ELF>p|@x@8 @hihipppa2a244 x = 888$$Ptd` ` ` QtdRtd PPGNU NoS|ͩ+n p" #@012a@AT% $@     }vRPeߗ`c75kΑ7 q3`%ۃ1R"  F x : % p_ I  gw d( wW {;   h  p4 @n  ` pb  }  i!  j3 `Xy X VIY \I!  0e @Zw X T%  u _  n&^  \ e' U~ `{  2 ZM pV- 0b  pd$m  @}W   iN? TY @" PTIA  hB I yR WI  ~C  0g  r `  dP  Pj  b Pb!  @T  V  g/ K  @  d b = pZI1  k p< b    PgS  0ii Wa  |&  s  PhC  `:__gmon_start___init_fini_ITM_deregisterTMCloneTable_ITM_registerTMCloneTable__cxa_finalize_Py_NoneStructPyBaseObject_TypePyObject_SetAttrPyObject_GetAttrPy_EnterRecursiveCallPy_LeaveRecursiveCallPyErr_OccurredPyObject_CallPyExc_SystemErrorPyErr_SetStringrandom_bounded_uint64PyExc_DeprecationWarningPyErr_WarnFormatPyExc_TypeErrorPyErr_Format_Py_DeallocPyObject_GC_UnTrackPyErr_FetchPyThread_free_lockPyErr_RestorePyBuffer_ReleasePyObject_GC_IsFinalizedPyObject_CallFinalizerFromDeallocPyUnicode_New_PyUnicode_FastCopyCharactersmemcpyPyExc_OverflowError_PyUnicode_ReadyPyLong_FromSsize_tPyErr_NormalizeExceptionPyException_SetTracebackPyDict_NewPyImport_ImportModuleLevelObjectPyCapsule_NewPyDict_SetItemPyObject_GetAttrStringPyDict_GetItemStringPyModule_GetNamePyExc_ImportErrorPyCapsule_IsValidPyCapsule_GetNamePyCapsule_GetPointerPyDict_SetItemStringPyExc_AttributeErrorPyErr_ExceptionMatchesPyErr_ClearPyThreadState_GetPyInterpreterState_GetIDPyModule_NewObjectPyModule_GetDictPyUnicode_TypememcmpPyObject_RichCompare_Py_TrueStruct_Py_FalseStructPyObject_IsTruePyLong_TypePyNumber_IndexPyLong_AsSsize_tPyExc_ValueErrorPyOS_snprintfPyErr_WarnEx_PyType_LookupPyErr_SetObjectPySlice_Newvsnprintf_Py_FatalErrorFuncPyDict_NextPyUnicode_ComparePyObject_IsSubclassPyTuple_NewPyTuple_PackPyUnicode_InternFromStringPyUnicode_DecodePyUnicode_FromStringAndSizePyBytes_FromStringAndSizePyObject_HashPyObject_GetItemPyExc_RuntimeErrormallocfreePyList_TypePyTuple_TypePyObject_GC_TrackPyErr_GivenExceptionMatchesPyUnicode_FromStringPyUnicode_ConcatPyImport_GetModulePyObject_FreePyLong_AsUnsignedLongPyLong_AsLongPyExc_IndexErrorPyCFunction_TypePyType_IsSubtypePyObject_GenericGetAttrPyType_Ready_PyObject_GetDictPtr_PyDict_GetItem_KnownHashPyMethod_TypePyImport_Import_PyThreadState_UncheckedGetPyObject_NotPyFrame_NewPyTraceBack_HerePyCode_NewEmptyPyUnicode_FromFormatPyUnicode_AsUTF8memmovePyMem_Realloc_PyObject_GenericGetAttrWithDictPyMem_MallocPyGILState_EnsurePyGILState_ReleasePyDict_Sizerandom_intervalPyNumber_InPlaceMultiplyPyNumber_MultiplyPyList_NewPyList_AsTuplePyList_AppendPyLong_FromLongPyUnicode_FormatPyNumber_RemainderPyUnicode_FromOrdinalmemsetPyErr_NoMemoryPyExc_BufferErrorPyObject_SetItemPyExc_NotImplementedErrorPyNumber_AddPyNumber_InPlaceAddPy_OptimizeFlagPyObject_GetBufferPyMem_FreePyExc_StopIterationPyObject_GetIterPyIndex_CheckPyExc_UnboundLocalErrorrandom_normalrandom_logisticrandom_gumbelrandom_lognormalrandom_laplacerandom_rayleighrandom_poissonrandom_exponentialPyBytes_FromStringstrlenrandom_noncentral_fPySlice_TypePyFloat_TypePyObject_Formatrandom_standard_cauchyPyBytes_TypePySequence_Tuplerandom_frandom_vonmisesrandom_waldrandom_noncentral_chisquarerandom_betaPySequence_Containsrandom_weibullrandom_standard_trandom_logseriesrandom_powerrandom_paretorandom_chisquarerandom_geometricrandom_zipfrandom_gammaPyExc_ZeroDivisionErrorPyObject_RichCompareBoolPyDict_DelItemPyType_ModifiedPyExc_NameErrorPyObject_SizePyEval_SaveThreadPyEval_RestoreThreadrandom_standard_gammaPyLong_FromSize_tPyNumber_FloorDividerandom_multivariate_hypergeometric_countPyNumber_Orrandom_multivariate_hypergeometric_marginalsrandom_multinomialPyNumber_MatrixMultiplyPySequence_ListPyNumber_NegativePyLong_FromUnsignedLong_PyLong_CopyPyNumber_AbsolutePyFloat_FromDoublerandom_hypergeometricPyNumber_SubtractPyNumber_TrueDividePyLong_FromLongLongrandom_negative_binomialsqrtrandom_triangularPyFloat_AsDoublerandom_standard_gamma_frandom_standard_normal_fillrandom_standard_normal_fill_frandom_uniformPyBool_Typerandom_standard_exponential_fill_frandom_standard_exponential_inv_fill_frandom_standard_exponential_fillrandom_standard_exponential_inv_fillrandom_standard_uniform_fillrandom_standard_uniform_fill_fPyImport_AddModulePyObject_SetAttrStringPy_GetVersionPyLong_FromStringPyImport_GetModuleDict_Py_EllipsisObjectPyCode_NewWithPosOnlyArgsPyImport_ImportModulePyThread_allocate_lockPyCMethod_NewPyCapsule_TypePyExc_Exception_PyDict_NewPresizedPyObject_MallocPyObject_IsInstancerandom_binomialPyNumber_InPlaceTrueDividePyException_SetCausePyObject_CallObjectPyInit__generatorPyModuleDef_Initrandom_standard_uniform_frandom_standard_uniformrandom_standard_exponentialexplog1prandom_standard_exponential_fexpflog1pfrandom_standard_normalrandom_standard_normal_fpowlogpowflogfsqrtfrandom_positive_int64random_positive_int32random_positive_intrandom_uintrandom_loggamrandom_gamma_fexpm1floorrandom_binomial_btperandom_binomial_inversion__isnanacosfmodrandom_geometric_searchrandom_geometric_inversionrandom_buffered_bounded_uint32random_buffered_bounded_uint16random_buffered_bounded_uint8random_buffered_bounded_boolrandom_bounded_uint64_fillrandom_bounded_uint32_fillrandom_bounded_uint16_fillrandom_bounded_uint8_fillrandom_bounded_bool_filllogfactoriallibm.so.6libc.so.6GLIBC_2.14GLIBC_2.2.50ui ui  L PL  @%X8@Ppppp|X3d~N8 P Qx :     `   \ [   ` X #  L p, `% L  o` +h , -   ` 2  : p( E0 4P JX 4x S 0 N p Z : i( @ ]H ` h a  Z d   Ec0 VXLpM X(p80OZMdi8P `X1 oL LV`h  5d0JXppWM`X(`8h?xO{`MmW`Zh@Wx.S @ U(Ph8 @H X `hx @ T $G   (`8 @sHX `|h0x > v K `n @]c .Z v(`8@J @2HHX@> `hpx@/ n@" ` ` ``  (8 @HX `;h0Sx` h@g _ V O   (к8` @H*Xq `hxf =е`M `@8 p$ ` Ѕ (8 @H@bX &@Zr              #  '   ( 0  8 6@ <H =P >X @` Ah p x       e f   i k   t {      ( 0 8 @ H P X ` h p x                   (08@HP X `h px !"