# SageMathCell online https://sagecell.sagemath.org/?q=eaqvai # ''' Main properties of the graph xQ24p | Ord.: 1215 / Size: 9045 / Diam.: 3 / Avg.dist: 2.86052 / 15-reg.? False / Girth: 3 xQ24pp | Ord.: 1224 / Size: 9180 / Diam.: 3 / Avg.dist: 2.85989 / 15-reg.? True / Girth: 3 xQ24pp2 | Ord.: 1224 / Size: 9180 / Diam.: 3 / Avg.dist: 2.85989 / 15-reg.? True / Girth: 3 Degree histogram xQ24p: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 135, 1080] Degree histogram xQ24pp: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1224] Degree histogram xQ24pp2: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1224] Symmetry properties of the graph xQ24p | Aut.group.ord.: 51840 / Cayley ? False --- vtx.trans. ? False -- edge.trans. ? False xQ24pp | Aut.group.ord.: 1296 / Cayley ? False --- vtx.trans. ? False -- edge.trans. ? False xQ24pp2 | Aut.group.ord.: 324 / Cayley ? False --- vtx.trans. ? False -- edge.trans. ? False Automorphism group structure C_n is the cyclic group of order n; x means direct product; : means semidirect product. xQ24p: O(5,3) : C2 | center order: 1 xQ24pp: ((((C3 x C3) : C3) : Q8) : C3) : C2 | center order: 1 xQ24pp2: ((C3 x C3 x C3) : C3) : (C2 x C2) | center order: 1 xQ24p distance distrib from vtx. 0: [1, 14, 128, 1072] xQ24pp distance distrib from vtx. 0: [1, 15, 138, 1070] xQ24pp2 distance distrib from vtx. 0: [1, 15, 128, 1080] ''' import networkx as nx xQ24p = Graph(r":~?Q~_?_??@_??@?A_??@?A?B_?_?_?_?_?_??D_?_?_?_?_@?E?J_@_@_@_@_@?E?J_@?O_@_@_@_A?F?K_A?P?U_A_A_A_A?F?K_A?P?U_A?Z_A_A_B?G?L_B?Q?V_B?[?`_B_B_B?G?L_B?Q?V_B?[?`_B?e_B_C?H?M_C?R?W_C?\?a_C?f?k_C_C?H?M_C?R?W_C?\?a_C?f?k_C?p_D?E?F?G?H_v_v_v_v_v_v_v_v_v_v_D?E?F?G?H`A`A`A`A`A`A`A`A`A`A_D?E?F?G?H`L`L`L`L`L`L`L`L`L`L_D?E?F?G?H`W`W`W`W`W`W`W`W`W`W_I?J?K?L?M`b`b`b`b`b`b`b`b`b`b_I?J?K?L?M`m`m`m`m`m`m`m`m`m`m_I?J?K?L?M`x`x`x`x`x`x`x`x`x`x_I?J?K?L?MaCaCaCaCaCaCaCaCaCaC_N?O?P?Q?R?w?x?y?z?{@c@d@e@f@g_N?O?P?Q?R@B@C@D@E@F@n@o@p@q@r_N?O?P?Q?R@M@N@O@P@QADAEAFAGAH_N?O?P?Q?R@X@Y@Z@[@\@y@z@{@|@}_]?^?_?`?a?w?x?y?z?{@s@t@u@v@w_g?h?i?j?k?w?x?y?z?{@~A?A@AAAB_q?r?s?t?u?w?x?y?z?{AIAJAKALAM_X?Y?Z?[?\@G@H@I@J@K@c@d@e@f@g_b?c?d?e?f@]@^@_@`@a@c@d@e@f@g_l?m?n?o?p@R@S@T@U@V@c@d@e@f@g_S?T?U?V?W?|?}?~@?@@@h@i@j@k@l_S?T?U?V?W@G@H@I@J@K@s@t@u@v@w_S?T?U?V?W@]@^@_@`@a@~A?A@AAAB_S?T?U?V?W@R@S@T@U@VAIAJAKALAM_]?^?_?`?a@]@^@_@`@aADAEAFAGAH_]?^?_?`?a@R@S@T@U@V@y@z@{@|@}_g?h?i?j?k@G@H@I@J@KADAEAFAGAH_q?r?s?t?u@G@H@I@J@K@y@z@{@|@}_g?h?i?j?k@R@S@T@U@V@n@o@p@q@r_q?r?s?t?u@]@^@_@`@a@n@o@p@q@r_]?^?_?`?a@B@C@D@E@F@h@i@j@k@l_g?h?i?j?k@X@Y@Z@[@\@h@i@j@k@l_q?r?s?t?u@M@N@O@P@Q@h@i@j@k@l_X?Y?Z?[?\?|?}?~@?@@@n@o@p@q@r_b?c?d?e?f?|?}?~@?@@@y@z@{@|@}_l?m?n?o?p?|?}?~@?@@ADAEAFAGAH_X?Y?Z?[?\@M@N@O@P@Q@~A?A@AAAB_X?Y?Z?[?\@X@Y@Z@[@\AIAJAKALAM_b?c?d?e?f@B@C@D@E@FAIAJAKALAM_l?m?n?o?p@B@C@D@E@F@~A?A@AAAB_b?c?d?e?f@M@N@O@P@Q@s@t@u@v@w_l?m?n?o?p@X@Y@Z@[@\@s@t@u@v@w_D?w?|_D@B@GAn_D@M@RAnAo_D@X@]AnAoAp_D?w?|_D@B@G_D@M@R_D@X@]_E?x?}_E@C@H_E@N@S_E@Y@^_E?x?}_E@C@H_E@N@S_E@Y@^_F?y?~_F@D@I_F@O@T_F@Z@__F?y?~_F@D@I_F@O@T_F@Z@__G?z@?_G@E@J_G@P@U_G@[@`_G?z@?_G@E@J_G@P@U_G@[@`_H?{@@_H@F@K_H@Q@V_H@\@a_H?{@@_H@F@K_H@Q@V_H@\@aanananananBVanananaoBWB[aoaoaoaoBWB[aoB_aoaoapBXB\apB`BdapapapBXB\apB`BdapBhapaqBYB]aqBaBeaqBiBmaqaqBYB]aqBaBeaqBiBmaqBq_I@c@hArAsAtAubvbvbvbvbvbvbvbv_I@n@sArAsAtAuc?c?c?c?c?c?c?c?_I@y@~ArAsAtAucHcHcHcHcHcHcHcH_IADAIArAsAtAucQcQcQcQcQcQcQcQ_N?w@cAvAwAxAyBVBWBXBYBwBxByBz_N@B@nAvAwAxAyB^B_B`BaC@CACBCC_N@MADAvAwAxAyBfBgBhBiCRCSCTCU_N@X@yAvAwAxAyBnBoBpBqCICJCKCL_]?w@sBBBCBDBEBVBWBXBYCDCECFCG_g?w@~BJBKBLBMBVBWBXBYCMCNCOCP_q?wAIBRBSBTBUBVBWBXBYCVCWCXCY_X@G@cA~B?B@BABbBcBdBeBwBxByBz_b@]@cBFBGBHBIBrBsBtBuBwBxByBz_l@R@cBNBOBPBQBjBkBlBmBwBxByBz_S?|@hAzA{A|A}BZB[B\B]B{B|B}B~_S@G@sAzA{A|A}BbBcBdBeCDCECFCG_S@]@~AzA{A|A}BrBsBtBuCMCNCOCP_S@RAIAzA{A|A}BjBkBlBmCVCWCXCY_]@]ADBBBCBDBEBrBsBtBuCRCSCTCU_]@R@yBBBCBDBEBjBkBlBmCICJCKCL_g@GADBJBKBLBMBbBcBdBeCRCSCTCU_q@G@yBRBSBTBUBbBcBdBeCICJCKCL_g@R@nBJBKBLBMBjBkBlBmC@CACBCC_q@]@nBRBSBTBUBrBsBtBuC@CACBCC_]@B@hBBBCBDBEB^B_B`BaB{B|B}B~_g@X@hBJBKBLBMBnBoBpBqB{B|B}B~_q@M@hBRBSBTBUBfBgBhBiB{B|B}B~_X?|@nA~B?B@BABZB[B\B]C@CACBCC_b?|@yBFBGBHBIBZB[B\B]CICJCKCL_l?|ADBNBOBPBQBZB[B\B]CRCSCTCU_X@M@~A~B?B@BABfBgBhBiCMCNCOCP_X@XAIA~B?B@BABnBoBpBqCVCWCXCY_b@BAIBFBGBHBIB^B_B`BaCVCWCXCY_l@B@~BNBOBPBQB^B_B`BaCMCNCOCP_b@M@sBFBGBHBIBfBgBhBiCDCECFCG_l@X@sBNBOBPBQBnBoBpBqCDCECFCG_I@c@h_I@n@sCz_I@y@~CzC{_IADAICzC{C|_J@d@i_J@o@t_J@zA?_JAEAJ_J@d@i_J@o@t_J@zA?_JAEAJ_K@e@j_K@p@u_K@{A@_KAFAK_K@e@j_K@p@u_K@{A@_KAFAK_L@f@k_L@q@v_L@|AA_LAGAL_L@f@k_L@q@v_L@|AA_LAGAL_M@g@l_M@r@w_M@}AB_MAHAM_M@g@l_M@r@w_M@}AB_MAHAMarBwB{arC@CDarCICMarCRCVarBwB{arC@CDarCICMarCRCVasBxB|asCACEasCJCNasCSCWasBxB|asCACEasCJCNasCSCWatByB}atCBCFatCKCOatCTCXatByB}atCBCFatCKCOatCTCXauBzB~auCCCGauCLCPauCUCYauBzB~auCCCGauCLCPauCUCYczczczczczD~czczczc{E?ECc{c{c{c{E?ECc{EGc{c{c|E@EDc|EHELc|c|c|E@EDc|EHELc|EPc|c}EAEEc}EIEMc}EQEUc}c}EAEEc}EIEMc}EQEUc}EY_N?w@cC~D?D@DAD^D_D`DaD~E?E@EA_N@B@nC~D?D@DADfDgDhDiEFEGEHEI_N@MADC~D?D@DADnDoDpDqEVEWEXEY_N@X@yC~D?D@DADvDwDxDyENEOEPEQ_]?w@sDJDKDLDMD^D_D`DaEJEKELEM_g?w@~DRDSDTDUD^D_D`DaERESETEU_q?wAIDZD[D\D]D^D_D`DaEZE[E\E]_X@G@cDFDGDHDIDjDkDlDmD~E?E@EA_b@]@cDNDODPDQDzD{D|D}D~E?E@EA_l@R@cDVDWDXDYDrDsDtDuD~E?E@EA_S?|@hDBDCDDDEDbDcDdDeEBECEDEE_S@G@sDBDCDDDEDjDkDlDmEJEKELEM_S@]@~DBDCDDDEDzD{D|D}ERESETEU_S@RAIDBDCDDDEDrDsDtDuEZE[E\E]_]@]ADDJDKDLDMDzD{D|D}EVEWEXEY_]@R@yDJDKDLDMDrDsDtDuENEOEPEQ_g@GADDRDSDTDUDjDkDlDmEVEWEXEY_q@G@yDZD[D\D]DjDkDlDmENEOEPEQ_g@R@nDRDSDTDUDrDsDtDuEFEGEHEI_q@]@nDZD[D\D]DzD{D|D}EFEGEHEI_]@B@hDJDKDLDMDfDgDhDiEBECEDEE_g@X@hDRDSDTDUDvDwDxDyEBECEDEE_q@M@hDZD[D\D]DnDoDpDqEBECEDEE_X?|@nDFDGDHDIDbDcDdDeEFEGEHEI_b?|@yDNDODPDQDbDcDdDeENEOEPEQ_l?|ADDVDWDXDYDbDcDdDeEVEWEXEY_X@M@~DFDGDHDIDnDoDpDqERESETEU_X@XAIDFDGDHDIDvDwDxDyEZE[E\E]_b@BAIDNDODPDQDfDgDhDiEZE[E\E]_l@B@~DVDWDXDYDfDgDhDiERESETEU_b@M@sDNDODPDQDnDoDpDqEJEKELEM_l@X@sDVDWDXDYDvDwDxDyEJEKELEM_O?x@d_O@C@oE~_O@NAEE~F?_O@Y@zE~F?F@_O?x@d_O@C@o_O@NAE_O@Y@z_P?y@e_P@D@p_P@OAF_P@Z@{_P?y@e_P@D@p_P@OAF_P@Z@{_Q?z@f_Q@E@q_Q@PAG_Q@[@|_Q?z@f_Q@E@q_Q@PAG_Q@[@|_R?{@g_R@F@r_R@QAH_R@\@}_R?{@g_R@F@r_R@QAH_R@\@}avBVBwE~avB^C@E~avBfCRE~avBnCIE~avBVBwavB^C@avBfCRavBnCIawBWBxF?F_awB_CAF?awBgCSF?awBoCJF?awBWBxawB_CAawBgCSawBoCJaxBXByF@F`axB`CBF@FhaxBhCTF@axBpCKF@axBXByaxB`CBaxBhCTaxBpCKayBYBzFAFaayBaCCFAFiayBiCUFAFqayBqCLFAayBYBzayBaCCayBiCUayBqCLc~D^D~E~F^c~DfEFE~Ffc~DnEVE~Fnc~DvENE~Fvc~D^D~c~DfEFc~DnEVc~DvENd?D_E?F?F_G?d?DgEGF?Fgd?DoEWF?Fod?DwEOF?Fwd?D_E?d?DgEGd?DoEWd?DwEOd@D`E@FAFaGAd@DhEHFAFiGId@DpEXFAFqd@DxEPFAFyd@D`E@d@DhEHd@DpEXd@DxEPdADaEAF@F`G@dADiEIF@FhGHdADqEYF@FpdADyEQF@FxGPdADaEAdADiEIdADqEYdADyEQ_^?x@tFJFKFLFMF^F_F`FaGJGKGLGM_h?xA?FRFSFTFUF^F_F`FaGRGSGTGU_r?xAJFZF[F\F]F^F_F`FaGZG[G\G]_Y@H@dFFFGFHFIFjFkFlFmF~G?G@GA_c@^@dFNFOFPFQFzF{F|F}F~G?G@GA_m@S@dFVFWFXFYFrFsFtFuF~G?G@GA_T?}@iFBFCFDFEFbFcFdFeGBGCGDGE_T@H@tFBFCFDFEFjFkFlFmGJGKGLGM_T@^A?FBFCFDFEFzF{F|F}GRGSGTGU_T@SAJFBFCFDFEFrFsFtFuGZG[G\G]_^@^AEFJFKFLFMFzF{F|F}GVGWGXGY_^@S@zFJFKFLFMFrFsFtFuGNGOGPGQ_h@HAEFRFSFTFUFjFkFlFmGVGWGXGY_r@H@zFZF[F\F]FjFkFlFmGNGOGPGQ_h@S@oFRFSFTFUFrFsFtFuGFGGGHGI_r@^@oFZF[F\F]FzF{F|F}GFGGGHGI_^@C@iFJFKFLFMFfFgFhFiGBGCGDGE_h@Y@iFRFSFTFUFvFwFxFyGBGCGDGE_r@N@iFZF[F\F]FnFoFpFqGBGCGDGE_Y?}@oFFFGFHFIFbFcFdFeGFGGGHGI_c?}@zFNFOFPFQFbFcFdFeGNGOGPGQ_m?