# SageMathCell online https://sagecell.sagemath.org/?q=vgwdgx # ''' Petrit Isufi (isufi.petrit@proton.me; August 17, 2026) Main properties of the graph Q7T4p | Ord.: 3220 / Size: 17605 / Diam.: 4 / Avg.dist: 3.66278 / 15-reg.? False / Girth: 3 Degree histogram Q7T4p : [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 210, 3010] Symmetry properties of the graph Q7T4p | Aut.group.ord.: 1 / Cayley ? False --- vtx.trans. ? False -- edge.trans. ? False ''' import networkx as nx Q7T4p = Graph(r":~?qS`p_?W\g?IBbB_`x?ioUWJoEIBM@j_vwT_JSDyBE@f_u?ZKIsDkA}@b_s?YGLiD[Av@_?q?XGLGEvAn@[?oOWOKkEeB[`{?k?VGJgEEBK@i?vWUGJGDuBC@e_t_ZsFSB}AH@H?dORwIaBkA?@D?b?QoI?DT@v@?_aoPgH[DAAb_{?__O_GwCoAa@QO]OOWGSC]AX@L_hWNOFoCKAO@L?f?SsFkB{AF@G_d?RgI]@{@H?i?ToKOESB`CB?^_Q_HgD_BE@f?xoO?HWCwAq@\?s?\GGGCoA]@Y?n?YOLcCGAK@P?m?VoLOEuAE@F?h?TOK?EkB\@C?c?SoIoECBG@n_C?D?B?AS@Q?t?[oAOAg@g@K?i?V?Mw@O@W?u?^?T_K?Fc?k?_?[?O?J?EGBuG[?K?G_FOCGAs@c?u_E_C_BoAG@M?r?ZoBoAW@[@E?g?Y?MGaO?Q?J?E_BpG?@?BwBiAj_C_NoMoIq?S@??z_jWc_?kAA@w@VOB?GOFcD^?L?`_]_UC?{AG@z@WoCoHOGGDr?S?d__oUS@SAW@{@XoD_GoFwDj?O?b_^oUs@CAOA?@ZpJoAOCcCAAw_N?R_OwKA?m@N@C_oWB?DCCSAy_L?S_PWJm?u@R@A?nGB_DOCIA|_M_ROOoJy@A@Y@E_pgCODoC[BFa\?GoIgG{EP?d?j?c?WSAWAmAP@`oFoJ?HGEH?_?k_b?WkAoA}AY@eoJOK?HOE\?f?o_dOX{A_BCAU@gOIOKWH[ERDD?T?VOR?Km@U@]@K_rGE?EkD?BR_W_X?SGLQ@c@d@P?tgEWE[CuBV_Y?Y?R_La@i@h@M_sWDoEgC}BQ_B?MoLwISEtBoag_?o?wBoB_Ae@loB_FgFKDMB[_K_L_M_I_Ez?c?Z_Z?TOLy?G?n?[?ZOSWL}?I?x?\?Z_S_Le?}@D?m_eoZKA?A_@]@M?ugCGDkA}A\@loG_K?EWC}B[am?GoKGFGD?B\_Q_W_NgICE|?e?p_a?SOL}@S@h@H_i?UKAkBSA]@T?iwD_EkDEAh@UOJOK_IODYAs_R_XOSgIwD~?g?r_h_TwKi@Q@g@R_k?YkU[@i@l?{?m?[KAwB[@x@[_zGE?E{BsAq@zoKOM?FkDeCA_X?[oMgJSGZ?r?y?\_UoPa@g@k?z_loc[B_AE@}@^@JgFGCOB}B?A[oMoFoG?EADCax?N?FwGCDsDO_]_O?OOJkIv?u?___oV_UY@m@A?}?nOmK?sAOAJ@aoBoHGGOEL?C?C?Q_OgK]?I?H?d_`_XC?W?S@K@B_og?w?kAKAH@`p\g@_C[CSBC_G_T?Q?Kq?c@L@G_rWAWCwCcBM_I?RoP_K}?i@P@E_sGAoDGC[BH_G?SoPwKm?w@W@J?sgBgDcCmBRazoF_JOH_Eh?V?m?eOYs@_AiAY@joE_IoHOEp?Z?j_dOYKBWAKAK@goLoGwGsEd?w?c?b_Y[BcAQAN@iOMoHOH?ElDw_]?QoQGL]@y@K@H?uG@WDGCqB^_E?SoROLe?Y@S@I?ug@wCsCiBZ_C?R_QoLq?Q@N@J_vW@ODCCoB]_A_D_IoH{D`Dx_B?C?IwI?Db?F?G_U?SGIm?c@X@P?jGAWDgCuAl_I?V?R_Iy?G?T?i_fOT{@gBCAc@ZoEoKWISDp?[?m_h_VK@sA{Af@XP]gBoD{DOAr_J_W?TOJU?o@`@P_lgCgE[BuA|_R?Y?MgJy?}@h?z?oGC?EgBmB@_O_YoN?Ji@C@c?{_mwCWESBsA{a|oI?M_GCEH?h?u?__WkAgBYAB@bOIoLoFoEN?k?v_^_XCAsB_@~@`OHoMWG?EF?r?__`_X[BOACAF@eOLOGWGcEZBpa}oJ_G_GgE\?o?^?aoX{BC@}AC@gOK_G?GSER?V?q?^?XK@_BI@}@doE_KwF{EX?C?L_Y?O?Ku?I?[?s__OXs?W?y@i@@?rwns?[?{@j@@_sGCOF?CSBW_P_[oPWLE@I@s@A?sgCoEoCIBR_N_ZOOoLQ@?@m@B_tgCGE{CQBV_U_NoPwLy@M@?@G?vwn{A_AAAP@koIOGOHGEt?i?`_b?Z[AkAGAL@mOJ?FoGwEz?p?d_dOT{BGAWAU@WOKoGoH[Db?s?b_e?T[BSAOAX@UP_GDoCcCsAl_W?Q_Q_Iy@w@N@P?lgFgDCCuAv_Z?S_R_Ja@m@R@M_mWF?DOC}Aq_[_ROS?JM@u@M@O_lW@GDoDMA{b?oA_IgI_Dz?J?j?i_Vs?oAmAb@_OBOJ?IOEB?N?k_hOVS?_AsAe@\oD?K?F[EF?T?o_]?Wc@WBC@x@aoC?KWFgELEA_G_VONWK]?c@]?y_qGAWD{BkBA_V?ROSWKI@_@M@Q?owEGC{DIBC_X?SOSoKU@e@Q@R_pgE_DKDOBF_Y_T?TOKaKF?x?k_]_YCBkAs@z@coN?J_FSEV?|?i_\_XcBWAk@v@eoLoIwF_E\?w?k?]OX{?{A{A?@joA?JwGCEp?H?o?__YKWQ?S@`@@_sg@WEGBwBR_E?WoNoLQ?Y@\?~_tgAOEgCIB\_H_YoOoLy?g@c@B_vwAgESCQBX_J?XoPOLi?_@g@D_uwok@CBQAC@mOFOLoHGD\?]?v_b?T{@[B_AL@WOE?MWGwDb?Y?y?boT[@kBWAO@UOF?LgHCDZ?C?O?P?R?JU?I?`?^?eOUsWY?K?a?^_e_U{?[@E@?@I?mGCgCCCiAx_R?O_QoJI?}@B@J_kwDWCcCyAz_U?Q_RwJq@Y@J@O?nWCwCoDAA}_S?P_SOKAFdEG_S_PoRWKE@S@G@M?mgA?EoCgAy_G_ZOQgJm?c@m@J?nGAWE{CmA|_I?[?R?Jy?i@r@K_oGAoFOCsB@_L_O_SGKaKR?[?`_g_WS@sAGAZ@`oF_FoHoEH?V?^_fOWk@_A?A^@bOE_GGI?EN?e?b_h_X{@{AOAf@gOG?HGI_ER?`?d?i_X[Wi@C@J@P_rGCWCoDGBL_Q_P_SgKy?M?h?h_\_YsAgAg@v@joIoHgF_Ep?k?f?]OYK?O@Y@N?|?sg?gA[Aa@z@ho@_D?DGBiBSbDoL?IwGKEx?t?k?^?ZkAwAq@}@nOK?JOF{E~?p?m?_?ZKBGAiA@@lOKoIoGGEv?v?p_aOTkB_AyAI@VOMOJoGkD^EK_\_VoO_JA@w@_@A_kWFgECCKAj_Z?W_OwIq?W@g@F?kw@gEcC]At_F_Y_Q?JY?O@j@G_lw@GEOCcAw_D?XOP_JeKZ?J?r_bOUSA[AiAC@XOI?IoGSDf?h?j_`_UkAgAoAF@ZOIoJGGcDn?k?l?a_VCAsAwAJ@[oK_KGHCEB?C?X_W_QOJiK\?D?Y?WoP_Jm?K?t?m_bOVc?[@[@]@F?nWE?D{C]A}_W_W?Q?KA@y@d@J_pwEoE[CoBG_Z_Y?RGKI@o@h@L?owFGEgCgBCbFoMoLWHSEJ?{?q?d_Ws?gBeA[@fOAoM_HsE^?K?u?foYC?sBYA_@coBoLoICEV?G?v_g_Xc?cB_AZ@eoDOG?IgEhEO_J?OOSWLY?_@A@Q?twAGCKDIBW_H?P?SoLE?e?}@R_sgA_B{DOBR_K?R?NGLm?s@E?|?vGBWC[BuB\_M?Q?MgLyKb?\?c_\_Z{@wAS@v@koDoHWF_Et?b?g_^oTcASAcA?@UoH_IWGCD\?^?i?__T{A?AYAB@WOGOHoFoDb?a?f_^_T[NMKf??_?qi?qc?IBbB_afpnhDkhqTeETd^@dhXGX]UgEWdn`eX\OXiViEZe?@fH`WNOT`E]_@oBha?AQ@^?y_aoSGJ[EYK~@q_}oaGQ[HyDRAs`^oqgYkYAFBBk`zp?g`kqcHFCma[pPGsKTAIvDeawp^Go{XIKzEgbXpggv{rkMjF_btp|h?K_qOnGabPqJhFKcQQ^HYcqq[HN[gYSbEcdMqiHiOjyURJSdnqyh]koALJKKeJrGhdkraYFLMekrX?souIZ]EfEpr]_]kYcZJ?C_Ao@g?{?a?R?I_DoBG@kYgZL?NfC_CWAS@M?h?T_JODwBCYkZN?Y_LoFGBk@y?~?__OoGgC[Yq@J?e_RoIGDKyK@V?k_UoJgtgue@`?p_XOKwEcBU\]?v_[OMWtoui@v?{_]rloF{CAAB@A_`rnOtwumAL@F_cOQWHSCmAX@L_fORwu?uqAb@Q_hoTGIkDYAn@W_koUguGuuAx@\_nRu?KCEEBD@b_qOXWuOuyBN@g_soYgL[EqBZ@m_vo[G]ojILgLofu?\GMkFYBn@w_{o]gN[FqLiLp_~O^wOCGE^uAB`AO`WOsG]LkLq`CoagP[GqCZAM`FocGQL?kLmLr`IOdWQsH]CpAX`LOewRcHuLoLs`NogIBOIIDFAcgN?hgS{IaLqLt`TOiwTcIuD\An`WOkWUSJMLsLu`YolgU{JaDrAy`\onGVkJyLuLv`_OoWWSKMEHBD`bOpwXDCGLxBJga_rWXsK}E`BP`hSR?YcZsZrPN@jouIIOLiEvB[`movgZ{iAFoIs_A@o@nchwS}I_DOag`SWiOTJI]DRAhpTGigTUIkDUqf`Toi{T_IpDXAl@UkhwTkIvD[AmPVOjkTxI]D]anpW?kCUCJBDaQf`WgkWUMJGDdAqpXchwUYJMDfas@YGlGUfI]Diat`Ywl_UqJYDlqfpZ_mOVWJrD|b?p`Sh{UyJdDua|@^_oOWZ?DB_b^XRwlwVKJmDzA~P_goyS}J_Drazp]wnwWKKNdNawP\?n?VoJ~EBbCHRwmGVQJpD{b?P`?pES}JbDta{`^OoGWQKQdOCGqDXBO`yPEGfcTxS@AO`YOtG^CPqI@DET?OdGVCLaFxC_aQPQdOCHaDxB_a?P@GdCSxS@A[`_OxG\COqHXDQ?KFAE~QgAD@BC`cOzGaCRAIki?`QOiGXcNAGhCwalI`Fub|q?H?g_YOVGOQgP|o~__COCGFCEACSiC^]NxG@c@Q@x@c_vI`FwB}`~`?W__OYGMQgP}G~k^yOFGGcCqBkiC^cNsF~CAAAP@O_|I`Fxb|`~x?c_WOTGNqg`uo{C]WNNFlBvP|C?[MFIaFZbo`wg|?]uN^Ftqg`v?