1
Geneticdiscoveryandtranslationaldecisionsupportfromexomesequencing1
of20,791type2diabetescasesand24,440controlsfromfiveancestries2
3
JasonFlannick1,2,JosepMMercader1,3,*,ChristianFuchsberger4,5,*,MiriamSUdler1,6,*,4
AnubhaMahajan7,8,*,JenniferWessel9,10,11,TanyaMTeslovich12,LizzCaulkins1,Ryan5
Koesterer1,ThomasWBlackwell4,EricBoerwinkle13,14,JenniferABrody15,Ling6
Chen6,SiyingChen4,CeciliaContreras-Cubas16,EmilioCΓ³rdova16,AdolfoCorrea17,7
MariaCortes18,RalphADeFronzo19,LawrenceDolan20,KimberlyLDrews21,8
AmandaElliott1,6,JamesSFloyd22,StaceyGabriel18,MariaEugeniaGaray-Sevilla23,9
HumbertoGarcΓa-Ortiz16,MyronGross24,SoheeHan25,SarahHanks4,NancyL10
Heard-Costa26,27,AnneUJackson4,MaritEJΓΈrgensen28,29,30,HyunMinKang4,Megan11
Kelsey21,Bong-JoKim25,HeikkiAKoistinen31,32,33,JohannaKuusisto34,35,JosephB12
Leader36,AllanLinneberg37,38,39,Ching-TiLiu40,JianjunLiu41,42,43,Valeriya13
Lyssenko44,45,AlisaKManning46,47,AnthonyMarcketta12,JuanManuelMalacara-14
Hernandez23,AngΓ©licaMartΓnez-HernΓ‘ndez16,KarenMatsuo4,ElizabethMayer-15
Davis48,ElviaMendoza-Caamal16,KarenLMohlke49,AlannaCMorrison50,Anne16
Ndungu7,MaggieCYNg51,52,53,ColmO'Dushlaine12,AnthonyJPayne7,Catherine17
Pihoker54,BroadGenomicsPlatform18,WendySPost55,MichaelPreuss56,BruceM18
Psaty57,58,RamachandranSVasan27,59,NWilliamRayner7,8,60,AlexanderPReiner61,19
CristinaRevilla-Monsalve62,NeilRRobertson7,8,NicolaSantoro63,Claudia20
Schurmann56,WingYeeSo64,65,66,HeatherMStringham4,TimMStrom67,68,Claudia21
HTTam64,65,66,FarookThameem69,BrianTomlinson64,JasonMTorres7,RussellP22
Tracy70,71,RobMvanDam42,43,72,MarijanaVujkovic73,ShuaiWang40,RyanPWelch4,23
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
2
DanielRWitte74,75,Tien-YinWong76,77,78,GilAtzmon79,80,NirBarzilai79,John24
Blangero81,LoriLBonnycastle82,DonaldWBowden51,52,53,JohnCChambers83,84,85,25
EdmundChan42,Ching-YuCheng86,YoonShinCho87,FrancisSCollins82,PaulSde26
Vries50,RavindranathDuggirala81,BenjaminGlaser88,ClicerioGonzalez89,MaElena27
Gonzalez90,LeifGroop44,91,JaspalSinghKooner92,SooHeonKwak93,Markku28
Laakso34,35,DonnaMLehman19,PeterNilsson94,TimothyDSpector95,EShyong29
Tai42,43,77,TiinamaijaTuomi91,96,97,98,JaakkoTuomilehto99,100,101,102,JamesG30
Wilson103,CarlosAAguilar-Salinas104,ErwinBottinger56,BrianBurke21,DavidJ31
Carey36,JulianaChan64,65,66,JosΓ©eDupuis27,40,PhilippeFrossard105,SusanR32
Heckbert106,MiYeongHwang25,YoungJinKim25,HLesterKirchner36,Jong-Young33
Lee107,JuyoungLee25,RuthLoos56,108,RonaldCWMa64,65,66,AndrewDMorris109,34
ChristopherJO'Donnell110,111,112,113,ColinNAPalmer114,JamesPankow115,Kyong35
SooPark92,116,117,AsifRasheed105,DanishSaleheen73,105,XuelingSim43,KerrinS36
Small95,YikYingTeo43,118,119,ChristopherHaiman120,CraigLHanis121,BrianE37
Henderson120,LorenaOrozco16,TeresaTusiΓ©-Luna104,122,FrederickEDewey12,Aris38
Baras12,ChristianGieger123,124,ThomasMeitinger67,68,125,KonstantinStrauch123,126,39
LeslieLange127,NielsGrarup128,TorbenHansen128,129,OlufPedersen128,Phil40
Zeitler21,DanaDabelea130,GoncaloAbecasis4,GraemeIBell23,NancyJCox131,Mark41
Seielstad132,133,RobSladek134,135,136,JamesBMeigs18,46,137,SteveRich138,JeromeI42
Rotter139,DiscovEHRCollaboration12,36,CHARGE,LuCamp,ProDiGY,GoT2D,ESP,43
SIGMA-T2D,T2D-GENES,AMP-T2D-GENES,DavidAltshuler1,6,46,140,141,142,NoΓ«lP44
Burtt1,LauraJScott4,AndrewPMorris7,143,JoseCFlorez1,6,46,144,MarkI45
McCarthy7,8,145,MichaelBoehnke446
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
3
1. ProgramsinMetabolismandMedical&PopulationGenetics,BroadInstitute,47
Cambridge,Massachusetts,USA.48
2. DivisionofGeneticsandGenomics,BostonChildrenβsHospital,Boston,49
Massachusetts,USA.50
3. DiabetesUnitandCenterforGenomicMedicine,MassachusettsGeneralHospital,51
Boston,Massachusetts,USA.52
4. DepartmentofBiostatisticsandCenterforStatisticalGenetics,Universityof53
Michigan,AnnArbor,Michigan,USA.54
5. InstituteforBiomedicine,EuracResearch,Bolzano,Italy.55
6. DiabetesResearchCenter(DiabetesUnit),DepartmentofMedicine,56
MassachusettsGeneralHospital,Boston,Massachusetts,USA.57
7. WellcomeCentreforHumanGenetics,NuffieldDepartmentofMedicine,58
UniversityofOxford,Oxford,UK.59
8. OxfordCentreforDiabetes,EndocrinologyandMetabolism,RadcliffeDepartment60
ofMedicine,UniversityofOxford,Oxford,UK.61
9. DepartmentofEpidemiology,FairbanksSchoolofPublicHealth,Indiana62
University,Indianapolis,IN,46202,US.63
10. DepartmentofMedicine,SchoolofMedicine,IndianaUniversity,Indianapolis,IN,64
46202,US.65
11. DiabetesTranslationalResearchCenter,IndianaUniversity,Indianapolis,IN,66
46202,US.67
12. RegeneronGeneticsCenter,RegeneronPharmaceuticals,Tarrytown,NY,10591,68
USA.69
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
4
13. HumanGeneticsCenter,DepartmentofEpidemiologyHumanGeneticsand70
EnvironmentalSciences,SchoolofPublicHealth,TheUniversityofTexasHealth71
ScienceCenteratHouston,Houston,Texas,USA.72
14. HumanGenomeSequencingCenter,BaylorCollegeofMedicine,Houston,Texas,73
USA.74
15. CardiovascularResearchUnit,DepartmentofMedicine,Universityof75
Washington,Seattle,WA,USA.76
16. InstitutoNacionaldeMedicinaGenΓ³mica,MexicoCity,Mexico.77
17. DepartmentofMedicine,UniversityofMississippiMedicalCenter,Jackson,78
Mississippi,USA.79
18. BroadInstituteofMITandHarvard,Cambridge,Massachusetts,USA.80
19. DepartmentofMedicine,UniversityofTexasHealthScienceCenter,SanAntonio,81
Texas,USA.82
20. CincinnatiChildren'sHospitalMedicalCenter,Ohio,Cincinnati,USA.83
21. BiostatisticsCenter,GeorgeWashingtonUniversity,Rockville,MD,USA.84
22. DepartmentofMedicineandEpidemiology,UniversityofWashington,Seattle,85
WA,USA.86
23. DepartmentsofMedicineandHumanGenetics,TheUniversityofChicago,87
Chicago,Illinois,USA.88
24. DepartmentofLaboratoryMedicineandPathology,UniversityofMinnesota,89
Minneapolis,Minnesota,USA.90
25. DivisionofGenomeResearch,CenterforGenomeScience,NationalInstituteof91
Health,Chungcheongbuk-do,RepublicofKorea.92
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
5
26. DepartmentofNeurology,BostonUniversitySchoolofMedicine,Boston,93
Massachusetts,USA.94
27. NationalHeartLungandBloodInstitute'sFraminghamHeartStudy,Framingham,95
Massachusetts,USA.96
28. StenoDiabetesCenterCopenhagen,Gentofte,Denmark.97
29. NationalInstituteofPublicHealth,UniversityofSouthernDenmark,Copenhagen,98
Denmark.99
30. GreenlandCentreforHealthResearch,UniversityofGreenland,Nuuk,Greenland.100
31. DepartmentofPublicHealthSolutions,NationalInstituteforHealthandWelfare,101
Helsinki,Finland.102
32. UniversityofHelsinkiandDepartmentofMedicine,HelsinkiUniversityCentral103
Hospital,Helsinki,Finland.104
33. MinervaFoundationInstituteforMedicalResearch,Helsinki,Finland.105
34. InstituteofClinicalMedicine,InternalMedicine,UniversityofEasternFinland,106
Kuopio,Finland.107
35. DepartmentofMedicin,KuopioUniversityHospital,Kuopio,Finland.108
36. GeisingerHealthSystem,Danville,PA,17822,USA.109
37. DepartmentofClinicalMedicine,FacultyofHealthandMedicalSciences,110
UniversityofCopenhagen,Copenhagen,Denmark.111
38. CenterforClinicalResearchandPrevention,BispebjergandFrederiksberg112
Hospital,TheCapitalRegion,Copenhagen,Denmark.113
39. DepartmentofClinicalExperimentalResearch,Rigshospitalet,Copenhagen,114
Denmark.115
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
6
40. DepartmentofBiostatistics,BostonUniversitySchoolofPublicHealth,Boston,116
Massachusetts,USA.117
41. GenomeInstituteofSingapore,AgencyforScienceTechnologyandResearch,118
Singapore.119
42. DepartmentofMedicine,YongLooLinSchoolofMedicine,NationalUniversityof120
Singapore,NationalUniversityHealthSystem,Singapore.121
43. SawSweeHockSchoolofPublicHealth,NationalUniversityofSingapore,122
Singapore.123
44. DepartmentofClinicalSciences,DiabetesandEndocrinology,LundUniversity124
DiabetesCentre,MalmΓΆ,Sweden.125
45. UniversityofBergen,Norway.126
46. DepartmentofMedicine,HarvardMedicalSchool,Boston,Massachusetts,USA.127
47. ClinicalandTranslationalEpidemiologyUnit,MassachusettsGeneralHospital,128
HarvardUniversity,Boston,MA,USA.129
48. UniversityofNorthCarolinaChapelHill,ChapelHill,NorthCarolina,USA.130
49. DepartmentofGenetics,UniversityofNorthCarolina,ChapelHill,NorthCarolina,131
USA.132
50. HumanGeneticsCenter,DepartmentofEpidemiologyHumanGeneticsand133
EnvironmentalSciences,SchoolofPublicHealth,TheUniversityofTexasHealth134
ScienceCenteratHouston,Houston,Texas,USA.135
51. CenterforDiabetesResearch,WakeForestSchoolofMedicine,Winston-Salem,136
NorthCarolina,USA.137
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
7
52. CenterforGenomicsandPersonalizedMedicineResearch,WakeForestSchoolof138
Medicine,Winston-Salem,NorthCarolina,USA.139
53. DepartmentofBiochemistry,WakeForestSchoolofMedicine,Winston-Salem,140
NorthCarolina,USA.141
54. SeattleChildren'sHospital,Washington,Seattle,USA.142
55. DivisionofCardiology,DepartmentofMedicine,JohnsHopkinsUniversity,143
Baltimore,Maryland,USA.144
56. CharlesR.BronfmanInstituteofPersonalizedMedicine,MountSinaiSchoolof145
Medicine,NewYork,NewYork,USA.146
57. CardiovascularHealthResearchUnit,DepartmentsofMedicine,Epidemiology,147
andHealthServices,UniversityofWashington,Seattle,Washington,USA.148
58. KaiserPermanenteWashingtonHealthResearchInstitute,Seattle,Washington,149
USA.150
59. PreventiveMedicine&Epidemiology,Medicine,BostonUniversitySchoolof151
Medicine,Boston,Massachusetts,USA.152
60. DepartmentofHumanGenetics,WellcomeTrustSangerInstitute,Hinxton,153
Cambridgeshire,UK.154
61. UniversityofWashington,Seattle,Washington,USA.155
62. InstitutoMexicanodelSeguroSocialSXXI,MexicoCity,Mexico.156
63. DepartmentofPediatrics,YaleUniversity,NewHaven,CT,USA.157
64. DepartmentofMedicineandTherapeutics,TheChineseUniversityofHongKong,158
HongKong,China.159
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
8
65. LiKaShingInstituteofHealthSciences,TheChineseUniversityofHongKong,160
HongKong,China.161
66. HongKongInstituteofDiabetesandObesity,TheChineseUniversityofHong162
Kong,HongKong,China.163
67. InstituteofHumanGenetics,TechnischeUniversitΓ€tMΓΌnchen,Munich,Germany.164
68. InstituteofHumanGenetics,HelmholtzZentrumMΓΌnchen,GermanResearch165
CenterforEnvironmentalHealth,Neuherberg,Germany.166
69. DepartmentofBiochemistry,FacultyofMedicine,HealthScienceCenter,Kuwait167
University,Safat,Kuwait.168
70. DepartmentofPathologyandLaboratoryMedicine,RobertLarner,M.D.College169
ofMedicine,UniversityofVermont,Burlington,Vermont,USA.170
71. DepartmentofBiochemistry,RobertLarnerM.D.CollegeofMedicine,University171
ofVermont,Burlington,Vermont,USA.172
72. DepartmentofNutrition,HarvardSchoolofPublicHealth,Boston,Massachusetts,173
USA.174
73. DepartmentofBiostatisticsandEpidemiology,UniversityofPennsylvania,175
Philadelphia,Pennsylvania,USA.176
74. DepartmentofPublicHealth,AarhusUniversity,Aarhus,Denmark.177
75. DanishDiabetesAcademy,Odense,Denmark.178
76. SingaporeEyeResearchInstitute,SingaporeNationalEyeCentre,Singapore.179
77. Duke-NUSMedicalSchoolSingapore,Singapore.180
78. DepartmentofOphthalmology,YongLooLinSchoolofMedicine,National181
UniversityofSingapore,NationalUniversityHealthSystem,Singapore.182
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
9
79. DepartmentsofMedicineandGenetics,AlbertEinsteinCollegeofMedicine,New183
York,USA.184
80. UniversityofHaifa,Facultyofnaturalscience,Haifa,Isarel.185
81. DepartmentofHumanGeneticsandSouthTexasDiabetesandObesityInstitute,186
UniversityofTexasRioGrandeValley,EdinburgandBrownsville,Texas,USA.187
82. MedicalGenomicsandMetabolicGeneticsBranch,NationalHumanGenome188
ResearchInstitute,NationalInstitutesofHealth,Bethesda,Maryland,USA.189
83. DepartmentofEpidemiologyandBiostatistics,ImperialCollegeLondon,London,190
UK.191
84. DepartmentofCardiology,EalingHospitalNHSTrust,Southall,Middlesex,UK.192
85. ImperialCollegeHealthcareNHSTrust,ImperialCollegeLondon,London,UK.193
86. Ophthalmology&VisualSciencesAcademicClinicalProgram(EyeACP),Duke-194
NUSMedicalSchool,Singapore195
87. DepartmentofBiomedicalScience,HallymUniversity,Chuncheon,Republicof196
Korea.197
88. EndocrinologyandMetabolismService,Hadassah-HebrewUniversityMedical198
Center,Jerusalem,Israel.199
89. UnidaddeDiabetesyRiesgoCardiovascular,InstitutoNacionaldeSaludPΓΊblica,200
Cuernavaca,Morelos,Mexico.201
90. CentrodeEstudiosenDiabetes,MexicoCity,Mexico.202
91. InstituteforMolecularGeneticsFinland,UniversityofHelsinki,Helsinki,Finland.203
92. NationalHeartandLungInstitute,CardiovascularSciences,Hammersmith204
Campus,ImperialCollegeLondon,London,UK.205
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
10
93. DepartmentofInternalMedicine,SeoulNationalUniversityHospital,Seoul,206
RepublicofKorea.207
94. DepartmentofClinicalSciences,Medicine,LundUniversity,MalmΓΆ,Sweden.208
95. DepartmentofTwinResearchandGeneticEpidemiology,King'sCollegeLondon,209
London,UK.210
96. FolkhΓ€lsanResearchCentre,Helsinki,Finland.211
97. DepartmentofEndocrinology,AbdominalCentre,HelsinkiUniversityHospital,212
Helsinki,Finland.213
98. ResearchProgramsUnit,DiabetesandObesity,UniversityofHelsinki,Helsinki,214
Finland.215
99. DiabetesPreventionUnit,NationalInstituteforHealthandWelfare,Helsinki,216
Finland.217
100. CenterforVascularPrevention,DanubeUniversityKrems,Krems,Austria.218
101. DiabetesResearchGroup,KingAbdulazizUniversity,Jeddah,SaudiArabia.219
102. InstitutodeInvestigacionSanitariadelHospitalUniversarioLaPaz(IdiPAZ),220
UniversityHospitalLaPaz,AutonomousUniversityofMadrid,Madrid,Spain.221
103. DepartmentofPhysiologyandBiophysics,UniversityofMississippiMedical222
Center,Jackson,Mississippi,USA.223
104. InstitutoNacionaldeCienciasMedicasyNutricion,MexicoCity,Mexico.224
105. CenterforNon-CommunicableDiseases,Karachi,Pakistan.225
106. CardiovascularHealthResearchUnitandDepartmentofEpidemiology,226
UniversityofWashington,Seattle,WA,USA.227
107. MinistryofHealthandWelfare,Seoul,RepublicofKorea.228
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
11
108. TheMindichChildHealthandDevelopmentInsititute,IcahnSchoolofMedicineat229
MountSinai,NewYork,NewYork,USA.230
109. ClinicalResearchCentre,CentreforMolecularMedicine,NinewellsHospitaland231
MedicalSchool,Dundee,UK.232
110. SectionofCardiology,DepartmentofMedicine,VABostonHealthcare,Boston,233
Massachusetts,USA.234
111. HarvardMedicalSchool,Boston,Massachusetts,USA.235
112. BrighamandWomenβsHospital,Boston,Massachusetts,USA.236
113. IntramuralAdministrationManagementBranch,NationalHeartLungandBlood237
Institute,NIH,Framingham,Massachusetts,USA.238
114. PatMacphersonCentreforPharmacogeneticsandPharmacogenomics,Medical239
ResearchInstitute,NinewellsHospitalandMedicalSchool,Dundee,UK.240
115. DivisionofEpidemiologyandCommunityHealth,UniversityofMinnesota,241
Minnesota,MN,USA.242
116. DepartmentofMolecularMedicineandBiopharmaceuticalSciences,Graduate243
SchoolofConvergenceScienceandTechnology,SeoulNationalUniversity,Seoul,244
RepublicofKorea.245
117. DepartmentofInternalMedicine,SeoulNationalUniversityCollegeofMedicine,246
Seoul,RepublicofKorea.247
118. LifeSciencesInstitute,NationalUniversityofSingapore,Singapore.248
119. DepartmentofStatisticsandAppliedProbability,NationalUniversityof249
Singapore,Singapore.250
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
12
120. DepartmentofPreventiveMedicine,KeckSchoolofMedicine,Universityof251
SouthernCalifornia,LosAngeles,California,USA.252
121. HumanGeneticsCenter,SchoolofPublicHealth,TheUniversityofTexasHealth253
ScienceCenteratHouston,Houston,Texas,USA.254
122. InstitutodeInvestigacionesBiomΓ©dicas,DepartamentodeMedicinaGenΓ³micay255
ToxicologΓa,UniversidadNacionalAutΓ³nomadeMΓ©xico,MexicoCity,Mexico.256
123. ResearchUnitofMolecularEpidemiology,InstituteofEpidemiology,Helmholtz257
ZentrumMΓΌnchen,GermanResearchCenterforEnvironmentalHealth,258
Neuherberg,Germany.259
124. GermanCenterforDiabetesResearch(DZDe.V.),Neuherberg,Germany.260
125. DeutschesForschungszentrumfΓΌrHerz-Kreislauferkrankungen(DZHK),Partner261
SiteMunichHeartAlliance,Munich,Germany.262
126. InstituteofMedicalInformatics,BiometryandEpidemiology,ChairofGenetic263
Epidemiology,Ludwig-Maximilians-UniversitΓ€t,Neuherberg,Germany.264
127. DepartmentofMedicine,UniversityofColoradoDenver,AnschutzMedical265
Campus,Aurora,Colorado,USA.266
128. NovoNordiskFoundationCenterforBasicMetabolicResearch,FacultyofHealth267
andMedicalSciences,UniversityofCopenhagen,Copenhagen,Denmark.268
129. FacultyofHealthSciences,UniversityofSouthernDenmark,Odense,Denmark.269
130. DepartmentofEpidemiology,ColoradoSchoolofPublicHealth,Aurora,CO,USA.270
131. VanderbiltGeneticsInstitute,VanderbiltUniversity,Tennessee,Nashville,USA.271
132. DepartmentofLaboratoryMedicine&InstituteforHumanGenetics,Universityof272
California,SanFrancisco,SanFrancisco,California,USA.273
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
13
133. BloodSystemsResearchInstitute,SanFrancisco,California,USA.274
134. DepartmentofHumanGenetics,McGillUniversity,Montreal,Quebec,Canada.275
135. DivisionofEndocrinologyandMetabolism,DepartmentofMedicine,McGill276
University,Montreal,Quebec,Canada.277
136. McGillUniversityandGΓ©nomeQuΓ©becInnovationCentre,Montreal,Quebec,278
Canada.279
137. DivisionofGeneralInternalMedicine,MassachusettsGeneralHospital,Boston,280
Massachusetts,USA.281
138. CenterforPublicHealthGenomics,UniversityofViriginiaSchoolofMedicine,282
Charlottesville,Virginia,USA.283
139. DepartmentsofPediatricsandMedicine,InstituteforTranslationalGenomicsand284
PopulationSciences,LosAngelesBioMedicalResearchInstituteatHarbor-UCLA285
MedicalCenter,Torrance,California,USA.286
140. DepartmentofGenetics,HarvardMedicalSchool,Boston,Massachusetts,USA.287
141. DepartmentofBiology,MassachusettsInstituteofTechnology,Cambridge,288
Massachusetts,USA.289
142. DepartmentofMolecularBiology,MassachusettsGeneralHospital,Boston,290
Massachusetts,USA.291
143. DepartmentofBiostatistics,UniversityofLiverpool,Liverpool,UK.292
144. CenterforGenomicMedicine,MassachusettsGeneralHospital,Boston,293
Massachusetts,USA.294
145. OxfordNIHRBiomedicalResearchCentre,OxfordUniversityHospitalsTrust,295
Oxford,UK.296
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
14
Abstract297
Protein-codinggeneticvariantsthatstronglyaffectdiseaseriskcanprovide298
importantcluesintodiseasepathogenesis.Herewereportanexomesequence299
analysisof20,791type2diabetes(T2D)casesand24,440controlsfromfive300
ancestries.Weidentifyrare(minorallelefrequency<0.5%)variantgene-level301
associationsin(a)threegenesatexome-widesignificance,includingaT2D-302
protectiveseriesof>30SLC30A8alleles,and(b)within12genesets,includingthose303
correspondingtoT2Ddrugtargets(p=6.1Γ10-3)andcandidategenesfromknockout304
mice(p=5.2Γ10-3).Withinourstudy,thestrongestT2Drarevariantgene-level305
signalsexplainatmost25%oftheheritabilityofthestrongestcommonsingle-306
variantsignals,andtherarevariantgene-leveleffectsizesweobserveinestablished307
T2Ddrugtargetswillrequire110K-180Ksequencedcasestoexceedexome-wide308
significance.Tohelpprioritizegenesusingassociationsfromcurrentsmallersample309
sizes,wepresentaBayesianframeworktorecalibrateassociationp-valuesas310
posteriorprobabilitiesofassociation,estimatingthatreachingp<0.05(p<0.005)in311
ourstudyincreasestheoddsofcausalT2Dassociationforanonsynonymousvariant312
byafactorof1.8(5.3).Tohelpguidetargetorgeneprioritizationefforts,ourdata313
arefreelyavailableforanalysisatwww.type2diabetesgenetics.org.314
315
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
15
Introduction316
Tobetterunderstandortreatdisease,humangeneticsoffersapowerfulapproachto317
identifymolecularalterationscausallyassociatedwithphysiologicaltraits1.318
Common-variantarray-basedgenome-wideassociationstudies(GWAS)have319
discoveredthousandsofgenomiclociassociatedwithhundredsofhumantraits2,320
andfurthercommonvariantanalysesindicatethatmostcomplextraitheritabilityis321
attributabletomodest-effectregulatoryvariants3-5.However,non-codingGWAS322
associationsarechallengingtolocalizetocausalvariantsorgenes6-10.323
324
Protein-codingvariantswithstrongeffectsonproteinfunctionordiseasecanoffer325
molecularβprobesβintothepathologicalrelevanceofagene13-15andpotentially326
establishadirectcausal16,17linkbetweengenegainorlossoffunctionanddisease327
risk18,19βespeciallywhenthereisevidenceofmultipleindependentvariant328
associations(anβallelicseriesβ)withinagene18-20.Severallinesofargument11,12329
predictthatstrong-effectvariants(allelicodds-ratios[OR]>2)willusuallyberare330
(minorallelefrequency[MAF]<0.5%)and,inmanycases,difficulttoaccurately331
studythroughcurrentGWASandimputationstrategies13,14.Wholegenomeor332
exomesequencing,bycontrast,allowsinterrogationofthefullspectrumofgenetic333
variation.334
335
Previousexomesequencingstudies,however,haveidentifiedfewexome-wide336
significantrarevariantassociations21-26forcomplexdiseasessuchastype2337
diabetes(T2D)24,27.Thispaucityoffindingsisdueinparttothelimitedsamplesizes338
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
16
ofpreviousstudies,thelargestofwhichinclude<10,000diseasecasesandfallshort339
ofthesamplesizesthatanalytic12andsimulation-basedcalculations28-30predictare340
neededtoidentifyraredisease-associatedvariantsunderplausiblediseasemodels.341
Toexpandourabilitytouserarecodingvariantstomakegeneticdiscoveriesand342
accelerateclinicaltranslation,wecollectedandanalyzedexomesequencedatafrom343
20,791T2Dcasesand24,440controlsofmultipleancestries,representingthe344
largestexomesequenceanalysistodateforT2D.345
346
Geneticdiscoveryfromsingle-variantandgene-levelanalysis347
348
Studyparticipants(SupplementaryTable1)weredrawnfromfiveancestries349
(Hispanic/Latino[effectivesize(Neff)=14,442;33.8%],European[Neff=10,517;350
24.6%],African-American[Neff=5,959;13.9%],East-Asian[Neff=6,010;14.1%],351
South-Asian[Neff=5,833;13.6%])andyieldedequivalentstatisticalpowertodetect352
associationasabalancedstudyof~42,800individualsorapopulation-basedstudy353
(assuming8%T2Dprevalence)of~152,000individuals.Powertodetect354
associationwasimprovedcomparedtothepreviouslargestT2Dexomesequencing355
study24of6,504casesand6,436controls,increasing(forexample)from5%to90%356
foravariantwithMAF=0.2%andOR=2.5(SupplementaryFigure1).357
358
Exomesequencingto40xmeandepth,variantcallingusingbest-practice359
algorithms,andextensivedataqualitycontrol(Methods;SupplementaryFigures360
2-5,SupplementaryTable2)producedadatasetwith6.33Mvariants,ofwhich361
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
17
2.3%arecommon(MAF>5%),4.2%low-frequency(0.5%<MAF<5%),and93.5%362
rare(MAF<0.5%)(SupplementaryTable3).Theseinclude2.26Mnonsynonymous363
variantsand871Kindels,morethantwicethenumbersanalyzedinthelargest364
previousT2Dexomesequencingstudy24.365
366
Wefirsttestedwhetheranyofthesevariants,regardlessofallelefrequency,367
exhibitedassociationwithT2D(βsingle-variantβtest;Methods,Supplementary368
Figure6).Basedonapreviouslydemonstratedenrichmentofcodingvariantsfor369
diseaseassociations31,weusedanexome-widesignificancethresholdofp=4.3Γ10-7.370
Eighteenvariants(tennonsynonymous)insevenlocireachedthisthreshold;13of371
these(eightnonsynonymous)reachedthetraditionalgenome-widesignificance372
thresholdofp<5Γ10-8(Figure1a,SupplementaryTable4).These18associations373
representasubstantialincreaseovertheoneassociationreportedfromthe374
previouslargestT2Dexomesequencingstudy24.However,onlytwoofthese18have375
notbeenpreviouslyreportedby(muchlarger)GWAS:avariantinSFI1376
(rs145181683,p.Arg724Trp;SupplementaryFigure7)thatfailedtoreplicatein377
anindependentcohort(N=4,522,p=0.90,Methods),andavariantinMC4R378
(rs79783591,p.Ile269Asn).379
380
MC4Rp.Ile269AsnwasthesolevariantwithassociationOR>2(Hispanic/Latino381
MAF=0.89%;p=3.4Γ10-7,OR=2.17[95%CI:1.63-2.89]).MC4Rhaslongestablished382
effectsonbody-weightanddiabetes32-34,andp.Ile269Asnspecificallyhasbeen383
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
18
showntodecreaseMC4Ractivity35,36withassociationstoobesityandT2Din384
smallerstudiesofaUnitedKingdomfamily37andaNativeAmericanpopulation36.385
386
Assingle-variantanalysishaslimitedpowertodetectassociationswithrarer387
variants12,wenextperformedtestsofassociationforsetsofvariantswithingenes.388
Weperformedtwogene-levelassociationtests:(a)aburdentest,whichassumesall389
analyzedvariantswithinageneareofthesameeffect,and(b)SKAT38,whichallows390
variabilityinvarianteffectsize(anddirection).391
392
Followingpreviousstudies22-24,weseparatelytestedsevendifferentβmasksβof393
variantsgroupedbysimilarpredictedseverity.Asthisanalysisstrategyledto394
2Γ7=14p-valuesforeachgene,wedevelopedtwomethodstoconsolidatethese395
resultsforeachtest(Methods;SupplementaryFigures8-10).First,weretained396
onlythesmallestp-valuebutcorrectedfortheeffectivenumberofindependent397
maskstested39,onaverage3.6pergene(βminimump-valuetestβ).Second,wetested398
allnonsynonymousvariants(i.e.missense,splicesite,andproteintruncating)but399
weightedeachvariantaccordingtoitsestimatedprobabilityofcausinggene400
inactivation12(βweightedtestβ,inessenceassessingtheeffectofgene401
haploinsufficiencyfromcombinedanalysisofprotein-truncatingandmissense402
variants;Methods).Weverifiedthattheminimump-valueandweighted403
consolidationmethodswerebothwell-calibrated(SupplementaryFigure11)and404
betweenthemproducedbroadlyconsistentbutdistinctresults:acrossthetenmost405
significantly-associatedgenes,p-valueswerenominallysignificantunderboth406
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
19
methodsforeightgenesbutvariedbyone-to-threeordersofmagnitude407
(SupplementaryTable5).WeemployedaconservativeBonferroni-corrected408
gene-levelexome-widesignificancethresholdofp=0.05/(2testsΓ2consolidation409
methodsΓ19,020genes)=6.57Γ10-7.410
411
Usingthisstrategy,gene-levelassociationsreachedexome-widesignificancefor412
MC4R,SLC30A8,andPAM(Figure1b,SupplementaryTables5-6).Allthreegenes413
liewithinpreviouslyT2DGWASlociandcontainpreviouslyidentifiedcodingsingle-414
variantsignals:p.Arg325Trpandaseriesof12protectiveproteintruncating415
variants(PTVs)forSLC30A819,40,p.Asp563Glyandp.Ser539TrpforPAM24,41,and416
p.Ile269AsnforMC4R.417
418
Inadditionto11previouslyobservedPTVs,theSLC30A8gene-levelsignalincludes419
92variants(103intotalwithcombinedMAF=1.4%;p.Arg325Trpwasnotincluded420
ingene-levelanalysis)andisassociatedwithT2Dprotection(weightedp=1.3Γ10-8,421
OR=0.40[0.28-0.55]).Manyvariantscontributedtothissignal:whenwe422
progressivelyremovedvariantswiththesmallestsingle-variantp-values,removal423
of33wasrequiredtoextinguishnominal(p<0.05)gene-levelsignificance(Figure424
1cd,SupplementaryFigure12).AlthoughSLC30A8(anditsproteinproductZnT8)425
werefirstimplicatedinT2Doveradecadeago40,theirmoleculardisease426
mechanism(s)remainpoorlyunderstood42,43βinpartbecauseofseemingly427
conflictingobservationsofthecommonrisk-increasingallelep.Arg325Trp428
(suggestedtodecreaseproteinactivity44)andtherarerisk-decreasingPTVs(also429
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
20
thoughttodecreaseproteinactivity19).Theprotectiveallelicseriesfromour430
analysisarguesthatdecreased,ratherthanincreased,riskisthemoretypicaleffect431
ofSLC30A8geneticvariation,anditfurtherprovidesmanyallelesthatcouldbe432
characterizedtooffermechanisticinsight.433
434
TheMC4R(combinedMAF=0.79%;minimump=2.7Γ10-10,OR=2.07[1.65-2.59])and435
PAM(combinedMAF=4.9%;weightedp=2.2Γ109,OR=1.44[1.28-1.62])gene-level436
signalsareduelargelyβbutnotentirelyβtoeffectsfromindividualvariants437
(p.Ile269AsnforMC4R,p.Asp563Glyandp.Ser539TrpforPAM).ForMC4R,gene-438
levelassociationdecreasedbutremainedsignificantafterremovingp.Ile269Asn439
(p=8.6Γ10-3;SupplementaryFigure13).Similarly,asshownpreviously34,45,440
associationwaslesssignificantafterconditioningonsampleBMI,bothforthe441
p.Ile269Asnsingle-variantsignal(p=1.0Γ10-5)andthegene-levelsignalnot442
attributabletop.Ile269Asn(p=0.035).443
444
Thegene-levelsignalinPAMalsoremainednominallysignificant(p<0.05)even445
afterremovingthe35strongestindividuallyassociatedPAMvariants,indicatinga446
contributionfromsubstantiallymorevariantsthanp.Asp563Glyandp.Ser539Trp447
(SupplementaryFigure14).Cellularcharacterizationofp.Asp563Glyand448
p.Ser539TrprecentlyidentifiedanovelmechanismforT2Driskthroughaltered449
insulinstorageandsecretion46.Ourresultsprovidemanymoregeneticvariantsβ450
identifiableonlythroughsequencing17βthatcouldbecharacterizedforfurther451
insightsintotheT2DriskmechanismmediatedbyPAM.452
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
21
453
Wefinallyassessedthe50most-significantgene-levelassociations(asmeasuredby454
minimump-valueacrossourfouranalyses;Methods)intwoindependentexome455
sequencedatasets:14,118individuals(3,062T2Dcasesand9,405controlsof456
EuropeanorAfrican-Americanancestry)fromtheCHARGEdiscoverysequence457
project47(CHARGE,SupplementaryTable7;50genesavailable)and49,199458
individuals(12,973T2Dcasesand36,226controlsofEuropeanancestry)fromthe459
GeisingerHealthSystem(GHS,SupplementaryTable8;44genesavailable).In460
eachreplicationstudy,MC4R,SLC30A8,andPAMallshowedburdentest461
associationsdirectionallyconsistentwiththosefromouranalysis.MC4R(minimum462
p=0.0058)andSLC30A8(minimump=0.043)furtherdemonstratednominally463
significantassociationsintheGHSburdenanalysis,andMC4R(minimump=0.026)464
achievednominalsignificanceintheCHARGESKATanalysis.Theweaker465
associationsinthereplicationstudiescomparedtoourstudy(Supplementary466
Tables7and8)couldbeduetoawinnerβscurseeffectcombinedwithdifferences467
inproceduresforvariantcalling,qualitycontrol,annotation,andassociationtesting.468
469
Morebroadly,acrossthegeneswithreplicationresultsavailableandwithburden470
p<0.05inouranalysis,weobservedanexcessofdirectionallyconsistentburdentest471
associations(31of46inCHARGE,one-sidedbinomialp=0.013;23of40inGHS,472
one-sidedbinomialp=0.21;overallone-sidedbinomialp=0.011;Supplementary473
Table9).Futurestudiesmaythereforeenableseveralmoreofthetopgene-level474
signalsfromouranalysistoreachexome-widesignificance.475
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
22
476
Furtherinsightsfromgene-levelanalysis477
478
SLC30A8,MC4R,andPAMillustratehowexome-widesignificantgene-level479
associationsprovideallelicseriesthatcouldbecharacterizedforpathogenic480
insightsintopreviouslyT2D-associatedbutstillincompletelyunderstoodgenes.We481
nextinvestigatedtheutilityoflesssignificantgene-levelassociationstoeither(a)482
geneticallyprioritizegeneswithnopriorevidenceofT2Dassociation,(b)predict483
theeffectorgeneatestablishedT2DGWASloci,or(c)predictwhetherlossorgainof484
proteinfunctionincreasesdiseaserisk.Weconductedthisanalysisatthelevelof16485
setsofgenesconnectedtoT2Dfromdifferentevidencesources(e.g.genes486
harboringdiabetes-associatedMendelianorcommonvariants,T2Ddrugtargets48,487
orgenesimplicatedindiabetes-relatedphenotypesfrommousemodels49;488
SupplementaryTable10;Methods).489
490
First,foreachgeneset,weaskedwhetheritsgeneshadmoresignificantgene-level491
associationsthanexpectedbychance.Weusedaone-sidedWilcoxonRank-Sum492
Testtocomparegene-levelp-valueswithineachgenesettothoseforrandomsetsof493
geneswithsimilarnumbersofvariantsandaggregatefrequencies(Methods).494
Twelveofthe16genesetsachievedp<0.05set-levelassociations(Figure2a-e,495
SupplementaryFigure15),includingthoseforT2Ddrugtargets(p=6.1Γ10-3)and496
forgenesreportedfrommousemodelsofnon-autoimmunediabetes(p=5.2Γ10-3)or497
impairedglucosetolerance(p=7.2Γ10-6).Followingapreviousstudythat498
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
23
retrospectivelyvalidateddrugtargetsfromthegeneticeffectsofPTVs27,these499
resultsdemonstratethevalueofgene-levelassociationstoprioritizecandidate500
genesβe.g.thosethatemergefromhigh-throughputexperimentalscreens50,51βfor501
furtherinvestigation.Ourstudyemphasizestheaddedpowerofincludingmissense502
variantsinthisanalysis:set-levelp-valuesfromanalysisofPTVsalonewerep>0.05503
foralmostallgenesets(although,notably,thedrugtargetgenesetremained504
significantatp=0.0061;SupplementaryFigure16).505
506
Next,weinvestigatedwhethereffectorgenesthatmediateGWASassociationsβ507
whichmostlycorrespondtovariantsofuncertainregulatoryeffectsβwerealso508
enrichedforcodingvariantgene-levelassociations.Wetestedforassociations509
withintwosetsofpredictedeffectorgenes:acuratedlistof11genesharboring510
likelycausalcommoncodingvariants(reportedfromarecentstudy17with511
posteriorprobabilityofcausalassociation>0.25fromgeneticsalone;Methods),and512
20genessignificantinatranscriptassociationanalysiswithT2D52.Geneswith513
likelycausalcodingvariantsdemonstratedasignificantset-levelassociationrelative514
tocomparisongenesets(p=8.8Γ10-3)andtogeneswithinthesameloci(p=0.028;515
Figure2e),evenwhenweconditionedgene-levelassociationsonallsignificant516
commonvariantsignals.Mostofthissignalwasduetothegene-levelSLC30A8and517
PAMassociations(p=0.082fortheotherninegenes).Bycontrast,thetranscript-518
associationbasedgenesetdidnotexhibitasignificantassociation(p=0.72).519
520
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
24
Extendingthisanalysis,wecuratedalistof94T2DGWASloci,and595genesthat521
laywithin250kbofanyT2DGWASindexvariant,froma2016T2Dgenetics522
review53.Amongthese595genes,40achievedap<0.05gene-levelsignal523
(SupplementaryTable11),greaterthanthe595Γ0.05=29.75expectedbychance524
(p=0.038).These40geneshadamongthemsignificantlymoreindirectprotein-525
proteininteractions(DAPPLE54p=0.03;observedmean=11.4,expectedmean=4.5)526
thandidthe184genesimplicatedbasedonproximitytoGWAStagSNPs(DAPPLE527
p=0.64),consistentwithagenesetofgreaterbiologicalcoherence.Rarecoding528
variantscouldtherefore,inprinciple,complementcommonvariantfinemapping6,55529
andexperimentaldata7,56tohelpinterpretT2DGWASassociations,althoughour530
resultsindicatethatmuchlargersamplesizeswillberequiredtoclearlyimplicate531
specificeffectorgenes.532
533
Finally,weassessedwhethergene-levelanalysiscouldhelppredictwhethergene534
inactivationincreasesordecreasesT2Drisk(i.e.theT2Dβdirectional535
relationshipβ18,19).Foreachgeneset,wecomparedtheORsestimatedfromgene-536
levelweightedanalysisofpredicteddamagingcodingalleles(Methods)to537
directionalrelationshipspreviouslyreported.Gene-levelORswere100%538
concordantwiththeknownrelationshipsforthesetofeightT2Ddrugtargets(4/4539
inhibitortargetsOR<1,4/4agonisttargetsOR>1;one-sidedbinomialp=3.9Γ10-3;540
Figure2f).541
542
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
25
Conversely,concordancesbetweengene-levelORestimatesandmouseknockout543
observationsweremoreequivocal(7/11diabetesgeneswithOR>1,binomial544
p=0.27;137/240increasedcirculatingglucosegeneswithOR>1,p=0.016;545
SupplementaryFigure17).Therelativelylowconcordancesforthesegenesets,546
despiteacleartrendtowardlower-than-expectedgene-levelp-valueswithinthem547
(SupplementaryFigure15),highlighthowcodingvariantsmightbeusedtoassess548
seeminglypromisingpreclinicalresults(particularlygiventheknownlimitationsof549
animalmodels57,58).Forexample,theprotectivegene-levelATMsignalweobserve550
(burdentestofPTVsOR=0.50,p=0.003)questionspreviousexpectations,basedon551
insulinresistanceandimpairedglucosetoleranceinAtmknockoutmice59,thatATM552
loss-of-functionshouldincreaseT2Drisk.EvidenceisevenlessfavorablethatATM553
haploinsufficiencystronglyincreasesT2Drisk,rejecting(forexample)OR>2at554
p=1.3Γ10-8.Thisobservationcouldberelevantintheongoingcharacterizationof555
ATMasapotentialmetformintarget60-62orifATMactivatorsareconsideredtotreat556
cardiovasculardisease63.557
558
ComparisonofrareandcommonvariantsinT2Dgeneticanalyses559
560
ThesubstantialnumberofrarecodingvariantT2Dassociationsweobserved561
promptedustore-evaluatearguments13,14,16,64abouttheirvalueingeneticstudies562
relativetocommonvariants,whichhavetheadvantageofbeingefficientlystudied563
(inmanymoresamplesthancurrentlycanbesequenced)througharray-based564
associationstudies55,65.Whilerecentstudieshaveemphasizedthemain565
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
26
contributionofcommonvariantstoT2Dheritability17,21,24,66,theyhavelacked566
powertofullyevaluatetherelativemeritsofrareversuscommonvariants(or,by567
implication,sequencingversusarray-basedstudies)todiscoverdisease-associated568
loci,explaindiseaseheritability,orelucidateallelicseries.569
570
Forafaircomparisonofdiscoveriespossiblefromsequencingandarray-based571
studies,wecollectedgenome-widearraydatawithinthesameindividualswe572
sequenced(availablefor34,529[76.3%of]individuals;18,233casesand17,679573
controls).Wethenimputedvariantsusingbest-practicereferencepanels67,68and574
conductedsingle-variantanalysisfollowingthesameprotocolasforthesequence575
data(βimputedGWASβ;SupplementaryTable12,Methods).Eightoftheten576
exome-widesignificantnonsynonymoussingle-variantassociationsfromour577
sequenceanalysisweredetectableintheimputedGWASanalysis,togetherwith578
genome-widesignificantnoncodingvariantassociationsin14additionalloci579
(Figure3a,SupplementaryTable13).Alltensingle-variantsequenceassociations580
werealsopresentontheIlluminaExomeArray(Methods),implyingtheabilityof581
array-basedassociationstudiestodetectexome-widesignificantsingle-variant582
associationsatequivalentsignificanceandatfarlestcostthanexomesequence583
associationstudies.584
585
WenextcomparedthecontributionstoT2Dheritabilityfromthestrongest586
(common)single-variantassociationsfromtheimputedGWAStothosefromthe587
strongest(mostlyrarevariant)gene-levelassociationsfromthesequenceanalysis.588
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
27
Usingageneticliabilitymodel69inwhichalldamagingvariantsinagenehavethe589
samedirectionofeffect(Methods),thethreeexome-widesignificantgene-level590
signalsexplainanestimated0.11%(MC4R),0.092%(PAM),and0.072%(SLC30A8)591
ofT2Dgeneticvariance.Theseestimatesareonly10-20%ofthevariances592
explainedbythethreestrongestindependentcommonvariantassociationsinthe593
imputedGWASofthesamesamples(TCF7L2,0.89%;KCNQ1,0.81%;andCDC123,594
0.35%)andifanythingoverstatetheheritabilityexplainedbyrarevariantsinthe595
gene-levelsignals,sincetheMC4RandPAMestimatesareattributablemostlytothe596
low-frequencyp.Ile269Asn(70.9%ofthegene-leveltotal)andp.Asp563Gly(83.3%)597
alleles.Weobtainedsimilarresultsinabroadercomparisonbetweenall(19)598
previouslyidentifiedindexSNPsachievingp<5Γ10-8intheimputedGWASandthe599
top19gene-levelsignalsfromoursequenceanalysis(Figure3b).600
601
TheseresultsargueagainstalargecontributiontoT2Dheritabilityfromrare602
variantsinthestrongestobservedgene-levelsignals,withonecaveat:asgene-level603
testsmayincludebenignallelesthatcandiluteevidenceforassociation,their604
aggregateeffectsmightunderestimatethetruecontributionofrarefunctional605
variantstoT2Dheritability12.However,whenweanalyzedallpossiblesubsetsof606
variationinthethreemostsignificantgene-levelsignals(Methods),noneexplained607
morethan20%oftheheritabilityofthesingle-variantTCF7L2association608
(maximumof0.18%forMC4R,0.15%forPAM,0.17%forSLC30A8).609
610
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
28
Wefinallyassessedwhetheranarray-basedstudycouldhavedetectedtheallelic611
seriesweobservedfromexomesequenceanalysis.Amongthevariantscontributing612
totheexome-widesignificantgene-levelassociationsinSLC30A8,MC4R,andPAM,613
95.3%werenotimputable(r2>0.4;Methods)fromthe1000Genomesmulti-614
ancestryreferencepanel67,and74.6%ofthoseinEuropeanswerenotimputable615
fromthelargerEuropean-focusedHaplotypeReferenceConsortiumpanel68.616
Similarly,90.2%ofvariants(79.7%ofEuropeanvariants)areabsentfromthe617
IlluminaExomeArray.618
619
Additionally,genesetassociationsusinggeneβscoresβ70(Methods)fromimputed620
GWASassociationsweresuggestive(fourgenesetsachievingp<0.05,nineachieving621
p<0.1;SupplementaryFigure18)butweakerthangenesetassociationsfromour622
sequenceanalysis.Someofthesegenesetassociationscanberecapturedinlarger623
array-basedstudies:scoresfromapublishedmulti-ancestryGWASof~110K624
samplesproducedp<0.05for12ofthe16genesetswestudied(Supplementary625
Figure19,Methods).However,evenherethegenes(andcorrespondingvariants)626
responsibleforthegenesetassociationswerebroadlydifferentbetweenthearray627
andsequence-basedstudies,asthetwomethodsoftenproduceduncorrelatedrank-628
orderingsofgeneswithingenesets(e.g.r=-0.11,p=0.57forthemousediabetesgene629
set;Figure3c).Collectively,theseresultsarguethatarray-basedGWASandexome630
sequencingarecomplementary,favoringlocusdiscoveryandenablingfull631
enumerationofpotentiallyinformativealleles,respectively.632
633
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
29
Useofnominallysignificantassociationsintranslationaldecisionsupport634
635
TheT2Ddrugtargetsweanalyzedexemplifytheopportunitiesandchallengesof636
usingcurrentexomesequencedatasetsintranslationalresearch.Gene-level637
associationsaresignificantacrossthesetargetsasaset(Figure2b),andrare638
variantspredictthecorrectdiseasedirectionalrelationshipforeachgene(Figure639
2f).However,rarevariantgene-levelsignalsforthesegenesarenowherenear640
detectableatexome-widesignificanceinourcurrentsamplesize:80%powerwould641
require110,000-180,000sequencedcases(220,000-360,000exomesinabalanced642
study,equivalentineffectivesamplesizeto750,000-1,200,000exomesfroma643
populationwithT2Dprevalence8%;Figure4a).644
645
Consequently,manyofthemoremodestassociations(e.g.p=0.05)incurrentsample646
sizesmayinfactpointtotherapeuticallyrelevantvariantsorgenes647
(SupplementaryFigure20)71,72.Ifthefalsepositiveratefortheseassociationsβ648
whichisexpectedtobegreaterthanthatforassociationsexceedingexome-wide649
significance71-73βcanbequantified74,75,thenamodestassociationsignalmay650
motivatefurtherexperimentationonagenewhilecompleteabsenceofan651
associationmayreduceenthusiasmforitsstudy.Forexample,theexpectedvalueof652
theexperimentcanbecalculatedbasedonthelikelihoodoftrueassociation,the653
costoftheexperiment,andthebenefitofitssuccess76,77(Figure4b).654
655
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
30
Wesoughttoquantifythefalsepositiveassociationratefornonsynonymous656
variantsobservedinourdataset,dependingonthep-valueobservedinsingle-657
variantanalysis.Wedevelopedamethodtousetheconsistencyofsingle-variant658
associationstatisticsbetweenoursequenceanalysisandaprevious24exomearray659
study(re-analyzedtoincludeonlythe41,967individualsnotinourcurrentstudy;660
Methods),togetherwithpublishedestimatesofthefractionofnonsynonymous661
associationsthatarecausalfordisease17,78,79,toestimatetheposteriorprobability662
oftrueandcausalassociation(PPA)forvariantsreachingdifferentlevelsof663
statisticalsignificance.WeprovideanoverviewofthismethodinFigure4c-f,a664
detaileddescriptioninMethods,anditssensitivitytomodelingassumptionsin665
SupplementaryFigure21.666
667
Weappliedthismethodtothreeclassesofvariants:genome-wide,withinT2D668
GWASloci,andwithingenesimplicatedinT2Dthroughprior(non-genetic)669
evidence.Modelparametersinthemiddleoftherangeweexplored(Methods)670
predictthat1.5%(95%CI:0.74%-2.2%)ofnonsynonymousvariantsthatachieve671
p<0.05aretrulyandcausallyassociatedwithT2D,increasingto3.6%(1.4%-5.9%)672
forvariantswithp<0.005,and9.7%(3.9%-15.0%)forvariantswithp<5Γ10-4673
(SupplementaryFigure22).Underthismodel,541(270-810)ofthe36,604674
nonsynonymousvariantswithp<0.05inourdatasetrepresenttrueandcausal675
associations.676
677
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
31
Withinthesetof94T2DGWASloci,weobservedevidenceofagreaterenrichment678
oftrueassociations:61.3%ofnonsynonymousvariantsachievingsequencep<0.05679
weredirectionallyconsistentintheindependentexomearrayanalysis(comparedto680
51.9%outsideofGWASloci).Were-calculatedamappingbetweensequencesingle-681
variantp-valueandPPAusingonlynonsynonymousvariantswithintheseloci.The682
resultingmodelpredictsthat2.0%(0.048%-4.0%)ofsuchvariantsoverall,8.1%683
(3.6%-12.4%)withsequencep<0.05,and17.2%(7.7%-24.1%)withsequence684
p<0.005representtrueandcausalT2Dassociations.Thissuggeststhatourdataset685
containsalargenumberofpotentiallystrong-effectvariantsinT2DGWASloci686
achievingnominalsignificance:of1059variantswithp<0.05,weestimateroughly687
60(26-93)of746withestimatedOR>2and41(18-63)of503withestimatedOR>3688
aretrueandcausalassociations(SupplementaryTables14-15).689
690
BeyondGWASloci,manyothergeneshaveevidenceβforexamplefromanimal80or691
cellularstudies50,56βthatmayleadaresearcherto(oftensubjectively)believethey692
areinvolvedinT2Dpathogenesis.WeextendedourapproachforPPAestimationto693
incorporatepriorevidencethatageneisrelevanttoT2D81,calibratingitfroma694
modelofthepriorassociationlikelihoodwithinT2DGWASloci(Figure4e-f;695
Methods).Underourmodel(SupplementaryTable16),apriorbeliefthatagene696
has(forexample)probability25%ofbeinginvolvedwithT2Dyieldsestimatesthat697
variantswithinitachievingp<0.05andp<0.005have10.7%and26.2%698
probabilitiesofbeingtrueandcausalT2Dassociations.699
700
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
32
Inthefuture,thesePPAcalculationscouldbeextendedtogene-levelassociations,701
whichwouldavoidconflictingresultsamongvariantswithinagenebutrequire702
larger-scalegene-levelreplicationdatathanwehadavailable.Additionalwork703
couldalsodevelopdataandmethodstoestimateobjective,ratherthansubjective,704
genepriorsandreducedependenceofourconclusionsonmodelingassumptions705
(SupplementaryFigure21).Still,thesePPAcalculationsprovideausefulinitial706
frameworktousegeneticsignalstosupportcost/benefitestimatesofβgo/no-goβ707
decisions82inthelanguageofdecisiontheory76,77(Figure4b).Tosupportuseofthis708
strategy,wehavemadeourexomesequenceassociationresultspublicallyavailable709
throughtheAMPT2DKnowledgePortal(www.type2diabetesgenetics.org),which710
supportsqueryingofallpre-computedsingle-variantassociationsandallowsusers711
todynamicallycomputesingle-variantandgene-levelassociationsaccordingto712
customcovariatesandcriteriaforsampleandvariantfiltering.713
714
Discussion715
716
OurresultspaintanuancedpictureofrarevariationandT2D,whichmayalsoapply717
toothercomplexdiseaseswithsimilargeneticarchitectures83.Ourgenesetanalyses718
showthatrarevariantgene-levelsignalsarelikelywidelydistributedacross719
numerousgenes,butthevastmajorityexplain,individually,vanishingamountsof720
T2Dheritabilityβevincedbythe>1Msampleslikelyrequiredtodetectexome-wide721
significantrarevariantsignalsinvalidatedtherapeutictargets.Gene-levelsignals722
thatdoreachexome-widesignificanceinouranalysis(suchasthoseinMC4Rand723
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
33
PAM)arenoteworthynotbecausetheyincludeunusuallystrongrarevariant724
associationsbutbecausetheyincludetypicalrarevariantassociationsboostedfrom725
nominaltoexome-widesignificancebylowfrequencyvariant(s)βwhich,726
empirically,canalsobedetectedbyarray-basedstudies.Therefore,formany727
complextraits(particularlythosewithmodestselectivepressurelikeT2D),the728
primaryvalueofexomesequencingbeyondarray-basedGWASmaybetoaid729
experimentalgenecharacterization84byidentifyingabroadseriesofrarecoding730
allelesβideallythroughmulti-ancestrysamplestocaptureasbroadasetofalleles731
aspossibleβratherthantodiscovernewdiseaseloci.Whole-genomesequencing732
willlikely,oneday,becomesufficientlycosteffectivetosubsumebotharray-based733