$%& (()08@*H+P,X-`.h/p0x12 345789:;?BCDEFGH I(0J8K@HLPMXN`OhPpQxRSTUVWXYZ[\] ^_`abcd f(g0h8i@jHlPXm`nhoppxqrsuvwxyz|}~ (08@HPX`hpx (08@HPX`hpx (0HH Ht+H5 % @% h%ڏ h%ҏ h%ʏ h% h% h% h% hp% h`% h P% h @% h 0% h %z h %r h%j h%b h%Z h%R h%J h%B h%: h%2 h%* hp%" h`% hP% h@% h0% h % h% h% h% h %ڎ h!%Ҏ h"%ʎ h#%Ž h$% h%% h&% h'p% h(`% h)P% h*@% h+0% h, %z h-%r h.%j h/%b h0%Z h1%R h2%J h3%B h4%: h5%2 h6%* h7p%" h8`% h9P% h:@% h;0% h< % h=% h>% h?% h@%ڍ hA%ҍ hB%ʍ hC% hD% hE% hF% hGp% hH`% hIP% hJ@% hK0% hL %z hM%r hN%j hO%b hP%Z hQ%R hR%J hS%B hT%: hU%2 hV%* hWp%" hX`% hYP% hZ@% h[0% h\ % h]% h^% h_% h`%ڌ ha%Ҍ hb%ʌ hc%Œ hd% he% hf% hgp% hh`% hiP% hj@% hk0% hl %z hm%r hn%j ho%b hp%Z hq%R hr%J hs%B ht%: hu%2 hv%* hwp%" hx`% hyP% hz@% h{0% h| % h}% h~% h% h%ڋ h%ҋ h%ʋ h%‹ h% h% h% hp% h`% hP% h@% h0% h %z h%r h%j h%b h%Z h%R h%J h%B h%: h%2 h%* hp%" h`% hP% h@% h0% h % h% h% h% h%ڊ h%Ҋ h%ʊ h%Š h% h% h% hp% h`% hP% h@% h0% h %z h%r h%j h%b h%Z h%R h%J h%B h%: h%2 h%* hp%" h`% hP% h@% h0% h % h% h% h% h%ډ h%҉ h%ʉ hATI1HU1QHtLI$H5 HH>HExHAHEuHHHEuHADZ]A\AWIAVIH5ZgAUIATUSHAPHLHHIHu(LLH5#4HHI H81'qLHu9L>LHSIMLHH؀ H5 4H81)LLHHtHMAuHHMuHAZD[]A\A]A^A_AWIAVIH5]fAUIATUSHAPHLHHIHu(LLH53HHL H81*qLHu9LALHVIMLHH H53H81)LLHHtHMAuHHMuHAZD[]A\A]A^A_AVIAUIHATUSD Ht5H; HuE1tHLLvAHMu)HUH\ AH8tE1[D]A\A]A^AVAUIATUQHxHȆ HuH Ht#H9tH H52H8E1L%¹ Mt I$H5dL-IHtHIHuLHtHIHAH DdHLHBdxkAH 3dLLH/dxHAH dLLHdix%E1H dLLHdIxIHMHZL]A\A]A^AVIHAUIATUDSHH%HIH@u#H]} LLH51H81^ML$(ID$ Mt ILLIL9v#H} ILLH51H81AuNH9sIHl$RLIPMH2H1H11Y^yI $uLE1HL[]A\A]A^UH5 H SHFHD$H HD$H HD$0H HD$8H HD$XHR HD$`H H$H' H$H H$HN H$Hʤ HD$HD$ fD$(D$*HD$@HD$HfD$PD$RHD$hHD$pfD$xD$zHDŽ$ HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$H$H H$H H$H' H$H H$ H! H$(Hڣ H$HH Z H$PHģ H$pH H$xH H$H/ H$H HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$EHDŽ$fDŽ$Ƅ$HDŽ$0HDŽ$8fDŽ$@Ƅ$BHDŽ$X3HDŽ$`fDŽ$hƄ$jHDŽ$$HDŽ$fDŽ$Ƅ$HDŽ$7H$H H$H H$H H$H H$Hw H$Hx H$8H H$@Hb H$`H H$hHL HDŽ$fDŽ$Ƅ$HDŽ$&HDŽ$fDŽ$Ƅ$HDŽ$=HDŽ$fDŽ$Ƅ$ HDŽ$ HDŽ$(fDŽ$0Ƅ$2HDŽ$HBHDŽ$PfDŽ$XƄ$ZHDŽ$p5HDŽ$xfDŽ$Ƅ$H$H- H$HF H$Hϣ H$H0 H$H H$H H$H H$H H$(H5 H$0H H$PHo H$XHؠ HDŽ$Q HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$ HDŽ$fDŽ$Ƅ$HDŽ$#HDŽ$fDŽ$ Ƅ$"HDŽ$8&HDŽ$@fDŽ$HƄ$JHDŽ$` H$xH H$H H$H H$HΟ H$H? H$H H$H H$H H$H H$ H HDŽ$hfDŽ$pƄ$rHDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$ HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$( HDŽ$0fDŽ$8Ƅ$:H$@H H$HH H$hH H$pHp H$HY H$HZ H$H[ H$HD H$H] H$H. H$H H$H HDŽ$P!HDŽ$XfDŽ$`Ƅ$bHDŽ$xHDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$ HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$%H$0HC H$8H$ H$XH H$`H H$H H$H H$H H$H H$Hk H$H̜ HDŽ$ fDŽ$(Ƅ$*HDŽ$@HDŽ$HfDŽ$PƄ$RHDŽ$hHDŽ$pfDŽ$xƄ$zHDŽ$HDŽ$fDŽ$Ƅ$HDŽ$ HDŽ$fDŽ$Ƅ$HDŽ$ HDŽ$fDŽ$Ƅ$H$HP H$Hƛ H$ H߇ H$(H H$HH H$PH H$pH# H$xH H$Hņ H$Hn H$Hg H$HX HDŽ$"HDŽ$fDŽ$Ƅ$HDŽ$02HDŽ$8fDŽ$@Ƅ$BHDŽ$X*HDŽ$`fDŽ$hƄ$jHDŽ$(HDŽ$fDŽ$Ƅ$HDŽ$+HDŽ$fDŽ$Ƅ$HDŽ$#H$H H$Hd H$H͚ H$HN H$8HN H$@H8 H$`HQ H$hH" H$Hs H$H HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$ HDŽ$ HDŽ$(fDŽ$0Ƅ$2HDŽ$H"HDŽ$PfDŽ$XƄ$ZHDŽ$pHDŽ$xfDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$H$HE H$H H$H H$H H$Hɖ H$Hژ H$(H H$0HĘ H$PH H$XH H$xH H$H HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$ Ƅ$"HDŽ$8HDŽ$@fDŽ$HƄ$JHDŽ$`HDŽ$hfDŽ$pƄ$rHDŽ$&H$HӁ H$H H$Hu H$H H$H H$Hx H$ H H$ Hb H$@ H; H$H HL HDŽ$fDŽ$Ƅ$HDŽ$*HDŽ$fDŽ$Ƅ$HDŽ$%HDŽ$fDŽ$Ƅ$HDŽ$ &HDŽ$ fDŽ$ Ƅ$ HDŽ$( !HDŽ$0 fDŽ$8 Ƅ$: HDŽ$P !HDŽ$X fDŽ$` Ƅ$b H$h H- H$p HF H$ H H$ H0 H$ H H$ H H$ H H$ H H$ H5 H$ H H$0 H H$8 Hؕ HDŽ$x HDŽ$ fDŽ$ Ƅ$ HDŽ$ HDŽ$ fDŽ$ Ƅ$ HDŽ$ HDŽ$ fDŽ$ Ƅ$ HDŽ$ HDŽ$ fDŽ$ Ƅ$ HDŽ$ HDŽ$ fDŽ$( Ƅ$* HDŽ$@ H$X H} H$` H H$ HE H$ HΔ H$ H? H$ H H$ HA} H$ H H$ H| H$ H HDŽ$H fDŽ$P Ƅ$R HDŽ$h LHDŽ$p fDŽ$x Ƅ$z HDŽ$ HDŽ$ fDŽ$ Ƅ$ HDŽ$ HDŽ$ fDŽ$ Ƅ$ HDŽ$ "HDŽ$ fDŽ$ Ƅ$ HDŽ$ [HDŽ$ fDŽ$ Ƅ$ H$ Hu{ H$( H H$H H{ H$P Hp H$p H H$x HZ H$ H H$ HD H$ H H$ H. H$ Hߔ H$ H HDŽ$0 ?HDŽ$8 fDŽ$@ Ƅ$B HDŽ$X .HDŽ$` fDŽ$h Ƅ$j HDŽ$ HDŽ$ fDŽ$ Ƅ$ HDŽ$ HDŽ$ fDŽ$ Ƅ$ HDŽ$ HDŽ$ fDŽ$ Ƅ$ HDŽ$ H$ H H$ H$ H$8 H H$@ H H$` H H$h H H$ H H$ H H$ Hx H$ H̑ HDŽ$ fDŽ$ Ƅ$ HDŽ$ HDŽ$( fDŽ$0 Ƅ$2 HDŽ$H HDŽ$P fDŽ$X Ƅ$Z HDŽ$p HDŽ$x fDŽ$ Ƅ$ HDŽ$ HDŽ$ fDŽ$ Ƅ$ HDŽ$ &HDŽ$ fDŽ$ Ƅ$ H$ H H$ HƐ H$ H H$ H H$( H H$0 H H$P H H$X H H$x Hv H$ Hn H$ H' H$ HX HDŽ$ HDŽ$ fDŽ$ Ƅ$ HDŽ$ HDŽ$ fDŽ$ Ƅ$" HDŽ$8 HDŽ$@ fDŽ$H Ƅ$J HDŽ$` HDŽ$h fDŽ$p Ƅ$r HDŽ$ HDŽ$ fDŽ$ Ƅ$ HDŽ$ H$ H H$ Hd H$ H H$ HN H$H H$ H8 H$@H H$HH" H$hH[ H$pH HDŽ$ fDŽ$ Ƅ$ HDŽ$ HDŽ$ fDŽ$ Ƅ$ HDŽ$ HDŽ$fDŽ$Ƅ$HDŽ$(HDŽ$0fDŽ$8Ƅ$:HDŽ$PHDŽ$XfDŽ$`Ƅ$bHDŽ$x HDŽ$fDŽ$Ƅ$H$Hs H$H H$Hs H$H H$H H$Hڍ H$H s H$Hč H$0H l H$8H H$XHk H$`H HDŽ$!HDŽ$fDŽ$Ƅ$HDŽ$"HDŽ$fDŽ$Ƅ$HDŽ$ HDŽ$fDŽ$Ƅ$HDŽ$.HDŽ$ fDŽ$(Ƅ$*HDŽ$@)HDŽ$HfDŽ$PƄ$RHDŽ$h(H$H+ H$H H$H H$H H$H H$Hx H$H> H$Hb H$ Hp H$(HL HDŽ$pfDŽ$xƄ$zHDŽ$ HDŽ$fDŽ$Ƅ$HDŽ$ HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$7HDŽ$fDŽ$Ƅ$HDŽ$0FHDŽ$8fDŽ$@Ƅ$BH$HHa