{K]KNPFibw@|ciG\qNCFbbs`yo}C^HIaF\Bn`xG|O]mNaFqqg`vWz{]SNLFkBwp{siG\wN?Fdbr`zG|o^NIbF?Bb@q?xs\AMlFWqgpoGws[cM]FPBh`u[iK[CMMFHbdpsWy_\hIbF@ba@q_x_\GMhFYoA?w_wATEMCFCbdPrGyS\SMmdPb`PpOxW[sM^FTbjxSWw[[UMNFLbg@t_zATGLHEjBV@kGuwZgLxdQBQ`iwtsZCLgEyb^HS_skYaL]EpbYPmovuTGLKEhBVpkgugZ_L}dQBRPiWt_ZKLjEwb^xS_s{YgLYErbZ@mOv]TGLOEibUpk?usZeLwbab_XSgpKXAKgEVbLPf_sITIKSELbIPe?rWXyLCdQbDPb_qKXaKvE^BPXSgpWWyKcETBMPfwsYTIKWENBHPdWrGY?LFdQbEPbwqWXWKrE\BQHSgpgX?KfEVBL@fWsETKKREcb_@uo}s`FIeDmbD@hOwC\mNmGQQh`ZopSYUMAF[BzqCk?gMKMAdRAw@aoso[EMxFwCHhSomCWoLLFABm`}HA]TKJaEKbRpogzk^cOgdRAwpbOt?[MM{FxcIXSwmOWwLRFDbo`~PBETMJdEMbT@p_{K^uOidRax`botS[YNCFyCIxSwm[W}LUFFBn`}pAuTMJgEOBTpp?z{^mOmdRayPcGtC[QN?F{CJw@W[[[FIfDtbEpiOwg]ANxGWQiP\_qSYyMUFbB~qFCicVYKeEnBbpwx?C`rIhDvBHpjwx?]QOAGXQiP\wq_YoMQFdC?qE[icV_KhElBcpxW~o`hIhDwbGpjWxO]WN|GYqiP]OqOYwMTFab~aEsigVeKmErbePyP?S`|IiDyBJpk?xg]gOEG^oB?x?wQTSJuEWBWPrW{s_MP?dTA|peGuG[yNMGCCMhTOn_XSLbFNBrq@HBmTSJxETbXPqw|?_SO{dTA}`d_uW[oNPGACNXTWnkXkLhFQBtqAPCUTUJ{EZbY`sg|__WPEdTa~PfGuk[}NXGEcPxTWnwXcLkFOBua@pCaTUJ~EXbZPsG|k_]P@bcb`XTWoCXgLmFPBtQA@CMTUKAEYbY@sW|W_aPCdUB?pfwvK\ONbGKCQxT_oOY?LsFSbvABHCqTWKDE\B\PtO|s_sPMdUB@`fWvW\UN^GHcRxT_o[XwLoFUBwAA`DATWKGE]b[Ptg}C_iPHdUBAPfovG\KNaGJcQhTgogYOL}FXbxqBhDIFqIt_F`qpo{isWYL@E~bl@|@@wafIlEFBO`mwzS^UO^GiQjP`wsOZoMmFuCGAIkisW_LDE{bjp{`AGalIlEGbP`n_z?^IOZGjqjPaOs[ZyMpFrCFAIKiwUwKZEkBdpyh@KabImDmbF@jOx_]kOSGhQj`ZopsYuMXFjcDQI[iwV?K]EmBe`z@@[ah?OBeBaHTomCW}L\FLbuQB@DUT[JaEOBV`rg|g_qPUdVAwpcGt{[{NZGLCTxTwmOXGLaFPBwQC@AeT]JdEQbWpsW}G`CObdVax`couS\GNbGLcHHTwm[XMLeFQbvAB`AUT]JgESBXprw|s_yOedVayPdGu?\?N^GNCHxTwmkXEL`FObwABxAa?aFLFCqk@\_qoZWMlFqb{AECj?VYKmEubh`{o~C`bIoDvBJploy_^MNqGTQk@\wr?ZOMhFsB{qD[j?V_KpEsbi`|W}s`ZIoDwbI`lOyk^WNmGVQk@]OqkZUMkFqBzqD{jCVeKtEzBk@vW~W`lIpDyBL`m?zC\wNvG[QkP]or[ZaMrFZB}AFK@GM[MIdWa|pfGvG\gMvF{cKhUGn_XcLrFYbm@~PBMTaJxEXb\@tozc^uOsdWa}`e_vS\]MyFyCLXUOnkX{LwFAboA?XBuTcJ{E^b]Pow{C^wO}dXA~Pg?vo[?NAF}cNxUOnwXsL|F?bop~pCATcJ~E\b^`oO{O^}OydXB?Pf_v{[EM}G?cMwAW[{[VIqE@BNPmwwO\}OAG]Ql@_Ws[YWMHFeCAAGcjOWGLGEeba`wh?caJIsEAbOPhwwk]KOIGbQl@_osGY_MKFbc@AG{jOWMLCEcbbPxH?SaPIsECBPPhOww]SOEG_ql@`GsWYUMGFdc@qG[jSWSKYEjBd@y@?waTItEEbCpiwxS]aONGdoD?y?wqTiKMEIBSPqo|G__PKdYbBpagtG[]NSGGcRhUgp?WkLRFGBrQAPC}TiKPEKBT@qO{w_WPOdYbC`bGtS[eNNGEcQXUoloXELgFVBna?`CeTkJ\EQBYPtwz{_IPIdZAv`cgug\_N?GBCQxUom?XKLjFWboQ?xCqTkJ`ERbZ@uW{G_OPM_I`sXUomGXOLlFYBoq@HC}TkJbESbZ`ug{O_SPOdZax@dWvG[ENIGGcTxUwmSXWLrFABqqAPDETmJeEVB\@og{o_WPQdZaxpdwvS[MNDGEcSxUwm_X_LuF?Bpa@pDQTmJhEWb[@oG{[_]PTdZaypdOvC[CNHGGCThV?moXgL|FFBraAxAa?kFQd[AzPegvw[ONNGKCIXV?mwXkL~FCbsABHAMToJnEZb\ppO|C_sOcd[A{@fGv_[UNQGHcHXV?nCXcLxFEBtAA`AYToJqEXb^@pg{s_iOfd[a{pfgt?[cNYGMCJxVGnOX{LHFHbuqBhBATqJuE^bQ`q_|S_{Opd[a|pg?sk[iNUGNcIgAw\K[^IxD{BM`h_xW]mO_GTqmP^GrkYYMNFkCGaDkjcVsK{Efbc@zH@k`\IyD|bP`iOxs]}NrGYqm`^_s[YeM]FoBzQEsjgVyLGEiBdp{G}w`pIyD~BOPigx_^CNnG[qm`^wsGYkMXFpb{AESjgWALCEjbe`z_~C`fIyE@BPPiGxk]yNqGYOE?y_xATuKBEKbV@s?}o^qO{d\b@@bOts\ANcF|CNXVWoSWeL]FPBxP~XByTuKEEIBVpsW}W^gO~d\b@pagt_\GNfFzCOHVWo_WkLYFQby@}xBiTuKHEKBUprw}k^oOzd]BA`cGuW\UMxF~COxV_osWuLfFUBm`~xCQTwKMEMBW@tgzk_APD`|AlgBO\W[d?CD]BBpbguC\KM{G@CPg?gjoW_K]EpBi@up?KaN?ED]BCPbwuK\QMvF}CQG?wjoWcK_Eqbi`v?~saB?GD]av@dOv[[]N[FyCOW@GjsUyKjE{Bc@zg~WaF?ID]av`d_vc[cN^FzcPG@WjsV?KmE}Bcp{?~_aJ?KD]awPdwvs[gN`F{cPg@gjsVCKoE~BdP{O~gaN?ZBjbcw@wjsVEKpE~bd`{W~kaP?OD^ax@eWsk[sNgG@CSGAGj{VIKsEeBep|X?KaR?QD^ax`egss[yNkF}CQgAWj{VMKuEfbf`{_~saV?SD^ay@ewt?[mNdF~CRGAgj{VQKxEcbe@{o~{a\?UD^aypeOsg[qNfG?cRwAwk?VWK{EibhPux?[al?WD_AzPfgtW[}MwGCCTwB_\a?sJ?DvBN`iwy?\qOHGgoEpW?m{X}LPFObma@PDI?wJ?DwBO@iOyG\uOCGhoFPW?nCXsLRFPbnA?hDQ?{J?DxBMpi_yO\kOEGioFpWGnKYIL^FSboq@hA]@?J@DyBP`j?yg]GOMGSOGPWGnWYMLYFTbna@xAe@CJ@DzbQ@jWyo\}OOGPoGpWGn_YAL[FUboAAHAQ?yFXFIoHPWGncYCL\FRBoQAPAU@KJ@D|BP@joy_]COKGROHpWOnkWoL`FYBpqBPAy@OJAD}BEPkOzS]QORGVoIPWOnsWsLbFVBqaA`BA@SJAD~BCpkgy{]UOTGWoIpWOn{WgLeFWBrAAxAi@WJAE?bDPkwzC]IOWGToJPWOoGWkL_FXbpaBHAu@[JBE@bG@lWwC]gO^GYOF_zOxY@_JBEABGPl_wG]YO_GYoKPWWoSWuLlF@braCPBY@cJBEBBF@lowO]]OZG[OKpWWo[WyLgFAbsAB`Be@gJBECBF`lGw[]aO\GXOLPWWocW}LiF?BsaBpBM@kJCEDBIPmgwo]oNnG\oLpW_osXELuFEbuP}@Bq@oJCEFBH@m?ww]sNpG]oMPW_o{XILpFCBup}PBy?}FZFJoMpW_p?XKLqFCbtP}XB}@wJCEGbHpmWwg]kNlG_ONPW_pGXOLsFDbtp|pBi@{JDDmBK`iGyW]IOZG\ONpWglsXeLQFSBpaB`BmA?JDDnBL@iWyc]MO\G]OOPWgm?XiLSFTBqQBpBuACJDDobL`igyk]SO^G^OOpWgmGXmLUFUBqqC@B}AGJDDpbMPiwys]WOaG_OG?z_xaAKJEDqBMpjWzC]aNqGcOPpWomSXwL[FXbs`}XCEAOJEDrBNPjgzO]gNlG`oQPWom[X{L]FYbrP|pCQASJEDsBNpjwyw][NnGaoQpWomcY?LWFVbrp}@CYAWJEDtbM`jOz?]_NpGboRPWwmoYGLdFBbt`~@C}A[JFDubPPkow?]mNxGgORpWwmwYKLfF?bu@~PCe@AF\FKoSPWwm{YML_F@BuP~XCiAcJFDwBQ@kGwK]sNsGdoSpWwnCYALaFABup}pCqAgJFDxBO`kWwS]iNvGfOTPX?nKWkLmFDBw`~hDUAkJGDyBE@l?wk^EN}GjOTpX?nWWqLhFEBv@~xD]AoJGDzbE`lOws]yO@GgoUPX?n_WeLjFFBvq?PDIAsJGD{bD@l_w_^?OBGhoG_zsDoUOJyEIbZPpG}C^wPS_maq`^Wp{ZaMTFrCAaCsDwUSJ{EOB[`qo}[_GOf_naq`^gqCZeMNFsC@QDCE?USJ}ELb\@q?}k_KOh_oaq`^wpoZiMQFuC@qC[EGUSK@EMb\`qW}O_OOc_paq`_OpwZ_MSFqcAQCkEOUUKBESB^@r?zo__Ol_qaqp__qcZyMXFZCCQDsAKM}MZ_raqp_gqKZ{MYFZcCaD{E_UUKEEQB^prWz__WOo_saqp_wqSZmM\F[cBQEKEgUUKGERB]@rozg_[Oi_taqp`Gq[ZqMVF\cBqD[EoUWKIEWbRpsW{C_iOr_uar@`gqgY_McF`CDqEcEwUWKMETbQPsg{K_oOt_var@`wqoYSM^FaCEQEsF?UWKOEVBQps?zw_sOw`|oHO{GxuBeJKEGbJph_yC\}ORG[o\@X_pGX_LLFPBoAA`BIBiJLDmBM`k?w_^GOKGXO\`XglsXuL`FCbxQ@hBMBmJLDnBN@kOwg^KOMGYO]@Xgm?XyLbFDbxq@xBUBqJLDobN`kgwo^OOOGZO]`XgmGX}LeFEbyqAHBaBuJLDpbO@kwww^WOQG[o^@XomOYCLiFHbmaBHCA@KFaFNO^`XomSYGLjFIBmqBPBiB}JMDrBPPl_xS\wORG\o_@Xom[YKLlFJBlaA`BqCAJMDsBPplow{\mOTG]o_`XomcYOLgFGBmAAxByCEJMDtbOPlGxG\qOWG^o`@XwmoWiLsFNBnqBpC]CIJNDubD`mgx[]?O^GcO``XwmwWoLuFKBoQC@CECMJNDvbEPm?xc]COaG`oHo{Wx}CQJNDwBE`mGxg]EOZGaOa`XwnCWeLqFLbpAB`CUCUJNDxBD@mWxs\{O\GbOb@Y?nKW{L~FObqp|pCyCYJODyBFpmwyG]WNnGfob`Y?nWX?LwFPbpP}@DAC]JODzbGPnGyO]KNpGcoc@Y?n_WuL{FQbpp}PCiCaJOD{bF@ngx{]QNrGdoc`Y?ngWyL}FOBq`|hCq@OFc`IAsP^Wq[YSMkFfb}qIcHSUaJ{ESBQptg|?