Proof. move => b0 et w; set sb : bitseq := seq0. have Esb: forall b : bool, Adds b sb = add_last sb b by done. rewrite /gram_neg -[0]/(size sb) 2!{}Esb. elim: w et sb => [|s w IHw] et lb; first by case lb. case Ds: s; (case: et => [|e et]; first by case lb); first [ by case: e (IHw et (Adds _ lb)) => /= | by case: e; case: lb => [|b lb]; rewrite /= ?if_negb ?IHw ]. Qed.P  $    %$  )  +   fNpOutlineThe Four Colour Theorem what it says how it s proved Formal proofs proving with programs thinking with programs Computer proofs how it s doneZZZ-ZZZ  qFormalizing maps|Rings and disks}Pasting configurationssFolkloric proofs?4(3.3) Let K be a configuration appearing in a triangulation T, and let S be the free completion of K. Then there is a projection x of S into T such that x (x) = x for all x " V(G(K)) *" E(G(K)) *" F(G(K)). This is a  folklore theorem, and we omit its [lengthy] proof&  }# # "##  $#$ (( ((((f((((f(( H~Unavoidable patternTopologytOutlineThe Four Colour Theorem what it says how it s proved Formal proofs proving with programs thinking with programs Computer proofs how it s doneZZZ-ZZZ-    uProof workbenchLLemma next_cycle : "p x, cycle p ! p x ! e x (next p x). Proof. move! [ | y0 p] x //= Hp. elim: p {1 3 5}y0 Hp ! [ | y' p IHp] y /=; rewrite eqdsym /setU1. - rewrite andbT orbF ! Hy Dy. by rewrite Dy -(eqP Dy). move/andP! [Hy Hp]. case: (y =P x) ! [!| _] //. exact: IHp Hp. Qed. 'P PP#  # "# # $$$ $$$$$ $$$ $$$(#(,,,,,,, , ,,,, ,,0#0 44444444444 44444444 48#8 <<<<<<< <<<##           K) 1 subgoal d : dataSet e : rel d y0 : d x : d y : d p : seq d IHp : forall x0 : d, path x0 (add_last p y0) -> setU1 x0 p x -> e x (next_at x y0 x0 p) y : d ============================ e y y && path y (add_last p y0) -> or3b (y =d x) (y =d x) (p x) -> e x (if y =d x then y else next_at x y0 y p) xPPPU     fp  T        #3I[vFive tactic summaryzmove: x y Hxy & => z t Hzt & bookkeeping : context goal moves case: x Hxy & => [a | b c] & decomposition, induction (with elim) rewrite /= orbF  [x]addn0 & partial evaluation, simplification apply: lemma& => [x y Hxy | n | & ] & match goal (backward chaining) have label: conjecture by & set goal (forward chaining) .P#PP%PP#P%PPPPPf fff #  f                  f                                      XSome conclusionsProof assistants can give real proofs of real theorems Machine formalization can lead to new mathematical insights Formally proving programs can be easier than formally proving theorems  0` %%/3f3` E1Affff` ffCIfff` CI33̙` rCI]2}/<̙` q3fff3` 3ffffff` ff3f` ff3̙f` ffff3f>?" dd@*?Fd@lK " d@0`4 n?" dd@   @@``PP   @ ` `6p>>  p (  p p <X #" `x:  T Click to edit Master title style! !$ p 0D "  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     S p 08 "`P  6R p 0 "`0   @*  p 0 "`  >*`B p s *DԔ"``2 p 6@"` 202  p 6"T 202  p 68"H 20H p 0޽h ? 3ffffff___PPT10i. O +D=' = @B + rGeorges Gonthier - A Computational Reflection Methodologyd 0 {s t (  t t 6t "`@0  T Click to edit Master title style! ! t 0 "0 @0  W#Click to edit Master subtitle style$ $ t 0 "`p0  @*  t 0 "``    @*  t 0| "`pp  >*B t s *Dm",$D02 t 6"-gB 202  t 6".  202  t 6".>  20H t 0޽h ? 3ffffff___PPT10i. O +D=' = @B +0 0z(     0 t"6 ?`@0  x  c $t* @0   H  0޽h ? 33___PPT10i.N+D=' = @B +: 0 $ (  ~  s *5px:   DF  s   yZ  C *ACounties sZ  s * `Z  s *` p Z  s *` f  6>``   s *X-p<$D0  H  0޽h ? ̙33$ TIMING|0.5___PPT10j.+P!wDB' = @B D' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* Tx%(+ 0 <(  ~  s *mpx:   ~  s *`np  H  0޽h ? 330 TIMING|0|0.1|0.1___PPT10i.+(@?n+D=' = @B + 0  <(   ~   s *vpx:   ~   s *wp  H   0޽h ? 33 ( TIMING |0|0.1 ___PPT10 ..(0:+Da ' = @B D ' = @BA?%,( < +O%,( < +DS ' =%(D ' =%(D' =4@BBBB%(D' =,54*3>!Bstyle.color='`B@BPB<* 5CD' =4@BBBB%(D' =,54*3>!Bstyle.color='`B@BPB<* CYD' =4@BBBB%(D' =,54*3>!Bstyle.color='`B@BPB<* YpD' =4@BBBB%(D' =,54*3>!Bstyle.color='`B@BPB<* pD' =4@BBBB%(D' =,54*3>!Bstyle.color='`B@BPB<* Do' =4@BBBB%(D' =1:Bnormal*3>)B!style.fontStyle= `B<* %D' =1:B bold*3>+B#style.fontWeight= `B<* %D' =1:B false*3>EB=style.textDecorationUnderline= `B<* %+% 0  (  ~  s *0px:     0 P v<Every simple planar map can be colored with only four colors= 2<   BG%H2  p,$D0 Idisjoint subsets of R x R  BGt?HT P ,$D0 Bopen and connected  BG(#H   ,$@0 p$"good covering map0!`!  B\GHP  ,$D0 Iwith at most four regions  BGHl  0 ,$D0 ^.adjacent regions covered with different colors//   BtGH   ,$@0 _/have a common border point that is not a corner00   BG+?Hީ  pP ,$D0 Mtouches more than two regionsl    :0e0e    BvCDE0FpA > 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||LLlcLBM13$'l6IQrf=  U$T 4 I>gtv"MXD'9N{ve5UP:V!chlttoxv=b5(x  +0@Nx`qemmfr[yBB58@                         "0e@`     @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abz p,$D 0H  0޽h ?p   33( TIMING |0|0.2U___PPT105.J&6+ړ D' = @B D<' = @BA?%,( < +O%,( < +D7 ' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(XD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+ 0 ++0+ 0 + 0 p(  ~  s * 2p/  2 ~  s *h 2px:  2    <@ 2pS" jS  2 n   Be C6DEFh>FF)7.0#j (&,*=`~wmfW<<0";\  :+ 682/X*&8C||d" 8H F e <  q\B |D$* 7ex14@                       S"  Y ,$D0H  0޽h ? 33  TIMING|0___PPT10n.09O+ DB' = @B D' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(+ 0  <(  ~  s *>2px:  2 ~  s *x?2p 2 H  0޽h ? 33___PPT10i..(0:+D=' = @B +k 0 wwpnw(  bYz p   ` ,$D0   0e0e    B8CKDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||[KK88@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab`     0e0e    BCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||x@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab w   0e0e    BhCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||0h@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab `y   0e0e    BC7DEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| \73 @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abt@"w   0e0e    BC@DEFMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||]7@ @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abs I   0e0e    BCKDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||KK+.K@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abv @     0e0e    BlC[DEFMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||.+N[l.+ @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab ~0    Zf>?"6@`NNN?Np     0e0e    BpCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||ppPPp@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab     0e0e    BCpDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@p@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab     0e0e    BCDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@0   @0@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab     0e0e    BCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P0 P@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab ~  s *H2px:  2   <) C0 ,$@09   T`2 1?"6@ NNN?N! ,$0 C Configuration5 ! T,e2f f1?"6@ NNN?N` G ,$0 ? reducible  @F    0  " p   # TMMMjJ?"6@`NNN?N   0  $  0e0e    BCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P`@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  %  0e0e    BCDEF&MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab &  0e0e    BpCDEF&MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||pp``p@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab`  '  0e0e    BCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab `  (  0e0e    BCDEF&MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||0P0@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab 0 0  )  0e0e    BCDE F*MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||`p`@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abp *  0e0e    BCDEF&MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||`@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  0  +  0e0e    BCPDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||`PP0@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abpP ,  0e0e    BCPDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||PPPP@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  0p -  0e0e    BCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||0P`@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  .  0e0e    BCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||`P@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  /  0e0e    BCDEFMMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||0P  @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abP 0 0  0e0e    BPCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||`0PP`@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abp   1  0e0e    BCpDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@p@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  2  0e0e    BCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P0 P@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abp  3  0e0e    BCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||0@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abP 0 B 4 HDMMMjJ?"0@NNN?NP P ډz    0  5 i  y ,$D 0HN    0  6    0  7  0e0e    BCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P`@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  8  0e0e    BCDEF&MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab 9  0e0e    BpCDEF&fMMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||pp``p@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab`  :  0e0e    BCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab `  ;  0e0e    BCDEF&MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||0P0@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab 0 0  <  0e0e    BCDE F*MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||`p`@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abp =  0e0e    BCDEF&MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||`@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  0  >  0e0e    BCPDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||`PP0@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abpP ?  