}AEFVFWFXFYFbFcFdFeGVGWGXGY_Y@NA?FFFGFHFIFnFoFpFqGRGSGTGU_Y@YAJFFFGFHFIFvFwFxFyGZG[G\G]_c@CAJFNFOFPFQFfFgFhFiGZG[G\G]_m@CA?FVFWFXFYFfFgFhFiGRGSGTGU_c@N@tFNFOFPFQFnFoFpFqGJGKGLGM_m@Y@tFVFWFXFYFvFwFxFyGJGKGLGM_T?}@i_T@H@tGz_T@^A?GzG{_T@SAJGzG{G|_U?~@j_U@I@u_U@_A@_U@TAK_U?~@j_U@I@u_U@_A@_U@TAK_V@?@k_V@J@v_V@`AA_V@UAL_V@?@k_V@J@v_V@`AA_V@UAL_W@@@l_W@K@w_W@aAB_W@VAM_W@@@l_W@K@w_W@aAB_W@VAMazBZB{FBFbGBazBbCDFBFjGJazBrCMFBFzGRazBjCVFBFrGZazBZB{GzazBbCDGzazBrCMGzazBjCVGza{B[B|FCFcGCa{BcCEFCFkGKa{BsCNFCF{GSa{BkCWFCFsG[a{B[B|G{H[a{BcCEG{a{BsCNG{a{BkCWG{a|B\B}FDFdGDa|BdCFFDFlGLa|BtCOFDF|GTa|BlCXFDFtG\a|B\B}G}H]a|BdCFG}Hea|BtCOG}a|BlCXG}a}B]B~FEFeGEa}BeCGFEFmGMa}BuCPFEF}GUa}BmCYFEFuG]a}B]B~G|H\a}BeCGG|Hda}BuCPG|a}BmCYG|HldBDbEBFBFbGBdBDjEJFBFjGJdBDzERFBFzGRdBDrEZFBFrGZdBDbEBGzHZdBDjEJGzHbdBDzERGzHrdBDrEZGzHjdCDcECFCFcGCdCDkEKFCFkGKdCD{ESFCF{GSdCDsE[FCFsG[dCDcECG{H[H{dCDkEKG{HcdCD{ESG{HsdCDsE[G{HkdDDdEDFEFeGEdDDlELFEFmGMdDD|ETFEF}GUdDDtE\FEFuG]dDDdEDG|H\H|dDDlELG|HdIDdDD|ETG|HtdDDtE\G|HldEDeEEFDFdGDdEDmEMFDFlGLdED}EUFDF|GTdEDuE]FDFtG\dEDeEEG}H]H}dEDmEMG}HeIEdED}EUG}HuIMdEDuE]G}Hm_^?x@tHBHCHDHEHVHWHXHYIBICIDIE_h?xA?HJHKHLHMHVHWHXHYIJIKILIM_r?xAJHRHSHTHUHVHWHXHYIRISITIU_Y@H@dG~H?H@HAHbHcHdHeHvHwHxHy_c@^@dHFHGHHHIHrHsHtHuHvHwHxHy_m@S@dHNHOHPHQHjHkHlHmHvHwHxHy_^@^AEHBHCHDHEHrHsHtHuINIOIPIQ_^@S@zHBHCHDHEHjHkHlHmIFIGIHII_h@HAEHJHKHLHMHbHcHdHeINIOIPIQ_r@H@zHRHSHTHUHbHcHdHeIFIGIHII_h@S@oHJHKHLHMHjHkHlHmH~I?I@IA_r@^@oHRHSHTHUHrHsHtHuH~I?I@IA_^@C@iHBHCHDHEH^H_H`HaHzH{H|H}_h@Y@iHJHKHLHMHnHoHpHqHzH{H|H}_r@N@iHRHSHTHUHfHgHhHiHzH{H|H}_Y?}@oG~H?H@HAHZH[H\H]H~I?I@IA_c?}@zHFHGHHHIHZH[H\H]IFIGIHII_m?}AEHNHOHPHQHZH[H\H]INIOIPIQ_Y@NA?G~H?H@HAHfHgHhHiIJIKILIM_Y@YAJG~H?H@HAHnHoHpHqIRISITIU_c@CAJHFHGHHHIH^H_H`HaIRISITIU_m@CA?HNHOHPHQH^H_H`HaIJIKILIM_c@N@tHFHGHHHIHfHgHhHiIBICIDIE_m@Y@tHNHOHPHQHnHoHpHqIBICIDIE_Z@I@e_Z?~@pIn_Z@OA@InIo_Z@ZAKInIoIp_Z@I@e_Z?~@p_Z@OA@_Z@ZAK_[@J@f_[@?@q_[@PAA_[@[AL_[@J@f_[@?@q_[@PAA_[@[AL_\@K@g_\@@@r_\@QAB_\@\AM_\@K@g_\@@@r_\@QAB_\@\AMa~BbBwFFFjF~a~BZC@FFFbGFa~BfCMFFFnGRa~BnCVFFFvGZa~BbBwG~HbHvIoa~BZC@G~HZH~Ioa~BfCMG~HfIJIoa~BnCVG~HnIRIob?BcBxFGFkG?b?B[CAFGFcGGb?BgCNFGFoGSb?BoCWFGFwG[b?BcBxH?HcHwInb?B[CAH?H[I?InJJb?BgCNH?HgIKInb?BoCWH?HoISInb@BdByFHFlG@IpJTb@B\CBFHFdGHIpJLb@BhCOFHFpGTIpb@BpCXFHFxG\Ipb@BdByHAHeHyb@B\CBHAH]IAb@BhCOHAHiIMb@BpCXHAHqIUbABeBzFIFmGAIqJUbAB]CCFIFeGIIqJMbABiCPFIFqGUIqJYbABqCYFIFyG]IqbABeBzH@HdHxbAB]CCH@H\I@bABiCPH@HhILbABqCYH@HpITdFDjD~FFFjF~InJRdFDbEFFFFbGFInJJdFDnERFFFnGRInJVdFDvEZFFFvGZInJ^dFDjD~G~HbHvdFDbEFG~HZH~dFDnERG~HfIJdFDvEZG~HnIRdGDkE?FGFkG?IoJSJgdGDcEGFGFcGGIoJKdGDoESFGFoGSIoJWdGDwE[FGFwG[IoJ_dGDkE?H?HcHwdGDcEGH?H[I?dGDoESH?HgIKdGDwE[H?HoISdHDlE@FIFmGAdHDdEHFIFeGIdHDpETFIFqGUdHDxE\FIFyG]dHDlE@H@HdHxIpJTJhdHDdEHH@H\I@IpJLJpdHDpETH@HhILIpJXdHDxE\H@HpITIpJ`dIDmEAFHFlG@dIDeEIFHFdGHdIDqEUFHFpGTdIDyE]FHFxG\dIDmEAHAHeHyIqJUJidIDeEIHAH]IAIqJMJqdIDqEUHAHiIMIqJYJ}dIDyE]HAHqIUIqJa__?y@uIrIsItIuJFJGJHJIJrJsJtJu_i?yA@IzI{I|I}JFJGJHJIJzJ{J|J}_s?yAKJBJCJDJEJFJGJHJIKBKCKDKE_d@_@eIvIwIxIyJbJcJdJeJfJgJhJi_n@T@eI~J?J@JAJZJ[J\J]JfJgJhJi__@_AFIrIsItIuJbJcJdJeJ~K?K@KA__@T@{IrIsItIuJZJ[J\J]JvJwJxJy_i@IAFIzI{I|I}JRJSJTJUJ~K?K@KA_s@I@{JBJCJDJEJRJSJTJUJvJwJxJy_i@T@pIzI{I|I}JZJ[J\J]JnJoJpJq_s@_@pJBJCJDJEJbJcJdJeJnJoJpJq__@D@jIrIsItIuJNJOJPJQJjJkJlJm_i@Z@jIzI{I|I}J^J_J`JaJjJkJlJm_s@O@jJBJCJDJEJVJWJXJYJjJkJlJm_d?~@{IvIwIxIyJJJKJLJMJvJwJxJy_n?~AFI~J?J@JAJJJKJLJMJ~K?K@KA_d@DAKIvIwIxIyJNJOJPJQKBKCKDKE_n@DA@I~J?J@JAJNJOJPJQJzJ{J|J}_d@O@uIvIwIxIyJVJWJXJYJrJsJtJu_n@Z@uI~J?J@JAJ^J_J`JaJrJsJtJu_d@_@e_d?~@{_d@DAK_d@O@u_e@`@f_e@?@|K^_e@EALK^K__e@P@vK^K_K`_e@`@f_e@?@|_e@EAL_e@P@v_f@a@g_f@@@}_f@FAM_f@Q@w_f@a@g_f@@@}_f@FAM_f@Q@wbFBrBwFNFzF~bFBZCIFNFbGNbFB^CVFNFfGZbFBfCDFNFnGJbFBrBwHFHrHvIwJcJgK_bFBZCIHFHZIFIwJKJwK_bFB^CVHFH^IRIwJOKCK_bFBfCDHFHfIBIwJWJsK_bGBsBxFOF{G?K`bGB[CJFOFcGOK`KtbGB_CWFOFgG[K`bGBgCEFOFoGKK`bGBsBxHGHsHwIvJbJfbGB[CJHGH[IGIvJJJvbGB_CWHGH_ISIvJNKBbGBgCEHGHgICIvJVJrbHBtByFPF|G@IxJdJhKabHB\CKFPFdGPIxJLJxKaKubHB`CXFPFhG\IxJPKDKaKybHBhCFFPFpGLIxJXJtKabHBtByHIHuHybHB\CKHIH]IIbHB`CXHIHaIUbHBhCFHIHiIEbIBuBzFQF}GAIyJeJibIB]CLFQFeGQIyJMJybIBaCYFQFiG]IyJQKEbIBiCGFQFqGMIyJYJubIBuBzHHHtHxK^bIB]CLHHH\IHK^KrbIBaCYHHH`ITK^KvbIBiCGHHHhIDK^K~dNDzD~FNFzF~IvJbJfK^LJdNDbENFNFbGNIvJJJvK^KrdNDfEZFNFfGZIvJNKBK^KvdNDnEJFNFnGJIvJVJrK^K~dNDzD~HFHrHvdNDbENHFHZIFdNDfEZHFH^IRdNDnEJHFHfIBdOD{E?FOF{G?IwJcJgdODcEOFOFcGOIwJKJwdODgE[FOFgG[IwJOKCdODoEKFOFoGKIwJWJsdOD{E?HGHsHwKaLMLQdODcEOHGH[IGKaKudODgE[HGH_ISKaKydODoEKHGHgICKaLAdPD|E@FQF}GAK_LKLOdPDdEPFQFeGQK_KsdPDhE\FQFiG]K_KwdPDpELFQFqGMK_L?L[dPD|E@HHHtHxIxJdJhdPDdEPHHH\IHIxJLJxdPDhE\HHH`ITIxJPKDdPDpELHHHhIDIxJXJtdQD}EAFPF|G@dQDeEQFPFdGPdQDiE]FPFhG\dQDqEMFPFpGLdQD}EAHIHuHyIyJeJiK`LLLPdQDeEQHIH]IIIyJMJyK`KtL`dQDiE]HIHaIUIyJQKEK`KxdQDqEMHIHiIEIyJYJuK`L@L\_`?z@vKZK[K\K]KnKoKpKqLZL[L\L]_j?zAAKbKcKdKeKnKoKpKqLbLcLdLe_t?zALKjKkKlKmKnKoKpKqLjLkLlLm_o@U@fKfKgKhKiLBLCLDLELNLOLPLQ_`@`AGKZK[K\K]LJLKLLLMLfLgLhLi_`@U@|KZK[K\K]LBLCLDLEL^L_L`La_j@JAGKbKcKdKeKzK{K|K}LfLgLhLi_t@J@|KjKkKlKmKzK{K|K}L^L_L`La_j@U@qKbKcKdKeLBLCLDLELVLWLXLY_t@`@qKjKkKlKmLJLKLLLMLVLWLXLY_`@E@kKZK[K\K]KvKwKxKyLRLSLTLU_j@[@kKbKcKdKeLFLGLHLILRLSLTLU_t@P@kKjKkKlKmK~L?L@LALRLSLTLU_o@?AGKfKgKhKiKrKsKtKuLfLgLhLi_o@EAAKfKgKhKiKvKwKxKyLbLcLdLe_o@[@vKfKgKhKiLFLGLHLILZL[L\L]_n@T@e_n?~AF_n@DA@_n@Z@u_o@U@f_o@?AG_o@EAA_o@[@v_p@V@g_p@@AHMF_p@FABMFMG_p@\@wMFMGMH_p@V@g_p@@AH_p@FAB_p@\@wbNBjBwFVFrF~bNBZCRFVFbGVbNB^CMFVFfGRbNBnCDFVFvGJbNBjBwHNHjHvJ?J[JgKgLCLOMGbNBZCRHNHZINJ?JKK?KgKsLgMGbNB^CMHNH^IJJ?JOJ{KgKwLcMGbNBnCDHNHnIBJ?J_JsKgLGL[MGbOBkBxFWFsG?KhLDLPMHbOB[CSFWFcGWKhKtLhMHMTbOB_CNFWFgGSKhKxLdMHbOBoCEFWFwGKKhLHL\MHbOBkBxHOHkHwI~JZJfbOB[CSHOH[IOI~JJJ~bOB_CNHOH_IKI~JNJzbOBoCEHOHoICI~J^JrbPBlByFXFtG@J@J\JhKiLELQbPB\CTFXFdGXJ@JLK@KiKuLibPB`COFXFhGTJ@JPJ|KiKyLebPBpCFFXFxGLJ@J`JtKiLIL]bPBlByHQHmHyMFbPB\CTHQH]IQMFMRbPB`COHQHaIMMFMVbPBpCFHQHqIEMFbQBmBzFYFuGAJAJ]JiMIMebQB]CUFYFeGYJAJMKAMIMUbQBaCPFYFiGUJAJQJ}MIMYbQBqCGFYFyGMJAJaJuMIbQBmBzHPHlHxKfLBLNbQB]CUHPH\IPKfKrLfbQBaCPHPH`ILKfKvLbbQBqCGHPHpIDKfLFLZdVDrD~FVFrF~I~JZJfKfLBLNMFMbdVDbEVFVFbGVI~JJJ~KfKrLfMFMRdVDfERFVFfGRI~JNJzKfKvLbMFMVdVDvEJFVFvGJI~J^JrKfLFLZMFMfdVDrD~HNHjHvdVDbEVHNHZINdVDfERHNH^IJdVDvEJHNHnIBdWDsE?FWFsG?J?J[JgdWDcEWFWFcGWJ?JKK?dWDgESFWFgGSJ?JOJ{dWDwEKFWFwGKJ?J_JsdWDsE?HOHkHwKiLELQMIMeMqdWDcEWHOH[IOKiKuLiMIMUdWDgESHOH_IKKiKyLeMIMYdWDwEKHOHoICKiLIL]MIMidXDtE@FYFuGAKgLCLOdXDdEXFYFeGYKgKsLgdXDhETFYFiGUKgKwLcdXDxELFYFyGMKgLGL[dXDtE@HPHlHxJ@J\JhMHMdMpdXDdEXHPH\IPJ@JLK@MHMTdXDhETHPH`ILJ@JPJ|MHMXdXDxELHPHpIDJ@J`JtMHMhM|dYDuEAFXFtG@MGMcModYDeEYFXFdGXMGMSdYDiEUFXFhGTMGMWNCdYDyEMFXFxGLMGMgM{dYDuEAHQHmHyJAJ]JiKhLDLPdYDeEYHQH]IQJAJMKAKhKtLhdYDiEUHQHaIMJAJQJ}KhKxLddYDyEMHQHqIEJAJaJuKhLHL\_a?{@wL~M?M@MAMNMOMPMQMzM{M|M}_k?{ABMBMCMDMEMNMOMPMQNBNCNDNE_u?{AMMJMKMLMMMNMOMPMQNJNKNLNM_a@aAHL~M?M@MAMjMkMlMmNFNGNHNI_a@V@}L~M?M@MAMbMcMdMeM~N?N@NA_k@KAHMBMCMDMEMZM[M\M]NFNGNHNI_u@K@}MJMKMLMMMZM[M\M]M~N?N@NA_k@V@rMBMCMDMEMbMcMdMeMvMwMxMy_u@a@rMJMKMLMMMjMkMlMmMvMwMxMy_a@F@lL~M?M@MAMVMWMXMYMrMsMtMu_k@\@lMBMCMDMEMfMgMhMiMrMsMtMu_u@Q@lMJMKMLMMM^M_M`MaMrMsMtMu__?y@u__@_AFNZ__@T@{NZN[__@D@jNZN[N\_`?z@v_`@`AG_`@U@|_`@E@k_a?