^gPT`JAsP^gqcYWMeFgb|aIsH[UaJ}EPbRPt?|G^mPV`KAsP^wqOY]MhFiB}AIKHcUaK@EQbS@tO{s^qPQ`LAsP_OqWYQMjFfB}aI[HkUcKBEWBT@tw|k_AOd`MAs`__rCYiMoFic?aCsHsUcKDETBT`uG|W_EOf_S`xPsKH{UcKEETbTpuW|[^wOg`OAs`_wqoYaMsFkB~QDKICUcKGEVBS`ug|c^{Ob`PAs``Gq{YeMmFlB~qCcIKUeKIE[bV`o_}?_KOj`QAsp`grGY}MDFoc@qDkISUeKMEXbU@ow}G_OOm`RAsp`wrOYsM?FpcAQD{I[UeKOEYbUpoG|o_SOo`SAspaGrWYwMAFmc@AEKAgNKMa`TAspaOr[YyMBFnc@QDSIkUiJ[E_b[@rw{s^wOi`UAtPZgsGZaM_FfB~QD[IsUiJ]EaB[`sG{{^{Ol`VAtP[?sSZeMaFgB~qDsI{UiJ`EbB\@sW|C_AOn`WAtP[Os[ZiMcFhC?aECJCUiJbEcB\`sg|O_EOp`XAt`[_pOZqMiFkcAQFKJKUkJdEIb^@tW|g_SOq_T`xps[JSUkJeEJB^Pt_|k_GOr`ZAt`[wp_Z{MlFic@QEcJ[UkJgEKb^pso|W_KOt`[At`\GpgZmMgFjc@qEsJcUkJjEHb]@tG|__OOw`\Atp\_psYYMtFmcBqF{JkUmJlENBRpto|{__P?`]Atp\op{Y_MnFoCCQFSJsUmJnEOBQPu?}C_cOz`^Atp]?qCYSMpFpCBAFcAoNOMc`_Atp]GpkYUMrFpcBQFkKCUmJqEMBR@u_|o_[O}``Au@]WqWYmMAFtcDAGsKKUoJsERbSPoW}o_iPF`aAu@]oq_YcMCFqCDqHCKSUoJvESbSpog}S_oP@`bAu@^?qKYgMFFrCEQG[K[UoJxEQBTPo?}[_sPC`cAu@^OqSYkM@FsCCqGkKcUqJzEVbU`pgz_`CPK_U`yPskKkUqJ{EWBUppozc_uPM`eAuP^grCYwMGF\CFAH{KsUqJ}ETBVPpGzk_yPO`fAuP^wqkY{MIF]CFaHKK{UqK@EUBVppWzW_}PI`gAuP_OqwYoMKFZcGAH[LCUsKBEZbWpq?{O^aPR`hAu`__rcZIMQF^B{aIcLKUsKDEXBX`qWz{^ePT`iAu`_orKZMMSF_BzQIsAwNSMe`jAu`_wrOZ?MTF_bzaI{L[UsKGEYbWPqo{G^]PP`kAu``GrWZCMNF`b{AISLcUuKIE_BZPrW{c^mOc`lAup`grgZ[M\FdB}ACkLkUuKME\bY@ro{k^qOe`mAup`wroZQMVFeB}aC{LsUuKOE]bY`r?{S^uOg`nAupaGrwZUMXFbB|ADKL{UuKQE^bZ@rO{[^kOb`}AmGE?]o\PBaGlowqJcMOazBd`rCVyKCMaFQPa`tCWw\XEQ@aFlFSozQKsMwbNBnGsO{ALKNCbTBqGto{qLcNObZBtGvO|aL{BGN[Mi`{C[W^HFIFsPr`|c\G^`FUFyPu`~C\w^xFaG?Pxa?c]gEW]{\VCBG}P@ANkOSb|CEG~p@qOCO_cBCHH@PAaO[OkcHCKHAoL?}?yqG[QFaFcaGa@GeGaQIaHCawaXGqGgQLaIcbgapG}GmQO_Y`{PtkPccdCYHHpEqQcPocjC\HJPFaQ{P{cpC_HKpGQRSQGcv?uBxBjgc`HuHIQ]aRCfwcxIAHOQ`aScggdPIMHUQcaUChWdhIY@mFrFVpJqTCR?dRCpHTPKaT[RKdXCsHUpLQTsRWd^CvHWPMAUKB_NgMoa\CkwfXJQHwQta]clgfpJ]H}Qwa_CmWgHJiICQza`cnGFG^S\bDDH^PPaV{S[e@DGH_pQQWSSgeFDJHaPRAWkSseLDMHbo~PVKBkNmMragcqgiPKmIeRKaiCrWihKyIkRNajcsGj@LEIqRQalCsw~?zQIwRTamctgjpL]I}RWaoCuWkHLiJCRZapcvGk`LuJIR]_]`}PukU[f@DgHopYQ[SUgfFDjHqPZA[kUsfLDmHrpZq\CV?fR?}B|BlgmPMmJeRkayCzWmhMyJkRnazc{Gn@NEJqRqa|C{wnXNQ@}FzFZp^Q]sVwfnD~H{P_A^KWCftEAH|p_q^cWOfzEDH~P`a^{^o\pEGI?paQ_SWggFEJIAPbA_kWsgLEMIBpbq`CX?gREPIDP~PvKXKgXESIEpdQ`sXWg^EVIGPeAaKXcgdEYIHpeqacXogj@AB~BmgrpP]K}SWbODEWsHPiLCSZbPdFGs`PuLIS]bRDFwsxQAAEF~F\piQcSYghFEjIQPjAckYshLEmIRpjqdCZ?hREpITPkad[COO?M{bYDJWuhQyLkSnbZdKGv@RELqSqb\DKwvXRQLwStb]dLg^ojiAKGAF^PoAfK[ChtFAI\poqfc[OhzFDI^Ppaf{[[i@FGI_pqQgSC[OEM~bddPGx`SUMYTEbfDPwxxSaM_THbgdQgyPSmMeTKbiDRWH?_O]@FUIfptqiC\_ibFXIhPuai[\kihF[IipvQis\winF^IkOQP?g{ENATYbpDUw{XTqNGT\bqdVg{pT}NMT_bsDWW|HUINSTb_dA@g|`UUNYTebvDXw|xUaN_ThbwdYg}PUmNeTkbyDZW}hUyAUGFF`p|qmC^_jbFxIxP}am[^kjhF{Iyp~Qms^wjnF~I{Q?AnKCoOONCc@D]x?XVqOGT|cAd^h?pV}OMU?cCD_X@HWIOSUBcDd`GHg_c]JGLJBQBao{_{kPGOJCqCQpS`GkVGRJEQDApk`Sk\GUJFoR`@O{YOoUPcKdchBPXMOuUScMDdXBhXYO{UVcNdeHC@XePAUY_faApw{aKkxGcJMqHQrsaWk~GfJOQIAsKaclDGiJPqIqscaolJB~D\oSP@g{eP]UgcWDiXEHYiPcUjcXdjHE`YuPiUmcZDjxExZAPoUpcFBqhFPZMPuUsc]DlXFhZYP{Uvc^dmHG@ZeQAUyc`DmxGXZqAeGNFdqPQvscWl~HFJ_QQAwKccmDHIJ`qQqwccomJHLJbQRaw{DOO_NKcgDqXIH[iQcVJchdrHI`[uQiVMcjDrxIx\AQoVPckdsgIg`C]ZHZJiQVAykdsmlH]JjqVqzCe?mrH`JlQWaz[eKmxHcJmoT`AO{yRKV^crdwHL@]ERQVactDwxLX]QRWVdcudxhLp]]R]Vg_jaCpx{fCnTHqJtq[q|cfOnZHtJvQ\a|{f[n`HwJwq]Q}Sfgnf@WCIBsHN`^URyVuc~D|xNx^aS?Vxd?d}hOP^mSEV{dAD~XOh^yAqGTFgq`r?Cg_oBIHK@Qab?[gkoHIKKAqbR?sgwoNINKCQcB@KDgOkNQdHEAxQX_qSgWLdIeBhQp_}SmWOdKECXRH`ISsWRdLeDG_?jqAwGWFiOwbAx`_oqWYKLeFBBh`yFEP[KJeFrC@aGpEWcKQeHg[`DsomWfKSEIRDPakpYWm`qcVbAxa{p_WpKXEKrE`bUa}WVKZEMBFHbgpuW{K]oxqK@`[p{W~K_EORGXcOqJBgGoeDrGpc[qOXHKdEQrHcMcbCWVKfERrI@dCqcXRKiOyaKX`_qiX\KqeZBM`fosFBjGqEEBIpdwrKXlKye^ROsDsOqNT`ucXbB@d[q}XfKve\bNpg]F[PfKKEURK@e_r_XvK~eaG\xE_ooXYKoeYRMHf_s?YHgseEBJXeGrSXqK|E_RPSNCbSWWKmEXBLXfKruYALDo{aLX`c{w]cNUflbvx{_}`BrGuEERrhyW|[]vN_FqRxSNObYWXNNFhrtxz_}A^ANdo|QLp`c{}]gNWfmRvP{K}XBuGveERs@yc|c]rN]FpBxkDwOsNU`{C[RBHyC|S]jNYFnRwh{yFqPqKKfgbsXyo|i]}Nbfrw^PFKos\eMwF]boXwW{_]X`|c\BBPu[za\zM}f`rqHxmFwPtKLFYBmPvoz{]GNHFdIMp`gzQ\rMyf^rpHxK{jB}GzeEblPvOzk]?NDFbBqsN{boWYMtfZRmxwC{U]LNJp?ANH`gzW\nM{F_bohww{pPyKLfJrfPsSyO\RMjFWWJw`k]nCBG}EEre@rkx{\HMiFUBkcOObyWZMWfNBfxsgy[\XMqp@QNp`kxc[|M_FQrhxtgyzCEG~eEreXr[yC\LMgFUrjsO[c?WZMYFMBgXsWya\[MnpAAOH`kxi[xMaFPriPtSz@CHH@EFB^HoSwQ[UMLFHbdSOgcEW[L|F@b`Xp[wu[^MUS`BB`nkwM[KMGFFBcHquGWQDKME~B_Hoswa[\MPFJgK?`o]pCMHBeFB^hoGw[[QMNFGrc{O{cOW[L~F?r`xpKwo[cMSPCAPH`ow?[CMCFDBbHqSxRCPHDEFRWPk{uiZYLrezR]SPGcUW\L`esBYplkvAZmLypCqP``suGZILjevB[Pm{vlCSHEeFRWhkkuoZ]LpeyR]{PSc[W\LbErBYHl{vGZiL{PDaPx`suOZLLhewB[hmkv`QOKMeqRXplOuqZeLuE{XBg|eGqQQKNEbBRPiCtOYmLYemwbPHKo{YLLIEgbTHi{tkY|hIEFbPphSswYiLWElrVsPociW]LFedbRhiKtcYwL^pFQQp`wsaYVLNEhBTXjcu@C]HJeFbQPh_s}YdLUEkrWKP{coW]LHeeRS@i[tYYsL\PGARH`{sWZAL{fJrkpxqHAQYKNeTbPhkKvs[oMrffWcPHko}XVLFEpB^XrCzO]]_pAF`zSQOo}XXLFepR^`rGzQ]^aQcfbBxdgsaZEL}fKrlPyAc}W^KlecbX@nwxg\jNOpHqS@`{qwYRLcf?Behuo|DCgKOEVRQhkowG[zMxfigdHIGp?YULef@Rf`vO|FCiHPeGBQxkwwK[|MufhGdXIOp?YWLff@rexu{|LCkHQeGBRHl?wA[wMwFhwdhIWp?YYLdF?bfHvC|P@bCNbuwdxI_p?YSLdf?rfPvG|RCoHSeGbRplWw][~M{FkWeHIgpCY^LjfABg@vg|dCqHTeGbS@l_wQ\AM|fiweXIopCXgLOesR`XsKzw]kaYCjRCPiGue[KMaF\RtkRSd[WaLMEtB`hsSzk]maZCjrCPhsui[MM^F\rt{R[pEXkLRewBaPskz{]va[CkRCXestOZXMHfRRnxzaBGG_FmPMaUXaKr]YhLlFDBgpw?|rCzHYEGrM@iguu[UMbf_Ru[RodiWbKwegrZ`p[yO]ANYPNQUpaKrcYcLnFCBhHwK|jC}HZeGrMXiSu}[PMdF^RusR{doWcLVewbbht?