H$PHF H$pHB H$xH0 H$HZ H$H H$H: H$H H$H H$H H$H H$H؊ HDŽ$XHDŽ$`fDŽ$hƄ$jHDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$ HDŽ$ H$8H̕ H$@H H$`H H$hH$HAH$H H$HAH$Hm H$HAH$HDŽ$(fDŽ$0Ƅ$2HDŽ$HHDŽ$PfDŽ$XƄ$ZHDŽ$pHDŽ$xfDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$.HDŽ$fDŽ$Ƅ$H$Hll H$HA H$(Hl H$0HA(H$PH# H$XHA0H$xH H$HA8H$H H$HA@H$H H$HAHHDŽ$9HDŽ$fDŽ$ Ƅ$"HDŽ$8)HDŽ$@fDŽ$HƄ$JHDŽ$`HDŽ$hfDŽ$pƄ$rHDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$ H$H H$HAPH$Ha H$ HAXH$@H H$HHA`H$hHz H$pHAhH$H[ H$HApHDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$(HDŽ$0fDŽ$8Ƅ$:HDŽ$P HDŽ$XfDŽ$`Ƅ$bHDŽ$xHDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$H$H H$HAxH$H H$HH$H H$HH$0H H$8HH$XH H$`HH$H H$HHDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$ fDŽ$(Ƅ$*HDŽ$@HDŽ$HfDŽ$PƄ$RHDŽ$hHDŽ$pfDŽ$xƄ$zHDŽ$H$Hf5 H$HH$H H$HH$H( H$HH$ H H$(HHH$HH HQ@H$PHDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$ HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$0HDŽ$8fDŽ$@Ƅ$BHDŽ$XHDŽ$`fDŽ$hƄ$jH$xHAH$Hč H$HAH$H% H$HAH$H H$HA H$Hm H$HA(H$8Hde H$@HA0H$pHDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$ HDŽ$ HDŽ$(fDŽ$0Ƅ$2HDŽ$H)H$`H" H$hHA8H$H H$H$HAHHPH$HY H$H$HBH$H$HHDŽ$PfDŽ$XƄ$ZHDŽ$pHDŽ$xfDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$ Ƅ$"H$(H' H$0HB H$PH H$XHB(H$xHb H$HB0H$H H$HB8H$H H$HB@HHH$H܆ H$HDŽ$8HDŽ$@fDŽ$HƄ$JHDŽ$` HDŽ$hfDŽ$pƄ$rHDŽ$4HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$ H$ HBH$@Hk H$HHBH$hH0 H$pHBH$HU H$HB H$H H$HB(H$HDŽ$fDŽ$Ƅ$HDŽ$( HDŽ$0fDŽ$8Ƅ$:HDŽ$P HDŽ$XfDŽ$`Ƅ$bHDŽ$xHDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$ HDŽ$fDŽ$Ƅ$H$HG H$HB0H$H H$HB8H$0H1_ H$8HB@H$XH} H$`HBHH$H| H$HBPH$Hi H$HBXHDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$ fDŽ$(Ƅ$*HDŽ$@THDŽ$HfDŽ$PƄ$RHDŽ$hHDŽ$pfDŽ$xƄ$zHDŽ$HDŽ$fDŽ$Ƅ$HDŽ$H$H H$HB`H$Hf H$H$(HBpH$HH H$PHBxH$pH H$xHH$ HXHDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$0HDŽ$8fDŽ$@Ƅ$BHDŽ$XHDŽ$`fDŽ$hƄ$jHDŽ$HDŽ$fDŽ$Ƅ$H$H4\ H$HH$H[ H$HH$H H$HH$HB~ H$HH$8H\z H$@HH°H$`HZ H H$hHDŽ$%HDŽ$fDŽ$Ƅ$HDŽ$3HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$ HDŽ$  HDŽ$(fDŽ$0Ƅ$2HDŽ$HHDŽ$PfDŽ$XƄ$ZHDŽ$pH$HBH$Hf H$H$HBH$H= H$H$0HB(H$H$HH$(H8HDŽ$xfDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$ Ƅ$"HDŽ$8HDŽ$@fDŽ$HƄ$JH$PH H$XHB0H$xH{e H$HB8H$H H$HB@H$H H$HBHH$H H$HBPH$Hw H$ HBXHDŽ$` HDŽ$hfDŽ$pƄ$rHDŽ$$ HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$(H$@Hx H$HHB`HhH$hHP HH$pH$HBH$H/ H$HBH$Hz H$HBH$HDŽ$0fDŽ$8Ƅ$:HDŽ$PHDŽ$XfDŽ$`Ƅ$bHDŽ$xHDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$ HDŽ$fDŽ$Ƅ$H$H} H$HB H$0H| H$8HB(H$XHI{ H$`HB0H$H} H$HB8H$Hy H$HB@H$H~ H$HBHHDŽ$HDŽ$ fDŽ$(Ƅ$*HDŽ$@HDŽ$HfDŽ$PƄ$RHDŽ$h HDŽ$pfDŽ$xƄ$zHDŽ$ HDŽ$fDŽ$Ƅ$HDŽ$ HDŽ$fDŽ$Ƅ$HDŽ$H$Hm| H$HBPH$ HL| H$(HBXH$HH9} H$PHB`H$pH. H$xHBhH$H H$HBpHDŽ$fDŽ$Ƅ$HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$0HDŽ$8fDŽ$@Ƅ$BHDŽ$X HDŽ$`fDŽ$hƄ$jHDŽ$R HDŽ$fDŽ$Ƅ$HDŽ$ HDŽ$fDŽ$Ƅ$H$Hz H$HBxH$Hz H$HH$ Hy H$ HH$8 Hx H$@ HH$` Hy H$h HH$ Hx H$ HDŽ$HDŽ$fDŽ$Ƅ$HDŽ$HDŽ$ fDŽ$ Ƅ$ HDŽ$ HDŽ$( fDŽ$0 Ƅ$2 HDŽ$H HDŽ$P fDŽ$X Ƅ$Z HDŽ$p HDŽ$x fDŽ$ Ƅ$ HDŽ$ H$ HH$ HUz H$ HH$!H H$!HH$(!Hz H$0!HH$P!Hr H$X!HH$ HHDŽ$ fDŽ$ Ƅ$ HDŽ$ HDŽ$ fDŽ$ Ƅ$ HDŽ$ HDŽ$ fDŽ$ Ƅ$ HDŽ$! HDŽ$!fDŽ$ !Ƅ$"!HDŽ$8!HDŽ$@!fDŽ$H!Ƅ$J!HDŽ$`!HDŽ$h!fDŽ$p!Ƅ$r!H$x!HZ H$!HH$!HLu H$!HH$!H&y H$!HH$!H`O H$!HH$"Hu H$ "HH$@"H H$H"HHDŽ$!KHDŽ$!fDŽ$!Ƅ$!HDŽ$! HDŽ$!fDŽ$!Ƅ$!HDŽ$!HDŽ$!fDŽ$!Ƅ$!HDŽ$"$HDŽ$"fDŽ$"Ƅ$"HDŽ$("HDŽ$0"fDŽ$8"Ƅ$:"HDŽ$P")H$h"Hr H$p"HH$"H)w H$"HH$"Hs H$"HH$"HM H$"HH$#Hp H$#H HDŽ$X"fDŽ$`"Ƅ$b"HDŽ$x" HDŽ$"fDŽ$"Ƅ$"HDŽ$"HDŽ$"fDŽ$"Ƅ$"HDŽ$" HDŽ$"fDŽ$"Ƅ$"HDŽ$"&HDŽ$"fDŽ$#Ƅ$#HDŽ$#HDŽ$ #fDŽ$(#Ƅ$*#H$0#Hv H$8#H(H$X#Hs H$`#H0H$#Hr H$#H8H$#Hs H$#H@H$#H@t H$#HHH$#Hn H$$HPHDŽ$@#HDŽ$H#fDŽ$P#Ƅ$R#HDŽ$h#HDŽ$p#fDŽ$x#Ƅ$z#HDŽ$# HDŽ$#fDŽ$#Ƅ$#HDŽ$# HDŽ$#fDŽ$#Ƅ$#HDŽ$#HDŽ$#fDŽ$#Ƅ$#HDŽ$$H$ $H s H$($HXH$H$Hr H$P$H`H$p$Hr H$x$HhH$$Hs H$$HpH$$H(p H$$HxHDŽ$$fDŽ$$Ƅ$$HDŽ$0$HDŽ$8$fDŽ$@$Ƅ$B$HDŽ$X$HDŽ$`$fDŽ$h$Ƅ$j$HDŽ$$HDŽ$$fDŽ$$Ƅ$$HDŽ$$HDŽ$$fDŽ$$Ƅ$$HDŽ$$ HDŽ$$fDŽ$$Ƅ$$H$$Hj H$$HH$%Hr H$%HH$8%H H$@%HH$`%Hm H$h%HH$%Hn H$%HH$%Hp H$%HHDŽ$$ HDŽ$%fDŽ$%Ƅ$ %HDŽ$ %HDŽ$(%fDŽ$0%Ƅ$2%HDŽ$H%8HDŽ$P%fDŽ$X%Ƅ$Z%HDŽ$p% HDŽ$x%fDŽ$%Ƅ$%HDŽ$% HDŽ$%fDŽ$%Ƅ$%HDŽ$%H$%Hhm H$%HH$&H:m H$&HH$(&Hk H$0&HH$P&Hp H$X&HH$x&Hl H$&HHDŽ$%fDŽ$%Ƅ$%HDŽ$% HDŽ$%fDŽ$%Ƅ$%HDŽ$& HDŽ$&fDŽ$ &Ƅ$"&HDŽ$8& HDŽ$@&fDŽ$H&Ƅ$J&HDŽ$`&HDŽ$h&fDŽ$p&Ƅ$r&HDŽ$& HDŽ$&fDŽ$&Ƅ$&H$&H2a H$&HH$&HLn H$&H$&HH$'Ho H$ 'H$H'HH$h'H(F H$p'HH$&HH$@'H`HDŽ$&HDŽ$&fDŽ$&Ƅ$&HDŽ$&HDŽ$&fDŽ$&Ƅ$&HDŽ$'HDŽ$'fDŽ$'Ƅ$'HDŽ$('HDŽ$0'fDŽ$8'Ƅ$:'HDŽ$P'HDŽ$X'fDŽ$`'Ƅ$b'HDŽ$x' H$'Hm H$'HH$'H8i H$'HH$'Hzh H$'HH$(Hk H$(H H$0(H|m H$8(H(H0Ƅ$'HHDŽ$'fDŽ$'HDŽ$'HDŽ$'fDŽ$'Ƅ$'HDŽ$' HDŽ$'fDŽ$'Ƅ$'HDŽ$'HDŽ$'fDŽ$(Ƅ$(HDŽ$(HDŽ$ (fDŽ$((Ƅ$*(HDŽ$@(HDŽ$H(fDŽ$P(Ƅ$R(H$X(Hl H$`(H$(HBH$(H8l H$(HBH$(Hf H$(HBH$(H! H$)HB H$ )Hu H$()HB(H$(HDŽ$h(HDŽ$p(fDŽ$x(Ƅ$z(HDŽ$(HDŽ$(fDŽ$(Ƅ$(HDŽ$(HDŽ$(fDŽ$(Ƅ$(HDŽ$( HDŽ$(fDŽ$(Ƅ$(HDŽ$)d HDŽ$)fDŽ$)Ƅ$)HDŽ$0)H$H)Hi H$P)HB0H$p)Hfk H$x)HB8H$)Hj H$)HB@H$)He H$)HBHH$)Hh H$)HBPHDŽ$8)fDŽ$@)Ƅ$B)HDŽ$X) HDŽ$`)fDŽ$h)Ƅ$j)HDŽ$)HDŽ$)fDŽ$)Ƅ$)HDŽ$) HDŽ$)fDŽ$)Ƅ$)HDŽ$) HDŽ$)fDŽ$)Ƅ$)HDŽ$) HDŽ$*fDŽ$*Ƅ$ *H$*Hj H$*HBXH$8*HSa H$@*HB`H$`*H*i H$h*H$*HBpH$*H? H$*HBxH$*H:? H$*HH$*HHDŽ$ *HDŽ$(*fDŽ$0*Ƅ$2*HDŽ$H*HDŽ$P*fDŽ$X*Ƅ$Z*HDŽ$p*HDŽ$x*fDŽ$*Ƅ$*HDŽ$*HDŽ$*fDŽ$*Ƅ$*HDŽ$*#HDŽ$*fDŽ$*Ƅ$*HDŽ$*!H$+HZ H$+HH$(+H= H$0+HH$P+He H$X+HH$x+He H$+HH$+H7= H$+HHDŽ$*fDŽ$*Ƅ$*HDŽ$+HDŽ$+fDŽ$ +Ƅ$"+HDŽ$8+%HDŽ$@+fDŽ$H+Ƅ$J+HDŽ$`+HDŽ$h+fDŽ$p+Ƅ$r+HDŽ$+HDŽ$+fDŽ$+Ƅ$+HDŽ$+'HDŽ$+fDŽ$+Ƅ$+H$+H; H$+HH$+H8f H$+HH$,H` H$ ,HH$@,Hg H$H,H$p,HH$,HN H$,HH$h,HHDŽ$+2HDŽ$+fDŽ$+Ƅ$+HDŽ$,HDŽ$,fDŽ$,Ƅ$,HDŽ$(, HDŽ$0,fDŽ$8,Ƅ$:,HDŽ$P,HDŽ$X,fDŽ$`,Ƅ$b,HDŽ$x,HDŽ$,fDŽ$,Ƅ$,HDŽ$,H$,H>: H$,HH$,H H$,HH$-He H$-H$8-HH$X-H_ H$`-HH$0-HXHDŽ$,fDŽ$,Ƅ$,HDŽ$,HDŽ$,fDŽ$,Ƅ$,HDŽ$,IHDŽ$,fDŽ$-Ƅ$-HDŽ$-HDŽ$ -fDŽ$(-Ƅ$*-HDŽ$@-HDŽ$H-fDŽ$P-Ƅ$R-HDŽ$h- HDŽ$p-fDŽ$x-Ƅ$z-H$-H8 H$-HH$-H)c H$-HH$-H;a H$-HH$-Hb H$.H$(.H(H$H.Hb H$P.H0H$ .HðHDŽ$-BHDŽ$-fDŽ$-Ƅ$-HDŽ$-HDŽ$-fDŽ$-Ƅ$-HDŽ$- HDŽ$-fDŽ$-Ƅ$-HDŽ$.HDŽ$.fDŽ$.