GWASandexomesequencing;evennow,itisatminimumanessentialmeansto734
expandimputationreferencepanelstopowergeneticdiscoveryfromGWAS.735
736
Ourresultsalsooutlineastrategyforusingexomesequencedatatoprioritizeor737
validategenesunderstudybybiologistsorpharmaceuticalindustryscientists.738
WehavepresentedaprincipledandempiricallycalibratedBayesianapproach739
(Figure4,SupplementaryTable16)toestimatetheassociationprobabilityfor740
anyvariantinourdataset.Whilecurrentlylimitedbyavailabledataandmodeling741
assumptions,itprovidesafirststeptoincreasetheinterpretabilityofexome742
sequenceassociationsevenabsentexome-widesignificance.Resultsandcustomized743
analysesfromourstudycanbeaccessedthroughapublicwebportal744
(www.type2diabetesgenetics.org),advancingthevisiontobroadlyuseexome745
sequencedataacrossmanyavenuesofbiomedicalresearch.746
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
34
Figurelegends747
748
Figure1:Exome-wideassociationanalysis.(a)AManhattanplotofexome749
sequencesingle-variantassociations.Genesclosesttovariantsachievingp<4.3Γ10β7750
(redline;atmostonepereach250KBregion)arelabeled.(b)AManhattanplotof751
gene-levelassociations;p-valuesshownaretheminimumacrossthefourgene-level752
analysesaftercorrectionforfouranalyses(Methods),withthemostsignificant753
geneslabeled.Redline:p=6.5Γ10-7.(c)Gene-levelassociationp-valuesforSLC30A8,754
usingtheburdentestonallelesinthe1/51%mask(themask,asdefinedin755
Methods,achievinggreateststatisticalsignificanceforSLC30A8),afterprogressive756
removalofvariantsinorderofincreasingsingle-variantassociationp-value.Theleft757
y-axis(blackline)showstheprogressivegene-levelp-value,thedashedlinep=0.05.758
Therighty-axis(blueline)showstheestimatedeffectsize(log10(OR)),withshaded759
blueindicatingthe95%confidenceintervalanddottedlineindicatingeffectsize=0.760
(d)VariantsobservedinSLC30A8within1/51%mask.Variantsarecoloredblue(if761
OR<1)orred(OR>1).Case(red)andcontrol(blue)frequenciesareshownfor762
eachvariant,withblackboxesshadedaccordingtothecontributionofeachvariant763
tothegene-levelsignal(computedbythedifferenceinlog10(p-value)afterremoval764
ofthevariantfromthetest).OR:oddsratio.765
766
Figure2:Genesetanalysis.(a-e)Boxplotsoftherankpercentiles(1beingthe767
highest)forgene-levelassociationswithin(a)11genesimplicatedinMaturity768
OnsetDiabetesoftheYoung(MODY);(b)8genesannotatedintheDrugBank769
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
35
databaseastheprimarytargetsofT2Dmedications;(c)31genesannotatedinthe770
MouseGenomeInformatics(MGI)databaseasharboringknockoutmutations771
causingnon-insulindependentdiabetes;(d)323genesannotatedintheMGI772
databaseasharboringknockoutmutationscausingimpairedglucosetolerancein773
mice;and(e)11geneswithstronggeneticevidenceforharboringcommoncausal774
codingvariants.P-valuescorrespondtoaone-sidedWilcoxonRank-Sumtest775
comparingtheassociationstothoseofmatchedcomparisongenes.(f)Estimated776
oddsratios(OR)ofdeleteriousnonsynonymousvariantsintheeightT2Ddrug777
targets.Targetsofagonistsarecoloredredandtargetsofinhibitorsarecolored778
blue.Errorbarsindicateonestandarderror.779
780
Figure3:Comparisonofexomesequencingtoarray-basedGWAS.(a)A781
Manhattanplotofsingle-variantassociationsinanarray-basedimputedGWASof782
thesubset(76%)ofthesamplesintheexomesequenceanalysisforwhicharray783
datawereavailable.Labelsandy-axisareequivalenttoFigure1a.(b)Theobserved784
liabilityvarianceexplained(LVE)bythetop19gene-levelassociationsfromthe785
exomesequenceanalysis(red;Exomes)andthetop19single-variantassociations786
(consideringonlyoneper250kb)fromtheimputedGWAS(blue;ImputedGWAS),787
aswellastheirratio(black;Ratio).SignalsarerankedbyLVEratherthanp-value.788
(c)Acomparisonofgenerankpercentilesaccordingtoexomesequencegene-level789
analysis(x-axis)andgenerankpercentilesaccordingtoproximitytoGWASsignals790
fromapublishedtransethnicT2DGWAS(y-axis;Methods).Genesshownarefrom791
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
36
thesetof31genesimplicatedinnon-insulindependentdiabetesfromknockout792
mice(thesetinFigure2c).793
794
Figure4:Translationaldecisionsupportfromexomesequencedata.(a)795
Estimatedpower,asafunctionoffuturesamplesize,todetectT2Dgene-level796
associations(atsignificancep=6.25Γ10-7)withaggregatefrequencyandoddsratios797
equaltothoseestimatedfromouranalysisineightestablishedT2Ddrugtargets(in798
Figure2f).(b)Aproposedworkflowforusingexomesequencedataingene799
characterization.Dependingonthepriorbeliefinthedisease-relevanceofthegene,800
thecostofexperimentalcharacterization,andthebenefitofvalidatingthegene,a801
decisiontoconductafurtherexperimentcouldbeinformedbytheprobabilitythat802
thegeneisrelevanttodisease,asestimatedfromexomesequenceassociation803
statistics(availablethroughwww.type2diabetesgenetics.org).(c-f)Tosupportthis804
workflow,weestimatedtheposteriorprobabilityoftrueandcausalassociation805
(PPA)fornonsynonymousvariantsinoursequenceanalysisbasedon(c)806
concordancewithindependentexomechipdataandpublishedestimatesofthe807
fractionofcausalcodingassociations(Methods).(d)PPAestimatesfor808
nonsynonymousvariantswithinT2DGWASlociareshownasafunctionofp-value809
(righty-axis,black;95%confidenceinterval,gray)togetherwiththetotalnumberof810
suchvariants(lefty-axis,red).ForvariantsoutsideofT2DGWASloci,wedeveloped811
amethodtofurthercompute(e)Bayesfactors,whichmeasuretheoddsoftrueand812
causalassociation,asafunctionofp-value,usingamodeloftheprioroddsoftrue813
andcausalassociationforvariantsinGWASloci(Methods).TheseBayesfactorscan814
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
37
be(f)combinedwithasubjectivepriorbeliefintheT2D-relevanceofagene(y-axis)815
toproducetheestimatedposteriorprobabilityoftrueandcausalassociationforany816
nonsynonymousvariantintheexomesequencedatasetbasedonitsobserved817
log10(p-value)(x-axis).Posteriorestimatesareshadedproportionaltovalue(red:818
low;white:high).Valuesshownareforthedefaultmodelingassumptionsof33%of819
missensevariantscausinggeneinactivationand30%oftruemissenseassociations820
representingthecausalvariant. 821
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
38
Funding822
BroadInstitute,USA:SequencingforT2D-GENEScohortswasfundedbythe823
NationalInstituteofDiabetesandDigestiveandKidneyDiseases(NIDDK)grant824
U01DK085526:MultiethnicStudyofTypeDiabetesGenesandNationalHuman825
GenomeResearchInstitute(NHGRI)grantU54HG003067:LargeScaleSequencing826
andAnalysisofGenomes.827
SequencingforGoT2DcohortswasfundedbyNationalInstituteofHealth(NIH)828
1RC2DK088389:Low-PassSequencingandHighDensitySNPGenotypinginType2829
Diabetes.830
SequencingforProDiGYcohortswasfundedbyNationalInstituteofDiabetesand831
DigestiveandKidneyDiseases(NIDDK)U01DK085526.832
SequencingforSIGMAcohortswasfundedbytheCarlosSlimFoundation:Slim833
InitiativeinGenomicMedicinefortheAmericas(SIGMA).834
AnalysiswassupportedbytheNationalInstituteofDiabetesandDigestiveand835
KidneyDiseases(NIDDK)grantU01DK105554:AMPT2D-GENESData836
CoordinationCenterandWebPortal.837
TheMountSinaiIPMBiobankProgramissupportedbyTheAndreaandCharles838
BronfmanPhilanthropies.839
TheWakeForeststudywassupportedbyNIHR01DK066358.840
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
39
Oxfordcohortsandanalysisisfundedby:TheEuropeanCommission(ENGAGE:841
HEALTH-F4-2007-201413);MRC(G0601261,G0900747-91070);National842
InstitutesofHealth(RC2-DK088389,DK085545,R01-DK098032,U01-DK105535);843
WellcomeTrust(064890,083948,085475,086596,090367,090532,092447,844
095101,095552,098017,098381,100956,101630,203141)845
TheFUSIONstudyissupportedbyNIHgrantsDK062370andDK072193.846
TheresearchfromtheKoreancohortwassupportedbyagrantoftheKoreaHealth847
TechnologyR&DProjectthroughtheKoreaHealthIndustryDevelopmentInstitute848
(KHIDI),fundedbytheMinistryofHealth&Welfare,RepublicofKorea(grant849
number:HI14C0060,HI15C1595).850
TheMalmΓΆPreventiveProjectandtheScaniaDiabetesRegistrywere851
supportedbyaSwedishResearchCouncilgrant(LinnΓ©)totheLundUniversity852
DiabetesCentre.853
TheBotniaandThePPP-Botniastudies(L.G.,T.T.)havebeenfinancially854
supportedbygrantsfromFolkhΓ€lsanResearchFoundation,theSigridJuselius855
Foundation,TheAcademyofFinland(grantsno.263401,267882,312063toLG,856
312072toTT),NordicCenterofExcellenceinDiseaseGenetics,EU(EXGENESIS,857
EUFP7-MOSAICFP7-600914),OllqvistFoundation,SwedishCulturalFoundationin858
Finland,FinnishDiabetesResearchFoundation,FoundationforLifeandHealthin859
Finland,SigneandAneGyllenbergFoundation,FinnishMedicalSociety,Paavo860
NurmiFoundation,HelsinkiUniversityCentralHospitalResearchFoundation,861
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
40
PerklΓ©nFoundation,NΓ€rpesHealthCareFoundationandAhokasFoundation.The862
studyhasalsobeensupportedbytheMinistryofEducationinFinland,Municipal863
HeathCareCenterandHospitalinJakobstadandHealthCareCentersinVasa,864
NΓ€rpesandKorsholm.TheskilfulassistanceoftheBotniaStudyGroupisgratefully865
acknowledged.866
TheJacksonHeartStudy(JHS)issupportedbycontractsHHSN268201300046C,867
HHSN268201300047C,HHSN268201300048C,HHSN268201300049C,868
HHSN268201300050CfromtheNationalHeart,Lung,andBloodInstituteandthe869
NationalInstituteonMinorityHealthandHealthDisparities.Dr.Wilsonissupported870
byU54GM115428fromtheNationalInstituteofGeneralMedicalSciences.871
TheDiabeticCohort(DC)andMulti-EthnicCohort(MEC)weresupportedby872
individualresearchgrantsandclinicianscientistawardschemesfromtheNational873
MedicalResearchCouncil(NMRC)andtheBiomedicalResearchCouncil(BMRC)of874
Singapore.875
TheDiabeticCohort(DC),Multi-EthnicCohort(MEC),SingaporeIndianEye876
Study(SINDI)andSingaporeProspectiveStudyProgram(SP2)weresupported877
byindividualresearchgrantsandclinicianscientistawardschemesfromthe878
NationalMedicalResearchCouncil(NMRC)andtheBiomedicalResearchCouncil879
(BMRC)ofSingapore.880
TheLongevitystudyatAlbertEinsteinCollegeofMedicine,USAwasfundedby881
TheAmericanFederationforAgingResearch,theEinsteinGlennCenter,and882
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
41
NationalInstituteonAging(PO1AG027734,R01AG046949,1R01AG042188,883
P30AG038072).884
TheTwinsUKstudywasfundedbytheWellcomeTrustandEuropean885
CommunityβsSeventhFrameworkProgramme(FP7/2007-2013).TheTwinsUK886
studyalsoreceivessupportfromtheNationalInstituteforHealthResearch(NIHR)-887
fundedBioResource,ClinicalResearchFacilityandBiomedicalResearchCentre888
basedatGuy'sandStThomas'NHSFoundationTrustinpartnershipwithKing's889
CollegeLondon.890
FraminghamHeartStudyissupportedbyNIHcontractNHLBIN01-HC-25195and891
HHSN268201500001I.ThisresearchwasalsosupportedbyNIAAG08122and892
AG033193,NIDDKU01DK085526,U01DK078616andK24DK080140,NHLBIR01893
HL105756,andgrantsupplementR01HL092577-06S1forthisresearch.Wealso894
acknowledgethededicationoftheFHSstudyparticipantswithoutwhomthis895
researchwouldnotbepossible.896
TheMexicoCityDiabetesStudyhasbeensupportedbythefollowinggrants:897
RO1HL24799fromtheNationalHeart,Lung,andBloodInstitute;ConsejoNacional898
deCienciayTecnologΔ±Β΄a2092,M9303,F677-M9407,251M,2005-C01-14502,and899
SALUD2010-2151165;andConsejoNacionaldeCienciayTecnologΔ±Β΄a(CONACyT)900
[FondodeCooperacioΒ΄nInternacionalenCienciayTecnologΔ±Β΄a(FONCICYT)C0012-901
2014-01-247974.902
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
42
TheKAREcohortwassupportedbygrantsfromKoreaCentersforDiseaseControl903
andPrevention(4845β301,4851β302,4851β307),andanintramuralgrantfrom904
theKoreaNationalInstituteofHealth(2016-NI73001-00).905
TheDiabetesinMexicoStudywassupportedbyConsejoNacionaldeCienciay906
TecnologΓagrantnumberS008-2014-1-233970andbyInstitutoCarlosSlimdela907
Salud,AC.908
TheAtherosclerosisRiskinCommunitiesstudyhasbeenfundedinwholeorin909
partwithFederalfundsfromtheNationalHeart,Lung,andBloodInstitute,National910
InstitutesofHealth,DepartmentofHealthandHumanServices(contractnumbers911
HHSN268201700001I,HHSN268201700002I,HHSN268201700003I,912
HHSN268201700004IandHHSN268201700005I).Theauthorsthankthestaffand913
participantsoftheARICstudyfortheirimportantcontributions.Fundingsupport914
forβBuildingonGWASforNHLBI-diseases:theU.S.CHARGEconsortiumβwas915
providedbytheNIHthroughtheAmericanRecoveryandReinvestmentActof2009916
(ARRA)(5RC2HL102419).CHARGEsequencingwascarriedoutattheBaylor917
CollegeofMedicineHumanGenomeSequencingCenter(U54HG003273and918
R01HL086694).FundingforGOESPwasprovidedbyNHLBIgrantsRC2HL-103010919
(HeartGO)andexomesequencingwasperformedthroughNHLBIgrantsRC2HL-920
102925(BroadGO)andRC2HL-102926(SeattleGO).921
TheinfrastructurefortheAnalysisCommonsissupportedbyR01HL105756922
(NHLBI,B.M.P.),U01HL130114(NHLBI,B.M.P.)and5RC2HL102419(NHLBI,E.B.).923
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
43
TheNHLBIExomeSequencingProject(ESP)wassupportedthroughtheNHLBI924
GrandOpportunity(GO)programandfundedthroughbygrantsRC2HL103010925
(HeartGO),RC2HL102923(LungGO),andRC2HL102924(WHISP)forproviding926
dataandDNAsamplesforanalysis.TheexomesequencingfortheNHLBIESPwas927
supportedbyNHLBIgrantsRC2HL102925(BroadGO)andRC2HL102926928
(SeattleGO).929
ThisresearchwassupportedbytheMulti-EthnicStudyofAtherosclerosis(MESA)930
contractsHHSN268201500003I,N01-HC-95159,N01-HC-95160,N01-HC-95161,931
N01-HC-95162,N01-HC-95163,N01-HC-95164,N01-HC-95165,N01-HC-95166,932
N01-HC-95167,N01-HC-95168,N01-HC-95169,UL1-TR-000040,UL1-TR-001079,933
andUL1-TR-001420.Theprovisionofgenotypingdatawassupportedinpartbythe934
NationalCenterforAdvancingTranslationalSciences,TSCIgrantUL1TR001881,935
andtheNationalInstituteofDiabetesandDigestiveandKidneyDiseaseDiabetes936
Research(DRC)grantDK063491.937
TheSanAntonioMexicanAmericanFamilyStudies(SAMAFS)aresupportedby938
thefollowinggrants/institutes.TheSanAntonioFamilyHeartStudy(SAFHS)and939
SanAntonioFamilyDiabetes/GallbladderStudy(SAFDGS)weresupportedbyU01940
DK085524,R01HL0113323,P01HL045222,R01DK047482,andR01DK053889.941
TheVeteransAdministrationGeneticEpidemiologyStudy(VAGES)studywas942
supportedbyaVeteransAdministrationEpidemiologicgrant.TheFamily943
InvestigationofNephropathyandDiabetes-SanAntonio(FIND-SA)studywas944
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
44
supportedbyNIHgrantU01DK57295.TheSAMAFSresearchteamacknowledges945
lateDr.HannaE.AbboudβscontributionstotheresearchactivitiesoftheSAMAFS.946
Samplescollection,researchandanalysisfromtheHongKongDiabetesRegister947
(HKDR)attheChineseUniversityofHongKong(CUHK)weresupportedbythe948
HongKongFoundationforResearchandDevelopmentinDiabetesestablished949
undertheauspicesoftheChineseUniversityofHongKong,theHongKong950
GovernmentResearchGrantsCommitteeCentralAllocationScheme(CUHK1/04C),951
aResearchGrantsCouncilEarmarkedResearchGrant(CUHK4724/07M),the952
InnovationandTechnologyFund(ITS/088/08andITS/487/09FP),andthe953
ResearchGrantsCommitteeTheme-basedResearchScheme(T12-402/13N).954
TheTODAYcontributiontothisstudywascompletedwithfundingfromNIDDKand955
theNIHOfficeoftheDirector(OD)throughgrantsU01-DK61212,U01-DK61230,956
U01-DK61239,U01-DK61242,andU01-DK61254;fromtheNationalCenterfor957
ResearchResourcesGeneralClinicalResearchCentersProgramgrantnumbers958
M01-RR00036(WashingtonUniversitySchoolofMedicine),M01-RR00043-45959
(ChildrenβsHospitalLosAngeles),M01-RR00069(UniversityofColoradoDenver),960
M01-RR00084(ChildrenβsHospitalofPittsburgh),M01-RR01066(Massachusetts961
GeneralHospital),M01-RR00125(YaleUniversity),andM01-RR14467(University962
ofOklahomaHealthSciencesCenter);andfromtheNCRRClinicalandTranslational963
ScienceAwardsgrantnumbersUL1-RR024134(ChildrenβsHospitalof964
Philadelphia),UL1-RR024139(YaleUniversity),UL1-RR024153(Childrenβs965
HospitalofPittsburgh),UL1-RR024989(CaseWesternReserveUniversity),UL1-966
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
45
RR024992(WashingtonUniversityinStLouis),UL1-RR025758(Massachusetts967
GeneralHospital),andUL1-RR025780(UniversityofColoradoDenver).Thecontent968
issolelytheresponsibilityoftheauthorsanddoesnotnecessarilyrepresentthe969
officialviewsoftheNationalInstitutesofHealth.970
Acknowledgements971
RuthLoosissupportedbytheNIH(R01DK110113,U01HG007417,R01DK101855,972
R01DK107786).973
AndrewPMorrisissupportedbytheNIH-NIDDK(U01DK105535);andaWellcome974
TrustSeniorFellowinBasicBiomedicalScience(awardWT098017).975
JoseCFlorezisanMGHResearchScholarandissupportedbyNIDDKK24976
DK110550.977
GraemeIBellissupportedbyP30DK020595.978
MichiganStateUniversityissupportedbyNIHGrant1K23DK114551-01.979
MarkIMcCarthyisaWellcomeTrustSeniorInvestigator(WT098381);anda980
NationalInstituteofHealthResearch(NIHR)SeniorInvestigator.Theviews981
expressedinthisarticlearethoseoftheauthor(s)andnotnecessarilythoseofthe982
NHS,theNIHR,ortheDepartmentofHealth.983
YoonShinChoacknowledgedsupportfromtheNationalResearchFoundationof984
Korea(NRF)grant(NRF-2017R1A2B4006508).985
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
46
Ching-YuChengissupportedbyClinicianScientistAward(NMRC/CSA-986
SI/0012/2017)oftheSingaporeMinistryofHealthβsNationalMedicalResearch987
Council.988
LuCAMP:WewishtothankA.Forman,T.H.LorentzenandG.J.Klavsenfor989
laboratoryassistance,P.Sandbeckfordatamanagement,G.Lademannfor990
secretarialsupport,andT.F.Toldstedforgrantmanagement.Thisprojectwas991
fundedbytheLundbeckFoundationandproducedbyTheLundbeckFoundation992
CentreforAppliedMedicalGenomicsinPersonalisedDiseasePrediction,993
Prevention,andCare(www.lucamp.org).TheNovoNordiskFoundationCenterfor994
BasicMetabolicResearchisanindependentResearchCenterattheUniversityof995
CopenhagenpartiallyfundedbyanunrestricteddonationfromtheNovoNordisk996
Foundation(www.metabol.ku.dk).FurtherfundingcamefromtheDanishCouncil997
forIndependentResearchMedicalSciences.TheInter99wasinitiatedbyTorben998
JΓΈrgensen(principalinvesitigator[PI]),KnutBorch-Johnsen(co-PI),HansIbsen,and999
TroelsF.Thomsen.ThesteeringcommitteecomprisestheformertwoandCharlotta1000
Pisinger.ThestudywasfinanciallysupportedbyresearchgrantsfromtheDanish1001
ResearchCouncil,theDanishCentreforHealthTechnologyAssessment,Novo1002
Nordisk,theResearchFoundationofCopenhagenCounty,theMinistryofInternal1003
AffairsandHealth,theDanishHeartFoundation,theDanishPharmaceutical1004
Association,theAugustinusFoundation,theIbHenriksenFoundation,theBecket1005
Foundation,andtheDanishDiabetesAssociation.DanielWitteissupportedbythe1006
DanishDiabetesAcademy,whichisfundedbytheNovoNordiskFoundation.1007
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
47
WethankallstudyparticipantsoftheDiabeticCohort(DC),Multi-EthnicCohort1008
(MEC),SingaporeIndianEyeStudy(SINDI)andSingaporeProspectiveStudy1009
Program(SP2)fortheircontributionsandtheNationalUniversityHospitalTissue1010
Repository(NUHTR)forbiospecimensamplestorage.1011
WethanktheJacksonHeartStudy(JHS)participantsandstafffortheir1012
contributionstothiswork.1013
ThisstudywasprovidedwithbiospecimensanddatafromtheKoreanGenome1014
AnalysisProject(4845-301),theKoreanGenomeandEpidemiologyStudy(4851-1015
302),andtheKoreaBiobankProject(4851-307,KBP-2013-11andKBP-2014-68)1016
thatweresupportedbytheKoreaCentersforDiseaseControlandPrevention,1017
RepublicofKorea.1018
ThePakistanGenomicResource(PGR)wouldliketothankallthestudy1019
participantsfortheirparticipation.PGRisfundedthroughendowmentsawardedto1020
CNCD,Pakistan.1021
TheKORAstudywasinitiatedandfinancedbytheHelmholtzZentrumMΓΌnchenβ1022
GermanResearchCenterforEnvironmentalHealth,whichisfundedbytheGerman1023
FederalMinistryofEducationandResearch(BMBF)andbytheStateofBavaria.1024
Furthermore,KORAresearchwassupportedwithintheMunichCenterofHealth1025
Sciences(MC-Health),Ludwig-Maximilians-UniversitΓ€t,aspartofLMUinnovativ.For1026
thispublication,biosamplesfromtheKORABiobankaspartoftheJointBiobank1027
Munich(JBM)havebeenused.1028
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
48
RonaldCMaandJulianaCChanacknowledgedsupportfromtheHongKong1029
ResearchGrantsCouncilTheme-basedResearchScheme(T12-402/13N),Research1030
GrantsCouncilGeneralResearchFund(Ref.14110415),theFocusedInnovation1031
Scheme,theVice-ChancellorOne-offDiscretionaryFund,thePostdoctoral1032
FellowshipSchemeoftheChineseUniversityofHongKong,aswellastheChinese1033
UniversityofHongKong-ShanghaiJiaoTongUniversityJointResearchCollaboration1034
Fund.WewouldalsoliketothankallmedicalandnursingstaffofthePrinceof1035
WalesHospitalDiabetesMellitusEducationCentre,HongKong.1036
AuthorContributions1037
Leadership.J.F.,N.P.B.,J.C.F.,M.I.M.,M.B.Analysisteam.J.M.M.,C.F.,M.S.U.,1038
A.Mahajan,T.W.B.,L.Chen,S.C.,A.E.,S.Hanks,A.U.J.,K.M.,A.N.,A.J.P.,N.W.R.,N.R.R.,1039
H.M.S.,J.M.T.,R.P.W.,L.J.S.,A.P.M.Projectmanagement/Supportroles.L.Caulkins,1040
R.K.,M.C.Datageneration.BroadGenomicsPlatform.T2D-GENES.A.C.,R.A.D.,S.G.,1041
S.Han,H.M.K.,B.-J.K.,H.A.K.,J.K.,J.Liu,K.L.M.,M.C.N.,M.P.,R.S.V.,C.S.,W.Y.S.,C.H.T.,1042
F.T.,B.T.,R.M.v.D.,M.V.,T.-Y.W.,G.Atzmon,N.B.,J.B.,D.W.B.,J.C.C.,E.Chan,C.-Y.C.,1043
Y.S.C.,F.S.C.,R.D.,B.G.,J.S.K.,S.H.K.,M.L.,D.M.L.,E.S.T.,J.T.,J.G.W.,E.Bottinger,J.C.,J.D.,1044
P.F.,M.Y.H.,Y.J.K.,J.-Y.L.,J.Lee,R.L.,R.C.M.,A.D.M.,C.N.P.,K.S.P.,A.R.,D.S.,X.S.,Y.Y.T.,1045
C.L.H.,G.Abecasis,G.I.B.,N.J.C.,M.S.,R.S.,J.B.M.,D.A.GoT2D.V.L.,L.L.B.,L.G.,P.N.,1046
T.D.S.,T.T.,K.S.S.LuCAMP.M.E.J.,A.L.,D.R.W.,N.G.,T.H.,O.P.ProDiGY.L.D.,K.L.D.,1047
M.K.,E.M.-D.,C.P.,N.S.,B.B.,P.Z.,D.D.SIGMA.C.C.-C.,E.CΓ³rdova,M.E.G.-S.,H.G.-O.,1048
J.M.M.-H.,A.M.-H.,E.M.-C.,C.R.-M.,C.Gonzalez,M.E.G.,C.A.A.-S.,C.H.,B.E.H.,L.O.,T.T.-1049
L.CHARGE.J.W.,E.Boerwinkle,J.A.B.,J.S.F.,N.L.H.-C.,C.-T.L.,A.K.M.,A.C.M.,B.M.P.,1050
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
49
S.W.,P.S.d.V.,J.D.,S.R.H.,C.J.O'D.,J.P.,J.B.M.Regeneron.T.M.T.,J.B.L.,A.Marcketta,1051
C.O'D.,D.J.C.,H.L.K.,F.E.D.,A.B.,D.C.KORA.T.M.S.,C.Gieger,T.M.,K.S.1052
ESP.E.Boerwinkle,M.G.,N.L.H.-C.,A.C.M.,W.S.P.,B.M.P.,A.P.R.,R.P.T.,C.J.O'D.,L.L.,1053
S.R.,J.I.R.1054
1055
Disclosures1056
PhilipZeitlerisaconsultantforMerck,Daichii-Sankyo,Boerhinger-Ingelheim,and1057
Janssen.1058
1059
BruceMPsatyservesontheDSMBofaclinicaltrialfundedbyZollLifeCorandon1060
theSteeringCommitteeoftheYaleOpenDataAccessProjectfundedbyJohnson&1061
Johnson. 1062
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
50
Methods1063
Sampleselection1064
Wedrewsamplesforexomesequencingfromsixconsortia(SupplementaryTable1065
1):1066
1. TheT2D-GENES(Type2DiabetesGeneticExplorationbyNext-generation1067
sequencinginmulti-EthnicSamples)consortium,anNIDDK-funded1068
internationalresearchconsortiumseekingtoidentifygeneticvariantsforT2D1069
throughmultiethnicsequencingstudies24.1070
2. TheSlimInitiativeinGenomicMedicinefortheAmericas:Type2Diabetes1071
(SIGMAT2D),aninternationalresearchconsortiumfundedbytheCarlosSlim1072
FoundationtoinvestigategeneticriskfactorsofT2DwithinMexicanandLatin1073
Americanpopulationsandtranslatethosefindingtoimprovedmethodsof1074
treatmentandprevention85.1075
3. TheGeneticsofType2Diabetes(GoT2D)consortium,anNIDDK-funded1076
internationalresearchconsortiumseekingtounderstandtheallelicarchitecture1077
ofT2Dthroughlow-passwhole-genomesequencing,deepexomesequencing,1078
andhigh-densitySNPgenotypingandimputation24.1079
4. TheExomeSequencingProject(ESP),anNHLBI-fundedresearchconsortiumto1080
investigatenovelgenesandmechanismscontributingtoheart,lung,andblood1081
disordersthroughwholeexomesequencing86.1082
5. TheLundbeckFoundationCentreforAppliedMedicalGenomicsinPersonalised1083
DiseasePrediction,Prevention,andCare(LuCamp)study,whichresearches1084
wholeexomevariationinDanishmetabolicdiseasesincludingdiabetes21.1085
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
51
6. TheProDiGY(ProgressinDiabetesGeneticsinYouth)consortium,anNIDDK-1086
fundedresearchconsortiumtoinvestigategeneticvariantsforchildhoodT2D.1087
Eachconsortiumprovidedindividual-levelinformationonT2Dcase-controlstatus1088
accordingtostudy-specificcriteriaaswellaskeycovariatesincludingage,sex,and1089
BMI(SupplementaryTable1).Inaddition,severalconsortiaprovideddataon1090
fastingglucose,2-hourglucosefollowingglucosechallenge,anduseofanti-1091
hyperglycemicmedications.Weexcludedascontrolsindividualswitha2-hour1092
glucosevalueβ₯11.1mmol/L(whichmeetsdiagnosticcriteriaforT2D)orwithany1093
twoofthefollowingfeaturessuggestiveofT2D:fastingglucoseβ₯7mmol/L,1094
hemoglobinA1cβ₯6.5%,orrecordedastakingananti-hyperglycemicmedication.1095
Weoptedtorequiretwoofthepreviousfeaturessincethereisroomforerrorin1096
each:fastingvaluesusedinT2Ddiagnosticcriteriaarerequiredtorepresentatleast1097
aneight-hourfast,accuracyvariesacrosshemoglobinA1cassays,andanti-glycemic1098
medicationsareoccasionallytakenbynon-diabeticindividuals.1099
1100
Allsampleswereapprovedforusebytheirhomeinstitutionβsinstitutionalreview1101
boardorethicscommittee,aspreviouslyreported21,24,85,86.Samplesnewly1102
sequencedatTheBroadInstituteaspartofT2D-GENES,SIGMA,andProDiGYare1103
coveredunderPartnersHumanResearchCommitteeprotocol#2017P000445/PHS1104
βDiabetesGeneticsandRelatedTraitsβ.1105
1106
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
52
Availabilityofsequencedataandphenotypesforthisstudyisavailableviathe1107
databaseofGenotypesandPhenotypes(dbGAP)and/ortheEuropeanGenome-1108
phenomeArchive,asindicatedinSupplementaryTable1.1109
1110
SampleSequencing1111
Forroughlyhalfthestudyparticipants(someofT2D-GENES24,GoT2D24,SIGMA-1112
T2D85,LuCAMP21,ESP86),exomesequencedatawereavailablefromprevious1113
studies.Fortheseindividuals(SupplementaryTable1),weobtainedaccesstoand1114
aggregatedBAMfilescontainingunalignedsequencereads,whichweregenerated1115
andanalyzedaspreviouslydescribed23,62,79,80.1116
1117
Fortheremainingparticipants,de-identifiedDNAsamplesweresenttotheBroad1118
InstituteinCambridge,MA,USAwheresampleswith(a)sufficienttotalDNA1119
quantityandminimumDNAconcentrations(asestimatedbyPicogreen)and(b)1120
highqualitygenotypes(asmeasuredbya24SNPSequenomiPLEXassay)were1121
advancedforsubsequentsequencing.Libraryconstructionwasperformedas1122
previouslydescribed87withsomeslightmodifications.InitialgenomicDNAinput1123
intoshearingwasreducedfrom3Β΅gto50ngin10Β΅Lofsolutionandenzymatically1124
sheared.Foradapterligation,dual-indexedIlluminapairedendadapterswere1125
replacedwithpalindromicforkedadapterswithunique8baseindexsequences1126
embeddedwithintheadapterandaddedtoeachend.1127
1128
In-solutionhybridselectionwasperformedusingtheIlluminaRapidCapture1129
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
53
Exomeenrichmentkitwith38Mbtargetterritory(29Mbbaited),including98.3%of1130
theintervalsintheRefseqexomedatabase.Dual-indexedlibrarieswerepooledinto1131
groupsofupto96samplespriortohybridization,withliquidhandlingautomated1132
onaHamiltonStarletLiquidHandlingsystem.Theenrichedlibrarypoolswere1133
quantifiedviaPicoGreenafterelutionfromstreptavidinbeadsandthennormalized1134
toarangecompatiblewithsequencingtemplatedenatureprotocols.1135
1136
Followingsamplepreparation,thelibrariespreparedusingforked,indexed1137
adapterswerequantifiedusingquantitativePCR(KAPABiosystems),normalizedto1138
2nM,andpooledbyequalvolumeusingtheHamiltonStarlet.Poolswerethen1139
denaturedusing0.1NNaOH.Denaturedsamplesweredilutedintostriptubesusing1140
theHamiltonStarlet.1141
1142
Clusteramplificationofthetemplateswasperformedaccordingtothe1143
manufacturerβsprotocol(Illumina)usingtheIlluminacBot.Flowcellswere1144
sequencedonHiSeq4000Sequencing-by-SynthesisKits,thenanalyzedusing1145
RTA2.7.3.1146
1147
Variantcallingandqualitycontrol1148
Sequencingreadsforallsamples(bothnewlysequencedandpreviouslysequenced)1149
wereprocessedandalignedtothehumangenome(buildhg19)usingthePicard1150
(broadinstitute.github.io/picard/),BWA88,andGATK89softwarepackages,following1151
best-practicepipelines;datafrompreviouslypublishedstudiesweretreatedthe1152
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
54
sameasdatafromthenewstudy(i.e.beginningfromunalignedreads)toensure1153
uniformityofprocessing.Singlenucleotideandshortindelvariantswerethencalled1154
usingaseriesofGATKcommands(versionnightly-2015-07-31-g3c929b0):1155
ApplyRecalibration,CombineGVCFs,CombineVariants,GenotypeGVCFs,1156
HaplotypeCaller,SelectVariants,andVariantFiltration.Variantswerecalledwithin1157
50bpofanyregiontargetedforcaptureinanysequencedcohort.1158
1159
Wecomputedhardcalls(theGATK-calledgenotypesbutsetasmissingata1160
genotypequality[GQ]<20threshold)anddosages(theexpectedalternateallele1161
count,definedasPr(RX|data)+2Pr(XX|data),whereRisthereferencealleleandX1162
thealternativeallele)foreachindividualateachvariantsite.Weusedhardcallsfor1163
qualitycontrolanddosagesindownstreamassociationanalyses.Wecomputed1164
dosagesontheXchromosome(outsideofthepseudo-autosomalregion)accounting1165
forsex,treatingmalesashaploid.1166
1167
Toperformdataqualitycontrol,wefirstcalculatedarangeofmetricsmeasuring1168
samplesequencingquality(SupplementaryFigure2).Wethenstratifiedsamples1169
byancestryandsequencecapturetechnologyandexcludedfromfurtheranalysis1170
samplesthatwereoutliersaccordingtoanymetric,basedonvisualinspectionby1171
comparisontoothersampleswithinthesamestratum.Afulllistofmetricsusedfor1172
exclusionandthenumberofsamplesexcludedbasedoneachmetricisshownin1173
SupplementaryTable2.1174
1175
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
55
Afterexclusionofsamples,wecalculatedanadditionalsetofvariantmetricsand1176
excludedanyvariantwithoverallcallrate<0.3,heterozygosityof1,orheterozygote1177
allelebalanceof0or1(i.e.100%or0%ofreadscallednon-referencefor1178
heterozygousgenotypes).Weintentionallychosethesenon-stringentinitialvariant1179
quality-controlthresholdsduetotheheterogeneityofcaptureandsequencing1180
technologiesusedinourstudy;weperformedmuchmorestringentvariantquality1181
controlduringsingle-variantorgene-levelassociationanalysis.Werefertothe1182
49,484samplesand7.02Mvariantspassingthisfirstroundofnon-stringentquality1183
controlastheβcleanβdataset.1184
1185
Additionalqualitycontrolforassociationanalysisinsequencedata1186
Followinginitialsampleandvariantqualitycontrol,weperformedadditional1187
exclusionsofsamplesfromassociationanalysis.First,wecomputedatransethnic1188
setofβancestryβSNPsforuseinidentity-by-descent(IBD)andprincipalcomponent1189
(PC)analysis.Webeganthisanalysiswithvariantsinthecleandataset(a)with1190
genotypecallrate>95%,(b)withminorallelefrequency(MAF)>1%ineach1191
ancestry,and(c)furtherthan250KbfromtheHLAregionoranestablishedT2D1192
associationsignal.WeLD-prunedvariantsusingPLINK90basedonmaximumr2=0.21193
(parametersβindep-pairwise5050.2).Weusedtheremaining171Kvariantsto1194
estimatepairwiseindividualIBDusingPLINK,andthetop10PCsofgenetic1195
ancestryusingEIGENSTRAT91.ForeachpairofindividualswithIBD>0.9,we1196
excludedtheindividualwiththelowercallrate(337duplicateexclusionsin1197
SupplementaryFigure2).Wethenexcluded,foreachofthefiveancestries,any1198
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
56
individualwhoappeared,basedonvisualinspectionofthefirsttwotransethnicPCs,1199
tolieoutsideofthemainPCclustercorrespondingtothatancestry(133ethnic1200
outliersinSupplementaryFigure2).Finally,weusedthesubsetoftransethnic1201
ancestrySNPsontheXchromosometocomparegeneticsextoreportedsex,using1202
PLINK,andexcludedalldiscordantindividuals(273sexdiscordancesin1203
SupplementaryFigure2).1204
1205
Atthisstagewealsoexcludedthe3,510childhooddiabetescasesfromtheSEARCH1206
andTODAYstudies.Weinitiallyhopedtoincludethesesamplesascasesinboth1207
single-variantandgene-levelanalysis,usingeitherPCsorlinearmixedmodelsto1208
adjustforanyancestrydifferencesbetweenthemandtheothersamples.However,1209
whilesingle-variantassociationstatistics(computedviaameta-analysisof1210
ancestry-levelassociations)remainedwell-calibratedwiththesestudiesincluded1211
(SupplementaryFigure23ab),gene-levelanalysisyieldedadramaticallyinflated1212
QQplot(SupplementaryFigure23cd).ExclusionoftheSEARCHandTODAYstudy1213
samples,samplesfailingqualitycontrol,andvariantsthatbecamemonomorphicas1214
aresultofthesesampleexclusions,yieldedanβanalysisβdatasetof45,2311215
individualsand6.33Mvariants.1216
1217
Afterthesethreeroundsofsampleexclusions,weidentifiedfivesetsofancestry-1218
specificβancestryβSNPs.Weusedthesameprocedureasforthetransethnic1219
ancestrySNPs(describedabove),exceptthatweappliedtheMAFthresholdonly1220
withintheappropriateancestry.WeusedtheseancestrySNPstoestimate,foreach1221
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
57
ancestry,pairwiseIBDvalues,geneticrelatednessmatrices(GRMs),andPCsforuse1222
indownstreamassociationanalysis.1223
1224
Additionally,fromtheIBDvalues,wegeneratedalistofunrelatedindividualswithin1225
eachancestrybyexcludingtheindividualwiththelowercallrateinanypairof1226
individualswithIBD>0.3(leadingto2,157excludedindividuals).Theresulting1227
βunrelatedsanalysisβsetconsistedof43,090individuals(19,828casesand23,2621228
controls)andyielded6.29Mnon-monomorphicvariants.Weusedthissetof1229
individualsandvariantsforsingle-variantandgene-leveltests(describedbelow)1230
thatrequiredanunrelatedsetofindividualsforanalysis.1231
1232
Wecarriedoutpowercalculations92forsingle-variantorgene-leveltestsassuminga1233
diseaseprevalenceof0.08toconvertpopulationfrequenciesandORstocaseand1234
controlfrequencies,andasamplesize(19,828casesand23,262controls)froman1235
analysisofonlyunrelatedindividuals.Ourpowercalculationsassumedthatallelic1236
effectswerehomogeneousacrossancestries.1237
1238
Variantannotation1239
WeannotatedvariantswiththeENSEMBLVariantEffectPredictor93(VEP,version1240
87).AnnotationswereproducedforallENSEMBLtranscriptswiththeβflag-pick-1241
alleleoptionusedtoassignaβbestguessβannotationtoeachvariantaccordingto1242
thefollowingorderedcriteriafortranscripts94:transcriptsupportlevel(TSL,i.e.1243
supportedbymRNA),biotype(i.e.protein_coding),APPRISisoformannotation(i.e.1244
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
58
principal),deleteriousnessofannotation(i.e.prefertranscriptswithhigherimpact1245
annotations),CCDS95statusoftranscript(i.e.ahigh-qualitytranscriptset),canonical1246
statusoftranscript,andtranscriptlength(i.e.longerpreferred).WeusedtheVEP1247
LofTee(https://github.com/konradjk/loftee)anddbNSFP(version3.2)96pluginsto1248
generateadditionalbioinformaticpredictionsofvariantdeleteriousness;fromthe1249
dbNSFPplugin,wetookannotationsfrom15differentbioinformaticalgorithms1250
(listedinSupplementaryFigure8)aswellastherecentmCAP97algorithm.As1251
theseannotationswerenottranscript-specific,weassignedthemtoalltranscripts1252
forthepurposeofdownstreamanalysis.1253
1254
Allsingle-variantanalysesreportedinthemanuscriptorfiguresareshownusing1255
theβbestguessβannotationforeachvariant(asdescribedabove).1256
1257
Single-variantassociationanalysisinsequencedata1258
Toperformsingle-variantassociationanalysis,westratifiedsamplesbycohortof1259
originandsequencingtechnology(i.e.samplesfromthesamecohortbutsequenced1260
atdifferenttimeswereanalyzedseparately).SamplesfromtheESPstudywere1261
treateddifferently,duetothelargenumberofcohortsandsequencingtechnologies1262
withinthestudy;westratifiedESPsamplesbyancestry(ratherthancohort)anddid1263
notfurtherstratifythembysequencingtechnology.Thisprocedureyielded251264
distinctsamplesubgroups(SupplementaryFigure6).1265
1266
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
59
Wethenexcludedvariantsseparatelyforeachsubgroup,basedonsubgroup-1267
specificmeasuresofcallrate,Hardy-Weinbergequilibrium(HWE),differentialcase-1268
controlmissingness,andalternateallelegenotypequality.Specificfiltersusedto1269
excludevariantsfromallsubgroupsareshowninSupplementaryFigure6;in1270
general,filterswerestrictβparticularlyformultiallelicvariantsandX-chromosome1271
variants.1272
1273
Forsomesubgroups,weusedstricterfiltersontopofthebasicfiltersifsubgroup-1274
specificquantile-quantile(QQ)plotsshowedanexcessofsignificantassociations.In1275
particular,theAshkenazisubgroupfromtheT2D-GENESstudyshowedminimum1276
heterogeneityinsequencingqualitybetweencasesandcontrols(owingto1277
resequencingperformedsubsequenttotheoriginalstudypublication)andrequired1278
significantfilterstoremoveartifactualassociations.Inaddition,duetoasignificant1279
imbalancebetweenthenumberofcasesandcontrolsintheESPstudies,we1280
excludedanyvariantsfromthatsubgroupwhichhadanassociationp-valueless1281
than0.3timesthep-valuefromFisherβsexacttest(undertheassumptionthat1282
covariatesintheanalysiswereinducingstatisticalartifacts).Thenumbersof1283
variantspassingthesefiltersineachsubgroupareshowninSupplementaryFigure1284
6.1285
1286
Foreachofthe25samplesubgroups,weconductedtwosingle-variantassociation1287
analyses.Inbothsingle-variantanalysis,wecollapsedallnon-referenceallelesat1288
multiallelicsitesintoasingleβnon-referenceβallele.1289
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
60
1290
First,weanalyzedall(includingrelated)samplesviatheEMMAXtest98,as1291
implementedintheEPACTS(genome.sph.umich.edu/wiki/EPACTS)software1292
package,usingtheGRMcomputedfromtheancestry-specificancestryvariants.We1293
includedinthemodelcovariatesforsequencingtechnology(whereappropriate)1294
butnotforPCsofgeneticancestry.Wedidnotincludecovariatesforage,sex,or1295
BMI.1296
1297
Second,weanalyzedunrelatedsamplesviatheFirthlogisticregressiontest99,also1298
asimplementedinEPACTS;weincludedinthemodelcovariatesforsequencing1299
technologyandforPCsofgeneticancestry(computedfromtheancestry-specific1300
ancestryvariants).ThenumberofPCsweincludedvariedbysubgroup;toselectthe1301
PCstobeincluded,weregressedT2Dstatusonsequencingtechnologyandthefirst1302
tenPCsandincludedinthemodelanyPCthatdemonstratednominal(p<0.05)1303
associationwithT2D,aswellasallhigher-orderPCs.1304
1305
Foreachofthe25Γ2=50single-variantanalyses,weinspectedQQplotsofvariant1306
associationstatisticsandincreasedthestringencyofthevariantfiltersifthe1307
distributionofassociationstatisticsappearedpoorlycalibrated.Thefiltersshownin1308
SupplementaryFigure6representthefinalvaluesatwhichwearrived.1309
1310
Wethenconducteda25-groupfixed-effectinverse-varianceweightedmeta-analysis1311
foreachoftheFirthandEMMAXtests,usingMETAL100.WeusedEMMAXresultsfor1312
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
61
associationp-valuesandFirthresultsforeffectsizeestimates.Forcomparison,we1313
conductedtwoadditionalmeta-analyseswithassociationZ-scoresweightedby(a)1314
sample-sizeand(b)thenumberofvariantcarriers.Wefoundthatthesample-size1315
weightedmeta-analysishadsignificantlyreducedpowertodetectassociationfor1316
variantswithfrequenciesthatvariedwidelybysamplesubgroup;forexample,1317
1,425East-Asianindividualscarriedp.Arg192HisinPAX4(N=6,032;p=1.2Γ10-21)1318
comparedtoonly28carriersacrossallotherancestries(N=39,199;p>0.2),yielding1319
aninverse-varianceweightedmeta-analysisp=7.6Γ10-22andasample-sizeweighted1320
meta-analysisp=1.0Γ10-6.Bycontrast,thenumber-of-carrierweightedmeta-1321
analysisyieldedsimilarresultsastheinverse-varianceweightedmeta-analysis.We1322
electedtousetheinverse-varianceweightedmethodduetoitswidespreaduse100.1323
Wedidnotconductrandom-effectsmeta-analyses.1324
1325
Replicationofrs1451816831326
Toassesswhetherthers145181683variantinSFI1(p=3.2Γ10-8intheexome1327
sequenceanalysis)representedatruenovelassociation,weobtainedassociation1328
statisticsfromthe4,522Latinospreviouslyanalyzedaspartofan8,214sample1329
LatinoGWASpublishedbytheSIGMA-T2Dconsortium101whodidnotoverlapwith1330
thecurrentstudy.Basedontheoddsratio(1.19)estimatedinouranalysisandthe1331
MAF(12.7%)inthereplicationsample,powerwas91%toachievep<0.05undera1332
one-sidedassociationtest.Theobservedevidence(p=0.90,OR=1.00)didnot1333
supportrs145181683asatrueT2Dassociation.1334
1335
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
62
Gene-levelanalysis1336
Wefirstfilteredvariants(or,moreaccurately,alleles,sinceincontrasttosingle-1337
variantanalysis,wetreatedmultiallelicvariantsascollectionsofindependent1338
biallelicvariants)accordingtosevendifferentannotationβmasksβ,rankedinorder1339
ofincreasingdeleteriousness.Thestrongestmaskconsistedofallelespredictedto1340
causelossoffunctionbytheLofTeealgorithm1341
(https://github.com/konradjk/loftee),whileweakermasksalsoincludedalleles1342
predicteddeleteriousbyprogressivelyfewerbioinformaticalgorithms.Eachmask1343
includedallallelesinhigherrankedmasksaswellasadditionalallelesspecificto1344
themask.Inthetwolowestrankedmasks(the1/51%and0/51%masks,which1345
includedallelespredicteddeleteriousbyoneorzerotools,respectively),wefiltered1346
allelesspecifictoeachmaskaccordingtoallelefrequencyusingacutoffofMAF=1%,1347
withMAFcomputedasthemaximumMAFacrossthefiveancestries.Afulllistand1348
definitionsofmasksareshowninSupplementaryFigure8;thecriterialistedin1349
thefigureareforallelesspecifictoeachmask.1350
1351
Tovalidatethattheseverityorderingofmaskscorrespondedtoanincreasing1352
likelihoodthatanalleleinthemaskwasdeleterious,weusedpreviouslypublished1353
dataassessingtheextenttowhichallmissensevariantsinthegenePPARGimpeded1354
adipocytedifferentiation(i.e.wereannotatedascausingPPARGlossoffunction).1355
Thesedatashowedatrendwherebyallelesinmoreseveremaskshadlower1356
predictedfunctionality(SupplementaryFigure9).1357
1358
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
63
Foreachmask,wegroupedallelesbygeneaccordingtoVEPannotationsof1359
impactedtranscript;weassignedvariantsintranscriptsofmultiplegenestoallsuch1360
genes.Foreachgene,wecreateduptothreegroupingsofalleles,correspondingto1361
differenttranscriptsetsofthegene.First,theβbestβgroupingconsistedofallelesin1362
themaskaccordingtotheβbestguessβallele-levelannotations.Second,theβallβ1363
groupingconsistedofallelesinthemaskaccordingtoanytranscriptofthegene.1364
Third,theβfilterβgroupingconsistedofallelesinthemaskaccordingtoprotein-1365
codingtranscriptsofthegenewithTSL<3.Formanygenes,twoormoreofthese1366
allelegroupingswereidentical.1367
1368
Additionally,weassignedmask-specificalleleweightsaccordingtotheiraggregate1369
predicteddeleteriousness.Tocalculateweights,weusedapreviouslypublished1370
model12inwhichmissensevariantsareamixtureoffullybenignvariantsandfully1371
loss-of-functionvariants,withaparameter0β€xβ€1determiningthefractionofloss-1372
of-functionvariants.WeassumedallallelesintheLofTeemaskwerefullloss-of-1373
functionvariants(x=1)andthatallsynonymousalleleswerefullybenign(x=0).We1374
thencalculatedthe(binned)frequencydistribution,truncatedatMAF<1%,of1375
biallelicLofTeeandbiallelicsynonymousalleles,usingtheseasreference1376
distributionsofthefrequencyofloss-of-functionandbenignalleles,respectively.1377
Foreachmask,wethencalculatedthebinnedandtruncatedfrequencydistribution1378
forallelesspecifictothemask(SupplementaryFigure10)andestimatedavalue1379
forx(byenumeratingandtestingarangeofpossiblevaluesbetween0and1)that1380
maximizedthelikelihoodoftheobservedfrequencydistribution.Wethenusedthe1381
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
64
estimatedvaluesofxforalleleweights,asshowninSupplementaryFigure8.1382
Becauseeachmaskconsistednotonlyofallelesspecifictothemaskbutalsoof1383
allelespresentinhigherrankedmasks,alleleswithinanygivenmaskhadarangeof1384
weights.1385
1386
Priortorunninggene-leveltests,weperformedadditionalqualitycontrolonsample1387
genotypes.Foreachofthe25samplesubgroups(thesamesubgroupsusedfor1388
single-variantanalysis),weidentifiedallvariantswithlowsubgroup-specificcall1389
rates,highsubgroup-specificdeviationsfromHWE,orhighsubgroup-specific1390
differencesbetweencaseandcontrolcallrates(specificcriteriaareshownin1391
SupplementaryFigure8).Foreachvariantfailinganyofthesecriteria,all1392
genotypesforindividualsinthesubgroup(regardlessofallele)weresetas1393
βmissingβ;formultiallelicvariants,allsubgroupgenotypesweresetasmissingifany1394
allelefailedanyqualitycontrolcriterion.1395
1396
Wethenconductedaseriesoftestsacrossthemasks.Weusedaburdentestand1397
SKAT38,bothasimplementedintheEPACTSsoftwarepackage.Theburdentest1398
assumesthattheeffectsizesofallanalyzedvariantsarethesame,whiletheSKAT1399
testallowseffectsizestovary102.Weconductedeachtestacrossallunrelated1400
individualspooledtogether(i.e.incontrasttosingle-variantanalysis,weperformed1401
aβmega-analysisβratherthanameta-analysis)andincludedtenPCcovariates1402
(computedfromthetransethnicancestrySNPs)aswellasindicatorcovariatesfor1403
the25samplesubgroups(thesameasdefinedinsingle-variantanalysis).Wedid1404
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
65
notincludecovariatesforage,sex,orBMIinouranalysis,astheyhadlittleeffecton1405
ourresults.1406
1407
Weimplementedsubgroup-specificgenotypefilters(asdefinedintheprevious1408
qualitycontrolstep)bymodifyingtheEPACTSsoftwaretosetspecifiedgenotypes1409
tomissingduringassociationtesting;weachievedallele-specifictestsfor1410
multiallelicvariants(i.e.inwhichonlyoneallelewaspresentinthemask)ina1411
similarmannerbysettingnon-referencegenotypestomissingforsamplesthat1412
carriedanalleleoutsideofthemask.WealsomodifiedtheEPACTSsoftwareto1413
acceptallele-specificweightsbymultiplyinggenotypes(ormoreaccurately,1414
genotypedosages)bytherelevantweightpriortoconductingtheformalburdenor1415
SKATanalysis.1416
1417
Consolidationoftestsacrossmasks1418
Historically,exomesequencingstudieshaveproducedseparategene-level1419
associationresultsforeachallelicmask.Whilestraightforwardtoreport,1420
interpretingmultiplep-valuesforeachgenecanbechallengingβparticularlyifthe1421
goalistodeterminewhetheraspecificgenedemonstratesassociationwitha1422
phenotype.Toaddressthischallenge,wedevelopedtwomethodstocollapse1423
associationresultsacrossdifferentallelicmasks.1424
1425
Thefirstmethod(βweightedtestβ)collapsesassociationsunderamodelwhereby1426
thephenotypiceffectsofallelesaredirectlyproportionaltotheirbioinformatically1427
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
66
estimateddeleteriousness.Intheβweightedburdenβtest,weusedthesumofthe1428
weightsofallelescarriedbyanindividualasapredictorvariableinplaceofthetotal1429
numberofallelescarried.IntheβweightedSKATβtest,wemultipliedthedefault1430
weightsusedintheSKATEPACTSimplementationbytheallelicweightswe1431
calculated.Fortheseweightedtestsweincludedallallelesinthe0/51%maskin1432
theanalysis.1433
1434
Becausebioinformaticallypredictedseverityisanimperfectproxytoactual1435
phenotypicseverity,wedevelopedasecondmethod,theβminimump-valuetestβ,to1436
collapseassociationsacrossmasks.Wechosetheminimump-valuetesttoprovidea1437
principledextensionofanadhocbutintuitivewaytointerpretmultiplep-valuesfor1438
agivengene:takethesmallestp-valueobservedacrosseachmaskandthencorrect1439
fortheeffectivenumberoftestsperformedforthegene.1440
1441
Toconducttheseminimump-valuetests,wefirstrantheburdenandSKATanalyses1442
foreachofthesevenmasksseparately,followingusualexomesequenceanalysis1443
protocolsbyusingnoweightsandincludingallallelesineachmask.Foreachgene,1444
wethenconvertedthesevenp-valuesintoasinglep-valueviatheformula1445
1β 1β π!"# !
whereeistheeffectivenumberofindependenttestsperformedacrossthemasks.1446
Toestimatee,weappliedapreviousapproach39originallydevelopedtocompute1447
theeffectivenumberofindependentp-valuesacrossasetofSNPs:1448
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
67
π β πΌ π! > 1 π! β 1!