{@w_a@aAH_a@V@}_a@F@lbBBVCDFJF^GJNZbBBrCRFJFzGVNZbBBjCIFJFrGNNZbBB^B{FJFfGBNZbBBVCDHBHVIBIsJGJsK[KoL[M?MOM{bBBrCRHBHrINIsJcK?K[LKLgM?MkNGbBBjCIHBHjIFIsJ[JwK[LCL_M?McN?bBB^B{HBH^HzIsJOJkK[KwLSM?MWMsbCBWCEFKF_GKK\KpL\M@MPM|N]NibCBsCSFKF{GWK\LLLhM@MlNHN]bCBkCJFKFsGOK\LDL`M@MdN@N]bCB_B|FKFgGCK\KxLTM@MXMtN]bCBWCEHCHWICIrJFJrbCBsCSHCHsIOIrJbJ~bCBkCJHCHkIGIrJZJvbCB_B|HCH_H{IrJNJjbDBXCFFLF`GLItJHJtK]KqL]bDBtCTFLF|GXItJdK@K]LMLibDBlCKFLFtGPItJ\JxK]LELabDB`B}FLFhGDItJPJlK]KyLUbDBXCFHEHYIEL~MNMzN\NhbDBtCTHEHuIQL~MjNFN\bDBlCKHEHmIIL~MbM~N\bDB`B}HEHaH}L~MVMrN\NpbEBYCGFMFaGMIuJIJuMAMQM}bEBuCUFMF}GYIuJeKAMAMmNIbEBmCLFMFuGQIuJ]JyMAMeNAbEBaB~FMFiGEIuJQJmMAMYMubEBYCGHDHXIDKZKnLZN[NgbEBuCUHDHtIPKZLJLfN[bEBmCLHDHlIHKZLBL^N[N{bEBaB~HDH`H|KZKvLRN[NodJD^EJFJF^GJIrJFJrKZKnLZL~MNMzdJDzEVFJFzGVIrJbJ~KZLJLfL~MjNFdJDrENFJFrGNIrJZJvKZLBL^L~MbM~dJDfEBFJFfGBIrJNJjKZKvLRL~MVMrdJD^EJHBHVIBN]NidJDzEVHBHrINN]OEdJDrENHBHjIFN]N}dJDfEBHBH^HzN]NqdKD_EKFKF_GKIsJGJsdKD{EWFKF{GWIsJcK?dKDsEOFKFsGOIsJ[JwdKDgECFKFgGCIsJOJkdKD_EKHCHWICK]KqL]MAMQM}NZNfdKD{EWHCHsIOK]LMLiMAMmNINZOBdKDsEOHCHkIGK]LELaMAMeNANZNzdKDgECHCH_H{K]KyLUMAMYMuNZNnOJdLD`ELFMFaGMK[KoL[N\NhOTdLD|EXFMF}GYK[LKLgN\ODdLDtEPFMFuGQK[LCL_N\N|dLDhEDFMFiGEK[KwLSN\NpOLdLD`ELHDHXIDItJHJtM@MPM|dLD|EXHDHtIPItJdK@M@MlNHdLDtEPHDHlIHItJ\JxM@MdN@dLDhEDHDH`H|ItJPJlM@MXMtdMDaEMFLF`GLM?MOM{N[NgOSdMD}EYFLF|GXM?MkNGN[OCdMDuEQFLFtGPM?McN?N[N{OWdMDiEEFLFhGDM?MWMsN[NoOKdMDaEMHEHYIEIuJIJuK\KpL\dMD}EYHEHuIQIuJeKAK\LLLhdMDuEQHEHmIIIuJ]JyK\LDL`dMDiEEHEHaH}IuJQJmK\KxLT_i?yA@N^N_N`NaNfNgNhNiOZO[O\O]_s?yAKNbNcNdNeNfNgNhNiObOcOdOe_i@IAFN^N_N`NaNrNsNtNuO^O_O`Oa_s@I@{NbNcNdNeNrNsNtNuOVOWOXOY_i@T@pN^N_N`NaNzN{N|N}ONOOOPOQ_s@_@pNbNcNdNeOBOCODOEONOOOPOQ_i@Z@jN^N_N`NaN~O?O@OAOJOKOLOM_s@O@jNbNcNdNeNvNwNxNyOJOKOLOM_t?zAL_t@J@|_t@`@q_t@P@k_u?{AM_u@K@}Or_u@a@rOrOs_u@Q@lOrOsOtbRBVCVFZF^GZNbNfObOrbRBbCIFZFjGNNbNrOVOrbRBrC@FZFzGFNbOBONOrbRBfB{FZFnGBNbNvOJOrbRBVCVHRHVIRJCJGKCKkKoLkMKMONKbRBbCIHRHbIFJCJSJwKkK{L_MKM[N?bRBrC@HRHrH~JCJcJoKkLKLWMKMkMwbRBfB{HRHfHzJCJWJkKkL?LSMKM_MsbSBWCWF[F_G[KlKpLlMLMPNLNeNiOebSBcCJF[FkGOKlK|L`MLM\N@NeNuOYbSBsCAF[F{GGKlLLLXMLMlMxNeOEOQbSBgB|F[FoGCKlL@LTMLM`MtNeNyOMbSBWCWHSHWISJBJFKBOsOwbSBcCJHSHcIGJBJRJvOsbSBsCAHSHsI?JBJbJnOsbSBgB|HSHgH{JBJVJjOsbTBXCXF\F`G\JDJHKDKmKqLmOuOybTBdCKF\FlGPJDJTJxKmK}LaOuPEbTBtCBF\F|GHJDJdJpKmLMLYOubTBhB}F\FpGDJDJXJlKmLALUOubTBXCXHUHYIUMJMNNJNdNhOdbTBdCKHUHeIIMJMZM~NdNtOXbTBtCBHUHuIAMJMjMvNdODOPbTBhB}HUHiH}MJM^MrNdNxOLbUBYCYF]FaG]JEJIKEMMMQNMbUBeCLF]FmGQJEJUJyMMM]NAbUBuCCF]F}GIJEJeJqMMMmMybUBiB~F]FqGEJEJYJmMMMaMubUBYCYHTHXITKjKnLjNcNgOcOtOxbUBeCLHTHdIHKjKzL^NcNsOWOtPDbUBuCCHTHtI@KjLJLVNcOCOOOtbUBiB~HTHhH|KjK~LRNcNwOKOtPHdZD^EZFZF^GZJBJFKBKjKnLjMJMNNJdZDjENFZFjGNJBJRJvKjKzL^MJMZM~dZDzEFFZFzGFJBJbJnKjLJLVMJMjMvdZDnEBFZFnGBJBJVJjKjK~LRMJM^MrdZD^EZHRHVIRNeNiOeOuOydZDjENHRHbIFNeNuOYOuPEdZDzEFHRHrH~NeOEOQOuPUdZDnEBHRHfHzNeNyOMOuPId[D_E[F[F_G[JCJGKCOtOxd[DkEOF[FkGOJCJSJwOtPDd[D{EGF[F{GGJCJcJoOtPTd[DoECF[FoGCJCJWJkOtPHP\d[D_E[HSHWISKmKqLmMMMQNMNbNfObd[DkEOHSHcIGKmK}LaMMM]NANbNrOVd[D{EGHSHsI?KmLMLYMMMmMyNbOBONd[DoECHSHgH{KmLALUMMMaMuNbNvOJd\D`E\F]FaG]KkKoLkNdNhOdOsOwd\DlEPF]FmGQKkK{L_NdNtOXOsPCd\D|EHF]F}GIKkLKLWNdODOPOsPSP_d\DpEDF]FqGEKkL?LSNdNxOLOsPGP[d\D`E\HTHXITJDJHKDMLMPNLd\DlEPHTHdIHJDJTJxMLM\N@d\D|EHHTHtI@JDJdJpMLMlMxd\DpEDHTHhH|JDJXJlMLM`Mtd]DaE]F\F`G\MKMONKNcNgOcd]DmEQF\FlGPMKM[N?NcNsOWd]D}EIF\F|GHMKMkMwNcOCOOd]DqEEF\FpGDMKM_MsNcNwOKd]DaE]HUHYIUJEJIKEKlKpLlOrOvd]DmEQHUHeIIJEJUJyKlK|L`OrPBPfd]D}EIHUHuIAJEJeJqKlLLLXOrPRP^d]DqEEHUHiH}JEJYJmKlL@LTOrPFPZ_k?{ABOnOoOpOqOvOwOxOyPjPkPlPm_k@KAHOnOoOpOqPBPCPDPEPnPoPpPq_k@V@rOnOoOpOqPJPKPLPMP^P_P`Pa_k@\@lOnOoOpOqPNPOPPPQPZP[P\P]_j?zAA_j@JAGPz_j@U@qPzP{_j@[@kPzP{P|bJBVCMFRF^GRN^NfOZOnOvPjPzbJBbCRFRFjGVN^NrO^OnPBPnPzbJBjC@FRFrGFN^NzONOnPJP^PzbJBnB{FRFvGBN^N~OJOnPNPZPzbJBVCMHJHVIJI{JGJ{KcKoLcMCMONCbJBbCRHJHbINI{JSK?KcK{LgMCM[NGbJBjC@HJHjH~I{J[JoKcLCLWMCMcMwbJBnB{HJHnHzI{J_JkKcLGLSMCMgMsbKBWCNFSF_GSKdKpLdMDMPNDNaNiO]bKBcCSFSFkGWKdK|LhMDM\NHNaNuOabKBkCAFSFsGGKdLDLXMDMdMxNaN}OQbKBoB|FSFwGCKdLHLTMDMhMtNaOAOMbKBWCNHKHWIKIzJFJzOoOwPkP{Q?bKBcCSHKHcIOIzJRJ~OoPCPoP{bKBkCAHKHkI?IzJZJnOoPKP_P{bKBoB|HKHoH{IzJ^JjOoPOP[P{bLBXCOFTF`GTI|JHJ|KeKqLeOqOyPmbLBdCTFTFlGXI|JTK@KeK}LiOqPEPqbLBlCBFTFtGHI|J\JpKeLELYOqPMPabLBpB}FTFxGDI|J`JlKeLILUOqPQP]bLBXCOHMHYIMMBMNNBN`NhO\P|Q@bLBdCTHMHeIQMBMZNFN`NtO`P|QLbLBlCBHMHmIAMBMbMvN`N|OPP|bLBpB}HMHqH}MBMfMrN`O@OLP|bMBYCPFUFaGUI}JIJ}MEMQNEP}QAbMBeCUFUFmGYI}JUKAMEM]NIP}QMbMBmCCFUFuGII}J]JqMEMeMyP}QUbMBqB~FUFyGEI}JaJmMEMiMuP}bMBYCPHLHXILKbKnLbN_NgO[OpOxPlbMBeCUHLHdIPKbKzLfN_NsO_OpPDPpbMBmCCHLHlI@KbLBLVN_N{OOOpPLP`bMBqB~HLHpH|KbLFLRN_O?OKOpPPP\dRD^ERFRF^GRIzJFJzKbKnLbMBMNNBdRDjEVFRFjGVIzJRJ~KbKzLfMBMZNFdRDrEFFRFrGFIzJZJnKbLBLVMBMbMvdRDvEBFRFvGBIzJ^JjKbLFLRMBMfMrdRD^ERHJHVIJNaNiO]OqOyPmP}QAdRDjEVHJHbINNaNuOaOqPEPqP}QMdRDrEFHJHjH~NaN}OQOqPMPaP}QUdRDvEBHJHnHzNaOAOMOqPQP]P}QYdSD_ESFSF_GSI{JGJ{OpOxPlP|Q@dSDkEWFSFkGWI{JSK?OpPDPpP|QLdSDsEGFSFsGGI{J[JoOpPLP`P|QTdSDwECFSFwGCI{J_JkOpPPP\P|QXQddSD_ESHKHWIKKeKqLeMEMQNEN^NfOZdSDkEWHKHcIOKeK}LiMEM]NIN^NrO^dSDsEGHKHkI?KeLELYMEMeMyN^NzONdSDwECHKHoH{KeLILUMEMiMuN^N~OJdTD`ETFUFaGUKcKoLcN`NhO\OoOwPkdTDlEXFUFmGYKcK{LgN`NtO`OoPCPodTDtEHFUFuGIKcLCLWN`N|OPOoPKP_dTDxEDFUFyGEKcLGLSN`O@OLOoPOP[dTD`ETHLHXILI|JHJ|MDMPNDPzP~dTDlEXHLHdIPI|JTK@MDM\NHPzQJdTDtEHHLHlI@I|J\JpMDMdMxPzQRQfdTDxEDHLHpH|I|J`JlMDMhMtPzQVQbdUDaEUFTF`GTMCMONCN_NgO[P{Q?QsdUDmEYFTFlGXMCM[NGN_NsO_P{QKdUDuEIFTFtGHMCMcMwN_N{OOP{QSQgdUDyEEFTFxGDMCMgMsN_O?OKP{QWQcdUDaEUHMHYIMI}JIJ}KdKpLdOnOvPjdUDmEYHMHeIQI}JUKAKdK|LhOnPBPndUDuEIHMHmIAI}J]JqKdLDLXOnPJP^dUDyEEHMHqH}I}JaJmKdLHLTOnPNPZ~~~~~~") xQ24pp = Graph(r":~?RG_?_??@_??@?A_??@?A?B_l???D?E?F?G_??D?E?F?G_??D?E?F?G_??D?E?F?G_??D?E?F?G_l_l?q_l?q?r_l?q?r?s`Y???H?I?J?K?l?u?v?w?x_??H?I?J?K_??H?I?J?K_??H?I?J?K_??H?I?J?K_l?u?v?w?x_l?u?v?w?x_l?u?v?w?x_l?u?v?w?x`Y`Y@b`Y@b@c`Y@b@c@daF?@?L?M?N?O?m?y?z?{?|@Z@f@g@h@i_@?L?M?N?O_@?L?M?N?O_@?L?M?N?O_@?L?M?N?O_m?y?z?{?|_m?y?z?{?|_m?y?z?{?|_m?y?z?{?|`Z@f@g@h@i`Z@f@g@h@i`Z@f@g@h@i`Z@f@g@h@iaGaGASaGASATaGASATAUas?@?V?W?X?Y?m@C@D@E@F@Z@p@q@r@s_@?V?W?X?YAGA]A^A_A`_@?V?W?X?Y_@?V?W?X?Y_@?V?W?X?Y_m@C@D@E@F_m@C@D@E@F_m@C@D@E@F_m@C@D@E@F`Z@p@q@r@s`Z@p@q@r@s`Z@p@q@r@s`Z@p@q@r@saGA]A^A_A`aGA]A^A_A`aGA]A^A_A`aGA]A^A_A`bJAtatBJatBJBKatBJBKBLb`?A?S?c?f?g?n@@@P@S@T@[@m@}A@AA_A?S?c?f?gAHAZAjAmAnAuBGBWBZB[_A?S?c?f?g_A?S?c?f?g_A?S?c?f?g_n@@@P@S@T_n@@@P@S@T_n@@@P@S@T_n@@@P@S@T`[@m@}A@AA`[@m@}A@AA`[@m@}A@AA`[@m@}A@AAaHAZAjAmAnaHAZAjAmAnaHAZAjAmAnaHAZAjAmAnbtBbbwAuBGBWBZB[auBGBWBZB[auBGBWBZB[auBGBWBZB[cDBbBtcGBbBtCDbbBtCDCGcM?B?T?d?h?j?o@A@Q@U@W@\@n@~ABAD_B?T?d?h?jAIA[AkAoAqAvBHBXB\B^_B?T?d?h?jBcBuCECICK_B?T?d?h?j_B?T?d?h?j_o@A@Q@U@W_o@A@Q@U@W_o@A@Q@U@W_o@A@Q@U@W`\@n@~ABAD`\@n@~ABAD`\@n@~ABAD`\@n@~ABADaIA[AkAoAqaIA[AkAoAqaIA[AkAoAqaIA[AkAoAqcaBcBuCECICKcPcdAvBHBXB\B^avBHBXB\B^avBHBXB\B^avBHBXB\B^cqBcBuCECICKcPCbctBcBuCECICKbcBuCECICKcPCbCrcxCPCbCrCvcz?C?U?e?i?k?p@B@R@V@X@]@oA?ACAE_C?U?e?i?kAJA\AlApArAwBIBYB]B__C?U?e?i?kBdBvCFCJCL_C?U?e?i?kCQCcCsCwCy_C?U?e?i?k_p@B@R@V@X_p@B@R@V@X_p@B@R@V@X_p@B@R@V@X`]@oA?ACAE`]@oA?ACAE`]@oA?ACAE`]@oA?ACAEaJA\AlApAraJA\AlApAraJA\AlApAraJA\AlApArdNBdBvCFCJCLcQCcCsCwCyc~awBIBYB]B_awBIBYB]B_awBIBYB]B_awBIBYB]B_d^BdBvCFCJCLcQCcCsCwCyc~DPbdBvCFCJCLbdBvCFCJCLcQCcCsCwCyc~DPD`cQCcCsCwCyc~DPD`Dd_A?P?Z?[?`?n?}@G@H@M@[@j@t@u@z_A?P?Z?[?`AHAWAaAbAgAuBDBNBOBT_A?P?Z?[?`BbBqB{B|CA_A?P?Z?[?`COC^ChCiCn_A?P?Z?[?`C|DKDUDVD[_n?}@G@H@M_n?}@G@H@M_n?}@G@H@M_n?}@G@H@M`[@j@t@u@z`[@j@t@u@z`[@j@t@u@z`[@j@t@u@zaHAWAaAbAgaHAWAaAbAgaHAWAaAbAgaHAWAaAbAgdid{BbBqB{B|CAcOC^ChCiCnc|DKDUDVD[auBDBNBOBTauBDBNBOBTauBDBNBOBTauBDBNBOBTdiDxdiDxEBeHDiDxEBECeKBbBqB{B|CAcOC^ChCiCnc|DKDUDVD[bbBqB{B|CAbbBqB{B|CAcOC^ChCiCnc|DKDUDVD[cOC^ChCiCnc|DKDUDVD[_C?R?]?_?b?p@?