Ƅ$.HDŽ$0.HDŽ$8.fDŽ$@.Ƅ$B.HDŽ$X.H$p.H H$x.H8H$.H6 H$.H@H$.H(b H$.HHHPH$.He` H$.H$/HBH$/HDŽ$`.fDŽ$h.Ƅ$j.HDŽ$.'HDŽ$.fDŽ$.Ƅ$.HDŽ$.$HDŽ$.fDŽ$.Ƅ$.HDŽ$.HDŽ$.fDŽ$.Ƅ$.HDŽ$.HDŽ$/fDŽ$/Ƅ$ /HDŽ$ /HDŽ$(/fDŽ$0/Ƅ$2/H$8/HW H$@/HBH$`/H4 H$h/HBH$/H_ H$/H$/HB(H$/H H$/HB0H$0H H$0HB8H$/HPHDŽ$H/HDŽ$P/fDŽ$X/Ƅ$Z/HDŽ$p/3HDŽ$x/fDŽ$/Ƅ$/HDŽ$/HDŽ$/fDŽ$/Ƅ$/HDŽ$/HDŽ$/fDŽ$/Ƅ$/HDŽ$/ HDŽ$/fDŽ$/Ƅ$/HDŽ$0= H$(0H H$00HB@H$P0HU H$X0HBHH$x0H_ H$0HBPH$0H[ H$0H$0HB`H$0HHHDŽ$0fDŽ$ 0Ƅ$"0HDŽ$80HDŽ$@0fDŽ$H0Ƅ$J0HDŽ$`0HDŽ$h0fDŽ$p0Ƅ$r0HDŽ$0HDŽ$0fDŽ$0Ƅ$0HDŽ$0HDŽ$0fDŽ$0Ƅ$0HDŽ$0HDŽ$0fDŽ$0Ƅ$0H$0H)P H$0HBhH$1HN H$ 1HBpH$@1H3Q H$H1HBxH$h1HXT H$p1HH$1H[ H$1HH$1HR H$1HHDŽ$1HDŽ$1fDŽ$1Ƅ$1HDŽ$(1HDŽ$01fDŽ$81Ƅ$:1HDŽ$P1HDŽ$X1fDŽ$`1Ƅ$b1HDŽ$x1HDŽ$1fDŽ$1Ƅ$1HDŽ$1HDŽ$1fDŽ$1Ƅ$1HDŽ$1H$1H H$1HH$2H"0 H$2HH$02HlU H$82HH$X2HP H$`2HH$2HL H$2HHDŽ$1fDŽ$1Ƅ$1HDŽ$1'HDŽ$1fDŽ$2Ƅ$2HDŽ$2"HDŽ$ 2fDŽ$(2Ƅ$*2HDŽ$@2 HDŽ$H2fDŽ$P2Ƅ$R2HDŽ$h2HDŽ$p2fDŽ$x2Ƅ$z2HDŽ$2HDŽ$2fDŽ$2Ƅ$2H$2HZ H$2HH$2H|0 H$2HH$2H^V H$3HH$ 3HX H$(3HH$H3HjZ H$P3HH$p3HM H$x3HHDŽ$2HDŽ$2fDŽ$2Ƅ$2HDŽ$2HDŽ$2fDŽ$2Ƅ$2HDŽ$3 HDŽ$3fDŽ$3Ƅ$3HDŽ$03HDŽ$83fDŽ$@3Ƅ$B3HDŽ$X3HDŽ$`3fDŽ$h3Ƅ$j3HDŽ$3H$3H( H$3HH$3HY H$3H$3HH$4HM H$4HH$84H:X H$@4HH$3HHDŽ$3fDŽ$3Ƅ$3HDŽ$3"HDŽ$3fDŽ$3Ƅ$3HDŽ$3HDŽ$3fDŽ$3Ƅ$3HDŽ$3HDŽ$4fDŽ$4Ƅ$ 4HDŽ$ 4HDŽ$(4fDŽ$04Ƅ$24HDŽ$H4HDŽ$P4fDŽ$X4Ƅ$Z4H$`4H H$h4HH$4H V H$4H H$4H- H$4H(H$4HO H$4H0H$5HT H$5H8H$(5HR H$05H@HDŽ$p4HDŽ$x4fDŽ$4Ƅ$4HDŽ$4HDŽ$4fDŽ$4Ƅ$4HDŽ$4"HDŽ$4fDŽ$4Ƅ$4HDŽ$4 HDŽ$4fDŽ$4Ƅ$4HDŽ$5HDŽ$5fDŽ$ 5Ƅ$"5HDŽ$85H$P5H" H$X5HHH$x5H N H$5HPH$5H H$5HXH$5H}) H$5H`H$5HH H$5HhHDŽ$@5fDŽ$H5Ƅ$J5HDŽ$`5HDŽ$h5fDŽ$p5Ƅ$r5HDŽ$5HDŽ$5fDŽ$5Ƅ$5HDŽ$5 HDŽ$5fDŽ$5Ƅ$5HDŽ$5#HDŽ$5fDŽ$5Ƅ$5HDŽ$6HDŽ$6fDŽ$6Ƅ$6H$6HAD H$ 6HpH$@6HS H$H6HxH$h6HR H$p6H$6HH$6H' H$6HH$6HL H$6HH$6H8HDŽ$(6HDŽ$06fDŽ$86Ƅ$:6HDŽ$P6HDŽ$X6fDŽ$`6Ƅ$b6HDŽ$x6HDŽ$6fDŽ$6Ƅ$6HDŽ$6HDŽ$6fDŽ$6Ƅ$6HDŽ$6]HDŽ$6fDŽ$6Ƅ$6HDŽ$6H$7H^L H$7HH$07HM H$87HH$X7HM H$`7HH$7HtN H$7HH$7HI H$7HHDŽ$6fDŽ$7Ƅ$7HDŽ$7HDŽ$ 7fDŽ$(7Ƅ$*7HDŽ$@7 HDŽ$H7fDŽ$P7Ƅ$R7HDŽ$h7 HDŽ$p7fDŽ$x7Ƅ$z7HDŽ$7 HDŽ$7fDŽ$7Ƅ$7HDŽ$7HDŽ$7fDŽ$7Ƅ$7H$7HK H$7HH$7HO H$8HH$ 8HN H$(8HH$H8H H$P8HH$p8HuO H$x8HH$8HQO H$8HHDŽ$7HDŽ$7fDŽ$7Ƅ$7HDŽ$8HDŽ$8fDŽ$8Ƅ$8HDŽ$08HDŽ$88fDŽ$@8Ƅ$B8HDŽ$X8HDŽ$`8fDŽ$h8Ƅ$j8HDŽ$8HDŽ$8fDŽ$8Ƅ$8HDŽ$8H$8H. H$8HH$8HhM H$8HH$9HsK H$9HH$89HDH H$@9HH$`9HNJ H$h9HHDŽ$8fDŽ$8Ƅ$8HDŽ$8 HDŽ$8fDŽ$8Ƅ$8HDŽ$8 HDŽ$9fDŽ$9Ƅ$ 9HDŽ$ 9HDŽ$(9fDŽ$09Ƅ$29HDŽ$H9HDŽ$P9fDŽ$X9Ƅ$Z9HDŽ$p9HDŽ$x9fDŽ$9Ƅ$9H$9H J H$9H H$9H*K H$9H(H$9HK H$9H0H$:HVG H$:H8H$(:HI H$0:H@HHH$P:H,L H$X:HDŽ$9 HDŽ$9fDŽ$9Ƅ$9HDŽ$9HDŽ$9fDŽ$9Ƅ$9HDŽ$9HDŽ$9fDŽ$9Ƅ$9HDŽ$: HDŽ$:fDŽ$ :Ƅ$":HDŽ$8: HDŽ$@:fDŽ$H:Ƅ$J:HDŽ$`:H$:HBH$:HI H$:HBH$:HL H$:HBH$:HK H$:HB H$;HJ H$x:H$ ;HDŽ$h:fDŽ$p:Ƅ$r:HDŽ$:HDŽ$:fDŽ$:Ƅ$:HDŽ$: HDŽ$:fDŽ$:Ƅ$:HDŽ$:HDŽ$:fDŽ$:Ƅ$:HDŽ$;HDŽ$;fDŽ$;Ƅ$;HDŽ$(;HDŽ$0;fDŽ$8;Ƅ$:;H$H;HB0H$h;HD H$p;HB8H$;HJ H$;HB@H$;HF H$;HBHH$;HB H$;HBPH$<HGI H$<H$@;HDŽ$P;HDŽ$X;fDŽ$`;Ƅ$b;HDŽ$x; HDŽ$;fDŽ$;Ƅ$;HDŽ$;HDŽ$;fDŽ$;Ƅ$;HDŽ$; HDŽ$;fDŽ$;Ƅ$;HDŽ$;HDŽ$;fDŽ$<Ƅ$<HDŽ$<H$8<HB`H$X<HF H$`<HBhH$<Hn H$<HBpH$<HI H$<HBxH$<HG H$<HDŽ$ <fDŽ$(<Ƅ$*<H$0<HDŽ$@<HDŽ$H<fDŽ$P<Ƅ$R<HDŽ$h<HDŽ$p<fDŽ$x<Ƅ$z<HDŽ$<HDŽ$<fDŽ$<Ƅ$<HDŽ$<HDŽ$<fDŽ$<Ƅ$<HDŽ$<HDŽ$<fDŽ$<Ƅ$<H$=HH$ =HG H$(=HH$H=HG H$P=HH$p=HF H$x=HH$=H H$=HH$=HJG H$=HH$<HDŽ$=HDŽ$=fDŽ$=Ƅ$=HDŽ$0=HDŽ$8=fDŽ$@=Ƅ$B=HDŽ$X=HDŽ$`=fDŽ$h=Ƅ$j=HDŽ$=HDŽ$=fDŽ$=Ƅ$=HDŽ$=HDŽ$=fDŽ$=Ƅ$=HDŽ$= H$=H>F H$=HH$>H@ H$>HH$8>H H$@>HH$`>H H$h>HH$>H H$>HHDŽ$=fDŽ$=Ƅ$=HDŽ$=HDŽ$>fDŽ$>Ƅ$ >HDŽ$ > HDŽ$(>fDŽ$0>Ƅ$2>HDŽ$H>HDŽ$P>fDŽ$X>Ƅ$Z>HDŽ$p>tHDŽ$x>fDŽ$>Ƅ$>HDŽ$> HDŽ$>fDŽ$>Ƅ$>H$>H8= H$>HH$>Hx H$>HH$?HHDŽ$>fDŽ$>Ƅ$>HDŽ$> HDŽ$>fDŽ$>Ƅ$>HDŽ$?OHDŽ$?fDŽ$ ?Ƅ$"?HDŽ$8?HDŽ$@?fDŽ$H?Ƅ$J?HDŽ$`?HDŽ$h?fDŽ$p?Ƅ$r?HDŽ$?H$?HC H$?HH$?HC H$?HH$?Hj: H$?H H$@H H$ @H(H$@@H9 H$H@H0HDŽ$?fDŽ$?Ƅ$?HDŽ$?HDŽ$?fDŽ$?Ƅ$?HDŽ$?HDŽ$?fDŽ$?Ƅ$?HDŽ$@HDŽ$@fDŽ$@Ƅ$@HDŽ$(@!HDŽ$0@fDŽ$8@Ƅ$:@HDŽ$P@HDŽ$X@fDŽ$`@Ƅ$b@H$h@H? H$p@H8H$@Hj; H$@H@H$@H? H$@HHH$@H= H$@HPH$AHB H$AHXH$0AH H$8AH`HDŽ$x@HDŽ$@fDŽ$@Ƅ$@HDŽ$@HDŽ$@fDŽ$@Ƅ$@HDŽ$@HDŽ$@fDŽ$@Ƅ$@HDŽ$@ HDŽ$@fDŽ$AƄ$AHDŽ$AHDŽ$ AfDŽ$(AƄ$*AHDŽ$@ANH$XAH; H$`AHhH$AH@ H$AH$AHxH$AH< H$AHH$AH|@ H$BHH$AH\$HDŽ$HAfDŽ$PAƄ$RAHDŽ$hA HDŽ$pAfDŽ$xAƄ$zAHDŽ$AHDŽ$AfDŽ$AƄ$AHDŽ$AHDŽ$AfDŽ$AƄ$AHDŽ$A HDŽ$AfDŽ$AƄ$AHDŽ$BHDŽ$BfDŽ$BƄ$BH$ BH> H$(BHH$HBH[> H$PBHH$pBH; H$xBHH$BH? H$BHH$BHyX H$BHH$BHK? H$BHHDŽ$0BHDŽ$8BfDŽ$@BƄ$BBHDŽ$XB HDŽ$`BfDŽ$hBƄ$jBHDŽ$BHDŽ$BfDŽ$BƄ$BHDŽ$BHDŽ$BfDŽ$BƄ$BHDŽ$BY HDŽ$BfDŽ$BƄ$BHDŽ$BH$CHD; H$CHH$8CH; H$@CHH$`CH: H$hCHH$CH; H$CHH$CH, H$CHHDŽ$CfDŽ$CƄ$ CHDŽ$ CHDŽ$(CfDŽ$0CƄ$2CHDŽ$HCHDŽ$PCfDŽ$XCƄ$ZCHDŽ$pCHDŽ$xCfDŽ$CƄ$CHDŽ$CHDŽ$CfDŽ$CƄ$CHDŽ$CHDŽ$CfDŽ$CƄ$CH$CH H$CHH$DHK H$DHH$(DHm9 H$0DHH$PDHH9 H$XDHH$xDH#9 H$DHH$DH4 H$DHHDŽ$C&HDŽ$CfDŽ$CƄ$CHDŽ$D HDŽ$DfDŽ$ DƄ$"DHDŽ$8DHDŽ$@DfDŽ$HDƄ$JDHDŽ$`DHDŽ$hDfDŽ$pDƄ$rDHDŽ$DHDŽ$DfDŽ$DƄ$DHDŽ$D H$DHg> H$DHH$DHi H$DH H(H$EH9 H$ EH$HEHBH$hEH5 H$pEHBHDŽ$DfDŽ$DƄ$DHDŽ$D HDŽ$DfDŽ$DƄ$DHDŽ$ED HDŽ$EfDŽ$EƄ$EHDŽ$(EHDŽ$0EfDŽ$8EƄ$:EH$@EHDŽ$PEHDŽ$XEfDŽ$`EƄ$bEHDŽ$xE HDŽ$EfDŽ$EƄ$EH$EH/ H$EHBH$EH3 H$EHB H$EH9 H$EHB(H$FH]/ H$FHB0H$0FH6 H$8FHB8H$XFH8 H$`FHB@HDŽ$E HDŽ$EfDŽ$EƄ$EHDŽ$E HDŽ$EfDŽ$EƄ$EHDŽ$EHDŽ$EfDŽ$FƄ$FHDŽ$FHDŽ$ FfDŽ$(FƄ$*FHDŽ$@FHDŽ$HFfDŽ$PFƄ$RFHDŽ$hFH$FH# HDŽ$pFfDŽ$xFƄ$zFH$FHDŽ$F HDŽ$FfDŽ$FƄ$FHDŽ$FHDŽ$FHDŽ$FHDŽ$FfDŽ$FƄ$FH+HteC C!H{Hst5{"t zHE0HSHHt 1`{HE{HE HsHEH}Ht%yH(HF1[]ATE1UQH52 PtHtC1HH{IHu wHuH H5NH8sHMuHrLZ]A\AWAVAUATIUS1H(LPH{Ht HHcHcAHwHHHHD$D|$ M9}KDH#HHuIM$HH;\$tH;u!IHL$HCHL$HHH9tHHu?Lct$ H5{KDHHI$HPH H81yHoMvuHo1H([]A\A]A^A_AWAVAUATIUSHH(LwH I9t NH*ItLLvIHuELtyHH@u1LMtHD$D$E1 D$E1HwHtBH8Ht:HIT$LH|$uH|$HHtH|$Hup|$MtHSHLAIHu:Lyp0LMHt IVLH5H81lH7& H H5 1lH& HH% H5U% 1kH% HH5 1kH% HH5W 1kH% HzH5 ! 