{U]}a_CmRC`fSt_ZbMNFSRohz}dsWcKzEkb[`p_yc]EN_POaVXaOtUZdMKfSrox{EIEQ{KQEjB[ppgyg]GN\OXPCG|uIIQ}KQEjR[xpky[]HN]PPaVxaOt[Z`MMFRrpPzuIMR?KQe^BV@moxA\[NGfpGh@KCpIX|L[ezRcPtS{c^DaccobChfwteZmMPfTbqX{]eEWdK~elB\xqOyo]KNcPQqW`aSs?YtLsfHRjHws}RDKKQe_RUpmgxK\YNFFoghhKWpIYALZeyrbxtk{_^BafCprCpgKuAZvMUFWBqp{mGAI|_raGpz{TCeSWeLBEmb^@qszA]VNeSqrCpg[tuZoMVFXBr@{uIeRKKREaBVhnCxM\dNKfrgi`KspKYHL^E{bd@ts{u^NaicrbCpggt}ZtMSfVbq`|AIkRNKREarW@nWxS\^NIfqgixL?pMXTLIEsRa@sw{W^IakCsRCxdWsiZRMGfRrph{mIqRQKReTrQplOwc\ONFFrGjPLKpMXXLJetRaXtC{_^L_sAH@{CToeiWfKlEeBYppOyc]PNfPVQYpa[quYXLjfDbiXxG}^D]HjeHrJ`hguo[VMiFcryCT{eoWgKmefRZXpkys]XNPPWAZHa_q{Y]LmFFBjXxk{xD`KSEVrRxlwwy\[NIFfWkPLkpOX_LOEvrbptS{i]]apcvBD@eCtAZ_MKFTbqpx}JGR\KSEWbSPlcwq\WNJfgGkhLwpOXcLMEubbPtc{o]`_saHP{KU[f?WhKqehR[hqWy{\hNSpYA[HacrKYfLrFFrjxug|TDhHpEIRKxi_vM[`MoFYrs[UgfEWhKsEiR[HqGzA\kNQPYrDHectSZaMPfXBkpyYJWRdKSeYbSXmKxG\dMrfhwlhMWpQXjLQExBchtszO]gavCxrDPeot[ZnMSfLBlxy}J]WiKuejr\Hqgxi\oNWp[A\Hagr]YoLtFJBdxvC|d@iCRBwgmPMkpSXoLXEyrdhr?zc]jaxczBDPfCtUZkMVFKRmXyqJgRlKTE[bT`msxM[qMyFjWmhMwpSXrLUezbd@rKzY]mazCzrDXfOtmZpL~FMRn`zYJmRoKTe\RV@nGw?[yMyflwn@NCpUXuL[e|R^Hrkzk]wa{eIrMxjKvkZyM]F\rvKVgfeWjK{ElB]xnkxy\wNXp]q]`akrsYtL{E~Bexvg|h@jCRbwwnhNWpUXzLZE{B^hr_zu]ta~C|rDhfou?ZDM@FPRoHzuJ}WlK}eoRWpoKx{]AN^P_A^Hasr{YyLcF@BfxwK|~E@H|EJRNxjkuQ[DM_F^RwCWGfuWlL?EnRWPoWyC\}N_p_q^`assAY}L`f@rgXv{|tR|KUe_bVxkOwA\CN?FnGohNwp[YBLHerr`hsc{M^BbBC~rDpgWsWZOMFFQbp@{QBWGgFqPaA_HawsMYLLdFBrhXwc}JEHI@EJbP@gwuU[GMefabw{WggEWmLCebrX`ocyK]JNcParDpggsaZLMDfProh{eKWSDKVEarQPkwwW\GNBFogphOWp]XTLMEwRcxr[zy^AiBeJrIphsvC[gM[F^bw[W{p]XVLNEwrdHrcz}^CbGDARDxdcs}ZcMTFMbo@{UKaSIKVeUbS@mSxW[zN?fpwLgac^JERIEEJrJXiCvK[lM]F_bxCXOgYWnKmEgb[xqwxy]BNcpdQ`pb?qyYcLte~BgXwg}`EUIFeKBJpiSvWZ|MaFarxSX[g_WoKnehr\hnwyI]DNdpeAaHb?r?YgLvF?BfpwW}XEXKWEWRTHm{vq[~NBfrWrPPKp_XaLTEyR^Ps?{O^MbLdDBE@eOtEZiL|fObpH{}KwSTKWeXRThnWwM\FNGFgWLoaiK{WpKrEjb]xoCyO]PNPPfqb@bCrMYnL{F?bhHxG{xE_IKeKRL@j?v_[BMdFcrrkYCgsWpKsekb]HoOyU]KNNPgabXbCrSYjLxF@Rhhws{~S[KWeYrT`nSwK\ENFFgGs`PspcXkLZEqR`XtK{i]gbQdFbEPestmZAMEFTBqpyeLKS^KXEZrV@kKwY\MNJfigsxbGr_YxLaFBbhxx_|F@nCTpiQcPbGraYrLafBri@xc|HEiIPeKbMPjOuK[GMgferssYkhGWqKxelRX@ocyc]SNRpjAchbKrgY~LdfDbj@uo|\ElIREKrMhk?uW[VMkfXbt{YwhMWrKzEoRXhp?ys\fNWpjqd@bKrmYyLfFCRjXu_|dEoISeKrN@jku][QMmFYRt[ZChSWrK|EnRY@pKyi\iNUPkbEXfkt{ZIMIFTblXyuB_GkFsPlBE`foscZTMKfXRmPzULiSmKYE^RQXlWws\\MxflgupQ{pgX}LEEtrbXtwzg]vbZdKBE`f{sYZWMMFVrlhzaLoSpKYE_BPplCwy\_MvfmWvHRGpgY@LFesrbpuCz_]rb\DKrE`gGsaZSMKFXBmHzQLuSsKYe_rRPl{xG[qMzfnGv`RSpiYELIEwBchrKzo]|b]dLbEhg[siZXMRFLBnPzyFII`a@anwMWa{^VSxKYeaBQplgw}[tM|fnwwHRgpiYHLJeurcHq{zw^?b`DMrEhggsoZ[MPFKBmh{EMES{KYearRHlwxE[pMzFmgw`bWqiYbLwFABihus|tFDI^ELbIpiOva[HMjFZrvc[Wh}WuKjehR]Pokyo\oN]ppqg@bWqqYfLyfBBjHvC||FGI_eLbJPi_vk[LMlF[bv{[ciCWuKleiR]xowyu\rN_O\@E?}qMUTCKZEVBTPn_w]\[MyFoWx`SSpoX\LUEpBaXuCzu^HbedPbF@dwtYZDMIFXBn`{IM[TFK[EVrTpkWwk\dMyfowxxS_poX_LVeqBaxtszk^CbgDQRF@eCt_ZHMGFVbmx{UMaWwKpEkbWPpCy}\wNbpsahXb_rGYjL`fCbk@vg}PFRK[eXRUhkww{[oN?Frwy`SspqXeLZErrb@rC{A^O_yaKP|k\Wi]WxKrelrY@pcxc]ANdPtqi@bcrOYwLdFEbeXwK}VFWIgeMRLHjcuU[ZMYF^Rxc\cicWxKtEkrX`poxi\}NepuaiXbcrUYsLefFRdxv{}\FZIiEMbL`jwuo[aM]F`bsC\oiiWyKuenrYHqKxy]FNOpvQipbgr]Z?LhfHBexw_|DF]IjeMbM@kCug[dM[FaRrc\{ioWyKwembYhqWxq]INMo\`EO}yNAWyKxEmrYpp{xs]JNNPwajXbgreY|LjfGRfXwS{~FbImEMrM`hCus[lM_Fcrs{]OiyWzKyecbZXqwyC]KNSPxRFXfWseZ[MRfOrphyeNKT^K\e\rP`lwxO\CNFFig{xU?puXwLEevrdHsS{_]bbsDWRFXfgs[Z_MTFNbqHyQNQTaK\e]rPxlcxW[~NHFhg|PUKpwX{LKexB^Pss{o]l_zaKp|{]ojIW{K}eeb[hnkyK]XNVPzQkpbor{YSLrE~Bgxxk|^FmIreNBNxhSvMZ|McFdBuK]{pwY?LJEwR^psc{i]qbwDYRF`gCsmZaM?FQbqpymNaTiK]E_bR@mKvq\JNJfjG}PbssEYaLvF@RiHu_|hFrIuENROphov][EMhFYRuk^OjYW|LBefR\Ho[ye\iNZP|QlpbssOY]LtF?Ri`uk|n@wCYB{G}xV?pyYHLNeyr_PswzW]wb{D[RFhggt?ZkM@fRrkpzeNqTqK]earSHmswG\OMrfkw~PVKp{XTLTeqbbxrw{g]rb|d\BFpdWtWZJMOfNrqhzQjiW}KjejRX`qGy?]UNYp~QmpbwqqYmLefGrgPx[|lF}IzeNbJPi{u[[cM`feBu{^{p{XZLWErrchsO{q]wc?D]RFpdotcZOMRFPRrXzeBqGtFwq?anXb{qyYsLiFIbhPuk}BT{K^eVbUhlSxW\JMuFmh?`Vsp}X^LZEtbdhsszK]{cAeNrK@j[um[mMbFXrvk_Wj}W~KoemBZ@q[yM\gN^Q@qo@b{rCYxLgfIBh@uc|~GGJ?eNrK`jKue[hMcfYbwC_ckCX?KqenRZpo?y]\pNcQAaoXc?rKY}Lne}Ri@vG}RGJJAEOBKxj{v?ZyMgf[rwSFgPkNqcEd`bG@e_u?ZXL|fSbm`{MO[UFK_EYRWHlgvw\RMufpH@xc?rSYyLle~Ri`u{}JGOJCeOBLXjkuwZ}MfF[Bw{`CkSX@KuEbr[xoKyu\uNfTarGHessaZ`MAFVBmx{}OeUKK_eZrQPmGwI\TM{FsHA`WsqAXoLHewr_ptWzs^IcIeORMHgovG[FMkF]rx[`Wk]X@KxEbR[hoCyq\{NeO]pEw~MOoUPK_e[rPpmWwC\YMyfrXBHXGqEXsLKEyb`pt{{E]^cLEOrMhhcvU[NMoF^RsC`kkgXBKzEeb\`o_zA\}NOqFAqhcKrmYSLufARk`v{|DG\JJEOrN@hSv[[JMqf_Brc`wkmXBK|Edb\xooyy]@NMqFqr@cKruYVLsfBRjpwG{|G_JKePBN`iCvi[PMYfaRssaCksXCK}egb]ppGx]]INRo^@F?~QPEU[KaE^bR`n[we[oNDfiHC`XsqGX~LMe}Ba`rC{I]hcQdfbG`g?s{ZoMJFKbopyiPKU^KaE_RRxnCwm[rNBfgxCxcOsCY_LxFCBe`w_|HGgJOePROXiguO[[M\FbbtcaclCXDLBEgrXHpsxu]ONUqIasXcSsMYcL`FFbf`xC|\GjKaeaBShkKwo[|NHFjxD`YSqIYHLRepBbHr[{e]paAAoGNobg^lGnJSEPRPPi_uI[YM[FbBuTYcqIYJLSepbbXrc{Y]jcWdibGpdSteZXM?fVRohymPcXEKjElBZPoGy{]ENUQKqt`cWqmYtLlf?rjxw[|ZGsJUePbJHjWuw[CMoFaBtsbSl[XEKlElrZpoSzA]HNVqLatxcWquYwLnf@bk`wg|bGvJWEPbJ`jcv?