@J@L@O@]@l@w@y@|_C?R?]?_?bAJAYAdAfAiAwBFBQBSBV_C?R?]?_?bBdBsB~C@CCDkDzEEEGEJ_C?R?]?_?bCQC`CkCmCp_C?R?]?_?bC~DMDXDZD]_p@?@J@L@O_p@?@J@L@O_p@?@J@L@O_p@?@J@L@O`]@l@w@y@|`]@l@w@y@|`]@l@w@y@|`]@l@w@y@|aJAYAdAfAiaJAYAdAfAiaJAYAdAfAiaJAYAdAfAidkDzEEEGEJegEXbdBsB~C@CCcQC`CkCmCpc~DMDXDZD]awBFBQBSBVawBFBQBSBVawBFBQBSBVawBFBQBSBVdkDzEEEGEJdkDzEEEGEJerEXEgetEXEgErdkDzEEEGEJewEXEgErEtbdBsB~C@CCcQC`CkCmCpc~DMDXDZD]bdBsB~C@CCbdBsB~C@CCcQC`CkCmCpc~DMDXDZD]cQC`CkCmCpc~DMDXDZD]_B?Q?\?^?a?o?~@I@K@N@\@k@v@x@{_B?Q?\?^?aAIAXAcAeAhAvBEBPBRBU_B?Q?\?^?aBcBrB}C?CBDjDyEDEFEI_B?Q?\?^?aCPC_CjClCo_B?Q?\?^?aC}DLDWDYD\EWEfEqEsEv_o?~@I@K@N_o?~@I@K@N_o?~@I@K@N_o?~@I@K@N`\@k@v@x@{`\@k@v@x@{`\@k@v@x@{`\@k@v@x@{aIAXAcAeAhaIAXAcAeAhaIAXAcAeAhaIAXAcAeAhdjDyEDEFEIfDeWEfEqEsEvbcBrB}C?CBcPC_CjClCoc}DLDWDYD\avBEBPBRBUavBEBPBRBUavBEBPBRBUavBEBPBRBUdjDyEDEFEIdjDyEDEFEIfDFSeWEfEqEsEvfDFSF^eWEfEqEsEvdjDyEDEFEIfDFSF^F`eWEfEqEsEvbcBrB}C?CBcPC_CjClCoc}DLDWDYD\bcBrB}C?CBbcBrB}C?CBcPC_CjClCoc}DLDWDYD\cPC_CjClCoc}DLDWDYD\_D?L?P?Q?R?q?y?}?~@?@^@f@j@k@l_D?L?P?Q?RAKASAWAXAYAxB@BDBEBF_D?L?P?Q?RBeBmBqBrBsDlDtDxDyDz_D?L?P?Q?RCRCZC^C_C`FFFNFRFSFT_D?L?P?Q?RD?DGDKDLDMEYEaEeEfEg_q?y?}?~@?_q?y?}?~@?_q?y?}?~@?_q?y?}?~@?`^@f@j@k@l`^@f@j@k@l`^@f@j@k@l`^@f@j@k@laKASAWAXAYFsaKASAWAXAYaKASAWAXAYaKASAWAXAYdlDtDxDyDzFsF{fFFNFRFSFTFsF{G?eYEaEeEfEgFsF{G?G@beBmBqBrBscRCZC^C_C`d?DGDKDLDMaxB@BDBEBFaxB@BDBEBFaxB@BDBEBFaxB@BDBEBFdlDtDxDyDzdlDtDxDyDzfFFNFRFSFTeYEaEeEfEgfFFNFRFSFTeYEaEeEfEgdlDtDxDyDzfFFNFRFSFTeYEaEeEfEgbeBmBqBrBscRCZC^C_C`d?DGDKDLDMbeBmBqBrBsbeBmBqBrBscRCZC^C_C`d?DGDKDLDMcRCZC^C_C`d?DGDKDLDM_D?V?c?d?e?q@C@P@Q@R@^@p@}@~A?_D?V?c?d?eAKA]AjAkAlAxBJBWBXBY_D?V?c?d?eBeBwCDCECFDlD~EKELEM_D?V?c?d?eCRCdCqCrCsFFFXFeFfFg_D?V?c?d?eD?DQD^D_D`EYEkExEyEz_q@C@P@Q@RFsGEGRGSGT_q@C@P@Q@R_q@C@P@Q@R_q@C@P@Q@R`^@p@}@~A?`^@p@}@~A?`^@p@}@~A?`^@p@}@~A?aKA]AjAkAlFsGEGRGSGTaKA]AjAkAlaKA]AjAkAlaKA]AjAkAldlD~EKELEMFsGEGRGSGTfFFXFeFfFgFsGEGRGSGTeYEkExEyEzFsGEGRGSGTbeBwCDCECFcRCdCqCrCsd?DQD^D_D`axBJBWBXBYG`axBJBWBXBYaxBJBWBXBYaxBJBWBXBYdlD~EKELEMdlD~EKELEMfFFXFeFfFgeYEkExEyEzfFFXFeFfFgeYEkExEyEzdlD~EKELEMfFFXFeFfFgeYEkExEyEzbeBwCDCECFG`GrcRCdCqCrCsG`GrH?d?DQD^D_D`G`GrH?H@beBwCDCECFbeBwCDCECFcRCdCqCrCsd?DQD^D_D`cRCdCqCrCsd?DQD^D_D`_G?O?a?g?k?t?|@N@T@X@a@i@{AAAE_G?O?a?g?kANAVAhAnArA{BCBUB[B__G?O?a?g?kBhBpCBCHCLDoDwEIEOES_G?O?a?g?kCUC]CoCuCyFIFQFcFiFm_G?O?a?g?kDBDJD\DbDfE\EdEvE|F@_t?|@N@T@XFvF~GPGVGZGcGkG}HCHG_t?|@N@T@X_t?|@N@T@X_t?|@N@T@X`a@i@{AAAE`a@i@{AAAE`a@i@{AAAE`a@i@{AAAEaNAVAhAnArFvF~GPGVGZaNAVAhAnAraNAVAhAnAraNAVAhAnArHPdoDwEIEOESFvF~GPGVGZfIFQFcFiFmFvF~GPGVGZe\EdEvE|F@FvF~GPGVGZbhBpCBCHCLcUC]CoCuCydBDJD\DbDfa{BCBUB[B_GcGkG}HCHGa{BCBUB[B_a{BCBUB[B_a{BCBUB[B_doDwEIEOESdoDwEIEOESfIFQFcFiFme\EdEvE|F@fIFQFcFiFme\EdEvE|F@doDwEIEOESfIFQFcFiFmHPHXe\EdEvE|F@bhBpCBCHCLGcGkG}HCHGcUC]CoCuCyGcGkG}HCHGdBDJD\DbDfGcGkG}HCHGbhBpCBCHCLbhBpCBCHCLHPHXHjcUC]CoCuCydBDJD\DbDfcUC]CoCuCydBDJD\DbDfHPHXHjHp_F?N?b?f?j?s?{@O@S@W@`@h@|A@AD_F?N?b?f?jAMAUAiAmAqAzBBBVBZB^_F?N?b?f?jBgBoCCCGCKDnDvEJENER_F?N?b?f?jCTC\CpCtCxFHFPFdFhFl_F?N?b?f?jDADID]DaDeE[EcEwE{F?_s?{@O@S@WFuF}GQGUGYGbGjG~HBHF_s?{@O@S@W_s?{@O@S@W_s?{@O@S@WHOHWHkHoHs``@h@|A@AD``@h@|A@AD``@h@|A@AD``@h@|A@ADaMAUAiAmAqFuF}GQGUGYaMAUAiAmAqaMAUAiAmAqH|aMAUAiAmAqHOHWHkHoHsdnDvEJENERFuF}GQGUGYfHFPFdFhFlFuF}GQGUGYe[EcEwE{F?FuF}GQGUGYbgBoCCCGCKcTC\CpCtCxdADID]DaDeazBBBVBZB^GbGjG~HBHFazBBBVBZB^azBBBVBZB^azBBBVBZB^dnDvEJENERdnDvEJENERfHFPFdFhFle[EcEwE{F?fHFPFdFhFle[EcEwE{F?dnDvEJENERfHFPFdFhFlHOHWHkHoHse[EcEwE{F?H|IDbgBoCCCGCKGbGjG~HBHFcTC\CpCtCxGbGjG~HBHFdADID]DaDeGbGjG~HBHFbgBoCCCGCKH|IDIXbgBoCCCGCKHOHWHkHoHscTC\CpCtCxdADID]DaDecTC\CpCtCxH|IDIXI\dADID]DaDeHOHWHkHoHs_E?M?`?h?i?r?z@M@U@V@_@g@zABAC_E?M?`?h?iALATAgAoApAyBABTB\B]_E?M?`?h?iBfBnCACICJDmDuEHEPEQ_E?M?`?h?iCSC[CnCvCwFGFOFbFjFk_E?M?`?h?iD@DHD[DcDdEZEbEuE}E~_r?z@M@U@VFtF|GOGWGXGaGiG|HDHE_r?z@M@U@V_r?z@M@U@VH{ICIVI^I__r?z@M@U@VHNHVHiHqHr`_@g@zABAC`_@g@zABAC`_@g@zABAC`_@g@zABACaLATAgAoApFtF|GOGWGXaLATAgAoApIhaLATAgAoApH{ICIVI^I_aLATAgAoApHNHVHiHqHrdmDuEHEPEQFtF|GOGWGXfGFOFbFjFkFtF|GOGWGXeZEbEuE}E~FtF|GOGWGXbfBnCACICJcSC[CnCvCwd@DHD[DcDdayBABTB\B]GaGiG|HDHEayBABTB\B]ayBABTB\B]ayBABTB\B]dmDuEHEPEQdmDuEHEPEQfGFOFbFjFkeZEbEuE}E~fGFOFbFjFkeZEbEuE}E~dmDuEHEPEQIhIpfGFOFbFjFkHNHVHiHqHreZEbEuE}E~H{ICIVI^I_bfBnCACICJGaGiG|HDHEcSC[CnCvCwGaGiG|HDHEd@DHD[DcDdGaGiG|HDHEbfBnCACICJH{ICIVI^I_bfBnCACICJHNHVHiHqHrcSC[CnCvCwIhIpJCd@DHD[DcDdIhIpJCJKcSC[CnCvCwH{ICIVI^I_d@DHD[DcDdHNHVHiHqHr_E?S?W?\?]?r@@@D@I@J@_@m@q@v@w_E?S?W?\?]ALAZA^AcAdAyBGBKBPBQ_E?S?W?\?]BfBtBxB}B~DmD{E?EDEE_E?S?W?\?]CSCaCeCjCkFGFUFYF^F__E?S?W?\?]D@DNDRDWDXEZEhElEqEr_r@@@D@I@JFtGBGFGKGLGaGoGsGxGy_r@@@D@I@JIhIvIzJ?J@_r@@@D@I@JH{IIIMIRIS_r@@@D@I@JHNH\H`HeHf`_@m@q@v@w`_@m@q@v@w`_@m@q@v@w`_@m@q@v@waLAZA^AcAdFtGBGFGKGLaLAZA^AcAdIhIvIzJ?J@aLAZA^AcAdH{IIIMIRISaLAZA^AcAdHNH\H`HeHfdmD{E?EDEEFtGBGFGKGLfGFUFYF^F_FtGBGFGKGLeZEhElEqErFtGBGFGKGLbfBtBxB}B~JUcSCaCeCjCkd@DNDRDWDXayBGBKBPBQGaGoGsGxGyayBGBKBPBQJUJcayBGBKBPBQayBGBKBPBQdmD{E?EDEEdmD{E?EDEEfGFUFYF^F_JUJcJgeZEhElEqErJUJcJgJlfGFUFYF^F_eZEhElEqErdmD{E?EDEEIhIvIzJ?J@fGFUFYF^F_HNH\H`HeHfeZEhElEqErH{IIIMIRISbfBtBxB}B~GaGoGsGxGycSCaCeCjCkGaGoGsGxGyd@DNDRDWDXGaGoGsGxGybfBtBxB}B~H{IIIMIRISbfBtBxB}B~HNH\H`HeHfcSCaCeCjCkIhIvIzJ?J@d@DNDRDWDXIhIvIzJ?J@cSCaCeCjCkH{IIIMIRISd@DNDRDWDXHNH\H`HeHf_F?U?Y?[?^?s@B@F@H@K@`@o@s@u@x_F?U?Y?[?^AMA\A`AbAeAzBIBMBOBR_F?U?Y?[?^BgBvBzB|C?DnD}EAECEF_F?U?Y?[?^CTCcCgCiClFHFWF[F]F`_F?U?Y?[?^DADPDTDVDYE[EjEnEpEs_s@B@F@H@KFuGDGHGJGMGbGqGuGwGz_s@B@F@H@KIiIxI|I~JAJVJeJiJkJn_s@B@F@H@KH|IKIOIQIT_s@B@F@H@KHOH^HbHdHg``@o@s@u@x``@o@s@u@x``@o@s@u@x``@o@s@u@xaMA\A`AbAeFuGDGHGJGMaMA\A`AbAeIiIxI|I~JAaMA\A`AbAeH|IKIOIQITaMA\A`AbAeHOH^HbHdHgdnD}EAECEFFuGDGHGJGMfHFWF[F]F`FuGDGHGJGMe[EjEnEpEsFuGDGHGJGMbgBvBzB|C?JVJeJiJkJncTCcCgCiCldADPDTDVDYKCazBIBMBOBRGbGqGuGwGzazBIBMBOBRJVJeJiJkJnazBIBMBOBRazBIBMBOBRKCKRdnD}EAECEFdnD}EAECEFKCKRKVfHFWF[F]F`JVJeJiJkJne[EjEnEpEsJVJeJiJkJnfHFWF[F]F`KCKRKVKXe[EjEnEpEsdnD}EAECEFIiIxI|I~JAfHFWF[F]F`HOH^HbHdHge[EjEnEpEsH|IKIOIQITbgBvBzB|C?GbGqGuGwGzcTCcCgCiClGbGqGuGwGzdADPDTDVDYGbGqGuGwGzbgBvBzB|C?H|IKIOIQITbgBvBzB|C?HOH^HbHdHgcTCcCgCiClIiIxI|I~JAdADPDTDVDYIiIxI|I~JAcTCcCgCiClH|IKIOIQITdADPDTDVDYHOH^HbHdHg_G?T?X?Z?_?t@A@E@G@L@a@n@r@t@y_G?T?X?Z?_ANA[A_AaAfA{BHBLBNBS_G?T?X?Z?_BhBuByB{C@DoD|E@EBEG_G?T?X?Z?_CUCbCfChCmFIFVFZF\Fa_G?T?X?Z?_DBDODSDUDZE\EiEmEoEt_t@A@E@G@LFvGCGGGIGNGcGpGtGvG{_t@A@E@G@LIjIwI{I}JBJWJdJhJjJo_t@A@E@G@LH}IJINIPIUKDKQKUKWK\_t@A@E@G@LHPH]HaHcHh`a@n@r@t@y`a@n@r@t@y`a@n@r@t@y`a@n@r@t@yaNA[A_AaAfFvGCGGGIGNaNA[A_AaAfIjIwI{I}JBaNA[A_AaAfH}IJINIPIUaNA[A_AaAfHPH]HaHcHhdoD|E@EBEGFvGCGGGIGNfIFVFZF\FaFvGCGGGIGNe\EiEmEoEtFvGCGGGIGNbhBuByB{C@JWJdJhJjJocUCbCfChCmKqdBDODSDUDZKDKQKUKWK\a{BHBLBNBSGcGpGtGvG{a{BHBLBNBSJWJdJhJjJoa{BHBLBNBSKqK~a{BHBLBNBSKDKQKUKWK\doD|E@EBEGKqK~LBdoD|E@EBEGKDKQKUKWK\fIFVFZF\FaJWJdJhJjJoe\EiEmEoEtJWJdJhJjJofIFVFZF\FaKDKQKUKWK\e\EiEmEoEtKqK~LBLDdoD|E@EBEGIjIwI{I}JBfIFVFZF\FaHPH]HaHcHhe\EiEmEoEtH}IJINIPIUbhBuByB{C@GcGpGtGvG{cUCbCfChCmGcGpGtGvG{dBDODSDUDZGcGpGtGvG{bhBuByB{C@H}IJINIPIUbhBuByB{C@HPH]HaHcHhcUCbCfChCmIjIwI{I}JBdBDODSDUDZIjIwI{I}JBcUCbCfChCmH}IJINIPIUdBDODSDUDZHPH]HaHcHh_H?L?S?T?U?u?y@@@A@B@b@f@m@n@o_H?L?S?T?UAOASAZA[A\A|B@BGBHBI_H?L?S?T?UBiBmBtBuBvDpDtD{D|D}_H?L?S?T?UCVCZCaCbCcFJFNFUFVFW_H?L?S?T?UDCDGDNDODPE]EaEhEiEj_u?y@@@A@BFwF{GBGCGDGdGhGoGpGq_u?y@@@A@BIkIoIvIwIxJXJ\JcJdJe_u?y@@@A@BH~IBIIIJIKKEKIKPKQKR_u?y@@@A@BHQHUH\H]H^KrKvK}K~L?