1kH% HWH5  1ekH% H4H5&! 1BkHs% HH5 1kHX% HH5 1jH=% HH5e 1jH"% HH5" 1jH% HH5O 1jH$ HbHHH1njH$ H=H5 1KjH$ HH5< 1(jH$ HH5 1jH~$ HH5 1iHc$ HH5 1iHH$ HH5 1iH-$ HkH5 1yiH$ HHH5 1ViH# H%H5 13iH# HH5 1iH# HH5 1hH# HH56 1hH# HH5K 1hHp# HvH5P 1hHU# HSHm$ H5 1ZhH3# H)H5 17hH# HH5  1hH" HH5 1gH" HH5 1gH" HH5 1gH" HzH5 1gH" HWH5a 1egHv" H4H56 1BgH[" HH5 1gH@" HH5h 1fH%" HH5 1fH " HH5 1fH! HH H5 1fH! H[H5 1ifH! H8H5 1FfH! HH5 1H fHy! HH5 1eH^! HH5 1eHC! HH5 1eH(! HH5x 1eH ! HcH5e 1qeH H@H5z 1NeH HH5_ 1+eH HL , L 1H  H H5 dH HAE11H H  Qj5 5 RRPRR1QdHPHB HhH5z 1vdH HEAE11Hw H x Qh5 5^ RRPRR1Q4dHPH H4L-A1T6L-A1;8L-pA1":L-WA1 EL->A1IL-%A1JL- A1KL-A1oAL-H0 H=i H= HH H H Hz Hk H\ y1H H5 H=J ]}AL-AH|$Ht HuYH|$ Ht HuYH|$(Ht HuXH= tFH=` ttLDH=襌H= Ht7H Hu'X =]HuH H5H8Y1H=p 1H H= HI H"H H= H5  H= bH=u 0H=a H=m H=N `H=: H HgH HfHnHDfHnHH=* flfHnH*H= ) fHnH0fHnflH1)y fHnH fHnfl)m fHnfl)m H5 H=r `H=^ H=J H HH5 HH fHnH!fHnH0H=( H H flH= H i H5- H= 1`H= MH= 7H=IZHHu~AL-ApHHRH5cHi H-HMuHUH=fZHHtA HHH5cH H-HMuHOUH=ZHH:A HHH5ZNcH H4-HMuHTH=nYHHA`HHPH5AbH H,AH HHH5bHW H,A0HHH5bH. H{,APHHH5dbH HJ,AHHH5}3bH H,AHH|H5LbH H+AHHZH5aH H+AHH#H5aHa H+AHHH5oaH8 HU+AHHH5>aH H$+AHHH5W aH H*AHHuH5&`H H*AHHTH5`H H*AHH,H5z`Hk H`*AHHH5I`HB H/*HMuHQH=VHHA`HHSH5_H H)A@HHH5|_H H)H*H)AHHeH56{_H Ha)HMuH%QH=EUHH H BH HH5?P[\)H HR HH5+[7)H H% HH5[)HMuHPH=TUHHuAL-x2H H HH5[(H H HH5{[(H H HH5V[(H H HH5k1[(H uHf HH5R [a(H PH9 HH58Z<(H +H  HH5Z(H H HH5Z'H H HH5xZ'HMuHOH=%SHHqH HG HH5-Z'H H HH5Z]'H H HH5Y8'H 'H HH5Y'H H HH5sY&H %Hf HH5YtY&H (H9 HH5JOY&H #H  HH5**Y&H H HH5 YZ&H H HH5X5&H \H HH5X&HMuHHMKLl$Lt$IHLLLH~FH=_ H5 1*HD$HHQH5) \*HD$ HDH|$HuLH5 H|$ HD$@MHD$HH|$ HuLHD$ H|$H;= @H;= @uH;= tQŅH|$Hu>LHD$H=v 1҅H5 )HD$HHH5( k)HD$ HH|$HuKH5 H|$ HD$4)HD$H]H|$ HuKH= HD$HD$ HH uKHD$uH5O (HD$HH H5 (HD$ HH|$Hu0KH=9 HD$ HD$HH! u KHD$ H<$Ht HuJH|$H$Ht HuJHD$H|$Ht HuJHD$AdfAdYAdLAd?Ae2Ae%AeAg AgH|$Ht Hu JHD$H|$ Ht HuJH DHD$ H=s}HL$(HT$HHt$ +0y6HHL$L-`HT$H4$AhfBcH H= HHH uoIH|$ Ht Hu[IHD$ H|$Ht Hu>IHD$H|$(Ht Hu!IHHL$HD$(HT$H4$AGLLLHHABH5 H= >&HD$(HHH H5_ HPH|$(HuHHD$(H= LH5 H=y %HD$(HHH H5 HOx{H|$(Hu&HHD$(H=v qLH|$Ht HuGHD$H|$Ht HuGHD$H<$Ht HuGH$H|$Ht HuGHD$H|$ Ht HuGHD$ H|$(Ht HulG111HHD$(/HH $HT$Ht$ @H5 H= 1$HD$(H H= H HuGH5 H=Z 1HD$(r$HD$(HH= H HuFH5 H= 1HD$(.$HD$(HH= Hz HuxFH5q H= 1HD$(#HD$(HH=5 H. Hu4FH55 H= 1HD$(#HD$(HjH= H HuEHD$(H`  KHJ uKHF iKHB ]KH> QKH: EKH6 9KH2 -KH޹H= H DLLLHH>H5 H=J "HD$(HHH H5 HjLH|$(HuDHD$(H=[ >IH5 H= ;"HD$(HHH+ H5T HLx{H|$(HuDHD$(H= HH<$Ht HueDH|$H$Ht HuIDHD$H|$Ht Hu,DHD$H|$Ht Hu DHD$H|$ Ht HuCHD$ H|$(Ht HuC111HHD$(+HHL$HT$H4$r<=BLLLHH<H= H;= H;= uH;= t HbH=K H54 HD$(HH6H Hl$`HD$XHHD$`rHD$HH|$(HuBHD$(H|$HuBH= H5 HD$ HD$HHH HHD$XHD$`qHD$(HH|$Hu`BHD$H|$(HuHBHD$(H|$Ht Hu+BHD$H|$Ht HuBHD$H<$Ht HuAH$H|$Ht HuAHD$H|$ Ht HuAHD$ H|$(Ht HuA111HHD$()HH $HT$Ht$9:H 11H=w 2BHD$(HHH5 H= HH|$(HuAHD$(H= HD$(HHH5 H=c >HH|$(Hu@HD$(H= HD$(HHH5 H= GH|$(Huw@HD$(T>HD$(H|H HHD$(H H@HHt$(1H= (HD$HZH|$(Hu @H5J H|$HD$(HHD$(HH<H5 H=P +G=H|$(Hu?HD$(H|$Hu?HD$H= WHD$HH H5 H= F H|$HuL?HD$)=HD$HHL HHD$H= H@HHt$1H=p 'HD$(HH|$Hu>H5 H|$(HD$GHD$HHH5 H=% FH|$Hu>HD$H|$(Huq>HD$(NH2 H  H9Hu)H Ht HH= .H= 聭HH= H H5 HH|$H- H5: HD$(H* H|$Hu(9HD$(H | HD$HD$(H# H| H9Hu)HG Ht HH=8 .H= ҬHH= H H5 CHH|$(H H5 HD$H H|$(Huy8HD$H HD$(HD$H| H H9Hu)H Ht HH=y .H=X #HH=G HX H5Y 蔮HH|$H+ H5 WHD$(H( H|$Hu7HD$(H HD$HD$(H H H9Hu)H Ht HH= .H= tHH= H H5 HH|$(H H5- HD$H H|$(Hu7HD$H ? HD$(HD$H. Ho H9Hu)H Ht HH= .H= ŪHH= H H5 6HH|$H) H5~ HD$(H& H|$Hul6HD$(H 11HD$H=L H HD$(7HD$(HH H5 H= s= H|$(Hu5HD$(,>HD$(HH H H5 %= Hv H5 H|$(= H^ H5 H|$(< Hn H5 H|$(< H6 H5 H|$(< H. H5g H|$(< HV H5W H|$(e< H H5O H|$(E< H H5 H|$(%<| H H5 H|$(<s H H5 H|$(;j H H5 H|$(;a H& H5 H|$(;X HN H5 H|$(;O HN H5O H|$(e;F H H5 H|$(E;= H H5 H|$(%;4 H H5 H|$(;+ H H5 H|$(:" Hn H5W H|$(: H H5 H|$(: Hn H57 H|$(: Hv H5 H|$(e:HN H5g H|$(E:H H5g H|$(%:Hn H5O H|$(:Hn H5 H|$(9H H5 H|$(9H. H5 H|$(9H H5_ H|$(9H H5 H|$(e9H H5 H|$(E9Hn H5O H|$(%9H H5 H|$(9H H5 H|$(8H6 H5 H|$(8H H5 H|$(8H H5 H|$(8wH H5 H|$(e8nH& H5? H|$(E8eH H5 H|$(%8\HN H5 H|$(8SH H5 H|$(7JHv H5_ H|$(7AHT$(H5 H= 78H|$(HAL-&sA5L-A6L-A7L-pA:L-TpA;L-8TAL-8AL-AL-FAL-*AL-AL-AL-֢AL-tAL-XAL-<A L-f A L-JAL-.AL-AL-AL-ڡAL-xAL-\AL-@AL-j$L-YA L-BAL-+A+ L-A+L-AL-A'L-ϠA)L-Al7L-AU9L-A>GL-sA'IL-\AWL-EAYL-.AAaL-AcL-AdL-AeL-̟AfL-oAgL-XAhL-AAiL-p*AjL-YAkL-BAlL-+AmL-AnL-AoL-ApL-ϞAqL-rArL-[AsL-DAtL-s-AuL-\AvL-EAwL-.AxL-AyL-AzL-A{L-ҝA|L-uA}L-^A~L-GAL-v0AL-_AL-HAL-1AL-AL-AL-AL-՜AL-xAL-aAL-JAL-y3AL-bAL-KAL-4AL-AL-}AL-HMu$HA~'L-z~AL-^HMu$HAn'L-z4AL-^HMu$HA('L-4AL-DA+H QH=֠ZL-H([]A\A]A^A_H= ^%f.@H=A H: H9tHֱ Ht H= H5 H)HH?HHHtH HtfD= u/UH=~ Ht H=R -/h ]{f.HG8HHGHHGHGHHGWd1~HGpHff.