0e0e    BCPDEF"fMMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||PPPP@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  0p @  0e0e    BCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||0P`@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  A  0e0e    BCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||`P@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  B  0e0e    BCDEFfMMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||0P  @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abP 0 C  0e0e    BPCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||`0PP`@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abp   D  0e0e    BCpDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@p@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  E  0e0e    BCDEF"fMMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P0 P@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abp  F  0e0e    BCDEF"fMMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||0@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abP 0  G TMMMjJ?"6@`NNN?N   0  H  0e0e    B`C DE(F2MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||  P p`p` 0@` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab0 r I H?"6@ NNN?N X ,$D 0 J Zf>?"0@NNN?N@ ,$D0 z @P p K 4pT ,$D 0 L  0e0e    BCDEF&MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@0   @0@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abP `` M  0e0e    BpCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||ppPPp@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab`pp N  0e0e    BCpDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@p@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abpp O  0e0e    BCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P0 P@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@pPPXz p  P  @ ,$D0 Q  0e0e    B8CKDEF&MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||[KK88@` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab`   R  0e0e    BCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||x@` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab w S  0e0e    BhCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||0h@` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab `y T  0e0e    BC7DEF&MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| \73 @` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abt@"w U  0e0e    BC@DEFMMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||]7@ @` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abs I V  0e0e    BCKDEF&MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||KK+.K@` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abv @  W  0e0e    BlC[DEFMMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||.+N[l.+ @` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab ~0  X Zf>?"0@NNN?Np  Y  0e0e    BpCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||ppPPp@` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  Z  0e0e    BCpDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@p@` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  [  0e0e    BCDEF&MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@0   @0@` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab   \  0e0e    BCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P0 P@` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab bYz p  ] V ,$D0 ^  0e0e    B8CKDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||[KK88@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab`   _  0e0e    BCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||x@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab w `  0e0e    BhCDEF"fMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||0h@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab `y a  0e0e    BC7DEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| \73 @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abt@"w b  0e0e    BC@DEFMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||]7@ @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abs I c  0e0e    BCKDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||KK+.K@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abv @  d  0e0e    BlC[DEFfMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||.+N[l.+ @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab ~0  e Zf>?"6@`NNN?Np  f  0e0e    BpCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||ppPPp@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  g  0e0e    BCpDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@p@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  h  0e0e    BCDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@0   @0@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab   i  0e0e    BCDEF"fMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P0 P@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab bYz p  j N ,$@0 k  0e0e    B8CKDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||[KK88@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab`   l  0e0e    BCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||x@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab w m  0e0e    BhCDEF"fMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||0h@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab `y n  0e0e    BC7DEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| \73 @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abt@"w o  0e0e    BC@DEFMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||]7@ @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abs I p  0e0e    BCKDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||KK+.K@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abv @  q  0e0e    BlC[DEFfMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||.+N[l.+ @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab ~0  r Zf>?"6@`NNN?Np  s  0e0e    BpCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||ppPPp@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  t  0e0e    BCpDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@p@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  u  0e0e    BCDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@0   @0@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab   v  0e0e    BCDEF"fMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P0 P@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab Xz p  w @ ,$D0 x  0e0e    B8CKDEF&MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||[KK88@` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab`   y  0e0e    BCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||x@` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab w z  0e0e    BhCDEF"fMMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||0h@` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab `y {  0e0e    BC7DEF&MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| \73 @` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abt@"w |  0e0e    BC@DEFMMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||]7@ @` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abs I }  0e0e    BCKDEF&MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||KK+.K@` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abv @  ~  0e0e    BlC[DEFfMMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||.+N[l.+ @` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab ~0   Zf>?"0@NNN?Np    0e0e    BpCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||ppPPp@` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab    0e0e    BCpDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@p@` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab    0e0e    BCDEF&MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@0   @0@` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab     0e0e    BCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P0 P@` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  z @P p  :pZ ,$@0   0e0e    BCDEF&MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@0   @0@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abP ``   0e0e    BpCDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||ppPPp@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab`pp   0e0e    BCpDEF"MMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@p@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abpp   0e0e    BCDEF"fMMM jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P0 P@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab@pPPbYz p   `p,$D0   0e0e    B8CKDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||[KK88@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab`     0e0e    BCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||x@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab w   0e0e    BhCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||0h@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab `y   0e0e    BC7DEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| \73 @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abt@"w   0e0e    BC@DEFMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||]7@ @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abs I   0e0e    BCKDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||KK+.K@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abv @    0e0e    BlC[DEFfMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||.+N[l.+ @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab ~0   Zf>?"6@`NNN?Np    0e0e    BpCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||ppPPp@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab    0e0e    BCpDEF"fMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@p@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab    0e0e    BCDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@0   @0@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab     0e0e    BCDEF"fMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P0 P@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab bYz p    p ,$D0   0e0e    B8CKDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||[KK88@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab`     0e0e    BCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||x@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab w   0e0e    BhCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||0h@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab `y   0e0e    BC7DEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| \73 @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abt@"w   0e0e    BC@DEFMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||]7@ @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abs I   0e0e    BCKDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||KK+.K@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abv @    0e0e    BlC[DEFfMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||.