[FMqfaruSb_laXFKmemr[Xooxe]QN[o^pFW~]PsUrKbeVbVhmOwY[sNHfkxFXZOqMX^L^ExR`prS{W]sc]DlRGxe?t}ZeMFfJrphzUPyUuKbeWRW@m[wO[oNFFlhFpZ[qMXaL_ewR`HrC{_]vc^dmBGxeOtsZaMDfKbqHzaQ?UxKcEXRPpmswm[wNJfoHGHZgqOXeLFezba@rc{o^@c`DmrH@e[saZnMGfMbrHziQEU{KcEYBQPmcwc[zNLfnGO?bo^pU}KcEYRQXmgwe[{NIFnXGpZ{qOXiLEEyra`rs{i]}cbeQBLXgsvW[UMZfdbv{c_mAXHKuEdr^@pgyG\fNbqQQwPccrYYWLwFErghu_}PHIJ`eQRLxhcva[[M^FYRxKckmGXHKwEeb]Ppsx}\iN`QRAwhccraYSLyfFbg@uk}FHLJbEQRMPhSvk[WM`FZBwccwmMXHKxedb]xpcyE\eNao_PFg~eQ_VHKdE\BS@kKxI\GMyFrXIH[gqSXtLOepBcpsczY^MchDqrHPfWtCZDMNfQblx{}QeVKKdE\rR`kWxA\JMwFsHI`cgroY\LcFGbhhvC}THTJfEQbNPhwuQ[bMbF[bx[dWm]XIK|efrWPqOyM\rNeQTqy@ckrwYhLefIBi`vg{|HWJgeQrNhigu[[hMfF]rr|\GqUX}LPerrdPs{zw]_`@AN`~SdkqUX~LQEsBd`t?zi]`cmDtRHXg?tIZIMUfSRmpyIQyVUKde_RSxkkx[\QMzffHJp\[qUYALSErBcxtKzo]\cnduBH`gKtcZVL}fURnxyQR?VXKeE`bTXl_v{\YN?FhhKHcosMYkLgf?BjXwC|NHaJleRBP@isueZxMmF_btD\oqWYHLVEtB^PtS{E]hcqDvRH`ggt]ZTL|fTbnhyiCEG~F|qXazxcosUYoLjE~Bj@vw|FHfJoERbIhjgvQ[WMbF\Rs[e_nAXMKjEmr\PpcyM\uNQQYQ{PcwqmY|LtfEbh@v[|LHiJpeRbJHjwvW[ZMcf]Bs{ekq[XYL^ezRb`sgzs]gcuDxRHpdku?ZmMMfQrnXyeRYVeKfEVBWHm{w{\LM}FihLp][q]X\LEe{bcXtG{C]qcveRrJpgwvi[cMhf_rt[GOQ@ViKfeVrPxnWxI\SM}fjHMP]kq]X_LGe|rcpswz{]lcxdzBHxeCscZwMNfRrnxyyRgVlKfeWbQXn?xA\ON?FjxMh]wq]XcLEE{RcPtC{A]pczDzrI@eSskZEMVFTbp@zaRmVoKgEXbQxk_xM\WNCfmXN@d?rMYWLcfIBjHwg|fVqKgEYBRHkGxQ\YNDflHNP^Kq_XhLLEordPtk{I]t`AaOP~kfoniXOKtEdBW`qoyw]ENZQ^Q}pd?rUYTLafJRihw[|nH}JzeSRL`h{u_ZzMqFbRv{f{noXPKuegBXPnozI]MN_T}RIHe{tAZJL}fVRq@{ESAVyKge[BSPkov{\]NGfmhOP^kqaXpLMErR_@t{{c]{d@d~BIHfGsyZML{fWBqXzuSGV|Kge[rRpk{vs\`NEFnhOh^wqcXsLSEsr_prC{u^D`BAO`~sg[o?XQKyeiRY`o[xc]SNbqaB?HdGrkYiLif?ReXxS}PIHK@ESbMxiKuk[AMYFdbxL_KqcXwLQEtr_XrS{m^AdDe@BIPfgtIZWMAFJrr@{MSWWDKhE]rSxlCwI[oNKfpHPh_WqeX{LWEvB`HrszS^KdFE@rIXfstcZ]MDfLrlX{uS]XRK~EirZxooxo\kNfQcB@HdKr}YkLoFBRfHuW}^AFC`b~xQP_kqeY?LUeuR`prgzM^OdHeBBIXgCt[ZYMFfMrl@{iSgWLKhe_bTxlkwO[{MsfqxQh_wqgYBL[exba`sGz_]\kFeTBOpjKvM[UM`f[Rrsh[o_XSLBelB[Hp[yG\qNNqeBAHdOsOYtLpFCBghvK|@IXKHETBPHjWvE[PM^F\BsKhgoeXSLDElr[`pGx}\lNPQerA`dOsUYwLqfCrg@u{{xCDD_oaPGh?EBAC@GQCkA`XdSrI`D_K`OPUX@ceIW[L]FZb~cN?HKJ@GodqBKA@qEqCVFIDyBNY?d@maMcHB@qRH`d?b@^AKAaaA`ICoy_QPKoqOiOXGSwOFJGDubBqF}RaKMJTe]cEs@?RELyFEdxBBQO\GrDIFPCLqs`e[~[_b`DAPa?SBWBeBfEgd^bKHfPF[cc`X?x`{pHsgcX^KrHFSkKAgBaBW@pAtqp@eh@Kcr_^?l?\GOk_SOWJwe\sE[HsQIMMFMDNQw@dx?tB?@h`baGhP[rG^qOOGMw[_YKMSJ\H{EWb~i@yM?NfG|dgBLXk\@MbV__Ad`n?y?joXwOYGcCRC?sRqIyIdEYRyX}D?y_d`DaPq?[GoQOOC`EaQQ?kGwQSOE`FaQsq[H?QWOG`GaRQ@KHGQ[OIaBAogQ_d?_XATCgcBWQodG_\AVChcBwR?dO_`AXCicCXIp@HKdAZCjcCwR_d`KfHXGIhcg_wkMC}HZGJog@JaXYDAH\GKog`Jp@iDEH^GLoh@K@@qDIH`GMoh`KP@yDMHbRIOi@K`AAGOJCRLoi`KpAIDUHfGPoj@LAXQDYHhGQoj`LPAYD]HjGRok@L`AaDaHlGSqZaDQXyDeHnGTpAPWkJSRaOl`ZA[cq{J[ReOn`[A\AECJcRiOp`\A\aESJkRmOr`]A]AEcJsRqOt`^A]aEsOgULH{G[HdGWGfs`rBAC~CMgWWf{`vBCD?CNGWggC`zBED@CNgWwgK`~BGDACOGXGgSaBCJ`da`qG[KoSOPC`eaaSqcggaLBNDDcPxP`C`KxBPDEcQWYOgwaTBRDFcQwY_h?aXCKDcHdWYohGa\BVDHcRxQ`D@L@BXDIcSWZOhWadBZDJcSwZ_h_ahB\DKcTWZohgalB^DLcTw[oiIG[JI_???QJ@`[}eanRIH}g???GBaB_Af`n`Rx`_}h??CUaf@S?okZsNhGkcqByiXa??SvJREDRBPgOve\aNgftcq[??TCWZNjgOCUAP|K[elR[How??iKow^WRfHuS{a]|Nv??KMfuSqk??TI^YRPo?PSp`{}v?@?@ahrC@|qG]JJS?o?O@oicpC^]_?_EPTPaK}~?@?QAirC`}A?A?nDUEHR{K?C@sIlKRFwhTpD_pM^bRahrSyq\|NOfpR{qjqJ@a_~GfERfhts{A]dNcfrdWCUBDH}TMMfORkHwS|Q]lNhIpGkEIb{q[`MafYRpHws|a^UTcPWKTfxsxI\HMuf[RqhzS}sP?UWg@dYCUBDh}dMSfRRiHvS{q]xNnItGkEJb|Q[lMWfTRnHxs}A^aTkWnNtgjsWyQlK]ekRVhmSwSj[p_^kPVgsceqXhLKeoR\HpHV@bC~YanPmhOSsiY\LaezR]qmREP}xD]bgQeHWctAZHLwe}d\EKr|yI|FedVQuhiSuYZTL~IzKYGjs^qPPJoeXRTHlCuq[ATwWtNwgjs`IQ@KEejRVHlswKjspkYeMIf`Bsh~H?g_tPQH}gaGktODI~K[EkRc@sC|_^sONgOSUI^iU?WxL]FIrh`zk}y^tOeGnC~SkCpsZFMZFTrwp}_~k`VO{H}hWPbkucZsMpfsb}X~\BCaBR|QorF`lsv}\mNFf}B~qEtC[fydaENR\@ogzq]YN{gASDQHdNtJDHBD?Ad`Y[meW}Kee]R~SkWcaSJI[Dkazp_gp}YDN|qpqR`PWiETnJseDbG@h?~xJGHRctAhpVgngW`K_eesrCPGU[gAddCkaZxTckIV~KUEOrJ@~}UUQ|HtDXAq@ZspmXCKpg?HX`KcfiS`JLdqBGPcSr[_@cqarP\OqGYqN]GJCRRGq?IR_JMDybJPk_xo`APYKbg?xNWjKU]KwEvbhqD`ESqO_CdBAn`Y?sKZuMqFtC[BHI?USaJHDgb?@oozs^iPzKdG@hRglGUgKKFGbqA?@B[qU_FdSAspZwp[Y[NRGDcObHa?aGeJNS@OPOYgP_IuE\BoAG`Yhcx?T@O@H`GokoY_NUGmDjERs@[DkC{B`Aw`ko}obcUmXOOEOX_TGMoH[E~C?aP@Z@dD?Z@q@Y?|ofGVoOWHNDkeSc@sFsD}CAAa@`oxOdgUsXROFoa?XOOsI_EQBiaDpZXdP?`@DCqavAOpdStK_PPbhpWI?f?UyQPKjEkSYQ[YAuHzDnCfBIxjp?eb\RbpD@YA_IBKIEDoChrJHk\?ibgRcO[`QGmCdcXYLhGDc]Y[eByI\DpCnRJXlt?mb}RdOa@T?mKeQX[LsGEC`I[mC{JHDqC|RJhq@?qdKRhoiPY_mSg?X]MTgEciy[qDgJ^DrDArJxrX?ucSReonp[wmggkX_LyGFCcA[}ESJgDyctBKHn|?ycjRgOtPUWmce}XaMDGFceq\EGiJPS@OcpVomkfSXcMIgGCgI\I?CBvDuBJQk`eSyW_`R@hug?OOGVYKwIOeXbiyAHK]fZ_@@BP\osKhWXfMpgGsrQ\Q?CCWDvb?Af@e_z[eURQhtW?OQKV_KKI`eYRnIATJCfU_@?wP]Gp[i[XiNAGHcli\]?CBkDxBGajHekyA_fQ{HuGMGT?VeMPJAeZBwqA`LMf__w`Up]_swk_XlNhGIStA]EGkJQS@O[OkonWYqUZKvfbsDYYdND@pAwa|pk`Y[r_]YOUHiczcFCH[JwEvdkbMHyT@YejRmo[OfGncZuTnKxFkCDqYpM|@pAaA}`opVgre]zOVhhcz{M?LOJzFRd|BM`~L@_esRrow?uWno\cV~Kyf~ctq]aF?E~D}bnQvhfX?Q_qRVhyW[?VoV{NGJcE\sAaBLL_fi`o@`p^w|KmeXwONgLCuI]MGmJRS@Ow?qOoC]{V]K|FvSEqZHNJB_BMb?`r`]cru^gOZhks{sS{OAKBGDeDbNaB`BYeyRupRp@_oO_kW`K}gIcFIZlN\DNBdB@QCHaor{_tO\HnC}CS{MiKEGUELrNyBlAAetRwpRo{?o[^SXAL?GNCHaZXNdDNBtbA@}hcssA_|Ojhls|[S{NkKHG?EAbOQBxBCexRuPn`JOogb_YBLAgNsRIZ|NhBfDPh~DCYaPPIgeSSIITDSPcUigB_@`n`AwosbuYELGGOcSa[@Nj?MB^AG``pB[sMYZO`gkSwI^Y?qE}CVBBqGPd_sO`CP]Hoc}{AOL{GxEGCRRKXgdBoeTRaH}GDwZwQGKPGlEZbPQCXCEe|R{oM_voc{WcPdK{easGyGxL{fr`HaJP_?pKj]YKNmgQCui^MC{GlEEBDAnPgs~O`HRZH|GTGasWiKVJAebb}YChLmft`YAJPaoqGk_YNN~GQsvI^YGsJUS@onpDgp_XYUZLGgASqIZhNnBICUbEPf@Y[sc_SOfHms~CLSPYKYE`dkbQY@|A]e{R{oz@R_pkZGV]LIGSCIy[HMVBvDMBF@lx]csi`POpHpCwkOGSwK\E|d|BQqDHBYe|RbPBPR_pw[KV~LJgIcIYZxMNCWDMBFpqHZsso_tOiHnsxCQKSwK_EfDqBRICDAif?RcowPR_qCYqVRLLGRCIq[DMTCZS@pP@`WqK]OXLLMG_s\A\II_KJEQBsr@PhtAqaMPxhswjWokXIN]KJEfcJQHdF{fKarBApcoxopAY^OlghC`I[uJaKJERbhrD`i@AwapPbhrwdookXOMqKZegSJiJpEcfOa[bApdGzsqCYaOnG]CZi\EKyKiE|CJBLpiKuy`^QOHuGt?qkZsNiK{ehB\AE@HUfYbXbJ@nO~SsIYdLRGWSeq\mGwJWS@pnpdovg_?YOLRekSKYSDMhD{EVb]a@XhktOY{OqHRCykW[X_LyGJEUBTHk\Ime^RjPc`eGvg`AXbLTEscKqPPMnFuEXByQGPJstU[IOrhhSz{_CXeNhGecqRT`pTBOdaRoQB@e_}casQELUfGCliYHNBFIEYbyQKhHCt[[jOtH]C{S\SXkNhGwCfBTxrXBUeBRmPw@ew}cbuQfLWE|CLaW|MzC\Dki?w|Wrc^QOvHXEkb^yExKsf]cfa``fPDce}YrNAGZstQ]YQsIPE\cUQ\PjOyA`oRThxxAwhsXwPXHyelRhaFDLWfgcPAi@fhDcg?YuMjg[csq]eP[HdE^CUQ`Xj[zE`rRRhyhFGf?X}PXIJEmBlqFPLOfbcaA]pg@DcegYxM{g\StI]UCOJiE_cqAhpjg|_`uRWHzG?WCSViLAHcDURVXzlBmepRupF`ZQ_M?[@ODXbPAX@UOty^EO{hkc|s@cAuI}EacqAcHjw}c`yRXh{GC_EWUQLEHcDJBVxw|BuesRwoJoMOlOYMRGI[EoBrQFpL[fq_\?