!!!
whereinourcaseMequalsthenumberofmasks(usuallyseven,exceptforgenes1449
thatlackvariantsinoneormoremasksorforwhichtwomasksareidentical)andΞ»i1450
aretheeigenvaluesoftheMΓMmatrixofcorrelationsamongthep-valuesofthe1451
mask-leveltests.Tocomputethemaskp-valuecorrelationmatrix,wefollowedthe1452
previousapproachbyfirstcalculatingthemaskgenotypecorrelationmatrix(i.e.,for1453
eachmask,producingavectorwiththenumberofvariantsinthemaskcarriedby1454
eachindividual,andthencalculatingcorrelationsofthevectors)andthen1455
transformingthegenotypecorrelationmatrixaccordingtothepreviously1456
empiricallyderived39polynomialequation:1457
π¦ = 0.2982π₯! β 0.0127π₯! + 0.0588π₯! + 0.0099π₯! + 0.6281π₯! β 0.0009π₯
wherexisthemeasuredcorrelationbetweenthenumberofallelescarriedandyis1458
theestimatedcorrelationbetweenp-values.1459
1460
Wenotethatthispolynomialequationwasinitiallydevelopedtotranslate1461
correlationsbetweenindividualvariantsandp-values,ratherthancorrelations1462
betweenaggregatesetsofvariantsandp-values,andthusmaynotbeasaccuratein1463
oursetting.However,genomiccontrolestimates(Ξ»=0.67)andQQplots1464
(SupplementaryFigure11)suggestedthatifanythingourmultipletestcorrection1465
wasconservativeformostgenes.Furthermore,evenifourgene-levelp-valueswere1466
Bonferronicorrectedforallsevenmasks,theresultsofourstudywouldremain1467
largelyunchanged:eachofSLC30A8,MC4R,andPAMwouldstillexceedexome-wide1468
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
68
significance(forboththeweightedandminimump-valuetests),andthegeneset1469
testswouldremainnearlyidentical(astheyarebasedongene-levelp-valueranks1470
ratherthanabsolutevalues).Futureworkcouldinvestigatetheapplicationofother1471
methodspreviouslydevelopedtocorrectforcorrelatedp-values103,104.1472
1473
Theapplicationoftwodifferentmethodsforcollapsingp-valuesacrossmasksfor1474
eachoftwotestsyieldedfouranalysesforeachgene,correspondingtoaweighted1475
burdenanalysis,aweightedSKATanalysis,anminimump-valueburdenanalysis,1476
andanminimump-valueSKATanalysis.Infact,foreachofthefouranalyses,1477
multiplep-valueswerepossibleforeachgene(correspondingtothedifferent1478
transcriptsetsusedforannotation).Toproduceasinglegene-levelp-valueforeach1479
ofthefouranalyses,wethuscollapsed(foreachgene)thesetofp-valuesacross1480
transcriptsetsintoasinglegene-levelp-valueusingthesameprocedureasforthe1481
minimump-valuetest(i.e.takingtheminimump-valuecorrectedfortheeffective1482
numberoftestsperformed).1483
1484
Forsomegenes(SupplementaryFigures12-14)weconductedadditionalgene-1485
levelanalysestodissecttheaggregatesignalsobserved.First,weperformedtests1486
foreachmaskseparately,includingonlyvariantsspecifictothemask(ratherthan1487
allvariants),tounderstandwhethertheaggregatesignalwasobservedinonlyone1488
asopposedtomultiplemasks.Second,weperformedtestsbyprogressively1489
removingvariantsinorderoflowestsingle-variantanalysisp-value,tounderstand1490
the(minimum)numberofvariantsthatcontributedstatisticallytotheaggregate1491
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
69
signal.Third,weperformedtestsconditionaloneachvariantseparately(i.e.1492
calculatingseparatemodelswitheachindividualvariantasacovariate),withthe1493
resultingp-valuescomparedtothefullgene-levelp-value,toassessthecontribution1494
ofeachvariantindividuallytothesignal.1495
1496
AnalysisofexomesfromtheGeisingerHealthSystem(GHS)1497
Weobtainedgene-levelassociationresultspreviouslycomputedfromananalysisof1498
49,199individuals(12,973T2Dcasesand36,226controls)fromtheGeisinger1499
HealthSystem.Werequestedassociationsummarystatisticsforthe50geneswith1500
thestrongestgene-levelassociationsfromouranalysis;44geneshadprecomputed1501
summarystatisticsavailable;pseudogeneUBE2NLandXchromosomegenes1502
MAP3K15,SLC16A2,MAGEB5,DGKK,andMAGEE2werenotavailable.1503
1504
GHSsequencedatawereprocessedandanalyzedaspreviouslydescribed27and1505
associationresultswereproducedforfour(nested)variantmasks:1506
1. M1:predictedloss-of-functionvariants,accordingtotheVEP,withMAF<1%β1507
similartotheLofTeemaskbutwithanadditionalMAF<1%filterandwithoutthe1508
LofTeefilteronprotein-truncatingvariantsannotatedbytheVEP.1509
2. M2:nonsynonymousvariantspredicteddeleteriousby5/5prediction1510
algorithmswithMAF<1%βsimilartothe5/5maskbutwithanadditionalfilter1511
onMAF<1%.1512
3. M3:allnonsynonymousvariantspredicteddeleteriousbyβ₯1/5bioinformatic1513
algorithmswithMAF<1%βsimilartothe1/51%mask.1514
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
70
4. M4:allnonsynonymousvariantswithMAF<1%βsimilartothe0/51%mask,1515
althoughnotidenticalasthe1%filterwasusedforallvariantsincludingthosein1516
theLofTeeand5/5masks.1517
1518
Foreachmask,associationresultswerecomputedvialogisticregressionunderan1519
additiveburdenmodel(withphenotyperegressedonthenumberofvariants1520
carriedbyeachindividual)withage,age2,andsexascovariates.Althoughthis1521
analysisprocedurewasbroadlyconsistentwiththeoneweusedforourexome1522
sequenceanalysis,wewerenotabletosynchronizeourproceduresforquality1523
control,annotation,andcollapsingassociationstatisticsacrossmasks.1524
1525
ToproduceasingleGHSp-valueforeachgene,weappliedtheminimump-value1526
procedureacrossthefourmask-levelresults.Weestimatedthecorrelationmatrix1527
usingthesameprocedureasforourexomesequenceanalysis,usingthecombined1528
GHSallelefrequenciesreportedacrossthefour(nested)masks.1529
1530
AnalysisofexomesfromtheCHARGEconsortium1531
WecollaboratedwiththeCHARGEconsortiumtoanalyzethe50geneswiththe1532
strongestgene-levelassociationsfromouranalysisin12,467individuals(3,0621533
T2Dcasesand9,405controls)fromtheirpreviouslydescribedstudy105.CHARGE1534
DNAsampleswereprocessedatBaylorCollegeofMedicineHumanGenome1535
SequencingCenterusingtheVCRome2.1designandsequencedinpaired-endmode1536
inasinglelaneontheIlluminaHiSeq2000ortheHiSeq2500platformwithamean1537
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
71
78-foldcoverage.Allsampleswerecalledtogetheranddetailsonsequencing,1538
variantcalling,andvariantqualitycontrolweredescribedindetailbyYuetal.1061539
1540
VariantsintheCHARGEexomeswereannotatedandgroupedintosevenmasks1541
usingthesameprocedureasfortheoriginalexomesequenceanalysis.Foreach1542
mask,CHARGEburdenandSKATassociationtestswereperformedintheAnalysis1543
Commons107usingalogisticmixedmodel108assuminganadditivegeneticmodel1544
andadjustedforage,sex,study,race,andkinship.1545
1546
ToproduceasingleCHARGEp-valueforeachgene,weappliedtheminimump-value1547
procedureacrossthefourmask-levelresults,asfortheGHSanalysis.1548
1549
Evaluationofdirectionalconsistencybetweenexomesequence,CHARGE,andGHS1550
analyses1551
Weexaminedtheconcordanceofdirectionofeffectsizeestimates(i.e.OR>1or1552
OR<1)betweenouroriginalexomesequenceanalysisandthosefromCHARGEand1553
GHS.Weusedburdenteststatisticsforthisanalysis,asSKATtestsdonotproduce1554
directionofeffects.Ofthe50genesadvancedforreplication,weconsideredthe461555
thatreachedburdenp<0.05foratleastonemask(i.e.ignoringthosewithevidence1556
forassociationonlyundertheSKATmodel).Wecomparedthedirectionofeffectto1557
thatestimatedbyburdenanalysisofthesame(oranalogous)maskintheGHSor1558
CHARGEanalysis.ForCHARGE,wecompareddirectionofeffectforthesamemask.1559
ForGHS,wecomparedusethefollowingapproximatemappingbetweenmasks:1560
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
72
LofTeetoM1;15/15,10/10,5/5,and5/5+LofTeeLCtoM2;1/51%toM3;and0/51561
1%toM4.Wethenconductedaone-sidedexactbinomialtesttoassesswhetherthe1562
fractionofresultswithconsistentdirectionofeffectswassignificantlygreaterthan1563
expectedbychance.1564
1565
GenerationofcandidateT2D-relevantgenessets1566
Toassesswhethergene-levelassociationstrengthcouldbeaninformativemetricto1567
usewhenprioritizingcandidategenesforfurtherstudyorexperimentation,we1568
comparedgene-levelassociationsforgenesinavarietyofgenesets1569
(SupplementaryTable10)togene-levelassociationstatisticsforrandomsetsof1570
genesmatchedwiththetargetsetbasedonthenumberandfrequenciesofvariants1571
(asdescribedbelow).Wedidsofor16setsofgenes:1572
1. ElevengenesharboringmutationsthatcauseMaturityOnsetDiabetesoftheYoung1573
(MODY).Weselectedgenesfromasetpreviouslydescribed24afterexcludingtwo1574
genes(ABCC8andKCNJ11)thatcancausemonogenicdiabetesorcongenital1575
hyperinsulinismdependingonwhetherthemutationstheyharborareactivating1576
orinactivating.1577
2. Eightgenesannotatedastargetsforantidiabeticmedications.Wedownloaded1578
medicationsannotatedasβDrugsUsedinDiabetesβorβBloodGlucoseLoweringβ1579
fromtheDrugBankdatabaseversion5.048.Afterexclusionofmedicationswith1580
morethantwoannotatedtargets,weadvancedforanalysisonlygenes(a)1581
annotatedasatargetofatleasttwocompoundsand(b)forwhichthe1582
therapeutictargetmodulationstrategywasconsistentlyannotatedacrossall1583
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
73
medications,whereannotationsofβinhibitorβ,βantagonistβ,andβinverse1584
agonistβwereinterpretedasreducingactivity,whileannotationsofβagonistβ,1585
βactivatorβ,orβinducerβwereinterpretedasincreasingactivity.These1586
restrictionsexcludedABCC8fromanalysis,asitwasannotatedasthetargetof1587
bothaninhibitorandanagonist;weelectedtomaintainthisexclusion,despite1588
multiplelinesofevidence109indicatinginhibitionofABCC8tobetheappropriate1589
anti-diabeticstrategy,tomaintainconsistentcriteriaacrossallgenesselectedfor1590
analysis.Additionally,weexcludedKCNJ11(whichwithABCC8encodestheATP-1591
sensitiveK(ATP)channeltargetedbysulfonylureas)fromanalysisbecauseboth1592
medicationslistedinDrugBankastargetingithadmorethantwotargets1593
(Glyburide,8,andGlimepiride,3).TheresultinggenesetwasthusGLP1R,IGF1R,1594
PPARG,INSR,SLC5A2,DPP4,KCNJ1,andKCNJ8.1595
3-14.TwelvesetsofgenesreportedasrelevanttoT2Dinmousemodels.Withinthe1596
MouseGenomeInformaticsDatabase,wesearchedforgenesmatchingvarious1597
diabetes-relevantβphenotypes,alleles,anddiseasemodelsβunderthebroader1598
categoryofβmousephenotypesandmousemodelsofhumandiseaseβ.We1599
constructedagenesetforeachphenotypedefinedinthedatabase,manyof1600
whichoverlapped.Forphenotypesassociatedwithincreaseddiabetesrisk,we1601
used:(3)βtype2diabetesortypeiidiabetesβ(i.e.non-insulindependent1602
diabetes;31genes),(4)βdiabetesmellitusβ(72genes),(5)βimpairedglucose1603
toleranceβ(327genes),(6)βincreasedcirculatingglucoseβ(365genes),(7)1604
βinsulinresistanceβ(181genes),and(8)βdecreasedinsulinsecretionβ(1331605
genes).Forphenotypesassociatedwithdecreaseddiabetesrisk,weused:(9)1606
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
74
βimprovedglucosetoleranceβ(239genes),(10)βdecreasedcirculatingglucoseβ1607
(481genes),(11)βincreasedinsulinsensitivityβ(178genes),and(12)βincreased1608
insulinsecretionβ(51genes).Forphenotypesassociatedwithdiabetesriskbut1609
withuncleardirectionofeffect,weused(13)βdecreasedcirculatinginsulinβ1610
(321genes)and(14)βincreasedcirculatinginsulinβ(215genes).1611
15. ElevengenessuspectedofharboringcommoncodingcausalvariantswithinT2D1612
GWASloci.Weanalyzedthesetofgenesfromarecentexomearrayanalysis171613
whichcontainedacodingvariantGWASsignalforwhichtheunweighted1614
posteriorprobabilityofcausalityexceeded25%.Althoughthefinalvalues1615
reportedbythestudyincludeanelevatedpriorforcodingvariants,weelectedto1616
usea25%unweightedposteriorthresholdtoenrichforthegeneswiththe1617
highestlikelihoodofmediatingtheobservedGWASsignal.Foranalysisofthis1618
geneset,werecomputedgene-levelassociationstatisticswithinthesetby1619
conditioningonallGWAStagSNPs(withinthelocus)reportedintheexome1620
arrayanalysis17;weusedp-valuesfromtheseconditionalgene-levelassociations1621
inthegenesetanalysis.1622
16. TwentygeneswithT2D-associatedtranscriptlevels.Weselectedgeneswith1623
significantassociationsinapre-publication52tissue-wideT2Dassociation1624
analysis(i.e.testingforassociationbetweenthegeneticcomponentoftissue-1625
levelgeneexpressionandT2D),withassociationsconsideredsignificantifthey1626
survivedBonferronicorrectionforalltestedgenesandalltestedtissues.Results1627
werecomputedwiththeMetaXcansoftwarepackage110usingSNPregression1628
coefficientstakenfromalargetrans-ethnicT2DGWASmeta-analysis111and1629
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
75
geneexpressionpredictionmodelsfromthePredictDBwebsite1630
(http://predictdb.org).1631
1632
Genesetanalysis1633
Foreachgeneset,ourgoalwastocomparethegenelevelp-valueswithinthesetto1634
thoseofgeneschosenatrandomfromthegenome.Tocontrolforgenevariabilityin1635
thenumberandfrequencyofvariantswithinthem,whichcouldconfound1636
comparisons,weconstructedcomparisongenesbymatchingonfourproperties:the1637
(1)numberofvariantsinanyofthesevenvariantmasks;(2)totalallelecountsover1638
allvariantsinanyofthesevenmasks;(3)numberoftestsacrossallvariantmasks1639
andtranscriptsets;and(4)effectivenumberoftestsacrossallvariantmasksand1640
transcriptsets(ascomputedfortheminimump-valuetest).Wescaledeach1641
propertytozeromeanandunitvariance.Foreachgene,wethenusedthe501642
nearestneighbors(definedusingEuclideandistanceinthescaledpropertyspace)1643
asmatchedcomparisongenes.1644
1645
Toconductagenesetanalysis,wethencombinedthegenesinthegenesetwithall1646
ofthecomparisongenesmatchedtoeachgeneintheset.Withinthecombinedlistof1647
genes,werankedgenesusingthep-valuesobservedfortheminimump-value1648
burdentest.Wethenusedaone-sideWilcoxonrank-sumtesttoassesswhether1649
genesinthegenesethadsignificantlyhigherranksthanthecomparisongenes.1650
1651
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
76
Forgenesetanalysis,weusedtheminimump-valuetest,ratherthantheweighted1652
test,undertherationalethat(a)weaimedtodetectassociationswithasmanygenes1653
aspossibleusinginformationfromasmanyvariantsaspossibleand(b)the1654
weightedtestmightnotdetectgenesthatdidnotfollowitsmodelofastrong1655
correlationbetweenvarianteffectsizesandmolecularannotation.Weusedthe1656
burdentestratherthanSKATbasedonadesiretohavemoreinterpretable1657
associationstatistics(e.g.effectsizeestimates).However,wedidnotquantitatively1658
andsystematicallycomparethepowerofeachofouranalysesinthissetting.1659
1660
Useofgene-levelassociationstopredicteffectorgenes1661
Inmostsituations,GWASassociationsimplicatecommonregulatoryvariants,which1662
seldomlocalizetospecificgenes.Toassesswhethergene-levelassociationsfrom1663
exomesequencingβwhicharecomposedmostlyofrarevariantsindependentfrom1664
anyGWASassociationsβcouldprioritizepotentialeffectorgeneswithinknownT2D1665
GWASloci,wecataloguedallgeneswithineachlocusreachingp<0.05forthe1666
minimump-valueburdentest.Wetookalistof94GWASlocifromarecentreview1667
article53andadvancedforanalysisthe595geneswithin250kbofanindexSNP.1668
1669
Wethensoughttocomparetwomethodstopredicteffectorgeneswithintheseloci.1670
First,weusedp<0.05accordingtotheminimump-valuegene-leveltestfromour1671
exomesequenceanalysistopredictcandidateeffectorgenes,producingalistof401672
genes(across32loci).Second,weusedproximitytotheindexSNP(aspredictedby1673
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
77
DAPPLE54)topredictcandidateeffectorgenes,producingalistof184genes(at1674
somelociDAPPLEannotatedmorethanonecandidateeffectorgene).1675
1676
Asaccuratelyassessingwhichofthesetwogenesetsismoreenrichedfortrue1677
effectorgeneswouldrequire(atminimum)significantexperimentalwork,weused1678
therelativenumberofproteininteractionswithineachgenesetasone(imperfect)1679
measureoftheirrespectivebiologicalβcoherenceβ.Toassesswhethereachset1680
encodesproteinswithmoreinteractionsthanwouldbeexpectedbychance,weran1681
DAPPLEthroughthepublicGenePatternportal1682
(https://software.broadinstitute.org/cancer/software/genepattern)withdefault1683
valuesforallparameters.The40geneswithminimump<0.05weresignificantly1684
moreenrichedforproteininteractions(p=0.03;observedmean=11.4,expected1685
mean=4.5)thanwerethe184genesimplicatedbasedonproximitytotheindexSNP1686
(p=0.64;observedmean=21.1,expectedmean=21.9).1687
1688
Whiletheseresultssuggestthatgene-levelassociationsmaybeusefulfor1689
prioritizingeffectorgenes,wenotethattheydonotimplicateanyspecificgenesand1690
thatDAPPLEisonlyonemeanstoassessbiologicalcoherenceofageneset(through1691
directandindirectproteininteractions).Evaluationofthebiologicalcandidacyof1692
thesegenesmayultimatelyrequirein-depthfunctionalstudies56.1693
1694
Useofgene-levelassociationstopredictdirectionofeffect1695
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
78
Intherapeuticdevelopment,itisoftenvaluabletoknowthedirectionofeffect1696
linkinggenemodulationtodiseaseriskβthatis,whetherinactivationoractivation1697
ofaproteinincreasesdiseaserisk.Wethusassessedwhethergene-levelassociation1698
analysisofpredicteddeleteriousvariantscouldbeusedtopredictthisdirectionof1699
effect.Forthisanalysis,weusedoddsratiosestimatedfromamodifiedweighted1700
burdentestprocedure,whichonlyincludedallelesfromthefourmaskswiththe1701
predictedmostdeleteriousvariants:LofTee,16/16,11/11,and5/51702
(SupplementaryFigure8).Weightsforvariantswereidenticaltothoseusedinthe1703
exome-wideweightedburdentest.Wechosethesefourmasksforanalysisto1704
balanceadesireforgreateraggregateallelecountpergene(i.e.missensevariantsin1705
additiontoprotein-truncatingvariants)withaneedtostronglyenrichfor1706
deleteriousvariants(>73%estimatedtobedeleteriousinmasksanalyzedvs.<50%1707
intheothermasks(SupplementaryFigure8).Inaddition,weusedtheweighted1708
testbecauseitwasexplicitlydesignedtoestimateaneffectofgene1709
haploinsufficiencybasedonbothprotein-truncatingandmissensevariants.1710
1711
TocomparethesedirectionofeffectestimatestothoseexpectedforT2Ddrug1712
targets,weassumedagonisttargetstohavetrueOR>1andinhibitorstohavetrue1713
OR<1.Foracomparisontoexpectationsformousegeneknockouts,wefirst1714
excluded473genesannotated,basedonmembershipinmultiplegenesets,tohave1715
bothexpectedOR>1andexpectedOR<1(thesegeneswereexcludedonlyfromthe1716
directionofeffectcomparisons;theyweremaintainedinallothergeneset1717
analyses).Thisleft389geneswithanexpectedOR>1,associatedexclusivelywith1718
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
79
mousetraitsindicativeofincreasedrisk(overlappingsetsof11βtype2diabetesor1719
typeiidiabetesβ,46βdiabetesmellitusβ,204βimpairedglucosetoleranceβ,2451720
βincreasedcirculatingglucoseβ,104βinsulinresistanceβ,and63βdecreasedinsulin1721
secretionβ),and467geneswithanexpectedOR<1,associatedexclusivelywithtraits1722
indicativeofdecreasedrisk(overlappingsetsof164βimprovedglucosetoleranceβ1723
genes,358βdecreasedcirculatingglucoseβgenes,95βincreasedinsulinsensitivityβ1724
genes,and18βincreasedinsulinsecretionβgenes).Genesetsforβdecreased1725
circulatinginsulinβandβincreasedcirculatinginsulinβwereexcludedfromthis1726
directionofeffectcomparisonduetotheunclearrelationshipbetweenthese1727
phenotypesandT2Drisk.1728
1729
AggregationandgenerationofSNParraydata1730
Becausethemostsignificantsingle-variantassociationsthatemergedfromour1731
exomesequenceanalysiswerewithcommonvariants,weaskedwhetheranarray-1732
basedgenome-wideassociationstudyinthesamesamplescouldhaveprovideda1733
lessexpensivemethodtodetectthesesameassociations.Toaddressthisquestion,1734
weaggregatedallavailableSNParraydatafortheexome-sequencedsamples1735
(SupplementaryTable12).DatafortheGoT2D24,SIGMA85,andT2D-GENES1736
consortiahavebeenpreviouslyanalyzed(unpublishedT2D-GENESdatawere1737
collectedfromarangeofSNParraysincludingAffymetrix5.0and6.0,Illumina1738
HumanHap610Kand1M,andtheIlluminaCardioMetabochip).Thenewly1739
sequencedsamplesfromtheT2D-GENESandSIGMAconsortiaweregenotypedona1740
customβGenomesForLifeβ(G4L)IlluminaInfiniumarray,including243,6621741
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
80
variantschosentouniquelyidentifyeachindividualinastudyandtoprovidea1742
backboneforimputationofcommonvariation.TheG4Larraywasprocessedbythe1743
ArrayslabofBroadGenomicsandcalledusingtheIlluminaGenCall(Autocall)1744
algorithm.1745
1746
AnalysisofSNParraydata1747
Aftergenotyping,the34,529samples(18,233casesand17,679controls;1748
SupplementaryTable12)bothintheexomesequenceanalysisandwithaSNP1749
arraycall-rate>95%wereadvancedforimputation.Toomitvariantsthatmight1750
degradeimputationquality,priortoimputationweexcludedvariantswithlow1751
genotypecallrate(<95%),strongdeviationfromHardy-Weinbergequilibrium1752
(p<10-6),differentialgenotypecallratebetweencasesandcontrols(p<10-5),orlow1753
frequency(MAF<1%).Wethenimputedautosomalvariants(SNVs,shortindels,and1754
largedeletions)viatheMichiganImputationServer112foreachoftworeference1755
panels:theallancestries1000GenomesPhase3(1000G)referencepanelof2,5041756
individuals67andtheHaplotypeReferenceConsortium(HRC)Panelof32,4701757
individuals68.Weusedthe1000G-basedimputationforallassociationanalysesand1758
theHRC-basedimputationtoassessthenumberofexomesequencevariants1759
imputablefromthelargestavailableEuropeanreferencepanel.Wenotethatthe1760
HRCpanelincludesonlySNPs(i.e.noindels)andonlyvariantsobservedatleastfive1761
timesinthesequencedatacontributedtotheHRC.1762
1763
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
81
Afterimputation,weperformedsampleandvariantqualitycontrol,aswellas1764
associationtests,analogoustotheexomesequencesingle-variantanalysis.By1765
contrastwiththeexomesequenceanalysis,wefoundthattheEMMAXtestproduced1766
moresuspiciouslookingassociationsthandidtheFirthtestandthususedonlythe1767
Firthtest(i.e.forbothp-valuesandORs)intheimputedGWASanalysis.1768
1769
Todeterminewhichvariantsintheexomesdatasetwereimputablefromthe1000G1770
orHRCpanel,wecalculatedwhichoftheexomevariantspassedimputedGWAS1771
qualitycontrolinanysamplesubgroup,withafurtherrestrictionofachievingr2>0.41772
inthatsubgroup.Onlyvariantsintheexomesdatasetthatwerepolymorphicinthe1773
imputedGWASsampleswereincludedinthisanalysis.Forcalculationsinvolving1774
theHRC-imputedGWAS(giventhattheHRCpanelisEuropean-specific),weonly1775
consideredvariantsvariableinfourEuropeancohorts(METSIM,Ashkenazi,1776
GoDARTS,andFHS)intheanalysis.1777
1778
GenesetanalysisusingSNParraydata1779
Inadditiontosingle-variantanalysis,weconductedgenesetanalysiswiththe1780
imputedGWASdata.WefirstusedthemethodimplementedinMAGENTA70to1781
assigngenescoresfromtheimputedGWASsingle-variantassociationresults;1782
MAGENTAgenescoresarebasedonproximitytoaGWASleadSNPaftercorrection1783
forpotentialconfoundingfactors.Inthesamewayasforgenesetanalysisfromthe1784
exomesequencegene-levelresults,wethenconductedaone-sidedWilcoxonrank-1785
sumtesttocomparethegenescorestothoseofmatchedcomparisongenes.1786
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
82
1787
AstheimputedGWASgenesetanalysisproducedfewersignificantgeneset1788
associationsthandidtheexomesequencegenesetanalysis,weinvestigated1789
whetheralargerarray-basedassociationstudywouldproducemoresignificant1790
genesetassociations(i.e.whetherthelackofgenesetassociationsintheimputed1791
GWASwasduetoafundamentallackofassociatedcommonvariantsnearthegenes1792
inthegenesetorsimplyduetoaninsufficientsamplesize).Forthisanalysis,we1793
downloadedsingle-variantassociationstatisticsfromthelargestavailablemulti-1794
ethnicarray-basedGWASforT2D111,convertedthemtoMAGENTAgenescores,and1795
thenforeachgenesetconductedaWilcoxonrank-sumtestasdescribedabove.1796
1797
LVEcalculations1798
Tocalculateliabilityvarianceexplained(LVE),weusedapreviouslypresented1799
formula69tocalculatetheLVEofavariantwiththreegenotypes(AA,Aa,andaa)and1800
correspondingrelativerisks(1,RR1,andRR2).Forthesecalculationsweassumed1801
HWE,implyingthefrequenciesofthethreegenotypestobePaa=Pa2,PAa=2Pa(1-Pa),1802
andPAA=(1-Pa)2,wherePaistheminorallelefrequency.Underthisassumption,LVE1803
canbeexpressedas1804
πΏππΈ = π!! π!! β π ! + 2π!(1β π!) π!" β π ! + 1β π! ! π!! β π !
whereπ = 2π!(1β π!)π!" + 1β π! !π!!,and1805
π!! = 0; π!" = π βΞ¦!! 1β π!" ; π!! = π βΞ¦!! 1β π!!
HereΞ¦!!isthenormalquantiledistribution,π = Ξ¦!!(1β π!!),andfaa,fAa,andfAA1806
aredefinedas1807
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
83
π!! =πΎ
π!! + 2π!(1β π!)π π ! + 1β π! !π π !; π!" = π π !π!!; π!! = π π !π!!
whereKisthediseaseprevalence.1808
1809
Theinputstotheseformulaeareestimatesofallelefrequency(foreitherindividual1810
variantsorsetsofvariants,dependingonwhethervariant-levelorgene-level1811
varianceistobecalculated),relativerisk,anddiseaseprevalence.Forindividual1812
variants,weusedthepointestimateoftheMAFfromouranalysistoestimateallele1813
frequency,whileforgenesweusedthepointestimateofcombinedallelefrequency1814
(acrossallalleles)inplaceofMAF.WeestimatedrelativerisksfromanalysisORs1815
andMAFs(π!)underanassumedprevalenceofK=0.08andanadditivegenetic1816
model,byiterativelysolvingtwoequations69:1817
π!! =πΎ
π!! + 2π! 1β π! π π ! + 1β π!
!π π !
1818
π π ! =ππ !
1+ π!!(ππ ! β 1)
wherei=1,2correspondtotheheterozygousandmajor-allelehomozygous1819
genotypes.Weusedamultiplicativemodelforodds-ratios;i.e.OR2=OR12.1820
1821
WeperformedLVEcalculationsasanintegraloverthedistributionofpotential1822
relativerisks,assumingthatthelogarithmofoddsratiosORifollowednormal1823
distributionswithmeansandvarianceequaltothoseestimatedfromouranalysis.1824
WhenpresentingthestrongestLVEvaluesfortheimputedGWASanalysis,weonly1825
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
84
consideredvariantsgenotypedinatleast10,000individualstoavoidpotential1826
artifactsresultingfromaspuriousassociationinasmallsamplesubgroup.1827
1828
Forgene-levelLVEcalculations,weusedthevariantmaskwithlowestp-valueto1829
calculateLVE.Aseachmaskmayhaveincludedamixtureofdisease-associatedand1830
benignalleles,thecalculatedLVEmayunderestimatethetrueLVEfordisease-1831
associatedalleleswithinthegene.TocalculateanupperboundontheLVEbyonly1832
disease-associatedalleles,weperformedaseriesofLVEcalculationsfor1833
progressivelylargersetsofalleles,ateachstepincludingallelesbyorderof1834
decreasingsingle-variantsignificance.Weperformedtwocalculationsforeachgene,1835
oneforriskallelesandoneforprotectivealleles,takingthemaximumofthetwoas1836
thefinalupperboundestimatedforLVEbythegene.WedidnotcalculateanLVE1837
boundunderamodelwherebyalleleswithinthegenecanbothincreaseand1838
decreaseriskofdisease.1839
1840
Estimatedpowertodetectgene-levelassociationswithT2Ddrugtargets1841
Toestimatethepoweroffuturestudiestodetectgene-levelassociationsingenes1842
witheffectsizessimilartothoseforestablishedT2Ddrugtargets,weused1843
aggregateallelefrequenciesandoddsratiosestimatedfromourgene-levelanalysis1844
andanassumedprevalenceofK=0.08tocalculateaproxyfortruepopulation1845
frequenciesandrelativerisks.Ineachcase,weusedoddsratiosandfrequencies1846
fromthevariantmaskyieldingthestrongestgene-levelassociation.Becauseon1847
averagethesedrugtargetshad5effectivetestspermask,weusedanexome-wide1848
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
85
significancethresholdofΞ±=1.25Γ10-7forpowercalculations.Wecalculatedpower1849
aspreviouslydescribed92.1850
1851
Estimatedfractionoftrueassociations1852
Wesoughttoquantifytheproportionoftrueassociations(PPA)fornonsynonymous1853
variantsobservedinourdatasetasafunctionofassociationstrengthasmeasured1854
bysingle-variantp-value.Wedefineatrueassociationasavariantwhich,when1855
studiedinlargersamplesizes,willeventuallyachievestatisticalsignificanceowing1856
toatrueORβ 1.Wedistinguishtrueassociationfromcausalassociation:causally1857
associatedvariantsarethesubsetoftrulyassociatedvariantsinwhichthevariant1858
itselfiscausalfortheincreaseindiseaserisk,asopposedtobeingtrulyassociated1859
duetoLDwithadifferentcausallyassociatedvariant.1860
1861
ToestimatePPA,weusedastrainingdataapreviousexomearraystudyfromthe1862
GoT2Dconsortiumspanning13Europeancohorts24.Astwoofthe13cohorts1863
includedinthepreviousstudycontributedsamplestothecurrentexomesequence1864
analysis,were-calculatedafixed-effectsinverse-varianceweightedmeta-analysis1865
foreveryvariantintheexomearraystudyafterexcludingallsamplesfromthese1866
twooverlappingcohorts.Thisyieldedacollectionofexomearrayassociation1867
statisticsfor206,373variants,withamaximumsamplesizeof50,567(maximum1868
effectivesamplesize41,967).1869
1870
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
86
Wethencomparedvariantdirectionofeffectestimatedfromourexomesequence1871
analysisof45,231individualstothoseestimatedfromtheindependentexomearray1872
analysisof41,967individuals.Toproduceanuncorrelatedsetofassociationstests1873
forthisanalysis,weprunedallcollectionsofvariantsusingtheLD-clumpprocedure1874
(parametersβclump-p10.1βclump-p20.1βclump-r20.01)ofthePLINKsoftware1875
package90,whichrequiredvariantstohavepairwiser2<0.01.Weperformedthis1876
procedurefor(a)nonsynonymousvariantswithin94previouslyestablishedT2D1877
GWASlociand(b)nonsynonymousvariantsexome-wide.Forthe1,0591878
nonsynonymousvariantswithinestablishedT2DGWASlociachievingp<0.05inthe1879
exomesequenceanalysis,thedirectionsofeffectwereconcordant(bothOR>1or1880
bothOR<1)withtheexomearrayanalysisfor61.3%ofvariants.Thisfraction1881
decreased(asexpected)forhigherp-valuethresholds(e.g.49.4%atp>0.5)and1882
whenonlyvariantsoutsideofT2DGWASlociwereanalyzed(51.9%atp<0.05).1883
1884
Toestimatethefractionoftrueassociationsamongthesetofvariantsachieving1885
significancebelowathresholdp(e.g.p<0.05),wemodeledthesetofvariantsasa1886
mixtureofproportionsxpoftrulyassociatedvariants(ORβ 1)and(1-xp)oftrulynon-1887
associatedvariants(OR=1).Weassumednon-associatedvariantshavea50%1888
chanceofaconcordantdirectionofeffectbetweenthetwoanalyses,andtruly1889
associatedvariantshaveagreaterchanceaccordingtotheirestimatedeffectsize.1890
Specifically,assumingthattheobservedeffectsizeforavariantfollowsanormal1891
distributionwithmeanequaltothetrueeffectandvariancethatscalesinversely1892
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
87
withsamplesize,weestimatedtheprobabilitypiofproducingaconcordanteffect1893
forvariantvias1894
p! = Pr π |Ξ²|,ππ!"π!"
> 0
where|Ξ²|istheabsolutevalueoftheestimated(fromtheexomesequenceanalysis)1895
logarithmoftheoddsratio,πistheestimatedstandarderrorofthelogarithmofthe1896
oddsratio,Nexistheeffectivesamplesizeoftheexomesequenceanalysis,andNeais1897
theeffectivesamplesizeoftheexomearrayanalysis.1898
1899
Theexpectedfractionofvariantsexhibitingconcordantdirectionofeffectisthen1900
π! =π! π₯!
!!!!!π!
+ 0.5 1β π₯!
whereVpisthenumberofvariantsintheset.Basedontheobservedfractionπ!of1901
variantswithconcordantdirectionsofeffect,wethusestimatedxpby1902
π₯! =
π! π! β 0.5 π!π! β 0.5 π!!
!!! (1)
Tocalculatea95%confidenceinterval(CI)forxp,wefirstestimateda95%CIforfp1903
usingtheJeffreysintervalmethod113,asimplementedintheRsoftwarepackage1904
(https://www.r-project.org),andwethenusedequation(1)toconvertitslower1905
andupperboundstolowerandupperboundsonthecorrespondingconfidence1906
intervalforxp.1907
1908
Probabilityofcausalassociation1909
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
88
Theestimatedvaluesforxpcanbeinterpretedasestimatesoftheposterior1910
probabilitythatavariantwithp<0.05inouranalysisistrulyassociatedwithT2D1911
ratherthanduetochance.Asourultimategoalwastoquantifytheprobabilityof1912
causalassociation,ratherthanjusttrueassociation,wemodeledtheprobabilityof1913
variantassociationasafunctionof(a)theprobabilityofcausalassociation(PPAc),1914
influencedinturnbythelikelihoodthatthevariantresultsingeneloss-of-function1915
aswellasthelikelihoodthatthegeneisrelevanttoT2D;and(b)theprior1916
probabilityofindirectassociation(PPAi),influencedinturnbythelikelihoodthat1917
thevariantisinLDwithanearbybutdifferentvariantthatiscausallyassociated1918
withT2D.Undertheassumptionthatcausalandindirectassociationsaredisjoint1919
events,thismodelexpressesPPAas1920
πππ΄ = πππ΄! + πππ΄!
1921
Preciselydeterminingwhichcodingvariantassociationsareinfactcausalrequires1922
finemappingofallnearbyvariantsinlargesamplesizes6,whichiscurrently1923
infeasibleforthemostlyrarevariantsobservedinourstudy.Sincewecouldnot1924
accuratelycalculatespecificvaluesofPPAcandPPAiforeachvariant,weinstead1925
usedestimatesoftheaveragetheproportionofassociationsthatarecausal(Ξ±),1926
whereπΌistheprobabilityofcausalassociationconditionalonatrueassociation,1927
ratherthantheabsoluteprobabilityofcausalassociation.Weconsideredtwomeans1928
toestimateΞ±.1929
1930
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
89
First,recentanalyseshaveattemptedtoassessthecontributionofnonsynonymous1931
variantstoT2Dorsimilartraits,eitherbydirectlyestimatingtheproportionof1932
associationsthatareduetononsynonymousvariants79orbymeasuringthe1933
proportionofheritabilityexplainedbynonsynonymousvariants78.Theseanalyses1934