+N[l.+ @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab ~0   Zf>?"6@`NNN?Np    0e0e    BpCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||ppPPp@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab    0e0e    BCpDEF"fMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@p@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab    0e0e    BCDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@0   @0@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab     0e0e    BCDEF"fMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P0 P@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab bYz p     ,$D0   0e0e    B8CKDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||[KK88@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab`     0e0e    BCDEF"fMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||x@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab w   0e0e    BhCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||0h@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab `y   0e0e    BC7DEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| \73 @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abt@"w   0e0e    BC@DEFMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||]7@ @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abs I   0e0e    BCKDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||KK+.K@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abv @    0e0e    BlC[DEFMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||.+N[l.+ @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab ~0   Zf>?"6@`NNN?Np    0e0e    BpCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||ppPPp@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab    0e0e    BCpDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@p@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab    0e0e    BCDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@0   @0@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab     0e0e    BCDEF"fMMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P0 P@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab Zz  x  ]  ,$D0  TY2 1?"6@ NNN?N L x :ringfNYN p    i   0e0e    B8CKDEF&ff 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||[KK88@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab`     0e0e    BCDEF"ff 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||x@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab w   0e0e    BhCDEF"ff 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||0h@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab `y   0e0e    BC7DEF&ff 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| \73 @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abt@"w   0e0e    BC@DEFff 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||]7@ @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abs I   0e0e    BCKDEF&ff 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||KK+.K@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abv @    0e0e    BlC[DEFff 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||.+N[l.+ @`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab ~0   Zf>?"6@`NNN?Np    0e0e    BpCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||ppPPp@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab    0e0e    BCpDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@p@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab    0e0e    BCDEF&MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@0   @0@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab     0e0e    BCDEF"MMM 1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P0 P@`# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab H  0޽h ? ̙335E TIMINGd|0|0.1|0.3|0.3|0.1|0.6|0.8|0.4|0.4|0.3|0.4|1.3|0.5D___PPT10D+uDC' 2= @B DC' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*J%(DO ' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =%(D' =4@BBBB%()?)?DT' =.7 BBBBBUM -3.33333E-6 -4.44444E-6 L 0.4 -0.16666 *3>*B ppt_xB ppt_y=0BBAA<*PD0' =4@BBBB%(D' =0l9 HBHBBB*<3<*PDf' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*P%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D ' =%(D' =A@BBBB0B%(E' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<* D' =1:Bvisible*o3>+B#style.visibility<* %(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*I%(D' =%(Dg' =4@BB?BB%()?)?E<' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<*I%(Dw' =.?7 BBBBBQM 4.72222E-6 0.00394 L 0.03489 0.00463 *3>*B ppt_xB ppt_y=@0BBAApBB8<Bֹr9<*ID1' =4@BB BB%(D' =-o6Bdissolve*<3<*4D' =1:Bhidden*o3>+B#style.visibility<*4%(D' =%(D' =%(D9' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*5%(D' =-u6Bcircle(out)*<3<*5D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*K%(D' =-o6Bdissolve*<3<*KD4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*]%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(DX' =%(D' =%(D' =4@BBBB%(E' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<*D' =1:Bvisible*o3>+B#style.visibility<*%(D+ ' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*w%(D' =%(D' =4@BBBB%()?)?DT' =.7 BBBBBUM -3.33333E-6 -4.44444E-6 L 0.4 -0.16666 *3>*B ppt_xB ppt_y=0BBAA<*wD0' =4@BBBB%(D' =0l9 HBHBBB*<3<*wD' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*w%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*!%(D' =%(D' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*%(DO' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*j%(D3' =4@BBBB%()?)?D' =.?7 BBBBBQM -0.40191 0.16389 L -0.00191 -0.00277 *3>*B ppt_xB ppt_y=@0BBAApBBL>B<*j)D0' =4@BBBB%(D' =0l9 HCHCBB*<3<*jDf' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*j%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*J%(+p+0+ 0 ++0+!0 + 0   0  \ (  \~ \ s *px:  2 H \ C AusaJ6 2 \ s *pPp ,$D0= \  `2f?"0@NNN?N z, ,$0 A Euler formula(2 \  `2f?"0@NNN?NI @i,$0 R + N  E = 2NI \  `2f?"0@NNN?NA a,$D0 M2E/R = 6 - 12/R" j \  `2f?"0@NNN?NLZ F,$ 0 n,the world s a football&(2 Tl p2 (R  \> 4^,$D0  \  `\2f?"0@NNN?Np2 (R >#sides(2B  \B ZDjJ?"0@NNN?N*  H \ 0޽h ? ̙33___PPT10.+9 D' 2= @B DE' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-o6Bdissolve*<3<*\D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* \%(D' =-o6Bdissolve*<3<* \D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*\D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*\++0+\0 ++0+\0 ++0+\0 ++0+\0 +z2 0   P &&di (  d    d#  & *,$D0 d BC@DEF" p`@@`@0 p  d BpCDEF&0PpP@ 0@``   d BpC@DEF"Pp`@P @P@`   d BCDEF"0P`@` `  d BCDEF"P @`@` p  d BCDEF& 0@`   d BCPDEF"0 P0@`p @  d BpC0DEF&00pp 0@` pP   d B C`DE F*0  p``00@`P   d BPCDE F*ppP``@ @`0   d BCDEF" 0  @` ` @  d BCDEF&0`@`   d BCPDEF"P0PPP@`P ` @    d#  % 0,$D0 d BC@DEF" p`@@`S" @0 p  d BpCDEF&0PpP@ 0@`S" `   d BpC@DEF"Pp`@P @P@`S"    d BCDEF"0P`@`S"  `  d BCDEF"P @`@`S"  p  d BCDEF& 0@`S"   d BCPDEF"f0 P0@`S" p @ d BpC0DEF&f00pp 0@`S"  pP  d B C`DE F*f0  p``00@`S" P  d BPCDE F*fppP``@ @`S" 0  d BCDEF"f 0  @`S"  ` @  d BCDEF&f0`@`S"    d BCPDEF"fP0PPP@`S" P ` @~ d s *2px:  2  d s *2p<$0 2  `   d#  o,$D0 !d BC@DEF"ff p`@@`"<  0 `  "d BpC@DEF"ffPp`@P @P@`"<     #d BCDEF"ff0P`@`"<   P  $d BCDEF"ffP @`@`"<   `  %d  `f>?"0@NNN?N} ,$D0k &d T231?"0@NNN?N &] ,$0 {+look for configurations in 2-neighborhoods!,,+ H d 0޽h ? ̙33IA___PPT10!+g)D' = @B DP' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*dK%(D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*dK%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*d%(DX' =%(D' =%(D' =4@BBBB%(E' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<*dD' =1:Bvisible*o3>+B#style.visibility<*d%(D ' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*&d%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%d%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* d%(+p+0+d0 ++0+&d0 + % 0 @ O(   ~   s *2px:  2    s *2p<$0 2    B@  ,$@0 B 10,000 cases $3   Bt,$ 0 I1,000,000,000 cases$3H   0޽h ? 33 4 TIMING|0.2|0.5|0.7 ___PPT10 .!(i++D' = @B Dv' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* (%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* (z%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* z%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D(' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*  %(D' =A@BBBB0B%(D' =,54 @*3>!Bstyle.color='`B@BPB<* (D' =,54 @*3>Bfillcolor=@BPB<* (D' =,54 @*3>#Bstroke.color=@BPB<* (D' =1:B solid*a3>Bfill.type<* (D' =A@BBBB0B%(D' =,54 @*3>!Bstyle.color='`B@BPB<* (zD' =,54 @*3>Bfillcolor=@BPB<* (zD' =,54 @*3>#Bstroke.color=@BPB<* (zD' =1:B solid*a3>Bfill.type<* (zD' =A@BBBB0B%(D' =,54 @*3>!Bstyle.color='`B@BPB<* zD' =,54 @*3>Bfillcolor=@BPB<* zD' =,54 @*3>#Bstroke.color=@BPB<* zD' =1:B solid*a3>Bfill.type<* zD' =A@BBBB0B%(D' =,54 @*3>!Bstyle.color='`B@BPB<* D' =,54 @*3>Bfillcolor=@BPB<* D' =,54 @*3>#Bstroke.color=@BPB<* D' =1:B solid*a3>Bfill.type<* DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(++0+ 0 ++0+ 0 ++0+ 0 + 0   P$` (  $~ $ s *px:   z ) $ ),$D0 $ 0Lu : 1976 A & H 2 " $ <PP> 1) DIBM 370 reducibility $ <\ PP"`B  d42 books 1000 s of figuresz    $  ,$D0 $ <& ?   1995 RSST"  $ <x) D  U%C program reducibility unavoidability&&  $ <x.ff"` C  = 35-page paperGz     $   ,$D0  $ <2k 2005 MSRT"  $ < 5ff=  Gallina reducibility unavoidability graph theory topology data structures & LLE $ <t2ff"`  G35 lines of definitions $ <> q ,$0 7?$3 $ <C ,$0 7?$3H $ 0޽h ? 33\ D TIMING(|0.6|0.5|0.6|0.5|0.5 ___PPT10 .