^PZws_eOTBL_fhSqyY|NVB`EcbfAexd_uCZsO~Hhc|[MoYSMfIZeWrWXn|B}efRuO|phWzGhmXmLaFAcOAY`NZCAEeBnQexfcuI[TP?hiS|sOsYYNGIZe`RWpq@CCeiRwPFpZY_MGoLNFhdLrQ@k_xUaCRTh{WcWt?]{SvLLeqReqGTLWfqa[bSQ?@I[lKZIMvG`cuY^eIGLQGDckaspkkzqaFRYH{wi?tK_kQ|JRErBoaG`L[fsalbTACHKclKZLM_gaSty^UJKLTGUC`aspkwyWaIRWH|gmGtW^SQPJRErriyGlLafvaVBTp}hHolKZOMpgbCuQ^aKcLWGqdDbAhlC{saLR[hqgc?lpOGhpTRpfPjPF?egWTLhfhSPyZhMVEgElc]qZx`Sug]oRJhmswkZKYwOvHtEDRYhzlCae{RbPnpjhCGfiWTLjFpcQQZTMND{EnCRQ_@`Sum^QPHhlcxCW[Y}PYIDeDRZ@w|CgevRcpypT?u?hoYCLkgDCQiZxMbFuCqbWQgXgOus_^PJHnsyS_CR_LaIfE`BZX|tCmf?RhqB@NWuKiqYCLmFyCRA[DMXC`Dmi@TFYfHTPFIDBBXQk`gOu{^rPLHocxk\SSaLeIOe`BZx~xCufCRfpw@Rgu[hWYCLoGASRaZtM`HCD^BYAsxmCve`@PMhASy{c{UQLhJXEwb]YCpC{bFRkQU`Y_ugj]ZbLxgTsRyLHMtGVDnbYqnPmOve`aPOGvSz[aGVSLkJAexR]YEtDAbgRiQJ`]gusk_ZeLxgIcSQNLMjGxDXbZarXm[ve_tPPg~cysQGU{gFS]I[tTKFsXCLoJcEyRkQITDwd@RnOa@dgvCmeZiMpG]CSqSpM~@DE[B[azpmkzCaBPRhTs{CD?YELrJsezBkQGxDOcSRooUp_?vOngZlMpGeSTIQ@ND@eEEB\Q~xmwzCacPTHIszcFGWmLuJ]ezrkQJDHke\RmotPmwwWpmZFLwFsSTaV`NJ?B@Hb]@qHcGucZpNgh_sri]Y?[A]EfB]RHhlsvc^PPVHbs{{M_TGf{STiJDDiaxP]goSWpH@[A_`P{hsTTOEOTGtcZwWILsE|RyIJHKsfg_Q?l@k_vsokYeLzFsSUYYTNR?n@^bZpnpaCtaZvNgglCkQ]i@sBIE|b^rD`jovo^PPYhZS{[Qw[?OvIOe}SDQC@DkcSRpilwfGwCaCSkL|GLSGAJ\H?fdT`PP@oPCshoZzO_GOSVAQlNKjLagB_qJPSKvw`?OeGmSeq]\UrDZFACXQhpntA?`VP\HOS|CUW[IPoIke~cGAEHIWe_RspHP[I_dP}huTTiwgmGw[buTcM?GOCLiJtImfibBa]pp@X?wAacPWGncrQ^IKcIEFCder_QJ@Daa~RQhywrghC[SUfM@gkCVaUHKcfkbSAfPpXZGwG`wPWGoSli]uLeIgFEDZr_iGLD_bAQ{HzgvweS[YTyMBGbcUAKLKEfoa}A[@ppWSwMaXPWGpCpy^EN?J^FFd~rUHo`EIc^RSh}G|Wmg[_U|L]FASWqP|LSfxaRAwd@Qc@RmilTpp|`]gxGmOZFMDgqCbyYlNfG@DXbcqyXlGwWbHQNhjC}c_oT{MSJnEvR`iKhG}eeRypq`XGxSnQZgMFHFssIY\NlFTDiBda}`iWw]bKQNhiC}{bcYEMVKOfCBdYKtK[enRcqP@_?x_pW[PMZGrcpqZ@MTHNEEBeRExnOwcbNRFHkSx[dgWmMYK`E~raYL@K[eqRaqDpcOxkqY[IMIGsSpqZLMLCfDpiAtGIf`T[jdcPBJPrh_gwi[UPhhbcua[]P[KwFNEDbaxq@EgeMRVHqGMOtc[}YOMKFTsYiYtLwfO_}bX@s@hkwq\bPjHjSui\ECOLnFOeUBbPuxEmelRZHsgGgvk\CXbMLf]SZAYtLmfR_gB``sXewww]CPkhjSvI[qAuMPFQE]RbhsDEselR\HrWKosw\IYDMNFRCZYYtLufN`dBh`vhHCw}^QPmHmCwI\YHOJcSAIOdNIi|VLBTFSBqAR`qC{]b]R[Hocy{HK\QNRHRfGbrQL|LofCRkOf`tO|wdc[bNQgwCvAZtMtAhFMBiqVhqO|_b`R[Hncz[JO\MMkHcfHRvYX`Loe~RiOnptgzGcK[eNbGwsvA[@MjCbFVCGQ_@q[~{b\PqHoszk?KFAMnGUDArdA?dFIbgR`hvg@oMo\_NiIJFISAaNLK{fBRnoEO]wzC^iRSMTGFs[yNxMEf_aSaxT?icLRsioTroH?_OzK_?R^MUFvS\IOdMEf`_V`BPu`?kfS[lNsGps\Q[LND?yAKBlQApNSx[^rPhGyswY\qJwIrFZEAbdxsDLyfMRmIlwowjw\mWUMWFRC\iZxM[f\T`Pc`XGz_pA[pMjgzcvy[xM{jLbMat@vHaoxc\bPvhoCxq\|UrEgDnbmbExrKz[boR_hrc{AmQLeJiF\eObe`vdFafARfHwT\{Z{ViM{KefLRoaNHMGfMRpI}gdOmXOMhCS|ikT\C\SWmM}K{fLrvYNPF{fXRtJ@W{?qG\}YDM[Fpc]iOdMqfbUGPypdg{?s_[xNhGps]q\dNIkZbzBM@wHhkxs]NPhG|szI]YOALBF`EUBfXxhEybwRkhxx@_o?]EXbM]FhS\ANdMqfgbdBB@w`ewxy]oPxg}czI]eP[LzFacqRfp}`FucuRqH{XFGwW]KQEM^f{s^aSDNGfqcaBcPwxHCy?^}P}hRC{a]mHUJfSCIPTNajHVQk^cfbR`xHHoyC_HP~hTs{a]qQsLXFdChrgY@PG?cSRqHzXAwuO]UQqMaGFs_IQ@NGfmcPBZpx`JsyI^\Q@HIs{a^ABKNLFnCybgqEHGEdlRvh|wMOxo][RtMbgZS_aV`N]fw_}bhpxxO?yO_iQAh_s|y^eCOMqFgDArhIBTGKeNRvh{wGgzs]aSUMdGOS_yXhN]fs_gBq@yPLOyU`KQCHhS|y^UHWJgSCiPdNijLVSk__lbspy`L{yY`VQDHWc|y^YD}NTFydURhqGxGUekRcH}wXO|W_?TcMfgeS`aYXMQfz`ibtq@XQCy_acQEhhsxQ^mCeNWGJDJBiIJDG[egRdh}wRo|c`ASwMhGnC`yYdMIfz`SbuaD`SKye`wQGHicwq^mDgNZFtDRbiaGLGaejRbh}wb?|oasTyLsFTSaQZHM]gEaPbvQKhWStK\URMHksyA_YHYJhSDIPtNqjPVUk``obvqM@X?ta\WQIhlCyI_YFWN_G|derV`tdGkemRhI@g]w}C`mUfLbfUcayY|MegEa@BwaGPZGuc\ZQKHkCxa_YGYNbGedZrZhtpGqepRei@gmGhs^GVhMIfVSbQZ\MigP_@`J`T?}Sng[_MnHEsvI\XOb?MA[aXP{p^{xU\^QMHmcyy`E?qDCCwBxqvhrWz?c\R\huDAKAOI_HzFsDqB]`uDKme{RlICXSi^pPegsSYiLdEyb`PrCnDtiAtHIf|TijkUPOJojWgW^UVRL~fXCcIZTMugP_\@X`QG}om{[IMqhGcuq\PObFIEfBzQY`uXBocbRVHtDBaj]MiLXFvCvrkyGLHGenRiiFDWS]?ZGNnHtFYCPqQTL_fUSMIrW|Wu{^_RtMsgeSsQZDMmg[Tkp|`nW~Cg?\iPQHHsuQ\`Owjcc?b``}POkzUapQSHkszQ`pV^GKFGb{qapupDwchRYHutBaniPCMqFyDOrYPutHSezRpIHt_kR?VWgCSdI_TUqmtXFGmF]b|ahplsz]ckR]HvDCypAPqNGFzdUR\@v@HYetRmiHtb[cO]eNwIqEhbmIQxLkf]SRjHhHw|w^qS`LWf[cdyZ\M}gfUWqU`r_~ghWY{MxhKCvI]@PMk{cJbhp~XR_uM\sQWhmc{Ia\YP@ZF}CDauPn{zicqR_HyTEQtMBKN|GOdZr`PvXKqf@RtIKgMO~w`WTyMIf\sea[HNEgq_}by`~xWSx?\wQYhpC{ibIHaJlSAiQtOQj`V[kcUloa@}h?Ck_[jM|HLsvi]XPd@DG?C?arXrWzucwR^HxtESD?_EOJJRe|BnaRdL}fgSXOlA?`Fkme\xM}gscfQ^@PzA~GAcLqzpvw{Gb\Q\h{TFkKg_KPAJsfORnyM`HwfqS]otQ?xCsng\KN?G{sfi]lPzARGCCUa~xt[{Ab}Q^HzDFkHw_QPdJ]fWroQOdH}flS]oiQ@PF?mO\mN@gpsgA]xPzCqDvI@tHagLTqjoUQjVG`gf?_WXANAfhSgQT\NkhGaKA]q@hcs{K]oQIHOs}ycaHEIEGFEAboxzlH?dCR{IQG[GhC_]WUNCFpcdYSTNqhG`uAfQA@aC{Q^QQZHPc}YcaFmIgGGeJBpPw|IAecRyIQG_OeS_cWvNDfechASpNihGarAtAAXeK{W_^QchbswydMJaJ^GIEZbph|tISeYRcISwdomg_iXxNFFyChYYTMQhRaXazt@ActSGiyTwjHtjkRcViOVLAfcB}YStJCfIShpP@UX@_s_]PN~HRcli[lQfDOD^CERRXxH?QdNQ{HpTI[TkUQOYKkFcsAaT@KEfEShpnpf@@kdc]SOeHiCxidy?ED{E`cFAVhxTAmdQRShrtJs?wKMK?GMcqRqqEHIeeiRgIVgBGXGWWO]HBFdsLiTPLUfPSnOH?rgp[_}QPNKGIciiYpMch]_V`i@cPA?cw]XOYhTcsq\LQ|CsDwHhD@IcxSIizTxJIDj{BgLeKlGPChrrYCDIoefReIVhAw}g`EU|NFffCjIUHMWhiTZqG`}hAOmO]YNMhUcli[tRSjAcVC?ACh\K{{]dQlh]CxyehUZGxGDcHazpx{|_d[R@hsDLQleQGOUGRdyRs@zlIyeNRgiYd[cc{`AOgJyFgRwqTxKsfQStIzxJPAc`WV~NPFscjyYTMehiT|OSADPCspW]bOChWCtY\lRikD_lcIqJPb[|G_SQohjCyafTW`CtDwiAdHygXTwjrUSjWGKpAsbIXANRGFskYYXMihtULo[aDpF?qY]fNmhXCsy\XRike_}cJqNX_g|O^gQqhiCyyfTXbAGGWCLrApyc~eeORShuDMirqAIOpG`EGRtP~xJMeiRlI\ThCIcSaOqLLfisEiU`Laf`T?JSwU_hs`eXWNUGOSlIZHNCi?UnOnpT@BOrE]lOeHYcuY\pS?lh`dAXQEhew|[`VQthlCzig@ZhBTCwCLbNHy|BCdkRVHvdOAv}HkJqSDiSDOyjtVgkiUoocpNXB_sI]pOuhZcty\|S?mI`NA`aFHh?|c_iRLhkC{Ag@[jCADycMaR`zLDadoRZHyDP[OsTeOzHRflCVaVDLmfhTDpE@VpBodc]tO{H[cvI]hSVCbDccNQVhzXCEdrR\HwtP[MCUgO}HcflsPqVPLufdTDoz@ZxB{cK]wPKh\Sva]XSVBvDtCOAQHzdDGduRYhxtP[TkWWP@IDenBvQV\MGfmTJPLp]Y_PQaiGT^I|TdYuH[pDeEJcOqapk[|wdxR]h{DQsVCXCPCHiEsbviVhL{fpTJPJ`dhCSe}Z\N^H]svy^HSlCxE[CPa\Pm_|}d{R_HytQsSOYEPFHyehbwAVtMAfkTJPS@_@C_g?YpN_h^cwQ]tSlErEvcQQd`rW}CbrQ~h|TSKZ{ZuPII[E|BwYNxK?fuTOp^@opCkiEZ~NaHASoI^\TBEFFGcRAhpog}IbFR@H}DSKR_VggDShIaTVynXXWlbVKpc`hpCwiq[TNbgscoa^dTBE\EkcRqk`q?