`b@f@m@n@o`b@f@m@n@o`b@f@m@n@o`b@f@m@n@oaOASAZA[A\FwF{GBGCGDL_aOASAZA[A\IkIoIvIwIxaOASAZA[A\H~IBIIIJIKaOASAZA[A\HQHUH\H]H^dpDtD{D|D}FwF{GBGCGDfJFNFUFVFWFwF{GBGCGDe]EaEhEiEjFwF{GBGCGDbiBmBtBuBvJXJ\JcJdJeL_LccVCZCaCbCcKrKvK}K~L?L_LcLjdCDGDNDODPKEKIKPKQKRL_LcLjLka|B@BGBHBIGdGhGoGpGqa|B@BGBHBIJXJ\JcJdJea|B@BGBHBIKrKvK}K~L?a|B@BGBHBIKEKIKPKQKRdpDtD{D|D}KrKvK}K~L?dpDtD{D|D}KEKIKPKQKRfJFNFUFVFWJXJ\JcJdJee]EaEhEiEjJXJ\JcJdJefJFNFUFVFWKEKIKPKQKRe]EaEhEiEjKrKvK}K~L?dpDtD{D|D}IkIoIvIwIxfJFNFUFVFWHQHUH\H]H^e]EaEhEiEjH~IBIIIJIKbiBmBtBuBvGdGhGoGpGqcVCZCaCbCcGdGhGoGpGqdCDGDNDODPGdGhGoGpGqbiBmBtBuBvH~IBIIIJIKbiBmBtBuBvHQHUH\H]H^cVCZCaCbCcIkIoIvIwIxdCDGDNDODPIkIoIvIwIxcVCZCaCbCcH~IBIIIJIKdCDGDNDODPHQHUH\H]H^_H?V?`?a?b?u@C@M@N@O@b@p@z@{@|_H?V?`?a?bAOA]AgAhAiA|BJBTBUBV_H?V?`?a?bBiBwCACBCCDpD~EHEIEJ_H?V?`?a?bCVCdCnCoCpFJFXFbFcFd_H?V?`?a?bDCDQD[D\D]E]EkEuEvEw_u@C@M@N@OFwGEGOGPGQGdGrG|G}G~_u@C@M@N@OIkIyJCJDJEJXJfJpJqJr_u@C@M@N@OH~ILIVIWIXKEKSK]K^K__u@C@M@N@OHQH_HiHjHkKrL@LJLKLL`b@p@z@{@|L_LmLwLxLy`b@p@z@{@|`b@p@z@{@|`b@p@z@{@|aOA]AgAhAiFwGEGOGPGQL_LmLwLxLyaOA]AgAhAiIkIyJCJDJEaOA]AgAhAiH~ILIVIWIXaOA]AgAhAiHQH_HiHjHkdpD~EHEIEJFwGEGOGPGQfJFXFbFcFdFwGEGOGPGQe]EkEuEvEwFwGEGOGPGQbiBwCACBCCJXJfJpJqJrL_LmLwLxLycVCdCnCoCpKrL@LJLKLLL_LmLwLxLydCDQD[D\D]KEKSK]K^K_L_LmLwLxLya|BJBTBUBVGdGrG|G}G~MLa|BJBTBUBVJXJfJpJqJra|BJBTBUBVKrL@LJLKLLa|BJBTBUBVKEKSK]K^K_dpD~EHEIEJKrL@LJLKLLdpD~EHEIEJKEKSK]K^K_fJFXFbFcFdJXJfJpJqJre]EkEuEvEwJXJfJpJqJrfJFXFbFcFdKEKSK]K^K_e]EkEuEvEwKrL@LJLKLLdpD~EHEIEJIkIyJCJDJEMLMZfJFXFbFcFdHQH_HiHjHkMLMZMde]EkEuEvEwH~ILIVIWIXMLMZMdMebiBwCACBCCGdGrG|G}G~cVCdCnCoCpGdGrG|G}G~dCDQD[D\D]GdGrG|G}G~biBwCACBCCH~ILIVIWIXbiBwCACBCCHQH_HiHjHkcVCdCnCoCpIkIyJCJDJEdCDQD[D\D]IkIyJCJDJEcVCdCnCoCpH~ILIVIWIXdCDQD[D\D]HQH_HiHjHk_I?M?^?_?c?v?z@K@L@P@c@g@x@y@}_I?M?^?_?cAPATAeAfAjA}BABRBSBW_I?M?^?_?cBjBnC?C@CDDqDuEFEGEK_I?M?^?_?cCWC[ClCmCqFKFOF`FaFe_I?M?^?_?cDDDHDYDZD^E^EbEsEtEx_v?z@K@L@PFxF|GMGNGRGeGiGzG{H?_v?z@K@L@PIlIpJAJBJFJYJ]JnJoJs_v?z@K@L@PI?ICITIUIYKFKJK[K\K`_v?z@K@L@PHRHVHgHhHlKsKwLHLILM`c@g@x@y@}L`LdLuLvLzMMMQMbMcMg`c@g@x@y@}`c@g@x@y@}`c@g@x@y@}aPATAeAfAjFxF|GMGNGRL`LdLuLvLzaPATAeAfAjIlIpJAJBJFMzaPATAeAfAjI?ICITIUIYaPATAeAfAjHRHVHgHhHldqDuEFEGEKFxF|GMGNGRfKFOF`FaFeFxF|GMGNGRe^EbEsEtExFxF|GMGNGRbjBnC?C@CDJYJ]JnJoJsL`LdLuLvLzcWC[ClCmCqKsKwLHLILML`LdLuLvLzdDDHDYDZD^KFKJK[K\K`L`LdLuLvLza}BABRBSBWGeGiGzG{H?MMMQMbMcMga}BABRBSBWJYJ]JnJoJsa}BABRBSBWKsKwLHLILMa}BABRBSBWKFKJK[K\K`dqDuEFEGEKKsKwLHLILMdqDuEFEGEKKFKJK[K\K`fKFOF`FaFeJYJ]JnJoJse^EbEsEtExJYJ]JnJoJsfKFOF`FaFeKFKJK[K\K`MzM~e^EbEsEtExKsKwLHLILMMzM~NOdqDuEFEGEKIlIpJAJBJFMMMQMbMcMgfKFOF`FaFeHRHVHgHhHlMMMQMbMcMge^EbEsEtExI?ICITIUIYMMMQMbMcMgbjBnC?C@CDGeGiGzG{H?MzM~NONPcWC[ClCmCqGeGiGzG{H?dDDHDYDZD^GeGiGzG{H?bjBnC?C@CDI?ICITIUIYbjBnC?C@CDHRHVHgHhHlcWC[ClCmCqIlIpJAJBJFdDDHDYDZD^IlIpJAJBJFcWC[ClCmCqI?ICITIUIYdDDHDYDZD^HRHVHgHhHl_K?N?Z?\?e?x?{@G@I@R@e@h@t@vA?_K?N?Z?\?eARAUAaAcAlB?BBBNBPBY_K?N?Z?\?eBlBoB{B}CFDsDvEBEDEM_K?N?Z?\?eCYC\ChCjCsFMFPF\F^Fg_K?N?Z?\?eDFDIDUDWD`E`EcEoEqEz_x?{@G@I@RFzF}GIGKGTGgGjGvGxHA_x?{@G@I@RInIqI}J?JHJ[J^JjJlJu_x?{@G@I@RIAIDIPIRI[KHKKKWKYKb_x?{@G@I@RHTHWHcHeHnKuKxLDLFLO`e@h@t@vA?LbLeLqLsL|MOMRM^M`Mi`e@h@t@vA?M|N?NKNMNV`e@h@t@vA?`e@h@t@vA?aRAUAaAcAlFzF}GIGKGTLbLeLqLsL|aRAUAaAcAlInIqI}J?JHM|N?NKNMNVaRAUAaAcAlIAIDIPIRI[NiaRAUAaAcAlHTHWHcHeHndsDvEBEDEMFzF}GIGKGTfMFPF\F^FgFzF}GIGKGTe`EcEoEqEzFzF}GIGKGTblBoB{B}CFJ[J^JjJlJuLbLeLqLsL|cYC\ChCjCsKuKxLDLFLOLbLeLqLsL|dFDIDUDWD`KHKKKWKYKbLbLeLqLsL|b?BBBNBPBYGgGjGvGxHAMOMRM^M`Mib?BBBNBPBYJ[J^JjJlJub?BBBNBPBYKuKxLDLFLOb?BBBNBPBYKHKKKWKYKbdsDvEBEDEMKuKxLDLFLONiNldsDvEBEDEMKHKKKWKYKbfMFPF\F^FgJ[J^JjJlJuNiNlNxe`EcEoEqEzJ[J^JjJlJufMFPF\F^FgKHKKKWKYKbM|N?NKNMNVe`EcEoEqEzKuKxLDLFLOM|N?NKNMNVdsDvEBEDEMInIqI}J?JHMOMRM^M`MifMFPF\F^FgHTHWHcHeHnMOMRM^M`Mie`EcEoEqEzIAIDIPIRI[MOMRM^M`MiblBoB{B}CFGgGjGvGxHAM|N?NKNMNVcYC\ChCjCsGgGjGvGxHAdFDIDUDWD`GgGjGvGxHANiNlNxNzblBoB{B}CFIAIDIPIRI[blBoB{B}CFHTHWHcHeHncYC\ChCjCsInIqI}J?JHdFDIDUDWD`InIqI}J?JHcYC\ChCjCsIAIDIPIRI[dFDIDUDWD`HTHWHcHeHn_J?O?[?]?d?w?|@H@J@Q@d@i@u@w@~_J?O?[?]?dAQAVAbAdAkA~BCBOBQBX_J?O?[?]?dBkBpB|B~CEDrDwECEEEL_J?O?[?]?dCXC]CiCkCrFLFQF]F_Ff_J?O?[?]?dDEDJDVDXD_E_EdEpErEy_w?|@H@J@QFyF~GJGLGSGfGkGwGyH@_w?|@H@J@QImIrI~J@JGJZJ_JkJmJt_w?|@H@J@QI@IEIQISIZKGKLKXKZKa_w?|@H@J@QHSHXHdHfHmKtKyLELGLN`d@i@u@w@~LaLfLrLtL{MNMSM_MaMh`d@i@u@w@~M{N@NLNNNU`d@i@u@w@~`d@i@u@w@~NhNmNyN{OBaQAVAbAdAkFyF~GJGLGSLaLfLrLtL{aQAVAbAdAkImIrI~J@JGM{N@NLNNNUaQAVAbAdAkI@IEIQISIZNhNmNyN{OBaQAVAbAdAkHSHXHdHfHmOUdrDwECEEELFyF~GJGLGSfLFQF]F_FfFyF~GJGLGSe_EdEpErEyFyF~GJGLGSbkBpB|B~CEJZJ_JkJmJtLaLfLrLtL{cXC]CiCkCrKtKyLELGLNLaLfLrLtL{dEDJDVDXD_KGKLKXKZKaLaLfLrLtL{a~BCBOBQBXGfGkGwGyH@MNMSM_MaMha~BCBOBQBXJZJ_JkJmJta~BCBOBQBXKtKyLELGLNa~BCBOBQBXKGKLKXKZKadrDwECEEELKtKyLELGLNNhNmNyN{OBdrDwECEEELKGKLKXKZKaOUOZfLFQF]F_FfJZJ_JkJmJtNhNmNyN{OBe_EdEpErEyJZJ_JkJmJtOUOZOffLFQF]F_FfKGKLKXKZKaM{N@NLNNNUe_EdEpErEyKtKyLELGLNM{N@NLNNNUdrDwECEEELImIrI~J@JGMNMSM_MaMhfLFQF]F_FfHSHXHdHfHmMNMSM_MaMhe_EdEpErEyI@IEIQISIZMNMSM_MaMhbkBpB|B~CEGfGkGwGyH@M{N@NLNNNUcXC]CiCkCrGfGkGwGyH@OUOZOfOhdEDJDVDXD_GfGkGwGyH@NhNmNyN{OBbkBpB|B~CEI@IEIQISIZbkBpB|B~CEHSHXHdHfHmcXC]CiCkCrImIrI~J@JGdEDJDVDXD_ImIrI~J@JGcXC]CiCkCrI@IEIQISIZdEDJDVDXD_HSHXHdHfHm_J?Q?X?f?i?w?~@E@S@V@d@k@rA@AC_J?Q?X?f?iAQAXA_AmApA~BEBLBZB]_J?Q?X?f?iBkBrByCGCJDrDyE@ENEQ_J?Q?X?f?iCXC_CfCtCwFLFSFZFhFk_J?Q?X?f?iDEDLDSDaDdE_EfEmE{E~_w?~@E@S@VFyG@GGGUGXGfGmGtHBHE_w?~@E@S@VImItI{JIJLJZJaJhJvJy_w?~@E@S@VI@IGINI\I_KGKNKUKcKf_w?~@E@S@VHSHZHaHoHrKtK{LBLPLS`d@k@rA@ACLaLhLoL}M@MNMUM\MjMm`d@k@rA@ACM{NBNINWNZ`d@k@rA@ACOUO\OcOqOt`d@k@rA@ACNhNoNvODOGaQAXA_AmApFyG@GGGUGXLaLhLoL}M@aQAXA_AmApImItI{JIJLM{NBNINWNZaQAXA_AmApI@IGINI\I_NhNoNvODOGaQAXA_AmApHSHZHaHoHrOUO\OcOqOtdrDyE@ENEQFyG@GGGUGXfLFSFZFhFkFyG@GGGUGXPBe_EfEmE{E~FyG@GGGUGXbkBrByCGCJJZJaJhJvJyLaLhLoL}M@cXC_CfCtCwKtK{LBLPLSLaLhLoL}M@dEDLDSDaDdKGKNKUKcKfLaLhLoL}M@a~BEBLBZB]GfGmGtHBHEMNMUM\MjMma~BEBLBZB]JZJaJhJvJya~BEBLBZB]KtK{LBLPLSPBPIa~BEBLBZB]KGKNKUKcKfdrDyE@ENEQKtK{LBLPLSNhNoNvODOGdrDyE@ENEQKGKNKUKcKfOUO\OcOqOtfLFSFZFhFkJZJaJhJvJyNhNoNvODOGe_EfEmE{E~JZJaJhJvJyOUO\OcOqOtfLFSFZFhFkKGKNKUKcKfM{NBNINWNZe_EfEmE{E~KtK{LBLPLSM{NBNINWNZdrDyE@ENEQImItI{JIJLMNMUM\MjMmfLFSFZFhFkHSHZHaHoHrMNMUM\MjMme_EfEmE{E~I@IGINI\I_MNMUM\MjMmbkBrByCGCJGfGmGtHBHEM{NBNINWNZcXC_CfCtCwGfGmGtHBHEOUO\OcOqOtdEDLDSDaDdGfGmGtHBHENhNoNvODOGbkBrByCGCJI@IGINI\I_PBPIPPbkBrByCGCJHSHZHaHoHrcXC_CfCtCwImItI{JIJLdEDLDSDaDdImItI{JIJLPBPIPPP^cXC_CfCtCwI@IGINI\I_dEDLDSDaDdHSHZHaHoHr_K?R?Y?g?h?x@?@F@T@U@e@l@sAAAB_K?R?Y?g?hARAYA`AnAoB?BFBMB[B\_K?R?Y?g?hBlBsBzCHCIDsDzEAEOEP_K?R?Y?g?hCYC`CgCuCvFMFTF[FiFj_K?R?Y?g?hDFDMDTDbDcE`EgEnE|E}_x@?@F@T@UFzGAGHGVGWGgGnGuHCHD_x@?@F@T@UInIuI|JJJKJ[JbJiJwJx_x@?@F@T@UIAIHIOI]I^KHKOKVKdKe_x@?@F@T@UHTH[HbHpHqKuK|LCLQLR`e@l@sAAABLbLiLpL~M?MOMVM]MkMl`e@l@sAAABM|NCNJNXNY`e@l@sAAABOVO]OdOrOsPCPJPQP_P``e@l@sAAABNiNpNwOEOFaRAYA`AnAoFzGAGHGVGWLbLiLpL~M?aRAYA`AnAoInIuI|JJJKM|NCNJNXNYaRAYA`AnAoIAIHIOI]I^NiNpNwOEOFaRAYA`AnAoHTH[HbHpHqOVO]OdOrOsdsDzEAEOEPFzGAGHGVGWfMFTF[FiFjFzGAGHGVGWPCPJPQP_P`e`EgEnE|E}FzGAGHGVGWPpblBsBzCHCIJ[JbJiJwJxLbLiLpL~M?cYC`CgCuCvKuK|LCLQLRLbLiLpL~M?dFDMDTDbDcKHKOKVKdKeLbLiLpL~M?b?BFBMB[B\GgGnGuHCHDMOMVM]MkMlb?BFBMB[B\J[JbJiJwJxb?BFBMB[B\KuK|LCLQLRPCPJPQP_P`b?BFBMB[B\KHKOKVKdKePpPwdsDzEAEOEPKuK|LCLQLRNiNpNwOEOFdsDzEAEOEPKHKOKVKdKeOVO]OdOrOsfMFTF[FiFjJ[JbJiJwJxNiNpNwOEOFe`EgEnE|E}J[JbJiJwJxOVO]OdOrOsfMFTF[FiFjKHKOKVKdKeM|NCNJNXNYe`EgEnE|E}KuK|LCLQLRM|NCNJNXNYdsDzEAEOEPInIuI|JJJKMOMVM]MkMlfMFTF[FiFjHTH[HbHpHqMOMVM]MkMle`EgEnE|E}IAIHIOI]I^MOMVM]MkMlblBsBzCHCIGgGnGuHCHDM|NCNJNXNYcYC`CgCuCvGgGnGuHCHDOVO]OdOrOsdFDMDTDbDcGgGnGuHCHDNiNpNwOEOFblBsBzCHCIIAIHIOI]I^PCPJPQP_P`blBsBzCHCIHTH[HbHpHqPpPwP~cYC`CgCuCvInIuI|JJJKPpPwP~QLdFDMDTDbDcInIuI|JJJKPCPJPQP_P`cYC`CgCuCvIAIHIOI]I^dFDMDTDbDcHTH[HbHpHq_I?P?W?j?k?v?