@HpHHpff.fATIUHSHHHt HՅu!H1Ht[LH]A\[]A\ff.HGHHGHHHHt 1DHGHHGHt;Ht6H9HOHVH9t(\Ht 1~\HtÐ1H91DF\f9G\u΋GX;FXuATUSH_H9^t|H_ H9^ tiH^(H9_(tVH_0H9^0tCH_8H9^8t0H^@H9_@tH^HH9_Ht HFPH9GPu{\St[]A\Ë^`19_`uLgHnMtOHtI<$1Ht,HtHt1HDI9Du%tHI<Hu1H|f11Hff.@Hu#10HtH HHPHfH H5 18Hu+10HtH_ HHPHHH H5R 18HGHHtfD'HGHHtfD#+AUIATIUHSHHGHHt]H=_!!u:LLHI:'MtHL[]A\A]&IHt"HE1[L]A\A]fH[]A\A])H H5s_H8"fAUATUSH^HH9=IIH@H1E11L^#HLHDHHHTHI9~H[]A\A]DUHGHL@t3H LH_H81;*AHEu&]fDH HHH5|_H81(Hmt 1]H 1ff.UHH HGHHn*H|$HT$Ht$'HEH= H9}tH9}HH}0HG H H9MH H9t~H H9tiH H9tTH H9t?H H9t*H H9tH H9)HmH|$HT$Ht$H}HtHEH/t^H} HtHE H/t7H}(HtHE(H/tHEHH@H ]3+ffH}@G1Ƀ 9AH5 HcHH&H}HtHEH/tHEH]H@fDK"uHUHH9B0uHNt]ATIHUH~HtIHID$LHH@pPHmItHL]A\HHL]A\DE1ff.UHSHHt:HHH}H/tH]H1[]@;H]H1[]fDH ff.@UHGHHunH$H}HtHEH/t?HHtHDžH/tHEH]H@ff uHUHlH9B0tHd]H٦ LGHHGMtI(t 1HL,1HDUSHHH- HHEHkHHEHt H/tAHEHHHHEHtH/t H1[]H1[]ffAUfIATIUHSHH(HGXHT$Ht$HD$HG`GXHD$HGhHGhH|$HD$H{XHt$Ht H|$|HD$HtHHD$HtHHD$Ht HHD$HT$IUI$HD$HEHH8L`HHT$HhHPHT$HPHtH/t=MtI,$tAHtHmtH(1[]A\A]HxfDkfLXfDH|$IEI$HEHtH/t8H|$HtH/tHH|$HtH/t(H([]A\A]fffATfHnfHnUflHLGXLg`GXHohHOhMtI(tLMtI,$t0HtHmt H]A\@HH]A\YfLHfDL8fDAUIATIUSHIHtTH5 HLALHHmItHL[]A\A]ÐHHL[]A\A]f.HE1[L]A\A]ff.@USHHH- HHEHkHHEHtH/HEH{ HHk HEHt H/tnHEH{(HHk(HEHtH/t?H{HHtHCHH/tH1[]H1[]f.ffYfDATIUHSHHHt HՅuAH{ Ht LՅu/H{(Ht LՅuH{H1Ht[LH]A\fD[]A\ff.H9t+HXHt/HJH~F1 fHH9t7H9tuf.HH9tHu1H;5 f1ff.fAUAATUSHH9H H9GHIH9F A|$ HUI9T$HEIL$H9@H@t Hu ED$ D8@ !H}HA cIL$0It$HA@HEȃU\DA9uBHH1Au&1@H1 H9ut1AH[]A\A]@I9uuHDL HHH; H;- uH9u8HmuHD$ :D$ @1AH[]A\A]@HfDHM0H}H@HE@L:fL5fDIt$HfDD@Dff.Ha H9Gu;HGHPHwUHt HcWHHcHHEfUHHHtoH.Hmt7H]ÐHtBHt GWHH f.HHD$HD$@GWHH HH뚐ATIH/t%Hf LH5QH81zA\f{fG<4w9HŒHcHfDf.f.HH @H5RH811Hff.f.f.AVAUIATIUHLwLCHHtCH@HHtHLLH]A\A]A^DHEHH]A\A]A^@Hq LH8@AVAUATUHSHHWDl$@HZpHHCHIMtI0H[]A\A]A^DHLu1HH1H^ LIHtHmuHMtFLLSI.ItHHL[]A\A]A^Ha HRH56QH81dHE1[L]A\A]A^ÐLXfDEu+L5ě NEuCH HF@1HL$H4$H4$HL$HIHfDHIHt9HY LHIHtHmt9ImLH*HmHH~ff.UHH$H$H$L$L$t@)$ )$0)$@)$P)$`)$p)$)$Hl$ H$D$HD$HH$HL$HOD$ 0HD$ HH=jDAUATIUSHHHGH$IHl$HD$tBHHOH $H( LH5nOH81,1H[]A\A]1LHHt4H$H@uHԘ LH5NH811@H $HuH[]A\A]AWIAVN4AUIATUSHHHHG1HL$HHD$0LL$HD$0HD$8HD$@HD$(Ht H/HD$0Ht|HD$8H9CITHLHHD$8HT$0IHL$(Ht~LfHPHHtcH9 uHT$0Ht$L)HD$(HD$0HHuHL$HT$(Ht$8HrIHL$(Huf.HHD$0HHt$(HFIHtMMID$IHt:H8HFH9Gu ID$IHt$(HuM9u&"fDHFH9GIM9IH8H9uH HT$HH5$MH81H|$(Ht H/hH|$0Ht H/JHH[]A\A]A^A_fD{ &Ht$H|$0LL)H<I<$Ht$(:HH.tH|$0fH( fDHKxfHt$(IM9H HT$HH5KH81H HT$H5KH819HHt$(H|$(HtH/t:H|$0Ht H/ua HH1[]A\A]A^A_K A 7 H|$(HufAUATIUHHH@H;5} HH(A$@HLnI@t'M9LL"*HEHHE1HL"HmIMIM@LLoImuu]LA\A]+H5JHt!H ]A\A]H8 Ht]LA\A]fDt)A$@t1 HHD]A\A]DH5J]LA\A]H1H@HxtHL]A\A]H) LH5JH81-ATfHnfHnUflHLLgHoHOMtI(tNMtI,$t2HtHmtH]A\fDHH]A\fLfDLfDIHH HHGH9tHu HGHuHIHGHHGHIHtHHHtHHHtHff.fAWAVAUATIUHSH8HM0L|$pL.HD$AM~pHA1AIHD$HFHLt$IELl$ ILL|$(IHHLEt$0HL$ ILImL|$0Hl$XZL9l$uH8[]A\A]A^A_M~ H|$~M9t61M~HLLH} LLd$I9uH8[]A\A]A^A_ÐL;l$uLH8HLI[]A\A]A^A_9 fHGHHGATUHSHHGH;R H;- tSHXpHtzH{tsHcIHHHSI,$LHD$HD$@Ht HyHGtH;Es}HDHH[]A\HXhHt_HCHtVHyulHH[]A\Ht HyHGtH9EvHUHHH[]A\HIHt@HH"HHtHt$HHt$HxHHCl1H͏ Ht$H88tHCHt$5ATIHUHHtIHID$LHH@pPHmItHL]A\HHL]A\DE1ff.LVIIM1fHI9tM9Duf.1fDITHBtv@tmL9tIXHt,HqH~S1HH9t?H;TufDLDHH9xHuH; ffDHI9k1ATIUHSHHHt HӅuQH} Ht LӅu?H}(Ht LӅu-H}HHt LӅuHp1Ht LH[]A\[]A\ff.UHH HGHH. HT$Ht$H|$ZHEHPHUHH; HB8HDžHDžHEHH|$HT$HEHt$hHpHtHDžpH/tHH H]fDfHDž HUHH9B0HH ]u@HHtHDžH/tHEH$@HEHp@H=A1HHtGHH9t.HXHtRHJH~q1DHH9t_H;tuHfDH H5qH81HHDHH9tHuH;5( tfDH) HNH5BHWH81(1@AWMAVMAUATUSH8HH$H$HHt$HT$$H$HDŽ$q$HDMMHD$$H@H$ HD$H@H$(H$HDŽ$H$HHD$$H@H$(HD$H@H$H$HDŽ$H$H6HD$$H@H$HD$H@H$H$HD$pH$HLMIHD$$H@ HD$HHD$H@ HD$P_H$HD$0HT$@H1MMHD$$H@(HD$XHD$H@(HD$`H|$@MHD$xH|$HHD$$Lh0HD$L`0WLT$E1MhLLMMHD$$H@8HD$ HD$Lh8Hl$(HD$8MMILHD$$ H@@HD$hHD$L`@MHD$L$E1L$HPHHD$H$L$MIHpHHD$(H$LL$HIċ$LIMLHILd$hL9$uMIL$L$H$L$H$HD$8HD$8HT$ HT$(H9LMHLI9HD$xHt$XHD$xHt$H9D$`GMHD$0HT$HHD$0HT$@H9D$PMMHD$pH$HD$pH$H9$]LMIH$H$(H$H$H9$H$H$ H$H$H9$FH$H$H$H$H9$H8[]A\A]A^A_@MHL$(E1LHLIL$L$L$VHL$hL$L$L$HM9uB@MYHE1fHLLLT$8L\$(IHL$ L\$(LT$8HM9uMHL$1HLLHHLI9uIHHL$@Hl$X1fDHLLHnHHI9uIHH$Hl$H1HLLH1HHI9uH$H$H$1HLLHHHH9$uH$H$1HLLHH$(HH9$uH$H$1HLLHiH$ HH9$urH$H1HLLH)H$HH9$uaff.@HG@t~HFHtt@tkH9t.HXHt*HJH~A1DHH9t/H;tufHH9tHu1H;5 f1D#t4@AWAVAUIATUHSHHGHHtIMt"HL[]A\A]A^A_IMuHك H8uH LH5hH81HHHtHHtH5G HIHteLHIHtjHI/Ht#I.t'Hmt*HpI3DLLHHm:H-1fDUSHHH-P HHEHkHHEHtH/HEH{ HHk HEHtH/HEH{(HHk(HEHt H/H{HHtHCHH/tpHpHEHpHtH/tBHH9tHtP8Hǃ~gHǃH1[]ff_fD,fDfDu'HHtHǃH/u|{rH=E61HWD_@GDHtWH H1LH9t)HRLIHLATUHSHHFHHW@@HXHt;HJH~{1fDHH9thH;luH[]A\f.HH9tHu1H;-r ΐE1JtH9tH|$IuIH|$L9uH1[]A\@HH[]A\H^H~1 HH9tH;|uSf1ff.fAWAVAUATUSH8HH$H$ HHIIAHDŽ$H$(A$AIAH$HzHDŽ$ICH$H$H$AIAH$HHDŽ$ICH$H$H$ABIAH$HHDŽ$ICH$H$H$AIA H$HHD$HIC H$H$HD$`LMIAIC(HD$PHIA(D|$MMHD$HD$XHD$`HD$(|$|IG0HD$H3IF0Hl$(1EHD$ L|$ M_8MHH8L\$@IIHD$0HL$8HHH̓|$Mw@M|$ H]@'LHUHIwHE1ɋ$EL$L$H$HT$xHt$pH|$hkH|$hHt$pL$HT$xHH$L$IM9uHD$0Ld$8Ht$0H9t$@GHLHHHl$ HH9\$IEHD$H\$XHD$H\$(H9D$PMD|$MHD$HH$HD$HH\$`H9$LMIH$H$H$H$H9$H$H$H$H$H9$$H$H$H$H$H9$H$H$(H$H$H9$ 8H8[]A\A]A^A_I<$HEHHsLT$pHD$hHHH$H8HEHH=DD$L\$LL$7LL$L\$DD$HHH$H8HEuAHHDD$L\$LL$LL$L\$DD$HHHHH$H8HEu5HHDD$L\$LL$LL$L\$DD$HHUHH HGHHT$Ht$H|$2HE`HEHH}H}8HmH|$HT$Ht$xH}PHtHEPH/tAH}XHtHEXH/tHEHH@H ]DffUhkH}H^EluMM0HU@E1Hu8H}@u'HH9P0H~H ]KHEff.fAWAVAUATUSHLoMzHIH1HI9tH9\uIH[]A\A]A^A_DHC0E1HD$@NdI9Hi H9CI9D${ A|$ HSI;T$ID$HsH9@H@t HDK A|$ Dȉ@@8uA ]LKH@ jIt$0IH@IDA9DA9u7HLL$E1HL$AIM91H[]A\A]A^A_f.L5g L9uuM9uuLHL$IHtH;g L$L;%g