suggestthat~10%ofT2Dassociationsarelikelytobeduetononsynonymous1935
variants.Asthesecalculationsapplytoallassociationsinthegenome,ratherthan1936
thoseinwhichatleastonenonsynonymousvariantachievessignificance,theylikely1937
underestimatetheproportionofnonsynonymousassociationsthatarecausal.1938
1939
Second,arecentexomearraystudyidentified40exome-widesignificant1940
nonsynonymousvariantassociationsandthencalculatedtheprobabilityofcausal1941
associationforeach(viacrediblesetanalysis)17.Thereportedaverageprobabilityof1942
causalassociationacrossthesevariantsof49.2%providesadirectestimateofΞ±.1943
Thisestimateislikelylessbiasedthanthatbasedongenome-wideanalysesofall1944
T2Dassociations,butitisbasedonasmallnumberofassociationsandthushasa1945
highvariance.1946
1947
Basedontheseconsiderations,weconsideredvaluesof10%,30%,and50%forΞ±.1948
andused30%asourdefaultvalueforanalysesreportedinthemainmanuscript.1949
Foranyvalueofxp,representingthefractionoftrueassociationsatagivenp-value1950
threshold,wecalculatedavalueforπ₯!! ,representingthefractionofcausal1951
associationsatagivenp-valuethreshold,asπ₯!! = πΌπ₯!.Underthismodel,usinga1952
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
90
differentvalueforΞ±(e.g.50%or10%)wouldscalePPAcestimateslinearly(e.g.5/31953
or1/3ashigh).1954
1955
Incorporationofpriorlikelihoodintoposteriorprobabilityestimations1956
Followingpreviouswork81,theposteriorprobabilityofcausalassociationπ₯!! canbe1957
expressedasacombinationoftheprioroddsofcausalassociationforthevariant,Ο1958
(i.e.thebelief,priortoobservinganygeneticassociationdata,thatthevariantis1959
causallyassociatedwithT2D),andtheBayesfactorforcausalassociationofthe1960
variantcalculatedfromgeneticassociationdata,BFc:1961
ππ! = π΅πΉ!π
1β π (2)
wherePOcistheposterioroddsofcausalassociationexpressedas1962
ππ! = πππ΄!/(1β πππ΄!) (3)
WeuseaβcβsubscriptinPOcandBFctoemphasizethattheyareposteriorodds(and1963
Bayesfactors)forcausalassociation,ratherthanjusttrueassociation.1964
1965
Givenanestimateπ₯!! oftheposteriorprobabilityofcausalassociation(i.e.PPAc)for1966
aclassofvariants(e.g.thosesatisfyingp<0.05),aswellasapriorprobabilityof1967
causalassociationΟforthesameclassofvariants,wecancalculateanestimateof1968
theaverageBayesfactorforvariantsintheclassas: 1969
π΅πΉ!! =
π₯!!
1β π₯!!1β ππ (4)
Here,π΅πΉ!! denotestheaverageBayesfactorforcausalassociation(i.e.theratioof1970
thelikelihoodoftheobserveddataunderthemodelofcausalassociationtothe1971
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
91
likelihoodoftheobserveddataunderthemodelofnoassociation)forvariantswith1972
p-valuebelowagivenp.Wenotethatthisequationindirectlyinfersanaverage1973
Bayesfactorfromadirectestimateofanaverageposterior(xpc)andaspecified1974
priorΟ,whichisdifferentfromhowBayesfactorsareusuallycalculated.1975
1976
UndertheassumptionthattherelationshipbetweenavariantβsΟandPOcis,given1977
itsobservedp-value,conditionallyindependentofallothervariantproperties(i.e.1978
dependenceonpropertiessuchassamplesizeisentirelycapturedbytheobserved1979
p-value),wecalibratedtherelationshipbetweenp-valueandBFpcusing1980
nonsynonymousvariantswithinGWASloci.WemodeledΟforsuchvariants1981
assuming(a)onaverage1.1geneswithin250kbofeachGWASsignalharbors1982
codingvariantsassociatedwithT2D;(b)missensevariantsareamixtureoffully1983
benignandfullyprotein-inactivatingvariants12;(c)onlyinactivatingmissense1984
variants;and(d)one-thirdofmissensevariantsareinactivating(asestimatedby1985
theaverageweightofmissensevariantsinourmasks).Basedonthe595genes1986
withinthe94T2DGWASlociinouranalysis,thisyieldedapriorestimateof1987
0.057 = 1.1Γ 94 595 Γ 0.33.1988
1989
ThegenepriorwasinspiredbytheoftenimplicitexpectationthataGWASsignal1990
usuallyrepresentsasinglecausalvariant114affectingasinglegene(although1991
multipleeffectorgenesmaybemorecommonthanpreviouslythought3).Toassess1992
thesensitivityofourresultstotheassumptionof1.1disease-relevantgenesper1993
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
92
T2DGWASlocus,werepeatedallcalculationswiththeadditionalchoicesof0.5and1994
2genesperGWASlocus(SupplementaryFigure21ab).1995
1996
Wecalculatedthevariantpriorbasedonthemeanweightofvariantsinourdataset1997
ascomputedfortheβweightedβgene-leveltest,astheseweightsweredesignedto1998
directlyestimatetheprobabilitythatvariantsinamaskcausefulllossoffunction.1999
Thiscalculationproducedapriorestimateof34.2%fornonsynonymousvariantsin2000
ourdataset,notfarfromapreviouslyreportedvalueof25%12.Wethususedavalue2001
of33%forthevariantpriorinourmainanalysis,withvaluesof40%and25%used2002
forcomparison(SupplementaryFigure21cd).2003
2004
Throughthepriorprobabilityofcausalassociationfornonsynonymousvariantsin2005
T2DGWASlociof0.057,andequations(1)-(4)above,weproducedalookuptable2006
mappingvariantp-valuestoBayesfactorsofcausalassociation(BFc).Forany2007
subsequentvariantvwithobservedp-valuep(v)andauser-specifiedprioronthe2008
relevanceofitsgenetoT2D,wethencalculateditsposteriorlikelihoodof2009
associationbymappingp(v)toBFcandthenemployingequations(2)and(3)to2010
calculateanestimatedposteriorprobabilityofcausalassociation(PPAc).Although2011
notpresentedhere,lowerandupperconfidenceintervalsonPPAccanalsobe2012
estimatedbyrepeatingthisprocedureusingthelowerandupperconfidence2013
intervalsforxpcinequation(4).2014
2015
SensitivityofPPActomodelingparameters2016
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
93
Theabovecalculationsrelyontwoparameters,thespecificvaluesofwhichwill2017
affectfinalPPAcestimates.First,theyrequireaparameterfortheproportionoftrue2018
nonsynonymousassociationsthatarecausal.Asdescribedaboveandinthetext,we2019
usedavalueβof30%βinbetweenapublishedestimateoftheproportionof2020
nonsynonymousassociationswithinGWASlocithatarecausal(49.2%)anda2021
publishedestimateoftheproportionofcausalassociationsthatarenonsynonymous2022
(~10%).Usingadifferentvalue(e.g.50%or10%)wouldscalethePPAcestimates2023
linearly(e.g.5/3or1/3ashigh).2024
2025
Inaddition,calculationsinvolvingauser-specifiedpriorrequireaparameterforthe2026
proportionofnonsynonymousvariantsinGWASlocithatcausallyinfluenceT2D2027
risk(priortoanyobservedassociations).ThisparameterdoesnotaffectPPAc2028
estimatesgenome-wideorwithinGWASloci,aswedirectlyestimatePPAcestimates2029
forthesegenesfromourdataandthereforedonotrequireauser-specifiedprior.2030
Althoughwedecomposethisparameterintotwoβaparameterfortheproportionof2031
geneswithinT2DGWASlocithatarerelevanttodiseaseandaparameterforthe2032
proportionofmissensevariantswithinagenethatresultinlossoffunctionβonly2033
theproductofthetwoparametersisusedinthemodel.SupplementaryFigure212034
showstheimpactofdifferentvaluesforthesetwoparameters.2035
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
94
References2036
1. Altshuler,D.,Daly,M.J.&Lander,E.S.Geneticmappinginhumandisease.2037Science322,881-8(2008).2038
2. Welter,D.etal.TheNHGRIGWASCatalog,acuratedresourceofSNP-trait2039associations.NucleicAcidsRes42,D1001-6(2014).2040
3. Boyle,E.A.,Li,Y.I.&Pritchard,J.K.Anexpandedviewofcomplextraits:from2041polygenictoomnigenic.Cell169,1177-86(2017).2042
4. Gusev,A.etal.Partitioningheritabilityofregulatoryandcell-type-specific2043variantsacross11commondiseases.AmJHumGenet95,535-52(2014).2044
5. Maurano,M.T.etal.Systematiclocalizationofcommondisease-associated2045variationinregulatoryDNA.Science337,1190-5(2012).2046
6. Gaulton,K.J.etal.Geneticfinemappingandgenomicannotationdefines2047causalmechanismsattype2diabetessusceptibilityloci.NatGenet47,1415-204825(2015).2049
7. Grotz,A.K.,Gloyn,A.L.&Thomsen,S.K.Prioritisingcausalgenesattype22050diabetesriskloci.CurrDiabRep17,76(2017).2051
8. Claussnitzer,M.etal.FTOobesityvariantcircuitryandadipocytebrowning2052inhumans.NEnglJMed373,895-907(2015).2053
9. Musunuru,K.etal.FromnoncodingvarianttophenotypeviaSORT1atthe20541p13cholesterollocus.Nature466,714-9(2010).2055
10. Rusu,V.etal.Type2diabetesvariantsdisruptfunctionofSLC16A11through2056twodistinctmechanisms.Cell170,199-212e20(2017).2057
11. Eyre-Walker,A.EvolutioninhealthandmedicineSacklercolloquium:genetic2058architectureofacomplextraitanditsimplicationsforfitnessandgenome-2059wideassociationstudies.ProcNatlAcadSciUSA107Suppl1,1752-62060(2010).2061
12. Zuk,O.etal.Searchingformissingheritability:designingrarevariant2062associationstudies.ProcNatlAcadSciUSA111,E455-64(2014).2063
13. Cirulli,E.T.&Goldstein,D.B.Uncoveringtherolesofrarevariantsincommon2064diseasethroughwhole-genomesequencing.NatRevGenet11,415-25(2010).2065
14. McClellan,J.&King,M.C.Geneticheterogeneityinhumandisease.Cell141,2066210-7(2010).2067
15. Plenge,R.M.,Scolnick,E.M.&Altshuler,D.Validatingtherapeutictargets2068throughhumangenetics.NatRevDrugDiscov12,581-94(2013).2069
16. Dickson,S.P.,Wang,K.,Krantz,I.,Hakonarson,H.&Goldstein,D.B.Rare2070variantscreatesyntheticgenome-wideassociations.PLoSBiol8,e10002942071(2010).2072
17. Mahajan,A.etal.Refiningtheaccuracyofvalidatedtargetidentification2073throughcodingvariantfine-mappingintype2diabetes.NatGenet50,559-2074571(2018).2075
18. Cohen,J.etal.LowLDLcholesterolinindividualsofAfricandescentresulting2076fromfrequentnonsensemutationsinPCSK9.NatGenet37,161-5(2005).2077
19. Flannick,J.etal.Loss-of-functionmutationsinSLC30A8protectagainsttype20782diabetes.NatGenet46,357-63(2014).2079
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
95
20. Rivas,M.A.etal.Humangenomics.Effectofpredictedprotein-truncating2080geneticvariantsonthehumantranscriptome.Science348,666-9(2015).2081
21. Lohmueller,K.E.etal.Whole-exomesequencingof2,000Danishindividuals2082andtheroleofrarecodingvariantsintype2diabetes.AmJHumGenet93,20831072-86(2013).2084
22. Purcell,S.M.etal.Apolygenicburdenofraredisruptivemutationsin2085schizophrenia.Nature506,185-90(2014).2086
23. Do,R.etal.ExomesequencingidentifiesrareLDLRandAPOA5alleles2087conferringriskformyocardialinfarction.Nature518,102-6(2015).2088
24. Fuchsberger,C.etal.Thegeneticarchitectureoftype2diabetes.Nature536,208941-7(2016).2090
25. Luo,Y.etal.Exploringthegeneticarchitectureofinflammatorybowel2091diseasebywhole-genomesequencingidentifiesassociationatADCY7.Nat2092Genet49,186-192(2017).2093
26. Jun,G.etal.Evaluatingthecontributionofrarevariantstotype2diabetes2094andrelatedtraitsusingpedigrees.ProcNatlAcadSciUSA(2017).2095
27. Dewey,F.E.etal.Distributionandclinicalimpactoffunctionalvariantsin209650,726whole-exomesequencesfromtheDiscovEHRstudy.Science2097354(2016).2098
28. Agarwala,V.,Flannick,J.,Sunyaev,S.,Go,T.D.C.&Altshuler,D.Evaluating2099empiricalboundsoncomplexdiseasegeneticarchitecture.NatGenet45,21001418-27(2013).2101
29. Kryukov,G.V.,Shpunt,A.,Stamatoyannopoulos,J.A.&Sunyaev,S.R.Powerof2102deep,all-exonresequencingfordiscoveryofhumantraitgenes.ProcNatl2103AcadSciUSA106,3871-6(2009).2104
30. Moutsianas,L.etal.Thepowerofgene-basedrarevariantmethodstodetect2105disease-associatedvariationandtesthypothesesaboutcomplexdisease.2106PLoSGenet11,e1005165(2015).2107
31. Sveinbjornsson,G.etal.Weightingsequencevariantsbasedontheir2108annotationincreasespowerofwhole-genomeassociationstudies.NatGenet210948,314-7(2016).2110
32. Govaerts,C.etal.Obesity-associatedmutationsinthemelanocortin42111receptorprovidenovelinsightsintoitsfunction.Peptides26,1909-192112(2005).2113
33. Larsen,L.H.etal.Prevalenceofmutationsandfunctionalanalysesof2114melanocortin4receptorvariantsidentifiedamong750menwithjuvenile-2115onsetobesity.JClinEndocrinolMetab90,219-24(2005).2116
34. Morris,A.P.etal.Large-scaleassociationanalysisprovidesinsightsintothe2117geneticarchitectureandpathophysiologyoftype2diabetes.NatGenet44,2118981-90(2012).2119
35. Tan,K.etal.Functionalcharacterizationandstructuralmodelingofobesity2120associatedmutationsinthemelanocortin4receptor.Endocrinology150,2121114-25(2009).2122
36. Thearle,M.S.etal.Greaterimpactofmelanocortin-4receptordeficiencyon2123ratesofgrowthandriskoftype2diabetesduringchildhoodcomparedwith2124adulthoodinPimaIndians.Diabetes61,250-7(2012).2125
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
96
37. Farooqi,I.S.etal.Clinicalspectrumofobesityandmutationsinthe2126melanocortin4receptorgene.NEnglJMed348,1085-95(2003).2127
38. Wu,M.C.etal.Rare-variantassociationtestingforsequencingdatawiththe2128sequencekernelassociationtest.AmJHumGenet89,82-93(2011).2129
39. Li,M.X.,Gui,H.S.,Kwan,J.S.&Sham,P.C.GATES:arapidandpowerfulgene-2130basedassociationtestusingextendedSimesprocedure.AmJHumGenet88,2131283-93(2011).2132
40. Sladek,R.etal.Agenome-wideassociationstudyidentifiesnovelrisklocifor2133type2diabetes.Nature445,881-5(2007).2134
41. Steinthorsdottir,V.etal.Identificationoflow-frequencyandraresequence2135variantsassociatedwithelevatedorreducedriskoftype2diabetes.Nat2136Genet46,294-8(2014).2137
42. Davidson,H.W.,Wenzlau,J.M.&O'Brien,R.M.Zinctransporter8(ZnT8)and2138betacellfunction.TrendsEndocrinolMetab25,415-24(2014).2139
43. Rutter,G.A.&Chimienti,F.SLC30A8mutationsintype2diabetes.2140Diabetologia58,31-6(2015).2141
44. Nicolson,T.J.etal.Insulinstorageandglucosehomeostasisinmicenullfor2142thegranulezinctransporterZnT8andstudiesofthetype2diabetes-2143associatedvariants.Diabetes58,2070-83(2009).2144
45. Chambers,J.C.etal.CommongeneticvariationnearMC4Risassociatedwith2145waistcircumferenceandinsulinresistance.NatGenet40,716-8(2008).2146
46. Raimondo,A.etal.Type2DiabetesRiskAllelesRevealaRolefor2147PeptidylglycineAlpha-amidatingMonooxygenaseinBetaCellFunction.2148bioRxiv(2017).2149
47. Wessel,J.etal.Low-frequencyandrareexomechipvariantsassociatewith2150fastingglucoseandtype2diabetessusceptibility.NatCommun6,58972151(2015).2152
48. Wishart,D.S.etal.DrugBank5.0:amajorupdatetotheDrugBankdatabase2153for2018.NucleicAcidsRes(2017).2154
49. Blake,J.A.etal.MouseGenomeDatabase(MGD)-2017:community2155knowledgeresourceforthelaboratorymouse.NucleicAcidsRes45,D723-2156D729(2017).2157
50. Wang,M.C.,Min,W.,Freudiger,C.W.,Ruvkun,G.&Xie,X.S.RNAiscreeningfor2158fatregulatorygeneswithSRSmicroscopy.NatMethods8,135-8(2011).2159
51. Xin,Y.etal.RNASequencingofSingleHumanIsletCellsRevealsType22160DiabetesGenes.CellMetab24,608-615(2016).2161
52. Torres,J.M.etal.Integrativecrosstissueanalysisofgeneexpression2162identifiesnoveltype2diabetesgenes.bioRxiv(2017).2163
53. Flannick,J.&Florez,J.C.Type2diabetes:geneticdatasharingtoadvance2164complexdiseaseresearch.NatRevGenet17,535-49(2016).2165
54. Rossin,E.J.etal.Proteinsencodedingenomicregionsassociatedwith2166immune-mediateddiseasephysicallyinteractandsuggestunderlying2167biology.PLoSGenet7,e1001273(2011).2168
55. Mahajan,A.etal.Fine-mappingofanexpandedsetoftype2diabeteslocito2169single-variantresolutionusinghigh-densityimputationandislet-specific2170epigenomemaps.bioRxiv(2018).2171
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
97
56. Thomsen,S.K.etal.Systematicfunctionalcharacterizationofcandidate2172causalgenesfortype2diabetesriskvariants.Diabetes65,3805-11(2016).2173
57. Jucker,M.Thebenefitsandlimitationsofanimalmodelsfortranslational2174researchinneurodegenerativediseases.NatMed16,1210-4(2010).2175
58. Seok,J.etal.Genomicresponsesinmousemodelspoorlymimichuman2176inflammatorydiseases.ProcNatlAcadSciUSA110,3507-12(2013).2177
59. Takagi,M.etal.ATMRegulatesAdipocyteDifferentiationandContributesto2178GlucoseHomeostasis.CellRep(2015).2179
60. Woods,A.,Leiper,J.M.&Carling,D.TheroleofATMinresponsetometformin2180treatmentandactivationofAMPK.NatGenet44,360-1(2012).2181
61. Yee,S.W.,Chen,L.&Giacomini,K.M.TheroleofATMinresponseto2182metformintreatmentandactivationofAMPK.NatGenet44,359-60(2012).2183
62. Zhou,K.etal.CommonvariantsnearATMareassociatedwithglycemic2184responsetometforminintype2diabetes.NatGenet43,117-20(2011).2185
63. Espach,Y.,Lochner,A.,Strijdom,H.&Huisamen,B.ATMproteinkinase2186signaling,type2diabetesandcardiovasculardisease.CardiovascDrugsTher218729,51-8(2015).2188
64. Bodmer,W.&Bonilla,C.Commonandrarevariantsinmultifactorial2189susceptibilitytocommondiseases.NatGenet40,695-701(2008).2190
65. Visscher,P.M.etal.10yearsofGWASdiscovery:biology,function,and2191translation.AmJHumGenet101,5-22(2017).2192
66. Scott,R.A.etal.Anexpandedgenome-wideassociationstudyoftype22193diabetesinEuropeans.Diabetes(2017).2194
67. 1000GenomesProjectConsortiumetal.Aglobalreferenceforhuman2195geneticvariation.Nature526,68-74(2015).2196
68. McCarthy,S.etal.Areferencepanelof64,976haplotypesforgenotype2197imputation.NatGenet48,1279-83(2016).2198
69. So,H.C.,Gui,A.H.,Cherny,S.S.&Sham,P.C.Evaluatingtheheritability2199explainedbyknownsusceptibilityvariants:asurveyoftencomplexdiseases.2200GenetEpidemiol35,310-7(2011).2201
70. Segre,A.V.etal.Commoninheritedvariationinmitochondrialgenesisnot2202enrichedforassociationswithtype2diabetesorrelatedglycemictraits.PLoS2203Genet6(2010).2204
71. Altshuler,D.etal.ThecommonPPARgammaPro12Alapolymorphismis2205associatedwithdecreasedriskoftype2diabetes.NatGenet26,76-802206(2000).2207
72. Sinner,M.F.etal.Lackofreplicationinpolymorphismsreportedtobe2208associatedwithatrialfibrillation.HeartRhythm8,403-9(2011).2209
73. Hirschhorn,J.N.,Lohmueller,K.,Byrne,E.&Hirschhorn,K.Acomprehensive2210reviewofgeneticassociationstudies.GenetMed4,45-61(2002).2211
74. Wacholder,S.,Chanock,S.,Garcia-Closas,M.,ElGhormli,L.&Rothman,N.2212Assessingtheprobabilitythatapositivereportisfalse:anapproachfor2213molecularepidemiologystudies.JNatlCancerInst96,434-42(2004).2214
75. Wakefield,J.ABayesianmeasureoftheprobabilityoffalsediscoveryin2215geneticepidemiologystudies.AmJHumGenet81,208-27(2007).2216
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
98
76. Lehmann,E.L.Someprinciplesofthetheoryoftestinghypotheses.Annalsof2217MathematicalStatistics21,1-26(1950).2218
77. Peterson,M.Anintroductiontodecisiontheory,x,317p.(Cambridge2219UniversityPress,NewYork,2009).2220
78. Finucane,H.K.etal.Partitioningheritabilitybyfunctionalannotationusing2221genome-wideassociationsummarystatistics.NatGenet47,1228-35(2015).2222
79. Pickrell,J.K.Jointanalysisoffunctionalgenomicdataandgenome-wide2223associationstudiesof18humantraits.AmJHumGenet94,559-73(2014).2224
80. Smith,S.B.etal.Rfx6directsisletformationandinsulinproductioninmice2225andhumans.Nature463,775-80(2010).2226
81. Stephens,M.&Balding,D.J.Bayesianstatisticalmethodsforgenetic2227associationstudies.NatRevGenet10,681-90(2009).2228
82. Wagner,J.etal.Adynamicmapforlearning,communicating,navigatingand2229improvingtherapeuticdevelopment.NatRevDrugDiscov17,150(2018).2230
83. Timpson,N.J.,Greenwood,C.M.T.,Soranzo,N.,Lawson,D.J.&Richards,J.B.2231Geneticarchitecture:theshapeofthegeneticcontributiontohumantraits2232anddisease.NatRevGenet(2017).2233
84. Starita,L.M.etal.Variantinterpretation:functionalassaystotherescue.AmJ2234HumGenet101,315-325(2017).2235
85. SIGMAType2DiabetesConsortiumetal.Associationofalow-frequency2236variantinHNF1Awithtype2diabetesinaLatinopopulation.JAMA311,22372305-14(2014).2238
86. Fu,W.etal.Analysisof6,515exomesrevealstherecentoriginofmost2239humanprotein-codingvariants.Nature493,216-20(2013).2240
87. Fisher,S.etal.Ascalable,fullyautomatedprocessforconstructionof2241sequence-readyhumanexometargetedcapturelibraries.GenomeBiol12,R12242(2011).2243
88. Li,H.&Durbin,R.FastandaccurateshortreadalignmentwithBurrows-2244Wheelertransform.Bioinformatics25,1754-60(2009).2245
89. DePristo,M.A.etal.Aframeworkforvariationdiscoveryandgenotyping2246usingnext-generationDNAsequencingdata.NatGenet43,491-8(2011).2247
90. Purcell,S.etal.PLINK:atoolsetforwhole-genomeassociationand2248population-basedlinkageanalyses.AmJHumGenet81,559-75(2007).2249
91. Price,A.L.etal.Principalcomponentsanalysiscorrectsforstratificationin2250genome-wideassociationstudies.NatGenet38,904-9(2006).2251
92. Skol,A.D.,Scott,L.J.,Abecasis,G.R.&Boehnke,M.Optimaldesignsfortwo-2252stagegenome-wideassociationstudies.GenetEpidemiol31,776-88(2007).2253
93. McLaren,W.etal.TheEnsemblVariantEffectPredictor.GenomeBiol17,1222254(2016).2255
94. Aken,B.L.etal.Ensembl2017.NucleicAcidsRes45,D635-D642(2017).225695. Pujar,S.etal.Consensuscodingsequence(CCDS)database:astandardized2257
setofhumanandmouseprotein-codingregionssupportedbyexpert2258curation.NucleicAcidsRes(2017).2259
96. Liu,X.,Wu,C.,Li,C.&Boerwinkle,E.dbNSFPv3.0:aone-stopdatabaseof2260functionalpredictionsandannotationsforhumannonsynonymousand2261splice-siteSNVs.HumMutat37,235-41(2016).2262
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
99
97. Jagadeesh,K.A.etal.M-CAPeliminatesamajorityofvariantsofuncertain2263significanceinclinicalexomesathighsensitivity.NatGenet48,1581-62264(2016).2265
98. Kang,H.M.etal.Variancecomponentmodeltoaccountforsamplestructure2266ingenome-wideassociationstudies.NatGenet42,348-54(2010).2267
99. Ma,C.,Blackwell,T.,Boehnke,M.,Scott,L.J.&Go,T.D.i.Recommendedjoint2268andmeta-analysisstrategiesforcase-controlassociationtestingofsingle2269low-countvariants.GenetEpidemiol37,539-50(2013).2270
100. Willer,C.J.,Li,Y.&Abecasis,G.R.METAL:fastandefficientmeta-analysisof2271genomewideassociationscans.Bioinformatics26,2190-1(2010).2272
101. SIGMAType2DiabetesConsortiumetal.SequencevariantsinSLC16A11are2273acommonriskfactorfortype2diabetesinMexico.Nature506,97-1012274(2014).2275
102. Lee,S.etal.Optimalunifiedapproachforrare-variantassociationtesting2276withapplicationtosmall-samplecase-controlwhole-exomesequencing2277studies.AmJHumGenet91,224-37(2012).2278
103. Han,B.,Kang,H.M.&Eskin,E.Rapidandaccuratemultipletestingcorrection2279andpowerestimationformillionsofcorrelatedmarkers.PLoSGenet5,2280e1000456(2009).2281
104. Conneely,K.N.&Boehnke,M.Somanycorrelatedtests,solittletime!Rapid2282adjustmentofPvaluesformultiplecorrelatedtests.AmJHumGenet81,22831158-68(2007).2284
105. Psaty,B.M.etal.CohortsforHeartandAgingResearchinGenomic2285Epidemiology(CHARGE)Consortium:Designofprospectivemeta-analysesof2286genome-wideassociationstudiesfrom5cohorts.CircCardiovascGenet2,73-228780(2009).2288
106. Yu,B.etal.RareexomesequencevariantsinCLCN6reducebloodpressure2289levelsandhypertensionrisk.CircCardiovascGenet9,64-70(2016).2290
107. Brody,J.A.etal.Analysiscommons,ateamapproachtodiscoveryinabig-2291dataenvironmentforgeneticepidemiology.NatGenet49,1560-3(2017).2292
108. Chen,H.etal.Controlforpopulationstructureandrelatednessforbinary2293traitsingeneticassociationstudiesvialogisticmixedmodels.AmJHum2294Genet98,653-66(2016).2295
109. Haghverdizadeh,P.,SadatHaerian,M.,Haghverdizadeh,P.&SadatHaerian,2296B.ABCC8geneticvariantsandriskofdiabetesmellitus.Gene545,198-2042297(2014).2298
110. Barbeira,A.N.etal.Exploringthephenotypicconsequencesoftissuespecific2299geneexpressionvariationinferredfromGWASsummarystatistics.bioRxiv2300(2017).2301
111. Mahajan,A.etal.Genome-widetrans-ancestrymeta-analysisprovides2302insightintothegeneticarchitectureoftype2diabetessusceptibility.Nat2303Genet46,234-44(2014).2304
112. Das,S.etal.Next-generationgenotypeimputationserviceandmethods.Nat2305Genet48,1284-7(2016).2306
113. Brown,L.D.,Cai,T.T.&Dasgupta,A.Intervalestimationforabinomial2307proportion.StatisticalScience16,101-133(2001).2308
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
100
114. WellcomeTrustCaseControlConsortiumetal.Bayesianrefinementof2309associationsignalsfor14lociin3commondiseases.NatGenet44,1294-3012310(2012).2311
23122313
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
a
0
5
10
15
20
25
30
Singleβvariant associations
Chromosome
βlo
g 10(p
)
1 2 3 4 5 6 7 8 9 11 13 15 18 22
ββββ
β
βββ
β
β
ββ
β
ββββββ
ββ
β
ββ
β
β
β
β
ββ
β
ββββ
β
ββββ
β
β
β
β
βββ
β
β
ββ
ββ
β
β
β
β
βββ
β
β
βββββββββββ
β
βββββββ
β
β
ββ
ββ
β
β
β
ββ
βββ
βββ
β
ββ
β
β
β
ββ
β
β
βββββ
β
ββ
ββ
β
β
ββ
β
β
β
β
β
ββ
β
β
β
ββββ
β
β
β
ββ
βββ
ββ
β
β
ββ
βββ
ββ
β
β
β
ββ
β
β
β
β
ββ
β
βββ
β
β
ββ
ββ
β
β
β
β
ββ
βββ
ββ
βββ
β
β
β
βββββββββ
βββββββ
ββββ
β
ββ
ββ
ββ
β
βββββ
β
β
ββ
β
ββββ
ββββ
β
ββββββ
βββββ
β
βββββ
ββ
ββββββ
β
ββ
β
β
β
β
βββ
β
βββ
β
β
ββ
βββ
β
ββ
β
β
β
β
βββ
β
β
βββββ
ββ
β
ββ
β
β
β
β
β
β
ββ
β
ββββ
β
ββββ
ββ
β
β
ββ
β
ββ
ββββ
βββ
β
β
βββ
β
ββββββββ
β
β
ββ
β
β
β
βββ
ββ
ββ
β
β
ββββββ
β
β
β
βββ
β
β
β
β
β
β
β
ββββ
β
ββββ
βββββ
β
β
ββ
β
β
ββ
βββ
β
ββββββββββββββ
β
β
β
ββββ
ββ
ββ
ββββββββ
ββ
βββ
ββββ
β
β
ββββββββββββ
β
ββ
β
β
β
βββ
ββ
β
ββ
ββββββ
β
β
βββββ
ββ
βββ
βββ
β
β
ββ
β
β
ββββ
β
βββββ
β
β
ββ
β
β
ββββ
β
β
β
β
β
β
ββ
β
β
β
ββ
β
β
β
βββββ
β
β
β
β
β
ββ
β
β
β
β
ββββ
β
β
ββ
ββ
β
ββ
βββ
β
ββ
βββ
ββββ
β
ββ
ββ
β
β
ββ
βββ
β
β
ββββββ
β
ββ
ββββ
β
β
β
β
ββ
β
βββββββββββ
ββ
ββ
βββββββ
β
βββ
ββ
β
ββββ
β
ββ
β
β
β
ββ
β
βββ
ββββ
ββββββββ
β
ββββ
ββ
βββββββ
β
β
βββββββ
β
β
ββββββ
β
ββ
β
β
β
ββ
β
ββββββ
βββββββ
β
βββ
ββ
β
ββ
β
ββββββ
β
β
ββ
ββ
βββ
β
β
β
ββββββ
β
β
β
β
ββββββ
β
β
ββββββββ
β
β
β
β
β
β
ββ
ββ
β
ββββββββββββββ
β
β
β
β
β
ββββββ
ββββ
β
β
ββββββ
β
ββ
β
βββββββββ
ββ
β
β
βββ
β
βββββββ
β
ββ
β
ββ
β
ββββββ
β
β
β
βββ
β
ββ
βββ
βββββββ
ββ
β
βββββ
ββ
βββββ
β
β
β
β
β
β
β
ββββ
ββ
ββ
β
βββ
ββββ
β
β
β
ββ
β
ββ
ββ
ββββ
β
β
β
β
ββ
β
ββββββββ
ββ
β
β
β
β
β
ββ
β
β
ββββ
β
β
ββ
β
β
ββ
β
βββ
β
βββ
ββββββββ
β
β
βββ
ββ
ββ
βββββ
ββ
β
β
βββββ
βββ
β
β
β
βββ
β
ββββ
β
β
βββ
β
β
β
ββ
β
β
β
ββ
βββ
β
ββ
β
ββ
ββββ
β
ββ
βββββββββββ
β
β
βββ
βββ
β
β
β
β
β
ββββ
ββ
β
ββ
β
ββββββ
β
βββββββββββ
β
ββ
β
β
ββββββ
β
β
β
β
ββ
ββββ
β
β
β
β
β
ββ
ββ
β
β
βββ
ββββββββ
β
ββ
β
β
βββ
β
βββ
β
βββββ
ββ
βββ
β
ββ
ββ
β
β
βββ
β
β
βββ
β
ββ
β
β
ββ
ββ
ββββββ
β
ββββββ
β
β
ββββββ
β
ββββββ
ββ
βββββββββββ
β
ββ
β
β
ββββ
β
ββββ
ββββ
β
β
β
βββ
β
ββββ
β
βββ
ββ
β
βββββββ
β
β
β
β
β
β
β
β
ββββ
β
ββββββ
ββββ
β
βββ
β
βββ
βββ
β
ββ
βββ
β
βββ
β
β
βββββββββ
β
ββ
βββββ
β
ββββ
ββ
β
ββ
β
β
ββ
ββ
β
β
ββ
β
β
ββββββ
β
ββββ
β
β
ββ
ββ
ββββ
ββ
ββ
β
ββ
ββ
βββ
β
ββ
β
β
ββ
β
β
ββ
βββ
β
ββ
β
β
ββ
βββ
β
β
ββ
β
β
βββββ
β
β
ββ
β
ββ
β
β
β
ββ
β
ββ
β
ββ
β
ββββ
βββ
β
β
β
β
β
β
β
βββββ
ββ
β
ββββ
β
β
β
β
ββ
β
β
βββ
β
β
β
β
β
βββββ
β
ββββ
β
ββββββ
β
β
β
β
β
β
β
ββ
ββββ
ββ
ββββ
β
β
β
βββ
β
β
β
β
β
ββββββ
β
βββ
β
ββββ
β
βββ
β
ββββ
βββ
ββ
β
βββ
β
ββ
β
ββββ
ββββ
β
ββββββββ
βββ
ββ
ββββββββ
β
β
ββ
ββββββ
β
βββ
β
β
β
ββ
β
β
β
βββββ
β
β
β
βββ
β
βββ
βββ
β
βββ
β
β
βββ
β
βββββ
βββ
β
β
β
ββ
ββ
β
ββ
ββββββββ
β
βββ
β
β
β
β
ββββ
β
ββββ
βββββ
β
β
β
βββββ
β
ββ
β
βββββββ
β
βββ
βββ
ββββ
β
βββ
ββ
βββ
β
β
ββββ
ββ
βββββ
β
ββ
β
β
βββββββββ
ββββ
ββββββββββ
β
ββββββ
ββ
β
ββ
β
ββββββββββββ
β
β
ββ
βββ
ββββ
β
β
βββ
β
ββ
β
ββββββ
ββ
β
ββ
β
β
βββ
β
β
β
β
β
β
β
β
ββ
βββββ
β
β
ββ
β
ββ
β
ββ
ββ
βββββ
β
ββ
β
βββ
β
ββ
β
βββ
β
βββ
β
β
β
β
β
ββββ
β
ββ
β
β
β
βββββ
β
β
β
βββ
β
β
ββ
β
β
β
β
β
β
β
ββββ
β
βββββ
β
β
ββ
β
βββ
β
βββ
β
ββββ
β
β
β
ββ
ββ
βββ
β
ββββββ
β
βββββ
ββ
ββ
β
ββββ
βββ
β
βββ
β
β
β
β
β
ββ
β
βββ
βββββββββ
ββββ
ββ
β
β
β
β
β
β
β
ββ
β
βββ
ββ
βββ
βββββ
βββ
β
β
β
βββ
βββ
ββ
ββ
ββββ
β
βββ
βββ
β
β
β
β
β
βββββββ
β
ββ
ββββ
β
β
ββ
ββββ
β
ββββββββββ
β
ββ
β
ββ
β
ββββ
β
β
βββ
β
β
βββββββββββ
β
β
β
β
ββ
ββββ
β
ββ
ββ
βββ
β
βββββββ
β
β
β
β
ββ
βββ
βββ
β
ββ
ββ
ββ
β
βββ
β
β
ββ
ββ
β
βββ
β
β
ββ
β
ββ
β
ββ
β
ββ
ββ
βββββ
ββ
βββ
β
β
βββ
β
β
β
ββββ
β
β
βββββ
β
βββββ
β
ββββββββ
β
β
β
ββ
ββββ
β
ββββββ
β
β
ββββ
β
β
ββ
βββ
β
β
ββββββ
βββ
ββββ
ββ
β
ββ
β
ββ
βββββββ
β
β
ββ
β
β
ββ
βββ
β
β
β
ββ
β
βββ
ββββββ
β
β
βββ
β
ββ
β
β
β
β
β
ββ
ββββ
β
β
β
β
ββ
β
β
β
β
ββ
β
βββ
ββ
β
β
ββ
β
β
β
βββ
β
β
ββ
β
β
ββββββ
β
ββ
β
ββββ
β
β
β
βββ
β
β
β
ββββ
ββ
ββ
ββ
β
ββ
β
ββ
βββ
β
ββ
ββ
β
β
ββββ
β
ββββββ
β
β
β
βββ
βββ
ββ
ββββ
β
ββββββ
ββ
β
β
ββ
β
β
β
β
β
β
β
ββββββ
β
β
β
β
β
ββ
ββ
β
β
βββ
β
β
β
β
ββ
ββββ
βββ
β
βββ
ββ
βββ
β
ββββββ
βββ
β
βββββββββ
ββββββ
ββ
β
ββ
ββ
βββ
βββ
β
β
β
ββ
β
β
β
ββ
β
βββ
ββ
ββ
β
β
β
βββ
β
β
β
β
β
β
ββββββββββ
β
ββ
β
β
ββ
ββ
β
β
β
β
β
β
β
β
β
β
β
βββ
ββββββ
β
β
ββ
βββ
ββ
β
β
β
β
β
βββ
β
β
β
βββ
β
β
β
βββ
ββ
ββ
β
β
β
βββββββ
β
βββββββββββββ
βββ
β
βββββ
β
ββββ
β
βββββ
β
β
ββββββ
βββββββ
β
β
ββ
β
β
β
β
βββββ
β
β
β
β
ββ
ββ
β
ββββ
ββ
ββ
β
ββ
ββ
β
β
ββ
βββ
βββββ
βββ
ββββ
β
β
β
ββ
β
ββ
β
β
ββββ
β
ββββ
ββ
ββ
β
β
ββββ
ββ
β
β
βββ
ββ
βββββ
βββ
β
ββ
βββββ
β
β
ββ
β
βββ
βββ
β
β
β
ββ
ββ
β
ββ
β
ββ
β
βββ
ββββ
β
β
ββββ
ββ
βββ
β
βββ
βββ
β
ββ
β
ββ
βββ
ββββ
β
ββ
β
ββ
β
β
ββββ
ββ
ββ
β
β
β
β
ββββ
β
ββ
β
βββ
ββββ
ββ
β
β
βββββ
β
β
β
βββ
ββ
ββ
β
β
ββββ
β
ββ
β
β
β
β
β
βββββ
ββ
βββ
βββ
β
β
ββ
β
βββββββ
β
ββ
β
βββ
β
β
β
ββ
β
ββ
β
β
β
β
β
βββ
β
ββ
βββ
β
ββ
β
β
β
β
β
β
β
ββββ
β
ββ
β
ββββ
β
β
βββ
β
βββ
β
βββββ
β
βββ
β
ββββ
β
β
β
β
ββ
β
ββ
β
βββββ
βββ
βββββββββ
β
β
β
β
β
ββ
ββ
β
ββ
ββ
β
β
ββββββββββββββ
β
βββββ
ββ
ββββββ
ββ
β
β
ββ
β
ββ
β
ββ
β
βββββ
β
β
β
β
ββββββββ
β
ββ
βββ
β
ββ
β
ββββ
ββ
β
β
β
ββ
ββ
βββββ
ββ
ββββββ
β
βββ
ββββ
β
β
ββ
ββ
βββββ
β
ββ
β
β
β
βββββββββββββ
βββ
ββ
β
βββββ
β
β
β
β
ββ
β
ββ
ββββββββββ
ββββββ
ββ
β
β
β
βββββ
β
β
βββββ
β
βββ
β
ββ
β
β
βββββ
β
β
β
β
βββββ
ββ
β
β
β
ββ
ββββββββ
β
ββ
β
ββββ
β
βββ
β
β
β
β
β
β
βββββ
β
βββββββββ
β
ββββ
β
β
β
β
βββ
β
ββββ
β
βββββββββββ
β
β
β
β
β
βββ
β
ββ
β
βββββ
β
β
ββββββββββ
β
ββββ
β
β
ββ
β
βββ
ββ
ββ
β
ββββββ
β
β
β
ββ
β
β
β
βββ
ββ
β
ββ
β
β
βββ
β
ββββ
β
ββββ
βββββββ
ββ
β
βββ
β
βββββββ
βββ
β
ββ
β
ββ
ββ
β
β
β
βββββ
β
ββ
β
β
ββ
β
β
β
ββ
β
β
βββββ
ββ
ββββ
β
β
βββββ
β
ββ
β
βββ
βββ
βββ
βββββ
β
β
β
β
ββββββ
β
ββ
β
ββββ
β
β
βββ
β
β
β
ββββ
β
ββ
β
βββ
ββββββββββββββ
β
β
ββββββ
β
β
β
ββββββββ
βββ
β
β
β
ββββ
β
ββββββββ
β
ββββββββ
β
β
β
β
ββ
β
β
ββββ
β
ββββ
β
β
β
β
β
ββ
β
βββ
β
β
β
β
βββ
β
β
β
βββ
β
ββ
ββββ
β
β
βββββββ
β
ββ
βββ
ββ
β
ββ
β
ββββ
β
β
β
ββ
β
β
ββ
β
ββ
ββ
ββ
β
ββ
β
β
β
βββββ
βββ
ββ
β
ββββββββ
β
ββ
βββ
ββββ
βββ
βββ
ββ
β
β
β
ββ
β
ββ
β
ββ
β
ββ
β
β
β
β
β
β
ββββββββ
β
β
β
β
β
β
β
β
β
β
ββββββββ
β
ββ
ββββββ
β
β
β
β
β
ββββ
β
β
β
β
β
β
β
βββ
ββ
β
β
β
β
βββ
ββ
ββ
β
β
ββββ
β
β
β
β
βββ
β
β
β
ββ
β
βββ
β
β
ββ
β
ββββ
β
β
β
βββββββββ
β
β
β
β
β
β
ββ
β
β
ββββββ
β
ββ
β
ββ
β
β
β
β
β
β
β
β
β
β
β
βββββββββ
β
β
ββ
ββββββ
β
βββββ
ββ
β
ββ
βββ
ββ
β
β
ββ
ββ
β
ββββββ
β
ββ
β
ββββ
β
β
β
βββββββββββββββ
ββ
β
ββ
βββ
β
β
βββββ
β
β
β
β
ββββββ
β
β
β
βββββββ
ββ
β
β
β
β
βββ
β
β
β
ββ
β
βββββ
ββ
ββ
β
β
βββ
β
ββββ
β
β
β
ββββ
β
ββββ
βββββββ
β
β
βββ
β
β
ββββββββββ
β
β
βββ
β
β
ββββββββ
βββ
ββ
β
β
β
β
β
ββ
ββ
ββββββ
β
β
β
βββββββββ
βββ
β
β
β
β
β
ββ
β
ββββ
β
β
β
β
ββ
β
β
β
β
β
ββ
β
β
β
ββββββ
βββββ
β
β
β
β
β
β
ββ
ββββ
βββββ
ββββββ
β
β
β
β
βββ
ββ
βββ
β
β
ββ
β
ββ
β
β
β
β
β
β
β
β
ββ
βββββ
β
βββ
β
ββββ
β
ββ
β
β
β
β
β
βββ
βββββ
β
ββ
β
βββ
ββ
β
βββββββββ
ββ
β
β
β
β
β
ββ
β
β
ββββ
β
ββ
βββ
β
β
β
β
β
βββββ
β
β
ββ
β
β
ββ
ββ
β
β
βββ
β
β
β
βββ
β
ββββββββββββ
ββ
β
β
βββ
β
ββββ
β
ββ
β
β
ββ
ββ
β
β
β
β
ββ
β
ββ
β
β
β
ββ
β
β
β
ββ
β
β
β
ββββββ
β
β
β
βββ
βββββ
βββββββββ
β
ββ
β
β
β
βββββββ
βββ
ββββ
β
β
β
β
βββββ
ββββ
β
β
β
β
β
β
β
βββββ
β
β
ββ
β
β
β
ββ
β
β
β
βββββββββββ
β
β
β
βββ
βββ
βββββ
β
β
ββ
β
ββ
βββ
β
β
β
ββ
βββββββ
β
ββ
ββ
βββββ
β
βββ
ββ
β
β
ββ
β
β
β
β
β
β
ββ
βββ
β
βββ
βββββ
ββββββ
β
ββββββ
ββ
ββ
β
β
ββ
β
βββ
ββ
β
β
ββ
β
βββ
β
β
β
β
β
β
β
ββββββ
β
ββββββ
β
ββββ
β
β
ββ
ββ
β
ββ
ββ
βββ
β
βββββββ
ββββ
β
ββ
ββ
β
ββ
β
ββββ
βββ
β
β
β
βββ
ββββββ
ββββββ
βββββ
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
β
ββββ
ββ
βββββββ
β
β
ββ
ββ
β
ββ
β
ββββ
βββ
β
β
ββ
β
β
β
β
β
ββββ
β
β
ββββββ
ββ
β
β
β
ββ
β
ββββ
β
β
βββ
β
ββ
β
ββββ
β
β
βββ
β
ββ
β
β
β
ββββ
β
βββββ
β
β
β
β
β
β
β
βββββ
ββββββ
β
βββ
β
β
ββ
ββ
β
ββββ
β
βββ
β
ββ
βββ
ββ
β
βββ
β
β
ββ
β
β
β
βββ
β
β
β
β
β
ββββ
ββ
ββ
β
β
β
β
β
βββββ
β
ββ
β
ββββββββ
β
ββ
β
β
ββ
β
β
β
βββββ
β
β
ββββ
β
β
β
ββ
ββ
β
β
β
ββββ
β
β
β
β
ββ
ββββ
β
β
β
β
ββ
β
β
β
β
β
βββ
β
βββ
β
β
β
βββββββ
ββ
ββββββββ
β
β
ββββ
βββ
βββ
β
ββββ
β
βββββββββββββββ
β
ββ
β
β
βββ
β
βββββ
β
ββ
βββ
ββ
ββββ
β
ββββ
β
βββ
β
βββββ
ββ
βββ
β
ββββββ
ββ
β
β
βββββ
β
ββ
β
β
β
ββ
β
ββ
β
β
β
β
ββ
ββ
βββββββββ
ββ
β
β
βββββ
ββ
ββ
β
β
ββ
ββ
β
ββ
β
ββ
β
ββ
ββ
βββ
β
βββ
ββ
ββ
β
ββ
ββ
β
β
β
β
β
βββ
β
β
ββ
β
βββ
β
β
βββββ
β
β
ββββββββββ
ββ
β
β
βββββ
βββββββ
β
β
β
β
β
ββ
ββ
β
β
ββββββ
β
βββββββ
β
ββββ
β
β
β
β
β
ββββ
βββ
β
ββ
ββ
βββββ
ββ
ββ
βββ
β
ββ
β
β
ββ
ββββββ
β
ββββββ
β
ββ
βββββ
ββ
ββββ
β
ββββββ
βββ
β
β
ββββ
β
ββ
β
βββββ
β
β
β
β
ββββ
β
βββ
β
β
β
β
ββ
β
β
ββββ
β
ββ
β
ββ
β
βββ
βββ
β
β
β
β
β
β
ββ
β
ββββββββββββ
β
β
β
ββ
β
β
β
β
ββββββ
β
βββ
β
ββ
β
β
ββ
β
β
β
β
ββ
β
ββββββββββ
β
β
ββ
β
ββββ
ββ
βββββββ
β
ββββ
ββ
βββ
β
βββββββ
β
ββ
β
βββββ
ββ
ββββββ
β
ββ
β
βββββ
β
ββ
ββ
βββ
β
ββ
β
ββββ
β
β
ββ
β
ββββ
β
β
β
βββ
β
ββββββββ
β
β
β
β
βββ
β
ββ
β
β
ββββββ
β
ββββ
β
β
β
βββββ
β
β
β
β
βββ
βββ
ββββββββ
β
ββ
ββ
βββββββ
β
βββββββββ
β
βββ
ββ
β
ββ
ββ
β
βββ
β
β
β
ββ
β
ββ
β
β
ββββββββ
ββ
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
βββ
β
βββ
β
β
β
β
ββββββββ
β
βββ
βββ
β
ββ
β
β
βββββββ
β
βββ
β
β
β
ββ
β
β
β
βββ
β
β
ββββ
β
βββββ
β
β
ββββ
β
β
ββ
β
β
β
β
ββββ
β
β
ββββ
β
ββ
β
ββ
β
β
β
β
β
βββ
ββ
βββββββ
β
ββββ
βββ
β
β
β
β
ββββ
β
β
β
β
ββββ
ββ
β
β
ββββ
βββ
βββ
β
β
ββ
β
ββββββ
β
ββββ
ββββββ
βββββ
β
β
ββ
β
β
β
ββ
β
ββ
ββ
ββββββ
βββ
β
βββββββββ
β
β
βββ
β
β
ββ
ββ
β
ββ
βββ
ββ
βββββββββββ
β
ββ
ββ
β
ββββ
βββ
β
ββββββ
βββ
ββ
ββ
ββ
ββ
ββ
β
β
ββ
β
β
ββββ
β
ββββ
β
ββββββ
β
ββ
β
β
ββ
βββ
β
βββ
ββ
β
βββ
ββ
βββ
β
β
ββ
β
ββββ
ββ
β
ββ
β
β
β
ββ
β
β
β
β
β
β
ββββ
β
β
β
β
ββ
β
ββββββ
β
βββββ
ββββββ
βββββββββββ
βββββββ
β
βββββ
β
βββββββ
β
β
ββ
β
βββ
β
ββ
ββ
βββ
βββββββ
β
ββ
ββ
β
β
β
β
ββββ
ββ
βββ
β
β
ββββββ
β
β
β
βββ
ββ
βββ
βββββ
β
ββ
β
β
β
ββ
ββββ
β
ββββββ
β
βββββ
ββ
β
β
β
β