}Ob\RAh{tSKY_ZGPOIOfIrxIM`KKfsTOqB@yXDCku\bNdHIsoy[XTX?BBdBvaIPY[z[^JQZHaCwyiq?[FTFMCSquPvc}Wd@RChqDTc@cN?MfGiDZro`{tIWeIRcijGC_]k\cPTI|FORxqT\KUfITUOJo}ozsakUDMeFrsaaWpMUik_\A?Px@D[k_\VNgHGCpi[TTXBiDRH~TFQblPwg}S^iODGKRgVkgFSiIadWAn\XYlcVLO??[OMKFGBd@r?xo\?McS{PZ_?_w_\OMkFYBm@v_{?]Gh{axBa@x?{o]_NSFkBw@{agAJ@DuFCBy@|_~?^gNwF}C?DOcVcT{MGGACBAA@@O_oO[GOIaRNh}g[OOcGSCJAE@B_`wP?TEhh`p@COaOPKGgCTAJ@DpS`EDUpBaAK`E_bWPoGyC]ANahQKQs]FEC_AO`G_c_QSHKCfDRCWtusMKHOChAT@Iod_QsH]IfGqPMp]y_`QiiKT_i}DdquT[v?A@p`K?eGRGHeCsAY`LaKqXeFECvA[@M_fWRoHyC}DTCXsq{M?FEC~A_@OOgOSKIIDEDTcYG[WS[IODHAd@Qoh_SsI]IkGsowohoTCIcDRAi@TOioZwTYPi`q@Toj?TcIsD[Am`V`DgiwbVBcAn`W?kGUGJEDcAqajqLcMOJMDgAs`Y_lWUoJYIoEDcZW[_UwJ]DoAx@[om_VSTaLyGvOx?moV[JoDxA|@]ong}cb]e`a]A}D@IdXSYjBT{jJtkqxqFGD}A~`_?oGWGKEECDYCUQMKMOKIEEBC@aOpOWkKWItGxCqG[gWsK[ENBG@cOqWXOTkPrIZoxOqgXWKmEWBK`e_rWj[bgUe`q`f?roX{L?E`BP@gpV@FSojBdBQ@hOsoY[LQEiBTamQMpgQFIEkBU`j_twZ?LaEqGze{sqSMSLgEtBZ@lov?ZcLsIzG{FWg[gZkLwE|B_@oOwO[KTwPxNgox_w_[SMKFFBc@qOxWjsbs`?a]a}T@Qd\S[jCT|jKDkyxuFKFKBe`r_xw\?MaFQD^c^CUCMWMeFSBj@toz?\cMsJ?G}hFw[o\kMwF\Bn@vo{G]Gb{eMRNox_{W]ONIFeBr`y?|GkGb}el`r@y_|_]sN[FnBw@{PWXG@LpBeBx@{o}_^SNmFwB{apAOIYEFMFyB|`~?~g^wN}G?Dac_cxsM[OCGBCAA@P?o_[OOJEH@huW[w_cOSGJCEaB`@w`?UMQCRqOxpAG`GOeGSCIaD`B?k_cJC}D|IAtJAg|UIj{UXJYDrsM[OqGYCLaF@Bg`wO}JIHBh}w[wa?PAGbCQAHPCoa[UUQGSBOxpD?acPSGjCUAJpE?kocQgP`sAKPEObKPgGtCZALpXhGhOxBgC[AM`FWboPyG}C^araPYa]FOH?C_aO`GWcSQKHFDfcbDESM_QOHHCdAQpH_csQ[JOHEiNW\?d?QaHQChaT@IgdWUaQM`sATpJ?dcQuH[CmaV`YPG|QfBgCnaW@KGeGREHcCrAsqQAdyH}JzSAIUTQAkXVykrUtJfw\Ge[ROHhCtAYpL_esUiQQStOyPLoe{RaHqCxa\@MglWceht`sa\`Mwf_RqHyC}A^PYxHPS@BhC~A^pO?gCSCIBDAAuAQigmFQIDDBaa@PGggSUIKDkcddQsMcSYIMDFac@QOhKSgJYHJigW\GhSSkIVDKAePROhkUuQWTUOy_iwWsMGFyCWaXpZ`HdKmiv`t`GOj?WwMIFzCXAYARQkIFYCaAk`bowo^oPeHhDnCetXkS?VwgDSlIcTWynxXgljVOoz_c_TgK_FFB}aL@LOm?cyjX`v`HOj_XCMOF}CYaYp[HHxVHBoAR@VOqW[cN}GuCuAwaRym}FaCfAn@d?xW_?PmHlDpcgD^SMgHOD^BI`r@?Ob_R[JcHOj@W\WQcJ?EUBea?pFOe{VIQaUGOzOdOUCKmFMCAAMpMGmWdEkZ`v@IokOX_M]GDC]A[`[xIPXLBnAU@WorG\?OKG|CxayASirEF_ClAq@e_yG_[P{HsDschdfcSCVygFSlicdXAn|XilkVPO{OdwUSKuFQCCANpMhI`YPBiAW@Xor_\KOQH?CzCiTi[MkHaDgBN@t@@OcCRmJlHTJVg\gRGJQE^BjAApGOf_V[QjUsoz_eWUgL?FVCEaOpNGm{dWls`v`L?lWYCMoGMCaa]`]@IuF_CtAu@g_zG_{QKH{Dwcjg]GRWJYEbBlAC@GwfsVcQnVIoy_ewUwLGFZCGaQ@NonKd_m_`t`M?lwYSMwGQCca^p]`JD\VDAD~IADJahLUQk?UZJZTs[MsHsDoBR@vPAWcgS?JuHXjlw\oRkJcEfBnAD@HWgCVmQsV`Ozof_VKLQF^CIaR@OOn_dinL`w@NOm_YgNAGUCea_p^HJX]pBpA^@\OtW]GOoHMDAA}aUy}MFSC~Az@j?{W`cQ_IDD|cmD|sMkI?DvBU`x@BOdCSMJ{H[j}W\gSCJoEmBqaEpIOg_VyQyWAOz_gOVcL]FeCMASpPGnwduoN`v`OonOZ?NMG\CiAa`^xJqIEJ~SCiVTQakhWAkvUvJhEBKN?IIDzBW`y@BodSSUK@H^O{OgoVsLcFhCNaT`P_oGd~BiAb`^_u_]gP?HVDEb?qWCMkIOD~BY`z@CGd_S[KCH_ozOhGW?LkFlCPaUPPwoSeDBmAd@_Ouw]wPGHZDGB@aW[M{IUEAB[@zpCgdoScRC`w@R?oWZcN_GeCmacp`@KUFaDLBA@m_}Ga[Q{ISECcpg\OSwKIEzBxAI@JwhSWSRF`tahs~icHQEhCSaiPdGycd]BDDE?iAdJyhTUUkAU[JZtsj@m?EBjAg``_v_^KPQH_DJBBQXS?wFYDQBC@nO}_agRAIVHdhggBGMwIeEHB_@|PDWeGSoKNHeOH?\wTOKSF@BzaJ@KWhcW_RL_V_{?igWkMCFwCVaX@ROpCe\?y@w`T_p_[KNqGoCrAepaPK}AICXAO@`_uo]WOiHECybCqYCD?GsC`BC@lo{w`WQMHmEICsWJWPkHCEHB[@y@B?c?R]KTHhOX_b_QOKSExBsaCPGGfCWkRRabB?d@Ye@SmjKU@jMTmAyX_x@qAM`HOpWZgNEGQC`A[`b@LUByC]AR@b?u_]OOeHBCxctgP?P{HMEDBY`xPA_cSRgKYHjocobOQ{ImE{BuaF@H_foWuRW`N@Eod?T_LyFmCMaRPNgpoerAhAM@IOjG[?N]G]CfA\`bhLiGyCiAl@oO}?`{QOHvENCusrKJ{G{CjAm@o_}G`cQQHwENcvGXOP{HWD\B``y`BOcgRqK_HmotObGQsI{EzBuAEpHWfge|DFE@hgt?aeDSojMUAJMdmIy]FACZAY`XOpg^KPEHRD@BGq[CMoGwCuAn`b_}_aOQgIBEQCwW]wPsH_D_BF`|PCgdSSGKdHpP?_boRCJAEOBzaH`IofwXKRbaE`FoeOUGKaFwCRaS@Nwq[fHCWAK`KokWXKNqG_Cga_@d@MUGsCbAY@X?q_^GPAHQD?bIQ[sPoH[C{Au@eow_acQqIHETCxwbgRcHyDlBI`pPDOdkSSKjHsPF_foSOJMEUBbAIpJ_gkXWRhacB@CqA_TRCiXTfj@dfYvH\PC^AZ`S?l?X[MMGkCmab@dpMmGqCwAl`YOr?[_P]H]DAbJq\cPgHsDeAt@eOxGb?QmIFEWCzWbWRkJUDpBL@qpD?d_SOKpHvPFOgOVKJwEaBh@}`K?g{XcRnaN@Oom_W[LEFKB|aWPQ?rKf`C^Aa`\Or_[sNwHaDHBLA]IXEGqDEAv@f_xo^sREIREYc{gbOR{J]E^BS@ro~oeOSgKuHxpEog?V?L?ErBg@~pKogsXmRsacb@T?yeLSsjOUBjNTmYyd_~C[A_`[_sGZ{MaG?Cnab`fHNYG{DHA{`iOxO\cOOGpDJBMa]{P{ISDyBT@tOzO_GPcIVE\c}GbGSkJuEjBh`w@?WbKSoK{H{pE_h_VsLGFSBta@@E_hcXyRyaL`ROmoYSMkFuCAaLPROrwfvC[Ab`\oso\[OAGECZAepfxNqGyDGA{@hoz?_[OWGvDIbOA^kP{IaE?BV`vp@w`[P}HfE_c~gbGTGKAEoBoaC@COb_ROLAH~pQ`_q_`RGiZTgjADfqvT\So_aL@SooOZCNCGHCVAM`LGsOgBCZAi@_ouO\kOSGxC\aY`ghOIGwDTBA@j?z__kPwHCCtbPa_[PsIkD}BU`vP@gbsQ]HkEbd@GboSwJ}EmBnAB`FodgRYLGIApCOc?WGLIFPCTAT`KgfcYQSEaH@GOoWYWMcGjCgA[@NOsggNCRAP@`?sw[oPWHPC|a^A`CPOHGD}BS`rPDwdGRyIEEeDAWagQSJ}EiBfAK@IWfWSaLLIDPQp_y_dRIi[ThJATfyvX\Wo`aJ@H_o?YkM]GgCiA\pRgs{gXCVAR`_Os_\?PQHTC{Ai@i@OuGeClBC@k_yw^gQwH~DXbSQ`sPOH]EHBU@u?~WdsS?I}EhDBwagQ_KSElBk`~@JogCUQLRIGPD_dGWkL[FYB}aTpOOlOYgSPaJ`I_p_Y{MeF}CkA_pZwtSgdCPAT``Ou?\ON}HXDAAy`ipPMGcCkBB@kOyo_?QuH}DybTqacPSHeDVB[@v@?weCSWK?EkDDWh_o`OSheTMist`Qs@ZmmlWPPD_e_T_LqF\CCAW`OgooYsSVaJ`LOjGZgM{GACpa`pawtkgpCPAZ@U_u_\{OEHcDCBG`j`PeGcCoAm@lO{G_ORKIHEUbVQbSPKHaD\BZ@w`?gd{SSL]ILhdGa_RGI{EvBla@`K?gkYEL^IMPDof?UOLyFhCEaKPQOswZ?S\aG`M_kg[?NEGMCXAcpjGuCg|CQA\`VowG]OO]GrDIBW`k`P}GeC{Ao@o_{g`?PgILEpbZqcCSsWQeOSDiXtRqlPWUl@U{Jjga_RsJAFBBrAAPEggwZILzIPPDOfoUGLuFfCDAL`PwuW[KSbaJ@LokWZoNOGJCZac@kwxChHCQAb@Y_pg]{OcG}DJbY@r`QUGeC~At`b_}?`KP}IWEsbhqcsPOI?DkBF`{PA_b_SqLiFXDHwagSCJYEOBtADPFOhg\ySgaJ@O_kwXCNWGUC\aepl_{_hRCVA``Y?qW]sOoG{DIbZPyXQiGaDDAs`d?|o`CPyIUEvBvad[SwWSgCSsIftYiopYClxVVkHGa_SkJ]EYByAFpGWe[Z_NiIUpDOh_V?KuFtCKaPPL?vC^iSmaJ@ROmOXSNmGYCbAYQ?@Q}GmDFAx`d_~?