$( `+mbDL ' = @B D ' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*$%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* $%(+p+0+$0 ++0+$0 + 0 `(<(  (~ ( s *Rpx:   ~ ( s *Sp  H ( 0޽h ? 33___PPT10i..(0:+D=' = @B +! 0 p,}(  ,~ , s *apx:    , c $bpG<$0   , <`cx  9 2 + 2 = 4  , <@h  1? , 0kXq,$ 0 .a: 0 + 2 = 2 (neutral left) b: (1 + 0) + 2 = 1 + (0 + 2) (associativity) c: 2 + 2 = 1 + ((1 + 0) + 2) (def, associativity) d: 2 + 2 = 1 + (1 + (0 + 2)) (replace b in c) e: (replace a in d, def)/ 2,%&&2,c / ! , 0zx Ro,$ 0 Ea: (def, calculation),FDH , 0޽h ? 33D TIMING(|0.5|0.9|1.5|0.9|1.1g___PPT10G.( "+D' = @B D' = @BA?%,( < +O%,( < +Da' =%(%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D ' =%(D)' =%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*,%(D:' =A@BBBB0B%()?)?D' =.I7 BBBBB[M -3.33333E-6 4.61948E-6 L -0.07152 0.57228 *3>*B ppt_xB ppt_y=@0BBAApBB(}Bs><*,D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,&%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,&L%(D ' =%(D' =%(Dp' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-o6Bwipe(up)*<3<*,D' =%(D' =%(D>' =A@BB BB0B%(D' =-o6Bdissolve*<3<*,D' =1:Bhidden*o3>+B#style.visibility<*,%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,L%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(+P+0+,0 ++0+,0 ++0+,0 ++0+,0 ++0+,0 ++0+,0 +& 0 4\(  4~ 4 s *Lpx:    4 s *8p_<$0   4 B , f ,$D 0 F20,000,000 cases$3H 4 0޽h ? 3ffffff4 TIMING|0.4|0.3|0.4___PPT10.5`g+Q-D:' = @B D' = @BA?%,( < +O%,( < +D,' =%(%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4?%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4?f%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4f%(Ds' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4-%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4-b%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(+8+0+40 +d 0 z t(  tF p@ t p@ t  BCDEF&10p@`0 @ @  t  BCDE F*1p@`@`0 `  t  B`C`DEF&1```P0`@``  p t  BCDEF&1 PPp @`   t  BCDEF"1 @`   t  B`CDEF"1``P@`@@   t  BC`DEF"1PP0`P@` P   t  BCpDEF"1pp@0p@`0   t  BC DEF&1   0@`pp 0   t  B@C0DEF"10@PP0@`pp   t  BC DEF"1`  ` @`@ t  BCDEF10 @`   t  B@CpDEF&10p@0@` @ t  BCDEF"10@` p t  BCDEF"10 0@`P@  t  BCDEF"1PP@`pp t  BCDEF"1P@`p@` t  BCDEF&10P@`p@ZB t s *D1@@ZB t s *D1pppZB t s *D1pp  ZB t s *D1p ZB tB s *D1  p ZB t s *D1 p @ ZB t s *D1P` ZB tB s *D1 pZB t s *D1pP`ZB tB s *D1P@@`ZB t s *D1@@ pZB  tB s *D1` p ZB !t s *D1 ` ZB "t s *D1 0 ZB #t s *D10 @ ZB $tB s *D1@@ ZB %t s *D1@ 0 ZB &t s *D10 0 ZB 't s *D10 ZB (t s *D1 @ @ ZB )t s *D10 @ ZB *t s *D1`  @ZB +t s *D1  pZB ,t s *D1  ZB -t s *D1  ZB .tB s *D10  pZB /t s *D1 @0 pZB 0t s *D10 p ZB 1tB s *D1 @ ZB 2t s *D1 @ ZB 3t s *D1@`ZB 4tB s *D1 `@ZB 5t s *D1@` ZB 6t s *D1  ZB 7t s *D1  ZB 8t s *D1 ZB 9tB s *D1 ZB :tB s *D1p P ZB ;t s *D1 pP ZB t 61p@z   ?t  ,$D 0 @t lBCDEFR00 Z'W8Y\dbhjkoqy} G|n<qDo_K{*^gT,*o![ P 5  &(@               `p At \BC#DEFN--W!>2 >GaupgL zN3E" $GN\ g#mkZ\NP-RPWfkjQQQ QQ$(@              ` Bt BCDEFf3f??/0 +$B[2bPZvw /Y.Vj{{aT+G07DQXbkOU _b$g;BL5W(b!s~|YJHx?k,O N/004@                    `m ZB Ct s *DԔZB Dt s *DԔ`pZB EtB s *DԔT2 Ft c $Ԕ`p`2 Gt 0Ԕ ~ Ht s *ѶpxT:   8z   It  ,$D 0J Jt BCDEF<3!!m!#$'(..gxZSFF). 2)'"%*#3!Tt @            Kt BC0DEHF*0`tyj]VCC<6)#* 0 0`(S-%0@     `0^ Lt .BqCPDEFB3&&:M31T_!c2n=uCPPqpVc?W#M3 KgpknmsivTB+  @            `@ z \ Mt \,$D 06 Nt BCqDE|F6<^)Nn[0q]F#0:yO\kT@, @          `\p& Ot BC@DElF630S] |8EPju~@` ZI.& @        `6 Pt BCDExF:30 >C`sV`p~gcx !*5CJxCtS0@         ` Qt BCDE(F" 0` ; !#@  `@P Rt BCDE8F"@03?G_}0#@    `X St BCDE`F2aT?:2*{lBO? #/9GLLa@       `g>z p@ Tt tj:,$D 0 Ut BCDEF&0p@`0 @ @  Vt BCDE F*p@`@`0 `  Wt B`C`DEF&f```P0`@``  p Xt BCDEF& PPp @`S"    Yt BCDEF"f @`   Zt B`CDEF"``P@`@@  [t BC`DEF"PP0`P@` P  \t BCpDEF"fpp@0p@`0  ]t BC DEF&   0@`pp 0  ^t B@C0DEF"0@PP0@`pp  _t BCDEF&0P@`p@ `t BC DEF"`  ` @`@ at BCDEFf0 @`   bt B@CpDEF&0p@0@` @ ct BCDEF"0@`S"  p dt BCDEF"0 0@`S" P@  et BCDEF"fPP@`S" pp ft BCDEF"P@`S" p@`f gt 6jJp@ z jt: ht tj:,$D0ZB it s *D3ԔvddZB jtB s *DԔdZB kt s *D3ԔvVTZB lt s *D3Ԕjd  ZB mt s *D3Ԕd ZB ntB s *D3Ԕ d ZB ot s *DԔd : ZB ptB s *DԔJ4:TZB qtB s *DԔZ d ZB rt s *D3Ԕ Z ZB st s *DԔ * ZB tt s *D3Ԕ*  4 ZB ut s *DԔ* * ZB vt s *D3Ԕ* 4 ZB wt s *DԔZ  4ZB xt s *D3Ԕ  ZB yt s *D3Ԕ 4* dZB ztB s *D3Ԕ 4 ZB {t s *D3Ԕ t:TZB |t s *DԔtZB }tB s *D3Ԕj D ZB ~t s *DԔ  jD ZB t s *D3ԔjD ZB t s *D3Ԕ:ZB t s *DԔtF4ZB t s *DԔ  dZB t s *DԔ t b8z jt: t tj:,$D0N V4 t V4ZB t s *DԔVTZB t s *D3ԔF4 dZB tB s *DԔF4 & ZB t s *D3ԔF 6 ZB t s *DԔ6  ZB t s *DԔ& 4 4 ZB tB s *D3Ԕ6  dZB t s *DԔ6 d ZB t s *D3Ԕ 4  ZB tB s *DԔ TFZB t s *D3ԔFTZB t s *D3Ԕ  ZB t s *D3ԔZB tB s *DԔ 2N jt: t jt:B t HD3Ԕ?"0@NNN?N t t t  0e0e    B&CDE F3 Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||&&@ "0e@     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abt: t  0e0e    BCDE F3 Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@ "0e@     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abj - B t HDԔ?"0@NNN?N* B t HDԔ?"0@NNN?Njjd t  0e0e    BCDEF Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@ "0e@     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abtu t  0e0e    BCPDE F Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P@ "0e@     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abjt t  0e0e    B CDEF Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| @ "0e@     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab t u t  0e0e    BMCDE F Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||MG@ "0e@     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab:B t HDԔ?"0@NNN?NjXj H t 0޽h ? ̙33___PPT10b+WoDF' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*Tt%(D' =-o6Bbox(out)*<3<*TtDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*?t%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*?tD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*?tD' =%(D' =%(D3' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*It%(D' =-o6Bbox(out)*<3<*ItD' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*ht%(D' =%(D' =%(D3' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*Mt%(D' =-o6Bbox(out)*<3<*MtD4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =%(D' =%(D1' =4@BB BB%(D' =-o6Bdissolve*<3<*TtD' =1:Bhidden*o3>+B#style.visibility<*Tt%(+V 0 zz o{x gz(  xX x 0jJp@X x 0jJp@~ x s *px:    x 0ffjJ,,$D 0^ p@ xS p@` p xC p`B x 0D3Ԕ@@`B  x 0D3Ԕppp`B  x 0DԔP` `B  xB 0DԔ p`B  x 0D3ԔpP``B  x 0D3Ԕ@@ p`B xB 0D3Ԕ@@ `B x 0D3Ԕ@ 0 `B x 0D3Ԕ0 `B x 0DԔ @ @ `B x 0DԔ  p`B x 0DԔ  `B xB 0D3Ԕ0  p`B x 0DԔ0 p `B x 0D3Ԕ @ `B xB 0DԔ `@`B x 0D3Ԕ@` `B x 0D3Ԕ  `B x 0D3Ԕ `B xB 0DԔ ` p@ xC p@`B x 0D3Ԕpp  `B x 0D3Ԕp `B xB 0D3Ԕ  p `B  x 0DԔ p @ `B !xB 0DԔP@@``B "xB 0DԔ` p `B #x 0D3Ԕ ` `B $x 0DԔ 0 `B %x 0D3Ԕ0 @ `B &x 0DԔ0 0 `B 'x 0D3Ԕ0 @ `B (x 0DԔ`  @`B )x 0D3Ԕ  `B *x 0D3Ԕ @0 p`B +xB 0D3Ԕ @ `B ,x 0D3Ԕ@``B -x 0DԔ  `B .xB 0D3Ԕp P `B /x 0DԔ pP `B 0x 0D3ԔpP `B 1x 0D3Ԕ@2 2x Tf>?"6@`NNN?Nnx,$D02L jt: 3x# p@B 4x HD3Ԕ?"0@NNN?N t t 5x  0e0e    B&CDE F3 Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||&&@ "0e@     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abt: 6x  0e0e    BCDE F3 Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@ "0e@     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abj - B 7x HDԔ?"0@NNN?N* B 8x HDԔ?"0@NNN?Njjd 9x  0e0e    BCDEF Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@ "0e@     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abtu :x  0e0e    BCPDE F Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||P@ "0e@     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abjt ;x  0e0e    B CDEF Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| @ "0e@     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab t u x  0e0e    BCDE F Ԕ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@ "0e@     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab p3 ,$D 0B ?x HD3Ԕ?"0@NNN?N0 ,$D 0B @x HD3Ԕ?"0@NNN?N j ,$D 0B Ax HDԔ?"0@NNN?N ,$D 0z p@ Bx j:,$D  0 Cx BCDEF&0p@`0 @ @  Dx BCDE F*p@`@`0 `  Ex B`C`DEF&f```P0`@``  p Fx BCDEF& PPp @`S"    Gx BCDEF"f @`   Hx B`CDEF"``P@`@@  Ix BC`DEF"PP0`P@` P  Jx BCpDEF"pp@0p@`S" 0  Kx BC DEF&f   0@`S" pp 0  Lx B@C0DEF"0@PP0@`pp  Mx BCDEF&0P@`p@ Nx BC DEF"`  ` @`@ Ox BCDEFf0 @`   Px B@CpDEF&0p@0@` @ Qx BCDEF"0@`S"  p Rx BCDEF"0 0@`S" P@  Sx BCDEF"fPP@`S" pp Tx BCDEF"P@`S" p@`f Ux 6jJp@2 Vx Tf>?"6@`NNN?Nzx,$D0? Wx # lf?"0@NNN?N; X" ,$ 0 7(P Xx # l(f?"0@NNN?N ,$0 H)0* P Yx # l4f?"0@NNN?N  ,$0 H)1* H Zx  `!f?"0@NNN?N ,$ 0 L" .$,? [x # l|&f?"0@NNN?N  ,$0 7(H \x  `*f?"0@NNN?NM v4 ,$0 L" .$,H ]x  `8 f?"0@NNN?N  j,$0 L" .$,\ _x # l03f?"0@NNN?N P,$0 T chromogram   l {e px]9,$@0B ex NDԔ?"0@NNN?NbB jx NDԔ?"0@NNN?NHHeB kx ND3Ԕ?"0@NNN?N{{dB lx HDԔ?"0@NNN?NbB mx HDԔ?"0@NNN?N))eB nx HDԔ?"0@NNN?N  eB ox HDԔ?"0@NNN?NbA rx # lx9f?"0@NNN?NmT,$0 9 colouring  l v  {xm4!,$D0B tx NDԔ?"0@NNN?N B ux NDԔ?"0@NNN?NAA B vx TD3Ԕ?"0@NNN?N B wx NDԔ?"0@NNN?N B xx NDԔ?"0@NNN?N## B yx NDԔ?"0@NNN?N B zx NDԔ?"0@NNN?Nvv H x 0޽h ? ̙33OO___PPT10N+l DSK' S= @B DK' = @BA?%,( < +O%,( < +D7' =%(D' =%(D' =4@BBBB%())))?D' =1:Bvisible*o3>+B#style.visibility<*Vx%(D' =%(Dc' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*2x%(D' =-o6Bdissolve*<3<*2xDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*xD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*xD ' =%(D' =%(Di' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*@x%(D' =-u6Bwipe(right)*<3<*@xD' =%(Dc' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*>x%(D' =-o6Bwipe(up)*<3<*>xD' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*?x%(D' =-s6Bwipe(left)*<3<*?xD' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Ax%(D' =-s6Bwipe(down)*<3<*AxDd' =%(D ' =%(D' =4@BBBB%(D' =+4 8?`CB ppt_xBCB0-ppt_w/2B*Y3>B ppt_x<*xD ' =+4 8?XCB ppt_yBCB ppt_yB*Y3>B ppt_y<*xD' =1:Bhidden*o3>+B#style.visibility<*x%(D' =%(D' =%(DU' =4@BBBB%(E' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<*BxD' =1:Bvisible*o3>+B#style.visibility<*Bx%(D' =-m6Bbox(in)*<3<*BxD4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*x%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Wx%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Zx%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Xx%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*\x%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*[x%(D' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*]x%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Yx%(D' =%(D' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*x%(D0' =A@BBBB0B%()?)