}@D@W@X@c@j@qADAE_I?P?W?j?kAPAWA^AqArA}BDBKB^B__I?P?W?j?kBjBqBxCKCLDqDxE?ERES_I?P?W?j?kCWC^CeCxCyFKFRFYFlFm_I?P?W?j?kDDDKDRDeDfE^EeElF?F@_v?}@D@W@XFxG?GFGYGZGeGlGsHFHG_v?}@D@W@XIlIsIzJMJNJYJ`JgJzJ{_v?}@D@W@XI?IFIMI`IaKFKMKTKgKh_v?}@D@W@XHRHYH`HsHtKsKzLALTLU`c@j@qADAEL`LgLnMAMBMMMTM[MnMo`c@j@qADAEMzNANHN[N\`c@j@qADAEOTO[ObOuOvPAPHPOPbPc`c@j@qADAENgNnNuOHOIPnPuP|QOQPaPAWA^AqArFxG?GFGYGZL`LgLnMAMBaPAWA^AqArIlIsIzJMJNMzNANHN[N\aPAWA^AqArI?IFIMI`IaNgNnNuOHOIaPAWA^AqArHRHYH`HsHtOTO[ObOuOvdqDxE?ERESFxG?GFGYGZQ[fKFRFYFlFmFxG?GFGYGZPAPHPOPbPce^EeElF?F@FxG?GFGYGZPnPuP|QOQPbjBqBxCKCLJYJ`JgJzJ{L`LgLnMAMBcWC^CeCxCyKsKzLALTLUL`LgLnMAMBdDDKDRDeDfKFKMKTKgKhL`LgLnMAMBa}BDBKB^B_GeGlGsHFHGMMMTM[MnMoa}BDBKB^B_JYJ`JgJzJ{Q[Qba}BDBKB^B_KsKzLALTLUPAPHPOPbPca}BDBKB^B_KFKMKTKgKhPnPuP|QOQPdqDxE?ERESKsKzLALTLUNgNnNuOHOIdqDxE?ERESKFKMKTKgKhOTO[ObOuOvfKFRFYFlFmJYJ`JgJzJ{NgNnNuOHOIe^EeElF?F@JYJ`JgJzJ{OTO[ObOuOvfKFRFYFlFmKFKMKTKgKhMzNANHN[N\e^EeElF?F@KsKzLALTLUMzNANHN[N\dqDxE?ERESIlIsIzJMJNMMMTM[MnMofKFRFYFlFmHRHYH`HsHtMMMTM[MnMoe^EeElF?F@I?IFIMI`IaMMMTM[MnMobjBqBxCKCLGeGlGsHFHGMzNANHN[N\cWC^CeCxCyGeGlGsHFHGOTO[ObOuOvdDDKDRDeDfGeGlGsHFHGNgNnNuOHOIbjBqBxCKCLI?IFIMI`IaPAPHPOPbPcbjBqBxCKCLHRHYH`HsHtPnPuP|QOQPcWC^CeCxCyIlIsIzJMJNPnPuP|QOQPdDDKDRDeDfIlIsIzJMJNPAPHPOPbPccWC^CeCxCyI?IFIMI`IaQ[QbQidDDKDRDeDfHRHYH`HsHtQ[QbQiQ|fDFSF^F`FcKCKRKVKXK[MzM~NONPNTeXEgErEtEwJUJcJgJlJmOUOZOfOhOodiDxEBECEHKqK~LBLDLINiNlNxNzOC`Y@b@c@d@eL_LcLjLkLlMLMZMdMeMfbbBtCDCGCHH|IDIXI\I`PBPIPPP^Pa_l?q?r?s?tFsF{G?G@GAG`GrH?H@HAc~DPD`DdDfHPHXHjHpHtQ[QbQiQ|Q}_??@?A?B?CAGASATAUAVAtBJBKBLBMcPCbCrCvCxIhIpJCJKJLPpPwP~QLQM") xQ24pp2 = Graph(r":~?RG_?_??@_??@?A_??@?A?B_l???D?E?F?G_??D?E?F?G_??D?E?F?G_??D?E?F?G_??D?E?F?G_l_l?q_l?q?r_l?q?r?s`Y???H?I?J?K?l?u?v?w?x_??H?I?J?K_??H?I?J?K_??H?I?J?K_??H?I?J?K_l?u?v?w?x_l?u?v?w?x_l?u?v?w?x_l?u?v?w?x`Y`Y@b`Y@b@c`Y@b@c@daF?@?L?M?N?O?m?y?z?{?|@Z@f@g@h@i_@?L?M?N?O_@?L?M?N?O_@?L?M?N?O_@?L?M?N?O_m?y?z?{?|_m?y?z?{?|_m?y?z?{?|_m?y?z?{?|`Z@f@g@h@i`Z@f@g@h@i`Z@f@g@h@i`Z@f@g@h@iaGaGASaGASATaGASATAUas?@?V?W?X?Y?m@C@D@E@F@Z@p@q@r@s_@?V?W?X?YAGA]A^A_A`_@?V?W?X?Y_@?V?W?X?Y_@?V?W?X?Y_m@C@D@E@F_m@C@D@E@F_m@C@D@E@F_m@C@D@E@F`Z@p@q@r@s`Z@p@q@r@s`Z@p@q@r@s`Z@p@q@r@saGA]A^A_A`aGA]A^A_A`aGA]A^A_A`aGA]A^A_A`bJAtatBJatBJBKatBJBKBLb`?A?S?c?f?g?n@@@P@S@T@[@m@}A@AA_A?S?c?f?gAHAZAjAmAnAuBGBWBZB[_A?S?c?f?g_A?S?c?f?g_A?S?c?f?g_n@@@P@S@T_n@@@P@S@T_n@@@P@S@T_n@@@P@S@T`[@m@}A@AA`[@m@}A@AA`[@m@}A@AA`[@m@}A@AAaHAZAjAmAnaHAZAjAmAnaHAZAjAmAnaHAZAjAmAnbtBbbwAuBGBWBZB[auBGBWBZB[auBGBWBZB[auBGBWBZB[cDBbBtcGBbBtCDbbBtCDCGcM?B?T?d?h?j?o@A@Q@U@W@\@n@~ABAD_B?T?d?h?jAIA[AkAoAqAvBHBXB\B^_B?T?d?h?jBcBuCECICK_B?T?d?h?j_B?T?d?h?j_o@A@Q@U@W_o@A@Q@U@W_o@A@Q@U@W_o@A@Q@U@W`\@n@~ABAD`\@n@~ABAD`\@n@~ABAD`\@n@~ABADaIA[AkAoAqaIA[AkAoAqaIA[AkAoAqaIA[AkAoAqcaBcBuCECICKcPcdAvBHBXB\B^avBHBXB\B^avBHBXB\B^avBHBXB\B^cqBcBuCECICKcPCbctBcBuCECICKbcBuCECICKcPCbCrcxCPCbCrCvcz?C?U?e?i?k?p@B@R@V@X@]@oA?ACAE_C?U?e?i?kAJA\AlApArAwBIBYB]B__C?U?e?i?kBdBvCFCJCL_C?U?e?i?kCQCcCsCwCy_C?U?e?i?k_p@B@R@V@X_p@B@R@V@X_p@B@R@V@X_p@B@R@V@X`]@oA?ACAE`]@oA?ACAE`]@oA?ACAE`]@oA?ACAEaJA\AlApAraJA\AlApAraJA\AlApAraJA\AlApArdNBdBvCFCJCLcQCcCsCwCyc~awBIBYB]B_awBIBYB]B_awBIBYB]B_awBIBYB]B_d^BdBvCFCJCLcQCcCsCwCyc~DPbdBvCFCJCLbdBvCFCJCLcQCcCsCwCyc~DPD`cQCcCsCwCyc~DPD`Dd_A?P?Z?[?`?n?}@G@H@M@[@j@t@u@z_A?P?Z?[?`AHAWAaAbAgAuBDBNBOBT_A?P?Z?[?`BbBqB{B|CA_A?P?Z?[?`COC^ChCiCn_A?P?Z?[?`C|DKDUDVD[_n?}@G@H@M_n?}@G@H@M_n?}@G@H@M_n?}@G@H@M`[@j@t@u@z`[@j@t@u@z`[@j@t@u@z`[@j@t@u@zaHAWAaAbAgaHAWAaAbAgaHAWAaAbAgaHAWAaAbAgdid{BbBqB{B|CAcOC^ChCiCnc|DKDUDVD[auBDBNBOBTauBDBNBOBTauBDBNBOBTauBDBNBOBTdiDxdiDxEBeHDiDxEBECeKBbBqB{B|CAcOC^ChCiCnc|DKDUDVD[bbBqB{B|CAbbBqB{B|CAcOC^ChCiCnc|DKDUDVD[cOC^ChCiCnc|DKDUDVD[_C?R?]?_?b?p@?@J@L@O@]@l@w@y@|_C?R?]?_?bAJAYAdAfAiAwBFBQBSBV_C?R?]?_?bBdBsB~C@CCDkDzEEEGEJ_C?R?]?_?bCQC`CkCmCp_C?R?]?_?bC~DMDXDZD]_p@?@J@L@O_p@?@J@L@O_p@?@J@L@O_p@?@J@L@O`]@l@w@y@|`]@l@w@y@|`]@l@w@y@|`]@l@w@y@|aJAYAdAfAiaJAYAdAfAiaJAYAdAfAiaJAYAdAfAidkDzEEEGEJegEXbdBsB~C@CCcQC`CkCmCpc~DMDXDZD]awBFBQBSBVawBFBQBSBVawBFBQBSBVawBFBQBSBVdkDzEEEGEJdkDzEEEGEJerEXEgetEXEgErdkDzEEEGEJewEXEgErEtbdBsB~C@CCcQC`CkCmCpc~DMDXDZD]bdBsB~C@CCbdBsB~C@CCcQC`CkCmCpc~DMDXDZD]cQC`CkCmCpc~DMDXDZD]_B?Q?\?^?a?o?~@I@K@N@\@k@v@x@{_B?Q?\?^?aAIAXAcAeAhAvBEBPBRBU_B?Q?\?^?aBcBrB}C?CBDjDyEDEFEI_B?Q?\?^?aCPC_CjClCo_B?Q?\?^?aC}DLDWDYD\EWEfEqEsEv_o?~@I@K@N_o?~@I@K@N_o?~@I@K@N_o?~@I@K@N`\@k@v@x@{`\@k@v@x@{`\@k@v@x@{`\@k@v@x@{aIAXAcAeAhaIAXAcAeAhaIAXAcAeAhaIAXAcAeAhdjDyEDEFEIfDeWEfEqEsEvbcBrB}C?CBcPC_CjClCoc}DLDWDYD\avBEBPBRBUavBEBPBRBUavBEBPBRBUavBEBPBRBUdjDyEDEFEIdjDyEDEFEIfDFSeWEfEqEsEvfDFSF^eWEfEqEsEvdjDyEDEFEIfDFSF^F`eWEfEqEsEvbcBrB}C?CBcPC_CjClCoc}DLDWDYD\bcBrB}C?CBbcBrB}C?CBcPC_CjClCoc}DLDWDYD\cPC_CjClCoc}DLDWDYD\_D?L?P?Q?R?q?y?}?~@?@^@f@j@k@l_D?L?P?Q?RAKASAWAXAYAxB@BDBEBF_D?L?P?Q?RBeBmBqBrBsDlDtDxDyDz_D?L?P?Q?RCRCZC^C_C`FFFNFRFSFT_D?L?P?Q?RD?DGDKDLDMEYEaEeEfEg_q?y?}?~@?_q?y?}?~@?_q?y?}?~@?_q?y?}?~@?`^@f@j@k@l`^@f@j@k@l`^@f@j@k@l`^@f@j@k@laKASAWAXAYFsaKASAWAXAYaKASAWAXAYaKASAWAXAYdlDtDxDyDzFsF{fFFNFRFSFTFsF{G?eYEaEeEfEgFsF{G?G@beBmBqBrBscRCZC^C_C`d?DGDKDLDMaxB@BDBEBFaxB@BDBEBFaxB@BDBEBFaxB@BDBEBFdlDtDxDyDzdlDtDxDyDzfFFNFRFSFTeYEaEeEfEgfFFNFRFSFTeYEaEeEfEgdlDtDxDyDzfFFNFRFSFTeYEaEeEfEgbeBmBqBrBscRCZC^C_C`d?DGDKDLDMbeBmBqBrBsbeBmBqBrBscRCZC^C_C`d?DGDKDLDMcRCZC^C_C`d?DGDKDLDM_D?V?c?d?e?q@C@P@Q@R@^@p@}@~A?_D?V?c?d?eAKA]AjAkAlAxBJBWBXBY_D?V?c?d?eBeBwCDCECFDlD~EKELEM_D?V?c?d?eCRCdCqCrCsFFFXFeFfFg_D?V?c?d?eD?DQD^D_D`EYEkExEyEz_q@C@P@Q@RFsGEGRGSGT_q@C@P@Q@R_q@C@P@Q@R_q@C@P@Q@R`^@p@}@~A?`^@p@}@~A?`^@p@}@~A?`^@p@}@~A?aKA]AjAkAlFsGEGRGSGTaKA]AjAkAlaKA]AjAkAlaKA]AjAkAldlD~EKELEMFsGEGRGSGTfFFXFeFfFgFsGEGRGSGTeYEkExEyEzFsGEGRGSGTbeBwCDCECFcRCdCqCrCsd?DQD^D_D`axBJBWBXBYG`axBJBWBXBYaxBJBWBXBYaxBJBWBXBYdlD~EKELEMdlD~EKELEMfFFXFeFfFgeYEkExEyEzfFFXFeFfFgeYEkExEyEzdlD~EKELEMfFFXFeFfFgeYEkExEyEzbeBwCDCECFG`GrcRCdCqCrCsG`GrH?d?DQD^D_D`G`GrH?H@beBwCDCECFbeBwCDCECFcRCdCqCrCsd?DQD^D_D`cRCdCqCrCsd?DQD^D_D`_G?O?a?g?k?t?|@N@T@X@a@i@{AAAE_G?O?a?g?kANAVAhAnArA{BCBUB[B__G?O?a?g?kBhBpCBCHCLDoDwEIEOES_G?O?a?g?kCUC]CoCuCyFIFQFcFiFm_G?O?a?g?kDBDJD\DbDfE\EdEvE|F@_t?|@N@T@XFvF~GPGVGZGcGkG}HCHG_t?|@N@T@X_t?|@N@T@X_t?|@N@T@X`a@i@{AAAE`a@i@{AAAE`a@i@{AAAE`a@i@{AAAEaNAVAhAnArFvF~GPGVGZaNAVAhAnAraNAVAhAnAraNAVAhAnArHPdoDwEIEOESFvF~GPGVGZfIFQFcFiFmFvF~GPGVGZe\EdEvE|F@FvF~GPGVGZbhBpCBCHCLcUC]CoCuCydBDJD\DbDfa{BCBUB[B_GcGkG}HCHGa{BCBUB[B_a{BCBUB[B_a{BCBUB[B_doDwEIEOESdoDwEIEOESfIFQFcFiFme\EdEvE|F@fIFQFcFiFme\EdEvE|F@doDwEIEOESfIFQFcFiFmHPHXe\EdEvE|F@bhBpCBCHCLGcGkG}HCHGcUC]CoCuCyGcGkG}HCHGdBDJD\DbDfGcGkG}HCHGbhBpCBCHCLbhBpCBCHCLHPHXHjcUC]CoCuCydBDJD\DbDfcUC]CoCuCydBDJD\DbDfHPHXHjHp_F?N?b?f?j?s?{@O@S@W@`@h@|A@AD_F?N?b?f?jAMAUAiAmAqAzBBBVBZB^_F?N?b?f?jBgBoCCCGCKDnDvEJENER_F?N?b?f?jCTC\CpCtCxFHFPFdFhFl_F?N?b?f?jDADID]DaDeE[EcEwE{F?_s?{@O@S@WFuF}GQGUGYGbGjG~HBHF_s?{@O@S@W_s?{@O@S@W_s?