β
ββ
β
ββ
β
ββ
ββββββββββ
β
ββ
ββ
βββββββ
β
β
ββ
β
β
ββ
βββ
β
β
β
βββ
β
βββ
β
ββββ
β
ββββ
β
ββ
β
β
ββ
β
ββ
β
ββ
ββββ
β
β
β
ββ
β
βββββββ
β
β
β
ββββββββββββββ
ββ
β
β
β
β
β
ββ
ββββ
βββ
ββ
ββββ
β
β
ββββ
βββ
β
ββ
β
ββ
β
β
β
βββββ
β
β
β
βββββ
β
β
ββ
β
β
β
β
β
β
β
β
β
β
ββ
ββ
β
β
β
β
β
βββ
β
βββββ
β
ββ
β
β
ββ
β
β
β
β
ββ
β
βββ
β
β
β
β
β
βββ
β
ββ
βββββ
β
βββ
βββ
ββ
β
β
ββ
β
ββ
βββ
βββββ
β
ββ
β
β
ββ
β
β
β
β
β
βββββββ
β
β
β
ββ
ββ
β
β
β
β
β
β
β
ββ
β
β
βββ
β
ββββ
ββ
β
βββββ
β
β
β
β
β
β
βββ
ββ
ββ
βββββ
β
ββββ
βββ
βββββ
β
β
ββββββ
ββββ
β
β
ββ
ββ
βββ
β
β
β
βββββ
ββββ
β
βββββ
β
β
β
βββ
ββ
β
β
β
β
ββ
β
β
ββ
β
β
β
β
β
β
β
β
βββ
ββ
ββ
β
ββ
βββ
β
β
β
β
ββ
ββββββ
β
β
β
ββββββ
βββ
β
β
β
ββ
βββββ
β
β
βββββββββ
β
βββββ
βββββ
β
β
βββ
βββ
βββ
β
β
ββ
β
ββββββββββ
β
β
β
β
ββ
β
β
β
βββ
βββββββ
β
ββββ
ββ
β
ββ
βββ
βββ
β
β
β
ββ
ββββββ
β
βββββ
ββ
βββββ
β
β
β
ββββ
β
βββ
β
ββ
β
βββ
β
ββ
ββ
β
β
ββ
β
β
β
β
ββ
β
ββββ
β
ββ
β
β
ββββββ
β
β
βββ
β
β
β
ββ
ββββββ
β
ββ
β
ββββββββββββββββββββββ
β
β
ββ
β
β
β
β
βββ
βββββββ
β
βββ
β
β
β
βββ
ββββ
β
β
ββ
βββ
β
ββ
β
β
ββββ
β
β
β
β
β
ββ
β
ββ
β
ββββ
β
β
β
β
β
ββββββ
ββ
β
β
β
β
β
β
β
ββ
ββββ
β
β
ββ
β
β
β
β
ββ
β
βββββ
β
βββββ
β
β
β
β
β
βββ
β
β
β
β
β
ββ
ββ
β
β
βββββ
β
β
β
ββ
β
β
β
β
ββ
ββ
β
βββββββ
β
β
β
ββ
ββ
β
ββ
β
β
ββ
β
β
β
β
ββ
β
ββ
βββββββββ
β
βββββ
β
ββ
β
β
βββββββ
β
β
βββ
βββ
β
ββββ
β
β
β
β
β
β
ββββ
β
β
β
β
β
β
β
βββββ
β
βββββ
β
ββ
β
β
β
β
β
β
ββ
β
ββββ
β
β
β
ββ
βββ
β
βββ
β
ββ
β
β
βββ
β
β
ββ
β
β
β
ββ
βββββββ
β
ββ
ββ
β
β
βββ
β
β
β
βββ
ββ
β
β
ββ
β
βββ
β
β
β
β
β
ββ
β
β
β
β
β
β
β
ββββ
ββ
β
βββ
βββ
β
β
ββ
β
β
βββ
β
ββββ
β
β
β
βββββ
ββ
ββ
β
ββ
ββββββ
β
βββ
β
ββββ
βββ
β
β
β
ββ
ββββ
β
β
β
β
ββ
β
ββ
β
βββ
β
β
β
ββ
ββ
β
β
β
ββββ
ββ
βββ
β
β
β
ββ
β
βββββββ
βββ
ββ
βββ
ββββββ
β
β
β
β
β
ββββ
β
β
βββ
βββββ
ββ
β
ββ
β
β
βββββ
β
β
β
ββ
β
β
β
β
β
βββ
β
ββ
β
β
βββ
βββ
βββββββββββ
ββ
β
ββ
ββββββββββ
β
βββ
β
β
βββ
βββ
β
ββββββ
ββ
βββ
β
ββ
β
β
β
β
β
β
β
ββ
β
β
βββ
β
β
β
β
ββ
ββββββ
β
β
β
β
β
ββ
β
β
βββ
β
β
β
βββββββ
β
β
ββ
β
ββββ
β
βββ
ββ
βββ
ββ
β
βββ
β
β
β
βββββ
βββββ
β
ββ
β
β
β
ββ
ββ
β
ββββ
β
β
βββββββ
β
βββ
ββ
β
β
β
ββ
βββββββ
βββββ
β
βββ
ββββ
βββ
β
β
β
ββββ
β
β
β
β
β
β
β
β
βββββββββββ
ββ
ββ
ββββ
β
β
βββββ
β
ββ
β
β
β
βββ
ββββββ
β
βββ
β
β
β
ββββββ
βββ
β
ββ
β
β
βββββ
ββ
β
β
β
βββββ
β
β
β
β
ββ
β
βββ
β
ββ
β
βββ
β
β
ββββββ
ββ
ββ
β
β
β
ββββ
ββββ
β
ββββββ
β
β
β
β
β
β
β
β
β
β
ββββ
β
β
β
βββββ
ββ
β
β
βββ
ββ
βββββββ
β
ββββ
β
βββ
β
β
ββ
β
β
β
β
ββ
βββ
ββ
ββββ
β
ββ
βββ
β
ββββ
βββ
ββ
β
βββ
β
β
β
β
ββββββββ
β
ββ
β
β
ββ
β
β
βββββββββββ
β
β
βββ
ββββββββββ
β
β
ββββ
β
β
β
ββββββ
ββ
β
ββ
ββ
β
ββ
β
ββββ
β
β
ββ
β
β
β
β
β
βββββ
β
β
βββββ
β
ββ
ββ
β
β
ββ
β
ββ
β
ββ
β
βββ
β
βββββ
β
β
ββ
β
βββ
β
β
β
β
β
βββββ
β
β
β
β
ββ
βββββ
β
β
β
β
ββ
β
β
β
ββ
ββ
ββ
β
β
β
β
ββββββ
β
ββββ
β
ββ
β
β
β
β
ββββ
β
β
β
ββ
βββββ
β
ββββ
ββ
ββ
β
β
β
β
ββ
β
βββ
β
β
ββ
ββββ
β
β
β
ββ
β
β
ββ
β
β
β
β
β
ββββββββββ
β
β
βββββββββ
β
β
ββ
ββββ
β
ββ
β
ββ
β
β
β
β
β
β
ββββ
β
β
β
ββββββ
β
βββββ
β
ββ
β
ββ
β
β
β
β
βββββ
βββββββββββ
β
β
βββββ
β
β
β
ββββββ
β
ββ
β
β
β
βββ
ββββ
β
β
ββ
β
βββ
β
βββββ
β
ββββ
β
ββ
β
ββ
β
ββ
β
βββββ
β
ββ
β
ββ
β
ββ
ββββ
β
ββ
β
β
βββββ
ββ
ββ
βββ
ββββ
ββ
ββββ
β
β
ββ
ββ
β
β
β
β
ββ
β
βββ
ββββ
β
ββββ
ββββββ
β
βββββββ
βββ
ββ
ββ
β
βββ
ββ
β
ββ
ββ
β
βββββ
β
βββ
ββ
ββ
β
ββ
ββ
β
β
ββ
ββ
β
ββ
β
βββ
β
β
β
β
β
β
ββ
ββ
β
ββ
βββββ
ββββ
ββββββ
β
ββββ
β
βββββ
βββ
β
ββ
βββ
ββ
β
βββββββββ
β
βββββ
ββ
ββββ
β
β
ββ
βββββ
β
β
β
βββββββββββ
ββ
βββ
ββ
β
ββββββ
βββ
β
ββββββ
β
β
ββ
β
ββ
β
ββ
ββββ
β
βββββ
β
βββ
β
β
β
β
ββββ
β
ββ
ββ
ββ
β
β
ββββ
ββ
β
β
ββ
βββ
β
βββββ
β
β
β
β
β
ββββ
ββ
ββ
ββ
β
βββββ
β
β
βββ
ββ
β
ββ
ββββ
β
β
β
β
β
ββββββββ
ββ
β
ββββββ
βββ
ββββββββ
β
β
β
β
β
β
βββββββββ
β
β
βββ
β
β
β
β
β
β
βββ
β
βββ
ββ
ββββββββ
βββ
β
ββ
ββ
βββ
β
β
β
β
ββ
β
βββ
ββ
ββ
β
βββ
β
β
β
βββ
ββββββββββββββββββββββββ
ββ
β
β
β
β
βββββββ
β
ββ
β
β
β
ββ
β
ββ
β
βββ
β
β
β
β
β
βββ
ββββββ
β
ββ
β
β
ββ
ββ
βββββββββ
β
βββ
βββββ
β
ββ
β
β
βββ
βββββ
βββ
β
β
ββββ
βββββββ
ββ
βββ
β
ββ
β
βββ
β
β
ββ
βββββ
β
β
β
β
ββ
β
ββ
β
β
β
β
β
β
β
ββββ
β
βββ
β
ββ
β
β
β
ββ
β
ββββ
β
β
βββ
β
β
β
ββ
ββ
β
β
βββ
ββ
β
βββ
β
β
ββ
βββββ
β
ββββ
ββ
β
βββββ
β
β
β
ββββββ
β
β
β
β
βββ
β
β
β
β
β
βββββ
ββ
β
β
β
ββ
β
β
βββ
β
β
β
β
βββ
β
β
β
ββ
β
β
β
ββββ
β
ββββ
β
β
β
β
ββββ
β
β
βββββ
β
β
ββ
β
ββ
βββ
β
β
ββββ
ββ
β
β
βββ
β
β
β
β
β
βββ
ββ
β
βββ
β
ββββ
β
βββ
β
β
β
ββ
β
β
β
ββ
ββ
β
β
βββββββ
β
ββ
β
β
β
ββ
ββ
βββ
β
β
β
β
β
β
ββββ
β
β
β
ββ
β
β
ββ
β
β
β
β
ββ
β
ββ
β
βββββ
β
ββ
β
β
β
β
β
ββ
ββ
ββββ
ββββ
β
β
βββ
β
ββββββ
β
β
β
β
βββββ
β
β
ββ
ββ
βββββ
β
β
ββ
β
ββ
ββ
β
ββ
βββ
β
ββ
βββ
β
βββ
β
βββ
β
β
β
β
β
β
β
βββ
β
β
ββ
βββ
β
ββββββββ
β
β
β
β
ββ
β
β
ββββ
β
ββββ
βββ
ββ
β
ββ
β
β
ββ
β
βββ
β
ββ
ββ
βββ
β
β
β
ββ
β
β
ββ
β
β
ββ
β
β
β
ββ
βββββ
β
βββββ
β
ββββ
β
ββ
β
βββββ
ββββ
β
ββ
β
β
ββ
ββββββ
β
βββ
β
ββββ
ββ
βββ
β
β
ββ
βββββββ
β
β
ββ
β
β
ββ
β
β
β
βββ
β
ββ
ββ
ββ
βββ
β
β
β
β
ββ
βββ
β
β
βββ
β
βββ
ββββ
β
β
βββ
β
β
βββββββ
β
β
βββ
β
β
β
β
β
ββ
ββ
βββ
βββ
β
ββββββββ
ββ
βββ
β
ββ
ββ
β
β
ββ
β
ββββββ
β
β
β
β
βββ
β
β
β
β
βββ
ββ
β
ββββββ
β
βββββ
β
ββ
β
β
βββ
β
βββ
β
β
β
βββββ
β
ββ
ββ
β
βββ
βββ
ββ
β
ββ
β
ββ
β
ββ
β
β
β
βββ
ββ
β
β
βββ
β
β
β
β
β
ββ
β
βββββ
βββββββ
β
ββ
ββ
βββββββ
β
βββ
β
β
β
ββ
β
ββββ
β
β
βββββββββββ
ββ
β
βββ
β
ββ
β
β
β
β
β
ββ
β
β
βββββββββ
ββββββ
β
ββ
β
βββββ
β
β
ββββ
β
βββ
β
ββ
β
β
β
ββββ
ββ
β
ββ
β
β
β
β
ββββ
β
β
ββ
β
β
β
β
β
β
β
β
β
ββ
ββ
β
β
βββ
β
ββββ
β
β
βββββ
β
βββ
β
β
β
ββ
β
ββ
βββββ
β
β
β
βββ
β
ββββββββ
β
β
ββ
ββ
ββ
βββ
β
β
β
β
ββ
βββββββ
β
β
ββββ
ββ
ββ
βββββ
ββββββββββ
ββ
β
ββββββββ
βββ
β
β
ββββ
β
ββββ
ββ
β
β
β
β
β
ββ
β
ββ
β
β
βββββ
β
β
ββββ
β
βββββββββ
β
βββ
β
ββββ
β
β
β
ββββ
β
β
β
β
β
β
ββ
β
β
βββ
β
β
β
β
β
ββ
β
ββ
β
ββββββ
β
ββββ
β
β
ββ
β
ββ
β
β
ββ
β
ββ
β
ββ
β
βββ
β
β
β
β
ββββ
ββ
β
β
ββββ
β
β
β
β
β
βββ
β
β
β
βββββ
ββββ
β
ββββββββ
ββ
β
ββ
β
β
β
ββ
β
β
β
β
βββββ
β
βββ
ββ
βββ
β
ββββββββββββ
βββ
βββββββ
β
β
ββ
β
β
βββββ
βββββ
ββββ
ββ
β
β
βββββ
β
βββ
β
βββ
β
β
ββ
β
ββ
ββ
ββ
β
ββββββ
ββ
β
ββ
ββ
ββ
β
βββββ
β
β
βββββ
β
ββ
ββββ
β
β
βββ
β
β
βββββ
β
βββ
β
ββ
β
βββ
β
ββ
ββ
β
ββ
β
βββ
β
β
β
β
β
ββ
β
β
β
β
β
β
ββββββ
ββ
β
ββ
β
β
β
βββββββββ
βββ
β
β
β
β
β
ββ
β
ββββ
β
β
ββ
β
ββββββββ
βββ
ββ
β
ββ
β
β
β
βββ
β
ββ
β
β
β
β
β
ββ
β
ββββ
β
β
β
ββ
β
β
β
βββββ
β
ββ
β
ββββββ
β
βββ
ββ
ββββββ
ββ
β
ββ
ββ
β
βββ
β
β
β
ββ
β
β
βββββ
β
βββ
β
β
β
β
βββββ
β
βββββ
ββ
ββ
ββ
ββββββ
ββββ
β
βββ
ββ
ββ
β
ββ
ββββ
ββ
β
β
β
β
βββ
ββ
β
β
βββββββ
β
β
β
β
β
ββ
ββββ
ββββ
β
β
β
β
βββββββββ
β
ββ
β
ββ
β
β
β
ββ
β
β
βββ
β
β
β
β
ββ
β
ββββ
β
β
ββββ
β
β
ββ
ββ
βββββ
β
ββ
β
β
β
β
ββ
β
β
ββββ
βββ
β
β
β
β
βββ
β
βββ
ββ
β
β
β
β
βββββ
ββ
βββββββββ
ββ
β
β
β
ββββ
β
βββ
ββ
β
β
β
β
β
β
βββ
β
βββ
ββββββββ
β
β
β
βββ
β
ββββββββ
β
β
β
βββ
β
β
β
βββββββββ
β
β
β
β
ββ
ββ
ββ
β
ββ
β
ββββ
ββ
β
β
β
β
βββββββ
β
βββ
β
βββββ
β
β
β
ββ
β
β
β
βββ
βββ
β
β
β
β
β
β
βββββ
ββββ
β
ββββββββ
β
β
β
β
β
ββββββββ
β
β
ββββββββββ
β
β
β
ββββ
β
βββ
β
β
β
β
β
ββ
βββ
β
βββ
β
β
β
βββ
β
ββ
β
βββββ
ββ
βββ
ββββββ
β
β
β
ββββ
β
ββ
β
ββ
ββ
ββ
β
β
β
βββ
β
ββ
β
βββ
β
βββ
β
β
β
βββ
β
β
β
ββ
β
β
β
ββ
ββ
β
β
β
β
β
β
β
β
βββ
β
βββ
β
βββ
β
β
βββ
β
β
ββ
β
ββ
ββββ
β
ββ
β
ββ
ββ
β
β
βββ
β
ββββ
β
βββ
β
ββββ
βββ
β
β
β
β
β
ββ
β
β
βββββββ
β
β
ββ
βββ
ββ
β
βββ
ββββ
ββ
βββββββββ
β
βββββ
β
ββββββ
β
β
β
β
β
βββ
ββ
β
ββ
ββ
ββ
βββ
β
β
β
β
βββ
βββ
β
β
β
β
β
β
β
βββ
β
ββ
β
ββββ
ββ
β
β
β
β
β
β
βββββ
β
βββββββββ
β
ββ
β
β
β
β
β
ββββ
ββ
β
β
ββββββ
β
βββββββββ
β
β
β
β
β
βββββββ
βββ
β
β
β
ββ
β
ββ
β
βββ
β
ββ
β
ββ
βββββ
β
ββ
βββ
ββ
ββ
βββ
ββ
ββ
β
βββ
β
β
β
β
βββ
βββββ
β
β
β
β
β
β
βββ
ββ
β
βββ
β
β
ββ
β
βββ
β
β
β
β
β
β
βββ
β
ββββ
ββββ
β
β
βββ
β
β
ββ
β
β
β
ββ
ββ
β
β
β
ββββ
β
ββ
ββ
β
β
β
β
βββ
βββ
β
ββββ
β
βββ
ββ
ββ
β
β
βββ
β
β
β
βββ
β
βββ
β
β
β
β
β
β
β
β
β
β
βββββββββββββ
β
ββ
β
β
ββββββββββββ
β
ββ
ββ
β
βββββ
β
ββ
β
β
βββ
β
βββ
β
β
βββββ
ββ
β
ββ
βββ
β
βββββ
ββ
β
β
ββ
ββ
β
β
βββ
ββ
β
β
β
β
βββ
β
ββ
β
β
ββ
β
β
β
β
β
β
β
βββ
βββ
β
βββ
ββ
ββ
β
β
β
β
ββββββ
βββ
β
ββ
β
β
ββ
β
β
β
βββββ
β
β
β
ββ
β
ββββ
β
ββββββββ
β
ββββ
β
β
β
ββββ
β
β
β
βββ
β
β
β
ββ
β
β
β
β
ββ
ββββββββ
β
β
ββββββ
β
β
ββββ
β
β
βββ
βββββ
β
ββ
β
β
βββ
β
ββ
ββ
β
βββ
ββ
βββ
β
β
β
β
βββββ
ββββββ
β
β
βββββ
β
ββ
β
β
β
ββββ
β
β
β
βββββ
ββ
β
ββββββ
β
ββββ
β
βββ
β
ββ
β
ββ
β
β
ββ
β
ββ
β
βββ
βββββββ
β
ββββββ
β
ββ
β
βββ
ββ
β
βββ
β
β
ββ
β
ββ
β
β
β
βββββ
β
βββ
β
βββββββ
β
β
ββ
β
β
β
ββββ
β
β
β
ββββ
ββ
β
ββ
β
β
β
ββ
ββ
ββ
β
ββ
βββ
β
β
β
ββ
β
β
β
β
βββ
ββ
β
β
β
ββββββ
β
ββββ
βββ
β
β
βββ
β
β
β
β
ββ
β
β
βββ
β
β
ββ
β
ββ
ββ
β
ββ
βββββ
β
β
βββββ
β
βββββ
ββββ
β
βββ
β
β
β
β
β
ββ
β
ββ
β
βββ
βββ
ββ
β
βββ
β
βββ
βββββ
ββ
ββββ
β
β
β
βββ
βββββββ
β
ββββββββ
ββ
ββββ
β
ββ
βββ
β
ββββ
β
βββ
β
ββββββ
β
ββββββββββ
β
ββββ
ββ
βββ
β
ββββββ
β
β
β
β
β
ββ
β
ββ
ββ
β
β
β
β
β
β
β
β
ββββββββ
β
βββββ
β
β
β
ββ
ββ
β
ββ
β
β
ββ
ββ
ββ
ββ
β
β
βββ
β
β
β
ββ
β
ββ
β
β
ββ
β
ββ
β
β
β
ββ
β
ββ
β
β
β
βββ
β
ββ
β
β
β
β
ββββ
β
ββββ
β
β
β
β
βββ
ββββ
β
ββ
β
β
β
βββ
β
β
β
β
βββ
βββ
β
βββββββββββ
β
βββ
βββ
β
β
ββ
ββββ
ββ
βββ
ββ
β
ββββ
β
βββ
β
β
β
β
βββββββ
β
β
ββββ
β
ββββ
β
β
β
β
βββ
ββ
ββ
β
β
β
β
β
βββββββββββ
β
β
ββ
β
β
ββ
ββ
ββ
ββ
β
β
β
β
βββ
β
ββ
β
β
β
ββ
β
ββββ
ββ
ββ
β
β
βββ
β
ββββ
β
β
β
β
β
ββ
ββββββ
βββ
β
βββββββ
β
β
β
βββ
β
ββββ
β
β
β
ββ
β
ββββββ
ββ
β
β
β
β
ββ
β
β
β
β
β
ββ
ββ
β
β
ββ
ββ
β
βββββ
β
βββββββ
βββ
ββ
β
β
β
βββββ
β
ββ
ββ
ββ
β
β
β
β
ββββ
β
β
β
ββββ
β
β
ββββ
ββ
ββ
β
β
ββ
β
β
ββ
β
β
ββ
β
ββ
βββ
ββ
β
β
βββββ
ββ
β
βββ
β
β
ββββ
ββ
β
β
β
ββββ
ββ
β
β
ββ
β
β
β
ββββ
β
β
βββ
β
β
βββ
β
β
βββ
ββββ
β
ββ
β
ββ
β
β
ββ
βββ
β
βββ
β
βββ
β
β
β
β
βββββ
β
βββ
ββ
β
ββ
β
β
β
β
β
ββ
ββ
β
β
βββ
β
ββ
β
βββ
β
β
β
ββββββ
ββ
βββββ
β
β
β
β
ββ
β
ββββ
β
ββ
ββ
β
β
ββββββ
ββ
ββββ
β
ββ
β
βββ
β
β
β
β
ββ
β
βββββββ
β
β
β
βββ
β
β
β
βββ
β
β
β
β
ββ
βββ
β
βββ
β
ββ
ββ
β
βββββββββ
β
β
ββ
βββ
β
β
β
ββ
ββ
β
ββ
βββββββββ
β
β
β
βββ
β
ββ
β
β
ββ
βββ
ββββ
βββ
β
ββ
β
βββ
β
βββββ
β
ββ
ββ
ββ
ββ
ββ
β
β
β
ββββ
ββ
ββ
β
βββββ
βββββββ
β
β
ββ
β
βββ
β
β
β
β
βββ
ββ
ββ
β
β
ββ
βββ
β
β
ββ
β
β
β
ββββ
β
ββ
β
ββ
β
β
β
ββ
β
βββ
ββββ
β
β
β
ββ
β
ββ
β
β
β
βββββββ
ββ
β
βββ
β
ββ
ββ
ββ
β
ββ
β
β
ββ
β
β
β
βββββββββ
β
βββββββ
β
ββ
β
β
β
β
βββββ
β
β
β
ββββββββ
ββββββββ
β
β
β
ββ
ββ
β
βββ
βββββ
β
ββββββ
β
ββ
ββββ
β
ββββββββ
β
β
β
βββ
ββ
ββ
ββ
ββ
ββ
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
ββ
β
β
βββββββββ
β
βββ
β
βββ
β
β
β
βββ
β
ββββ
β
β
ββ
β
βββββ
β
ββββ
β
ββββ
β
β
βββββ
β
βββ
β
βββ
ββ
ββ
β
βββ
β
β
β
ββ
β
β
β
β
β
β
ββ
β
ββββββ
ββ
βββ
β
β
ββ
β
β
β
βββ
β
β
β
βββ
β
β
β
β
β
ββ
ββ
β
ββ
β
βββββ
β
ββ
β
β
β
β
β
β
β
β
β
βββ
β
ββββ
β
β
β
β
β
β
βββ
β
β
ββ
β
ββ
ββββ
β
β
β
β
βββββ
β
β
β
β
β
β
β
ββ
ββ
β
ββ
ββ
ββββββ
β
βββ
β
β
β
β
β
βββ
ββ
β
β
βββββ
β
ββββββ
β
β
β
β
ββ
β
β
β
β
ββ
β
ββββββββββ
β
ββββ
βββββ
β
βββ
β
β
β
β
β
ββ
ββ
β
ββ
β
βββββββ
β
β
βββ
β
ββ
β
β
ββββββ
β
β
β
β
ββ
β
β
β
βββββ
β
β
β
β
β
β
ββββββ
β
βββββββ
β
β
β
ββ
β
β
ββββββ
β
ββββββ
β
ββ
β
ββββββββββ
β
ββ
β
β
β
ββ
ββββ
β
β
β
β
βββ
β
β
β
ββββ
βββ
ββ
β
ββ
β
βββ
ββ
ββββββββββββ
ββ
ββββ
β
β
βββ
β
β
β
β
β
ββ
ββ
β
β
β
ββ ββ
β
ββ
β
ββ
ββββ
β
ββ
β
β
ββ
β
ββ
β
ββββ
β
βββ
β
ββββ
β
β
β
β
ββ
β
ββββ
β
ββ
ββ
β
β
ββ
β
β
β
ββββββ
β
ββ
β
β
ββ
β
ββ
β
β
βββ
β
β
β
ββββββ
β
β
β
ββ
β
β
β
β
ββββ
β
β
ββ
β
β
ββ
βββ
β
β
β
β
ββ
β
ββ
β
βββββ
β
β
β
β
β
βββ
β
β
β
β
ββ
β
βββ
β
ββββ
β
β
β
βββββ
β
β
β
β
β
β
ββ
β
ββββββ
β
β
β
β
β
β
β
β
β
β
β
ββββ
ββββ
β
βββββ
ββ
ββ
β
βββββ
ββββ
βββ
ββββββ
β
ββββββββββββ
β
ββ
β
β
ββ
β
β
β
β
β
ββ
β
β
β
β
ββ
β
β
ββ
β
βββ
β
ββ
β
ββ
ββ
ββ
ββ
β
β
β
ββ
ββ
β
ββββ
β
ββ
β
β
β
β
ββ
ββ
β
β
β
β
β
β
βββ
β
β
βββββββ
β
βββ
ββ
ββ
βββ
β
β
β
β
β
βββ
ββββ
β
β
β
β
β
ββ
ββ
β
ββ
ββ
β
ββ
βββ
β
ββ
ββ
β
β
β
β
ββ
ββ
βββ
β
β
ββ
β
βββ
β
β
β
β
β
β
ββββ
β
β
βββ
β
β
ββ
ββββββββ
β
β
β
β
β
β
βββ
β
ββ
β
β
β
β
ββββ
β
βββ
β
ββββββ
ββ
β
β
β
β
β
β
β
βββ
β
β
ββββββββββ
β
ββ
β
βββ
β
β
βββ
β
β
β
β
β
βββ
βββ
β
βββββ
ββ
β
β
β
β
β
β
βββββ
β
ββ
ββββ
β
β
β
βββ
β
βββ
β
ββ
β
β
ββ
β
ββββββββββ
β
βββββββββ
β
βββ
β
βββββ
β
β
β
ββββββββββββββ
β
ββ
ββ
ββ
β
β
βββ
β
β
β
β
βββ
β
ββ
ββββββ
β
β
ββ
β
ββ
ββ
β
βββββ
β
ββ
ββ
ββ
β
β
ββββ
β
βββ
β
β
β
β
ββββ
β
ββ
ββ
βββ
β
β
ββ
β
β
β
ββββ
ββ
β
βββββ
ββ
β
β
β
β
β
β
β
β
β
β
β
βββ
ββ
ββ
βββββ
β
β
βββ
β
β
βββββ
ββ
βββββ
β
β
βββ
β
ββββ
β
β
β
ββ
β
ββ
β
β
β
β
βββ
β
β
β
ββ
βββ
β
β
ββ
β
ββ
ββ
β
β
β
ββ
β
β
β
β
β
ββ
β
βββ
β
β
β
β
β
ββ
ββ
β
β
β
ββββ
β
β
β
β
β
βββ
βββ
βββββββ
β
ββ
β
ββ
β
ββ
βββ
β
ββββ
βββ
ββββββ
β
ββββ
ββ
β
βββ
ββ
β
β
β
β
β
β
β
ββββββ
ββ
β
βββββ
β
β
ββββ
β
ββ
ββ
β
β
βββββββ
β
ββ
ββ
βββ
β
ββββ
β
β
ββ
β
β
β
β
ββ
β
ββ
β
ββ
β
β
β
ββ
ββ
β
ββ
βββ
β
ββ
β
ββ
β
βββ
β
βββ
β
β
β
β
β
β
β
β
ββββ
ββββββ
β
β
β
β
β
β
βββ
β
ββββ
ββ
β
ββ
ββ
β
β
β
β
ββ
β
β
β
β
β
β
β
ββ
βββββ
β
ββ
β
βββββββββββ
ββββ
β
β
ββββ
β
β
ββ
ββββ
β
βββββ
β
ββ
β
ββββ
β
βββββ
β
β
β
β
β
ββββ
β
ββ
βββ
βββ
ββ
ββ
β
βββ
ββ
ββββββββββββ
ββ
β
β
β
β
βββ
βββ
β
β
ββ
β
β
β
ββ
β
βββ
ββ
β
βββ
βββ
ββ
β
β
β
β
β
β
β
ββ
ββ
ββ
β
β
ββββ
β
β
β
ββ
ββββββ
β
ββββββ
β
ββ
β
ββ
β
βββββββ
β
βββββ
β
β
ββ
ββ
ββββ
β
β
β
β
ββ
β
β
ββ
β
β
β
β
β
ββββ
β
ββ
ββ
β
β
ββ
β
ββββ
ββ
β
β
β
ββ
β
β
ββ
β
ββ
β
β
ββββ
β
β
ββ
β
ββ
βββββ
β
βββββββββββββββββββββ
β
ββ
ββ
ββ
β
β
ββ
β
β
β
β
β
β
β
β
β
βββ
β
β
β
ββ
β
βββ
β
βββ
β
ββ
β
ββββ
β
βββ
β
βββ
β
β
β
β
ββ
β
βββ
β
ββ
ββ
β
β
ββ
β
βββ
β
β
β
β
ββ
ββ
β
β
ββββββββββββ
ββββββββββββ
βββ
ββββ
ββ
β
βββ
β
β
β
β
β
β
β
β
ββ
β
β
ββ
β
β
β
β
β
β
β
ββ
β
ββ
βββββ
β
ββββ
ββ
ββ
β
ββ
β
β
β
β
β
ββ
β
β
βββ
ββββββββ
β
β
β
β
ββ
β
β
ββ
β
ββ
β
β
β
ββ
β
ββ
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
ββ
β
βββ
β
β
ββ
ββ
βββ
β
β
ββββ
β
β
β
ββ
β
βββ
βββββ
ββ
ββ
β
ββββββ
ββββ
β
ββ
β
β
β
βββββββββββ
ββββββ
β
ββ
β
β
ββ
β
ββββ
β
β
β
β
β
ββ
ββ
β
β
ββββββββ
β
ββ
βββ
β
βββ
β
β
β
ββ
β
β
β
β
β
ββ
ββ
ββ
ββ
β
ββ
β
β
β
ββ
ββ
β
β
βββ
β
β
β
β
βββββ
βββββ
β
ββββββ
βββ
β
ββββ
β
β
β
β
β
ββ
βββββ
βββ
β
ββ
β
ββ
β
βββββ
ββββββββββ
βββ
βββ
β
β
ββ
β
ββ
β
ββββ
β
ββ
β
β
ββ
β
βββ
β
βββ
β
β
β
ββββββ
ββ
βββ
ββββββ
β
β
ββ
βββββββ
β
β
β
β
ββ
β
ββββ
β
βββ
βββ
β
β
ββ
β
ββ
ββ
βββββ
β
β
β
β
β
βββββββ
β
β
β
ββββββ
β
βββ
β
ββ
β
ββ
ββββ
β
βββββββ
β
β
ββ
βββ
βββ
β
βββββββ
β
β
β
β
ββββ
β
ββββ
βββ
βββββ
β
ββ
β
βββ
β
βββ
β
ββββββ
β
ββββ
β
β
ββββ
β
ββ
β
βββ
β
β
β
β
β
ββ
β
β
ββββ
β
ββ
β
βββ
β
βββ
β
β
β
β
ββββ
β
β
β
ββββ
β
β
β
β
β
β
β
ββββ
ββββ
β
β
β
ββ
ββ
ββ
βββ
ββ
ββββββββββββ
β
β
β
ββ
β
ββββ
β
βββ
β
ββ
βββ
βββ
β
ββββ
β
ββ
β
ββ
β
β
β
βββ
ββ
ββββββ
ββ
ββ
ββ
β
β
β
β
β
β
β
β
β
β
βββ
β
ββββββ
β
β
β
β
β
βββββ
β
ββ
β
β
β
ββββ
β
β
β
ββ
β
βββ
ββ
β
β
ββ
β
βββ
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
ββ
β
ββ
β
β
β
β
β
βββ
β
β
ββ
β
β
β
β
β
β
β
ββββ
β
β
ββ
β
ββββββ
β
βββ
β
β
β
β
ββ
βββββββ
β
β
β
ββ
β
β
ββ
βββββ
β
β
β
β
β
β
β
β
ββββ
ββ
β
ββ
βββββββ
β
β
β
β
ββ
β
β
β
β
ββββββ
β
ββ
β
β
ββββββ
ββ
β
β
ββ
ββ
β
β
β
β
β
βββ
β
ββββ
β
β
β
ββββ
β
ββββ
ββββ
β
β
ββββββ
β
βββ
β
ββ
β
β
ββββββ
β
βββ
ββ
ββ
βββ
β
ββββ
βββ
β
ββββββββββββ
β
ββ
β
βββββ
β
β
β
ββββ
β
ββ
ββ
ββ
ββ
β
β
ββ
ββββ
β
β
βββββ
ββ
ββ
ββ
ββ
β
β
β
β
β
β
β
β
β
β
β
ββ
β
βββ
ββ
β
β
β
β
β
β
β
ββ
β
βββ
β
ββ
β
β
ββ
ββββ
β
β
β
β
β
ββ
β
βββ
β
βββ
β
ββββ
β
ββ
β
β
β
β
ββ
β
β
β
β
β
β
ββββ
ββ
βββββ
β
βββββ
β
βββ
β
β
βββ
β
β
ββ
β
ββββββ
β
ββββββββ
β
β
βββ
β
βββββββ
β
β
β
ββ
β
ββ
β
β
β
ββββ
β
ββ
ββ
ββββ
β
ββ
ββ
βββ
β
βββ
β
β
β
βββ
β
ββ
β
ββββββ
βββ
β
βββ
ββ
β
ββββ
ββ
β
β
β
ββ
βββ
β
β
ββ
βββββββββ
β
β
βββ
β
β
βββ
ββ
ββββββ
β
ββ
β
β
βββ
β
ββ
β
ββ
β
βββ
β
β
β
βββββββββ
β
β
β
ββ
βββββ
βββββ
β
β
β
ββ
β
β
βββ
ββ
β
β
ββ
ββ
β
β
β
β
β
ββ
β
βββ
β
β
β
ββββββ
ββββ
β
β
β
β
β
βββ
βββ
β
β
ββ
β
ββ
ββ
ββ
ββ
β
β
ββββ
β
β
β
ββ
β
βββ
β
βββ
ββββ
ββ
β
β
β
β
β
βββ
β
β
β
ββ
β
βββ
β
ββββ
ββ
ββ
ββ
β
β
βββββββ
β
β
ββ
βββ
β
ββ
β
β
ββ
ββ
β
ββ
β
βββββββ
β
βββ
β
ββ
β
β
β
ββββ
β
βββββββ
β
βββββββ
β
βββ
ββ
β
ββ
ββββ
β
β
ββ
β
ββ
β
ββ
ββ
β
β
β
β
β
β
β
βββ
β
β
βββ
β
ββββ
β
β
ββ
β
ββ
ββββ
β
βββββββ
ββ
β
β
ββ
β
β
β
ββ
β
β
β
β
β
βββ
β
β
ββββ
β
β
ββ
β
ββ
β
βββ
βββββββ
β
ββ
ββ
βββ
ββββ
ββ
β
β
β
ββββββ
β
ββββ
β
β
ββββ
β
β
β
ββββ
β
β
ββ
β
ββββ
β
ββ
βββ
β
βββββββ
β
β
β
β
ββββββββββ
β
β
ββ
βββ
β
ββ
β
β
β
β
ββ
β
β
ββ
β
ββ
β
β
β
β
ββ
βββ
ββ
β
βββββ
β
β
βββββ
βββββββββ
β
β
ββββ
β
β
ββ
β
βββ
β
ββ
β
ββ
β
β
β
β
β
β
β
β
β
β
β
β
β
ββββ
ββ
β
β
β
βββ
β
β
ββββ
β
β
ββββ
ββ
ββββ
ββ
βββ
β
β
ββ
ββ
β
β
β
β
ββββββββββββββββββββββ
β
ββββββ
βββ
β
βββββββ
β
β
β
β
β
ββ
ββ
β
ββββββ
β
β
β
ββ
β
β
ββ
βββββββββ
β
ββ
β
βββ
β
β
β
β
ββββ
β
βββ
ββββββββββββ
β
ββ
β
βββββββ
β
βββββββ
ββ
β
βββββ
ββ
β
β
β
ββ
β
ββ
ββ
β
ββ
ββββββ
β
β
β
β
ββ
β
β
βββ
β
βββββββββββ
β
ββ
β
ββ
ββ
β
β
βββ
β
β
β
ββ
ββββ
β
βββββββ
β
ββ
ββββββββββββ
β
β
β
βββ
β
ββ
βββ
β
β
β
β
β
ββ
ββ
β
ββββ
ββββββ
ββ
β
β
ββ
β
ββ
β
β
β
ββββ
β
β
β
β
β
β
ββββ
β
ββ
β
β
β
βββ
ββββββββ
βββ
β
β
βββββββ
β
β
ββ
β
β
ββββ
ββ
ββ
βββββββ
β
β
ββββββββββ
β
β
β
ββββ
β
β
β
βββ
β
ββ
ββ
β
ββββββββββ
β
β
ββ
β
β
ββ
β
β
ββ
βββ
β
βββ
β
ββββ
β
ββββ
β
β
β
β
ββ
ββ
β
β
β
β
β
β
β
β
ββββ
β
β
β
ββ
β
ββββββ
ββ
ββ
β
ββ
β
β
β
ββ
β
β
β
ββββββ
ββββ
ββββ
ββββ
β
β
β
β
ββ
ββββββββ
β
ββ
β
β
βββ
β
ββββ
β
βββ
β
ββββ
β
βββ
β
ββββ
β
β
β
β
β
β
β
β
β
ββ
ββ
β
β
β
β
ββ
β
β
ββ
β
βββ
βββ
β
ββ
β
β
β
β
β
βββ
β
ββ
β
ββ
β
βββ
ββ
β
β
β
ββ
β
β
ββββ
ββ
ββββββ
β
ββ
β
βββββββ
β
ββ
β
β
β
β
β
βββ
ββ
β
ββ
β
ββ
ββ
β
β
β
β
ββββ
β
βββββββ
β
ββββββββ
β
ββ
ββ
βββ
βββ
ββ
βββ
ββ
β
β
βββββββ
β
βββ
β
β
βββ
β
βββ
β
ββββ
β
β
β
β
β
β
β
β
βββββ
β
ββ
β
β
ββ
βββββ
β
β
ββ
β
βββ
β
ββββββββββββ
β
ββββββ
ββββββ
ββββ
βββ
ββ
β
β
ββββββ
β
β
β
β
β
ββ
βββ
β
ββ
ββββ
β
β
ββ
β
β
β
ββββ
ββββ
ββ
β
β
β
βββββββββ
β
β
β
βββββββ
β
β
βββββ
β
β
β
β
β
β
β
β
βββββ
βββββ
ββ
βββ
βββ
βββββββ
β
β
β
β
β
β
ββ
ββββ
β
β
ββββββ
β
βββββ
β
ββ
β
β
β
β
β
β
ββ
β
β
ββ
β
β
β
β
β
ββ
β
β
β
β
ββββ
βββ
β
β
βββ
β
β
β
βββ
β
βββββββββββ
ββββ
β
β
β
ββ
β
β
β
β
ββ
βββ
β
βββ
β
ββ
β
β
β
β
βββ
β
β
β
β
ββ
β
β
β
ββ
β
ββββββββ
β
β
β
β
β
ββ
ββ
β
β
β
β
ββ
βββ
β
β
ββ
β
ββ
ββ
β
β
β
β
β
β
β
β
β
ββββ
β
β
β
β
ββ
ββ
β
β
ββββββ
β
βββ
ββ
β
β
ββ
β
β
β
ββββ
β
β
β
ββ
β
β
β
β
ββ
ββ
ββββ
β
β
ββ
β
β
β
β
β
β
β
ββββ
βββββ
β
ββββ
βββ
ββ
β
βββββ
β
β
ββ
β
βββββββ
β
ββββββ
β
βββββββββββββ
β
β
ββββ
β
β
β
βββββ
βββββ
β
ββ
β
ββββββ
β
β
β
β
β
βββ
β
β
β
β
β
β
β
β
ββββ
ββ
ββ
β
β
βββ
ββ
β
β
β
β
ββ
βββββββ
ββ
β
β
β
βββββ
ββ
ββ
ββββββ
ββββ
β
β
β
β
β
ββ
β
β
β
β
β
β
ββββ
ββ
β
ββ
β
ββββ
ββββ
β
β
β
ββββ
β
ββ
ββ
ββ
βββ
β
βββ
β
βββββββ
β
β
β
ββββββββββ
ββ
β
β
βββββ
β
ββββββ
β
βββ
β
β
βββββ
β
β
β
β
β
ββ
β
ββ
β
ββ
βββ
β
β
β
β
β
βββ
β
ββ
β
ββββ
β
ββ
ββββ
β
β
β
β
β
β
β
β
β
β
β
βββ
β
β
ββ
β
β
β
βββββββββ
β
ββββ
ββββ
β
β
ββ
β
β
β
ββ
β
βββββββββββββ
ββββββββββββββββ
β
ββ
ββββββββββββββββ
β
β
ββββββ
β
β
β
ββ
βββ
ββββ
ββ
β
β
β
β
β
β
β
ββ
β
β
β
β
ββ
β
βββββ
β
β
β
β
β
β
β
β
ββββ
β
β
β
ββββββ
β
βββ
β
β
β
ββ
β
β
ββ
β
β
β
β
β
β
β
β
β
βββββ
β
β
β
ββββββ
β
ββββββ
β
βββ
ββ
βββ
β
β
β
ββββ
ββ
ββββ
β
ββ
ββ
β
β
βββ
β
βββ
β
β
β
β
ββββββ
β
ββββββ
β
β
β
βββ
β
βββββ
βββ
β
β
β
β
β
ββββ
β
β
ββ
βββββββ
β
βββ
ββββ
β
βββ
β
β
βββββ
β
ββββ
β
β
β
β
β
ββ
βββ
β
βββ
β
ββ
ββββββ
ββ
β
β
ββββ
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
βββ
β
βββββββββ
ββ
βββ
ββ
β
β
ββ
ββ
β
ββ
β
βββ
β
ββββ
β
ββ
β
β
β
β
βββββ
ββ
β
βββ
β
ββ
β
β
ββββ
β
ββ
β
βββββββββββββ
β
ββ
β
β
β
β
β
β
β
ββ
ββ
β
β
β
β
β
ββ
β
ββββ
β
βββββ
β
ββ
β
ββββ
β
ββ
β
β
ββ
β
βββββββββ
β
β
β
β
β
βββ
ββ
β
ββ
ββββ
ββ
βββββ
β
βββββ
β
β
β
β
ββ
β
ββ
βββββββ
β
ββ
ββ
ββ
β
ββββ
β
ββ
β
βββββββ
β
ββ
ββββ
β
β
β
ββββββββ
β
βββ
β
βββ
βββ
β
βββ
βββ
β
ββββ
β
β
β
β
βββ
β
β
ββ
βββ
βββ
β
βββ
β
β
β
ββ
β
β
β
ββββββ
β
βββ
β
ββ
β
ββ
ββ
β
β
β
ββ
ββββ
β
β
ββββββββββ
ββ
βββ
β
βββ
β
ββ
βββ
ββββ
β
ββ
β
β
ββ
β
ββββ
βββββββββ
ββββ
β
β
ββ
ββ
β
β
β
β
β
ββ
β
ββ
βββ
β
ββ
ββ
β
β
β
β
βββ
β
β
βββββββ
β
βββ
βββ
ββ
β
β
ββ
β
ββ
β
β
ββ
βββ
β
ββ
ββββ
βββ
β
β
β
ββ
ββ
βββββββ
β
βββββββ
ββββ
βββββββ
βββ
ββββββ
β
β
β
β
β
β
β
β
ββββ
β
β
βββββββββ
ββββ
ββ
ββ
β
ββ
β
βββ
β
β
ββ
β
ββββββββββ
β
βββ
β
ββ
ββ
β
ββββ
ββββ
ββ
β
β
β
β
ββ
ββ
βββ
ββ
βββ
ββ
β
ββββββββββββ
β
βββββ
β
βββ
β
ββ
β
βββ
β
ββ
ββββββ
βββ
β
β
β
βββ
β
βββ
ββ
βββββ
βββ
β
β
β
β
ββ
ββββ
β
β
β
ββ
ββ
β
ββ
ββ
β
β
ββ
ββ
β
ββββ
β
βββ
βββ
β
β
β
ββ
β
ββ
β
ββ
β
β
β
β
ββ
βββ
β
β
βββ
ββ
ββββ
ββ
β
ββ
ββ
β
β
β
βββ
β
β
ββββ
β
β
β
ββ
β
ββ
β
β
βββββ
β
β
βββ
βββββ
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
βββββββββββ
ββββ
β
β
β
β
β
β
βββ
β
β
β
β
βββ
β
β
β
β
β
β
βββββ
β
βββ
β
ββ
β
βββ
βββ
β
ββββ
β
β
β
ββββ
βββββ
β
ββββββ
β
β
ββ
β
ββββββββββ
β
β
ββ
β
β
ββββββ
β
β
ββββ
β
βββββ
ββ
βββββ
β
β
β
ββββββ
ββ
β
ββ
ββ
β
β
ββββ
βββ
β
β
β
βββββ
β
βββ
β
ββββββ
β
ββ
βββββ
ββ
β
ββ
β
βββββββββ
βββ
β
βββ
β
βββ
β
β
ββ
βββββββ
β
ββββ
β
β
βββ
ββββ
ββββββ
β
βββ
ββββ
β
βββ
β
ββββ
ββ
β
βββββ
β
βββ
ββ
β
βββββββ
β
ββ
β
ββ
β
β
β
ββββ
β
ββ
β
β
ββ
ββββ
ββ
β
β
β
β
β
β
ββ
β
ββ
β
β
β
ββ
βββββ
ββ
β
ββββ
β
β
β
ββββ
ββββ
β
β
β
ββ
β
ββββ
β
β
ββ
β
βββββββ
β
β
ββββββββββββ
ββ
β
β
ββββββ
ββ
β
β
ββ
β
β
βββ
β
β
βββ
β
β
ββ
ββ
ββ
ββ
βββββ
ββ
βββββββββ
β
β
ββ
ββ
β
β
ββ
ββ
β
ββββ
β
ββββ
β
β
βββ
β
β
β
ββ
β
β
ββββ
β
β
βββββ
β
ββ
β
ββ
β
β
β
βββββββ
ββ
βββ
β
β
β
β
βββ
β
βββββββ
β
β
ββββ
β
β
ββ
β
ββ
β
β
β
ββ
β
ββ
βββββ
β
β
ββ
β
ββ
β
βββ
ββ
ββββββββββ
β
β
β
ββββ
β
ββββ
β
ββ
β
ββ
ββββββ
β
ββ
β
β
β
β
βββββ
β
ββββ
β
ββββββββ
β
β
β
ββ
ββ
β
βββββ
ββ
ββ
β
β
βββββ
β
ββ
β
βββββ
β
βββ
β
βββββββ
β
β
β
ββββ
ββ
β
β
ββ
ββ
ββββ
β
ββββββ
β
βββ
β
ββββ
β
β
β
β
β
β
β
βββ
β
ββ
βββββ
β
β
β
β
β
β
β
ββ
ββ
β
ββββ
β
β
ββ
β
βββ
βββ
β
β
β
ββββββββ
β
ββββ
ββ
βββββ
βββββ
βββββ
β
β
β
ββ
β
ββ
ββ
β
β
βββ
β
β
βββ
βββ
β
β
β
βββ
β
ββ
β
ββ
β
βββ
β
β
β
βββ
ββ
ββ
β
β
ββ
β
β
β
ββββββββ
β
βββββββ
β
ββ
β
ββββ
β
βββββββ
β
β
β
β
βββ
β
β
β
β
ββ
ββ
βββββ
β
βββ
β
β
β
β
ββ
β
β
ββ
β
βββββββββ
ββββββ
βββ
β
β
β
β
βββ
β
β
ββ
β
βββ
β
ββββ
β
β
ββ
βββ
β
ββ
β
β
β
β
βββ
β
β
ββ
βββ
β
ββββ
β
β
βββ
β
β
βββ
β
ββ
β
β
ββ
β
β
β
ββββββ
β
βββββ
β
βββ
β
β
βββ
β
β
β
ββ
β
ββββ
β
ββ
ββ
βββββββ
β
β
β
β
βββ
βββ
β
βββββ
β
β
β
β
β
β
β
ββ
β
β
β
ββββββ
ββββ
β
β
β
ββ
β
β
β
βββ
β
β
β
ββ
βββ
ββ
β
βββ
β
ββ
βββ
β
β
β
β
β
β
ββ
β
β
β
ββ
βββ
β
βββββββ
β
β
ββ
β
ββββ
ββ
βββββ
ββ
ββ
ββββ
β
ββ
β
β
β
β
ββ
β
β
β
β
β
β
β
β
ββββββ
βββ
β
β
β
β
β
β
β
βββ
β
β
β
β
β
β
β
β
βββ
β
ββββββ
β
β
β
ββββββ
ββ
ββ
β
β
β
β
ββ
βββ
βββββ
β
ββββββββββ
β
β
ββββ
ββββ
β
ββ
β
βββ
β
ββββ
β
βββββββ
ββ
ββββββββ
β
β
β
ββ
β
β
β
βββββ
β
β
ββββ
ββ
β
ββ
ββββ
β
β
ββββββ
ββ
β
ββββ
β
βββββββββββββ
β
β
β
β
β
β
ββββ
β
βββββββ
βββββ
β
β
β
ββ
β
ββββ
β
β
βββ
ββ
βββ
β
ββββββ
β
ββ
β
β
β
ββ
β
β
ββ
β
β
β
βββββ
β
β
β
β
β
β
βββ
β
β
β
ββββ
βββββ
ββ
ββ
β
β
β
β
ββ
ββ
β
β
βββββ
βββββ
β
β
β
β
βββββ
ββ
ββ
β
β
ββ
ββββββββ
β
β
β
β
ββ
β
ββ
ββ
β
βββ
β
β
ββ
βββ
β
ββ
ββββ
β
ββ
β
ββ
β
β
ββ
βββββββ
β
ββ
ββββββ
β
ββ
β
β
ββββ
β
β
βββ
β
ββ
β
ββββββ
β
β
ββ
β
βββββ
β
β
β
β
βββ
ββββββ
β
β
β
β
β
β
ββββ
β
βββ
ββββ
ββββββ
β
β
β
β
ββββ
β
ββ
β
β
ββ
β
ββ
β
β
β
β
βββββ
β
βββ
β
βββββ
ββββββββββββββββββββββ
ββββββ
β
ββ
ββ
βββββββββββ
βββ
β
β
ββ
β
β
β
β
β
ββ
βββ
βββ
ββ
β
β
ββ
β
βββ
ββ
β
β
ββ
ββ
β
β
β
β
ββ
βββ
βββ
β
βββ
βββ
β
ββ
β
ββ
ββββ
βββ
βββββ
β
ββ
ββ
β
ββ
β
β
β
β
β
β
β
β
βββββ
β
β
β
β
β
ββ
β
β
ββββ
ββ
β
ββ
β
β
ββ
β
ββ
β
β
β
β
β
ββ
ββ
β
β
β
β
β
β
βββ
β
β
β
ββ
β
βββ
βββ
β
ββ
β
β
β
βββ
β
β
βββ
β
ββββββββββ
ββ
ββ
β
β
β
ββ
β
βββ
ββ
βββββ
β
ββ
βββββ
β
ββββββββββββββ
β
β
β
β
β
β
β
β
ββ
ββ
ββ
β
β
βββ
ββ
β
β
β
β
ββ
β
β
β
ββ
ββββ
β
β
β
β
β
βββββββββ
ββ
ββ
ββ
β
βββββ
βββββββ
β
ββββ
β
ββββ
β
β
β
β
β
ββββ
ββ
ββ
β
ββ
β
βββ
β
ββββββ
ββ
ββββ
β
ββ
ββ
β
β
β
ββ
βββ
β
ββ
βββ
β
β
βββ
ββ
βββββββ
ββ
ββ
ββ
β
ββ
β
β
βββ
ββββ
β
βββββ
β
β
β
β
βββββ
ββ
βββ
β
βββββ
ββ
βββ
ββ
β
β
β
β
ββββββ
β
βββ
β
β
β
ββββ
ββββ
β
βββββ
β
β
β
β
β
β
β
ββ
β
β
β
βββ
β
ββ
β
β
β
β
β
βββ
βββ
βββ
β
β
β
β
β
β
β
ββ
ββ
β
ββββ
ββ
β
βββ
ββ
ββββββ
β
ββ
β
β
ββ
β
β
β
ββββββββ
β
β
ββββ
β
ββββ
β
β
β
ββ
β
ββββββββ
β
βββ
ββ
ββ
β
β
β
β
β
ββ
β
β
β
ββ
ββββ
β
βββ
ββ
β
βββ
β
ββββββ
ββ
ββ
β
β
β
β
βββββ
β
ββ
ββ
ββ
βββ
β
ββ
β
ββββββ
ββ
β
βββ
β
ββββ
ββ
ββ
β
βββ
β
β
β
β
β
βββ
β
β
β
β
β
βββ
β
β
β
β
ββββ
βββ
β
βββββ
βββ
β
β
β
ββββ
βββββ
β
ββββ
β
β
β
β
βββ
βββ
β
β
β
β
ββ
ββββ
ββ
β
ββ
βββ
ββ
β
ββ
ββ
β
β
β
ββ
βββββ
β
ββ
ββ
ββ
β
ββ
ββ
β
ββ
β
βββ
β
βββββββ
β
βββ
ββ
β
β
ββββ
β
ββ
β
β
ββ
β
β
β
βββββββ
ββ
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
ββββ
β
ββ
β
β
ββ
β
β
β
β
ββ
β
βββββ
β
ββ
β
ββ
β
β
βββ
β
β
β
β
β
β
β
β
ββ
β
ββββββ
β
βββ
βββββ
β
β
β
β
ββββββ
ββ
ββ
β
β
β
βββ
βββββ
ββββββββββ
β
ββ
β
β
ββ
β
β
β
β
β
βββ
βββ
ββ
ββββ
β
β
β
β
ββββ
β
βββ
β
β
βββ
β
ββ
β
β
β
β
β
β
ββ
βββ
β
ββ
β
β
β
βββ
β
β
β
βββ
β
β
β
ββββββ
β
ββββ
β
βββββββ
ββ
β
ββββ
β
βββββ
β
βββ
βββββ
ββ
ββββ
β
ββ
βββββ
β
β
β
β
β
β
β
ββ
β
β
β
ββ
β
β
ββ
β
β
βββββββ
βββ
ββ
βββ
β
β
ββββ
ββ
βββ
β
ββ
βββ
β
ββββ
β
βββ
βββ
β
β
β
β
ββββββ
ββ
ββ
β
β
ββ
ββββββββ
ββββββ
β
β
ββ
βββ
β
β
β
ββ
β
β
ββββ
β
ββββββββββ
β
ββ
β
ββββ
βββ
ββ
β
βββ
ββ
βββ
β
ββ
ββββββββββ
β
β
β
ββββ
β
β
β
β
ββββ
β
βββββ
β
ββ
ββ
ββ
β
ββ
ββ
ββ
βββ
βββββββ
β
βββββββββ
β
ββββββ
β
β
β
ββ
β
ββββ
ββββ
β
ββββββ
β
β
βββββ
β
ββ
β
βββ
β
ββ
β
β
β
β
ββ
β
β
βββββββββ
ββ
ββ
β
βββββββ
β
ββ
β
ββ
β
β
ββββ
β
β
βββββββββ
βββββ
β
β
β
β
βββ
ββββ
ββ
β
β
β
ββ
ββββ
β
β
ββββ
β
β
βββ
ββββ
β
ββ
βββ
βββ
β
β
β
βββββββ
ββββ
β
β
β
β
β
ββ
β
βββββ
β
β
βββββ
β
ββ
β
ββ
ββ
β
β
β
β
β
β
ββββ
β
β
ββ
β
βββ
ββββ
β
β
β
β
ββ
βββββ
ββ
β
ββββ
β
ββ
β
ββ
β
ββ
ββ
βββββ
β
β
β
ββ
β
β
β
ββββββββ
β
β
β
β
β
ββ
β
β
β
ββββββββββββ
β
ββββββββ
β
βββ
β
βββββ
β
ββ
β
βββ
βββββ
β
β
ββ
β
β
ββ
β
βββ
β
ββ
βββ
β
βββββ
β
ββββββ
β
β
β
β
ββββββ
β
βββββ
βββ
βββββ
ββ
β
β
ββ
ββββ
β
ββ
β
β
ββ
β
β
β
β
β
β
ββ
ββ
ββ
ββ
ββ
βββββ
ββββ
βββ
β
β
β
βββββββββ
β
β
β
β
ββββ
β
βββββββ
βββ
ββ
β
ββ
β
ββ
ββ
β
β
β
ββ
β
β
β
β
β
ββ
β
β
β
β
β
βββ
β
ββ
β
β
β
β
β
ββ
β
ββ
β
β
ββββ
ββ
βββ
β
βββ
β
ββ
ββ
β
β
ββββ
ββ
β
ββββ
ββ
βββ
ββ
βββ
ββ
β
βββ
β
ββ
β
β
βββββ
β
β
ββββ
β
ββ
β
β
β
ββ
β
βββ
β
ββ
β
β
β
βββ
β
ββ
β
β
β
β
ββ
β
β
βββ
β
β
β
βββ
β
ββ
β
ββ
ββ
β
β
β
ββ
β
β
β
β
β
β
βββ
β
β
β
β
βββ
ββ
ββ
βββββ
β
β
β
β
ββ
βββ
β
β
ββ
β
β
ββ
ββ
ββββββ
β
β
ββ
β
β
ββ
β
β
ββ
β
ββ
β
β
β
βββββββββββ
β
βββββββ
βββ
ββ
β
β
β
β
ββββ
β
β
ββ
βββ
βββ
β
ββββββββββ
β
β
β
β
ββββ
β
β
β
β
β
β
β
β
ββ
ββ
ββ
βββ
ββ
βββββ
β
ββ
β
ββ
βββ
β
β
β
β
β
β
β
β
β
β
β
β
ββ
β
ββββ
β
βββββββββ
ββββ
β
β
β
ββββ
βββ
β
β
βββ
β
β
β
βββ
β
βββββ
ββββββ
β
β
β
ββ
ββββ
ββ
β
ββ
β
β
ββββββββββββ
β
ββ
β
ββ
β
βββ
β
β
β
β
ββββ
β
β
ββ
ββ
β
βββ
ββββββ
β
ββ
β
β
β
β
βββ
β
βββ
β
ββββ
βββββ
β
ββ
βββββ
β
β
ββ
ββ
ββ
ββββ
β
β
ββββ
β
ββββββ
β
βββββ
β
β
βββββ
β
ββ
β
β
β
ββββ
ββ
β
β
ββ
β
β
β
ββ
β
β
β
βββ
ββ
β
ββ
ββ
β
β
ββ
β
βββ
ββ
β
β
βββ
β
ββ
β
β
βββ
ββ
β
β
β
β
β
ββ
ββ
β
β
β
ββββ
ββ
β
βββ
β
ββ
βββ
β
βββ
β
ββ
β
ββββββββββ
β
ββ
β
β
β
β
ββββ
β
βββββ
βββββ
βββ
ββββ
β
β
β
β
ββ
ββ
ββββ
ββ
β
ββ
βββββ
β
βββ
β
β
β
β
β
ββ
β
ββ
β
βββββ
β
βββ
β
βββ
ββββ
ββββββ
β
βββ
βββββ
β
ββ
β
β
β
β
βββ
βββββ
ββ
ββ
ββ
βββββ
β
β
β
βββ
ββββ
ββ
ββββ
βββ
β
β
βββββ
βββ
β
ββββββ
β
ββ
β
ββββββββ
β
β
β
β
β
β
β
β
β
ββββββ
β
β
βββ
β
ββββ
β
βββββββ
β
β
β
β
ββ
β
ββ
β
β
β
β
ββ
β
ββββ
β
ββ
ββ
β
β
ββ
β
β
βββ
β
β
βββ
β
β
βββ
β
ββ
β
β
βββ
β
βββ
ββ
βββββββ
β
β
βββ
β
βββββ
βββ
β
ββ
β
ββ
βββ
βββ
β
β
β
β
ββ
β
ββ
ββ
β
βββ
β
ββ
β
β
ββββ
ββ
β
β
βββ
ββββ
β
βββββ
β
β
β
ββ
β
ββ
β
βββββββ
ββ
ββ
β
βββ
β
ββ
ββ
β
ββ
β
β
β
ββββββββββ
βββββββββββ
β
β
β
βββ
β
β
β
ββ
β
βββ
β
ββββ
β
β
β
ββββββββ
β
βββββββ
β
βββ
β
β
βββββββ
β
β
β
β
βββ
β
βββββ
βββββββ
β
ββββββββ
ββββββ
ββ
ββββ
β
ββ
ββ
βββ
β
ββ
β
β
β
β
β
β
β
ββββββ
β
β
β
β
β
ββββββ
β
ββ
ββ
ββ
β
βββββββ
ββ
βββββ
ββ
ββ
β
β
β
ββ
β
β
βββββ
ββ
βββ
β
β
ββ
ββββββ
β
ββ
β
ββ
β
β
β
ββββ
β
ββ
β
β
β
β
ββ
β
ββββ
ββ
β
ββ
β
ββ
β
βββββββββ
β
β
β
β
β
β
β
β
βββββ
β
β
β
β
βββββββ
β
ββββ
ββ
β
β
βββ
β
ββ
ββ
β
β
ββ
ββββ
β
βββ
β
ββ
β
β
ββββ
β
ββββ
β
β
β
ββ
ββ
βββββ
ββ
ββββββββ
ββ
ββββββββββ
β
β
β
β
βββββ
βββ
β
ββ
βββββββββ
β
β
ββββ
β
ββ
β
β
ββ
ββ
βββββ
β
β
β
β
ββ
β
β
β
β
ββ
β
βββββ
ββ
ββ
ββ
ββ
β
βββββ
β
β
ββββββ
β
βββ
β
β
βββ
β
β
ββ
β
ββ
β
β
ββββ
ββ
βββββ
β
βββ
β
βββ
β
β
β
β
βββ
ββ
β
β
β
β
ββ
β
βββ
βββ
βββ
ββ
ββ
β
βββ
β
β
βββββ
ββ
β
β
β
β
ββ
ββββ
β
ββ
β
β
β
βββββ
β
β
ββ
β
βββββ
ββ
β
β
βββ
βββ
β
ββββββββ
βββ
β
βββββ
β
βββββ
β
ββ
β
β
β
ββ
β
βββ
β
ββββββ
ββ
β
βββ
β
βββ
βββ
β
βββ
βββββ
ββ
ββ
β
β
ββ
β
β
β
β
βββ
ββ
β
ββ
ββ
β
ββ
βββ
β
ββ
β
ββββββ
ββ
β
β
βββ
β
β
β
β
β
β
βββ
β
β
βββββββ
β
βββ
β
βββ
βββ
β
β
β
ββ
βββββ
ββ
β
β
ββ
β
ββ
ββββ
β
β
β
βββ
ββ
β
β
β
ββ
βββ
β
ββββ
β
β
ββ
β
β
β
βββ
ββ
β
β
β
β
ββ
β
β
βββ
β
βββ
β
β
ββββ
β
βββ
β
β
βββββ
βββ
βββββββ
ββ
ββ
β
β
ββ
ββ
β
ββ
βββββ
β
βββββ
β
ββββ
β
β
ββββββ
β
βββββ
βββ
ββ
β
β
ββββββ
β
β
β
β
β
β
β
ββ
β
ββ
β
βββ
β
β
β
ββββββββ
βββ
β
ββ
β
β
β
ββ
βββ
ββββββββ
β
ββββ
ββββββββββββ
β
β
ββ
βββ
βββββββ
β
β
β
β
ββ
β
β
β
β
β
β
β
ββ
β
βββ
β
βββββ
βββ
β
ββ
β
ββ
β
ββββ
β
ββ
ββ
βββ
ββ
β
β
β
β
βββ
β
ββ
β
ββ
βββββ
β
β
β
β
β
β
ββ
βββ
β
ββ
β
ββ
ββ
β
βββ
βββββ
ββ
ββ
β
ββ
ββ
β
β
β
β
β
ββ
β
β
β
β
β
βββ
ββ
ββββββ
β
β
ββ
βββ
ββ
ββ
βββββββ
ββ
β
β
βββ
β
β
β
βββ
βββ
βββββββββ
β
β
β
β
β
β
ββββ
β
β
β
β
β
β
β
β
β
β
β
βββ
β
ββ
ββ
βββ
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
βββββ
β
β
ββββ
ββ
β
β
β
β
ββ
β
βββββ
β
ββββββ
β
βββ
β
β
ββ
β
β
ββ
β
β
ββ
βββββββ
β
β
ββ
β
β
ββ
β
β
β
ββ
β
βββ
β
βββ
βββ
β
β
β
βββ
ββ
β
β
β
β
ββ
ββββββββββββ
β
β
ββββ
ββ
β
β
ββ
ββββββ
ββ
ββββ
β
βββββββ
β
β
β
ββ
β
β
β
β
β
ββ
β
β
β
ββββ
β
β
βββ
ββββββ
βββ
ββββ
ββββ
ββ
β
β
ββ
β
β
βββββ
ββ
ββ
β
β
β
β
β
ββ
βββ
ββ
βββ
ββ
β
ββ
β
ββββ
β
βββ
β
βββ
β
β
β
β
β
βββ
β
ββββββββ
β
βββββ
β
β
β
βββ
βββ
βββ
β
β
βββ
β
ββ
ββ
βββ
β
β
ββββ
ββββββββ
β
ββ
βββ
ββββ
β
βββ
β
ββββββ
ββββββ
β
β
ββ
βββ
ββ
β
β
ββ
ββββ
ββ
ββ
βββββββ
β
ββββββββ
ββ
βββββββ
ββ
β
ββ
β
β
ββ
β
β
ββ
ββ
β
ββ
β
βββββ
βββ
β
β
β
ββββββ
β
ββββ
β
ββ
β
β
βββ
ββ
βββββ
ββββ
β
β
β
β
ββ
ββ
β
βββββ
βββ
β
β
β
ββββ
β
ββββ
ββ
β
βββββββ
β
ββ
ββ
β
β
β
β
ββββββ
β
β
ββ
β
βββ
β
ββ
β
β
β
β
βββ
β
β
β
β
β
βββββββ
βββ
β
ββ
ββββ
βββ
β
β
β
β
β
β
β
ββ
β
βββββ
ββ
β
ββ
β
β
β
ββ
ββββ
β
βββββββ
β
βββ
ββββββ
βββ
ββ
β
ββ
ββ
β
ββ
ββββββ
β
β
ββββ
β
β
β
ββββ
βββ
β
β
β
β
β
β
βββββ
β
ββββββ
β
βββββββ
ββ
ββ
β
βββββ
βββββ
ββ
β
β
ββββ
ββββ
β
β
βββ
β
βββ
ββ
β
ββββββ
β
ββ
β
ββ
ββ
β
βββββββ
β
βββββ
β
ββ
ββββ
β
β
β
ββββ
β
ββββ
β
βββ
β
ββ
β
β
βββββ
β
ββ
β
βββ
β
βββ
β
β
β
β
βββ
ββ
β
ββ
β
ββ
β
β
ββ
βββ
β
β
ββ
β
ββββββ
β
ββ
ββββ
β
β
β
βββ
β
β
β
β
ββ
β
β
ββ
β
β
β
β
ββββββ
β
β
ββββ
β
β
ββββ
βββ
ββ
β
β
β
β
β
β
ββ
β
β
ββ
β
ββ
ββ
β
βββ
βββββββββ
β
ββββ
β
ββββ
ββββββββββ
β
β
β
β
β
βββββ
β
β
β
β
ββββββββββ
βββββ
β
β
β
β
β
β
ββ
βββ
β
β
βββ
ββββ
β
β
β
β
β
β
β
β
βββββ
β
β
β
β
β
β
β
ββ
ββ
β
β
ββ
βββ
β
βββ
β
ββ
ββββ
β
β
β
ββ
ββββ
ββ
ββ
β
βββ
ββ
β
β
ββ
βββ
β
ββ
β
ββ
β
β
βββ
β
ββ
ββ
β
β
β
ββ
ββ
β
β
β
β
β
β
β
β
ββ
βββ
β
β
ββ
β
ββ
β
β
β
β
β
β
βββ
β
ββββ
β
β
β
β
β
β
β
β
β
βββ
βββββββ
β
ββ
β
β
ββ
ββ
ββ
βββ
β
β
ββββ
ββ
β
ββ
β
β
β
β
β
β
β
β
ββββ
β
β
ββ
β
βββββββββ
ββββββββ
β
β
βββ
β
β
βββ
β
ββ
β
βββββ
β
β
β
βββ
β
ββββ
β
βββββ
β
βββ
ββββ
ββ
β
ββ
β
β
β
β
β
ββ
βββ
βββββββββ
ββ
β
β
ββββ
ββββββ
β
ββ
ββ
β
ββ
β
β
β
β
ββ
β
β
ββ
ββββ
β
ββββββ
β
β
β
β
βββ
β
β
βββββββ
β
βββββ
β
ββββββ
β
βββ
β
ββ
ββ
β
β
βββββ
β
β
β
βββ
β
βββ
β
β
β
β
β
β
β
ββ
β
β
ββββ
β
β
β
β
ββββββ
β
β
β
ββ
β
β
ββ
β
β
ββββββ
β
β
β
ββ
βββ
β
βββ
ββ
ββββ
ββββββββββ
β
β
β
βββ
ββ
β
β
β
β
β
βββ
β
β
ββ
β
β
β
βββ
β
ββ
βββ
ββββ
ββ
ββββ
ββββββ
β
βββ
βββ
ββ
β
ββ
β
ββ
β
β
βββ
β
β
β
ββ
β
β
β
ββββ
β
β
ββ
β
βββββ
β
ββ
β
ββ
βββββ
β
β
β
ββ
ββ
β
β
ββββ
β
β
β
ββββββββ
β
β
βββ
ββ
β
βββ
β
βββ
ββββ
β
β
β
β
β
β
βββββ
β
ββββββ
β
β
β
β
ββββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
ββββ
β
ββ
β
β
β
ββ
ββ
β
βββ
βββββ
β
ββ
βββ
β
β
β
ββββββββ
β
βββββ
β
β
β
ββ
β
β
βββ
β
β
ββ
β
β
β
ββ
ββββ
β
ββββββββββ
β
ββββββββ
ββββ
ββ
ββ
β
β
β
β
β
β
ββ
β
ββ
ββββ
β
β
β
βββ
β
β
β
β
ββ
β
β
β
β
β
β
β
βββ
β
β
βββββ
β
ββ
β
β
ββ
β
ββ
β
ββ
β
β
ββ
ββ
β
β
ββ
ββ
β
ββ
β
β
β
ββ
β
βββββββββ
βββ
β
β
βββ
β
βββββββββ
β
β
β
β
ββ
β
ββββββ
β
β
ββ
β
ββββββ
ββ
βββββββ
ββ
β
β
β
β
βββββββ
β
ββ
β
ββββ
βββ
ββ
β
β
β
βββ
β
β
β
ββ
β
β
ββββ
β
ββββββββ
β
β
βββββββββ
β
βββ
β
ββ
ββ
β
β
βββ
ββ
β
βββ
ββ
ββ
βββ
βββ
ββ
ββ
ββ
β
β
β
ββ
ββ
β
β
β
ββββ
β
ββββββββββ
ββββββ
β
βββ
ββββ
ββββ
ββ
β
βββββ
β
β
β
ββ
β
β
β
βββββββ
βββ
β
β
ββ
β
β
βββ
β
ββββ
β
β
β
βββββββββββ
β
β
βββ
ββ
ββ
β
ββ
β
ββββ
ββ
β
β
β
βββ
β
β
β
β
βββ
β
β
β
β
βββββββββ
β
ββββ
ββ
ββ
ββ
ββ
β
β
β
ββββββ
β
β
ββ
ββ
β
βββ
β
ββ
ββββββββββ
β
β
βββ
β
β
βββββββ
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
ββββ
β
ββββ
βββββ
ββββ
β
β
β
ββββββββββββββ
ββββββββββ
ββ
ββββ
ββ
βββββ
β
β
β
β
β
β
β
β
β
ββ
βββ
β
β
β
βββ
β
β
ββ
β
ββ
β
ββββ
ββ
β
β
ββββ
β
β
β
ββββ
β
β
β
ββββββ
β
β
β
βββββββ
β
ββ
β
β
ββββ
β
β
β
ββ
β
βββββ
ββ
β
ββ
β
β
β
β
β
β
ββ
β
ββ
β
β
β
ββββ
β
β
ββββββ
β
β
β
ββββββ
ββ
βββββ
β
βββ
β
ββββββββββ
ββββ
β
βββ
β
ββββββββ
β
ββ
βββββ
β
ββ
β
βββββ
ββββ
ββ
β
β
β
β
βββ
β
β
β
β
ββ
β
β
β
ββ
β
ββββ
ββ
β
βββββ
ββ
ββ
βββ
β
β
βββ
βββ
β
β
β
ββ
β
β
β
ββββββ
β
β
β
β
β
β
βββ
β
ββββ
βββ
ββ
β
ββββββ
β
ββ
β
β
β
β
β
β
β
βββ
β
βββββ
β
β
ββ
β
ββββββ
β
β
β
βββ
β
β
ββββ
ββ
ββ
ββ
β
ββ
β
ββ
β
ββ
β
β
β
ββββββββ
ββ
β
β
βββ
β
β
β
βββ
β
β
ββ
ββ
β
β
β
βββ
ββ
ββ
βββ
βββ
βββββββ
β
ββββ
β
βββββ
ββββββ
β
βββββ
β
ββ
ββββ
β
β
ββ
βββββ
βββ
ββ
β
βββ
ββ
β
ββ
β
ββ
β
ββ
βββ
ββ
ββ
βββββ
ββ
ββ
β
βββββ
β
ββ
β
β
β
βββββββ
β
ββββββ
β
β
β
βββββββββββ
β
β
β
ββ
β
ββ
ββββ
β
βββ
β
β
βββββ
ββββ
βββ
ββ
β
ββ
β
βββββββββββ
βββ
β
β
β
β
β
β
β
β
ββ
ββββ
β
β
ββ
β
β
β
β
ββββββ
β
β
ββ
ββββββββββββββ
β
β
β
ββ
β
βββ
ββββββ
ββββ
β
βββ
β
β
β
βββββ
ββ
ββ
βββ
β
ββββ
βββ
ββ
βββ
β
β
β
βββ
β
ββββββββ
ββ
β
ββ
β
ββ
β
β
βββββ
β
β
β
β
β
ββ
ββββββββ
β
β
ββ
β
ββ
β
ββββββ
β
ββ
ββββ
ββ
β
ββ
β
ββ
β
ββ
β
ββββ
β
ββββββββββ
β
ββ
β
β
ββββββ
ββ
ββ
β
β
ββ
β
β
β
β
β
β
β
β
β
β
βββββββ
β
βββ
β
ββββ
β
β
βββββ
β
ββ
β
βββ
β
βββββ
β
β
ββ
βββ
βββ
β
β
β
βββββββββββ
β
βββ
β
ββ
β
βββββ
βββ
β
β
βββ
β
βββββββ
β
β
ββ
β
β
βββ
β
β
ββ
β
ββ
β
ββ
ββ
ββ
βββ
β
βββββ
ββββ
β
ββββββ
β
ββββββ
β
βββ
ββββ
β
β
β
ββ
β
β
β
β
β
ββββ
β
ββ
β
β
β
β
ββ
β
βββ
β
ββ
β
ββββ
β
βββ
β
β
β
ββββ
β
β
ββ
ββ
βββββββ
β
βββ
β
ββββ
β
ββββ
ββ
β
ββββ
ββ
ββ
βββ
ββββ
β
β
ββ
β
ββ
β
β
ββββββ
β
βββββ
β
ββ
β
β
β
ββββ
β
β
β
β
ββββ
β
ββ
β
β
ββββ
βββ
βββββ
β
βββββ
β
β
βββ
β
β
βββ
β
β
β
β
βββ
β
βββ
β
ββ
β
β
β
βββββββββββββ
βββ
β
ββ
β
ββ
β
ββββββββ
β
β