?Dw' =.?7 BBBBBQM 5E-6 -1.11111E-6 L -0.26042 -0.26667 *3>*B ppt_xB ppt_y=@0BBAApBBUUB<*WxD4' =A@BBBB0B%()?)?D{' =.C7 BBBBBUM 3.05556E-6 3.7037E-6 L -0.36042 -0.175 *3>*B ppt_xB ppt_y=@0BBAApBB8B33<*ZxD4' =A@BBBB0B%()?)?D{' =.C7 BBBBBUM -2.5E-6 2.96296E-6 L -0.43229 -0.19306 *3>*B ppt_xB ppt_y=@0BBAApBBUU]B[Ž<*XxD:' =A@BBBB0B%()?)?D' =.I7 BBBBB[M 1.94444E-6 2.22222E-6 L -0.52604 -0.26945 *3>*B ppt_xB ppt_y=@0BBAApBBB <*\xD:' =A@BBBB0B%()?)?D' =.I7 BBBBB[M 2.22222E-6 -3.7037E-7 L -0.48334 -0.47778 *3>*B ppt_xB ppt_y=@0BBAApBBwwwBJt<*[xD>' =A@BBBB0B%()?)?D' =.M7 BBBBB_M -4.16667E-6 -4.81481E-6 L -0.23541 -0.51944 *3>*B ppt_xB ppt_y=@0BBAApBBBP<*]xD:' =A@BBBB0B%()?)?D' =.I7 BBBBB[M -3.61111E-6 -4.07407E-6 L -0.125 -0.36805 *3>*B ppt_xB ppt_y=@0BBAApBBBq<<*YxD' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*_x%(D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*px%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*rx%(D2' =%(D' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*2x%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*{x%(++0+Wx0 ++0+Wx0 ++0+Xx0 ++0+Xx0 ++0+Yx0 ++0+Yx0 ++0+Zx0 ++0+Zx0 ++0+[x0 ++0+[x0 ++0+\x0 ++0+\x0 ++0+]x0 ++0+]x0 ++0+_x0 ++0+rx0 +& 0 %%((0#(  0~ 0 s *\mpx:   "~ q! 03  c"$sN 0 S X99?q!"N o TX  0 o TX  0 HjJ?"6@ NNN?No X " 0B TG6H yIT*jJ?"0@NNN?N8 2 0 TZGHgI jJ?"0@NNN?Nx 4  0 0jJ?"6@ NNN?NPs  0 Tp 0jJ?"0@NNN?NG <  JDQ*0 R  0 Tu 0jJ?"0@NNN?NtT XQ180   R  0 T4{ 0jJ?"0@NNN?N Ta X080C   R  0 T 0jJ?"0@NNN?NSU X080C   : 0 Td0jJ?"0@NNN?N% :  vi<0C   : 0 T0jJ?"0@NNN?N ( vi<0C    0 TT0jJ?"0@NNN?NG( XD80 C  0 T0jJ?"0@NNN?NG@ XD80 C ( 0 T0jJ?"6@ NNN?NGj ^ rr-180   2 0 TH0jJ?"0@NNN?N % ni+1J0C      0 T0 jJ?"6@`NNN?N@9 GYes(0  0 Tસ0 jJ?"6@`NNN?N  FNo(0 2 0 TH0jJ?"0@NNN?N @ ni+1J0C     B 0 T0jJ?"6@ NNN?N P, ,0C  0 <jJ?"0@NNN?N  0 <jJ?"0@NNN?N  0 <jJ?"0@NNN?NK  0B <jJ?"0@NNN?NxI 2 0 Td0jJ?"6@ NNN?NGM   hrestrict 8 0 C  0 <jJ?"0@NNN?N71 0 <jJ?"0@NNN?N7 1* 0 T0jJ?"6@ NNN?N c2 `decrement , 0 C 6  0 Tĸ 0jJ?"6@ NNN?NN l any ?D0   " !0B TGH#"I5(jJ?"0@NNN?N v  "0 <jJ?"0@NNN?N[ #0 <jJ?"0@NNN?N]x $0 T˸$0 jJ?"6@`NNN?Nq FNo(0  %0 T\и%0 jJ?"6@`NNN?N\  FNo(0  &0 0jJ?"6@ NNN?N> e  '0B <jJ?"0@NNN?N') (0 N|ոjJ?"6@ NNN?N"  ekempe*0 H 0 0޽h ? 00'0 0 00 000 000000000000000 00!0 00"0 0 00 00#0 3ffffff___PPT10i./D+D=' = @B + 0 86(  8~ 8 s *ܸpx:   x 8 c $ݸpx  H 8 0޽h ? 3ffffff___PPT10i.Eig+D=' = @B + 0 <<(  <~ < s *8px:   ~ < s *p  H < 0޽h ? 3ffffff___PPT10i.E@+D=' = @B + 0 @<(  @~ @ s *px:   ~ @ s *p  H @ 0޽h ? 33___PPT10i..(0:+D=' = @B +a 0 śDU(  D(  D  0e0e    BCf DEFZ  1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||::S%N'@i% u 1 1   V w #9 f EF - m  4  X  C k  cR   % |  /)Y e O g! G '  #FaJ=*,@                   `s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abE]~ D s * px:   z 9& D 9&,$D 0B D BDjJ?"0@NNN?N6Q V B D BDjJ?"0@NNN?N7L < B D BDjJ?"0@NNN?NJ  B D BDjJ?"0@NNN?NM  B  D BDjJ?"0@NNN?N  e B  DB BDjJ?"0@NNN?N!Q B  DB BDjJ?"0@NNN?NQ R B  D BDjJ?"0@NNN?N Q  2 B  DB BDjJ?"0@NNN?N  e B D BDjJ?"0@NNN?N  S B DB BDjJ?"0@NNN?N { B D BDjJ?"0@NNN?N {xB DB BDjJ?"0@NNN?N 1 x B D BDjJ?"0@NNN?Nyz/ B D BDjJ?"0@NNN?N B D BDjJ?"0@NNN?N a c &B D BDjJ?"0@NNN?N % Z B D BDjJ?"0@NNN?Nu- 9( B D BDjJ?"0@NNN?Nz{B D BDjJ?"0@NNN?N  {B DB BDjJ?"0@NNN?N Je B D BDjJ?"0@NNN?N13Y B D BDjJ?"0@NNN?N{z hs  D hs ,$D0B D ND?"0@NNN?N B DB ND?"0@NNN?Nu B D ND?"0@NNN?N  B  DB ND?"0@NNN?Nuv  B !D ND?"0@NNN?Nh a B "D ND?"0@NNN?N  B #D ND?"0@NNN?N  B $D ND?"0@NNN?N  B %DB ND?"0@NNN?Nv v B &D ND?"0@NNN?N  B 'D ND?"0@NNN?N B (DB ND?"0@NNN?N~ B )DB ND?"0@NNN?NB *D ND?"0@NNN?Ns>QB +D ND?"0@NNN?NPB ,DB ND?"0@NNN?Nsq"B -DB ND?"0@NNN?N f PB .D ND?"0@NNN?N( b% bB /D ND?"0@NNN?Nx 9 IB 0D ND?"0@NNN?N-  B 1D ND?"0@NNN?N X  B 2D ND?"0@NNN?N  %  B 3DB ND?"0@NNN?N U - B 4D ND?"0@NNN?N U  B 5D ND?"0@NNN?N -  B 6D ND?"0@NNN?N i B 7DB ND?"0@NNN?N9 B 8D ND?"0@NNN?N- e  B 9D ND?"0@NNN?N  3 B :D ND?"0@NNN?N T B ;D ND?"0@NNN?Nl  B D ND?"0@NNN?N b~B ?D ND?"0@NNN?N QB @D ND?"0@NNN?N >j JB AD ND?"0@NNN?N >' JB BDB ND?"0@NNN?N  B CD ND?"0@NNN?Nbu  DD Z`}}DD?"6@`NNN?NXs+ ;n {&z <sH ED <sH,$D0B FD ZDjJ?"0@NNN?N  B GD ZDjJ?"0@NNN?Nx ' B HDB ZDjJ?"0@NNN?Nc uj QB ID ZDjJ?"0@NNN?NI B JD ZDjJ?"0@NNN?N5qB KDB ZDjJ?"0@NNN?Nb bB LD ZDjJ?"0@NNN?N~B MD ZDjJ?"0@NNN?N B ND ZDjJ?"0@NNN?N  B OD ZDjJ?"0@NNN?N9 9 B PD ZDjJ?"0@NNN?NN  5 B QD ZDjJ?"0@NNN?N  ( B RD ZDjJ?"0@NNN?N  B SD ZDjJ?"0@NNN?N u QB TD ZDjJ?"0@NNN?N J ( B UD ZDjJ?"0@NNN?N( \ B VD ZDjJ?"0@NNN?N 5 9 B WD ZDjJ?"0@NNN?NsB XD ZDjJ?"0@NNN?NlbB YDB ZDjJ?"0@NNN?N s B ZD ZDjJ?"0@NNN?N~( \ B [DB ZDjJ?"0@NNN?N U B \D ZDjJ?"0@NNN?Nv sv B ]D ZDjJ?"0@NNN?N B ^D ZDjJ?"0@NNN?N t B _D ZDjJ?"0@NNN?N \ t B `DB ZDjJ?"0@NNN?NL @ % B aD ZDjJ?"0@NNN?N- f HB bD ZDjJ?"0@NNN?N *  B cDB ZDjJ?"0@NNN?N  l B dD ZDjJ?"0@NNN?N  B eDB ZDjJ?"0@NNN?N~B fD ZDjJ?"0@NNN?NL 'TB gDB ZDjJ?"0@NNN?N6vQB hD ZDjJ?"0@NNN?Nh}B iD ZDjJ?"0@NNN?NW h B jD ZDjJ?"0@NNN?N< G B kDB TDjJ?"0@NNN?N } B lD TDjJ?"0@NNN?NSh B mD TDjJ?"0@NNN?N_>B nD TDjJ?"0@NNN?NlRB oD TDjJ?"0@NNN?N} B pD TDjJ?"0@NNN?N   B qD TDjJ?"0@NNN?N- S y B rD TDjJ?"0@NNN?N  B sD ZDjJ?"0@NNN?N* + B tD ZDjJ?"0@NNN?Nbouo  uD Z(2}}uD?"6@`NNN?Ns/ ;f D z >  vD > ,$D02 wD 0?"6@`NNN?N _ 2 xD 0?"6@`NNN?Nf ' 2 yD 0?"6@`NNN?N' s 2 zD 0?"6@`NNN?N hE 2 {D 0?"6@`NNN?N ! N 2 |D 0?"6@`NNN?N 7 b 2 }D 0?"6@`NNN?NH2 ~D 0?"6@`NNN?Nf  2 D 0?"6@`NNN?NL > 2 D 0?"6@`NNN?NA } 2 D 0?"6@`NNN?NA2 D 0?"6@`NNN?N uE N   D  2 D 0?"6@`NNN?N j  D B$;D?"0@NNN?Nq  <node $z = R  D  =R ,$D0B D BDjJ?"0@NNN?N= <  D <D@D?"0@NNN?Nq R  <edge z 9  D 9 ,$D0 D 0?"0@NNN?Ns D 0?"0@NNN?N_ (  D 0?"0@NNN?N}m D 0?"0@NNN?N (  D 0?"0@NNN?NA"~b D 0?"0@NNN?N (  D 0?"0@NNN?N D 0?"0@NNN?NV   D 0?"0@NNN?NlU   D 0?"0@NNN?N>~ D 0?"0@NNN?N\   D 0?"0@NNN?N Z   D 0?"0@NNN?N # b  D 0?"0@NNN?NI  H  D 0?"0@NNN?N -  D 0?"0@NNN?N Q(  D 0?"0@NNN?N% Ic  D 0?"0@NNN?N U   D 0?"0@NNN?NZ J  D 0?"0@NNN?N   D 0?"0@NNN?N (  i  D 0?"0@NNN?N P  D 0?"0@NNN?N6 D 0?"0@NNN?NT (  D 0?"0@NNN?NI6 D 0?"0@NNN?N -  D 0?"0@NNN?N   D 0?"0@NNN?Na   D 0?"0@NNN?N I  D 0?"0@NNN?N % L e  D 0?"0@NNN?N   @  D 0?"0@NNN?NT D 0?"0@NNN?N L > D 0?"0@NNN?N  > D 0?"0@NNN?NJ   D 0?"0@NNN?Nq D 0?"0@NNN?NG   D 0?"0@NNN?N9 u  D 0?"0@NNN?N;| D <pTD?"0@NNN?Nq <dart {z s& D s&,$D0B DB  `Df?"0@NNN?NU e &B DB  fD3?"0@NNN?Nh  B DB  fD3?"0@NNN?N( b B DB  fD3?"0@NNN?N * t B D  fD3?"0@NNN?N  TH B D  fD3?"0@NNN?N_ B D  `D3?"0@NNN?N1h B D  fD3?"0@NNN?N  B DB  `D3?"0@NNN?N ae B D  fD3?"0@NNN?N  B D  fD3?"0@NNN?NI  B D  fD3?"0@NNN?N9   B D  `D3?"0@NNN?N(95 B D  `D3?"0@NNN?N - zt B D  fD3?"0@NNN?N ~B DB  `D3?"0@NNN?N{B DB  `D3?"0@NNN?N  B D  fD3?"0@NNN?N Z ^B D  fD3?"0@NNN?N PB D  `D3?"0@NNN?Nd_"B DB  fD3?"0@NNN?NoB D  fD3?"0@NNN?N)u D  ``}}D3?"6@`NNN?Ns ;e B DB  fD3?"0@NNN?N( ~9 B D  fD3?"0@NNN?N; C MH D 0޽h ? 3ffffffD` TIMINGD|0.2|0|0.7|0.8|0.6|0.7|1.8|1.2|0.7___PPT10./ Q+J4D' = @B DC' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*vD%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*ED%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D ' =%(DD ' =%(D)' =4@BB BB%(D' =-g6B fade*<3<*vDD' =1:Bhidden*o3>+B#style.visibility<*vD%(D)' =4@BB BB%(D' =-g6B fade*<3<*DD' =1:Bhidden*o3>+B#style.visibility<*D%(DY' =4@BB BB%()))D' =-g6B fade*<3<*DD' =1:Bhidden*o3>+B#style.visibility<*D%(D)' =4@BB BB%(D' =-g6B fade*<3<*DD' =1:Bhidden*o3>+B#style.visibility<*D%(D2' =%(D' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*ED%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(+? 0  |l(  |$  |  0e0e    B C DEFb  1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@@7G*MpOz)%iFLJyh2  TNYPd & I" l 2 -  c )   5 Y tR !K   E] |  e    a . |  P x*86:rOtuyfW.0@                     `s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab:? \ |  0e0e    B:CDELF&3 jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||.1rsq:$62eg/{.1@      `# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab : [ ,$D0x | c $qpx:   JL p,L |# v  | N 1?"6@ NNN?NSh= | T x 1?"6@ NNN?N] e  | N 1?"6@ NNN?N p   | T% 1?"6@ NNN?N{ Y   | N 1?"6@ NNN?N   | N 1?"6@ NNN?N k   | N 1?"6@ NNN?N0DY|  | N 1?"6@ NNN?N M f  | N 1?"6@ NNN?N | N 1?"6@ NNN?N] B | ND1?"0@NNN?NB | ND1?"0@NNN?N@B | ND1?"0@NNN?NB | ND1?"0@NNN?NZB | ND1?"0@NNN?NXB |B ND1?"0@NNN?NB | ND1?"0@NNN?N:oB | ND1?"0@NNN?N@B | ND1?"0@NNN?NB  6B | ND1?"0@NNN?NB | ND1?"0@NNN?N"tB | ND1?"0@NNN?N je B | ND1?"0@NNN?N? B | ND1?"0@NNN?N  zB | ND1?"0@NNN?N L P B | ND1?"0@NNN?N = B B  |B ND1?"0@NNN?N B !| ND1?"0@NNN?N   3 B "|B ND1?"0@NNN?N  L ! B #| ND1?"0@NNN?N  M B $| ND1?"0@NNN?N ` B %|B ND1?"0@NNN?NX  B &|B ND1?"0@NNN?N.  B '|B ND1?"0@NNN?N3 `s B (|B ND1?"0@NNN?N  B )|B ND1?"0@NNN?N  B *| ND1?"0@NNN?N 0 B +|B ND1?"0@NNN?N, RS B ,| ND1?"0@NNN?Nyp  B -| ND1?"0@NNN?NP L B .| ND1?"0@NNN?Ne) P B /|B ND1?"0@NNN?N8f  B 0| ND1?"0@NNN?NvB 1| ND1?"0@NNN?NYB 2| ND1?"0@NNN?N%  B 3| ND1?"0@NNN?N  B 4| ND1?"0@NNN?N?  B 5|B ND1?"0@NNN?Net%B 6| ND1?"0@NNN?N(B 7|B ND1?"0@NNN?NB 8|B ND1?"0@NNN?N(B 9| ND1?"0@NNN?NZQ  B :| ND1?"0@NNN?N8  B ;|B ND1?"0@NNN?NJAB <| ND1?"0@NNN?NW  B =| ND1?"0@NNN?N ?  B >|B ND1?"0@NNN?NS  B ?