{@O@S@WHOHWHkHoHs``@h@|A@AD``@h@|A@AD``@h@|A@AD``@h@|A@ADaMAUAiAmAqFuF}GQGUGYaMAUAiAmAqaMAUAiAmAqH|aMAUAiAmAqHOHWHkHoHsdnDvEJENERFuF}GQGUGYfHFPFdFhFlFuF}GQGUGYe[EcEwE{F?FuF}GQGUGYbgBoCCCGCKcTC\CpCtCxdADID]DaDeazBBBVBZB^GbGjG~HBHFazBBBVBZB^azBBBVBZB^azBBBVBZB^dnDvEJENERdnDvEJENERfHFPFdFhFle[EcEwE{F?fHFPFdFhFle[EcEwE{F?dnDvEJENERfHFPFdFhFlHOHWHkHoHse[EcEwE{F?H|IDbgBoCCCGCKGbGjG~HBHFcTC\CpCtCxGbGjG~HBHFdADID]DaDeGbGjG~HBHFbgBoCCCGCKH|IDIXbgBoCCCGCKHOHWHkHoHscTC\CpCtCxdADID]DaDecTC\CpCtCxH|IDIXI\dADID]DaDeHOHWHkHoHs_E?M?`?h?i?r?z@M@U@V@_@g@zABAC_E?M?`?h?iALATAgAoApAyBABTB\B]_E?M?`?h?iBfBnCACICJDmDuEHEPEQ_E?M?`?h?iCSC[CnCvCwFGFOFbFjFk_E?M?`?h?iD@DHD[DcDdEZEbEuE}E~_r?z@M@U@VFtF|GOGWGXGaGiG|HDHE_r?z@M@U@V_r?z@M@U@VH{ICIVI^I__r?z@M@U@VHNHVHiHqHr`_@g@zABAC`_@g@zABAC`_@g@zABAC`_@g@zABACaLATAgAoApFtF|GOGWGXaLATAgAoApIhaLATAgAoApH{ICIVI^I_aLATAgAoApHNHVHiHqHrdmDuEHEPEQFtF|GOGWGXfGFOFbFjFkFtF|GOGWGXeZEbEuE}E~FtF|GOGWGXbfBnCACICJcSC[CnCvCwd@DHD[DcDdayBABTB\B]GaGiG|HDHEayBABTB\B]ayBABTB\B]ayBABTB\B]dmDuEHEPEQdmDuEHEPEQfGFOFbFjFkeZEbEuE}E~fGFOFbFjFkeZEbEuE}E~dmDuEHEPEQIhIpfGFOFbFjFkHNHVHiHqHreZEbEuE}E~H{ICIVI^I_bfBnCACICJGaGiG|HDHEcSC[CnCvCwGaGiG|HDHEd@DHD[DcDdGaGiG|HDHEbfBnCACICJH{ICIVI^I_bfBnCACICJHNHVHiHqHrcSC[CnCvCwIhIpJCd@DHD[DcDdIhIpJCJKcSC[CnCvCwH{ICIVI^I_d@DHD[DcDdHNHVHiHqHr_E?S?W?\?]?r@@@D@I@J@_@m@q@v@w_E?S?W?\?]ALAZA^AcAdAyBGBKBPBQ_E?S?W?\?]BfBtBxB}B~DmD{E?EDEE_E?S?W?\?]CSCaCeCjCkFGFUFYF^F__E?S?W?\?]D@DNDRDWDXEZEhElEqEr_r@@@D@I@JFtGBGFGKGLGaGoGsGxGy_r@@@D@I@JIhIvIzJ?J@_r@@@D@I@JH{IIIMIRIS_r@@@D@I@JHNH\H`HeHf`_@m@q@v@w`_@m@q@v@w`_@m@q@v@w`_@m@q@v@waLAZA^AcAdFtGBGFGKGLaLAZA^AcAdIhIvIzJ?J@aLAZA^AcAdH{IIIMIRISaLAZA^AcAdHNH\H`HeHfdmD{E?EDEEFtGBGFGKGLfGFUFYF^F_FtGBGFGKGLeZEhElEqErFtGBGFGKGLbfBtBxB}B~JUcSCaCeCjCkd@DNDRDWDXayBGBKBPBQGaGoGsGxGyayBGBKBPBQJUJcayBGBKBPBQayBGBKBPBQdmD{E?EDEEdmD{E?EDEEfGFUFYF^F_JUJcJgeZEhElEqErJUJcJgJlfGFUFYF^F_eZEhElEqErdmD{E?EDEEIhIvIzJ?J@fGFUFYF^F_HNH\H`HeHfeZEhElEqErH{IIIMIRISbfBtBxB}B~GaGoGsGxGycSCaCeCjCkGaGoGsGxGyd@DNDRDWDXGaGoGsGxGybfBtBxB}B~H{IIIMIRISbfBtBxB}B~HNH\H`HeHfcSCaCeCjCkIhIvIzJ?J@d@DNDRDWDXIhIvIzJ?J@cSCaCeCjCkH{IIIMIRISd@DNDRDWDXHNH\H`HeHf_F?U?Y?[?^?s@B@F@H@K@`@o@s@u@x_F?U?Y?[?^AMA\A`AbAeAzBIBMBOBR_F?U?Y?[?^BgBvBzB|C?DnD}EAECEF_F?U?Y?[?^CTCcCgCiClFHFWF[F]F`_F?U?Y?[?^DADPDTDVDYE[EjEnEpEs_s@B@F@H@KFuGDGHGJGMGbGqGuGwGz_s@B@F@H@KIiIxI|I~JAJVJeJiJkJn_s@B@F@H@KH|IKIOIQIT_s@B@F@H@KHOH^HbHdHg``@o@s@u@x``@o@s@u@x``@o@s@u@x``@o@s@u@xaMA\A`AbAeFuGDGHGJGMaMA\A`AbAeIiIxI|I~JAaMA\A`AbAeH|IKIOIQITaMA\A`AbAeHOH^HbHdHgdnD}EAECEFFuGDGHGJGMfHFWF[F]F`FuGDGHGJGMe[EjEnEpEsFuGDGHGJGMbgBvBzB|C?JVJeJiJkJncTCcCgCiCldADPDTDVDYKCazBIBMBOBRGbGqGuGwGzazBIBMBOBRJVJeJiJkJnazBIBMBOBRazBIBMBOBRKCKRdnD}EAECEFdnD}EAECEFKCKRKVfHFWF[F]F`JVJeJiJkJne[EjEnEpEsJVJeJiJkJnfHFWF[F]F`KCKRKVKXe[EjEnEpEsdnD}EAECEFIiIxI|I~JAfHFWF[F]F`HOH^HbHdHge[EjEnEpEsH|IKIOIQITbgBvBzB|C?GbGqGuGwGzcTCcCgCiClGbGqGuGwGzdADPDTDVDYGbGqGuGwGzbgBvBzB|C?H|IKIOIQITbgBvBzB|C?HOH^HbHdHgcTCcCgCiClIiIxI|I~JAdADPDTDVDYIiIxI|I~JAcTCcCgCiClH|IKIOIQITdADPDTDVDYHOH^HbHdHg_G?T?X?Z?_?t@A@E@G@L@a@n@r@t@y_G?T?X?Z?_ANA[A_AaAfA{BHBLBNBS_G?T?X?Z?_BhBuByB{C@DoD|E@EBEG_G?T?X?Z?_CUCbCfChCmFIFVFZF\Fa_G?T?X?Z?_DBDODSDUDZE\EiEmEoEt_t@A@E@G@LFvGCGGGIGNGcGpGtGvG{_t@A@E@G@LIjIwI{I}JBJWJdJhJjJo_t@A@E@G@LH}IJINIPIUKDKQKUKWK\_t@A@E@G@LHPH]HaHcHh`a@n@r@t@y`a@n@r@t@y`a@n@r@t@y`a@n@r@t@yaNA[A_AaAfFvGCGGGIGNaNA[A_AaAfIjIwI{I}JBaNA[A_AaAfH}IJINIPIUaNA[A_AaAfHPH]HaHcHhdoD|E@EBEGFvGCGGGIGNfIFVFZF\FaFvGCGGGIGNe\EiEmEoEtFvGCGGGIGNbhBuByB{C@JWJdJhJjJocUCbCfChCmKqdBDODSDUDZKDKQKUKWK\a{BHBLBNBSGcGpGtGvG{a{BHBLBNBSJWJdJhJjJoa{BHBLBNBSKqK~a{BHBLBNBSKDKQKUKWK\doD|E@EBEGKqK~LBdoD|E@EBEGKDKQKUKWK\fIFVFZF\FaJWJdJhJjJoe\EiEmEoEtJWJdJhJjJofIFVFZF\FaKDKQKUKWK\e\EiEmEoEtKqK~LBLDdoD|E@EBEGIjIwI{I}JBfIFVFZF\FaHPH]HaHcHhe\EiEmEoEtH}IJINIPIUbhBuByB{C@GcGpGtGvG{cUCbCfChCmGcGpGtGvG{dBDODSDUDZGcGpGtGvG{bhBuByB{C@H}IJINIPIUbhBuByB{C@HPH]HaHcHhcUCbCfChCmIjIwI{I}JBdBDODSDUDZIjIwI{I}JBcUCbCfChCmH}IJINIPIUdBDODSDUDZHPH]HaHcHh_H?L?S?T?U?u?y@@@A@B@b@f@m@n@o_H?L?S?T?UAOASAZA[A\A|B@BGBHBI_H?L?S?T?UBiBmBtBuBvDpDtD{D|D}_H?L?S?T?UCVCZCaCbCcFJFNFUFVFW_H?L?S?T?UDCDGDNDODPE]EaEhEiEj_u?y@@@A@BFwF{GBGCGDGdGhGoGpGq_u?y@@@A@BIkIoIvIwIxJXJ\JcJdJe_u?y@@@A@BH~IBIIIJIKKEKIKPKQKR_u?y@@@A@BHQHUH\H]H^KrKvK}K~L?`b@f@m@n@o`b@f@m@n@o`b@f@m@n@o`b@f@m@n@oaOASAZA[A\FwF{GBGCGDL_aOASAZA[A\IkIoIvIwIxaOASAZA[A\H~IBIIIJIKaOASAZA[A\HQHUH\H]H^dpDtD{D|D}FwF{GBGCGDfJFNFUFVFWFwF{GBGCGDe]EaEhEiEjFwF{GBGCGDbiBmBtBuBvJXJ\JcJdJeL_LccVCZCaCbCcKrKvK}K~L?L_LcLjdCDGDNDODPKEKIKPKQKRL_LcLjLka|B@BGBHBIGdGhGoGpGqa|B@BGBHBIJXJ\JcJdJea|B@BGBHBIKrKvK}K~L?a|B@BGBHBIKEKIKPKQKRdpDtD{D|D}KrKvK}K~L?dpDtD{D|D}KEKIKPKQKRfJFNFUFVFWJXJ\JcJdJee]EaEhEiEjJXJ\JcJdJefJFNFUFVFWKEKIKPKQKRe]EaEhEiEjKrKvK}K~L?dpDtD{D|D}IkIoIvIwIxfJFNFUFVFWHQHUH\H]H^e]EaEhEiEjH~IBIIIJIKbiBmBtBuBvGdGhGoGpGqcVCZCaCbCcGdGhGoGpGqdCDGDNDODPGdGhGoGpGqbiBmBtBuBvH~IBIIIJIKbiBmBtBuBvHQHUH\H]H^cVCZCaCbCcIkIoIvIwIxdCDGDNDODPIkIoIvIwIxcVCZCaCbCcH~IBIIIJIKdCDGDNDODPHQHUH\H]H^_H?V?`?a?b?u@C@M@N@O@b@p@z@{@|_H?V?`?a?bAOA]AgAhAiA|BJBTBUBV_H?V?`?a?bBiBwCACBCCDpD~EHEIEJ_H?V?`?a?bCVCdCnCoCpFJFXFbFcFd_H?V?`?a?bDCDQD[D\D]E]EkEuEvEw_u@C@M@N@OFwGEGOGPGQGdGrG|G}G~_u@C@M@N@OIkIyJCJDJEJXJfJpJqJr_u@C@M@N@OH~ILIVIWIXKEKSK]K^K__u@C@M@N@OHQH_HiHjHkKrL@LJLKLL`b@p@z@{@|L_LmLwLxLy`b@p@z@{@|`b@p@z@{@|`b@p@z@{@|aOA]AgAhAiFwGEGOGPGQL_LmLwLxLyaOA]AgAhAiIkIyJCJDJEaOA]AgAhAiH~ILIVIWIXaOA]AgAhAiHQH_HiHjHkdpD~EHEIEJFwGEGOGPGQfJFXFbFcFdFwGEGOGPGQe]EkEuEvEwFwGEGOGPGQbiBwCACBCCJXJfJpJqJrL_LmLwLxLycVCdCnCoCpKrL@LJLKLLL_LmLwLxLydCDQD[D\D]KEKSK]K^K_L_LmLwLxLya|BJBTBUBVGdGrG|G}G~MLa|BJBTBUBVJXJfJpJqJra|BJBTBUBVKrL@LJLKLLa|BJBTBUBVKEKSK]K^K_dpD~EHEIEJKrL@LJLKLLdpD~EHEIEJKEKSK]K^K_fJFXFbFcFdJXJfJpJqJre]EkEuEvEwJXJfJpJqJrfJFXFbFcFdKEKSK]K^K_e]EkEuEvEwKrL@LJLKLLdpD~EHEIEJIkIyJCJDJEMLMZfJFXFbFcFdHQH_HiHjHkMLMZMde]EkEuEvEwH~ILIVIWIXMLMZMdMebiBwCACBCCGdGrG|G}G~cVCdCnCoCpGdGrG|G}G~dCDQD[D\D]GdGrG|G}G~biBwCACBCCH~ILIVIWIXbiBwCACBCCHQH_HiHjHkcVCdCnCoCpIkIyJCJDJEdCDQD[D\D]IkIyJCJDJEcVCdCnCoCpH~ILIVIWIXdCDQD[D\D]HQH_HiHjHk_I?M?^?_?c?v?z@K@L@P@c@g@x@y@}_I?M?^?_?cAPATAeAfAjA}BABRBSBW_I?M?^?_?cBjBnC?C@CDDqDuEFEGEK_I?M?^?_?cCWC[ClCmCqFKFOF`FaFe_I?M?^?_?cDDDHDYDZD^E^EbEsEtEx_v?z@K@L@PFxF|GMGNGRGeGiGzG{H?_v?z@K@L@PIlIpJAJBJFJYJ]JnJoJs_v?z@K@L@PI?ICITIUIYKFKJK[K\K`_v?z@K@L@PHRHVHgHhHlKsKwLHLILM`c@g@x@y@}L`LdLuLvLzMMMQMbMcMg`c@g@x@y@}`c@g@x@y@}`c@g@x@y@}aPATAeAfAjFxF|GMGNGRL`LdLuLvLzaPATAeAfAjIlIpJAJBJFMzaPATAeAfAjI?ICITIUIYaPATAeAfAjHRHVHgHhHldqDuEFEGEKFxF|GMGNGRfKFOF`FaFeFxF|GMGNGRe^EbEsEtExFxF|GMGNGRbjBnC?C@CDJYJ]JnJoJsL`LdLuLvLzcWC[ClCmCqKsKwLHLILML`LdLuLvLzdDDHDYDZD^KFKJK[K\K`L`LdLuLvLza}BABRBSBWGeGiGzG{H?MMMQMbMcMga}BABRBSBWJYJ]JnJoJsa}BABRBSBWKsKwLHLILMa}BABRBSBWKFKJK[K\K`dqDuEFEGEKKsKwLHLILMdqDuEFEGEKKFKJK[K\K`fKFOF`FaFeJYJ]JnJoJse^EbEsEtExJYJ]JnJoJsfKFOF`FaFeKFKJK[K\K`MzM~e^EbEsEtExKsKwLHLILMMzM~NOdqDuEFEGEKIlIpJAJBJFMMMQMbMcMgfKFOF`FaFeHRHVHgHhHlMMMQMbMcMge^EbEsEtExI?ICITIUIYMMMQMbMcMgbjBnC?C@CDGeGiGzG{H?MzM~NONPcWC[ClCmCqGeGiGzG{H?dDDHDYDZD^GeGiGzG{H?bjBnC?C@CDI?ICITIUIYbjBnC?C@CDHRHVHgHhHlcWC[ClCmCqIlIpJAJBJFdDDHDYDZD^IlIpJAJBJFcWC[ClCmCqI?ICITIUIYdDDHDYDZD^HRHVHgHhHl_K?N?Z?\?e?x?{@G@I@R@e@h@t@vA?_K?N?Z?\?eARAUAaAcAlB?BBBNBPBY_K?N?Z?\?eBlBoB{B}CFDsDvEBEDEM_K?N?Z?\?eCYC\ChCjCsFMFPF\F^Fg_K?N?Z?\?eDFDIDUDWD`E`EcEoEqEz_x?{@G@I@RFzF}GIGKGTGgGjGvGxHA_x?{@G@I@RInIqI}J?JHJ[J^JjJlJu_x?{@G@I@RIAIDIPIRI[KHKKKWKYKb_x?{@G@I@RHTHWHcHeHnKuKxLDLFLO`e@h@t@vA?LbLeLqLsL|MOMRM^M`Mi`e@h@t@vA?M|N?NKNMNV`e@h@t@vA?