`kQMHiExcAqeCPCIODsBJ`}PB_c?RULsGJDKWaOScJiEWBxAFPGGeoZiO`IXPCohOUwKqFrCNAO`LgvW`WSraJ@S_ngY?MGGdCca\@mxRQGmDRAz@gOwgaWQSHtE{COaekPCIgDvBP@p`CwckR[LxGedLn") Q7T4pnx = Q7T4p .networkx_graph() # List of graphs to process graphs = [('Q7T4p ',Q7T4p)] def count_k_cycles(G, k): count = 0 visited = set() def dfs(path, start, depth): nonlocal count current = path[-1] # Early exit if we?re going too deep if depth == k: if start in G.neighbors(current): # Normalize to avoid duplicates cycle = tuple(sorted(path)) if cycle not in visited: visited.add(cycle) count += 1 return for neighbor in G.neighbors(current): if neighbor not in path and neighbor >= start: dfs(path + [neighbor], start, depth + 1) for v in G.vertices(): dfs([v], v, 1) return count # each cycle counted twice (once forward, once reverse) def algebraic_connectivity(G): """ Compute the algebraic connectivity (Fiedler value) of a graph G. INPUT: - G: a SageMath Graph OUTPUT: - The second-smallest eigenvalue of the Laplacian matrix of G """ L = G.laplacian_matrix() eigenvalues = L.eigenvalues() eigenvalues.sort() if len(eigenvalues) < 2: return 0 # Trivial case: empty or isolated vertex graph return eigenvalues[1] def check_all_isomorphisms(graph_list): n = len(graph_list) print("\n Isomorphism check of all pairs (a dot means the pair ARE isomorphic):") for i in range(n): label_i, G_i = graph_list[i] for j in range(i + 1, n): label_j, G_j = graph_list[j] if G_i.is_isomorphic(G_j): # print(".", end="") print(f"{label_i} IS isomorphic to {label_j}") else: print(f"{label_i} NOT isomorphic to {label_j}") def non_isomorphic(graph_list): reps = [] labels = [] for label, G in graph_list: if not any(G.is_isomorphic(H) for _, H in reps): reps.append((label, G)) labels.append(label.strip()) # remove extra spaces if you want return labels def isomorphic(graph_list): labels = [] for i, (label, G) in enumerate(graph_list): if any(i != j and G.is_isomorphic(H) for j, (_, H) in enumerate(graph_list)): labels.append(label.strip()) return labels def compare_graphs_list(graphs): canon = {} count =1 for label, G in graphs: s6 = G.canonical_label().sparse6_string() # print(f"{label.strip():15} : {s6[:40]}...") canon.setdefault(s6, []).append(label.strip()) print("\n noniso ->",len(canon)) print("\nGroups:") for group in canon.values(): if len(group) > 1: print(count,"Isomorphic :", ", ".join(group)) count=count+1 else: print(count,"Unique :", group[0]) count=count+1 print("\n START \n") #noniso = non_isomorphic(graphs) #print(len(noniso), " non-isomorphic -> ",noniso) #iso=isomorphic(graphs) #print(len(iso), " isomorphic -> ",iso,"\n") compare_graphs_list(graphs) nonisographs = graphs # Print properties for each graph in the list print("\n Main properties of the graph\n") for label, graph in nonisographs: print(f"{label} | Ord.: {graph.order()} / Size: {graph.size()} / Diam.: {graph.diameter()} / Avg.dist: {graph.average_distance().n(digits=6)} / 11-reg.? {graph.is_regular(k=11)} / Girth: {graph.girth()} ")# / Alg.conn. {algebraic_connectivity(graph).n(digits=6)} ")# / Domin. number: {graph.dominating_set(value_only=True)} ") print("Degree histogram Q7T4p :", nx.degree_histogram(Q7T4pnx)) print("\n Symmetry properties of the graph\n") for label, graph in nonisographs: print(f"{label} | Aut.group.ord.: {graph.automorphism_group().order()} / Cayley ? {graph.is_cayley()} --- vtx.trans. ? {graph.is_vertex_transitive()} -- edge.trans. ? {graph.is_edge_transitive()}" ) ''' print("\n Properties of the graphs as at arXiv\n") for label, graph in nonisographs: print(f"{label} & {graph.average_distance().n(digits=6)} & {graph.girth()} & {algebraic_connectivity(graph).n(digits=6)} & {graph.automorphism_group().order()} \\\\ ") ''' # Check isomorphisms # print(f"Are isomorphic G5 and G6? {G5.is_isomorphic(G6)}") #check_all_isomorphisms(nonisographs) print("\n") # automorphism group structure print(" Automorphism group structure") print(' C_n is the cyclic group of order n; x means direct product; : means semidirect product.\n') AQ7T4p = Q7T4p.automorphism_group() print('Q7T4p :', AQ7T4p.structure_description(), ' | center order:',AQ7T4p.center().order()) print("\n") # Compute the distance distribution from a given vertex v in graph G # Returns a list where the i-th element is the number of vertices at distance i from v def distance_distribution(G, v): from collections import Counter distances = G.shortest_path_lengths(v) distribution = Counter(distances.values()) result = [distribution[d] for d in sorted(distribution)] return result print("\n") for label, graph in nonisographs: print(f"{label} distance distrib from vtx. 0: {distance_distribution(graph, 0)}") ''' # Counting k-cycles for each graph print("\nNumber of k-cycles for k=3 up to 5") for label, graph in nonisographs: print(f"{label} "," & ".join(str(count_k_cycles(graph, k)) for k in range(3, 6))) # from 0 versio Molodtsov  for name, G in nonisographs: fname = name.strip() + "_adjlst.txt" s = "; ".join( "{}-{}".format(v, ",".join(map(str, G.neighbors(v)))) if G.neighbors(v) else str(v) for v in G.vertices(sort=True) ) with open(fname, "w") as f: f.write(s) # from 0 for label, _ in nonisographs: base = label.strip() G = globals()[base + "nx"] with open(f"{base}_edges.txt", "w") as f: f.write(",".join( f"{{{u},{v}}}" for u, v in sorted((min(u, v), max(u, v)) for u, v in G.edges()) )) ''' # from 1 for label, _ in nonisographs: base = label.strip() G = globals()[base + "nx"] with open(f"{base}_Zedges.txt", "w") as f: f.write(",".join( f"{{{u+1},{v+1}}}" for u, v in sorted((min(u, v), max(u, v)) for u, v in G.edges()) )) print("\n DONE \n") ## ##