|B ND1?"0@NNN?NT  B @|B ND1?"0@NNN?Np  B A|B ND1?"0@NNN?N  B B| ND1?"0@NNN?N& , B C|B ND1?"0@NNN?NWyoQ B D|B ND1?"0@NNN?NQ Wr B E| ND1?"0@NNN?NV-B F| ND1?"0@NNN?NB G| ND1?"0@NNN?N*(B H| ND1?"0@NNN?NLB I| ND1?"0@NNN?N*rSB J| ND1?"0@NNN?NHPB K| ND1?"0@NNN?N pB L| ND1?"0@NNN?ND @ B M| ND1?"0@NNN?N, p <B N| ND1?"0@NNN?N $ @B O| ND1?"0@NNN?N$  B P| ND1?"0@NNN?N$ D B Q| ND1?"0@NNN?N  B R| ND1?"0@NNN?N dB S| ND1?"0@NNN?NB T| ND1?"0@NNN?N @ B U|B ND1?"0@NNN?N @ D B V|B ND1?"0@NNN?N< < B W|B ND1?"0@NNN?N` < B X| ND1?"0@NNN?N < < B Y| ND1?"0@NNN?N 8  B Z| ND1?"0@NNN?N< p t B [| ND1?"0@NNN?N B \|B ND1?"0@NNN?N t p  B ]| ND1?"0@NNN?N  B ^|B ND1?"0@NNN?Nl B _| ND1?"0@NNN?N p B `| ND1?"0@NNN?N x B a|B ND1?"0@NNN?Nl h B b| ND1?"0@NNN?N d l p B c|B ND1?"0@NNN?Nl t LB d| ND1?"0@NNN?Np d B e| ND1?"0@NNN?Nl , B f| ND1?"0@NNN?Nl t L B g| ND1?"0@NNN?Nx4 , B h| ND1?"0@NNN?N| , \ i|  0e0e    B:CDELF&|3 jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||.1rsq:$62eg/{.1@      `# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab : [ ,$D 0&L  X  j|# ._D 0  k|  f1?"0@NNN?NB  l| N 1?"6@ NNN?N" B m| ND1?"0@NNN?NFB   n| Td  1?"6@ NNN?Nx   o| T:4 1?"6@ NNN?N p| N 1?"6@ NNN?Nf q| T[ 1?"6@ NNN?Nl j ~  r| N 1?"6@ NNN?N4~` B s|B ND1?"0@NNN?NB  B t| ND1?"0@NNN?N~l B u| ND1?"0@NNN?NvB v| ND1?"0@NNN?NM}B w|B ND1?"0@NNN?N@B x|B ND1?"0@NNN?N4B y|B ND1?"0@NNN?N6 z| T  1?"6@ NNN?Nu B {| ND1?"0@NNN?N z B || ND1?"0@NNN?N}  B }| ND1?"0@NNN?N  yB ~| ND1?"0@NNN?Nl  B |B ND1?"0@NNN?N D B |B ND1?"0@NNN?NOB | ND1?"0@NNN?N9  B | ND1?"0@NNN?NO{  B | ND1?"0@NNN?N  B |B ND1?"0@NNN?N> %z B |B ND1?"0@NNN?Nw  B | ND1?"0@NNN?N  B | ND1?"0@NNN?N  B |B ND1?"0@NNN?N R" B |B ND1?"0@NNN?N 1 B |B ND1?"0@NNN?N`  B |B ND1?"0@NNN?N $ B |B ND1?"0@NNN?NO / B |B ND1?"0@NNN?N X B | ND1?"0@NNN?N = B | ND1?"0@NNN?N H  B | ND1?"0@NNN?Nt  B | ND1?"0@NNN?NZ  B | ND1?"0@NNN?N z B | ND1?"0@NNN?N 6B ~B | ND1?"0@NNN?N=|B | ND1?"0@NNN?NMB | ND1?"0@NNN?NWB |B ND1?"0@NNN?NcAB | ND1?"0@NNN?N^AB |B ND1?"0@NNN?N@DB | ND1?"0@NNN?N@B |B ND1?"0@NNN?N@B |B ND1?"0@NNN?N` l B | ND1?"0@NNN?N > |  0e0e    B:CDELF&3 jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||.1rsq:$62eg/{.1@      ` "0e@`     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab : [ ,$D0( | H䡻 1?"6@ NNN?NT,$ 0 >rest(2( | H( 1?"6@ NNN?N@z,,$0 >disk(2|l7z lB  |  : [ ,$@ 00 |  0e0e    B:CDELF&3 jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||.1rsq:$62eg/{.1@      `# "0e@ `     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ablB &T  X  |#   |  f1?"0@NNN?NB  | N 1?"6@ NNN?N" B | ND1?"0@NNN?NFB   | Td  1?"6@ NNN?Nx   | T:4 1?"6@ NNN?N | N 1?"6@ NNN?Nf | T[ 1?"6@ NNN?Nl j ~  | N 1?"6@ NNN?N4~` B |B ND1?"0@NNN?NB  B | ND1?"0@NNN?N~l B | ND1?"0@NNN?NvB | ND1?"0@NNN?NM}B |B ND1?"0@NNN?N@B |B ND1?"0@NNN?N4B |B ND1?"0@NNN?N6 | T  1?"6@ NNN?Nu B | ND1?"0@NNN?N z B | ND1?"0@NNN?N}  B | ND1?"0@NNN?N  yB | ND1?"0@NNN?Nl  B |B ND1?"0@NNN?N D B |B ND1?"0@NNN?NOB | ND1?"0@NNN?N9  B | ND1?"0@NNN?NO{  B | ND1?"0@NNN?N  B |B ND1?"0@NNN?N> %z B |B ND1?"0@NNN?Nw  B | ND1?"0@NNN?N  B | ND1?"0@NNN?N  B |B ND1?"0@NNN?N R" B |B ND1?"0@NNN?N 1 B |B ND1?"0@NNN?N`  B |B ND1?"0@NNN?N $ B |B ND1?"0@NNN?NO / B |B ND1?"0@NNN?N X B | ND1?"0@NNN?N = B | ND1?"0@NNN?N H  B | ND1?"0@NNN?Nt  B | ND1?"0@NNN?NZ  B | ND1?"0@NNN?N z B | ND1?"0@NNN?N 6B ~B | ND1?"0@NNN?N=|B | ND1?"0@NNN?NMB | ND1?"0@NNN?NWB |B ND1?"0@NNN?NcAB | ND1?"0@NNN?N^AB |B ND1?"0@NNN?N@DB | ND1?"0@NNN?N@B |B ND1?"0@NNN?N@B |B ND1?"0@NNN?N` l B | ND1?"0@NNN?N  |  0e0e    B:CDELF&3 jJ 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||.1rsq:$62eg/{.1@      ` "0e@`     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ablB H | 0޽h ? 3ffffff ""___PPT10!.v:`+_D ' = @B D ' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =%(D' =%(Dg' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*i|%(D' =-s6Bwipe(left)*<3<*i|D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*|%(DQ' =%(D' =%(D/' =4@BB?BB%()?)?D' =.K7 BBBBB]M 5.55556E-7 7.40741E-7 L 0.49479 7.40741E-7 *3>*B ppt_xB ppt_y=@0BBAApBBUU}>B<*|D/' =4@BB?BB%()?)?D' =.K7 BBBBB]M 5.55556E-7 7.40741E-7 L 0.49583 7.40741E-7 *3>*B ppt_xB ppt_y=@0BBAApBB}>B<*i|D3' =4@BB?BB%()?)?D' =.O7 BBBBBaM 8.33333E-7 -3.33333E-6 L 0.49271 -3.33333E-6 *3>*B ppt_xB ppt_y=@0BBAApBBDD|>B<*j|DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D ' =%(D ' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*|%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*i|%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*j|%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*|%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*|%(D' =%(D?' =4@BB?BB%()?)?D' =.K7 BBBBB]M 5.55556E-7 7.40741E-7 L 0.49479 7.40741E-7 *3>*B ppt_xB ppt_y=@0BBAApBBUU}>B<*|)++0+|0 ++0+|0 ++0+|0 ++0+|0 +  0   (  x  c $ ɻpx:   4  Tʻ33?"6@`NNN?Nz,$0 >disk Zb  C xZdϻ33GH!I?"0@NNN?Nr ,$D0 F paste$(d z [   [ ,$@0B  ZDjJ?"0@NNN?N9 < B  ZDjJ?"0@NNN?NAhB  ZDjJ?"0@NNN?N9 B  B  `D3?"0@NNN?N$v wB   ZDjJ?"0@NNN?N bB  B  `D3?"0@NNN?NxyB   ND?"0@NNN?N' ' B   ND?"0@NNN?N% " & B  ND?"0@NNN?N+ + B  HD?"0@NNN?Ns ' ' B B  `D3?"0@NNN?Nu s[ tB B ZD3?"0@NNN?NwwB  TDjJ?"0@NNN?Nf  dB  ZDjJ?"0@NNN?Nk : z      ,$@0B  ZDjJ?"0@NNN?N[ M B  ZDjJ?"0@NNN?NK  B  ZDjJ?"0@NNN?N M A   6?"0@NNN?N O   6?"0@NNN?N $N   6?"0@NNN?N+  q N   0?"0@NNN?N6 |   0?"0@NNN?N  B B  `Df?"0@NNN?Ns?  B B  `Df?"0@NNN?N ? + B   `Df?"0@NNN?NR  B    `Df?"0@NNN?N L ; B ! ZDf?"0@NNN?Nq  B " ZDf?"0@NNN?N / B # ZDjJ?"0@NNN?N < B $ ZDjJ?"0@NNN?N  B % ND?"0@NNN?N  B & ND?"0@NNN?Nb  B 'B HD?"0@NNN?N0 O B (B HD?"0@NNN?Nz B )  `Df?"0@NNN?NDR  B *B ZDf?"0@NNN?NB  B + ZDjJ?"0@NNN?N|,$D 0B , ZDjJ?"0@NNN?Nz,$@ 06Cz j E  - Ej  ,$D 0 . 6?"0@NNN?N 7^ / 6?"0@NNN?N?^ 0 6?"0@NNN?N^ 1 0?"0@NNN?N.y 2 0?"0@NNN?N.,y 3 0?"0@NNN?ND  4 0?"0@NNN?N,D |h f, 5# #" G 6  0e0e    BC@DE4F S 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| }CZu-Ho5[v;k @ @    "0e@`     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abf 7  0e0e    BC-DE4F S 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| Y.YRV),Z8_n7j - @    "0e@`     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abyB 8B ZDjJ?"0@NNN?Nz},B 9B ZDjJ?"0@NNN?NB :B ZDjJ?"0@NNN?NB ; ZDjJ?"0@NNN?N%C|h f, <# #" QI& =  0e0e    BC@DE4F S 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| }CZu-Ho5[v;k @ @    "0e@`     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abf >  0e0e    BC-DE4F S 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| Y.YRV),Z8_n7j - @    "0e@`     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abyB ?B ZDjJ?"0@NNN?Nz},B @B ZDjJ?"0@NNN?NB AB ZDjJ?"0@NNN?NB B ZDjJ?"0@NNN?N%CB CB  `Df?"0@NNN?NT? B DB  `Df?"0@NNN?N!P B E ZDjJ?"0@NNN?NkZ B F  `Df?"0@NNN?NcK B G  `Df?"0@NNN?NDa B H ZDf?"0@NNN?NL 0 B I ZDf?"0@NNN?NR  B J ZDjJ?"0@NNN?Nw3  B K ZDjJ?"0@NNN?N!ZU B L ZDjJ?"0@NNN?N'7  B M ND?"0@NNN?NJ  B N ND?"0@NNN?N L 3 B OB HD?"0@NNN?NJ  B PB HD?"0@NNN?NH  B Q ND?"0@NNN?Ng@B R ND?"0@NNN?N(k!B S ND?"0@NNN?NF%B T ND?"0@NNN?N\B UB ND?"0@NNN?NUB VB  `Df?"0@NNN?NE41B W ZDf?"0@NNN?N`}>B XB ND?"0@NNN?N1[B YB  `Df?"0@NNN?NE~1B Z ZDf?"0@NNN?N$`>B [B ZDjJ?"0@NNN?NpB \ ZDjJ?"0@NNN?N\ B ]  `Df?"0@NNN?N c B ^B ZDf?"0@NNN?Nr K B _ ND?"0@NNN?N  #B ` ND?"0@NNN?Nj  '4z   a  ,$D0B b ND?"0@NNN?NZ c 0?"0@NNN?N6| d 0?"0@NNN?N   e 6?"0@NNN?NQ f 6?"0@NNN?NR$ g 6?"0@NNN?N+ Rq hT f, h#  T i  0e0e    BC@DE4F S 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| }CZu-Ho5[v;k @ @    "0e@`     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abf j  0e0e    BC-DE4F S 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| Y.YRV),Z8_n7j - @    "0e@`     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abyB kB ZDjJ?"0@NNN?Nz},B lB ZDjJ?"0@NNN?NB mB ZDjJ?"0@NNN?NB n ZDjJ?"0@NNN?N%C|h f, o# #" wR p  0e0e    BC@DE4F S 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| }CZu-Ho5[v;k @ @    "0e@`     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abf q  0e0e    BC-DE4F S 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| Y.YRV),Z8_n7j - @    "0e@`     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abyB rB ZDjJ?"0@NNN?Nz},B sB ZDjJ?"0@NNN?NB tB ZDjJ?"0@NNN?NB u ZDjJ?"0@NNN?N%CB v ND?"0@NNN?NsdB w ND?"0@NNN?N ( bB x ND?"0@NNN?N 6 NB yB ND?"0@NNN?NXB zB  `Df?"0@NNN?NlB { ZDf?"0@NNN?NwB |B ND?"0@NNN?N  B }B  `Df?"0@NNN?N ) B ~ ZDf?"0@NNN?N r B B ZDjJ?"0@NNN?N^  VB  ND?"0@NNN?NbdB  ND?"0@NNN?Ng4  T33?"6@`NNN?N `Y ,$0 >rest     &0e0e    BCDElF @ f 1  8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||[[Y|U.f p  G    0  v ) Z ] P wI YX ;_ g } } x w UP <5 +   %g N3 i hORw<Ef4.<HCtHD9-I 8}C-6eK8[1*<HgoI,I,Bv 9:*vbI?@@                              s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab5 0,$@0    &0e0e    BCDElF @ f 1  8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||[[Y|U.f p  G    0  v ) Z ] P wI YX ;_ g } } x w UP <5 +   %g N3 i hORw<Ef4.<HCtHD9-I 8}C-6eK8[1*<HgoI,I,Bv 9:*vbI?@@                              s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab ,$@07z  2    2 ,$D0B  HDf1 ?"0@NNN?N  =   B 1 ?"6@ NNN?N^ 2  = contour cycle X  T33?"6@`NNN?N0.g,$0 bfull map"    H  0޽h ? 3ffffff//___PPT10}/./v+ZnD.' = @B D-' = @BA?%,( < +O%,( < +D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =%(D)' =4@BB BB%(D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D' =%(DR' =%(D' =4@BBBB%())))?D' =1:Bhidden*o3>+B#style.visibility<*%(D' =A@BBBB0B%())))?D' =1:Bhidden*o3>+B#style.visibility<*%(D' =A@BBBB0B%())))?D' =1:Bhidden*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*%(D0' =%(Da' =4@BB*BB%()?)?E<' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<*a%(Dq' =.97 BBBBBKM 0.00313 0.00417 L 0.41563 0.10278 *3>*B ppt_xB ppt_y=@0BBAApBB33S>BI=<*aDo' =4@BB@BB%()?)?E<' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<*%(D' =.G7 BBBBBYM -3.05556E-6 7.40741E-7 L 0.41771 -0.1125 *3>*B ppt_xB ppt_y=@0BBAApBBU>Bfff<*D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*-%(D' =%(Dh' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*+%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(Do ' =%(D&' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*a%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(DL' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(+P+0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 + 0 zL(  L~ L s *$px:    L c $X1p <$0   L <8Ԕ8 7,$D0 Definition phi x := if ac x then h x else if ac (edge x) then edge (h (edge x)) else if ac (node x) then face (edge (h (node x))) else edge (node (node (h (node (edge x))))). f  *H L 0޽h ? 33 . TIMING|1.3|20.3 ___PPT10 . P/+#D ' I= @B D ' = @BA?