β
ββ
β
ββββ
β
β
ββββ
β
ββ
β
βββ
βββ
βββββββ
β
ββ
β
β
ββ
β
β
βββ
ββ
β
ββββββββββ
β
β
β
βββ
β
ββ
β
ββ
β
β
ββββββ
βββ
β
βββ
βββ
β
ββ
βββ
β
ββββ
ββ
βββ
β
β
ββ
β
βββββ
ββ
ββ
β
β
β
β
β
β
ββ
β
ββ
β
βββ
β
βββ
ββ
βββββ
ββββββ
βββββ
β
βββ
β
β
β
β
ββ
ββ
ββ
β
β
β
βββ
β
β
ββ
β
β
βββ
β
β
β
β
βββ
ββ
β
β
β
β
β
β
βββ
βββββββββββ
ββ
β
β
β
β
ββ
βββ
β
ββββ
β
β
β
β
ββ
β
β
β
β
ββββ
βββ
β
β
β
β
β
ββ
β
ββ
ββββ
ββ
β
β
ββ
ββ
β
β
β
β
βββ
ββββββββ
β
ββ
β
β
βββ
β
ββββ
βββ
β
ββ
ββββββ
β
β
β
β
β
ββββ
β
ββ
β
β
βββββ
β
β
β
β
β
β
β
ββ
βββββ
β
βββββββ
ββ
β
βββ
β
β
β
β
ββ
ββ
β
βββββ
ββ
β
ββββ
β
β
βββ
β
ββββ
β
β
ββ
β
β
ββ
β
ββββ
βββ
β
β
β
ββ
ββ
ββ
βββ
β
β
ββ
β
β
β
β
β
β
ββ
β
βββ
β
β
β
ββ
β
ββ
β
β
β
ββ
β
β
ββ
β
β
β
β
β
β
ββ
β
β
ββββ
β
βββββ
ββ
βββ
ββββ
β
β
ββ
β
β
βββββ
β
β
β
β
βββββ
β
β
β
βββ
β
βββ
β
β
ββββββ
β
β
ββ
βββ
β
ββ
β
β
β
β
ββ
β
βββ
ββ
βββ
β
β
β
β
ββ
β
β
β
ββββ
β
ββ
β
β
β
βββ
ββ
βββ
β
β
βββ
β
ββ
β
ββ
βββ
ββ
ββ
ββ
ββ
ββ
ββββ
ββ
β
β
β
β
β
βββββ
β
ββββ
β
βββββββ
β
β
β
β
β
β
βββββββββββ
β
ββ
PAX4
SLC30A8WFS1 KCNJ11SLC16A11
SFI1MC4R
b
0
2
4
6
8
10
Geneβlevel associations
Chromosome
βlo
g 10(p
)
1 2 3 4 5 6 7 8 10 12 14 17 20 23
β
β
βββββββ
β
ββ
ββ
ββ
β
βββββββ
ββββββ
β
ββ
ββ
β
βββ
β
β
β
βββββ
β
ββ
β
β
β
ββ
βββ
βββ
β
ββ
β
βββ
ββ
β
ββββ
β
ββββββ
β
βββ
β
β
ββ
β
ββ
β
ββββ
β
β
βββ
β
ββ
β
ββ
βββββββ
β
β
βββ
ββ
ββ
β
β
βββββββ
β
β
ββββββ
β
ββββ
β
βββββββββββββ
β
ββ
β
β
β
βββ
β
βββββββ
β
ββββββββββββ
β
ββ
β
β
ββββ
β
ββ
ββ
β
ββ
β
βββββ
ββββ
β
ββ
β
ββββ
β
ββ
β
βββ
β
β
β
βββββββββ
β
β
ββββββββ
β
ββ
β
β
β
β
β
βββ
β
β
ββ
ββ
β
β
βββ
β
β
ββ
ββββ
β
β
β
ββββ
β
β
β
β
ββ
β
βββ
ββββ
β
β
β
βββββ
ββ
β
β
ββββ
β
βββ
ββ
β
β
ββ
β
β
β
βββ
β
ββββ
ββ
β
β
β
βββββ
β
ββ
β
β
β
β
β
β
β
βββββββ
βββ
β
β
β
ββ
β
ββ
β
βββ
βββ
β
βββββ
β
ββββββ
β
ββββββββ
βββ
β
β
βββ
ββ
βββ
βββ
β
ββ
β
β
ββ
β
ββββββ
β
β
β
ββββ
β
ββ
βββββββ
β
ββ
β
β
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
βββ
β
ββββ
β
β
β
β
βββ
β
βββββ
ββββ
βββ
β
βββ
β
βββββ
β
β
β
β
β
βββ
β
β
ββ
βββ
β
β
β
β
ββ
β
β
β
β
ββ
β
β
β
β
β
β
β
β
ββββ
β
ββββ
β
βββββ
ββ
β
ββ
β
β
β
βββ
β
β
β
ββ
β
ββ
β
β
βββ
ββ
β
β
β
ββ
β
β
β
β
ββ
ββ
ββ
ββββ
ββ
βββ
β
βββ
β
β
βββββ
β
β
ββ
ββ
ββ
ββ
β
βββββββ
β
βββ
β
β
βββ
β
ββββ
β
β
βββ
β
β
βββββ
ββ
ββ
β
βββ
ββ
β
βββ
ββ
β
β
β
βββ
β
ββ
β
β
β
β
ββββββ
β
ββ
β
βββ
β
βββββ
β
βββ
β
βββ
ββ
ββ
β
β
β
ββ
ββ
β
ββ
β
β
β
β
β
β
ββ
β
β
ββ
ββ
βββ
ββ
β
ββ
β
ββ
ββ
ββββ
ββ
β
β
β
β
β
β
ββ
ββββββ
ββ
β
β
ββ
ββββββ
β
ββ
ββ
β
ββ
β
β
βββ
β
ββββ
β
ββ
β
β
β
βββββ
β
βββββ
ββ
β
β
β
β
β
β
βββββ
β
β
ββ
β
ββ
β
β
ββ
β
β
βββ
ββββββ
β
β
β
βββ
ββ
βββ
β
β
βββ
β
βββββ
ββββ
β
ββ
ββ
β
β
β
βββ
β
β
β
β
ββ
β
β
ββββ
β
ββ
β
β
βββββββ
β
βββ
ββββ
β
ββ
ββ
βββββββ
β
β
β
β
β
ββ
β
β
β
β
βββ
β
β
ββββ
β
β
β
ββββββββββ
ββ
β
β
β
βββ
β
βββ
β
β
β
ββ
β
β
ββ
β
β
ββ
ββ
ββ
β
ββββ
β
β
ββ
β
ββββ
β
βββ
β
βββ
ββ
β
ββ
β
βββ
ββ
β
β
ββββββ
β
ββββ
β
β
β
ββ
β
β
β
β
β
β
βββββββ
β
ββββββ
β
β
β
β
ββ
β
β
β
ββββββ
β
ββ
β
ββ
β
β
β
ββ
β
ββ
β
β
βββββ
β
ββββββ
β
β
βββ
β
β
β
ββββββ
β
β
β
βββββ
ββββ
ββββ
ββββ
β
β
β
β
β
ββββββ
β
βββ
β
βββββ
ββ
β
β
β
β
ββ
β
βββ
β
ββ
ββ
βββ
β
β
βββ
β
β
ββ
ββββ
β
ββ
β
β
β
β
β
βββββ
ββ
β
βββ
β
ββββ
β
βββ
β
ββ
βββββ
β
βββββ
ββ
βββββ
β
βββ
β
β
β
βββββββ
ββ
β
ββββββ
β
ββ
β
β
β
ββββ
β
ββββ
β
β
β
ββ
ββ
β
β
β
β
β
ββββ
β
β
ββββ
β
β
β
β
βββ
β
β
ββββββββββββ
β
β
βββ
β
β
βββ
β
β
β
β
β
β
β
β
ββ
β
ββ
β
β
ββββββ
β
β
β
βββββββββββββ
β
ββ
ββββ
β
ββ
βββ
β
ββββββββ
β
βββ
β
β
β
βββ
β
βββ
β
βββββ
β
ββββββ
β
ββ
β
ββ
β
ββββ
β
β
ββ
ββ
βββββββ
β
β
ββ
β
β
ββ
ββ
βββ
β
βββ
βββ
β
β
ββ
β
βββββββββββ
β
β
β
β
β
β
βββββ
β
β
β
ββ
β
β
β
ββ
βββ
β
β
β
β
β
β
β
ββββ
β
ββ
β
β
β
β
β
βββ
β
ββββββ
βββ
β
βββ
β
β
β
ββ
β
ββ
β
β
β
ββββ
β
ββ
β
β
β
βββ
ββ
βββ
β
β
β
β
ββ
β
β
β
β
βββββ
β
β
β
ββββββ
β
β
ββ
ββ
β
ββ
β
ββββ
ββ
βββββββ
ββ
β
ββββ
β
β
ββββ
β
βββ
β
β
ββ
ββ
β
β
β
ββ
β
ββ
β
ββββββββββ
β
β
β
ββ
β
ββ
β
β
β
β
β
β
ββ
β
βββββββ
ββ
β
β
ββ
ββ
ββ
ββ
β
βββ
β
β
β
β
β
β
β
ββ
βββββββ
β
ββ
β
β
β
ββββ
β
β
β
βββ
β
ββββ
ββ
β
βββ
β
βββ
β
βββ
ββ
βββ
ββ
ββββ
ββ
β
β
β
β
βββββββ
β
ββββββ
β
ββ
β
β
β
ββ
β
ββ
β
β
ββ
β
β
β
ββββ
β
β
β
β
β
β
ββ
β
βββ
ββ
β
ββ
β
β
β
ββ
β
β
β
β
ββ
βββββ
β
ββββ
β
β
β
β
β
β
ββββ
β
βββ
β
βββ
β
β
β
ββ
ββ
β
βββ
β
β
βββ
βββ
β
β
ββ
β
ββ
β
βββ
β
β
β
β
β
β
β
ββ
β
β
β
β
β
ββββ
β
β
ββ
β
ββ
β
βββββ
β
β
βββββ
ββββ
β
βββββ
ββββ
β
β
β
ββ
β
ββββββ
β
β
ββββ
β
β
β
βββββββ
β
βββββββββ
β
ββ
ββββ
ββββββ
β
ββ
β
ββββ
ββ
ββ
β
βββ
β
ββ
βββ
β
β
β
β
ββ
βββββ
β
β
β
βββ
β
ββ
β
β
β
β
βββ
β
βββββ
β
β
ββ
β
β
β
βββ
β
β
ββββ
β
β
β
βββ
ββ
β
ββ
βββ
β
βββββ
β
ββ
ββ
β
ββ
β
β
ββ
ββββ
β
ββ
β
β
β
β
βββ
β
β
β
βββββββ
β
β
ββββββ
ββ
β
ββ
β
β
β
βββ
β
ββ
β
ββ
ββββ
β
β
ββ
ββ
β
β
βββββ
β
β
ββ
ββ
β
β
β
β
β
ββββββ
β
β
β
β
β
βββ
β
β
ββ
β
β
ββ
ββ
ββββββ
βββ
βββββ
β
β
β
ββ
β
ββ
β
β
βββ
β
ββββββ
β
β
ββββββ
β
ββ
βββ
ββ
β
β
β
ββββββ
β
ββββ
β
βββ
β
β
ββββ
β
β
β
ββββββββ
β
β
β
ββ
β
β
β
β
β
ββ
β
β
ββββββ
β
β
β
β
β
β
β
ββββ
β
β
β
β
β
βββ
β
ββββ
β
ββ
β
β
ββ
βββββ
β
β
β
β
β
β
ββ
βββββββ
ββ
β
β
βββββββββ
β
β
β
β
β
β
ββββββ
β
β
β
β
β
βββ
ββ
β
ββ
β
ββ
β
β
β
ββββββ
β
β
β
ββ
β
ββ
ββ
β
β
β
β
β
ββββββββ
β
β
βββ
β
βββββββββ
β
β
β
ββ
ββ
ββββββββ
β
β
ββ
β
βββ
β
ββ
β
βββββββ
ββββ
β
ββ
β
ββββββ
β
βββ
β
β
ββββββββ
β
βββββ
βββββ
β
β
ββ
ββββ
β
β
β
βββ
β
β
ββ
β
β
β
ββ
β
ββ
ββββ
β
βββββββ
βββ
β
ββββ
β
βββ
β
ββ
β
ββ
β
ββ
β
ββ
β
β
β
β
βββββββ
β
ββ
ββ
β
β
β
ββ
βββ
β
β
β
β
ββ
βββββ
β
β
β
ββββββββ
β
β
β
β
βββββ
ββ
βββββ
β
β
ββ
ββββ
β
βββ
β
β
β
β
β
β
β
βββββ
β
β
β
β
βββ
β
ββ
βββββββββββ
β
β
β
β
β
β
β
ββ
β
β
βββββββββ
ββ
β
β
βββββββ
β
ββ
β
βββ
β
βββ
β
β
ββββ
ββ
ββββββ
β
β
ββ
β
β
ββ
β
β
ββ
β
β
β
βββ
β
ββββ
ββ
ββββββ
ββ
ββ
ββ
ββ
β
β
βββ
β
β
β
β
β
βββββ
β
ββ
β
βββ
β
ββ
β
ββ
β
ββ
β
βββββ
ββββ
β
β
β
β
β
β
ββ
ββ
β
β
β
ββββ
ββ
β
βββββ
β
β
β
β
β
βββββ
βββ
ββ
β
β
βββββ
β
β
ββ
ββ
β
ββ
β
β
β
β
β
β
ββββββ
ββββ
β
β
βββββ
β
β
β
β
β
β
βββ
β
ββ
ββ
β
β
β
ββ
ββ
β
β
ββ
ββ
β
β
βββββ
β
β
βββββββββ
β
β
βββ
β
β
ββ
ββ
β
β
β
βββ
β
β
β
βββ
β
βββββββ
ββββββ
β
β
ββ
β
ββ
β
β
β
β
ββ
β
β
β
β
β
β
ββββ
β
ββ
β
β
β
β
β
ββ
β
β
β
βββ
β
ββ
β
β
β
ββββ
β
β
β
β
β
β
ββββββββ
β
β
β
β
β
β
ββββ
β
β
β
βββ
β
ββ
ββββ
β
β
βββ
β
ββββ
ββββ
β
βββ
β
ββββ
ββββ
β
β
β
β
βββ
β
βββ
β
β
β
β
β
ββ
β
βββ
β
β
β
ββ
ββ
βββ
β
β
β
β
βββββ
β
β
βββ
β
β
ββ
β
β
ββ
ββ
β
ββββ
β
β
βββββ
β
β
β
β
β
β
β
β
ββββββ
βββ
β
ββ
β
β
βββββ
β
β
β
β
β
βββ
β
βββ
β
ββ
β
βββ
β
β
ββ
βββ
β
β
β
β
ββ
β
β
β
β
β
β
β
β
ββ
β
β
βββ
ββββββββ
βββ
β
βββββ
ββ
βββ
β
ββ
βββββββ
βββ
βββββ
β
ββββ
ββ
βββββββ
β
β
βββ
β
β
β
βββ
β
βββ
β
ββββββ
β
β
β
β
ββ
β
βββββββ
βββ
β
β
ββββ
β
β
ββββ
ββββ
β
β
β
β
β
βββββ
β
β
β
ββ
β
β
ββ
β
β
β
βββ
β
β
βββββ
β
βββ
ββββ
β
ββ
β
β
β
β
β
βββββ
βββ
βββ
β
ββ
βββ
β
β
ββ
β
βββββββ
β
β
β
β
β
βββββββ
β
ββ
β
βββ
β
β
β
ββββββ
β
β
β
ββββ
β
β
β
ββ
ββ
βββββββββ
β
βββ
ββ
β
βββ
β
β
β
ββ
β
ββ
β
ββ
β
β
ββ
β
βββ
β
ββ
β
ββ
β
β
ββ
β
ββ
β
β
β
β
ββββββββββββββ
β
β
ββ
βββ
β
β
βββββ
β
β
β
ββββ
β
β
ββ
β
β
β
β
ββ
β
β
ββ
β
ββ
β
β
ββββββββββ
β
β
βββ
β
ββ
β
β
β
β
β
β
β
β
ββ
β
β
β
βββ
βββ
ββ
β
ββ
β
β
β
ββ
β
βββ
β
ββ
β
β
βββββββββ
β
ββ
β
ββ
β
ββ
ββ
β
β
β
ββ
β
ββ
β
ββββββββ
βββ
β
ββ
ββ
β
βββββ
ββββ
β
β
βββ
ββββββββ
β
βββ
β
βββββ
β
βββββββ
β
β
β
ββββ
βββββ
β
ββββββββββ
β
ββ
β
β
βββββββ
β
β
βββ
β
β
β
β
β
ββββ
ββ
β
β
β
β
β
ββ
βββ
ββ
β
β
β
β
β
β
β
β
β
β
ββ
β
ββ
β
β
β
βββ
β
β
β
β
βββββ
β
βββββ
β
βββ
ββ
βββ
β
βββββ
ββ
β
ββ
ββ
β
ββββ
β
ββ
ββββββ
β
β
β
βββ
ββββ
ββββ
β
ββ
β
ββ
βββ
ββ
βββ
β
β
β
ββ
ββ
β
β
βββββββββ
β
ββ
βββ
β
β
β
β
β
β
ββββββββββββ
β
β
β
ββ
β
β
β
ββββ
ββ
β
ββ
ββ
β
β
ββββ
β
ββ
βββ
βββββββ
β
β
β
β
ββ
ββ
β
β
ββ
β
β
β
β
ββ
β
β
β
β
β
β
βββ
β
β
β
ββββ
β
βββ
β
ββ
ββ
β
β
β
β
β
β
β
β
βββ
β
ββββ
β
ββ
βββ
β
ββββββ
β
β
β
β
β
ββ
ββββ
β
β
βββββββββ
β
β
β
ββ
β
β
ββ
ββ
ββββ
β
ββ
β
β
β
β
βββ
β
β
β
β
ββββ
β
β
β
βββ
βββ
β
β
β
ββ
β
β
β
β
β
β
β
ββ
β
ββ
ββ
β
β
βββ
β
β
ββ
β
βββ
β
βββ
ββ
β
ββ
β
β
β
ββ
β
βββββ
β
ββββ
β
ββ
β
β
β
β
ββββ
β
βββ
β
β
βββ
ββ
β
ββ
ββ
β
βββββ
β
β
βββ
β
ββ
β
ββ
βββ
β
β
β
ββ
ββ
β
β
βββ
βββββ
β
β
β
β
β
β
ββ
βββ
β
βββββββββββ
βββββββ
β
βββ
β
β
ββ
β
β
βββββ
ββββ
β
β
β
β
β
ββ
β
βββ
β
ββ
β
β
β
βββ
β
β
ββ
β
βββ
ββ
ββ
β
β
β
β
β
ββββ
β
β
βββββ
βββ
β
β
ββ
β
ββ
ββ
β
β
β
ββ
β
β
β
ββ
ββ
βββ
β
ββββ
βββ
β
βββββ
β
β
β
βββ
β
ββ
β
β
β
βββ
ββ
β
ββββ
β
βββ
ββ
βββββββββ
β
ββ
β
βββ
ββ
β
βββββ
β
ββ
β
β
β
β
β
ββββββββ
ββ
ββββ
β
βββββββ
β
β
β
ββ
ββββββββ
β
β
β
ββββββββ
β
ββ
β
β
β
β
β
βββββ
β
ββ
β
β
β
ββ
β
β
β
ββββ
β
ββββ
β
β
βββ
β
β
β
β
ββ
β
β
β
ββββββ
β
βββββ
β
β
βββ
β
ββ
β
β
β
ββββ
β
β
ββ
ββββ
β
ββ
β
β
β
β
βββ
ββ
β
ββ
β
ββββ
β
β
β
β
β
β
ββ
β
βββ
β
ββ
βββββ
β
β
β
β
β
β
β
β
β
ββ
β
β
ββββ
β
ββ
β
ββ
β
βββ
βββ
β
ββββββββ
β
ββββ
β
ββ
β
ββββ
βββ
β
ββββ
βββ
β
β
β
ββββββββ
βββββ
β
β
β
βββββββ
β
ββ
β
β
βββ
βββ
ββ
β
ββ
β
βββ
β
β
β
β
β
ββ
ββ
β
β
β
β
β
β
β
β
ββββ
β
ββ
ββββββββββββ
ββββββ
β
ββββ
β
β
ββββ
ββ
βββ
ββ
β
βββββββββββ
β
β
β
ββ
β
β
βββ
β
βββββ
ββ
β
βββ
β
βββββ
β
ββββββ
ββββ
ββββ
β
β
βββ
β
β
β
ββββ
β
β
β
β
β
βββ
ββ
β
ββ
βββ
β
β
β
β
β
β
β
βββ
β
β
ββ
ββββ
β
ββ
ββ
β
β
β
β
ββββ
β
β
ββββ
β
ββββ
ββ
β
β
β
β
β
β
β
β
β
ββ
βββ
β
ββββ
ββ
β
ββ
β
ββ
β
β
β
ββββββ
ββ
β
βββ
β
ββββ
β
β
β
ββ
ββββββββ
β
ββββ
ββ
βββ
β
β
β
ββ
β
β
β
βββ
β
β
β
β
β
β
β
β
βββ
ββββββ
β
β
β
βββ
β
β
βββ
β
βββ
βββββ
β
β
β
ββ
ββββ
β
ββββββ
β
β
β
β
β
β
β
βββββββ
β
βββ
ββ
β
β
β
β
ββ
β
β
βββ
β
ββ
β
βββ
β
β
β
ββ
β
ββββββ
β
βββββββ
β
β
ββ
ββββββββ
β
ββββ
ββββ
β
β
ββ
β
ββ
ββ
β
ββ
β
ββ
β
βββ
β
ββββ
βββ
β
ββ
β
βββββ
β
β
β
ββββ
β
βββ
β
βββββ
β
β
β
β
ββ
β
β
ββββββ
β
β
βββ
β
β
ββββ
β
β
βββββ
β
β
ββ
ββ
β
ββ
ββ
ββ
β
ββ
β
βββ
β
β
βββ
β
β
β
ββ
β
β
βββββββ
β
β
β
β
ββββββββββ
β
ββ
ββ
βββββββ
β
ββ
β
βββββββ
β
ββββ
β
ββ
β
β
β
βββββββ
β
β
β
β
β
ββ
β
β
βββββββ
β
β
β
βββ
β
ββ
ββ
βββββ
β
ββββββββ
β
βββ
β
βββββββ
β
β
β
ββ
β
ββββ
β
βββββ
β
β
β
β
β
β
β
β
ββββ
β
ββ
βββ
β
ββ
β
ββ
ββ
ββ
βββ
β
β
β
β
β
β
β
β
β
βββββ
ββ
βββ
β
βββ
βββββ
β
β
β
β
β
ββββ
β
βββ
β
ββ
βββββ
β
β
βββββ
β
ββ
βββββ
ββ
β
ββ
ββ
β
β
ββ
β
β
β
ββ
ββ
ββββ
β
β
βββββββ
β
ββ
β
β
ββ
β
ββ
β
ββ
ββ
βββββ
β
ββββββ
β
β
ββββ
ββ
ββ
β
β
βββ
β
ββ
β
β
β
β
βββ
β
β
ββββ
β
β
β
βββββ
β
β
βββ
β
β
ββ
β
β
β
β
β
ββ
βββββ
β
β
β
β
β
β
β
βββ
β
βββ
β
β
β
β
β
βββββ
β
β
β
ββ
β
β
ββββ
β
β
β
ββ
β
β
β
ββββββ
β
β
ββββ
ββββ
β
β
β
β
ββββ
β
β
ββββ
β
ββ
βββ
ββ
β
ββ
β
β
β
βββββ
βββ
β
β
ββ
β
β
β
β
β
β
ββββββ
β
β
β
β
ββ
ββ
β
β
β
ββ
β
β
β
ββ
ββ
β
ββ
β
ββ
β
ββ
β
ββ
β
βββ
βββ
β
βββ
β
β
βββ
β
ββ
β
ββ
ββββββ
β
βββ
β
βββ
β
βββ
ββββ
β
β
β
ββ
ββ
β
ββ
β
β
ββββ
β
βββ
ββββ
β
β
β
ββ
ββ
βββ
β
ββ
β
β
β
β
βββ
β
β
ββ
β
β
βββββββββ
β
β
β
ββ
β
β
ββ
β
βββ
β
βββ
β
ββββββ
β
β
ββ
β
β
β
βββ
ββ
ββ
β
β
ββ
β
ββββββ
β
β
β
β
β
β
β
βββββ
β
βββ
β
β
β
β
β
β
ββ
β
β
β
β
β
ββββ
β
ββββ
β
βββ
β
β
ββββ
ββ
β
ββββ
β
ββ
β
β
β
βββ
ββ
β
ββ
β
β
β
βββββ
β
β
β
β
β
β
β
ββ
β
β
β
ββββ
β
β
β
β
β
β
ββ
β
β
β
β
ββ
βββ
ββ
ββββ
β
ββ
β
β
β
ββ
β
ββββ
β
ββ
β
ββββ
ββ
βββββ
β
ββββ
β
β
ββ
β
ββ
β
β
β
β
β
ββ
β
βββββ
β
βββββ
β
βββ
β
ββ
ββ
βββ
β
ββββ
ββ
β
ββββββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
ββ
ββββ
β
β
βββββ
β
ββ
β
β
β
βββ
βββ
ββ
ββββ
β
βββ
β
βββ
β
β
ββ
β
β
ββ
β
ββ
βββ
β
βββ
β
β
ββ
β
βββ
β
ββββ
β
β
ββββ
β
ββ
β
ββ
β
β
ββ
ββ
β
β
ββββ
β
ββ
β
ββ
β
ββ
ββ
β
β
βββββ
βββ
β
β
β
β
ββ
β
β
βββ
ββ
β
β
β
β
β
β
ββ
β
β
ββββββ
ββ
ββββββ
β
ββ
β
ββ
β
β
β
ββ
β
βββ
β
β
ββ
ββ
ββ
β
β
βββββ
βββ
ββ
β
ββ
β
ββββ
β
β
β
β
ββ
β
β
βββββ
β
β
β
β
β
β
β
β
βββ
β
β
β
ββ
β
ββ
β
β
ββββββ
ββ
β
β
ββ
β
β
β
β
β
βββ
β
ββ
β
ββ
β
β
β
ββ
β
β
β
β
βββββββ
ββ
β
β
ββ
ββ
βββ
ββ
β
β
βββ
ββββ
ββββ
β
βββ
β
β
β
β
ββββββ
β
βββ
β
βββ
ββββ
β
β
β
β
β
β
β
ββ
β
ββ
β
ββββ
ββββββ
β
ββββββββ
β
β
ββ
ββββ
β
β
β
β
ββββββββ
β
β
β
βββ
β
ββ
β
βββ
β
ββββ
βββ
βββββββββββ
β
βββ
βββ
β
β
β
β
β
β
β
ββββββ
β
β
βββ
ββ
β
β
ββ
βββ
β
ββ
β
β
β
ββ
β
ββββ
β
β
β
ββ
β
ββ
β
β
β
ββ
ββββββ
β
βββββββββββ
β
β
β
β
β
β
β
ββ
ββββ
β
ββββ
β
ββββ
β
ββ
β
β
β
ββ
ββ
ββ
ββββββ
β
β
β
β
ββ
β
β
ββ
β
β
ββ
β
ββ
ββ
ββ
β
β
β
β
ββ
βββ
βββ
βββββββ
β
β
β
βββββ
ββ
β
β
ββββ
β
ββ
βββ
β
β
β
β
ββ
β
βββββ
β
β
ββ
βββ
β
βββ
βββ
ββ
β
β
β
ββ
ββ
β
ββ
ββ
ββ
β
βββββ
β
ββββ
β
β
β
ββ
ββββββ
ββ
β
β
ββββ
β
β
β
β
β
β
β
β
βββ
β
β
β
β
ββββββ
β
ββββ
β
β
βββ
ββ
ββββ
ββββ
β
βββ
βββ
β
β
βββ
β
βββ
ββ
β
β
β
β
β
β
β
ββ
β
βββ
β
βββββββββ
ββ
β
ββ
β
βββ
ββ
ββ
β
βββββ
β
βββββ
β
ββββ
ββ
β
β
β
β
β
ββ
β
β
βββ
βββ
ββ
β
β
β
ββ
β
β
β
ββ
ββ
ββββ
βββ
βββ
β
β
ββ
β
β
βββββββββββββ
β
β
β
β
ββ
β
β
ββ
ββ
β
βββ
ββββ
β
β
ββ
β
β
β
ββββ
β
β
β
β
β
ββ
β
β
ββ
β
β
β
β
β
ββ
β
ββ
β
ββββββββββ
β
ββ
β
ββββββ
β
β
ββββββ
β
β
β
ββββ
β
β
β
β
ββ
βββββ
βββ
β
β
β
ββββ
β
ββ
β
ββββββ
β
β
β
ββββ
β
β
β
β
βββββ
β
ββ
β
β
ββ
ββ
β
β
β
β
ββ
β
ββ
β
β
βββ
β
ββ
β
β
β
β
β
ββββ
β
β
β
β
β
ββ
βββ
β
ββββββ
β
β
β
β
ββ
β
ββ
β
ββββ
βββ
ββ
β
ββ
β
β
ββ
βββ
ββ
β
β
β
β
β
β
β
βββββββββββ
ββ
βββ
ββ
β
β
β
β
β
β
β
ββ
β
βββ
β
β
βββ
β
βββ
β
ββββββ
βββββ
β
β
ββ
ββ
β
β
ββββ
ββ
βββββββββββ
β
β
βββ
βββ
β
ββ
β
β
ββ
βββ
β
β
β
ββ
βββββββββββ
ββ
β
β
β
ββ
β
β
ββββ
ββ
β
ββ
β
β
β
ββ
β
β
β
β
β
ββ
β
β
ββ
βββ
β
β
β
β
β
ββ
β
β
β
β
β
βββ
ββββββββ
ββ
ββ
β
ββ
ββ
βββ
β
β
βββ
β
βββ
β
βββ
β
β
β
β
β
β
β
βββ
β
β
β
βββββββ
β
βββ
β
β
β
ββ
β
β
ββ
β
β
β
β
ββ
β
β
βββββ
β
β
β
ββ
ββ
βββββ
β
βββββ
ββ
β
β
β
ββ
ββ
β
βββββββ
β
ββ
βββ
βββ
β
ββββββ
β
β
ββββ
β
βββ
β
β
β
ββ
β
β
ββ
β
β
β
ββ
ββ
ββ
β
β
βββββββ
ββββ
ββ
β
ββ
β
β
β
β
β
ββ
β
β
βββ
βββββββ
ββββββββ
ββββ
β
β
β
βββ
β
ββββ
β
ββββ
β
β
β
ββ
β
β
β
ββ
β
βββ
β
β
β
ββ
ββ
ββββββ
β
β
ββββ
ββ
ββββββ
ββ
β
ββββ
β
ββ
ββ
ββ
β
β
β
β
ββ
β
βββ
β
βββ
β
βββββββ
β
β
βββ
β
ββ
βββ
βββββ
β
ββ
β
ββ
ββ
βββββ
β
ββ
β
βββ
β
β
β
βββββββ
ββ
ββ
β
βββββββ
β
β
β
β
β
ββ
ββ
β
β
β
ββββ
β
β
β
β
β
β
β
βββββ
β
ββ
β
βββββββ
ββββ
β
β
β
ββ
β
β
ββ
β
β
β
βββ
β
β
ββββ
β
β
β
β
βββ
β
ββββ
β
β
β
β
β
β
ββ
β
β
ββββββββββββ
β
β
ββ
βββ
ββ
β
ββββββββββ
β
β
ββ
β
β
β
ββ
β
β
β
β
ββββ
β
β
βββ
β
β
β
β
ββ
β
ββββ
β
β
β
β
β
ββββββ
β
β
β
ββββ
β
β
ββ
β
β
β
β
β
β
βββ
β
βββ
β
β
βββ
ββ
ββ
β
ββββββββββ
β
β
ββ
β
ββββ
ββ
β
ββ
β
β
β
β
β
βββ
ββββ
β
β
β
β
β
β
β
β
β
β
βββββ
ββ
β
β
ββββββ
β
βββββ
β
β
β
β
ββ
βββ
β
β
ββββ
βββ
β
ββ
β
β
ββββ
βββ
ββ
ββ
β
βββ
β
βββ
β
β
β
ββββββ
β
β
β
β
β
βββ
β
ββ
β
β
ββββ
β
ββ
β
β
β
β
β
βββ
β
ββββ
ββ
ββ
β
βββ
β
βββ
β
βββ
β
βββ
βββ
ββ
β
β
β
βββββββ
ββ
β
ββββ
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
βββ
ββ
ββββ
ββ
β
β
β
β
ββ
β
ββββββββ
β
β
β
βββββ
β
β
β
ββββ
β
β
β
ββββββββββ
β
ββ
ββ
β
β
β
βββββββ
β
ββ
β
β
β
β
ββββ
β
β
ββ
β
β
ββ
β
β
ββ
βββββββ
ββ
β
β
β
β
β
ββ
β
β
β
β
βββ
β
β
β
β
β
β
β
βββββ
β
ββββ
β
βββ
β
βββ
β
ββββ
β
ββ
β
β
β
βββ
β
β
β
β
β
βββ
ββ
β
βββββββ
β
βββ
β
ββββ
β
ββ
β
βββ
β
ββ
β
ββββ
β
βββ
βββ
β
β
β
β
ββ
β
βββ
ββ
ββ
β
β
βββ
β
βββ
β
β
β
βββββ
β
βββ
β
ββ
β
β
β
ββ
β
β
ββββ
β
ββ
β
β
β
β
ββ
β
βββββββ
β
βββ
β
β
ββββ
ββ
β
β
β
β
β
βββ
β
βββ
ββ
β
β
βββ
β
β
βββ
β
β
ββ
β
ββ
β
β
β
β
ββ
β
β
β
β
β
βββ
ββ
β
β
βββββββββ
β
β
β
β
ββ
β
ββββ
β
βββ
ββ
β
β
ββββββ
ββ
β
β
βββ
β
βββββ
β
ββββ
β
ββ
β
β
βββ
ββ
βββ
β
β
β
β
βββ
β
βββββ
β
ββ
β
β
β
ββ
β
ββ
β
β
β
β
β
ββ
β
β
β
β
β
ββ
β
ββ
β
β
βββ
β
ββ
β
ββββββ
βββ
βββ
β
β
ββββββ
ββββββ
β
ββ
β
βββββ
ββ
βββββ
β
ββ
β
β
β
ββ
βββ
β
β
β
β
β
β
ββ
ββ
β
ββββββββββββββββ
β
βββ
βββ
ββββ
ββ
β
β
β
β
βββ
β
ββ
β
β
β
βββββββ
β
β
βββββββ
β
ββ
β
β
β
βββ
β
β
βββββ
βββ
β
βββββ
β
β
β
βββ
β
ββββ
ββ
β
β
β
β
β
β
β
β
β
ββ
ββ
ββ
β
ββ
ββ
β
ββ
β
βββ
β
ββββ
ββ
β
ββ
β
β
β
βββ
β
β
βββ
ββ
β
ββ
β
βββ
ββ
ββββββ
ββββ
β
β
β
ββ
ββ
ββββ
β
ββ
β
ββ
β
ββ
β
ββ
β
ββββ
β
β
ββ
β
β
β
ββ
β
βββ
β
β
β
ββββββ
β
β
β
ββ
β
β
ββββββ
β
ββ
βββ
β
ββ
β
β
β
β
βββββ
β
βββ
βββββ
ββ
ββββββββ
β
β
ββ
β
β
ββ
β
β
β
βββββββ
β
β
βββββββββ
β
ββββββ
β
β
βββ
β
βββ
ββ
ββ
β
β
βββ
β
ββ
β
β
βββββ
βββ
β
βββ
β
βββββ
β
ββ
ββ
βββββ
β
βββββ
β
βββββββββ
β
β
βββββββ
β
β
ββ
ββββ
ββ
β
β
β
β
βββ
β
β
ββ
β
β
β
ββ
β
ββ
β
β
ββ
β
β
β
ββ
ββ
β
β
β
β
βββ
β
ββ
β
β
β
ββββ
β
β
β
β
β
β
β
β
β
ββββ
β
β
βββββ
ββββ
ββ
β
β
ββ
ββββ
β
ββ
β
ββ
ββ
β
β
β
β
β
β
ββ
ββ
β
β
β
β
ββββ
β
β
β
βββ
β
β
β
β
βββββββββββ
β
β
βββ
β
ββ
ββ
βββββββ
βββ
β
ββββββ
βββ
β
β
β
ββ
ββββ
β
β
βββββ
β
βββ
ββ
β
β
β
β
ββββββ
β
β
β
β
ββ
β
β
β
β
β
β
ββββββ
ββ
β
β
β
βββββ
β
β
β
β
β
ββ
β
β
βββββ
β
βββ
ββββββββ
ββ
β
β
βββ
β
β
ββββ
β
βββ
ββ
βββββ
β
ββ
β
ββββ
ββ
ββββ
β
β
βββββ
β
β
β
β
βββββ
ββ
β
β
ββββ
β
ββββ
β
ββ
β
β
β
ββ
β
β
β
βββ
β
βββββββ
β
β
ββββββ
β
β
β
β
β
β
ββββββββββ
β
ββ
β
β
β
β
β
β
β
β
β
β
β
ββ
β
βββββ
β
β
β
β
βββ
β
β
β
β
ββββ
β
β
β
ββββ
β
βββ
β
β
ββββ
βββββββ
β
β
β
βββββββ
β
ββ
β
β
βββ
β
β
βββββ
β
ββββββ
β
ββ
β
β
ββββββ
β
β
β
β
β
β
β
ββ
β
ββββ
β
β
β
ββ
β
βββ
β
ββββ
β
ββββββββββ
β
β
βββ
β
β
β
β
β
βββββ
β
βββ
ββ
β
β
β
βββ
β
β
β
β
β
βββββ
ββ
β
β
βββββ
β
β
β
β
ββ
βββββββββ
βββ
β
ββ
β
βββββ
β
ββ
β
β
ββ
β
β
β
βββββββ
ββ
β
ββ
βββ
ββ
ββ
β
βββ
ββ
ββ
β
β
βββ
ββ
β
β
β
β
β
βββββ
ββ
β
β
ββ
ββββββββ
β
ββββ
ββ
β
β
β
β
ββ
β
βββ
β
β
β
β
β
β
β
β
β
ββ
β
ββββ
βββββββ
β
β
β
β
β
β
β
β
β
ββββ
β
ββ
ββββ
β
ββ
ββ
βββ
ββ
β
β
ββ
β
ββββ
β
β
β
ββββ
β
βββββ
βββ
β
β
β
ββ
ββββββ
β
β
β
β
ββ
β
ββββββ
ββ
βββ
β
ββ
β
β
β
ββββ
βββ
ββ
β
βββ
β
βββ
β
ββ
β
β
β
ββ
ββββββββ
ββ
ββ
β
β
βββ
β
β
β
ββ
β
βββ
β
ββββββ
β
β
β
ββββ
β
βββββ
β
ββ
β
β
β
β
βββ
β
β
β
β
βββββ
β
ββββββββ
β
β
β
ββ
ββββ
β
ββ
β
β
βββ
β
β
β
ββββββ
β
ββββ
β
ββ
ββ
ββββ
βββ
β
β
β
βββββ
β
β
βββββββ
ββ
ββββ
β
β
ββ
β
ββ
β
β
ββ
β
β
ββ
ββ
β
β
ββ
ββ
β
β
β
βββ
β
β
ββ
β
ββββ
β
ββββ
β
ββ
β
βββ
β
ββ
β
β
β
βββ
β
β
β
β
β
β
β
βββ
βββββ
β
β
β
β
ββ
β
β
β
ββ
β
β
ββ
ββ
β
β
ββ
β
βββ
β
βββ
β
β
ββ
β
ββββ
β
β
β
βββββββ
ββββ
β
ββ
β
β
ββ
β
β
β
β
β
β
β
β
ββ
ββ
β
β
β
ββ
ββ
β
β
β
ββββ
β
β
β
ββββ
ββ
βββββ
β
β
β
ββββ
βββ
β
β
β
β
β
β
ββββββ
β
ββ
ββββ
β
βββββββββ
β
β
β
βββββββ
β
ββββββββββ
ββ
β
β
βββββ
β
β
β
β
β
β
ββ
β
βββ
β
βββ
β
ββ
β
βββ
ββββ
β
β
β
ββββββ
β
βββββ
β
ββ
β
β
β
βββ
β
ββββββββ
β
ββββ
β
β
ββ
β
βββ
ββ
βββ
β
ββ
β
β
ββ
β
ββ
β
β
ββ
β
β
β
β
β
βββ
β
ββ
β
β
β
β
ββββ
β
β
ββ
β
β
β
β
β
βββββββββ
β
β
β
βββ
βββββββββ
β
ββββββββ
β
ββββββ
β
ββ
β
βββββ
β
β
β
ββ
ββ
ββ
ββ
ββ
ββ
β
β
β
β
β
β
ββββββββββββββ
ββ
βββ
βββββ
ββ
ββ
β
β
β
β
β
ββ
ββββ
β
β
βββββ
β
ββββ
β
βββ
β
ββ
β
β
ββββββ
β
ββ
ββ
β
ββββ
β
βββ
β
ββββββ
βββββ
β
βββ
β
β
β
βββ
β
β
βββ
β
βββ
β
βββ
β
ββ
β
β
β
β
β
βββ
β
β
βββ
β
β
ββββ
β
β
β
β
βββββ
β
β
β
β
β
ββββ
β
βββββββββ
β
β
β
ββββββ
β
β
β
β
β
β
βββββββ
β
ββ
βββ
ββ
β
β
β
ββββββββ
β
ββ
ββ
β
βββββββ
β
β
ββ
β
β
ββ
β
βββ
βββββ
β
β
β
ββ
βββ
β
ββ
β
β
ββ
β
β
β
β
ββ
βββ
β
βββββ
β
β
ββββ
β
ββββ
β
ββ
βββββββββββ
β
βββ
ββ
ββββ
β
β
β
β
β
β
β
ββ
βββββββ
β
ββ
βββββ
ββ
ββ
β
βββ
β
ββ
ββ
ββ
ββ
β
β
ββββ
βββββ
β
β
β
β
β
β
β
ββββββββ
β
βββ
ββ
ββββββ
β
βββββ
β
β
β
βββ
β
β
β
β
ββ
β
β
ββ
β
β
β
β
ββ
β
β
β
β
ββββ
β
ββ
ββ
β
β
β
βββββ
β
ββββββββββββ
β
β
ββ
β
β
β
β
ββ
β
β
β
ββ
β
β
β
β
β
β
βββββ
β
β
β
β
βββ
ββ
ββ
β
βββ
β
β
β
ββ
ββ
ββββ
βββββββ
β
βββββ
β
β
β
β
β
β
β
ββββββββ
βββ
βββ
β
β
βββββ
β
βββββ
β
β
β
ββ
β
ββ
β
ββββ
β
ββββ
β
β
β
β
β
βββββ
βββββ
βββββ
β
β
β
βββββ
β
βββββββββββββββ
ββ
βββββ
ββββββββ
βββ
βββ
βββ
β
β
β
β
ββββ
β
βββββ
β
β
β
ββ
β
ββββ
β
β
ββ
ββββ
β
ββββ
β
ββ
β
β
β
β
β
β
β
β
ββββ
βββ
β
ββββββ
ββ
β
β
β
ββ
ββββββ
β
ββββ
β
ββ
βββ
β
ββ
β
βββ
ββ
β
β
β
β
β
β
ββ
β
ββββ
β
ββ
β
ββββββ
β
βββ
ββ
β
β
ββ
β
ββ
β
β
β
ββββ
β
β
ββ
β
β
β
β
βββ
β
βββ
βββ
β
ββ
β
ββ
ββ
β
βββ
β
β
β
ββ
β
β
β
β
β
β
ββ
β
βββ
β
ββ
β
β
ββ
β
βββ
β
β
ββββ
ββ
β
β
β
β
β
β
β
ββ
β
ββ
β
β
β
β
β
β
β
β
β
ββ
β
β
β
βββ
β
β
β
β
ββββ
ββ
β
βββ
β
ββ
β
β
βββ
ββ
β
β
β
β
ββ
β
ββββββ
β
ββββββ
β
β
β
β
β
β
ββ
β
βββ
β
β
β
ββ
ββ
β
βββ
β
ββ
ββ
β
β
β
β
βββββ
β
β
β
ββ
β
β
ββ
β
ββ
β
β
ββ
β
β
β
β
β
β
β
ββββββ
β
β
βββ
β
βββββββ
β
β
β
ββ
β
ββββ
β
βββββββ
β
βββ
β
β
βββ
β
βββ
β
ββ
β
βββ
ββββ
ββ
β
βββ
ββββββ
β
ββ
β
βββ
β
βββββ
βββββ
β
β
ββββββββ
β
β
β
β
β
β
βββββ
β
β
β
ββ
β
ββ
β
βββ
β
βββ
β
β
β
β
ββ
β
β
β
β
ββ
ββββ
β
β
ββ
βββ
ββ
β
β
βββ
β
βββββββ
β
β
β
ββ
β
β
β
β
β
ββ
βββ
β
β
ββ
β
β
β
βββββββ
ββ
β
ββ
β
β
β
β
ββ
β
β
ββ
ββββ
β
β
ββ
βββ
β
βββ
β
β
β
βββββββ
ββ
β
ββ
ββ
β
ββ
β
β
β
β
β
ββ
β
β
β
β
β
β
β
ββ
ββ
β
β
β
β
ββββββββββ
ββ
β
β
β
β
β
β
ββ
β
β
β
β
ββ
β
β
β
ββ
β
β
β
β
ββ
β
β
β
βββ
β
β
ββ
ββ
β
β
β
βββ
β
β
β
β
β
β
βββ
β
β
ββ
ββ
β
ββ
β
β
ββββ
ββββββββ
β
β
β
β
ββββββ
β
β
β
ββ
ββββ
β
β
β
ββ
β
ββββββββββ
β
β
β
βββ
β
β
β
ββ
β
β
β
ββββ
βββ
β
βββββββββββ
β
βββ
β
β
ββββββ
βββ
β
β
ββββ
β
βββ
βββ
β
β
β
ββββββ
β
ββββββββββ
β
ββ
β
ββ
β
ββββ
β
βββ
β
ββββ
ββ
β
β
β
βββββββ
βββ
β
β
β
β
β
β
β
β
β
ββ
ββ
β
β
β
βββββ
β
β
β
ββββββ
β
β
ββββ
β
βββ
ββ
β
ββ
βββββ
β
ββ
ββ
β
ββ
β
β
βββββ
βββ
ββ
ββ
β
β
ββββββββ
β
ββ
ββ
βββ
β
βββββ
β
ββ
β
βββββ
ββ
ββββββββ
β
β
β
ββ
β
β
ββ
ββββββββ
β
βββ
β
β
β
ββ
β
β
β
β
β
ββ
ββ
ββ
ββββ
ββ
β
β
β
β
β
β
β
ββ
β
β
ββ
β
ββ
βββββ
β
β
β
ββ
β
βββ
β
β
β
β
β
β
β
β
ββββ
β
β
ββββ
ββββ
β
β
βββ
β
β
β
β
ββββββ
β
β
ββββ
ββ
β
ββββββββ
β
βββββ
β
ββββ
βββ
β
β
βββ
β
ββββββ
β
β
ββ
β
β
β
β
ββ
β
ββββββ
β
β
ββ
β
ββββ
β
βββ
β
βββββ
β
βββββ
β
β
β
β
βββ
β
β
ββ
ββ
ββ
β
ββββββββββ
β
βββ
β
βββ
ββ
ββ
β
βββ
β
β
β
ββ
β
ββ
β
βββ
ββ
ββ
β
β
ββββ
β
ββ
β
β
ββ
β
β
βββββ
β
β
ββ
ββββ
β
β
β
ββ
β
ββββ
βββββ
β
β
β
β
β
β
β
β
β
β
β
ββ
β
ββ
β
ββ
β
β
β
βββββββββββββ
β
ββ
β
βββββ
β
ββββββ
β
ββ
β
β
β
β
ββ
β
ββ
ββ
β
β
β
β
ββ
β
ββ
β
β
ββββ
β
β
β
β
β
β
βββββ
β
β
β
β
βββ
ββ
β
ββ
β
β
βββ
β
ββ
β
βββββ
β
βββββββββββββββ
β
β
ββ
ββββ
β
ββ
β
ββββ
β
β
β
ββββ
β
β
β
ββββββ
β
βββββ
β
ββ
β
β
ββ
β
βββ
β
β
β
ββ
β
βββ
β
β
β
ββββββ
ββ
βββββββββββββ
β
β
ββ
ββ
β
βββ
β
ββ
β
β
βββββ
ββ
ββ
β
β
ββββββββ
β
ββ
β
βββ
β
ββ
βββ
ββ
β
β
β
β
βββ
ββ
β
ββ
β
β
β
β
β
βββ
ββ
β
ββββ
β
ββ
β
ββ
β
βββ
β
βββ
β
ββ
β
β
β
β
β
β
β
βββ
β
ββ
ββ
ββ
β
ββ
ββ
ββββ
β
β
β
β
ββββ
β
ββ
β
β
β
βββ
β
β
β
β
β
β
βββ
β
β
βββ
ββ
β
β
β
βββ
β
β
β
β
ββ
βββ
β
β
β
β
β
β
ββ
ββ
β
ββββ
β
ββββ
ββ
β
ββ
β
β
β
βββ
β
β
β
β
β
β
β
ββββββ
β
ββ
β
β
β
β
β
β
β
β
ββ
β
ββ
β
βββββ
β
β
β
ββββββ
β
ββββββ
β
β
β
β
β
β
β
β
β
ββ
β
ββ
β
βββ
β
βββββ
β
ββββ
ββββ
β
βββ
ββββ
βββ
β
β
β
ββ
β
β
β
β
β
β
β
βββ
β
βββββ
β
ββ
β
β
β
β
βββββ
β
ββββββ
β
β
β
βββββ
β
β
β
β
β
β
ββ
ββ
β
ββ
β
β
βββ
β
β
β
β
β
ββ
ββ
β
β
βββ
β
ββ
β
ββ
β
ββ
β
βββ
β
β
β
β
β
β
β
ββ
ββ
β
ββ
ββ
βββββββββ
β
β
ββ
ββ
ββββ
β
ββββ
β
ββ
ββ
β
β
ββ
β
βββββββ
β
β
β
β
ββββββββ
βββ
β
β
β
ββββββββ
β
β
ββ
ββββ
β
ββ
ββ
ββ
β
β
ββ
ββββ
β
β
β
ββ
β
ββ
ββββββ
β
ββββ
β
β
ββ
β
β
β
β
βββ
β
ββββ
β
β
β
β
β
β
β
βββ
ββββ
ββ
β
β
βββββββ
β
β
β
ββ
β
β
β
β
β
ββ
βββββββ
β
ββββββ
β
β
ββ
β
β
β
βββ
β
β
β
β
ββ
β
β
β
ββ
β
β
β
β
ββ
β
β
βββ
β
βββ
β
ββ
β
ββ
β
β
β
β
β
ββ
β
ββ
β
ββββββ
ββ
β
ββββ
β
β
ββ
βββ
ββ
β
β
βββββ
β
βββββββ
β
β
ββ
β
β
β
β
β
β
β
β
ββ
β
ββ
βββββ
β
β
ββββ
β
β
β
β
β
β
ββ
ββββ
β
β
ββ
β
β
β
βββββ
β
ββββ
ββ
β
β
β
β
β
β
βββββββ
β
β
β
β
β
ββ
β
β
β
ββ
βββ
βββββββ
β
ββββ
β
ββ
βββ
β
ββ
β
β
β
β
β
β
βββββββ
βββ
β
βββββββ
β
ββββββ
ββ
βββ
β
β
βββββ
β
β
βββ
β
β
β
β
β
β
ββ
ββ
β
ββ
β
ββ
ββ
β
ββ
β
ββββ
β
β
ββββ
βββ
β
βββ
β
β
β
β
β
βββ
β
ββ
β
ββ
β
β
β
β
β
β
ββ
β
ββββ
β
β
β
ββββββ
β
β
β
β
β
β
β
β
β
ββββ
β
β
β
β
β
β
β
ββ
β
β
β
ββ
ββ
β
β
β
β
β
ββ
βββ
β
ββ
β
βββββ
ββ
ββ
β
ββββ
β
βββββββββββ
β
β
β
β
βββββ
β
ββββββ
β
β
β
β
β
ββ
ββ
β
β
β
βββ
β
ββ
ββ
βββββ
β
β
β
β
ββ
β
β
ββ
β
β
β
ββ
β
β
β
ββ
β
β
ββ
β
ββ
βββββββ
β
ββ
β
β
βββ
ββ
ββ
β
β
β
β
β
ββ
β
β
β
β
βββ
β
βββββ
β
ββ
ββ
β
β
β
β
β
βββ
β
β
β
β
β
β
β
β
β
βββ
β
βββββ
β
ββ
β
ββ
β
β
β
β
ββββ
β
ββ
β
β
ββ
β
β
ββ
β
βββ
βββ
ββββ
β
β
ββ
ββ
β
β
ββ
β
ββ
β
ββ
β
β
ββ
βββββββββ
β
ββ
β
ββββββ
βββ
β
β
β
β
ββ
β
β
βββ
βββ
β
β
ββ
β
βββ
β
βββ
βββ
ββββββ
β
ββ
ββ
β
β
β
β
β
βββββββ
β
β
β
β
β
β
ββ
β
β
ββ
ββ
ββ
β
βββ
β
β
β
β
β
βββ
β
β
ββββ
β
βββββ
β
β
ββ
ββββ
β
ββββ
β
ββββ
β
βββ
β
β
β
β
β
ββ
β
ββ
β
ββββββ
β
βββββ
β
β
β
βββββ
β
β
ββ
ββ
ββ
β
β
ββββ
β
ββ
β
β
β
βββ
β
β
β
β
β
β
βββ
β
βββββ
β
ββ
β
βββ
β
β
β
β
β
β
β
β
βββ
β
ββ
β
ββββββββ
β
β
β
β
β
ββ
β
ββ
β
β
β
β
β
β
ββββββ
β
β
β
βββ
β
ββ
β
ββ
β
β
β
βββ
ββββββ
βββ
β
β
β
βββββββββ
β
β
β
β
β
ββββ
β
β
ββββ
β
β
ββ
ββββ
ββββ
βββ
β
β
β
β
β
ββ
β
ββ
ββ
β
β
ββ
βββββββ
β
β
ββββββββ
β
β
β
ββ
β
ββ
β
β
β
β
β
βββββ
β
β
β
β
ββ
β
ββ
β
ββ
β
β
β
ββββ
β
β
β
β
ββ
ββββ
β
β
β
βββ
β
β
β
ββ
ββ
β
β
β
β
β
ββ
β
β
β
βββ
β
β
β
ββ
β
β
ββββ
βββββ
β
ββ
ββββ
β
β
β
βββββ
β
β
β
ββββββ
ββ
β
ββ
β
ββββ
β
ββ
ββ
βββ
β
βββββ
β
βββββββ
β
ββββ
β
βββ
β
β
β
β
βββ
β
ββ
β
β
β
βββββββ
ββ
ββ
β
β
ββββ
β
β
β
ββ
β
β
β
βββ
β
ββ
β
ββ
β
βββ
ββ
β
ββββ
β
β
β
β
ββ
βββββ
ββ
ββββββ
ββ
β
ββ
β
β
β
ββββ
β
ββββ
β
β
ββ
β
ββββ
ββββ
β
β
β
β
β
βββ
β
ββββββββββ
β
ββββ
β
β
β
βββ
β
ββββ
β
ββββββ
β
β
ββ
ββββββββ
ββ
βββ
β
β
β
β
β
ββ
βββ
ββββββ
β
β
ββ
β
β
ββ
β
β
βββ
β
ββ
β
ββ
β
ββ
β
β
β
β
βββ
β
ββ
β
β
β
ββ
β
β
β
β
ββ
β
β
β
ββ
β
β
β
ββ
β
βββ
ββββββββ
β
β
β
ββ
β
ββ
βββ
β
β
ββ
ββββ
β
ββ
β
ββ
β
β
β
ββ
ββ
β
β
βββββ
ββ
β
βββββ
βββ
ββ
β
β
β
ββ
β
β
ββ
β
ββ
βββββ
β
ββββββ
β
ββββ
β
β
β
β
ββ
β
β
ββββββ
ββ
β
β
ββ
β
β
β
ββββ
β
β
β
ββ
ββ
βββ
β
β
β
β
β
ββββ
β
ββ
β
β
ββ
β
ββββββ
β
β
β
β
ββ
βββ
β
β
β
β
β
β
β
β
βββββββββ
β
β
β
β
βββ
β
β
β
ββββββ
ββ
βββββββ
β
β
β
β
β
ββ
β
ββ
β
ββββ
β
β
β
ββ
β
β
β
ββββ
β
ββββββββββββ
β
β
ββ
β
β
β
β
β
ββ
ββ
β
β
βββ
β
β
β
ββ
β
β
βββ
β
βββ
β
ββββ
β
βββ
β
ββ
β
ββββ
βββ
βββββββ
β
β
β
β
β
βββ
β
β
β
β
β
βββ
βββ
β
ββ
β
β
ββββ
β
β
βββββ
β
β
β
ββββ
β
ββ
βββ
ββββ
β
ββββββββ
β
β
β
ββ
ββ
ββββ
β
βββ
β
βββ
β
ββββββ
β
β
ββ
β
β
β
β
β
β
β
β
β
β
ββββ
ββ
ββββ
β
ββ
ββ
β
β
βββ
ββββββ
β
β
βββ
ββ
β
β
β
ββ
β
ββ
β
ββ
β
β
β
β
β
ββ
β
β
β
ββββββ
β
β
β
βββββ
β
ββββββ
β
β
βββ
ββ
β
βββ
β
βββ
β
β
β
β
β
β
βββ
β
β
β
ββ
β
ββ
β
βββββββ
β
ββββββ
β
βββ
β
ββββ
βββ
β
β
βββββ
β
β
ββ
β
βββ
βββββ
β
β
β
β
β
βββ
ββββββββ
ββ
β
β
ββ
β
βββββββ
β
β
β
β
β
β
βββ
β
β
ββ
ββ
β
β
β
ββ
β
β
β
β
ββ
ββ
β
βββββ
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
ββ
ββ
β
β
β
β
βββ
β
βββ
β
β
ββββββ
β
βββββββ
β
β
β
β
βββββββββββββ
β
ββββ
β
ββ
β
β
β
β
β
ββββ
β
β
β
β
ββββββ
β
ββ
β
β
β
βββ
β
βββββ
ββ
ββ
ββ
β
ββ
ββββ
ββ
β
βββ
β
β
β
ββββ
β
β
β
β
β
βββ
βββ
ββββββ
β
βββ
ββββ
β
β
ββ
ββ
β
βββββ
β
ββ
βββββ
β
β
β
ββββ
ββ
ββββ
β
β
βββββββ
β
ββββββ
ββ
β
β
β
ββ
β
βββββββ
ββββββ
ββ
βββ
ββ
β
ββ
β
β
ββ
ββ
β
β
ββ
β
βββββββ
β
ββββ
β
βββββββ
β
βββ
β
β
β
β
β
β
β
β
ββ
β
β
β
β
ββββββ
ββ
ββ
β
ββββββββββ
β
β
ββ
β
β
β
ββ
β
βββ
β
ββ
ββ
β
β
ββββ
ββ
β
β
β
β
β
ββββ
β
β
βββ
βββ
β
β
β
ββ
β
βββ
β
βββ
ββ
ββ
β
β
β
β
β
β
β
β
β
β
β
ββ
β
ββββββ
βββ
β
βββββ
β
β
β
β
β
βββββ
ββ
βββ
ββ
β
ββ
ββ
β
β
β
β
β
ββ
β
β
ββββ
β
β
β
β
βββ
ββββ
ββββββββ
β
βββββββ
β
ββ
βββ
β
β
β
βββββββ
β
β
β
ββββ
β
β
β
β
β
β
β
ββ
β
β
β
β
ββββ
β
ββ
ββ
β
β
β
β
ββββ
ββ
βββ
β
ββ
β
βββ
ββββ
βββ
ββ
β
ββ
ββ
ββ
β
β
β
β
ββ
β
β
ββ
ββββ
β
ββ
β
β
β
ββββ
β
β
ββ
β
β
β
β
ββββ
β
β
β
ββ
ββββ
β
βββββ
β
β
β
ββββ
β
ββ
β
β
β
β
β
β
ββ
β
β
β
β
β
βββββ
β
βββββ
ββ
ββ
ββ
ββ
β
ββ
β
β
ββ
β
β
β
β
β
ββ
β
β
β
βββββ
β
ββ
β
βββββββββ
β
ββ
ββ
β
β
β
β
ββββ
ββββ
βββ
β
βββ
β
ββββ
β
ββ
β
β
ββββ
β
β
βββ
ββββββ
β
βββ
β
ββββββ
β
β
β
β
β
β
β
βββββββββββ
β
β
β
ββ
β
β
ββ
β
β
ββ
ββββββββββββ
β
βββ
ββ
β
β
ββ
β
β
ββ
β
ββ
β
β
β
β
ββ
β
βββ
β
β
β
β
β
β
βββ
β
ββ
β
β
ββββ
ββ
βββ
β
βββ
β
β
β
β
β
ββ
β
β
β
β
ββ
β
β
ββ
ββ
β
β
βββ
ββββ
βββ
β
β
β
βββ
ββ
β
β
β
ββ
β
β
ββββββββ
β
ββ
ββ
ββ
β
β
β
βββ
ββ
β
ββββββ
β
ββ
β
ββ
βββββ
β
ββββ
ββββ
βββ
βββ
βββ
βββββ
ββ
ββ
ββ
β
β
β
β
β
β
β
βββ
β
ββββββββββ
ββ
β
ββ
ββββ
β
ββ
β
β
β
ββββ
β
β
β
β
ββββ
β
β
βββββ
ββ
β
β
β
β
ββ
β
ββββ
ββ
β
ββ
ββ
β
ββ
ββ
β
ββββββ
β
β
βββ
βββ
ββ
β
β
β
ββ
β
ββ
β
βββ
β
β
β
β
βββ
βββββββββ
ββ
β
β
β
β
β
β
ββ
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
βββ
β
ββ
β
βββ
β
βββββββββ
β
β
β
ββ
β
β
β
β
β
β
β
ββ
β
β
ββ
β
β
β
β
ββββββ
ββ
β
ββ
βββ
β
βββ
β
ββββ
β
β
β
βββββ
β
β
β
ββ
β
βββββββ
β
β
β
ββ
ββ
β
β
β
ββ
β
β
β
β
β
β
βββββββββ
β
β
ββ
β
β
βββ
β
β
ββββββ
β
ββ
β
β
β
β
β
βββ
β
βββ
ββ
ββ
β
β
β
β
β
β
βββ
β
β
β
βββββ
β
β
ββ
ββ
β
β
ββ
ββ
β
ββββ
β
β
β
ββ
βββ
ββββββββ
β
β
β
βββ
β
βββββββ
ββ
ββ
β
ββ
ββββ
ββ
ββ
β
ββββ
β
β
β
β
ββββ
β
β
βββ
β
β
ββ
ββ
ββ
β
βββββββββββββββ
β
ββ
ββ
ββββ
β
β
β
β
β
β
β
βββββββββ
β
β
β
βββββ
β
β
β
β
ββββ
β
β
βββ
β
β
β
ββ
ββ
βββ
ββ
β
β
β
β
ββ
β
β
β
β
β
β
ββββββ
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
βββ
β
ββ
βββββ
ββ
ββ
β
ββ
β
β
β
β
βββββ
βββ
β
β
β
β
β
β
β
ββββββ
βββ
β
β
β
βββ
β
ββ
ββ
β
ββ
β
ββββββ
β
β
β
β
β
β
βββββββ
ββββ
β
β
β
βββββββ
β
β
β
β
ββββ
β
β
β
ββ
β
ββ
β
β
βββ
ββ
β
β
ββ
β
ββ
β
ββ
βββββ
βββ
ββ
βββ
ββ
β
β
β
β
β
β
βββ
β
ββ
β
ββββββ
ββββ
β
β
β
β
β
β
ββ
β
ββ
β
βββ
β
β
ββ
β
βββββ
β
βββ
β
β
β
β
β
β
βββ
β
βββ
β
β
β
β
βββ
β
ββββ
βββ
β
ββββ
β
β
β
βββββ
β
ββββββββββββββββ
β
ββ
β
β
ββ
β
β
β
β
ββββ
β
β
ββ
βββ
β
βββ
β
βββββββ
β
ββββ
β
βββββββ
ββ
ββ
ββββ
ββ
β
βββ
β
β
β
β
β
β
ββ
ββ
βββββ
β
ββββββ
ββ
β
βββββββββ
ββ
ββ
β
ββ
β
β
β
β
ββββ
β
β
β
βββ
β
ββ
ββ
ββ
β
β
ββββ
β
βββ
β
β
βββββββ
β
β
β
βββββ
β
β
ββ
ββββββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
βββββ
β
β
βββββ
ββ
β
β
βββ
β
ββ
β
β
β
βββ
β
ββββββ
ββ
ββββββ
ββ
β
β
β
β
β
β
βββ
ββ
ββββ
β
β
β
β
β
ββ
β
ββ
β
ββ
β
β
β
β
β
β
ββ
β
ββββββ
β
ββ
ββ
β
β
β
ββββββ
β
β
βββ
β
ββ
β
β
ββββββββββββββββββ
β
βββ
βββββ
β
β
β
ββ
β
ββββββββββ
ββ
βββ
β
β
βββββ
β
βββ
β
β
β
β
βββββββββ
βββ
β
β
β
β
β
β
β
ββ
βββ
ββ
βββ
β
β
β
ββ
β
β
β
β
ββββ
β
β
β
β
β
β
β
β
β
β
β
β
ββ
β
βββββββ
ββ
βββββ
β
βββ
β
βββββββ
β
ββ
ββ
ββββββββββββββ
β
β
ββββββ
ββββ
β
β
β
ββ
ββ
ββ
β
βββββ
β
β
β
β
ββ
β
β
β
ββ
β
β
ββββ
βββ
β
ββββββ
β
ββ
β
β
β
β
βββββ
β
ββ
β
ββ
βββ
ββ
ββ
β
β
ββββ
β
β
βββ
β
β
β
βββ
β
βββ
ββββ
β
β
β
β
β
β
β
ββ
β
β
ββ
β
β
ββ
β
β
β
ββββββ
β
β
β
ββββ
β
ββ
β
β
β
ββ
β
β
β
βββββββββ
β
βββ
β
β
β
β
β
ββ
ββ
β
ββββββ
ββββββ
ββ
β
ββ
β
βββ
β
ββββ
β
β
ββ
β
β
βββ
β
β
ββ
β
βββ
β
β
β
β
ββ
β
β
β
β
β
βββββ
β
β
β
ββ
β
βββββββββββ
β
β
β
βββββββ
β
ββ
βββ
βββββ
βββ
βββββ
β
βββ
β
βββ
β
β
βββββ
β
β
ββββ
β
ββ
ββ
ββ
β
β
β
βββ
β
β
β
β
β
β
ββββ
ββ
β
β
β
β
β
ββ
β
β
β
β
ββββ
β
ββ
ββ
βββ
ββ
β
β
β
β
β
β
β
ββββ
β
βββββ
ββ
β
β
ββ
β
β
β
ββ
ββ
β
ββ
β
β
β
ββββββββββ
β
β
β
β
β
β
βββββ
β
ββββ
β
ββ
β
β
β
ββ
β
βββββ
β
β
β
β
β
ββ
β
ββββββ
ββ
β
β
ββ
β
β
β
β
β
β
βββββββ
β
ββ
MC4R
PAM
SLC30A8
IGFBPL1BICD1
ING3 HNF1AMAP3K15
PDX1
c
0 20 40 60 80
1eβ
071e
β05
1eβ
031e
β01
SLC30A8 progressive geneβlevel analysis
# variants removed
Pβ
valu
e
02
46
log(
Odd
s R
atio
)
d SLC30A8 variants
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Glu2
Gly
@@@@@
p.Thr7Met
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Asn
11His
@@@@@
p.Met17CysfsTer6
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Tyr1
8His
@@@@@
p.Tyr18Cys
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Ala1
9Val
@@@@@
c.71+2T>A
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Lys
34Glu
@@@@@
p.Glu44Asp
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Leu
45Met
@@@@@
p.Gly49Ser
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Cys
53Ty
r
@@@@@
p.His54Leu
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Glu6
1Glnf
sTer
26
@@@@@
p.Glu66Lys
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Leu
74Arg
@@@@@
p.Ile80Met
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Phe
82Le
u
@@@@@
p.Ala87Thr
οΏ½οΏ½οΏ½οΏ½οΏ½
c.271
+1G>A
@@@@@
p.Ser113Asn
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Leu
118P
ro
@@@@@
p.Ser124Leu
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Ser
125L
eu
@@@@@
p.Arg131Trp
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Gly1
35Val
@@@@@
p.His137Pro
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Arg
138T
er
@@@@@
c.419-1G>C
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Glu1
40Ala
@@@@@
p.Ile141Leu
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Cys
150T
yr
@@@@@
p.Trp152Arg
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Val1
57Met
@@@@@
p.Arg165His
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Arg
165C
ys
@@@@@
p.Gln174Ter
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Ala1
75Val
@@@@@
p.Ile179Thr
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Ser
182P
ro
@@@@@
p.Ala188Ser
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Asn
189A
sp
@@@@@
c.572+1G>A
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Cys
200T
er
@@@@@
p.His203Arg
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Asn
211S
er
@@@@@
p.Val214Ile
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Ala2
16Pro
@@@@@
p.Val219Glu
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Gln2
27Te
r
@@@@@
p.Ser230Arg
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Ser
230A
sn
@@@@@
p.Ile237Thr
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Lys
241A
sn
@@@@@
p.Lys241Gln
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Tyr2
44Cys
@@@@@
p.Tyr244His
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Asp
248A
sn
@@@@@
p.Pro249Ser
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Ile2
66Val
@@@@@
p.Ile272Val
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Ile2
72Met
@@@@@
p.Tyr284Ter
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Asp
295G
lu
@@@@@
p.Asp295Asn
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Gly2
96Arg
@@@@@
p.Leu308Gln
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Met3
10Val
@@@@@
p.Gln312Arg
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Val3
19Ile
@@@@@
p.Thr321Ile
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Ser
327T
hrfsT
er55
@@@@@
p.Ser327Thr
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Gln3
28Te
r
@@@@@
p.Val330Phe
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Arg
331G
ln
@@@@@
p.Ala335Asp
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Leu
347P
ro
@@@@@
p.Ile349Phe
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Ile3
49Asn
@@@@@
p.Met351Leu
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Asp
356H
is
@@@@@
p.Pro359Leu
οΏ½οΏ½οΏ½οΏ½οΏ½
p.Pro
367S
er
Case
Control
Contribution
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
a
Bac
kgro
und
Gen
e se
t
0.0
0.2
0.4
0.6
0.8
1.0
ββββββ
β
β
β
β
β
p=0.0012
Per
cent
iles
Monogenic b
β
Bac
kgro
und
Gen
e se
t
0.0
0.2
0.4
0.6
0.8
1.0
ββββββ
β
β
p=0.0061
Drug targets c
Bac
kgro
und
Gen
e se
t
0.0
0.2
0.4
0.6
0.8
1.0
βββββββββ
ββββ
ββββ
βββ
β
βββ
ββ
ββ
ββ
β
p=0.0052
Mouse NIDD d
Bac
kgro
und
Gen
e se
t
0.0
0.2
0.4
0.6
0.8
1.0
p=7.2eβ06
Mouse impairedglucose tolerance e
Bac
kgro
und
Gen
e se
t
0.0
0.2
0.4
0.6
0.8
1.0
ββ
β
β
ββββ
ββ
β
p=0.0088
GWAS genes f
1/ 2
.71/
1.6
11.
62.
7
Odd
s R
atio
T2D drug target effect sizes
GL
P1R
IGF
1R
PP
AR
G
INS
R
Agonists
1/ 2
.71/
1.6
11.
62.