`e@h@t@vA?aRAUAaAcAlFzF}GIGKGTLbLeLqLsL|aRAUAaAcAlInIqI}J?JHM|N?NKNMNVaRAUAaAcAlIAIDIPIRI[NiaRAUAaAcAlHTHWHcHeHndsDvEBEDEMFzF}GIGKGTfMFPF\F^FgFzF}GIGKGTe`EcEoEqEzFzF}GIGKGTblBoB{B}CFJ[J^JjJlJuLbLeLqLsL|cYC\ChCjCsKuKxLDLFLOLbLeLqLsL|dFDIDUDWD`KHKKKWKYKbLbLeLqLsL|b?BBBNBPBYGgGjGvGxHAMOMRM^M`Mib?BBBNBPBYJ[J^JjJlJub?BBBNBPBYKuKxLDLFLOb?BBBNBPBYKHKKKWKYKbdsDvEBEDEMKuKxLDLFLONiNldsDvEBEDEMKHKKKWKYKbfMFPF\F^FgJ[J^JjJlJuNiNlNxe`EcEoEqEzJ[J^JjJlJufMFPF\F^FgKHKKKWKYKbM|N?NKNMNVe`EcEoEqEzKuKxLDLFLOM|N?NKNMNVdsDvEBEDEMInIqI}J?JHMOMRM^M`MifMFPF\F^FgHTHWHcHeHnMOMRM^M`Mie`EcEoEqEzIAIDIPIRI[MOMRM^M`MiblBoB{B}CFGgGjGvGxHAM|N?NKNMNVcYC\ChCjCsGgGjGvGxHAdFDIDUDWD`GgGjGvGxHANiNlNxNzblBoB{B}CFIAIDIPIRI[blBoB{B}CFHTHWHcHeHncYC\ChCjCsInIqI}J?JHdFDIDUDWD`InIqI}J?JHcYC\ChCjCsIAIDIPIRI[dFDIDUDWD`HTHWHcHeHn_J?O?[?]?d?w?|@H@J@Q@d@i@u@w@~_J?O?[?]?dAQAVAbAdAkA~BCBOBQBX_J?O?[?]?dBkBpB|B~CEDrDwECEEEL_J?O?[?]?dCXC]CiCkCrFLFQF]F_Ff_J?O?[?]?dDEDJDVDXD_E_EdEpErEy_w?|@H@J@QFyF~GJGLGSGfGkGwGyH@_w?|@H@J@QImIrI~J@JGJZJ_JkJmJt_w?|@H@J@QI@IEIQISIZKGKLKXKZKa_w?|@H@J@QHSHXHdHfHmKtKyLELGLN`d@i@u@w@~LaLfLrLtL{MNMSM_MaMh`d@i@u@w@~M{N@NLNNNU`d@i@u@w@~`d@i@u@w@~NhNmNyN{OBaQAVAbAdAkFyF~GJGLGSLaLfLrLtL{aQAVAbAdAkImIrI~J@JGM{N@NLNNNUaQAVAbAdAkI@IEIQISIZNhNmNyN{OBaQAVAbAdAkHSHXHdHfHmOUdrDwECEEELFyF~GJGLGSfLFQF]F_FfFyF~GJGLGSe_EdEpErEyFyF~GJGLGSbkBpB|B~CEJZJ_JkJmJtLaLfLrLtL{cXC]CiCkCrKtKyLELGLNLaLfLrLtL{dEDJDVDXD_KGKLKXKZKaLaLfLrLtL{a~BCBOBQBXGfGkGwGyH@MNMSM_MaMha~BCBOBQBXJZJ_JkJmJta~BCBOBQBXKtKyLELGLNa~BCBOBQBXKGKLKXKZKadrDwECEEELKtKyLELGLNNhNmNyN{OBdrDwECEEELKGKLKXKZKaOUOZfLFQF]F_FfJZJ_JkJmJtNhNmNyN{OBe_EdEpErEyJZJ_JkJmJtOUOZOffLFQF]F_FfKGKLKXKZKaM{N@NLNNNUe_EdEpErEyKtKyLELGLNM{N@NLNNNUdrDwECEEELImIrI~J@JGMNMSM_MaMhfLFQF]F_FfHSHXHdHfHmMNMSM_MaMhe_EdEpErEyI@IEIQISIZMNMSM_MaMhbkBpB|B~CEGfGkGwGyH@M{N@NLNNNUcXC]CiCkCrGfGkGwGyH@OUOZOfOhdEDJDVDXD_GfGkGwGyH@NhNmNyN{OBbkBpB|B~CEI@IEIQISIZbkBpB|B~CEHSHXHdHfHmcXC]CiCkCrImIrI~J@JGdEDJDVDXD_ImIrI~J@JGcXC]CiCkCrI@IEIQISIZdEDJDVDXD_HSHXHdHfHm_J?Q?X?f?i?w?~@E@S@V@d@k@rA@AC_J?Q?X?f?iAQAXA_AmApA~BEBLBZB]_J?Q?X?f?iBkBrByCGCJDrDyE@ENEQ_J?Q?X?f?iCXC_CfCtCwFLFSFZFhFk_J?Q?X?f?iDEDLDSDaDdE_EfEmE{E~_w?~@E@S@VFyG@GGGUGXGfGmGtHBHE_w?~@E@S@VImItI{JIJLJZJaJhJvJy_w?~@E@S@VI@IGINI\I_KGKNKUKcKf_w?~@E@S@VHSHZHaHoHrKtK{LBLPLS`d@k@rA@ACLaLhLoL}M@MNMUM\MjMm`d@k@rA@ACM{NBNINWNZ`d@k@rA@ACOUO\OcOqOt`d@k@rA@ACNhNoNvODOGaQAXA_AmApFyG@GGGUGXLaLhLoL}M@aQAXA_AmApImItI{JIJLM{NBNINWNZaQAXA_AmApI@IGINI\I_NhNoNvODOGaQAXA_AmApHSHZHaHoHrOUO\OcOqOtdrDyE@ENEQFyG@GGGUGXfLFSFZFhFkFyG@GGGUGXPBe_EfEmE{E~FyG@GGGUGXbkBrByCGCJJZJaJhJvJyLaLhLoL}M@cXC_CfCtCwKtK{LBLPLSLaLhLoL}M@dEDLDSDaDdKGKNKUKcKfLaLhLoL}M@a~BEBLBZB]GfGmGtHBHEMNMUM\MjMma~BEBLBZB]JZJaJhJvJya~BEBLBZB]KtK{LBLPLSPBPIa~BEBLBZB]KGKNKUKcKfdrDyE@ENEQKtK{LBLPLSNhNoNvODOGdrDyE@ENEQKGKNKUKcKfOUO\OcOqOtfLFSFZFhFkJZJaJhJvJyNhNoNvODOGe_EfEmE{E~JZJaJhJvJyOUO\OcOqOtfLFSFZFhFkKGKNKUKcKfM{NBNINWNZe_EfEmE{E~KtK{LBLPLSM{NBNINWNZdrDyE@ENEQImItI{JIJLMNMUM\MjMmfLFSFZFhFkHSHZHaHoHrMNMUM\MjMme_EfEmE{E~I@IGINI\I_MNMUM\MjMmbkBrByCGCJGfGmGtHBHEM{NBNINWNZcXC_CfCtCwGfGmGtHBHEOUO\OcOqOtdEDLDSDaDdGfGmGtHBHENhNoNvODOGbkBrByCGCJI@IGINI\I_PBPIPPbkBrByCGCJHSHZHaHoHrcXC_CfCtCwImItI{JIJLdEDLDSDaDdImItI{JIJLPBPIPPP^cXC_CfCtCwI@IGINI\I_dEDLDSDaDdHSHZHaHoHr_K?R?Y?g?h?x@?@F@T@U@e@l@sAAAB_K?R?Y?g?hARAYA`AnAoB?BFBMB[B\_K?R?Y?g?hBlBsBzCHCIDsDzEAEOEP_K?R?Y?g?hCYC`CgCuCvFMFTF[FiFj_K?R?Y?g?hDFDMDTDbDcE`EgEnE|E}_x@?@F@T@UFzGAGHGVGWGgGnGuHCHD_x@?@F@T@UInIuI|JJJKJ[JbJiJwJx_x@?@F@T@UIAIHIOI]I^KHKOKVKdKe_x@?@F@T@UHTH[HbHpHqKuK|LCLQLR`e@l@sAAABLbLiLpL~M?MOMVM]MkMl`e@l@sAAABM|NCNJNXNY`e@l@sAAABOVO]OdOrOsPCPJPQP_P``e@l@sAAABNiNpNwOEOFaRAYA`AnAoFzGAGHGVGWLbLiLpL~M?aRAYA`AnAoInIuI|JJJKM|NCNJNXNYaRAYA`AnAoIAIHIOI]I^NiNpNwOEOFaRAYA`AnAoHTH[HbHpHqOVO]OdOrOsdsDzEAEOEPFzGAGHGVGWfMFTF[FiFjFzGAGHGVGWPCPJPQP_P`e`EgEnE|E}FzGAGHGVGWPpblBsBzCHCIJ[JbJiJwJxLbLiLpL~M?cYC`CgCuCvKuK|LCLQLRLbLiLpL~M?dFDMDTDbDcKHKOKVKdKeLbLiLpL~M?b?BFBMB[B\GgGnGuHCHDMOMVM]MkMlb?BFBMB[B\J[JbJiJwJxb?BFBMB[B\KuK|LCLQLRPCPJPQP_P`b?BFBMB[B\KHKOKVKdKePpPwdsDzEAEOEPKuK|LCLQLRNiNpNwOEOFdsDzEAEOEPKHKOKVKdKeOVO]OdOrOsfMFTF[FiFjJ[JbJiJwJxNiNpNwOEOFe`EgEnE|E}J[JbJiJwJxOVO]OdOrOsfMFTF[FiFjKHKOKVKdKeM|NCNJNXNYe`EgEnE|E}KuK|LCLQLRM|NCNJNXNYdsDzEAEOEPInIuI|JJJKMOMVM]MkMlfMFTF[FiFjHTH[HbHpHqMOMVM]MkMle`EgEnE|E}IAIHIOI]I^MOMVM]MkMlblBsBzCHCIGgGnGuHCHDM|NCNJNXNYcYC`CgCuCvGgGnGuHCHDOVO]OdOrOsdFDMDTDbDcGgGnGuHCHDNiNpNwOEOFblBsBzCHCIIAIHIOI]I^PCPJPQP_P`blBsBzCHCIHTH[HbHpHqPpPwP~cYC`CgCuCvInIuI|JJJKPpPwP~QLdFDMDTDbDcInIuI|JJJKPCPJPQP_P`cYC`CgCuCvIAIHIOI]I^dFDMDTDbDcHTH[HbHpHq_I?P?W?j?k?v?}@D@W@X@c@j@qADAE_I?P?W?j?kAPAWA^AqArA}BDBKB^B__I?P?W?j?kBjBqBxCKCLDqDxE?ERES_I?P?W?j?kCWC^CeCxCyFKFRFYFlFm_I?P?W?j?kDDDKDRDeDfE^EeElF?F@_v?}@D@W@XFxG?GFGYGZGeGlGsHFHG_v?}@D@W@XIlIsIzJMJNJYJ`JgJzJ{_v?}@D@W@XI?IFIMI`IaKFKMKTKgKh_v?}@D@W@XHRHYH`HsHtKsKzLALTLU`c@j@qADAEL`LgLnMAMBMMMTM[MnMo`c@j@qADAEMzNANHN[N\`c@j@qADAEOTO[ObOuOvPAPHPOPbPc`c@j@qADAENgNnNuOHOIPnPuP|QOQPaPAWA^AqArFxG?GFGYGZL`LgLnMAMBaPAWA^AqArIlIsIzJMJNMzNANHN[N\aPAWA^AqArI?IFIMI`IaNgNnNuOHOIaPAWA^AqArHRHYH`HsHtOTO[ObOuOvdqDxE?ERESFxG?GFGYGZQ[fKFRFYFlFmFxG?GFGYGZPAPHPOPbPce^EeElF?F@FxG?GFGYGZPnPuP|QOQPbjBqBxCKCLJYJ`JgJzJ{L`LgLnMAMBcWC^CeCxCyKsKzLALTLUL`LgLnMAMBdDDKDRDeDfKFKMKTKgKhL`LgLnMAMBa}BDBKB^B_GeGlGsHFHGMMMTM[MnMoa}BDBKB^B_JYJ`JgJzJ{Q[Qba}BDBKB^B_KsKzLALTLUPAPHPOPbPca}BDBKB^B_KFKMKTKgKhPnPuP|QOQPdqDxE?ERESKsKzLALTLUNgNnNuOHOIdqDxE?ERESKFKMKTKgKhOTO[ObOuOvfKFRFYFlFmJYJ`JgJzJ{NgNnNuOHOIe^EeElF?F@JYJ`JgJzJ{OTO[ObOuOvfKFRFYFlFmKFKMKTKgKhMzNANHN[N\e^EeElF?F@KsKzLALTLUMzNANHN[N\dqDxE?ERESIlIsIzJMJNMMMTM[MnMofKFRFYFlFmHRHYH`HsHtMMMTM[MnMoe^EeElF?F@I?IFIMI`IaMMMTM[MnMobjBqBxCKCLGeGlGsHFHGMzNANHN[N\cWC^CeCxCyGeGlGsHFHGOTO[ObOuOvdDDKDRDeDfGeGlGsHFHGNgNnNuOHOIbjBqBxCKCLI?IFIMI`IaPAPHPOPbPcbjBqBxCKCLHRHYH`HsHtPnPuP|QOQPcWC^CeCxCyIlIsIzJMJNPnPuP|QOQPdDDKDRDeDfIlIsIzJMJNPAPHPOPbPccWC^CeCxCyI?IFIMI`IaQ[QbQidDDKDRDeDfHRHYH`HsHtQ[QbQiQ|_??@?A?B?C?l?q?r?s?t@Y@b@c@d@eaGASATAUAVFsF{G?G@GAL_LcLjLkLlatBJBKBLBMG`GrH?H@HAMLMZMdMeMffDFSF^F`FcKCKRKVKXK[MzM~NONPNTeXEgErEtEwJUJcJgJlJmOUOZOfOhOodiDxEBECEHKqK~LBLDLINiNlNxNzOCbbBtCDCGCHH|IDIXI\I`PBPIPPP^PacPCbCrCvCxIhIpJCJKJLPpPwP~QLQMc~DPD`DdDfHPHXHjHpHtQ[QbQiQ|Q}") xQ24pnx = xQ24p.networkx_graph() xQ24ppnx = xQ24pp.networkx_graph() xQ24pp2nx = xQ24pp2.networkx_graph() # List of graphs to process graphs = [('xQ24p ', xQ24p),('xQ24pp ', xQ24pp),('xQ24pp2 ', xQ24pp2)] 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)} / 15-reg.? {graph.is_regular(k=15)} / Girth: {graph.girth()} ")# / Alg.conn. {algebraic_connectivity(graph).n(digits=6)} ")# / Domin. number: {graph.dominating_set(value_only=True)} ") 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("Degree histogram xQ24p:" , nx.degree_histogram(xQ24pnx) ) print("Degree histogram xQ24pp:", nx.degree_histogram(xQ24ppnx) ) print("Degree histogram xQ24pp2:", nx.degree_histogram(xQ24pp2nx) ) ''' 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') AxQ24p = xQ24p.automorphism_group() AxQ24pp = xQ24pp.automorphism_group() AxQ24pp2 = xQ24pp2.automorphism_group() print('xQ24p:', AxQ24p.structure_description(), ' | center order:',AxQ24p.center().order()) print('xQ24pp:', AxQ24pp.structure_description(), ' | center order:',AxQ24pp.center().order()) print('xQ24pp2:', AxQ24pp2.structure_description(), ' | center order:',AxQ24pp2.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") ## ##