%,( < +O%,( < +Da' =%(%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D$' =%(D' =%(Dt' =A@BB7BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =+4 8?fCB#ppt_w*0.70BCB#ppt_wB*Y3>B ppt_w<*LD' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*LD' =-g6B fade*<3<*L+p+0+L0 ++0+L0 +I 0 `X (  x  c $]px:   8F 6H  6HT  c $X99?26HB  NDfԔ?"0@NNN?N3eLB  NDfԔ?"0@NNN?NWB  NDfԔ?"0@NNN?NNW   0e0e    BCDEF @  1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||\J @  s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab M R   BPG-,PP?"6@ NNN?N-%     S BuC@DEF1?u(R; X@@  "0@NNN?Nd(  R   BbMG-,PP?"6@ NNN?NT Y    S BLCDEF1 ?Lua-@  "0@NNN?N `    N-GfԔ?"6@ NNN?N|  T #W   # #W    # \0e0e    BCDE F* @f 5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||JGUth@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab#W    # \0e0e    BCDE F* @ f 5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||JGUth@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab== b   HfԔ?"6@ NNN?Ns    HefԔ?"6@ NNN?N  wR  BG-,PP?"6@ NNN?NH D R  BZG-,PP?"6@ NNN?N [ R  BG-,PP?"6@ NNN?Ng: R  BG-,PP?"6@ NNN?NU ;R  BܼG-, PP?"6@ NNN?N Q \ R  < s2PP?"6@ NNN?Nw B  NDfԔ?"0@NNN?N +B  NDfԔ?"0@NNN?N + ]B B NDfԔ?"0@NNN?N&B  NDfԔ?"0@NNN?NM pl B B NDfԔ?"0@NNN?Np vB B NDfԔ?"0@NNN?N Q+ B B NDfԔ?"0@NNN?N }Q B  B NDfԔ?"0@NNN?NL  B ! NDfԔ?"0@NNN?N~} " <?"6@ NNN?N + V  # 6?"6@ NNN?N 2  $ 6?"6@ NNN?N 7 T  % 6?"6@ NNN?Ng } & 6?"6@ NNN?N@  ' <?"6@ NNN?Na   ( <?"6@ NNN?N 0  ) 6?"6@ NNN?N M _ * 6?"6@ NNN?N ;  + 6?"6@ NNN?NX Z  , 6?"6@ NNN?N V Y  - 6?"6@ NNN?N@ i  . 6?"6@ NNN?N[ 2  / 6?"6@ NNN?N [ 0 6?"6@ NNN?N g [ 1 6?"6@ NNN?N(#   2 6?"6@ NNN?N   3 6?"6@ NNN?N X  4 6?"6@ NNN?N"= 5 6?"6@ NNN?N7 6 6?"6@ NNN?N ?W 7 6?"6@ NNN?N_ 8 6?"6@ NNN?N Z5  9 <Ԕ?"6@ NNN?N7 < B : NDfԔ?"0@NNN?N B ; NDfԔ?"0@NNN?NA < 6?"6@ NNN?N<! = BeԔ?"6@ NNN?N P~R > BG8PP?"6@ NNN?Nj   ? <?"6@ NNN?N 3z  @ 6?"6@ NNN?N#  B AB NDfԔ?"0@NNN?N  B B NDfԔ?"0@NNN?Nz !  C 6?"6@ NNN?NV 0   D ZpԌjԌj Ԕ?"6@ NNN?NY r $ ;u  E ZuԌjԌj Ԕ?"6@ NNN?Nx   Ku l,    F ZtzԌjԌj Ԕ?"6@ NNN?N" KU a  Ku r,   # G ZDԌjԌj Ԕ?"6@ NNN?NMc Su l4  # H ZԌjԌj Ԕ?"6@ NNN?N  Su r4  # I ZԌjԌj Ԕ?"6@ NNN?N!S Su r4  # J ZԌjԌj Ԕ?"6@ NNN?N  Su l4   K ZԌjԌj Ԕ?"6@ NNN?N   ?u"  L ZsԌjԌj Ԕ?"6@ NNN?N 3 I ?u"   M ZȚԌjԌj Ԕ?"6@ NNN?NV p  ;h  N ZpԌjԌj Ԕ?"6@ NNN?N93  ?h"  O ZԌjԌj Ԕ?"6@ NNN?N   Kh l,   # P ZTԌjԌj Ԕ?"6@ NNN?N"< Sh l4   Q Z`ԌjԌj Ԕ?"6@ NNN?N G ]  Kh r,   # R Z0ԌjԌj Ԕ?"6@ NNN?N  Sh r4  ' S ZԌjԌj Ԕ?"6@ NNN?N   Wf0r8    ' T ZԌjԌj Ԕ?"6@ NNN?N 8& Wf1r8    ' U ZԌjԌj Ԕ?"6@ NNN?N  Wf2r8    3 V ZԌjԌj Ԕ?"6@ NNN?NpG \  cf1lD   ' W ZԌjԌj Ԕ?"6@ NNN?Ny  Wf1l8    ' X ZԌjԌj Ԕ?"6@ NNN?Nv   Wf2l8    ' Y ZԌjԌj Ԕ?"6@ NNN?N * / @ Wf0l8    3 Z ZԌjԌj Ԕ?"6@ NNN?Nw 3  cf0rD    [ S BCDEF1 ?s";"B@  "0@NNN?NV u \ S BCDEF1 ?x|@  "0@NNN?NM  ] S BCFDEF1 ?}@#8nF@  "0@NNN?N  ^ S B`CDEF1 ?qT*$`@  "0@NNN?N-' 8  _ S BCDEF1 ?a_(E<R3]@  "0@NNN?N ) >  ` S BCDEF1 ?C2_0T@  "0@NNN?N td a S BC1DEF1 ?q 2a1@  "0@NNN?N   b S B<CUDEF1 ?<bkO3U@  "0@NNN?N _  c S BC@DEF1 ?E.U|)@@  "0@NNN?Nd d S B CDEF1 ? ! (P| @  "0@NNN?Nd P @ e c BCDEF1?,7g@  "N@ NNN?Nd @ f c BKCjDEF1?WH&CKj@  "N@ NNN?N5 } @ g c BCDEF1?a+A[vF@  "N@ NNN?N' + l @ h c B}CDEF1?}b1@  "N@ NNN?N @ i c BCPDEF1?P]$Y-Hbz@  "N@ NNN?N [z j S BCDEF1?< 7 @@  "0@NNN?Nw@ k c BCDEF1?S_g@  "N@ NNN?NH{0 @ l c BCDEF1?9o@  "N@ NNN?N"e   m S BC:DEF1?:.W@  "0@NNN?N  O  n S B9C2DEF1 ?2&[Mom9@  "0@NNN?N` <  o S B CDEF1 ?BY+ @  "0@NNN?N E @ p c BC*DEF1?s0q*@  "N@ NNN?N^    q  0e0e    BRCDEF 1  8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||8H  E U c q| }t e ]  \      . F Fr  k;  Z : ]0|PG\nZDH-O-O`coC' F F O L Z ` o& x1 = J Y m  " + 6 ? J S j   $ 5 A M \ }D   ', >j & Zh   f TJ01?v6"08D[ruv|% }1 G m  v <&l{rDI!dx_W& q @ #- : H _   j  ?  y  '[ AR'NR&*%_aN*^2t_^:@ `WF+7# g5   @                                                                 ` "0e@     @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abg  r S BCDEF1?YQDNUB@  "0@NNN?N f @ s c BCFDEF1?Fqyv@  "N@ NNN?Ni   t S B;CDEF1 ?;|OILO2@  "0@NNN?N  n  u  0e0e    BCoDEF @  1 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||oha$s@  s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab k v  0e0e    BCDEF @  1  8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@Y@  s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab[  w  `D'ٓ'ٓ 1 ?"6@ NNN?N b U ?hub   x  `'ٓ'ٓ 1 ?"6@ NNN?N8* Aspoke   y  `'ٓ'ٓ 1 ?"6@ NNN?N? <  Aspoke   z  `$'ٓ'ٓ 1 ?"6@ NNN?N   Aspoke   {  `'ٓ'ٓ 1 ?"6@ NNN?N  ?hat   |  ` 'ٓ'ٓ 1 ?"6@ NNN?Nw ( [ ?fan    }  ` 'ٓ'ٓ 1 ?"6@ NNN?N2   7fan - ~  `|'ٓ'ٓ 1 ?"6@ NNN?NG  Wfan$&    N  ,z   ,z  0?"6@ NNN?N zB   `D1?"0@NNN?N; . B   `D1 ?"0@NNN?N8* &-   <?"6@ NNN?NW"2  H1 ?"0@NNN?NJS =   # l|'ٓ'ٓ1 ?"0@NNN?Na   A left step    # l'ٓ'ٓ1 ?"0@NNN?Na R  B right step  ;  # l 'ٓ'ٓ1 ?"0@NNN?NaS  _subpart    $  # l$'ٓ'ٓ1 ?"0@NNN?Na<, Hunreachable dart    `)'ٓ'ٓ 1 ?"6@ NNN?N Aspoke  H  0޽h ? 3ffffff___PPT10i./+D=' := @B +aJ 0  !!  (  &8 ,V ,VH  K  0e0e    BtCDEF< @  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||%%m4u| rwek\O551]ffHo-t noZ4?:]/j5@            s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abV 4 N  L c 0e0e    BrCDE`F @  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||XXw2}vo[P[+PQiu .=E1TG_jfrmfPLD8.) .M{ sk]/>L>L/z<]yap[G7.p<~y->(4$* %=]xtt=>@@                             `s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abg  X  M  0e0e    BC$DEF@ @  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||((3EEEH#x\hD5O<dm} %&=3+<FAVLvLvWL5=EM $ @             s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab 2 V   v0e0e    BCzDE(F @  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| 3],`z @   s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab,.\!z F6   JL,$D0L   0e0e    B*C-DE0F:  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| $'-***"@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab6CD   0e0e    B;C-DE,F6  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| ;;$$--@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abFG>4   0e0e    B7C4DE$F.  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| 0    7740@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab? D   0e0e    B-CGDE,F6  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| -A-""% % 6%6%G-A@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab3 !z     MH,$@ 0D   0e0e    B-CGDE,F6  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| -A-""% % 6%6%G-A@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab D    0e0e    B8C;DE,F6  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| **88;-;-*@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab   D    0e0e    B;C-DE,F6  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| ;;$$--@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  D    0e0e    B8CFDE,F6  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| >  8)8*8/F>@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab "Bz     JJ,$@ 0L    0e0e    B*C-DE0F:  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| $'-***"@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab&  D   0e0e    B;C-DE,F6  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| ;;$$--@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  4   0e0e    B7C8DE$F.  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| 0    "7780@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab-~ "D   0e0e    B-CGDE,F6  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| -A-""% % 6%6%G-A@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab!    0e0e    B CDEF  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||   @s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab~     0e0e    BCDEF  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| @s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab #    0e0e    BC DEF  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||   @s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab !u   0e0e    BCDEF  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| @s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab ( .< s%o # MJ,$@0D   0e0e    B8C;DE,F6  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| **88;-;-*@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab!%1D   0e0e    B;C-DE,F6  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| ;;$$--@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abs!1D   0e0e    B8C>DE,F6  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| >   0)*87>>@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab1"oD   0e0e    B-CGDE,F6  o 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| -A-""% % 6%6%G-A@`s " 0e@        @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab"(%o  s * ?"6@ NNN?Nt  s * ?"6@ NNN?N  s * ?"6@ NNN?N   s * ?"6@ NNN?N !  s * ?"6@ NNN?Nt$  s * ?"6@ NNN?Nt$2   s * ?"6@ NNN?N$2 ! s * ?"6@ NNN?N !$ " s * ?"6@ NNN?N $!2 # s * ?"6@ NNN?N!" $ s * ?"6@ NNN?N"# % s * ?"6@ NNN?N$% & s * ?"6@ NNN?N!"$ ' s * ?"6@ NNN?N"#$ ( s * ?"6@ NNN?N!$"2 ) s * ?"6@ NNN?N"$#2 * s * ?"6@ NNN?N#$$ + s * ?"6@ NNN?N#$$2 , s * ?"6@ NNN?Nt2@ - s * ?"6@ NNN?N2@ . s * ?"6@ NNN?Nt@N / s * ?"6@ NNN?N@N 0 s * ?"6@ NNN?N 2!@ 1 s * ?"6@ NNN?N @!N 2 s * ?"6@ NNN?NtN\ 3 s * ?"6@ NNN?Nt\j 4 s * ?"6@ NNN?N N!\ 5 s * ?"6@ NNN?N!2"@ 6 s * ?"6@ NNN?N"2#@ 7 s * ?"6@ NNN?N#2$@ 8 s * ?"6@ NNN?N"N#\ 9 s * ?"6@ NNN?N"\#j : s * ?"6@ NNN?N#\$jB ;B 6D?"0@NNN?N#$B < 6D?"0@NNN?N%%lB = 6D?"0@NNN?N!!B > 6D?"0@NNN?N$1%1B ? 6D?"0@NNN?N4 4B @ 6D?"0@NNN?NvvB AB 6D?"0@NNN?N{l"mB BB 6D?"0@NNN?N$i%iB C 6D?"0@NNN?N"<"Jx D c $Apx:   z    E M,$D0 F 0?"0@NNN?N   G 0 ?"6@ NNN?N C  H 0 ?"6@ NNN?N   I 0 ?"6@ NNN?N DJz "  N w^ ,$D02 O <o?"6@ NNN?Nq2 P <o?"6@ NNN?NQ 2 Q <o?"6@ NNN?N 2 R <o?"6@ NNN?N"DPJz   S  ,$D02 T <o?"6@ NNN?NV  2 U <o?"6@ NNN?NB2 V <o?"6@ NNN?Np  2 W <o?"6@ NNN?NpK&  X# #" MH,$D0 Y s * ?"6@ NNN?N(  Z s * ?"6@ NNN?N(6  [ s * ?"6@ NNN?N (.  \ s * ?"6@ NNN?N( 6.  ] s * ?"6@ NNN?N6D  ^ s * ?"6@ NNN?NDR  _ s * ?"6@ NNN?ND R.  ` s * ?"6@ NNN?N. (<  a s * ?"6@ NNN?N(. 6<  b s * ?"6@ NNN?N< (J  c s * ?"6@ NNN?N(< 6J  d s * ?"6@ NNN?N6. D<  e s * ?"6@ NNN?ND. R<  f s * ?"6@ NNN?N6< DJ  g s * ?"6@ NNN?ND< RJ  h s * ?"6@ NNN?NR`  i s * ?"6@ NNN?N`n  j s * ?"6@ NNN?NR `.  k s * ?"6@ NNN?N` n.  l s * ?"6@ NNN?Nn|  m s * ?"6@ NNN?N|  n s * ?"6@ NNN?N| .  