7
Odd
s R
atio
T2D drug target effect sizes
SL
C5A
2
DP
P4
KC
NJ
1
KC
NJ
8
Inhibitors
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
a
0
5
10
15
20
25
30
Imputed GWAS associations
Chromosome
βlo
g 10(p
)
1 2 3 4 5 6 7 8 9 11 13 15 18 22
ββ
ββ
β
β
ββββ
β
β
β
β
β
β
β
β
β
β
ββββ
β
β
β
β
β
β
β
β
β
β
β
β
ββ
ββ
ββ
β
β
ββββ
β
β
βββ
ββ
β
β
β
ββ
ββ
ββ
β
βββ
β
βββββ
ββ
β
ββ
ββ
β
β
ββ
βββ
ββ
β
ββ
β
β
β
ββ
β
β
β
β
β
β
β
β
ββββββ
β
βββ
ββ
β
β
β
β
ββ
ββββ
β
ββ
βββ
β
β
ββ
ββββ
βββ
β
β
β
β
β
β
ββ
β
β
β
βββββ
ββ
β
ββββ
ββ
βββ
β
β
β
β
ββ
β
β
β
β
β
ββ
ββ
β
β
β
β
β
ββ
β
β
ββ
β
β
β
β
β
β
β
β
β
ββ
β
β
ββ
βββ
β
β
β
β
ββ
ββ
ββ
β
β
βββ
β
β
β
β
β
ββ
ββ
β
β
β
ββ
β
β
β
βββ
ββ
βββ
β
ββ
ββ
β
β
β
β
β
βββ
β
β
β
β
ββ
β
ββ
ββ
β
ββ
β
ββ
β
β
βββ
β
ββ
β
βββ
β
β
β
β
βββ
β
β
β
β
ββ
β
β
ββββ
ββ
β
β
β
ββ
β
ββββ
β
ββ
β
β
ββ
ββ
β
β
β
β
βββββββββ
β
ββ
ββββ
β
ββ
β
β
ββ
β
β
βββ
β
ββ
β
ββ
β
β
ββ
βββ
β
βββ
β
ββ
β
β
β
βββ
β
β
β
β
β
β
β
β
β
β
βββ
β
β
β
β
β
ββ
ββ
ββββ
βββ
ββ
ββ
ββ
βββββ
β
β
β
β
ββ
β
β
β
β
βββ
β
β
βββ
β
β
ββ
βββββ
ββ
ββββ
β
β
β
β
ββ
β
β
ββ
β
βββ
β
βββ
β
β
ββββ
ββββ
ββββ
ββ
β
β
ββ
ββ
β
β
β
β
β
β
ββ
β
β
β
ββ
β
β
β
β
β
βββ
β
β
ββ
β
β
β
β
ββ
β
β
β
ββ
β
β
β
β
ββ
ββ
ββ
β
β
βββ
ββββ
β
β
β
β
ββββββββββββββββββ
β
ββ
β
ββββββββ
β
β
ββ
β
ββ
β
βββ
β
ββ
β
β
β
ββ
β
ββ
ββ
ββ
βββ
β
ββ
β
β
βββββ
β
β
β
ββ
β
βββββ
ββ
β
βββ
ββ
βββ
β
β
ββββ
β
β
β
β
ββ
β
β
β
β
β
βββ
β
ββ
βββ
β
β
βββ
ββ
β
β
β
βββββ
β
β
β
β
ββ
β
β
ββββ
βββββ
βββ
β
β
β
ββ
β
β
β
β
ββ
β
β
ββ
ββ
β
ββββ
βββββ
ββ
β
ββ
β
ββ
β
β
β
β
ββ
ββ
β
β
β
β
β
ββ
β
βββ
β
β
β
β
ββ
β
β
β
ββ
β
β
ββ
β
β
ββββ
β
β
β
β
β
β
β
ββ
β
β
βββββββ
β
β
ββ
β
β
βββ
βββ
β
β
ββ
β
β
βββ
β
β
β
β
β
ββ
β
β
β
βββ
ββ
ββ
β
β
β
β
β
βββββββ
βββββββ
β
βββ
βββββββββ
β
β
β
β
β
β
β
βββ
βββ
β
ββ
ββ
βββ
β
β
ββββββββββ
β
β
βββββ
β
β
ββββ
βββ
β
β
β
ββ
βββ
β
β
β
ββ
β
ββββββββββββββββββββββββββ
β
βββββββββ
ββ
ββ
β
βββ
βββ
β
ββ
ββββββ
β
β
β
ββ
β
β
β
β
ββ
β
β
βββ
βββ
ββ
β
ββ
β
β
ββ
β
ββββ
β
β
β
β
βββ
β
β
β
ββ
β
β
ββ
ββ
β
ββ
ββ
β
β
β
β
β
ββ
β
ββ
β
ββ
β
β
ββ
ββββ
β
β
β
β
βββ
β
β
β
β
β
β
βββββ
β
β
β
β
β
β
β
β
β
ββββ
β
β
ββ
β
ββ
ββ
βββ
β
β
β
ββ
β
β
β
β
ββ
β
βββ
βββ
β
β
β
ββ
β
β
βββ
β
β
ββ
β
βββ
β
β
β
β
ββ
β
ββ
β
β
β
β
β
βββ
βββ
βββ
β
ββ
β
β
β
β
β
β
β
β
β
β
ββ
ββ
βββββ
ββ
β
β
β
β
βββ
β
β
β
β
β
βββ
β
β
β
ββββββββββββββββββββββ
β
βββββββββββββ
β
β
ββ
β
βββββ
ββββββββββ
β
β
ββ
β
βββ
ββ
β
β
β
β
β
ββ
ββββ
ββ
β
β
β
β
β
ββ
β
ββββ
ββ
ββ
ββ
β
β
β
ββ
β
ββ
β
ββ
ββ
ββββ
β
ββ
β
β
β
ββ
β
β
ββ
β
β
β
β
β
β
βββ
ββ
β
ββ
ββββββ
βββ
βββββ
β
βββββ
ββ
β
β
ββ
βββ
βββ
ββ
ββββ
β
β
β
β
β
β
ββββ
β
β
β
β
β
ββββ
ββ
ββ
β
ββββ
ββ
β
ββ
ββββββ
ββββββββββββ
β
β
ββ
β
ββ
β
ββ
β
β
ββ
β
β
β
β
β
ββ
ββ
β
ββ
β
βββββββ
β
β
ββ
β
β
ββ
β
ββ
ββββ
β
ββββ
ββ
β
βββ
β
βββββ
β
βββββ
ββββββββ
β
β
β
β
ββ
ββ
ββ
β
β
β
β
ββββ
β
β
ββ
β
ββββ
βββ
β
β
β
β
β
β
β
ββββ
ββββ
β
β
β
ββ
β
ββ
βββ
ββ
β
β
ββ
β
ββ
β
ββββ
βββββ
βββ
ββ
β
ββ
β
βββββββ
β
β
βββ
β
β
ββ
β
ββ
ββ
β
β
βββββββ
βββββ
ββββ
β
ββββ
β
β
ββ
β
β
ββ
β
β
ββ
β
β
β
β
βββ
ββ
βββ
ββ
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
β
ββ
ββ
β
β
β
β
ββ
β
β
ββ
β
β
ββ
βββ
ββ
ββ
ββ
ββ
β
β
β
β
ββ
β
β
β
β
βββ
ββββββββ
β
βββ
β
β
ββ
ββ
ββ
β
β
β
βββββ
β
β
ββββ
ββ
β
βββ
β
β
β
β
β
β
ββ
β
β
βββ
β
β
β
ββββββ
β
β
β
ββ
β
ββ
β
ββββ
β
β
ββ
β
β
β
β
β
β
β
ββ
β
βββ
β
β
β
ββ
β
β
β
βββ
ββ
β
β
β
β
β
βββ
β
ββ
ββ
β
β
β
β
ββ
β
ββββ
β
β
β
β
β
β
β
β
β
β
β
βββββ
β
β
β
βββ
β
β
β
ββ
β
ββ
β
ββ
ββββ
β
βββ
β
ββ
β
β
ββ
ββ
β
ββββββ
β
ββ
β
ββ
β
β
β
β
β
ββ
β
β
ββ
ββ
β
βββ
β
β
β
ββ
β
β
β
ββ
β
ββ
β
β
β
ββ
β
β
β
β
β
ββ
ββ
ββββ
ββ
β
ββ
β
β
ββ
β
ββ
β
β
β
ββββββ
βββ
ββ
β
β
β
ββ
βββββ
β
β
β
βββββββββββββββββ
ββ
β
ββ
β
β
βββ
β
βββββββββ
ββ
β
β
β
β
β
ββ
ββ
β
β
β
β
β
β
β
β
ββ
β
β
β
βββ
β
β
β
βββββββ
ββ
β
β
β
ββ
βββ
β
βββββ
β
β
β
β
β
ββ
β
β
β
βββ
ββββ
ββ
ββββ
β
β
ββ
β
ββ
ββ
β
βββ
βββββββ
β
ββββββββ
β
ββ
β
β
ββ
β
ββ
ββ
ββ
β
β
β
β
β
ββ
ββ
βββββ
β
β
β
β
β
β
βββββββββββββ
β
ββ
β
ββββ
β
ββββββββββββββββββββββββ
ββ
βββ
β
ββββ
β
ββββββββββββ
ββ
ββββ
β
βββββββββββββ
β
βββββ
ββββ
β
βββ
β
β
β
ββ
β
β
ββ
β
β
β
ββ
β
βββ
β
ββ
β
β
β
βββ
β
β
β
ββ
β
β
β
β
β
β
β
βββ
ββ
ββββββ
β
β
β
ββ
β
ββ
β
βββ
ββ
ββ
β
βββββ
β
ββββββ
βββ
β
ββ
β
β
β
βββββββββ
β
β
ββ
β
β
ββ
β
βββ
ββ
β
β
β
β
β
β
β
β
β
ββββββ
β
βββ
ββ
β
β
ββ
β
β
βββ
β
ββ
β
β
ββ
β
β
β
βββ
β
β
β
ββ
ββββ
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
β
ββββ
β
ββ
β
βββ
ββ
β
β
β
β
β
β
ββ
β
ββ
β
βββββββ
β
βββββββ
ββ
β
β
β
βββ
β
βββ
ββββββ
β
βββββ
ββββ
β
βββ
β
βββ
βββ
β
β
β
β
β
β
β
β
β
β
β
β
β
ββ
βββββββββββ
ββ
β
β
β
β
β
β
β
β
βββ
β
β
β
β
β
β
β
β
ββ
βββ
β
β
ββββ
β
β
β
ββ
βββ
β
β
β
β
β
β
ββ
ββββ
β
ββ
ββββββ
β
β
β
ββ
β
ββ
β
β
βββ
ββββ
ββ
β
β
βββ
ββ
ββββ
ββ
ββ
ββ
β
β
ββββ
β
β
β
β
ββ
β
ββ
β
ββββ
β
β
β
β
β
β
ββ
β
β
β
ββ
β
β
β
β
ββ
β
β
β
ββββ
β
βββ
βββββ
β
ββ
β
β
β
ββ
β
ββ
β
β
β
β
β
β
ββ
β
β
β
β
β
ββ
βββ
β
βββ
β
ββ
β
β
β
β
β
ββ
β
β
β
β
βββ
β
ββ
ββ
ββ
β
ββ
β
β
β
β
β
β
ββ
ββ
β
ββ
β
βββ
ββ
β
β
βββ
ββ
β
ββ
ββββ
β
ββ
β
βββββ
ββ
ββ
ββ
β
β
β
ββ
βββββ
β
β
β
ββ
β
β
βββ
β
βββββββ
β
β
β
β
βββ
β
β
β
β
β
β
β
ββ
β
β
β
β
β
ββ
ββ
β
β
β
ββ
βββ
βββββ
ββ
ββ
ββ
β
β
β
β
β
β
ββ
β
β
β
β
ββ
ββ
β
ββββ
β
ββββββββ
ββ
β
ββ
β
ββ
β
β
ββ
ββ
β
β
β
ββ
βββ
ββ
ββ
β
β
ββ
ββββ
βββ
β
β
β
βββ
β
β
βββ
ββββ
β
ββββ
β
ββββββββ
β
β
ββββ
βββ
β
β
β
βββ
βββ
β
β
β
β
β
β
β
β
ββ
β
βββββ
β
ββ
β
β
ββ
ββ
β
βββ
β
ββββ
β
ββ
β
β
βββ
β
ββ
β
ββββββ
β
ββ
β
ββ
β
β
β
β
β
β
β
β
ββ
β
ββββ
β
β
βββ
β
β
ββ
β
β
βββ
β
β
β
β
βββ
βββββ
β
βββ
β
β
β
ββ
ββ
ββ
β
ββ
β
βββ
β
ββββ
ββ
ββ
β
β
β
β
β
β
β
β
β
ββ
ββ
ββββ
βββ
ββββ
β
β
ββ
β
β
β
ββ
β
β
βββ
β
β
ββββ
β
β
β
ββ
β
ββ
β
ββ
βββ
β
β
β
ββ
β
βββ
β
βββββββ
βββ
β
ββββ
β
β
β
β
β
β
ββββ
β
β
β
ββββ
β
ββββ
β
β
ββ
ββ
ββ
β
β
β
ββββββββββββ
β
ββ
β
β
β
β
ββ
βββ
β
ββββββ
β
β
βββββ
βββββββ
ββ
β
β
β
β
β
β
β
β
βββ
β
ββ
ββ
β
ββ
β
β
β
β
β
ββ
βββ
β
ββ
β
βββ
ββ
βββ
β
β
β
β
ββ
β
β
βββ
β
β
β
ββ
β
β
ββ
β
ββ
β
βββ
β
β
β
β
β
ββββββββ
β
β
β
β
β
ββ
β
β
β
ββ
ββ
β
β
β
β
β
βββββ
β
β
β
ββ
βββ
βββ
ββ
β
βββ
β
β
β
β
βββββ
β
ββ
ββ
βββ
β
β
β
ββ
β
ββ
βββββ
β
ββ
βββ
ββ
βββββββ
β
β
β
βββ
β
β
β
β
β
β
β
β
β
β
β
ββ
β
βββ
β
βββ
β
β
β
βββ
β
ββ
β
ββ
β
β
ββββ
ββ
β
ββ
β
ββ
β
β
βββββββ
β
β
β
ββββββ
ββ
β
ββ
ββ
ββ
β
β
β
β
ββββ
ββ
β
β
β
ββ
β
β
βββ
β
ββ
ββ
β
β
β
βββββ
ββ
ββββββββββ
β
β
βββ
β
β
βββ
β
β
β
ββββ
ββ
β
βββββ
β
ββββ
ββ
β
β
ββ
β
ββββ
β
ββ
β
β
β
β
β
β
β
ββ
β
β
ββ
β
ββ
βββ
ββββ
β
β
β
β
ββββ
β
ββ
β
β
β
β
β
β
β
β
β
ββ
βββββ
β
β
β
βββ
β
β
β
β
β
ββ
β
β
β
β
β
ββ
β
β
β
β
ββ
β
β
β
ββ
ββββ
β
β
β
ββ
β
β
β
ββ
β
ββ
βββ
β
β
ββ
ββ
β
β
β
ββ
ββββ
β
β
βββ
β
βββββ
β
βββ
β
ββ
ββ
β
ββββ
β
β
ββ
β
ββ
β
ββ
β
β
ββ
βββ
ββ
ββββ
β
ββ
β
β
β
βββββββ
β
ββββ
β
ββ
ββββββββββββ
β
ββ
β
β
β
β
β
β
β
β
βββ
β
β
ββββ
ββ
β
ββ
β
β
βββ
ββ
ββ
βββ
β
ββ
β
β
β
β
β
β
β
β
β
ββ
β
β
β
ββ
β
β
β
β
ββββ
βββ
β
β
β
ββ
β
βββ
β
βββββ
β
β
β
β
ββββ
β
β
β
β
β
β
β
β
ββ
ββ
β
ββ
β
β
β
βββ
ββ
ββ
β
ββ
β
ββ
β
β
β
β
ββ
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
ββ
β
ββ
ββ
β
β
β
ββ
βββββ
β
β
β
β
ββββββββββ
ββββ
β
β
β
βββ
β
β
β
β
ββββ
ββββ
ββ
β
ββ
β
ββ
β
β
ββ
ββ
ββββ
β
β
β
β
ββ
β
β
βββ
β
βββββββββββββββββββββ
ββ
β
β
βββββ
β
βββββββ
βββ
β
β
β
ββ
βββββββββββββββββ
βββ
β
βββ
β
β
β
ββββββ
ββββ
β
β
ββ
βββββββββββ
ββββ
β
β
ββββββ
β
ββ
ββ
ββ
β
β
β
βββ
β
β
β
βββ
βββββββ
β
βββ
β
ββ
β
β
βββ
β
β
β
β
β
ββ
β
β
β
β
β
β
β
ββ
β
β
ββ
β
βββ
β
βββ
β
β
βββ
ββββ
β
β
β
ββ
β
β
ββ
βββ
β
β
β
β
ββ
ββ
β
β
ββββ
ββ
β
ββββ
β
β
β
β
β
β
ββ
ββ
β
ββ
β
β
ββ
β
ββ
β
ββ
β
ββ
β
ββ
β
βββ
βββ
β
ββ
ββ
β
ββ
β
ββ
ββ
β
β
β
β
β
β
β
β
β
ββ
β
β
βββββ
ββββ
β
β
β
ββββ
ββ
β
β
β
β
β
βββ
β
β
β
β
β
β
β
β
β
β
β
βββββ
β
βββββ
β
βββ
β
ββ
ββ
β
ββ
β
ββ
ββ
β
βββ
β
ββ
β
βββββββββ
βββββ
β
ββ
β
ββ
β
β
β
β
βββ
β
ββ
β
β
β
βββ
β
ββ
β
β
βββββββββββββββββββ
β
β
ββββββββββ
β
β
β
ββ
ββ
β
ββ
β
β
β
β
β
ββ
ββ
β
β
βββ
ββββ
ββββββ
β
β
ββ
β
β
β
ββ
β
β
ββ
βββ
βββ
ββββ
ββββββββ
β
βββββ
ββββ
β
β
βββ
β
ββββββββββ
β
ββ
β
β
β
β
β
β
β
β
β
β
β
βββββ
β
βββββββββββββ
ββ
ββ
β
β
ββ
β
βββββ
β
β
βββββββ
β
β
ββ
ββ
β
β
ββ
βββ
β
βββ
β
βββ
β
β
β
β
ββ
ββ
ββ
β
β
β
β
β
βββ
β
β
βββββ
ββββββββ
β
β
βββββ
β
βββββββββββββ
β
ββββββ
β
β
βββ
β
β
ββ
ββ
β
βββββββββ
β
ββββββββββββββββββββ
β
β
β
ββ
β
β
ββ
ββ
βββ
β
ββ
β
ββββββ
ββ
βββ
β
ββ
ββββββββ
β
βββββ
ββ
β
βββ
β
β
β
β
β
β
β
ββββ
β
ββ
ββ
β
β
β
ββ
β
ββ
ββ
ββ
β
ββββββ
β
βββββββ
ββ
β
ββββββ
ββββββ
β
βββββββ
βββ
βββ
βββ
ββββ
β
β
β
βββ
ββ
β
β
β
β
β
β
βββββ
β
β
β
β
βββββ
β
ββ
βββββ
β
β
β
ββββββ
ββ
β
ββ
β
β
βββ
β
βββ
β
ββ
β
ββββ
β
β
ββ
β
β
ββ
ββ
β
β
β
βββ
β
β
βββ
ββ
β
β
β
β
β
β
β
β
β
β
β
ββββββ
β
β
β
β
ββββ
β
β
β
β
β
βββ
ββ
β
βββ
β
β
β
β
βββ
ββ
β
β
β
β
β
βββ
ββ
β
ββ
βββ
β
βββ
β
β
β
ββ
β
β
β
β
β
ββ
β
ββββ
β
ββ
ββββββ
β
βββ
β
ββββββββββββββ
β
β
β
βββββββββββββ
β
ββββ
β
βββββββββββββββ
β
βββββ
β
ββββββ
β
ββ
β
β
β
β
βββββββββββ
β
ββββββββ
β
β
ββββ
β
βββββ
ββββ
β
β
ββ
β
β
β
ββ
β
β
β
βββ
β
β
βββββ
β
β
β
β
ββ
β
ββ
β
β
β
β
βββ
ββββ
ββ
β
β
β
β
β
β
ββ
ββββ
ββ
β
β
β
βββββ
ββ
ββ
β
β
β
ββ
ββ
β
ββββ
ββββββββ
β
β
βββββ
β
ββ
ββ
β
β
β
β
β
β
ββ
ββ
β
ββ
ββββββββ
β
β
β
ββββ
ββ
ββββ
β
β
β
β
β
ββ
β
β
β
β
β
ββ
ββββ
β
β
β
β
β
β
β
ββββ
β
β
β
β
β
βββββ
β
ββββ
β
ββ
ββ
β
ββ
β
ββ
β
β
β
ββ
β
β
β
β
β
β
β
ββ
β
ββββββ
β
β
ββββ
ββββββββ
β
βββββββββββββββββ
βββββββββββ
β
β
β
β
βββ
ββ
βββ
β
ββ
ββ
β
β
ββββββ
β
β
ββ
ββββ
ββ
β
β
ββββββ
β
ββ
β
βββββ
β
β
ββ
ββ
βββ
βββ
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
βββ
β
ββ
ββ
β
βββ
ββ
β
β
ββ
βββββββ
ββ
β
ββ
β
β
ββ
β
β
βββββ
β
β
ββ
ββββ
ββ
β
β
ββββββββ
βββββββ
ββ
β
β
β
ββ
ββββ
β
ββββ
β
β
βββ
β
ββ
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
ββββ
ββ
β
β
β
ββ
β
βββ
βββ
β
β
β
β
β
β
β
ββ
β
β
βββ
β
β
β
β
ββ
βββ
β
β
β
β
β
ββββ
β
βββ
β
β
β
β
ββ
βββ
β
β
β
βββ
β
β
ββββ
βββββββββββ
ββ
ββββββ
βββββββ
ββ
β
β
βββ
β
β
β
β
β
β
β
β
ββ
β
ββββββββββββββ
β
β
ββ
β
β
β
β
β
β
βββββ
β
ββ
ββ
βββ
βββ
β
β
β
ββ
β
β
β
ββ
β
βββββ
ββ
β
ββββββ
β
β
ββ
ββ
ββββ
β
β
β
ββ
βββ
ββ
β
βββββββββββββ
β
ββ
β
ββ
βββ
ββ
β
βββ
β
β
ββ
ββββββ
ββββββββββ
β
β
β
ββ
β
β
ββββββββββββ
β
βββββ
β
β
ββ
β
β
β
ββ
βββββ
ββββββ
β
β
β
β
β
β
ββ
βββββββ
ββ
β
ββ
β
β
ββ
β
βββ
β
β
ββ
ββ
βββ
β
βββ
β
β
β
β
β
β
β
βββ
β
β
β
ββ
ββ
β
β
ββ
βββββ
β
βββ
β
ββ
β
β
β
ββ
βββββ
β
βββ
β
β
β
β
β
ββ
βββββββ
ββ
ββ
β
ββ
ββ
β
β
βββββ
β
β
β
ββ
ββ
ββ
β
β
β
β
β
ββββ
β
β
ββ
ββ
β
β
βββββ
β
βββββββ
βββ
β
β
ββββ
βββ
βββ
β
β
β
ββ
ββ
β
ββ
β
β
β
β
β
ββ
β
βββ
β
β
β
ββββ
ββ
ββ
β
ββ
β
βββ
ββ
β
β
β
β
β
β
ββ
β
β
β
β
ββ
β
ββ
β
β
ββ
β
β
ββ
β
ββ
β
ββββ
βββ
β
β
ββ
β
βββ
β
β
β
β
β
β
β
β
βββ
β
β
ββ
β
ββββ
β
β
β
β
ββ
β
β
ββ
ββ
ββ
ββ
βββ
β
ββ
β
β
βββ
β
ββββ
β
βββββ
ββ
β
β
β
ββ
β
β
β
β
ββ
ββββ
βββββ
ββ
ββ
β
ββ
βββ
β
β
ββ
ββ
ββββ
β
β
β
β
ββ
β
βββ
ββ
β
β
β
ββ
β
β
β
β
β
β
βββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
βββ
β
ββ
βββ
ββ
ββ
β
β
β
ββ
ββ
β
ββ
β
βββ
β
β
ββ
β
ββββββ
ββ
ββββββββ
β
ββββββββ
β
βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
β
βββββββ
ββ
βββββββββββββββββββββββββββββββββββββββββββββββ
β
β
β
β
β
βββ
ββ
β
ββ
ββ
ββ
β
β
β
β
β
β
ββββββ
β
β
β
β
β
β
β
ββ
β
β
ββ
ββββββ
ββ
ββ
βββ
ββ
βββ
β
β
β
ββ
β
βββ
β
β
β
β
β
ββ
βββ
β
ββββββββββ
ββ
ββ
ββ
β
β
β
β
ββ
β
β
β
β
β
ββ
ββ
ββ
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
ββββ
β
β
β
β
β
β
β
β
ββ
β
βββ
ββββ
ββ
ββββ
β
β
β
β
ββββββ
βββ
β
β
ββ
ββββββ
ββ
β
β
β
βββββ
ββββ
ββββ
β
β
β
β
β
β
β
β
β
β
ββ
ββ
ββ
ββ
β
β
ββ
ββ
βββ
β
β
ββ
βββββ
β
β
ββ
β
β
βββ
ββββ
ββ
β
ββ
β
β
β
β
β
ββ
ββββββββ
β
β
βββ
βββ
β
β
ββ
β
β
β
β
β
ββββββββββββ
β
ββββββββββββββββββββββββββββββββββββ
β
β
ββββββββββββββββββββββββββββ
ββ
ββ
β
β
β
β
β
βββ
β
β
β
β
ββ
ββ
β
β
β
β
β
ββββ
β
β
β
β
β
β
β
βββ
β
β
βββ
ββββββββ
β
ββ
ββββ
β
β
βββ
β
β
ββ
β
β
β
β
β
β
β
β
ββ
β
β
ββ
βββ
β
βββ
ββ
β
β
βββ
β
βββββββββββββββββββββ
β
ββ
βββββ
ββ
ββββ
β
β
β
ββ
β
ββββ
β
β
β
ββββ
β
β
ββ
β
β
ββ
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
ββ
β
ββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
βββ
β
β
β
ββ
β
β
βββ
ββββ
β
β
β
β
β
β
β
β
β
βββββ
β
β
β
β
βββ
β
β
β
β
β
β
β
β
β
β
β
β
ββ
βββ
ββ
β
β
β
ββ
ββ
β
β
β
β
β
ββ
β
β
β
β
β
ββ
βββ
β
β
β
β
β
β
ββ
ββββββββ
ββ
β
βββββββ
ββ
ββ
β
ββ
βββ
β
β
βββββ
β
β
β
β
ββββ
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
ββ
β
ββββ
β
ββ
β
β
βββ
ββ
β
β
ββ
β
β
βββ
β
β
β
β
β
ββββ
ββ
ββ
β
β
β
β
ββ
β
β
ββ
β
βββ
β
ββ
ββ
βββ
β
β
β
β
β
β
β
ββ
β
β
β
β
β
ββ
β
β
β
β
β
β
βββββββ
β
βββ
β
β
β
β
β
ββ
β
β
βββ
β
ββ
β
β
βββ
ββββββββ
β
ββ
ββββββ
β
ββββ
β
βββ
ββ
β
ββ
β
β
β
β
βββ
β
β
ββ
ββ
ββββ
β
ββ
β
βββ
ββ
ββββββββ
β
ββββββββ
β
ββββββββββββββ
ββ
ββββββββββ
ββ
βββ
β
ββ
β
βββββββ
β
βββββ
β
β
β
ββ
β
ββββββ
β
ββ
β
βββ
β
βββ
β
ββ
ββ
β
β
βββ
β
ββββββββββ
β
βββββ
ββ
β
ββ
ββ
ββ
β
βββ
β
β
β
βββ
β
ββ
ββββ
β
β
β
β
βββ
β
βββ
β
β
ββ
β
β
β
ββββ
β
βββββ
β
β
β
β
ββββββ
ββ
βββ
β
ββ
β
ββ
ββ
β
β
ββ
ββββ
β
βββββ
β
ββ
β
β
ββ
ββ
βββββ
β
β
ββ
ββ
βββ
ββ
ββ
ββ
β
β
β
β
β
ββ
ββ
β
β
β
βββ
β
β
ββ
β
β
β
ββ
ββ
ββ
β
β
ββββββ
β
β
β
βββ
β
β
β
ββ
ββ
βββ
β
βββββ
β
β
β
β
β
β
ββ
ββββββββ
β
ββββββ
β
ββ
ββ
β
β
β
ββββ
βββββββ
β
ββββ
β
ββββ
β
βββββββββββββββββ
ββββββββ
β
β
ββ
β
ββ
β
ββββββ
β
ββ
β
β
β
β
βββ
βββ
ββ
β
β
β
βββββ
ββ
β
β
ββββββ
β
β
β
β
β
β
ββ
β
β
β
ββ
β
β
β
ββ
β
β
β
ββ
β
βββ
β
ββ
ββ
ββ
β
ββ
β
β
β
β
β
β
βββ
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
βββ
ββ
ββββ
β
β
βββ
β
β
β
β
βββ
β
β
ββ
β
β
ββββ
β
β
ββββ
βββββ
ββ
β
β
β
β
β
ββββ
βββ
β
β
β
ββ
β
β
β
β
ββ
ββ
βββββ
β
ββββ
ββ
β
β
ββ
β
ββ
β
ββ
β
βββββββββ
ββ
β
ββ
ββ
βββββββββ
β
ββββββββ
β
ββββββββββββββββββββ
β
βββ
β
ββββ
βββ
β
β
β
ββ
β
β
β
ββ
β
β
ββ
β
β
βββ
β
β
β
β
β
ββ
β
β
β
β
β
β
β
ββ
β
β
ββ
β
β
ββ
ββββ
β
β
β
β
β
β
ββ
β
βββ
ββ
β
ββββββ
β
ββββ
β
ββ
ββ
β
β
ββββ
β
β
ββ
ββββ
β
ββ
ββ
ββ
β
βββ
ββ
β
β
β
ββ
β
β
β
β
ββ
ββ
ββ
βββββ
β
β
β
βββ
β
ββββ
ββ
β
ββ
β
β
β
β
β
β
β
β
ββ
βββββ
βββ
ββββ
β
βββ
β
ββ
β
βββ
ββ
ββ
ββ
β
β
β
β
β
ββ
ββ
β
β
βββ
ββ
ββ
β
β
βββ
β
ββ
β
β
β
β
βββ
β
β
βββ
ββββββββββ
β
β
βββ
β
ββββ
β
β
βββββββββββββββββ
β
β
β
βββββ
ββ
β
β
β
β
ββ
β
β
β
β
β
β
β
ββ
ββββ
β
β
β
β
ββββββββββ
β
β
β
β
β
β
β
ββ
ββ
β
β
β
β
βββββββββ
β
β
ββ
β
β
β
β
ββ
ββ
βββ
β
ββ
ββ
β
βββ
β
β
β
β
β
β
ββ
βββ
βββββββ
β
β
β
β
β
β
β
β
βββ
β
ββ
β
ββββββ
β
β
ββ
β
ββ
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
ββ
ββ
β
ββ
β
βββββ
β
ββ
β
β
βββββ
βββ
β
β
ββ
β
ββ
ββ
β
β
ββββββββ
ββ
βββ
βββββ
β
β
β
ββββ
ββββ
ββ
β
β
β
βββ
β
β
ββ
β
β
β
βββ
β
β
β
β
β
β
βββ
ββ
β
β
β
ββ
β
β
β
βββββ
β
β
ββ
ββββββ
β
β
ββ
ββ
β
ββ
ββ
β
β
ββ
ββ
β
β
ββ
ββ
β
β
β
β
β
βββ
β
β
ββ
β
β
β
ββ
βββ
ββ
β
β
βββ
β
β
ββ
βββββ
β
β
βββ
β
β
β
β
β
β
ββ
β
β
ββββββ
β
ββββββ
β
ββ
β
β
βββββ
β
β
ββ
ββ
ββ
β
ββββββ
βββ
β
β
ββ
ββ
βββ
β
β
β
βββ
ββ
β
β
βββ
β
β
β
β
βββ
β
βββββ
βββ
β
ββ
β
β
β
ββ
β
β
β
ββ
β
ββββββββ
β
β
β
ββ
βββ
β
β
ββ
β
β
ββ
ββββββ
β
ββ
β
β
ββ
ββ
ββ
βββ
βββββ
β
ββ
ββ
ββ
β
ββββ
β
β
β
ββββ
β
β
ββββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
ββββ
β
β
β
β
β
βββββ
β
β
ββ
ββββ
ββββββββββ
β
ββββ
ββ
β
ββ
β
ββ
β
βββ
ββββββββββββββββββ
β
β
β
ββ
β
ββ
β
β
βββββ
βββββββ
ββ
β
β
β
β
β
β
βββ
β
β
β
β
ββββ
β
β
β
βββββ
βββ
β
β
ββ
β
β
ββ
ββ
β
β
β
β
β
β
ββ
βββ
β
β
β
βββ
ββ
β
β
ββ
β
β
β
β
β
β
β
β
β
ββ
β
βββ
β
βββββββ
ββ
β
β
βββ
ββββββββββββββββββββββββββββββββ
β
β
βββ
β
β
β
ββ
ββ
β
β
ββ
β
β
βββ
βββββββ
β
ββ
β
β
β
β
β
ββββ
β
ββ
β
β
β
ββ
βββ
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
βββ
βββββ
β
βββ
ββ
ββ
βββ
ββ
β
β
β
β
β
β
β
β
β
βββββ
β
ββ
β
β
β
ββ
β
ββ
β
β
β
ββ
β
ββββ
β
ββ
β
β
β
β
ββ
β
β
β
ββ
β
βββ
ββββ
β
β
β
βββ
β
β
β
β
βββ
β
ββ
β
ββββ
β
βββββ
ββ
β
β
β
ββ
β
β
β
β
ββ
ββ
βββ
ββ
βββ
β
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
βββββ
β
ββββ
ββ
β
β
β
β
β
β
β
β
β
ββ
ββββ
β
ββ
β
ββ
ββ
β
β
β
β
β
ββ
β
β
β
β
β
ββ
ββ
β
β
β
ββ
β
βββ
β
β
ββ
ββββ
β
β
β
β
β
β
ββ
ββ
β
β
β
β
β
βββββββββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
βββ
β
β
β
ββ
β
ββ
β
ββ
ββ
ββ
β
ββββββββββββββββββββββββββββββββββββββ
ββββββ
β
β
β
βββββββββββββ
β
βββ
β
ββ
β
ββββββββββββββββββ
β
β
βββ
ββ
β
βββ
β
β
β
ββ
β
β
β
βββββ
β
β
β
ββββββββββ
ββ
β
β
β
β
β
β
β
β
βββ
β
β
β
β
βββ
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
βββ
ββ
β
ββ
β
ββββββ
β
ββ
ββ
β
βββ
β
ββ
β
β
ββ
ββ
β
β
β
β
β
ββ
β
ββ
ββ
β
βββ
ββ
βββββββ
β
ββββββ
ββ
β
β
β
ββ
β
β
ββββββ
βββ
β
ββ
β
βββββββββββββββββββββββββββββββββ
β
βββββ
ββ
ββ
β
β
β
ββ
β
β
βββ
β
ββ
β
ββ
ββ
βββ
β
β
ββ
β
ββ
β
β
ββ
ββ
ββ
β
ββ
β
β
β
β
β
ββ
β
β
β
ββββββββββββββββ
β
β
β
β
βββ
β
ββ
β
β
β
ββ
ββ
βββ
β
β
ββ
ββ
βββ
ββ
β
β
ββ
βββ
βββββ
β
ββ
β
β
β
β
ββ
β
β
β
β
β
β
β
ββ
βββ
ββ
β
ββ
β
β
β
β
β
β
βββ
β
βββ
ββ
β
ββ
β
β
β
β
β
ββ
β
β
βββ
β
βββ
βββ
β
β
ββ
β
β
β
βββ
ββ
β
β
β
β
βββ
ββ
β
ββ
β
β
β
β
β
β
βββ
ββ
β
β
β
ββββ
β
β
β
ββ
β
β
β
β
β
ββ
βββββ
β
ββ
β
β
β
ββ
β
β
β
ββββββ
ββ
β
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
βββββ
β
β
β
ββ
βββ
ββ
β
β
β
β
ββ
ββ
ββββ
βββ
ββββ
ββββββ
βββ
ββ
ββ
β
βββ
β
ββ
β
β
β
β
β
β
β
β
ββββββββ
β
β
ββ
β
ββ
β
β
ββ
βββ
β
ββ
β
β
ββ
ββββ
β
β
β
β
ββ
ββββ
β
β
β
ββββ
β
ββ
β
βββ
ββ
ββ
β
βββ
β
β
ββ
βββ
ββ
β
β
ββ
βββββββ
β
ββ
β
βββ
ββ
β
βββ
β
β
β
βββ
β
βββββ
β
β
ββ
ββββ
β
βββ
βββββββ
β
β
β
β
β
β
β
βββ
β
βββ
β
ββ
ββ
β
β
β
ββ
ββ
ββ
ββ
β
β
β
ββ
βββββ
β
βββββ
ββ
ββ
β
β
ββ
ββ
β
ββ
β
ββββ
βββ
ββ
βββ
βββ
ββ
β
βββ
β
β
ββββ
β
ββ
βββ
β
β
β
β
βββ
β
β
ββ
β
βββ
β
β
ββ
β
β
β
β
β
β
β
β
ββ
β
βββββββ
β
β
β
ββ
β
β
βββββ
β
β
ββ
β
β
β
β
β
β
ββ
β
β
β
β
β
β
ββββββ
β
βββ
βββ
β
β
β
ββββ
β
β
β
ββ
ββ
β
β
β
β
ββ
β
β
β
β
ββ
ββ
ββ
ββββββββ
βββββββββ
ββββββββ
ββββββββββββββββββββββββββββββββ
β
β
βββββββ
β
βββ
ββββββββββββββ
β
βββββββββ
β
β
ββββββββ
βββ
ββββ
βββ
βββββ
ββ
β
β
β
β
β
β
β
βββ
ββ
β
ββ
ββ
β
β
β
β
β
ββββββββ
ββββ
β
βββββββββββ
ββ
βββββ
β
β
β
β
ββββ
β
ββ
ββ
βββ
ββ
β
β
ββ
ββ
β
ββ
β
β
β
β
ββ
β
β
ββββ
β
ββββ
β
β
β
β
β
ββ
ββββ
β
β
β
β
ββ
ββ
ββ
ββ
ββ
ββ
β
β
β
β
β
β
β
ββββ
β
β
β
ββ
β
β
β
ββ
βββ
β
ββ
ββ
ββ
β
β
βββββ
β
βββ
ββββ
ββ
β
ββ
β
β
ββ
β
β
ββ
ββ
ββββββ
β
βββ
ββ
ββ
ββ
β
ββ
βββ
β
ββ
βββ
β
β
β
β
β
βββ
ββ
β
ββββ
ββ
β
β
β
β
β
β
β
β
βββ
β
β
β
β
β
β
βββ
ββ
ββ
β
β
ββββ
β
β
β
β
βββββ
ββββ
β
βββββββ
ββ
ββββ
ββ
β
β
β
β
β
ββ
β
β
β
βββββ
β
βββββ
β
βββ
β
ββ
ββ
ββ
ββ
β
β
βββ
β
β
β
ββββ
ββ
ββ
ββββ
βββ
ββ
β
β
ββ
ββ
β
β
β
β
β
β
β
ββ
β
βββ
ββββ
ββ
ββ
β
β
β
β
βββ
β
ββ
βββ
β
βββ
β
ββ
ββ
β
β
β
β
β
β
β
β
β
βββ
β
βββ
β
β
β
βββ
β
ββ
ββ
β
ββββ
β
β
β
β
β
β
ββ
β
β
βββββ
β
β
β
ββ
β
β
ββ
β
βββ
β
β
β
ββ
β
ββββββββββββ
β
β
βββ
βββ
ββ
ββ
βββββ
β
βββ
β
β
β
β
β
β
β
ββ
ββ
ββ
βββ
β
ββ
β
β
β
βββββ
ββ
β
βββ
βββββββ
ββ
ββ
β
βββ
ββββ
β
βββββ
β
β
β
ββ
β
ββ
ββ
β
β
β
β
β
β
β
βββ
ββ
ββ
βββ
β
βββ
β
β
ββ
βββ
β
βββββ
β
ββ
β
β
ββββ
ββ
ββ
β
βββ
ββ
β
β
βββ
ββ
ββ
β
β
β
βββ
β
ββ
βββ
βββ
β
βββ
β
ββββ
β
ββ
βββββ
βββ
ββ
ββββββ
β
βββ
β
ββ
β
β
β
ββ
β
β
β
β
β
ββ
β
ββ
β
β
ββββ
β
β
ββ
β
β
β
ββββ
βββββ
β
β
β
βββ
ββ
β
β
β
β
ββ
βββ
ββ
β
β
ββββββ
β
ββ
β
βββ
β
β
β
β
ββ
β
β
β
β
ββ
β
ββ
β
ββ
β
β
βββ
β
β
β
β
ββ
βββ
β
ββ
β
ββ
β
ββ
ββ
β
β
β
β
ββ
β
β
β
β
β
β
β
ββ
β
β
β
βββ
β
β
β
β
βββ
β
β
βββ
βββ
β
βββ
β
βββ
β
β
βββ
β
β
β
β
β
ββ
β
ββ
β
β
β
βββββββ
β
β
β
β
β
β
β
β
ββ
ββ
β
ββ
β
βββ
β
β
βββ
β
β
β
β
β
β
β
β
βββββββ
ββ
β
β
ββ
β
β
ββ
β
β
β
β
β
β
β
β
ββ
β
β
βββ
β
β
ββ
β
β
β
β
β
β
β
β
β
β
βββ
β
β
ββ
β
βββ
β
βββ
β
ββ
ββββ
β
βββββββ
βββ
ββββ
ββββ
β
ββ
β
β
β
β
ββ
ββ
ββββ
ββ
β
βββ
β
ββ
β
ββ
β
ββ
ββ
β
β
β
ββ
ββββ
βββ
ββ
ββββββββββββ
ββ
βββββββββββββββββ
β
ββββ
β
β
βββββββ
β
ββ
β
ββ
β
βββ
ββββ
β
β
β
β
β
β
β
β
β
β
βββ
β
ββ
β
β
β
β
β
βββ
ββ
βββ
β
ββ
βββ
β
β
β
β
β
β
ββ
ββ
β
ββ
βββ
β
β
β
β
β
β
β
ββ
ββββββββββ
ββ
ββββ
ββ
β
ββ
β
βββ
β
β
β
ββββ
β
ββββ
β
β
β
β
β
β
βββ
β
β
ββ
β
ββ
β
β
β
β
β
β
β
ββ
βββ
β
β
ββ
ββ
β
β
β
β
βββ
β
β
β
β
βββ
β
βββ
β
βββββ
β
ββ
ββ
β
βββ
ββ
β
ββ
ββ
ββ
ββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
ββ
β
ββ
ββ
β
ββ
ββββ
ββββ
ββ
βββ
β
ββ
β
βββ
β
βββ
βββ
ββ
β
ββββ
β
βββ
β
ββ
β
β
β
ββ
β
βββ
β
β
β
β
β
β
β
ββ
β
β
ββ
β
β
ββ
ββ
βββββββββββ
β
β
βββ
β
β
βββ
β
β
ββ
β
β
β
ββ
β
βββ
β
β
ββ
ββ
β
ββ
βββββββββββββ
ββ
βββββ
β
βββ
β
ββββ
βββ
β
βββ
β
ββ
βββ
ββββββ
βββ
ββββ
β
ββ
β
β
βββ
ββ
ββββ
β
ββ
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
ββ
β
β
β
β
ββββ
β
β
β
ββ
β
β
β
ββββ
β
βββ
β
β
ββ
β
ββ
β
β
β
β
β
β
β
βββββ
β
ββ
β
βββ
β
ββ
β
β
ββββββββ
β
β
ββ
ββββ
βββ
β
β
β
β
ββ
β
βββββ
ββββ
βββ
β
ββ
βββββββ
β
βββ
ββ
ββ
ββββ
ββ
β
ββ
βββ
β
β
ββββββ
β
β
βββ
β
βββββ
β
β
βββ
β
β
β
β
β
β
ββ
β
β
β
ββββββ
β
ββ
β
β
βββ
β
β
β
βββ
β
β
β
β
β
β
β
β
β
β
ββ
βββ
β
β
β
β
ββββββββββββββ
βββ
β
ββββββββββββ
β
β
β
ββββ
β
β
β
ββ
β
β
βββ
β
β
β
β
β
β
ββ
ββββ
β
β
β
ββββ
β
β
ββ
ββ
β
β
βββββ
ββ
β
β
β
β
ββ
ββ
β
β
β
β
β
ββ
βββββββ
βββ
ββ
β
β
β
ββ
β
βββββ
β
β
β
ββ
β
βββββ
β
β
β
β
β
βββ
β
β
β
β
ββ
β
ββββββββ
βββ
βββ
ββββββ
βββ
ββββββββ
β
ββββ
ββ
βββββ
β
β
βββ
β
β
β
ββ
β
β
β
ββ
ββββββ
ββ
β
β
βββ
β
β
β
βββ
βββ
β
ββββ
βββ
β
β
ββ
β
ββ
ββ
β
ββββ
ββ
ββ
β
β
β
ββ
β
ββββ
β
ββ
βββββ
β
β
ββ
ββ
β
β
ββ
β
ββββ
βββββ
β
β
β
ββ
ββ
ββ
β
β
β
ββ
ββ
ββ
β
ββ
ββ
β
ββ
β
βββ
β
ββ
β
ββ
β
ββ
β
β
β
βββ
ββ
ββββββββ
β
ββββ
β
β
ββ
β
ββββ
ββ
β
β
ββ
ββ
βββ
β
β
ββ
ββ
β
β
β
β
βββββ
β
ββ
ββ
βββ
βββ
β
β
β
βββ
β
β
β
β
βββ
β
βββ
β
βββ
β
ββ
ββ
ββ
β
βββββ
β
β
ββββ
βββ
β
ββ
β
ββββββββ
β
βββ
βββ
β
β
βββββ
β
β
β
β
β
ββ
ββ
ββ
β
β
ββ
ββββ
β
β
ββ
β
β
ββ
β
ββ
β
β
β
β
ββ
βββ
ββ
ββ
β
βββββ
β
β
βββ
ββ
ββ
β
ββ
β
ββ
βββββ
βββ
β
ββ
β
ββββββ
β
ββββ
ββ
β
βββ
β
β
β
βββ
β
β
βββ
β
ββββ
βββ
β
β
ββββββββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
ββ
βββββββ
β
β
ββ
β
β
β
β
β
βββ
ββ
β
βββββββ
β
β
β
β
ββ
ββββ
ββ
β
β
β
β
βββ
β
β
β
ββ
β
β
ββββ
ββ
β
βββββ
β
ββ
β
βββ
β
β
ββββ
β
β
β
β
ββ
β
ββ
ββββββ
β
β
β
β
β
βββ
ββ
β
β
ββ
β
β
β
β
β
β
β
ββ
βββ
β
β
βββββ
β
ββ
βββ
β
ββ
β
ββββββ
β
ββββββββββββββββ
β
β
βββ
ββββ
β
βββ
β
β
β
βββ
ββ
β
ββ
β
β
β
ββββ
β
ββ
β
βββββ
ββββ
β
βββ
ββ
β
ββ
β
β
ββ
β
ββ
β
ββββ
β
ββββ
βββββ
β
βββ
ββββ
βββ
β
β
β
β
β
βββ
β
ββ
ββ
β
β
ββ
ββ
βββ
β
β
β
β
ββ
β
ββ
βββ
β
β
ββ
β
β
β
ββ
ββ
β
ββββββ
β
β
β
βββ
βββββ
β
ββ
β
βββ
βββββββββββ
β
βββββββ
ββ
ββββ
ββββ
βββ
β
ββ
β
β
ββββ
βββββββββββββ
β
β
βββ
β
β
ββββ
β
β
ββ
β
ββ
βββ
β
ββ
β
β
β
β
ββ
βββ
β
β
ββ
βββ
β
β
β
β
ββ
βββ
ββββ
β
ββ
β
ββ
β
ββ
ββ
β
β
β
β
ββ
β
β
β
βββ
βββββββ
β
ββ
β
ββ
β
β
βββ
ββββ
β
ββ
β
β
β
β
ββ
β
β
ββ
β
β
ββββββ
β
ββββ
ββ
β
ββ
β
β
βββ
ββ
β
ββ
β
ββ
βββ
ββ
β
ββ
ββ
β
β
β
β
β
β
β
β
β
ββ
β
β
ββ
ββββ
β
β
β
β
β
ββ
βββββ
β
β
β
β
β
β
βββββ
β
β
β
βββ
ββ
β
ββ
β
β
β
βββββ
β
β
β
β
βββββββ
β
β
β
β
β
β
β
β
β
ββ
ββ
β
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
ββ
ββ
β
β
βββ
β
β
βββ
β
β
β
β
β
β
ββββββββ
β
β
β
β
β
ββ
β
β
β
ββ
ββ
β
βββββ
βββ
βββ
ββ
β
βββ
β
β
β
β
βββββββββ
ββ
β
ββ
ββ
β
β
β
β
β
ββ
ββ
ββββ
β
ββ
β
β
β
β
β
β
β
β
βββ
β
ββ
βββββββ
βββ
ββ
βββ
β
β
βββ
ββ
β
β
β
ββ
β
β
β
β
β
βββ
β
β
β
β
βββ
ββββ
β
ββ
β
βββ
ββ
β
βββββ
βββ
β
β
β
ββββ
β
β
β
ββ
βββββ
β
β
β
ββ
β
β
βββ
β
β
βββ
β
ββββββ
β
β
β
β
β
βββββββ
β
ββ
β
ββ
β
β
βββ
β
β
β
β
β
ββ
β
ββββββ
β
β
ββ
ββ
β
β
β
β
β
βββ
ββββ
β
ββ
ββ
β
ββ
β
ββ
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
βββ
ββ
βββ
ββ
βββββ
β
ββββββββββββ
β
ββ
ββββββ
βββ
ββ
β
β
β
ββββ
β
β
β
β
β
ββ
ββ
β
ββ
β
β
βββ
β
β
β
β
ββ
βββ
β
β
ββ
ββ
β
β
β
βββ
ββ
β
βββ
ββ
βββ
β
β
β
β
βββ
β
β
β
β
βββ
β
β
ββ
βββ
β
βββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
β
ββ
ββ
ββ
β
β
βββ
ββ
β
βββ
β
ββ
β
ββ
β
β
β
β
β
β
β
ββ
β
β
ββ
β
β
β
β
β
ββ
ββ
ββ
βββ
β
βββ
β
β
β
βββββββ
β
ββββ
β
βββ
β
βββββββ
β
β
βββββββββββ
βββ
ββ
β
β
β
β
β
β
β
ββββ
β
β
ββ
β
ββ
β
β
βββ
β
β
ββββ
ββββββ
β
β
β
β
ββ
β
β
β
β
β
β
β
ββ
ββ
β
β
ββ
β
β
ββ
βββ
β
β
ββ
βββ
β
ββ
ββ
β
β
ββ
β
βββ
ββββ
β
ββ
β
β
ββ
βββ
β
βββ
β
β
β
ββ
β
β
ββββ
ββ
β
β
β
β
β
ββ
β
ββ
β
ββββ
β
β
ββ
β
β
ββ
β
βββ
ββ
β
β
β
β
β
βββ
β
βββ
β
β
βββ
β
β
ββ
βββ
β
ββ
β
ββ
ββ
βββ
ββ
β
β
ββ
βββ
ββ
β
β
ββ
ββ
β
βββ
βββ
β
β
β
βββ
β
β
β
ββ
β
ββ
ββ
β
ββ
ββ
ββ
βββ
β
βββ
ββ
ββββ
βββ
ββ
ββββ
β
β
β
β
β
β
ββββ
β
β
β
β
β
βββ
βββ
ββ
ββ
β
ββ
β
βββ
β
ββ
β
β
β
β
β
β
ββ
β
ββββ
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
βββ
β
β
β
β
β
ββ
β
ββ
ββ
β
β
β
β
ββ
β
β
β
ββββββ
β
β
β
β
β
ββ
βββ
β
β
βββ
β
β
β
ββ
β
β
ββ
β
β
β
β
ββ
β
β
β
ββ
βββ
β
ββ
β
β
β
β
β
βββ
βββ
β
β
β
β
β
ββ
ββ
βββ
β
βββ
β
β
ββ
β
ββ
β
ββ
ββ
ββ
ββ
βββ
ββ
ββ
ββ
βββ
β
β
β
β
ββ
ββ
βββ
β
β
β
ββ
β
β
β
β
β
ββββββββ
ββ
βββ
β
βββββββ
ββ
β
β
β
ββ
β
β
β
ββ
β
βββ
βββ
β
β
β
β
β
β
βββββ
β
β
β
β
β
ββ
ββ
βββββββ
ββ
β
βββββββ
β
ββββββ
β
βββββββββββββ
β
ββββββ
β
βββββ
β
βββ
β
βββ
β
βββ
β
βββββββ
β
βββββ
β
β
β
β
ββ
βββββββ
ββ
ββββ
β
ββββ
β
β
β
ββββββ
ββ
ββ
ββ
ββββββββββββ
βββββββ
βββ
ββ
ββ
β
ββββ
β
ββ
β
β
β
β
β
ββ
ββ
ββ
β
β
ββ
β
βββ
ββ
β
β
β
β
β
ββ
β
β
ββββ
β
β
β
β
ββ
β
β
β
βββ
β
βββ
β
ββ
β
ββββ
ββ
β
β
ββ
ββββ
β
ββ
β
ββββ
β
β
ββ
βββββββββββ
β
β
β
ββ
β
β
ββββ
β
β
βββββ
β
β
βββ
β
βββββ
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
ββ
ββ
β
β
ββ
ββ
β
ββ
β
ββ
β
ββ
β
β
β
ββ
βββ
β
β
β
β
β
β
β
β
β
β
βββ
ββ
βββββ
β
ββ
ββ
β
β
β
ββ
β
β
β
β
β
ββ
β
ββββββ
ββ
β
β
β
ββ
β
β
β
ββ
β
β
β
β
β
β
β
β
β
ββββββ
ββ
ββββββ
β
β
β
β
β
ββ
β
β
β
β
β
βββββββ
ββ
ββ
ββ
ββ
β
β
β
β
β
ββββ
β
βββ
βββ
β
β
β
β
ββ
β
β
β
βββ
ββ
β
βββ
βββ
β
ββ
β
βββ
β
β
ββ
ββ
β
ββ
ββ
βββ
β
β
β
ββ
ββββ
βββ
β
βββ
β
ββ
β
β
β
β
ββ
β
β
βββ
β
β
β
ββ
β
β
β
β
β
β
β
β
βββ
β
ββββ
βββ
β
βββ
ββ
β
βββ
β
β
β
ββ
βββ
βββββ
ββ
βββ
ββ
β
β
β
ββ
β
βββββ
β
β
β
βββββ
ββ
β
ββ
β
ββ
ββ
β
β
β
β
β
β
β
βββ
β
ββ
β
ββ
β
βββββ
β
β
β
β
β
β
β
β
β
ββ
β
β
β
βββββ
β
β
ββ
β
β
β
ββ
β
ββ
ββ
β
β
ββββ
βββ
β
ββββ
β
ββ
ββ
β
βββββββββ
β
β
β
β
β
β
β
βββββββ
β
βββ
ββββ
β
β
β
β
ββββ
β
ββ
β
β
βββ
β
β
β
β
β
βββ
βββ
β
β
ββ
ββ
β
β
β
β
ββ
ββ
β
β
β
βββ
β
β
ββ
ββ
β
β
β
ββββ
β
ββ
β
ββ
ββ
ββ
β
βββ
βββ
ββ
β
β
ββ
β
β
β
ββ
ββ
β
ββ
β
βββ
β
β
βββββ
β
ββ
β
ββ
ββ
ββββ
β
β
β
β
β
ββ
β
β
β
β
ββ
β
ββββββββ
ββ
βββββ
ββ
ββββββββββ
β
βββββββββββββββ
βββββββββ
β
β
β
β
β
ββ
β
βββββββ
β
β
β
β
β
ββββββββββββββββββββββββββββ
ββ
β
β
ββ
β
β
β
β
βββββ
ββ
β
β
ββββββ
βββ
β
β
β
ββββ
ββ
β
βββ
β
βββ
ββ
β
β
β
ββββ
ββ
βββ
βββ
ββ
ββ
β
βββ
β
β
βββ
ββ
ββ
β
βββ
β
βββββ
ββββββββββ
ββ
ββββ
β
β
β
ββββββββ
β
βββ
β
βββ
ββ
β
β
βββ
β
ββ
βββ
β
ββ
β
β
ββββ
β
β
β
ββββ
βββ
βββ
β
β
β
ββ
β
ββ
β
ββββ
ββββββββ
βββ
ββ
ββ
β
βββ
βββ
β
β
ββ
β
ββ
βββ
β
β
βββ
β
β
β
ββ
β
β
β
ββ
β
ββββ
β
β
β
ββ
β
β
β
β
β
β
βββ
β
βββ
ββ
β
β
ββ
β
β
ββ
β
ββ
ββ
β
β
β
β
β
β
ββ
β
β
β
β
β
ββββββββββ
ββ
ββ
β
ββ
β
βββ
β
β
ββ
β
βββββ
ββ
β
β
β
β
ββ
β
β
β
β
β
β
ββ
ββ
β
β
ββββ
β
β
βββ
β
β
β
ββ
β
ββββ
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
β
ββ
βββββββββ
β
ββ
ββ
β
β
β
βββ
ββ
β
β
ββ
ββ
β
β
β
ββ
β
β
ββ
β
β
ββ
β
ββ
β
β
β
β
β
β
β
β
ββββββββ
ββββ
β
βββ
βββ
β
β
β
β
β
ββ
β
ββ
β
ββ
βββ
ββ
β
ββββ
β
β
β
ββ
ββ
ββ
ββ
ββββββ
β
ββ
β
β
β
ββ
β
β
β
β
ββ
β
ββ
β
ββ
βββ
β
β
β
β
β
β
β
β
ββ
ββ
ββ
ββ
ββ
ββ
β
β
ββ
β
βββ
β
ββ
ββ
ββββ
β
β
β
ββ
βββ
β
ββ
β
β
β
βββ
ββ
β
ββββββ
β
β
β
β
ββββββββ
β
β
β
β
β
ββ
ββββ
β
β
ββ
β
β
βββ
β
β
ββ
β
ββ
β
β
ββββ
β
β
βββ
β
β
β
ββ
βββββ
βββ
β
β
β
β
β
β
β
β
β
ββ
ββ
β
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
βββ
βββ
β
ββ
βββ
β
β
β
ββ
ββ
β
ββ
ββ
β
β
β
β
β
β
β
ββββββββββββββββββββ
βββ
ββ
β
β
βββββββββββββββ
β
β
β
ββ
βββββββ
β
β
ββ
β
β
β
ββ
ββ
βββ
β
ββββ
β
β
β
β
β
ββββ
βββββββββββββββββββββββββββ
ββ
ββ
β
β
ββββ
βββββββββββ
β
β
ββ
β
β
ββ
β
β
β
β
β
β
ββββ
β
β
β
β
β
β
β
β
β
ββ
βββ
β
β
β
β
βββ
ββ
βββββββββββ
β
β
ββ
β
β
β
β
β
β
β
βββ
β
β
β
ββ
β
β
ββ
β
ββ
β
βββ
β
βββ
βββββ
ββ
β
β
β
β
ββ
β
βββ
β
ββ
ββ
β
β
ββ
β
β
β
ββ
β
β
βββ
β
β
β
ββ
β
βββ
β
β
β
β
ββ
β
β
β
β
β
β
β
β
βββ
ββ
β
β
β
β
β
β
ββ
ββββ
β
ββ
ββ
β
β
β
β
ββ
β
ββββ
β
β
β
β
β
ββ
ββ
ββ
β
β
β
β
β
ββ
β
βββ
β
βββ
βββ
β
ββ
β
β
βββββ
β
β
ββ
β
β
β
β
β
β
β
β
β
ββββββββ
β
βββ
β
ββ
β
ββββ
β
ββββββ
β
β
β
ββ
ββ
β
β
βββ
β
β
β
β
β
ββ
ββ
β
ββ
ββ
βββ
ββ
ββ
β
β
β
ββ
β
β
β
ββ
β
βββββ
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
βββββββββββ
β
β
ββ
β
ββ
βββββ
β
βββ
ββ
βββββββ
β
β
βββ
β
β
β
β
ββ
β
β
β
β
ββ
ββββ
β
βββ
β
ββ
β
ββ
βββββ
β
β
β
ββ
β
ββββ
β
β
β
ββ
β
β
β
β
ββ
βββββββββ
ββ
ββ
ββ
βββ
ββ
β
ββ
β
ββ
β
β
β
β
β
ββ
βββ
β
β
β
β
β
β
ββ
β
β
β
βββ
β
ββ
β
βββββ
β
β
βββ
β
β
ββ
β
ββ
β
ββ
β
ββββ
β
ββ
β
ββ
βββ
β
β
β
β
βββ
ββββ
β
ββ
ββ
ββ
β
β
β
ββ
β
βββββ
β
βββ
β
β
β
β
β
ββ
β
ββ
β
β
β
β
ββ
ββ
β
ββ
β
β
β
β
β
ββββ
ββββββββββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
ββββββ
β
β
β
βββ
β
ββ
β
β
β
β
ββββββ
β
ββββββββ
ββ
β
β
ββ
β
β
β
ββ
β
β
ββ
β
β
ββ
β
β
ββ
β
ββ
β
β
βββ
β
β
β
ββ
βββββ
β
ββ
ββ
β
β
ββββββ
β
ββ
β
βββββ
β
β
β
ββ
ββ
β
β
ββ
β
β
β
β
ββ
ββ
β
β
ββ
βββ
ββββ
β
ββ
β
βββββ
ββ
β
ββ
βββββ
β
β
ββ
β
βββ
ββ
β
β
β
β
βββ
ββ
βββββ
β
β
β
β
ββ
ββ
β
ββββ
β
β
β
β
β
β
ββ
β
β
β
β
ββ
β
β
β
β
βββββββ
β
β
β
ββ
β
βββββ
β
ββ
β
β
βββ
β
ββ
βββ
ββ
ββ
β
β
β
β
ββ
ββ
βββ
β
β
βββ
β
β
β
β
ββ
βββ
β
βββ
β
βββ
β
β
β
βββ
β
β
β
β
ββββββββββ
β
β
ββββ
β
β
ββββββββββββββββββββββββββββββββββββββββββββ
βββββ
β
β
β
ββββ
βββ
βββ
ββ
βββ
β
βββββ
β
β
β
β
β
β
β
ββββ
ββ
β
βββ
ββ
β
β
β
β
ββ
ββ
β
βββ
β
ββ
β
βββ
βββ
ββ
β
ββ
ββββββββββ
β
ββ
βββ
β
β
ββ
β
β
β
β
β
β
β
β
β
β
ββ
β
βββ
βββ
ββ
β
β
β
β
β
ββββ
β
β
βββ
β
β
β
β
β
ββββ
β
β
β
β
ββ
β
β
β
β
β
β
ββββββββ
ββ
β
β
ββ
βββ
βββ
β
ββ
β
ββ
βββ
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
ββ
β
β
ββ
ββ
β
β
ββ
ββ
β
β
ββββ
β
β
β
β
β
βββββ
β
β
β
β
ββ
β
β
β
ββββββββ
β
β
β
β
ββ
β
ββ
β
ββ
β
β
β
β
β
ββ
β
β
β
β
ββ
ββ
β
β
ββ
β
β
β
β
β
βββββ
β
β
β
β
β
β
ββ
β
βββ
ββββββ
β
βββ
β
ββ
β
β
β
ββββ
β
ββ
ββββ
β
β
βββββ
β
β
β
β
βββ
ββ
β
β
β
β
ββββββ
β
β
β
β
β
β
ββ
β
β
ββ
ββ
β
ββββ
β
ββ
β
β
β
β
β
β
β
βββ
ββββ
ββ
β
β
β
β
βββ
β
βββ
β
β
ββ
ββ
β
β
β
β
β
ββ
β
ββ
β
β
β
ββ
β
β
β
β
ββββ
β
ββββ
βββββββββ
ββ
βββββββββ
ββββ
β
ββ
βββ
βββββββββββββββββββ
β
β
βββ
β
β
ββ
ββ
β
β
β
β
β
β
β
β
β
βββ
β
β
β
ββ
ββ
β
β
ββ
ββ
β
ββ
ββ
ββ
β
ββ
β
β
βββββ
ββββββββββββ
β
βββββββββββββββ
ββ
β
βββ
β
β
β
β
β
ββ
β
β
β
β
ββββ
β
β
β
β
β
βββ
ββ
β
ββ
β
β
ββ
β
β
β
βββ
β
β
β
β
β
β
ββββββ
βββ
β
ββ
β
β
β
ββ
β
ββ
β
ββ
β
β
ββ
β
β
ββ
ββ
β
β
ββββ
β
ββ
ββ
β
ββ
β
ββ
β
βββββ
ββ
β
β
ββ
β
β
β
β
βββ
β
β
β
ββββββββ
β
β
β
β
ββ
β
ββ
βββββ
β
β
β
ββ
β
βββ
β
β
βββ
β
ββ
β
β
β
β
β
β
β
β
β
β
ββββ
β
βββ
β
β
βββββββββ
ββββββββ
βββββββββββββββ
β
β
ββ
β
β
β
β
ββ
β
ββ
ββ
β
β
β
ββ
β
β
β
β
β
ββ
β
β
β
ββ
ββ
β
ββ
β
β
β
β
ββ
β
β
ββ
ββ
β
β
β
β
β
β
βββ
β
ββ
ββ
ββ
ββ
β
β
β
β
ββ
β
ββ
ββ
β
ββ
β
βββ
ββ
βββββββββββββββββββββββ
β
β
β
ββββ
β
ββββ
β
ββ
ββββ
β
βββ
ββ
βββ
βββ
βββ
β
β
β
ββ
β
β
β
ββββ
β
ββ
βββ
β
β
ββββ
β
β
ββ
βββ
ββ
β
β
ββββ
ββ
β
ββ
β
ββ
β
β
β
β
ββ
β
β
β
β
β
β
ββ
β
ββββββ
β
β
β
β
β
β
β
β
β
ββ
β
β
βββ
ββββ
ββ
β
ββββ
β
βββββ
ββββ
β
β
ββ
ββ
β
β
ββ
β
ββ
ββββ
βββ
β
ββββββββββ
β
βββββββββ
β
ββββ
ββ
β
β
β
ββ
β
ββ
ββββ
βββ
ββ
ββ
β
β
β
ββ
β
β
β
β
ββββ
β
β
β
β
β
βββ
β
ββ
β
β
ββββ
β
β
ββββββ
β
βββββ
ββ
ββββ
ββββββ
β
β
β
βββ
β
β
β
β
β
β
ββ
β
ββ
β
β
ββ
βββββ
ββ
β
β
β
ββ
β
ββ
βββ
ββ
β
ββ
β
β
βββ
ββ
β
β
β
βββ
β
ββ
β
β
ββ
β
β
β
βββ
β
ββ
β
ββ
β
β
β
β
β
β
ββ
β
β
β
β
β
ββ
βββ
β
β
β
ββββ
β
βββ
βββ
β
β
ββ
β
β
β
ββ
β
β
βββββββ
β
β
ββ
β
β
β
ββββ
β
β
β
ββββ
β
βββββββ
βββ
ββ
β
β
β
β
β
ββ
β
β
β
β
β
βββ
β
β
β
β
β
ββ
βββ
β
ββ
βββ
β
β
β
β
β
β
β
β
β
ββββ
β
β
β
β
ββ
β
β
ββββββββββββ
β
βββ
β
βββ
β
β
β
ββ
ββ
ββ
ββ
β
ββ
ββ
β
β
β
β
ββ
β
ββ
β
ββ
βββ
β
ββ
ββ
β
ββ
ββββ
β
β
β
β
β
β
ββββ
βββ
ββ
β
β
ββββ
β
ββββ
βββββββ
ββ
βββββββββββββ
βββββββββ
βββββββ
β
β
β
β
ββββ
ββ
β
β
βββββββ
ββββββββ
β
βββ
βββββ
β
β
β
βββββββ
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
ββ
ββ
ββ
β
β
β
ββββββ
β
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
ββ
ββ
β
β
β
β
β
β
ββ
βββ
β
β
ββ
β
β
β
β
β
β
β
β
β
β
ββ
β
ββ
β
βββ
β
ββ
β
β
β
β
β
ββ
β
βββ
β
β
β
β
β
ββββ
β
β
β
β
β
β
β
β
βββ
βββ
β
ββ
β
ββ
β
ββ
β
ββββ
ββ
β
β
β
β
β
β
β
β
β
ββ
ββ
β
ββ
ββββββ
βββββ
β
β
β
ββ
β
β
ββ
β
β
ββ
β
β
β
β
βββββ
β
β
β
ββ
β
β
β
β
ββ
ββ
β
β
β
βββ
β
ββββββ
β
β
β
β
βββ
ββ
βββ
β
β
β
β
β
βββ
β
β
βββββ
β
β
βββ
β
β
β
ββ
β
ββ
ββ
β
β
β
β
βββ
β
β
β
β
β
β
β
β
β
ββ
ββ
βββ
β
βββββββββββ
β
β
β
ββ
β
β
ββββββ
βββββββββββββββ
β
β
ββ
ββββ
β
β
β
β
β
ββ
ββ
β
βββ
ββ
β
β
β
β
βββββ
βββ
β
βββββ
β
β
β
βββββ
ββββββ
βββββ
βββββ
ββββββ
β
β
β
β
β
β
β
βββ
β
β
ββ
β
β
ββββ
ββ
β
β
β
β
β
βββ
β
βββ
β
β
βββ
ββ
β
β
ββ
ββ
β
βββββββββββββ
ββ
β
β
ββ
β
β
ββ
β
ββ
ββ
β
β
ββββ
βββ
β
βββ
ββββββ
ββ
ββββ
β
β
β
β
ββββ
ββ
β
β
ββ
βββ
β
ββ
β
β
ββ
β
β
β
ββ
ββ
ββββ
β
ββ
β
ββ
β
βββ
β
β
β
β
β
βββ
βββ
ββββ
β
β
ββ
β
β
β
β
ββ
β
ββ
β
β
ββ
β
ββ
β
β
β
β
β
ββ
β
β
βββββ
β
ββ
β
β
β
ββ
β
β
β
β
β
β
β
β
ββ
ββ
β
β
ββ
β
β
β
β
ββ
ββ
βββ
β
βββββ
β
β
β
β
β
ββ
β
ββ
β
βββ
ββββ
β
β
β
ββββ
β
ββ
βββ
β
ββ
β
ββ
βββββ
ββ
β
ββ
β
β
β
β
ββ
β
β
β
β
ββ
β
β
β
β
β
β
β
ββ
ββ
ββ
β
β
βββ
β
β
βββ
βββ
βββ
β
β
ββ
ββ
β
βββ
ββ
β
β
β
β
ββ
β
β
β
β
βββ
ββ
ββ
β
ββ
ββββ
ββ
β
β
β
βββ
β
β
β
β
βββ
β
β
β
β
β
ββ
β
β
βββ
β
β
β
β
ββ
β
β
ββ
β
β
ββ
β
β
βββ
β
β
βββ
β
ββ
ββ
ββββ
β
β
βββββ
ββββββ
β
ββββ
β
β
β
ββ
β
ββ
βββββ
βββ
β
ββ
β
ββ
β
β
β
ββ
β
β
β
β
β
β
ββ
βββ
ββ
β
β
β
β
β
β
ββββ
β
β
ββ
βββ
β
β
β
β
β
β
ββ
ββ
βββββ
ββ
β
β
β
ββ
β
β
β
β
β
ββ
β
ββ
β
βββ
β
β
β
ββ
β
β
β
β
ββββββ
βββββββ
β
β
β
β
β
ββ
β
ββββ
β
ββββββ
β
β
β
β
ββ
β
β
β
β
β
βββββ
β
β
β
β
ββ
β
β
β
β
ββ
β
β
β
β
β
β
β
β
ββ
β
β
β
ββ
β
ββ
βββ
β
ββ
β
β
β
βββ
β
βββ
β
β
β
β
β
β
β
β
β
β
ββββββββββ
ββββ
β
ββββ
β
ββββββββ
ββββ
β
βββββ
β
βββ
ββββ
β
β
βββ
β
β
β
β
β
βββ
ββ
ββ
ββ
β
ββ
β
ββ
β
β
ββ
β
β
β
β
β
β
ββ
ββ
βββ
βββ
βββββ
ββ
ββ
ββ
ββ
β
β
ββ
ββ
βββββ
ββ
β
β
β
βββ
β
ββ
β
βββ
βββ
β
ββ
β
β
ββ
β
β
β
β
βββ
ββ
β
β
β
β
β
β
β
β
βββ
β
ββ
ββ
ββ
β
ββ
β
β
β
ββ
β
ββ
βββ
ββ
ββ
β
ββ
β
β
βββ
β
β
β
ββ
ββ
βββββ
β
β
βββ
β
βββ
β
ββ
β
β
ββ
β
β
β
β
ββ
β
ββββββββ
β
β
β
β
ββ
β
β
βββ
β
ββββββββββ
β
β
β
β
β
β
β
ββ
β
β
β
βββ
ββ
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
ββ
βββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
β
ββββ
β
β
β
β
β
β
β
β
β
β
β
β
β
ββββ
β
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
ββ
β
ββββ
β
β
βββ
ββ
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
ββ
ββ
β
β
β
ββ
β
ββ
ββ
ββββ
βββββββ
βββ
ββββ
β
ββ
βββ
β
β
ββ
β
βββ
β
ββ
ββ
β
ββ
β
β
β
β
βββ
β
ββ
β
βββ
ββ
β
β
β
β
ββ
β
β
ββ
β
β
ββ
β
βββ
β
β
ββ
ββ
β
ββββ
β
ββ
ββ
β
ββ
ββ
ββ
β
ββ
ββ
β
β
β
β
βββ
β
β
β
ββ
ββ
βββ
β
βββ
β
β
ββ
β
β
β
ββ
ββ
β
β
ββ
ββ
βββββββββ
β
β
β
β
ββ
ββ
βββ
β
ββ
β
ββ
β
β
β
ββ
ββββ
β
β
β
βββ
β
ββββββββ
β
β
β
ββ
β
β
ββ
ββββ
β
β
β
β
β
β
β
β
β
ββ
β
ββ
ββ
β
β
β
β
ββ
β
β
β
β
ββ
ββ
β
β
β
ββ
β
β
βββ
βββ
β
β
β
β
ββ
ββββ
β
ββββ
ββ
ββ
β
β
β
β
βββ
β
β
ββ
β
β
ββ
β
β
ββ
ββ
ββββ
ββββ
β
ββββββ
β
βββ
β
β
ββββ
β
β
β
ββ
ββ
ββ
ββββββββ
β
βββββ
βββββββββββββββββ
β
β
βββββ
β
β
β
β
β
ββ
β
ββ
βββββ
β
ββββ
β
β
ββββββ
β
βββ
β
βββββββββ
β
β
ββ
β
ββ
β
β
β
β
β
β
β
β
β
β
ββ
β
βββββ
β
β
β
β
β
ββ
β
ββ
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
βββ
β
β
β
β
β
β
β
β
βββ
ββ
β
β
βββββ
β
β
β
ββ
β
β
β
βββ
β
β
β
βββ
β
β
β
β
β
β
β
β
β
ββ
ββββ
β
ββββ
β
β
β
βββ
βββ
β
β
β
β
β
βββ
ββββββ
β
ββ
β
β
βββ
β
β
ββ
β
ββ
ββ
β
β
β
β
β
ββββββ
β
β
β
β
β
β
β
β
ββ
βββ
ββ
ββ
β
β
ββ
ββ
β
β
ββ
β
β
ββ
β
βββββββββ
β
β
β
ββββ
β
ββββββββ
βββββββββ
βββββ
βββ
β
ββββ
ββ
β
βββββ
ββ
β
ββ
ββ
ββ
β
β
ββ
β
ββ
βββ
β
ββ
β
β
β
β
β
β
ββ
ββ
β
β
β
β
β
ββ
β
ββββββββ
ββ
β
β
ββ
ββ
βββ
β
β
ββ
ββ
β
ββ
β
β
β
β
β
β
ββ
β
β
β
ββ
β
ββ
ββ
β
β
ββ
β
β
β
βββ
β
β
ββ
β
ββ
β
β
β
β
β
βββββ
βββ
ββ
ββ
β
ββ
βββ
β
β
ββ
β
ββ
βββ
ββ
β
β
βββ
β
β
β
β
β
β
β
β
βββ
β
ββββ
ββ
ββ
β
β
β
β
β
ββ
βββ
β
β
βββ
β
β
ββ
ββββ
β
ββ
β
β
β
βββββββββββββββββββββββββββββββββ
β
β
β
ββββ
ββ
ββββ
β
β
β
ββ
βββ
βββ
βββ
β
β
β
β
β
β
ββ
β
β
β
β
β
ββ
βββ
β
β
β
βββ
β
ββ
βββββββ
ββ
βββ
β
ββ
β
ββ
ββ
β
β
β
ββ
βββ
β
β
ββ
βββ
ββ
β
β
β
β
β
β
ββ
ββ
ββββ
ββ
β
β
ββ
ββ
β
β
β
ββ
β
β
β
βββ
β
β
ββββ
ββ
ββββββββ
β
ββ
ββββ
β
β
ββ
ββ
βββββββ
β
β
ββββββββ
β
βββββββββ
ββββ
β
β
β
β
ββ
ββ
β
β
β
β
β
β
β
ββ
β
β
β
ββ
β
β
β
β
β
β
β
β
β
ββββββ
β
β
β
β
β
β
β
β
βββ
β
β
β
ββ
βββ
β
β
β
β
β
ββ
βββ
β
ββ
ββ
β
ββ
ββββ
ββββ
β
βββ
β
ββ
β
ββββββ
ββ
β
βββββββ
β
ββ
βββββββββββββ
β
β
β
β
β
ββ
β
β
ββββ
β
β
β
β
β
β
β
ββ
β
β
β
βββ
ββ
ββββ
β
ββββ
β
β
β
β
βββ
β
ββ
β
ββ
β
β
β
β
β
β
ββ
ββ
β
β
β
ββ
ββ
β
ββ
β
β
ββ
ββ
ββ
β
βββ
β
β
ββ
ββββ
β
βββ
β
β
ββ
β
ββ
β
β
β
β
ββββ
β
β
ββ
β
ββββ
ββ
β
β
β
ββββ
βββββ
β
β
ββ
ββ
ββββ
β
ββ
ββ
β
β
β
β
ββ
β
ββ
β
ββ
β
β
β
ββ
β
β
β
β
ββ
β
β
β
β
β
β
ββ
β
β
β
β
β
ββ
β
β
β
β
β
βββ
βββ
βββ
ββ
βββ
β
β
β
ββββ
β
ββ
βββ
ββββββββ
ββ
ββ
ββ
β
β
β
β
βββ
β
β
ββ
βββββ
ββ
β
β
β
β
β
β
ββββ
ββ
β
ββ
βββ
ββββ
β
β
ββββ
βββ
β
β
ββββ
ββ
βββββ
β
βββ
β
β
ββ
β
βββ
β
ββ
β
β
β
β
βββ
β
ββ
ββ
β
β
β
ββ
β
β
β
β
βββ
ββ
β
β
β
βββ
β
βββ
βββ
β
β
ββ
βββ
ββ
ββ
β
β
βββ
β
ββ
ββ
β
β
β
ββ
β
β
βββββββ
β
β
β
βββ
ββββ
β
ββ
β
β
ββ
ββ
ββ
β
β
ββ
β
ββ
β
β
β
ββ
ββ
ββ
β
β
β
ββ
βββ
ββββ
βββ
β
ββ
β
ββ
ββββββ
β
ββ
β
βββ
β
βββ
β
β
β
β
β
ββ
β
β
ββ
β
β
β
ββ
β
β
β
β
β
ββ
β
βββ
β
βββ
β
ββ
β
β
ββ
β
β
ββ
βββ
β
ββ
ββ
β
β
βββββββββββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
ββ
ββββ
β
β
ββ
β
ββ
β
βββββ
ββ
βββ
ββ
β
β
β
β
β
β
β
β
β
ββ
β
β
ββββ
β
β
β
β
β
ββ
β
β
β
ββ
ββ
β
β
ββ
ββ
β
ββ
β
β
β
ββ
ββ
ββ
βββ
β
ββ
β
ββ
β
ββββ
β
β
β
β
βββ
β
β
β
β
ββ
β
βββββ
β
ββββ
β
β
βββββ
βββ
β
β
β
β
β
β
βββ
ββ
β
βββ
β
β
ββ
β
β
β
ββ
β
βββββ
β
βββ
β
ββ
βββ
β
ββ
β
ββ
β
βββ
β
β
β
β
β
β
β
β
ββ
βββ
ββ
βββ
β
ββ
ββ
β
β
βββ
ββ
β
β
β
β
β
ββ
βββββ
β
β
βββββββ
β
ββ
ββββ
β
β
β
β
ββ
β
ββ
β
ββ
β
β
β
β
β
β
β
ββ
β
β
β
β
β
ββββ
β
β
βββ
βββ
ββ
β
β
ββββββ
β
ββ
β
β
ββ
β
ββ
βββ
β
β
β
β
β
β
ββββ
β
β
β
β
β
ββββ
β
β
ββ
β
β
ββββ
ββ
β
ββ
β
βββ
β
β
ββ
β
β
β
β
ββ
β
ββββ
β
ββββ
ββββ
β
β
β
ββ
ββ
β
β
ββββββ
β
βββ
β
β
β
ββ
ββ
βββββ
β
β
β
ββ
β
ββ
βββ
ββ
β
β
β
ββ
β
ββ
β
β
βββ
ββββ
β
β
β
β
β
β
β
β
β
β
β
β
β
ββ
β
ββ
β
β
ββ
β
ββ
β
ββ
β
β
β
β
βββ
ββ
βββ
ββ
ββββ
β
β
ββ
βββββββββββββββββββ
β
ββ
β
βββ
β
βββββ
ββββ
ββββββββββ
β
β
ββββββββββββββββββββ
β
βββ
β
βββ
ββ
β
β
β
ββ
β
βββ
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
ββββ
ββ
β
ββ
β
β
β
β
β
ββ
β
β
β
β
ββββ
ββββββββ
β
βββ
ββ
ββ
β
βββ
βββ
β
ββ
β
β
βββ
β
β
βββββββββββββ
β
ββ
β
ββββ
β
β
β
β
β
β
ββ
β
β
ββ
β
β
ββ
ββββ
β
β
β
β
β
β
ββββ
ββ
β
ββ
β
β
ββ
β
ββ
β
β
β
βββ
β
βββ
β
ββ
βββ
ββββ
β
β
β
βββββββ
ββ
ββββ
ββ
ββ
β
β
βββββ
β
β
βββββββββββββ
ββ
β
ββ
β
β
β
β
β
ββββ
β
β
ββ
β
β
β
β
β
β
βββββββββββ
β
ββ
β
β
β
βββ
ββ
β
β
β
βββ
ββ
β
ββββ
βββ
β
ββ
ββ
β
β
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
ββ
βββ
β
ββββββ
β
β
β
β
β
ββββ
β
β
ββ
βββββ
β
β
β
ββββ
ββ
β
β
β
β
β
ββ
ββ
β
β
β
ββ
ββ
β
ββ
ββ
β
ββ
β
β
β
β
β
β
β
β
β
β
βββ
ββ
ββ
ββ
β
ββ
βββββ
β
ββ
β
β
ββ
ββ
β
β
β
β
β
βββ
ββββ
ββ
β
ββ
β
ββ
ββ
β
ββ
β
βββββββ
β
β
β
β
ββ
βββββ
β
β
β
β
βββββ
βββ
β
β
ββ
ββββ
ββ
β
ββ
β
β
β
βββ
β
ββ
β
β
β
β
ββ
β
β
ββ
βββ
β
ββββ
β
β
ββ
β
β
β
β
ββ
β
β
ββββββ
β
β
ββ
β
β
β
β
β
ββββ
β
β
β
ββ
ββ
β
β
β
ββ
β
β
β
β
β
β
ββ
ββ
β
β
βββ
β
β
β
ββββ
ββ
β
ββ
ββ
β
β
β
ββ
β
ββ
ββ
βββ
ββββ
β
β
β
β
β
βββ
βββ
β
β
ββ
β
β
β
β
β
ββ
ββ
ββ
β
β
β
ββ
ββ
β
βββ
ββ
ββ
ββ
β
β
β
β
β
βββ
β
β
β
β
ββ
β
ββββ
β
β
β
β
ββββ
β
β
ββ
ββ
β
β
β
β
β
β
β
β
βββββ
β
ββ
ββ
β
β
β
β
ββ
βββ
ββ
β
β
β
β
ββ
ββ
β
ββββ
β
ββββ
β
β
β
β
ββ
ββββ
β
β
ββ
ββ
ββββ
ββββ
β
β
β
βββββ
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
ββ
ββββββ
ββ
β
ββ
ββ
β
β
β
β
ββ
ββ
ββ
β
β
β
β
ββββββ
ββ
βββββ
β
ββ
β
β
β
β
ββββ
β
β
β
β
β
ββββββ
β
β
β
β
ββ
β
βββ
β
β
ββ
β
β
β
β
β
β
β
βββ
β
ββ
βββββ
β
ββ
β
β
β
β
β
ββββββββ
β
βββ
β
ββ
β
β
β
ββ
β
ββ
β
β
ββ
β
ββ
ββββββββ
β
β
β
β
β
ββ
β
β
β
β
β
β
ββ
ββ
ββ
ββ
β
ββ
β
ββ
β
βββ
ββ
ββββ
βββ
β
β
β
ββ
ββ
β
β
β
β
ββββββ
β
ββ
β
β
β
β
β
β
β
β
β
β
β
βββ
β
β
β
β
ββ
β
β
β
ββ
β
β
ββββ
β
β
β
β
ββ
βββ
β
β
ββ
ββ
βββ
ββ
β
βββ
β
β
βββββ
β
β
β
βββ
β
ββ
β
βββββββββββ
β
β
β
β
β
β
β
β
β
β
β
β
βββββ
β
ββ
ββ
β
β
βββ
β
β
β
β
ββββββ
ββ
β
ββ
β
ββ
β
β
βββββ
β
β
ββ
β
β
β
ββ
β
β
β
βββββββ
βββββ
βββββββββββββββ
β
β
β
ββ
β
β
β
βββ
β
βββ
β
β
ββββ
βββ
β
ββ
β
β
β
βββ
β
βββ
β
β
β
ββ
β
β
β
ββ
β
β
ββ
β
β
β
ββ
ββ
β
βββ
β
β
β
β
ββββ
ββ
β
β
ββββββ
βββ
β
ββ
βββ
β
β
β
β
βββ
ββββ
β
βββ
βββ
β
β
βββ
β
β
β
β
β
β
β
β
ββ
β
β
β
ββ
β
ββββββββββ
ββ
β
ββββ
β
βββ
ββ
β
β
β
β
β
β
β
β
β
β
ββ
β
β
ββ
β
ββ
β
β
ββ
β
ββ
β
ββ
β
β
β
β
ββ
β
β
β
β
β
β
β
ββββββ
β
β
ββ
β
β
ββ
ββββ
βββ
ββ
βββ
β
βββ
ββ
β
β
ββββββ
β
ββ
β
β
β
ββ
βββ
β
β
β
β
ββ
ββ
β
β
ββββ
ββ
β
β
β
β
βββ
ββ
β
β
ββ
ββ
βββ
β
β
β
β
ββ
β
β
β
ββ
β
β
β
βββ
β
ββ
β
ββ
β
β
βββββββββ
β
β
β
βββ
ββ
ββββ
β
β
ββββ
β
βββ
β
β
β
β
β
ββ
β
ββ
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
ββ
β
ββ
β
β
ββββ
β
β
ββ
β
β
βββ
ββ
β
ββ
β
β
β
ββ
ββββ
ββββ
β
ββ
β
ββ
β
ββ
ββ
β
βββ
β
β
β
β
βββββ
βββ
ββββ
β
β
ββ
β
ββ
β
βββββ
ββββββ
β
ββ
β
β
ββ
β
ββ
ββ
β
βββ
βββ
ββββββββ
β
ββ
β
β
ββ
β
βββ
β
β
ββ
ββββ
β
βββ
ββββ
β
ββ
ββββ
ββ
ββββ
ββ
β
β
β
β
β
β
ββ
ββ
β
ββ
β
βββ
β
β
β
β
β
β
β
β
β
β
β
β
βββ
ββ
β
β
ββ
βββ
β
β
ββ
βββββββββ
β
βββ
β
ββββββ
ββββ
β
β
β
ββ
β
β
βββ
β
β
β
β
ββ
ββ
β
βββ
ββββ
β
ββ
β
β
β
β
β
β
β
βββββ
ββββ
ββββ
β
ββββββ
ββ
β
β
β
βββ
ββ
βββ
β
β
β
β
ββ
β
β
β
βββ
β
β
ββ
β
β
β
β
β
β
β
ββ
β
ββ
β
β
β
β
βββ
βββ
β
ββ
βββ
β
β
β
βββββββ
β
β
β
ββ
β
ββ
βββ
β
β
β
β
β
β
β
βββ
ββ
βββ
ββ
β
βββ
ββ
β
β
β
βββββ
β
β
β
ββ
ββ
βββ
β
β
β
βββ
ββ
β
β
β
ββ
β
β
ββ
β
β
β
ββ
β
β
β
ββ
β
β
βββ
β
β
β
β
β
β
ββ
β
β
β
ββ
β
β
β
βββ
ββββ
ββ
βββ
β
ββ
β
ββ
ββ
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
β
ββ
ββ
β
β
βββ
ββ
ββββ
βββ
β
β
βββ
β
ββββ
β
β
β
ββββ
β
β
β
β
βββββ
β
β
ββ
β
β
ββ
β
β
ββ
β
β
ββ
ββ
β
β
β
β
β
ββββ
ββ
βββββ
β
β
ββ
β
βββββ
β
β
β
β
β
β
β
βββ
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
β
ββ
β
βββ
β
β
ββ
ββ
β
β
β
β
βββ
β
β
β
ββ
β
ββ
β
ββ
β
βββ
β
β
β
β
ββββββββββ
β
β
β
ββ
ββββ
ββ
β
β
β
βββ
ββββββ
ββ
β
β
ββ
β
β
β
βββ
β
β
β
βββ
β
βββ
βββ
β
ββ
β
β
β
β
ββ
β
ββββ
ββββ
ββββ
βββ
ββ
ββ
ββββ
β
βββ
β
βββ
ββ
ββ
β
β
ββββ
β
β
β
β
β
β
β
ββββ
β
β
β
β
β
β
βββ
β
ββββββ
ββ
β
β
β
β
β
ββ
β
β
β
β
β
ββ
β
βββ
β
β
β
ββββββ
β
ββ
β
ββββ
βββ
β
β
ββ
ββ
βββ
ββ
β
β
β
β
β
β
β
ββ
β
β
β
β
β
ββ
βββ
β
β
βββ
β
β
βββββ
ββ
βββ
ββββ
β
β
β
βββ
β
ββ
ββ
ββ
ββββ
β
ββ
β
ββββ
ββ
β
β
β
β
β
βββ
β
ββ
β
β
β
β
ββ
β
ββ
βββ
β
ββ
β
β
ββ
βββββ
ββ
β
βββ
βββββ
β
β
β
β
β
β
β
β
ββββ
βββ
ββ
ββ
ββββββββββββ
ββ
β
β
β
β
β
ββ
ββ
β
ββββ
ββββββ
β
ββ
βββ
ββ
ββββ
β
β
β
ββ
ββ
β
β
β
β
β
β
βββ
ββ
β
ββ
β
ββ
ββ
β
β
β
βββ
β
ββββ
β
β
β
β
β
β
β
β
β
β
β
ββ
β
ββ
ββ
ββ
βββ
β
ββ
ββ
ββ
β
ββ
β
ββ
ββββ
β
β
β
β
β
β
βββ
β
ββ
β
ββββ
ββββββ
β
β
ββ
ββ
β
β
β
β
β
β
β
βββββ
β
β
ββ
β
β
β
ββββββββββββ
β
ββ
β
ββββββββ
ββ
ββ
β
β
β
β
β
β
β
β
ββ
β
β
β
β
ββ
β
ββ
ββββ
β
β
ββ
β
ββ
β
βββ
β
ββ
ββ
β
β
β
ββ
ββ
β
β
β
β
β
β
β
β
ββ
β
ββ
β
β
ββ
ββ
β
β
βββ
β
β
βββ
β
β
ββ
β
ββ
β
β
β
β
ββββ
β
β
ββ
β
β
β
β
β
β
ββ
β
β
β
ββββ
ββ
β
ββ
β
β
β
ββββ
β
ββββ
β
ββββ
β
ββ
β
β
ββββββββ
ββ
βββ
β
β
β
β
β
β
β
β
ββ
β
βββ
β
β
βββββββ
β
ββ
β
ββββ
βββ
βββ
β
β
ββ
ββββ
β
β
β
β
β
ββ
β
β
β
βββββββββββ
β
β
β
βββ
β
β
β
β
βββ
β
ββ
ββ
β
ββββ
β
β
β
β
βββ
βββββββ
β
β
β
β
ββ
βββ
β
β
ββ
β
β
β
β
β
β
β
βββ
ββ
β
ββ
β
β
β
β
βββββ
β
ββ
β
β
β
β
β
β
β
β
ββββ
β
ββββββββ
β
β
β
β
β
β
β
β
βββ
β
β
βββββ
β
βββββ
βββ
ββββββ
β
ββββββββββββββββββββββββββββββ
β
βββ
β
βββββ
β
βββ
ββ
β
β
ββ
β
β
β
ββ
β
β
β
β
β
β
β
β
βββ
ββ
βββ
ββ
β
β
β
β
ββ
β
β
βββ
β
β
βββ
ββββββββ
ββββ
β
βββββββ
ββββ
βββββββββ
βββ
βββββββββββββββββββββββββββββββββββββββ
β
βββββββββββ
β
β
β
βββ
β
βββ
β
βββββββ
ββββ
ββββ
ββ
β
β
ββ
β
β
βββ
β
βββββ
β
βββ
β
ββββββββ
ββββββββββββββββββ
β
βββββ
β
βββββ
β
β
ββββββββββββββ
β
βββ
β
βββ
β
βββββββββββββββββ
β
βββββ
βββββββββ
β
ββββ
β
ββββ
β
β
β
ββββ
β
βββββ
ββββββ
β
βββ
β
βββ
βββ
β
ββ
β
β
β
β
ββ
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
ββ
β
β
ββ
ββ
β
β
ββ
β
β
β
β
β
β
β
β
β
β
βββ
β
β
β
ββ
β
β
βββ
βββ
β
ββ
β
β
ββββ
β
β
β
β
ββ
ββ
ββββ
βββββββββββ
β
βββββββββββ
β
β
β
ββββββββββββββ
ββ
β
β
β
β
ββ
β
β
ββββ
ββ
β
βββ
β
ββ
β
β
βββ
ββββ
β
β
β
ββ
β
β
ββ
βββ
β
βββββ
β
β
β
ββββ
β
β
β
ββ
ββ
β
β
ββ
ββ
ββ
βββ
β
β
β
ββ
β
ββ
β
β
β
β
ββ
βββ
ββ
ββ
β
ββ
βββ
β
β
β
βββ
ββ
β
βββ
β
β
β
β
β
β
ββ
β
βββ
β
βββββ
β
β
ββ
β
β
β
β
β
β
ββ
ββ
ββββ
β
β
β
β
β
β
β
β
βββ
β
β
βββ
βββ
β
β
β
β
β
β
β
ββ
β
β
ββ
ββ
β
β
βββ
β
ββ
β
ββββ
β
ββ
β
ββ
β
β
βββ
β
β
ββ
β
β
β
β
β
β
ββ
β
ββ
β
β
ββββββββ
β
β
ββ
β
βββ
β
β
β
βββ
ββββ
β
β
β
β
ββ
β
ββββ
β
β
β
β
β
ββ
β
β
β
β
β
βββ
ββ
β
β
β
β
β
β
β
β
β
β
β
ββ
ββ
β
β
β
β
βββ
β
β
ββ
β
βββββ
β
βββ
β
βββ
ββ
ββ
β
β
β
β
ββ
β
β
β
β
ββ
β
β
β
β
ββ
β
βββ
ββ
ββββ
ββ
β
βββ
β
β
β
β
β
βββ
ββ
β
β
β
β
β
ββββ
β
ββ
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
ββ
β
βββ
β
β
β
β
β
β
ββ
β
β
β
β
ββ
β
ββ
β
β
β
β
β
ββββ
β
β
β
β
β
βββ
β
βββββ
βββ
ββ
ββββ
ββ
β
βββ
ββ
β
ββ
β
βββ
ββ
β
ββ
ββ
βββββ
ββ
β
ββ
ββ
β
β
β
βββββ
β
βββ
ββββ
ββββ
β
β
ββ
ββ
ββ
ββββββ
β
ββ
βββββββ
β
β
βββ
ββ
β
βββ
β
ββ
β
β
ββ
β
ββ
β
β
βββββββ
β
ββ
β
βββ
β
βββ
ββ
β
ββ
β
ββββ
β
β
ββββ
βββ
βββ
β
β
β
β
βββ
βββββββββββ
β
ββ
ββ
βββ
ββ
ββ
β
ββ
β
β
β
β
β
β
βββββββ
β
β
β
β
β
β
ββ
β
β
β
ββββ
β
β
βββ
β
ββ
β
β
βββ
βββ
βββ
βββ
β
ββ
ββ
β
β
β
β
ββ
β
ββ
β
βββ
β
ββ
β
β
βββ
β
ββ
β
β
β
β
βββ
β
β
βββ
β
β
βββββ
β
β
β
β
βββ
β
β
β
ββ
β
βββ
β
ββ
βββ
β
βββ
β
β
β
β
ββ
β
β
ββββββ
β
β
β
β
ββ
ββ
β
ββ
β
ββ
β
ββ
β
β
ββ
β
β
βββ
β
ββ
β
βββββ
β
ββ
β
β
βββ
βββββ
β
β
β
β
β
β
ββ
β
β
β
β
β
β
ββ
β
β
βββ
β
β
β
β
β
ββ
βββ
ββ
β
ββ
β
β
ββ
β
β
β
β
β
ββ
β
β
β
β
βββ
ββ
ββ
β
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
β
ββ
ββ
β
β
β
β
β
β
ββ
β
β
β
ββ
β
β
β
β
βββ
ββ
β
ββ
β
β
β
β
β
βββ
β
β
β
ββ
β
ββ
β
β
βββββββββ
β
β
β
β
β
ββ
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
β
βββββ
ββ
β
ββ
β
β
β
β
ββ
ββββββ
ββββββ
β
β
βββββββ
β
β
βββ
β
βββββ
β
ββ
β
βββ
β
ββββββ
β
βββββ
βββββββββ
β
β
β
β
β
β
ββ
ββββ
ββββ
β
β
β
β
ββ
β
β
ββ
β
ββ
ββ
β
β
β
β
β
β
ββ
β
ββ
β
β
β
β
β
ββ
ββ
ββ
β
β
ββ
β
β
β
β
ββ
β
ββ
β
ββ
β
ββ
ββ
β
β
β
ββ
β
ββββ
β
βββββ
ββ
βββββ
βββ
β
ββ
β
ββββββ
β
ββββ
β
β
ββββ
β
β
ββ
β
β
β
β
ββ
βββ
ββ
ββ
β
ββ
βββ
β
β
ββ
β
β
βββ
ββ
ββ
β
β
ββββ
β
ββ
β
β
β
ββ
β
β
ββ
β
β
β
ββ
β
β
βββ
βββ
β
ββ
β
ββ
β
β
β
ββ
ββββ
β
ββ
ββββ
βββ
β
β
β
β
β
ββ
βββββ
β
βββ
ββ
β
ββ
β
ββββ
β
β
ββββββββββ
β
ββ
βββββββ
ββ
ββββ
ββ
βββββ
ββββββ
β
β
ββββ
β
β
β
β
β
β
β
β
βββ
β
β
ββ
ββ
β
β
ββ
ββ
β
ββββ
βββ
ββ
ββ
ββ
ββ
β
β
β
βββ
β
β
ββββ
β
ββ
ββ
β
βββ
β
βββ
β
β
ββ
β
β
β
β
β
ββ
β
β
ββ
β
β
β
β
β
β
βββ
β
β
β
β
βββ
β
β
β
β
β
β
βββ
β
ββ
ββ
β
β
β
β
β
βββ
β
ββββββββββββββββββββββββββββ
β
βββ
β
ββββββββββββββββββββββββββββ
β
β
β
ββ
β
ββ
β
ββ
β
ββ
β
β
β
βββ
ββ
β
β
β
ββ
ββ
β
β
βββ
β
ββββββ
β
βββ
βββββ
β
β
βββββββββ
β
β
β
β
β
ββ
β
ββ
βββ
β
βββββ
β
ββββββ
β
β
β
β
β
ββ
βββ
β
β
β
β
β
ββββ
βββββββββ
β
β
β
ββ
β
β
ββ
ββ
β
ββ
ββ
β
β
β
β
β
β
β
ββ
β
ββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
βββ
β
β
ββ
β
β
β
β
β
ββ
ββββ
ββ
ββ
ββ
β
ββ
β
β
β
β
βββββ
β
ββ
β
β
β
β
β
βββ
β
β
β
β
β
β
ββββ
β
β
βββββββββββ
βββ
βββ
β
ββ
β
β
ββ
β
β
β
β
ββ
ββ
β
ββ
ββ
β
β
β
ββ
ββ
β
β
βββ
β
ββββ
β
β
β
β
β
ββββ
β
βββ
ββ
ββ
β
ββ
β
βββ
β
β
ββ
β
ββββββ
ββ
βββββ
β
β
β
β
β
β
β
β
βββ
β
ββ
β
βββ
β
β
β
βββ
ββ
ββ
βββ
β
ββ
β
β
ββ
βββ
ββββ
β
β
ββββ
ββ
β
β
β
ββββββββ
β
β
ββ
ββ
βββββ
β
β
ββ
β
β
ββ
β
β
β
ββ
ββ
ββ
β
β
ββββββ
β
β
β
β
β
ββββ
β
β
β
ββ
β
β
β
ββ
β
β
β
β
ββ
β
β
β
β
β
β
β
ββββ
β
β
β
β
ββ
β
β
β
β
ββ
β
βββ
ββββ
β
βββ
β
ββ
ββ
ββ
β
β
ββ
β
β
β
ββββ
β
β
β
β
β
β
βββ
ββ
β
ββββ
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
βββ
β
β
β
βββββ
β
β
ββ
βββ
β
βββ
β
β
β
βββ
ββ
β
β
βββ
ββ
β
βββ
β
β
β
β
β
βββ
ββ
ββ
β
ββββ
β
ββ
β
β
ββ
ββ
ββ
ββββ
β
βββ
β
β
β
ββ
ββ
β
ββββ
ββ
ββ
β
β
ββ
ββββ
β
β
ββ
β
β
β
β
β
ββ
β
ββ
β
βββ
β
β
β
β
β
ββ
β
ββ
β
βββ
ββ
β
β
ββ
β
β
ββ
ββ
β
βββ
β
β
β
β
β
β
ββ
ββ
βββ
β
β
β
β
β
β
βββ
β
β
ββββββββββββ
ββ
β
β
β
β
β
ββββ
β
β
β
ββ
β
ββ
βββ
β
βββ
β
β
β
ββββ
ββ
ββ
β
β
ββ
β
β
β
β
β
ββ
ββ
ββ
βββ
β
ββ
βββ
ββ
ββ
β
β
ββ
β
β
β
βββ
ββ
β
β
β
β
ββ
β
β
βββ
β
ββ
β
βββββ
β
β
β
β
β
ββββ
ββ
β
β
ββββ
ββ
ββ
βββ
β
βββββββββββ
βββββ
β
ββ
β
β
βββ
ββ
β
β
βββββ
β
β
β
β
βββ
ββββ
β
β
β
β
ββ
β
βββ
β
ββ
βββββββ
ββ
βββββ
βββββ
β
ββββββββββββββ
β
ββββββββββ
βββββββ
ββββββββββ
β
β
ββββ
β
β
β
ββ
β
ββ
β
ββ
β
ββ
ββ
β
β
β
ββββββ
β
βββ
β
β
β
β
βββ
β
β
ββ
β
ββ
ββ
β
ββ
β
ββ
ββββ
β
βββ
βββββββ
β
ββββ
ββ
β
β
β
ββ
β
β
ββ
β
ββ
β
ββ
β
βββ
β
β
β
βββββ
β
β
ββββ
β
β
β
β
β
βββ
ββ
ββ
ββ
β
ββββ
ββ
β
β
ββββββ
βββ
βββββ
βββ
β
β
β
β
ββ
β
ββ
βββ
β
β
β
β
β
ββ
β
βββ
β
βββ
ββββββ
β
β
ββ
β
β
β
β
β
β
ββββ
ββ
β
ββ
β
β
ββ
ββ
β
β
β
β
β
β
ββ
β
β
ββ
β
βββ
ββ
β
βββ
β
ββ
ββ
β
βββ
β
β
βββ
ββ
β
β
β
β
β
β
ββββββ
β
β
β
β
β
β
βββββ
β
ββ
β
ββ
β
β
β
βββββββββ
β
ββ
β
βββ
β
βββββ
β
β
β
βββ
β
βββ
β
β
β
β
β
β
ββ
β
β
ββ
βββ
ββ
β
β
β
β
β
ββ
β
β
β
β
β
ββ
β
βββ
ββββ
β
β
β
β
ββ
β
β
β
β
β
β
ββ
β
β
ββ
β
β
β
β
ββββ
ββββ
ββββββ
ββββ
β
βββββ
β
βββ
β
βββ
β
βββββββ
β
βββ
β
β
ββ
β
β
ββ
β
β
βββ
ββ
β
β
β
ββββ
βββ
β
β
β
βββ
β
ββ
ββ
β
ββ
β
β
βββββ
β
ββ
β
β
β
ββ
ββ
βββ
ββ
β
ββ
β
ββ
ββ
β
βββ
β
β
ββββ
ββ
ββ
β
ββ
β
β
βββ
β
β
ββ
ββ
β
β
ββ
β
βββ
β
βββββ
β
β
β
βββ
β
ββ
β
ββ
β
β
ββ
ββ
ββ
β
ββββ
β
βββ
ββ
β
β
β
βββ
ββ
β
β
β
βββ
β
ββ
ββββββββ
β
β
βββ
β
β
ββ
β
β
β
β
β
β
β
β
ββ
ββ
β
β
β
ββ
ββββ
ββ
β
β
βββ
βββ
β
ββ
βββββ
βββ
ββ
β
β
ββ
β
β
β
ββ
ββ
β
β
β
β
βββ
β
β
β
β
ββ
β
ββββββββββββ
ββ
ββββββββ
β
ββ
β
ββββ
β
βββββ
β
βββββββββ
β
ββββ
ββββββββ
β
β
ββ
βββ
β
β
ββ
β
ββ
β
β
β
ββ
ββββββ
β
β
β
ββ
ββ
βββ
β
β
β
β
β
β
ββ
ββ
β
β
β
ββ
β
β
ββ
β
ββ
β
β
β
β
β
β
ββ
βββ
β
β
β
β
ββ
βββ
β
ββ
β
β
ββββ
ββββββ
ββ
β
β
β
ββ
β
β
β
ββ
β
ββ
ββββ
ββββ
β
ββββ
β
ββ
β
ββ
β
β
ββ
β
ββ
ββ
ββ
ββ
ββ
β
ββ
βββββ
β
β
β
β
β
β
β
β
β
β
ββββββ
β
β
β
β
β
βββ
β
β
ββββββ
ββββ
β
ββ
β
ββββ
β
β
β
β
β
ββ
β
ββ
ββ
β
β
ββ
β
βββ
ββ
β
β
β
β
β
β
β
β
β
β
ββ
β
βββ
ββ
ββ
β
β
β
βββ
ββ
β
β
β
ββββ
β
β
β
β
β
β
β
β
β
ββ
ββ
β
ββ
β
β
ββββ
β
ββ
β
β
β
β
β
β
β
βββ
ββ
β
β
β
ββ
ββ
β
ββ
β
β
ββ
βββ
β
βββββ
β
β
ββ
ββ
β
β
βββ
βββ
ββ
β
ββ
ββ
β
βββ
β
β
β
ββ
ββββ
β
β
βββ
ββ
β
β
β
β
βββββ
β
ββββββββββββ
βββ
β
βββββ
β
β
β
βββ
β
ββ
β
β
β
βββ
β
β
β
βββ
ββ
β
βββ
β
ββ
βββ
βββ
ββββββββββ
ββ
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
ββββββ
ββ
β
β
ββββ
β
β
ββ
ββββββββ
β
ββ
βββ
β
ββ
ββ
ββββ
β
ββ
β
β
ββββ
β
β
ββββ
ββ
β
β
β
βββ
β
βββββββββββ
ββ
ββ
β
β
βββββ
β
β
ββ
β
ββ
β
β
βββ
βββ
β
β
βββ
ββ
ββ
ββ
β
β
β
β
β
β
β
β
β
β
β
βββ
β
βββ
β
βββ
β
ββββββ
β
βββ
β
ββ
ββββ
β
β
β
β
β
ββ
β
β
ββ
β
β
β
ββ
β
β
β
β
β
βββ
β
ββ
β
β
ββββ
ββ
ββ
ββ
β
ββββ
βββββ
ββ
β
βββ
β
β
β
ββββ
ββββ
β
ββββ
β
ββ
βββ
β
β
βββ
β
ββββ
βββ
β
βββ
β
ββ
β
ββ
ββ
ββ
β
β
β
β
ββββββββββ
ββ
ββ
β
ββ
β
β
βββ
ββ
ββ
β
β
ββ
β
ββ
β
βββ
β
β
β
β
β
ββββ
β
β
ββ
ββββ
β
β
β
β
β
β
β
β
β
ββ
ββββ
ββ
ββ
β
β
ββββ
ββ
ββ
β
β
β
β
β
ββ
β
β
β
β
β
ββ
β
β
β
β
β
β
ββ
ββ
β
ββ
β
β
β
βββββ
β
β
ββ
β
β
β
β
ββ
ββ
βββ
β
βββ
βββ
ββ
ββ
β
βββ
β
ββββ
ββββββ
ββ
β
β
β
β
ββ
ββ
β
βββ
β
ββ
β
β
βββ
β
β
β
βββββββββββββ
ββ
β
β
β
ββ
ββ
βββββ
ββ
βββ
β
β
β
β
ββ
β
ββ
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
ββ
βββ
β
βββ
β
ββ
ββ
β
β
ββ
β
βββ
β
β
βββββββ
ββ
β
ββ
ββ
β
β
β
ββ
ββ
β
β
β
ββ
ββ
ββ
ββββββββ
β
β
β
β
β
ββ
β
β
β
β
ββ
β
βββ
β
β
β
ββββ
ββββ
ββ
ββββ
ββ
β
β
β
β
β
β
β
β
β
βββββ
ββ
β
β
β
β
β
βββ
β
β
ββ
ββ
β
β
βββ
β
ββ
βββ
β
β
βββ
β
ββ
β
β
β
β
β
β
β
β
β
β
βββ
βββββ
β
βββ
ββ
ββββ
β
βββββ
β
β
β
ββ
β
β
ββ
β
ββββ
β
β
ββββββββ
β
β
β
ββ
ββ
βββ
β
β
ββββ
β
β
β
ββ
β
βββ
β
βββ
β
ββ
β
β
ββββ
β
β
βββ
β
ββ
β
β
ββββββ
β
β
ββ
βββββ
β
β
ββ
ββ
β
β
βββ
β
βββ
ββ
βββ
β
βββ
β
β
ββ
β
ββ
β
β
ββββββ
β
ββββ
β
β
ββ
β
β
β
β
ββ
β
ββββββ
ββββ
β
βββββββββββ
β
βββββ
βββββ
β
βββ
β
ββββ
β
βββββ
β
ββ
β
β
β
ββββββ
β
βββ
β
βββ
β
β
β
β
βββ
ββ
β
ββββββ
ββ
ββ
ββ
ββ
β
β
βββ
ββ
ββ
β
ββ
β
β
βββ
β
ββ
β
ββββ
β
ββ
β
β
βββ
β
β
ββ
βββββ
ββ
βββββ
β
ββββββββ
ββ
β
β
ββ
β
β
β
βββ
β
β
β
β
ββ
β
ββ
β
ββ
β
β
ββ
β
ββ
β
ββ
β
β
β
ββ
β
β
β
ββ
β
β
ββ
β
βββ
ββ
β
β
β
β
β
ββ
β
β
β
ββββββ
β
ββ
β
β
β
β
β
β
ββ
β
β
β
ββ
β
β
ββ
β
β
β
βββ
β
β
ββ
β
ββ
β
ββ
β
β
ββ
ββ
β
β
β
β
βββ
β
βββ
β
β
β
β
ββ
ββββ
β
β
β
β
β
βββ
β
β
β
βββ
β
β
β
βββ
β
β
β
β
β
βββ
β
ββββββ
β
ββββββ
β
ββββββββ
β
β
β
β
β
β
ββββ
β
βββ
ββ
β
β
βββββββ
β
β
β
β
ββ
ββ
βββ
ββββ
β
β
β
ββ
β
β
β
ββ
ββ
β
β
β
ββ
β
ββββ
β
β
β
β
βββ
β
βββ
β
ββββ
ββ
β
β
β
ββ
β
β
β
β
β
β
ββ
β
β
β
β
ββ
βββββββ
ββ
β
β
ββ
β
β
βββ
β
ββ
β
β
ββ
β
ββ
β
β
β
ββββββ
β
β
β
βββ
ββ
β
ββ
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
β
β
β
β
β
βββ
β
ββ
β
ββ
β
β
β
βββββ
βββ
ββββββ
β
β
β
β
β
ββ
β
β
ββ
βββ
β
βββββββββ
β
βββββββββββββββββββββββββββββββββββββββββββββββββ
β
β
β
β
β
β
β
β
ββ
β
β
ββ
β
βββ
β
ββ
ββ
β
β
β
β
β
ββ
β
ββ
ββ
β
β
ββ
ββ
β
β
β
β
βββ
βββ
ββ
β
βββββββββ
β
β
β
β
β
β
ββββββββββ
ββ
ββ
β
β
β
β
TCF7L2
KCNQ1
CDC123
CDKAL1SLC30A8IGF2BP2
CTBP1ASCL2KCNJ11 HNF4A
KIF11ZMIZ1IRS1 JAZF1 SFI1
GPSM1SPRY2EML4PPARGWFS1
b
ββ β
ββ β β β β β β β β β β β β β β
5 10 15
0.00
20.
004
0.00
60.
008
LVE of top 50 Imputed GWAS and sequence associations
Rank
LVE
β
β
β
β ββ β
ββ β β β β β β β β β β
ββ
β
β
β
β
β
β
β
β β ββ
ββ β β β
β
0.15
0.20
0.25
0.30
Rat
ioExomesImputed GWASRatio
c
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
β
β
ββ
ββ
ββ
β
β
β
β
0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Rank comparison for mouse NIDD genes
Exomes Percentile
GW
AS
Per
cent
ile
GADD45GIP1
PPP1R3CPPP1R3A
SNAP25
SLC2A4
SLC2A2
CYB5R4
CDKAL1
PRKCI
PPARD
HNF1A
HMGA1
FOXM1
FEM1B
PDX1
PBX1NOS3
MAFA
MADD
LEPRIRS2
IRS1
CTF1
ASIP
AKT2
LEP
INS
GCK
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
β
ββ
β
β
β
β
β
β
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint
Exomes
p-value cutoff
Exome chip
Fraction concordant
Frac
tion
true
asso
ciat
ions
Calibrate from prior model at GWAS loci
1.1 effector genes per locus
1/3 of missense mutations loss-of-function
0.5 0.6 0.7 0.8 0.9 1.0
0.0
0.2
0.4
0.6
0.8
1.0
0.5 0.6 0.7 0.8 0.9 1.0
0.0
0.2
0.4
0.6
0.8
1.0
0.5 0.6 0.7 0.8 0.9 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Researcher gene or variant prior
Compare direction of effect
Fraction of causal coding associations
Mahajan et al, 2018 (0.49) Finucane et al, 2015 (~0.10)
Pickrell, 2014 (~0.10)
0.001 0.005 0.020 0.050
020
040
060
080
0
Causal associations at T2D GWAS loci
Pβvalue
# as
soci
atio
ns
0.0
0.2
0.4
0.6
0.8
1.0
Est
imat
ed fr
actio
n ca
usal
ass
ocia
tions
TotalFrac. causal
0.001 0.005 0.020 0.050
23
45
Map to Bayes Factor
Pβvalue
Bay
es F
acto
r
1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.0
0.2
0.4
0.6
0.8
Probability of nonsynonymous variant association
Observed βlog10(P)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Prio
r pr
obab
ility
of g
ene
rele
vanc
e
Gene
PriorCostBenefitVariantassoc.
Gene-levelassoc. Customize
PosteriorDecision
Portal
0 50000 150000 250000
0.0
0.2
0.4
0.6
0.8
1.0
Predicted power to detect known T2D drug targets
Sample Size
Pow
er
INSRGLP1RPPARGDPP4SLC5A2IGF1RKCNJ1KCNJ8
a b Decision support from exome sequence data
c d e f
.CC-BY-NC-ND 4.0 International licenseacertified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under
The copyright holder for this preprint (which was notthis version posted July 31, 2018. ; https://doi.org/10.1101/371450doi: bioRxiv preprint