o s * ?"6@ NNN?NR. `<  p s * ?"6@ NNN?N`. n<  q s * ?"6@ NNN?NR< `J  r s * ?"6@ NNN?N`< nJ  s s * ?"6@ NNN?Nn. |<  t s * ?"6@ NNN?N|. <  u s * ?"6@ NNN?Nn< |J  v s * ?"6@ NNN?N|< J  w s * ?"6@ NNN?NJ (X  x s * ?"6@ NNN?N(J 6X  y s * ?"6@ NNN?NX (f  z s * ?"6@ NNN?N(X 6f  { s * ?"6@ NNN?N6J DX  | s * ?"6@ NNN?NDJ RX  } s * ?"6@ NNN?NDX Rf  ~ s * ?"6@ NNN?Nf (t  s * ?"6@ NNN?N(f 6t  s * ?"6@ NNN?Nt(  s * ?"6@ NNN?N(t6  s * ?"6@ NNN?N6f Dt  s * ?"6@ NNN?NDf Rt  s * ?"6@ NNN?N6tD  s * ?"6@ NNN?NDtR  s * ?"6@ NNN?NRJ `X   s * ?"6@ NNN?N`J nX   s * ?"6@ NNN?NRX `f   s * ?"6@ NNN?N`X nf   s * ?"6@ NNN?NnJ |X   s * ?"6@ NNN?N|J X   s * ?"6@ NNN?N|X f   s * ?"6@ NNN?NRf `t  s * ?"6@ NNN?N`f nt  s * ?"6@ NNN?NRt`  s * ?"6@ NNN?N`tn  s * ?"6@ NNN?Nnf |t  s * ?"6@ NNN?N|f t  s * ?"6@ NNN?Nnt|  s * ?"6@ NNN?N|tz <h  <h,$D02  <o?"6@ NNN?Nx  2  <o?"6@ NNN?N6 ! 2  <o?"6@ NNN?N F  2  <o?"6@ NNN?NE < 2  <o?"6@ NNN?N Lr 2  <o?"6@ NNN?N F 0 2  <o?"6@ NNN?N  h2  <o?"6@ NNN?No  # lI:f?"0@NNN?N/ ,$0 LEuler: (n + 1)2 + n2 + 1  2n(n+1) = 2'  H  0޽h ? 3ffffff((___PPT10(./+LDq(' := @B D,(' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*S%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*N%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*E%(D2' =%(D' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*N%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(DF' =%(D' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*S%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*%(D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =4@BBBB%())))?D' =1:Bhidden*o3>+B#style.visibility<*%(DH' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<* %(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*E%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*X%(DH' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*X%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<* %(D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*X%(+8+0+0 + 0  P<(  P~ P s *lkpx:   ~ P s *lp  H P 0޽h ? 33___PPT10i..(0:+D=' := @B + 0 99 33T9(  T$ T 0Xz ~ Q,$D0 1 subgoal d : dataSet e : rel d ============================ forall (p : seq d) (x : d), cycle p -> p x -> e x (next p x) P%         , b"2 T 0$ ~ Q,$D0 1 subgoal d : dataSet e : rel d y0 : d p : seq d x : d Hp : path y0 (add_last p y0) ============================ setU1 y0 p x -> e x (next_at x y0 y0 p) 0Pc  +                  ` T 0  ~ Q,$D!0 2 subgoals d : dataSet e : rel d y0 : d x : d y : d ============================ e y y0 && true -> (y =d x) || false -> e x (if y =d x then y0 else x) subgoal 2 is: e y y && path y (add_last p y0) -> or3b (y =d x) (y =d x) (p x) -> e x (if y =d x then y else next_at x y0 y p) DPA  5      b       bW T 0 ~ Q,$D$0 b2 subgoals d : dataSet e : rel d y0 : d x : d y : d Hy : e y y0 Dy : y =d x ============================ e x (if y =d x then y0 else x) subgoal 2 is: e y y && path y (add_last p y0) -> or3b (y =d x) (y' =d x) (p x) -> e x (if y =d x then y else next_at x y0 y p) 2P]        a            AV T  6(pS" ~ <$@&0   T 0 ~ Q,$D;0 1 subgoal d : dataSet e : rel d y0 : d x : d y : d p : seq d IHp : forall x0 : d, path x0 (add_last p y0) -> setU1 x0 p x -> e x (next_at x y0 x0 p) y : d Hy : e y y Hp : path y (add_last p y0) ============================ or3b (y =d x) (y =d x) (p x) -> e x (if y =d x then y else next_at x y0 y p) }PPPU     f  ,        #3        q T 0 ~ Q,$D=0 r1 subgoal d : dataSet e : rel d y0 : d x : d y : d p : seq d IHp : forall x0 : d, path x0 (add_last p y0) -> setU1 x0 p x -> e x (next_at x y0 x0 p) y : d Hy : e y y Hp : path y (add_last p y0) ============================ or3b false (y =d x) (p x) -> e x (next_at x y0 y p) UPPPU     f  >  #3        I  T 0 ~ Q,$D?0 mSubtree proved! &P     T N1?"6@ NNN?N, m, ,$@%0~  T s *px:     T N1?"6@ NNN?Nm, ,$@0  T N1?"6@ NNN?Nm, E,$@0 T N1?"6@ NNN?N9m, ,$@ 0 T N1?"6@ NNN?Nwm, , ,$@#0 T N1?"6@ NNN?N m, s ,$@:0 T N1?"6@ NNN?Np m,  ,$@<0 T N1?"6@ NNN?N m, F ,$@>0~ T s *dp@( Z   8 T ZG0 Hߞ1?"6@ NNN?N,$D0 < proof script  0 T ZTG2H1?"6@ NNN?N 2( ,$D0 4goalUz LF6 T 4,$D0 T Z( G9H?1?"6@ NNN?NF6H 7context T N 1?"6@ NNN?NL|6 T Z G&H1?"6@ NNN?N,$D"0 : other goal   T 0 ) ,$0 1e  -  } T# hr ,$@0`2 T 0 c  } T 0C"? - `2 T 0 @ 6`2 T 0  m`2  T 0  Q ZB !T s *D c `2 "T 0p z `2 #T 0x 5  q I $T#   ,$@0 %T <p n  1e &T <q 5  1e 'T < `Q G 1e (T <" "  1e )T <$ b I 1e *T <(>   1e2 +T 0n s ,$@02 ,T 0ik,$@0 -T <- ,$@ 0 1x .T <& j ,$ 0 Rnext p x.  /T <$8J~,$D0 ?cycle p 0T <<,$D0 1pz   1T } ,$D90 2T B,BG H h Drecursion assumption` 3T 0 D H T 0޽h ?_PTTTT2T 3ffffff~ TIMING|49.3|9.8|22.7|8.3|8.2|12.7|4.8|12.9|16.6|2|101.2|4.5|52.1|22.2|27.8|3.3|1.1|0.8+~___PPT10 ~.AS+0DGy' := @B Dy' = @BA?%,( < +O%,( < +D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,T%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*+T%(D' =4@BBBB%(E' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<*0TD' =1:Bvisible*o3>+B#style.visibility<*0T%(D' =%(Dm' =%(D' =4@BBBB%(E' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<*$TD' =1:Bvisible*o3>+B#style.visibility<*$T%(D' =A@BBBB0B%(E' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<*TD' =1:Bvisible*o3>+B#style.visibility<*T%(D' =4@BBBB%(E' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<*/TD' =1:Bvisible*o3>+B#style.visibility<*/T%(D' =%(D' =%(D!' =4@BBBB%(D' =,54ff*3>Bfillcolor=@BPB<*,TD' =1:B solid*a3>Bfill.type<*,TD' =1:B true*]3>Bfill.on<*,TD' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*-T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0T%(Dj' =%(D' =%(D!' =4@BBBB%(D' =,54f*3>Bfillcolor=@BPB<*+TD' =1:B solid*a3>Bfill.type<*+TD' =1:B true*]3>Bfill.on<*+TD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*.T%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =%(Do' =%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*.T%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*-T%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*T%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*,T%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*+T%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*0T%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =%(D-' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* T%(D' =4@BBBB%(D' =1:Bhidden*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bhidden*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(De' =%(D ' =%(D' =A@BBBB0B%(E' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<*TD' =1:Bvisible*o3>+B#style.visibility<*T%(D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D ' =%(D7 ' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T %(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T'%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T'0%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T08%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T8A%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*TAM%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*TMd%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Td%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T5%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T5R%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*TRx%(DX' =%(D' =%(D' =4@BBBB%(E' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<*1TD' =1:Bvisible*o3>+B#style.visibility<*1T%(D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =%(Du' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* T%(++0+T0 ++0+T0 ++0+T0 ++0+T0 ++0+T0 ++0+T0 ++0+T0 ++0+ T0 ++0+T0 ++0+T0 ++0+T0 ++0+T0 ++0+T0 ++0+T0 ++0+T0 ++0+T0 ++0+-T0 ++0+.T0 ++0+.T0 ++0+0T0 ++0+0T0 + 0  X<(  X~ X s *px:   ~ X s *tp  H X 0޽h ? 33___PPT10i.$ò+D=' := @B +  0  \(  x  c $Hpx:     c $Hp<$0  H  0޽h ? 3ffffffme___PPT10E./pk+[W_D' := @B D' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*7%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*7s%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*s%(+8+0+0 +r Nm+zhmrzgeu< DArW<f P b{ " P܆ y B s< 7E XO 1hier - A Computational Reflection Methodology$Verifying the Four Colour Theorem150 years of historySo what about it ?Outline The TheoremThe formal theoremOutlineColouring by induction Cubic maps Small ringsThe proof in a nutshellProgress in verificationOutlineThe Poincar principleReflecting reducibility Border colouring (Tait 1880)Chord flips (Kempe 1879)Model checking colouringsChromogram twiddlingCorrectness proofOutlineFormalizing mapsRings and disksPasting configurationsFolkloric proofs?Unavoidable pattern TopologyOutlineProof workbenchFive tactic summarySome conclusions  Fonts UsedDesign TemplateSlide TitlesMicrosoft ResearchD 4<Version*)'&%%$--'Root EntrydO) =P@PicturesGCurrent UsernSummaryInformation(      =%&'()@  !"#$%&'(*+,-./0123456789:;<=>?Fabien A. P. Petitcolas2_xP &Dr Fabien A. P. PetitcolasDr Oh+'0    0 < H T`h Four colours theorem<Georges Gonthier - A Computational Reflection Methodologygonthie44Microsoft PowerPoint@@л*@@E>@GߙHGg  1՜.+,D՜.+,D    On-screen Show' &ArialTimes New Roman Wingdings MSResearchArial Unicode MSSymbol<Georges Gonthier - A Computational Reflection Methodology$Verifying the Four Colour Theorem150 years of historySo what about it ?Outline The TheoremThe formal theoremOutlineColouring by induction Cubic maps Small ringsThe proof in a nutshellProgress in verificationOutlineThe Poincar principleReflecting reducibility Border colouring (Tait 1880)Chord flips (Kempe 1879)Model checking colouringsChromogram twiddlingCorrectness proofOutlineFormalizing mapsRings and disksPasting configurationsFolkloric proofs?Unavoidable pattern TopologyOutlineProof workbenchFive tactic summarySome conclusions  Fonts UsedDesign TemplateSlide TitlesMicrosoft ResearchD 4<Version  y--$xx--'--%!!9--'3ff--&$$%%&')*****) '&%%$--'--&$$% % & ' ) *****)'&%%$--'--&$$%%&')*****)'&%%$--'@Arial-. 2 %' Verifying the."System-@Arial-.  2 2'FY.-@Arial-.  2 2-oY.-@Arial-. 33 2 23uY.-@Arial-.  2 29rY.-@Arial-. 2 2@Colour Theorem.-@Arial-. 2 O'Georges Gonthier.-@Arial-. 12 X'Microsoft Research Cambridge.-!Microsoft Research Summer SchoolGeorges Gonthier՜.+,D՜.+,D    On-screen Show' &ArialTimes New Roman Wingdings MSResearchArial Unicode MSSymbol<Georges Gont  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijkmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$&'()*+,=Root EntrydO)PicturesGCurrent User%SummaryInformation(PowerPoint Document(lP DocumentSummaryInformation8)