uM9u:I,$DtIEnErKH[]A\A]A^A_f.LL$$I,$L$AuLL$L$@A@HsHHEt$I@ It$HHL$LL$A|$ @LL$$L$1A9D`A9DSATUHHGHGHx_HPHv5HuDgGII HL]A\fDH]A\@E1HtDgH]LA\fHe H52 IH8S렐H@`HtmHHtaHHtWHf H9Eu'@H(HmIYHLHH5Q获HHuI)uHuHd H5QLH8HGt{HGHPHvHtOHt1D@HtHcWHHcHHE@GWHH f.GWHH HUHH@`HtvHHtjHHt`Hd H9EuH8Hmt)H]HH5PlHHuHHHD$HD$?HuHkc H5KH8fATUHHGHGHPHv2HHtJHcAH9HD]A\E1HtDgDHDDH]DA\@GWHH HcAH9tH)c H5H8Af.GWHH HHcAH9uHD]A\f.Hu%HtfDH@`HtfHHtZHHtPH:c H9Eu'@HHmAH*HH5O趴HHu7H)Ha H5|IAH8ff.AUATIUSHHHb H9FHnHEHHHcFHHcHEHH\ID$H;b H;` HXpHt|H{tuHHHQHLSHmH[]A\A]fHGH;}b H;X` uHG11H9IDHH[]A\A]ÐHXhHtgHCHt^HHHL[]A\A]HID$H(H9v)ID$HHH[]A\A]ÐHG1HHHlHLa@HID$H(H0fDHID$H;va PH;Q_ HfHxIHtHImHDHI"HuH\ H5DH8H@DAVAUATIUHHHH;=^ tH5^ tbfHUBtUM4$LjE1 uLeH= fLLAI}MHL]A\A]A^DHEt+H@8HDHtHLH1]A\A]A^IHtfI$HI$IEHELMH=[ uG1LHAIMt"ImKL>fE143IHtEE1!IHuHZ H5 H8cfD1LHIHgZ H5 H80qff.AVH?IAUIATIUHHHH5K\ H9IUtHB8IDHHL%H HdH= {u(1LLIMujIHHE1]LA\A]A^DIUBlLb1 H= 1uHAI+MtHL]A\A]A^Hu!H5K[ H9I}t@HG8IDHt2HLLL]1A\A]A^f.Im\LhHH 1f.IHIHTHI9uIELMH= 1HLAI+MHmHf.IUBM6Lb1 uImH=I MLHW H5F H8fE1v1HL#IYIHuHW H5 H8H1HLL1]A\A]A^ff.AWAVAUIATAUHSH(H= IHH@XMwhIGhfH$IG`AGXHD$HHH8Hu H9GLu MHW I9tL;!X LE1H51 EAHD D׃HcHD;t1f~0H9})HcHTA9}߉9|A9A9}HHHD;pjL I$H3~ 1LLHHt6XlHI,$uLHmHtH([]A\A]A^A_I,$uLH([]A\A]A^A_KHAHHHxXIH1W H0t111LGRfH!V H5Z E1H=x} c~$IXMW`MGhMwhD$AGXHt H/Mt I*vMt I(|E.H5_ HDG AD׃1V1ufDIGXfH$IG`AGXHD$IGhIGhHD$ELHIM~$IXHD$Mo`D$IohAGXIGhHt H/Mt ImHt HmH= EHD-h DHcHD;t1fDU9)HcHDA9}׉IGXfH$IG`AGXHD$IGhIGhHD$LDHS1H=;IHHHHHkImILG1A9A9 HcHLE;p;D9-L DL$)PIcHHHHHD9HMHHD9HMHtHHHL$AEpM D-ٍ I$EImuLH$HtHHD$HHH\$HtHH$HHtH\$H,HHH$HH,DD9-T A@IcHHHH/ HcD-! D- HLD9LL$$L$uLwLD$L$LD$L$=IGXfAH$IG`AGXHD$IGhIGhHD$H=Hy H5 HGHH;Q N1=HHzH|$H|$HHHIH{Q H9Q cH8H+THaLD*H5c~ HL$HVHL$HIHLn H@Hn %HHЈ Hy DpHf L I$HcHL^HHHP IHD$LD$SLD$HD$I8M H/z/pHD$pLD$HL$5LP H+P H@HHGP8HtH2H }7/HD$H=c HD$Hff.HHcHdIHI?H?JHʃHL)H?H!H)HHH4!fDHy;HHH9HHHHWPHOPHHHPHHWHOHPHxAUHN ATUH-w L(XHEHLAŹH 6jIH=6HmtADH Y6?H=j u]A\A]HxfD1ff.fATHv LOL9t.IXHLAM~E1 HI9t7H;TuH;=N H?LtLA\LA\DHWpHOxLH>HG@HFdMLL9H9AD M9AL9AE D!DOAADHH)HH=o NoVPAotjobf oin`AoptFoz ~0oy ~pAo@ t"or0v@oI0AoP0tH H92H~IHaLnIEI|$H/Ml$HEHvH^H5l HFID$LHHHH^H/ID$H5k LHHIMIEH5s LHHIIEHIEMHH}Hm HEHk< I9D$Mt$MM|$III,$fHnfInHLfl)$I.IHm@MI/=ImuL螰HHH[]A\A]A^A_AmOHDH $H=4H1[]A\A]A^A_;fDL(bfDH; A FOH5H8~f.Lدg1yIHt!HHְI.IqMxA HO$A ZOHxLh諲fDLHIL8hHt$LMH$Hl$I;fDH: A aOH5H8߯nf.{HAkOD[IKI/6IHtHH蓯ImHtKH.tOI,$ALBDL0MOL@AWAVAUIATUSHHG H;t: t"HLg HL[]A\A]A^A_Hp HH_pHcGdL5p HHD$H91H;IGHHt_MtI/tDHLIHI.tHH9\$MLHfDL8fDH [92H=MIE1LHIHtMHHmH٬@H z \E2H=HMtI.uL蠬M1I$I} H/t"Me I$MHPI$Me qfDcאE1L`DAUH5l ATIUHGHHHHI|$XŮIHHH^IHEMHHEt,I,$t L]A\A]@LȫL]A\A]H谫I,$uA1DTE1H 9H=9\L]A\A]H;HHEt6I,$A1uLAHmA1uH#뇐HfDAVAUATUSHHH1ܨIHpLHcCdI\I9sLI}rHHID$I;D$ HEIT$H,HID$Hmt8IL9wLHgI,$u^LHD$ZHD$JHHfDH-m HcwdHEH@hHH@HHHH[]A\A]A^@A1I,$AHuLݩDDH H=H1[]A\A]A^DHLI,$uL莩HmAHA 1uHs딐AHA1HIHt0HH蝩I,$ LHD$%HD$ AFA0*A 1 ff.AUATUSHHx;H1IHMLkxHcCdI\I9sHI}ZHHtrID$I;D$ HEIT$H,HID$Hmt4IL9wLH I,$uULH$GH$CH8fDI,$L0AH H=1H[]A\A]HLEbI,$uLΧHm0AuHt$ $讧$t$ DH5a\ H="m mv0?kfD0AVf0A>I,$0A)Lt$ $-$t$ AUATUSH1HH#LkpIHcCdI\I9sHI}蕩HHt}ID$I;D$ HEIT$H,HID$Hmt?IL9wL.HI,$u`LHD$聦HD$Lf.HhfDI,$A0uLKH 9DH=}1H[]A\A]HLuWI,$uLHmA0uHA0I,$A#0usfDAVAUIATUSHHcH蔨HIƅL%1 I$ZHHfHnfInHflLe(EL%Y ID$HH0H= un1LHI&MtIHmI<$M$HL[]A\A]A^L%y1 I$KcHHm6t~H XH=E1sHL[]A\A]A^I.t:I,$t[x6@L`HL[]A\A]A^HH=L8fDHt$ $t$ mLfDL1H諫IH0f.t6(H. H5hH8ff.AWIAVAUATAUHHEIcAyHH;-/ IH@t H;0 LH+II$HI$Mt_HLLA6IImtfH DH=/Hmt4DL]A\A]A^A_DA1IHuLŢH踢fDL訢fDL蘢eLHզI5DA/IWff.fAWAVAUATUSHH$ T$ LxXHcH0WHcH0pWHcH0RWtzHcH08Wt`HcH0WtFHcH0Wt,HcH0WtHcH01ACH$01H$8l5H$@5H$H5H$P8xH$X8`H$`71҃tH$h7H9AGddC99L7L$0L$M9{1I裡$HHHk[ L=%HcHHT[ HEAf$@OHHPHE LH$*H [ IH ףp= ףHHB)HD$ HZ HE(HIHHH?H4HH)HHHH)ÉHH1)HAfA$Hu1 IIM)MyAD$-IIMIIIHMcMcHL$0L)¾LD$(HT$JHT$LD$(HHL$0I@ Iq0IyH@HEH~5 HL$8LL$0LD$(HT$BHT$LD$(LL$0HL$8HMM]ILH1HAo  HH9uLHHL9I)I)IvMH4LLHHL9A4H@4HCI9~rAtHHC@tI9~[AtHC@tI9~GAtHC@tI9~3AtHC@tI9~AtHC@tI9~ At@tH\$ MIIYH ףp= ףLM0HU HHCHD$ HU HE8LIHLH?J<"LHH)HIHHH)‰1)HAfAHu1 IH)My C-HHHɿHIHLcHL)LcHT$HT$HI@ PIw0IH@HEH~ HT$HT$HMMUILL 1HfoAHH9uLHHL9I)I)IvL HL LHHL9D 3H7D HFI9~kH|3HF@|2I9~U|3HF@|2I9~B|3HF@|2I9~/|3HF@|2I9~|3HF@|2I9~ t3@4H\$ I_L}@H>S H{HH/S HEH莤IH~@ IV0INH@HDHT$ L}H]P8fHz0HrH@HE<taM1LL}MII9taIz 4LjMtHL)L9J  uHrH<uHD$ LJ< 諞fHmEH=_ LAH0I.DH JH=sA<$xsH DAH=DP$$H[]A\A]A^A_@H& H5jH8躚I.tDAHHm]H蛙PfDHHT$胗HT$I.uLhfDIFHHD$ ?fIyHIHL(HA<$HL$aHL$HIiAH7D;8IH]@AHDHDŽ$p$H$F L$8L$M9t"I!HDŽ$x$H$? L$@L$M9t"IHDŽ$$H$( ~L$HL$M9t"IHDŽ$$H$ /L$PL$ M9t"I4HDŽ$$H$J L$XL$(M9t"IHDŽ$$H$6 L$`L$0M9t"IHDŽ$$H$ tFL$hL$8M9t"IKHDŽ$$H$H$0L$(H$pHHLHLHiH$8H$xHHHH[HЃ3H$@H$HHHH HЃH$HH$HcHHH0"HЃH$PH$H-HHH:#HЃH$XH$HHHH#HЃt_H$`H$HHHH"HЃt-H$hH$HHHH$HH$J8H$H$@HSHHHH HHHiH$L$HHHIMzH3H$L$PHHIMHH$L$XHHIM HH$ L$`HvHIM!HH$(L$hH@HIMl!Ht_H$0L$pHHIMB!Ht-H$8L$xHHIM"HLH9s H9 HD$$Do$ DUDo$0Do$@Do$PDo$`o$pD)$o$o$D)$ o$o$D)$0H$ )$`o$o$o$D)$@HPX)$pD)$P)$)$)$)$)$)$-IcH̠ H;`H HƒYuHcHH;`H $uHcHH;`H uHcHkH;`]H uHcH6H;`(H uHcHH;`H tTuHcHH;`H t#uHcHH9`o$o$o$o$ )$H$o$0o$@)$ o$P)$0H@Xo$`)$@o$po$)$Po$)$`o$)$po$)$)$)$)$)$)$H̠mH;`_H MHcH̠8H;`*H RMHcH̠H;`H MHcH̠H;`H MHcH̠H;`H MHcH̠yhH;`u^H MHcH̠y;H;`u1H YMHcH̠yH9`:AFDd$ L$EH$@H$pHAAWH$8LL$AYAZH|$$DH H H H?H1H)f.1fH H5JB 1H8JAAHDH H5B H8=f$/@H H5A H8xHa H5A H8H)ك,^HcHcAHGALHNLAoN(HD7 HNhA]Ao#Ht7H Ao(.AtiAoqAuAo[XAo`fAtDAoiAmAospAoX^AtAoiAmAospAoX^ЉމЃ)9t8HHHcHH@HĀH@HԀHDŽ$H"HDŽ$taHDŽ$tPHDŽ$t?HDŽ$ t.HDŽ$(tHDŽ$0t HDŽ$8HcH$@qH@H9H$@fHn$@$Pt$`t$pȃt HH@VH$H躋DH H5 ? H8EAH'H H5> H8 })HcH$ ALFL$ AJ L$ LYBo LH|$HcINL$ B ML $LI8HxBo MLD$(LD7 Ht7NH4MH$ B o Ll$0L$ HI4 ABoBBo Bo 4AtbHL$H4$LT$(L\$0oaf)d$AobAcAoE)$$GAt"oafAoBACAou)$wЉ)9t8 HH0HcH0HpHİHpH̰HDŽ$0HDŽ$8taHDŽ$@tPHDŽ$Ht?HDŽ$Pt.HDŽ$XtHDŽ$`t HDŽ$hHcH$prHpH9H$pfHn$p$t$t$Ѓt HHpVH$H[5HLrH1bH] H5; H8D11PH+ H5d; H8o$ o$0o$@L$ o$P)$o$`o$p)$ I]Xo$)$0o$)$@o$)$Po$)$`o$)$po$)$o$)$)$)$)$)$AFTDU IcHĠxH;`jH HHȃUHcHԠ=H;`/H UHcHԠH;`H ~UHcHԠH;`H IUHcHԠH;`H UHcHԠymH;`ucH UHcHԠy@H;`u6H UHcHԠyH;`u McJELcJDPMcJDPMcJDPMcJDPvMcJDPWMcJf<1H$j)H$H$H$H$ &H$(H$01҃tH$8H9AGddCH$0HcIHHcҍuHHHDPt!HcHHHDPtH$H|$P~H|$Xu HDŽ$H|$`u HDŽ$tnH|$hu HDŽ$tUH|$pu HDŽ$tH/HII9u|$ ykH$@H$pHAWH$AH$8L$fL$3nL$D$0XZL$@M|1IHMHL9ub1҅H$Y,1HD$PH$HÃH$HD$XtjH$HD$`tWH$HD$htDH$HD$pt1H$HD$xtH$H$tH$H|$PgHDŽ$MI JJH?H1H)…1fDVLH$pH$xH$nH$]H$LH$;H$*H$HKH0HcH0HpHİHpH̰MHcɍCH0HH0HpH̰HpHİMHcɍCH0HH0HpH̰HpHİMOHcɍCH0HH0HpH̰HpHİM HcɍCH0HH0HpH̰HpHİMHcɍCH0HH0HpH̰HpHİMHcɍCH0HH0HpH̰HpHİM?HcɍCH0HH0HpH̰HpHİ1181mH$(H$$J>IH^fH$@H$pHAWH$AH$8L$bL$iL$D$0A[[ML$@NDUL$HH$o$ IEXo$0o$@o$Po$)$)$ o$`o$po$)$0o$)$@o$)$Po$)$`o$)$po$)$)$)$)$)$)$AFDUDKA.DT$(L$&hL$DT$(AM~jH$@HD$(L$HH$1l$0Dl$8DMIHLE1LLH轀L|$(I9uADl$8l$0DDT$(dH$ DT$(H$0HPXHcHH9qH$(H$DT$ 'jDT$ DT$ L$@gDT$ AH$H~iL$@vL$HH$I1D|$ LIELHLADLHHD$(II9HD$(uD|$ DcPeDUH$@H$@H?H1H)1H HHH?H1HH)QӸ̸ź~t1EI?H/tHL|$(I9uEbdH$(H$h"XNDE11IHMHH9uqeA$dH IH=Ǘ@b;eH GH=蜗Jbff.ATUSHH- IHHEHnt G`1tID$pHC01tID$xHC81tI$HC@1tID$hHC(ID$@HAD$dC$ID$XHCID$PHCAD$`C I$H{H/t.LcI9t 1[]A\fDI,$t!HCbfLbfDH H5H8c[]A\H5Y H=( MY .H=H 0H{HtH/tHCL#bAUATUHHGH5 HHDIMID$H5: LHH'HI$HH!I$HHEH5I HHHIHEHMHEHtGEeHH L`H=6 H&jHHmt.H]A\A]@H afDLa_HHD$`HD$H]A\A]@Ae3DH mH=L觔H1]A\A]ciISiHAg3I,$uL`럐+iIAj3Hm}HW`pfAm3Ar3ATIUHHHGHtHHHEHLP0HHt`H(tHs HH]A\_f+H pH=`蓓H1]A\f+@AUIATUHHlcIHtHL]A\A]Hi H8atbHEH5e HHHHHIEtEHELHHHt5HHEHHEHt)IHcH^VLHogHƾHt1H ZH=ux7gHZHt$ s^t$ ff.fAUATUHHGHHIIH5^ HHHLLH[HEx9HAHEtHD]A\A]@H]HD]A\A]H. HEtQH kH=A胑HD]A\A]fD;fH[, fHt$ d]t$ HPH H5tAH81,e>AUATUSHH `HIŋClL%# I$`HHfHnfInHflLe(EL%/ ID$HHH=#~[u`1LHIaMt;HmHL[]A\A]f.L% I$Y`HHm)tnH H=sE1HL[]A\A]DImt)I,$tJH[HL[]A\A]fL[fDHt$ [t$ }L[fDL1H;cIH@f.8H H5H8P\ff.UHHHHHEH5 HH HHH HEH5 HHHH}HWHUHt)Ht H]fDHHD$ZHD$H]þZHH H=Z1H]fHH= E1L 0RH (HH8H51+bXZ1H]ÐHyH5HvL1f.HbH ZTfDbfDHt$Yt$)ff.AVAUATUHHHGH5 HHoIMrID$H5 LHHII$HI$MxH_HEH5  HHHHH{HEH5X HHHIHEHMHEHID$H5f LHHHI$HHI$HH=A HWIH}HmH5C LWHHI,$HLaWIHEHmImIMHPIIHt2HL]A\A]A^HWLWLWHL]A\A]A^ÐLWHW1YI,$uL|WH ME1H=WH$HVHH A@H AHH HH5BATL H81YX%ZH ]H=訅HH[]A\A]E1 ;VH>%H5 HHVeVHHD$IfDGWHH HHcAH9Hz H5#H8#RUHLAof.GWHH HcAH9?fHF HHD$HFH$NI1]H= 1yGT&uH 9H=a\fH-UH0TH$XTHHH H5XL jAH lHvH81W^$_Dp%a:%H@`HtoHHtcHHtYH H9Eu&HxHmAHrOHH5H-HHu.$gSHH H5H8#PfD$.ff.AUIATUHut10IMtSH LHLID$HID$H7 ID$ID$ ID$(Hx L]A\A]fI,$t9E1]LA\A]DH9 H5 18Iyf.LHNfDAWAVAUATUSH(L% Ll$`Ht$HT$M9CHc߅PL ) IMοQIHMgH 1LI$HH Mw(IG H=- HH4H} I$LpHEHDžI/oT$`o\$po$o$o$o$o$o$o$o$o$o$o$  0@P`MtAE8IELP8IH0HpH/LpIH0I$HIAU`AoMhAoExIMXAoUPHHD$hExMhU`]dHHE@HLeHUPALHDžfInŃHfHnflEpH9s"HHH9v H8xHLHMPI9+E1I}.NIHMt I.SH}P NIHLHSIIMHIH I9GMwIVHdMt IcWIHcHEIII/ILuPL9M5@L Q IMDLJHy I9GqLSHHtwHD$}MH|$IH/rVJhLIDJLuPL9sHE~D$ID$HPHUxLJNH\IfDLI[IEH(L[]A\A]A^A_fCH PH=Mp}HEE1HHEHtMtI,$uLhIfDHXIfDKIfDM!C닐H#CAItFH Ƽ#CH= |jf.I.E11 BALHH xDH=Ö|HE1)DIIAGAWHH IDI/uzE1+BALTHfH JBAH=: |HmWHHJH  BH={E1%H +BH={uxIE/DLJIAGAWHH HII/&CA%H +&CH=qD{E1 pABH= 18HH HGIH9t=HXHHyH1HH9H;TuMxIAAxdvxvpvhv`vXvPvHv@v8v0v(v vvv6L HHtDHHH9LHuH; :fD1E18fDMH DHD$H=#yHD$H@ATUHHG@DWdHwpHOxH<$IHD$LE'MH$H9L9AD I9M9AD !AR„HD$H)HxH=oD)L$o)T$PAo)$tsof)d$ oi)l$`Aop)$tLo~ )|$0oy )|$pAo` )$t%oF0)D$@oI0)$AoP0)$DЃAt"HH4HtH HLPIHĐL;HH~H; H诀HEIHEHtHL]A\HDHL]A\f.H$H9L9 AR„RHD$H)HxH=:o.Dfv)l$o1)$)t$Ptao^)\$ oy)$)|$`t@on )l$0oq )$)t$pto^0)\$@oa0)$)$DЃAHH4HtHLHDŽĐHTPHHH <gDE1H=6v,H vQ/H=9vHL]A\fDHHD$HHD$PIH$AHFHD$HAHD$XI@H$AHFHD$ HAHD$`I@H$AHFHD$(HAHD$hI@H$AHF HD$0HA HD$pI@ H$AXHF(HD$8HA(HD$xI@(H$A0HF0HD$@HA0H$I@0H$AHF8HD$HHA8H$I@8H$H HHxH9HXHHqH~ 1f.H;THH9uH HJH5HWH81HHmH ,S/E1H=FtHL]A\H ]-^/E1H=stHEHGHHD$HHDŽ$HD$PAHFHD$HAHDŽ$HD$XAHFHD$ HAHDŽ$HD$`AHFHD$(HAHDŽ$HD$hAeHF HD$0HA HDŽ$HD$pA=HF(HD$8HA(HDŽ$HD$xAHF0HD$@HA0HDŽ$H$AHF8HD$HHA8HDŽ$H$H??YH[ H5bH8$@3HHH9HuH; DAUIATUHSH10IMtzH< LHLID$HH I\$ID$I\$ I\$(Hx2H[ HI$pID$LIDŽ$H[]A\A]I,$t9HE1[L]A\A]H H5 18IJfL>fDHHX@HtHfPH 1HD$H=kqHD$H@HHcd@HtHfLH 5P1HD$H=KNqHD$H@ATIUHHGH5s HHHHID$t_HELHHHtOHMHQHUHtFHtH]A\fHHD$IHRHD$HHD$IEID$LMH=tw81LLAI>MIm{=IHfHnfInHfl@H=n iBHtH=T=B1LHfDH; LKIHhImI@LD$LHLD$HIULLD$HILLD$HILLD$HLD$LD$I(L|E1Do[Hmt1pHt$1T$NT$t$QHHx.HHH OHEHܡ H5efH81L-[E1E1E1E1wDE1j[fDHݺr[fDIUHbIEL LpLxqfDHI H5UH81[cfDLX@[QHվ[fD[)fHH# H5RH81HHtmHLH+HH@LE11HL3ILHD$nLD$P1[cIHuHg H5QH80L1HIIHf.H(H LD$H5&TH81LD$I,$LQ[LE1E1E1E1G[+E1E1I(t`u1IHNLH H5cHEH% H81CMtMI$E11Y[HI$T5L%AAH LD$ E11Y[E11E1E1E11۾#[E1fDAWAVAUIATIUHSHXH H9H$H&PH=ooHoP oX0o`@ohP$op`oxp$oo$$oo$o$$$ $0$@$P$`$pI9Ht$LPOH/o(opHox o@`$oh0oHp$op@ooo$$oxPo$oHEH5 $H$$$$$ $0$@HHHdHE{HUHBHHGHHEHcAH9fAQHmaID$H5 LHHHHHEHEHPHH'H EUHH HcAH9!A-HmL$HADD$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$H$HkHĠHHHX[]A\A]A^A_DHEAAHDEH HHcAH9HunHufH H5TH8EHAE1Hx HWuAAHDEpEUHH HHcAH9Hr H5TH8HAfEUHH HcAH9nfEUHH HHcAH9@H! HH}H9HXHHqH~1H;THH9uH= HJH5PHWH81<y*z*fDH H=\?1fDE11Hi H%I|$H9%HXH"HqH~1H;THH9uH} HJH5ROHWH81|*MD*9f*!HvH**HHH H5}H8 y*H H5|H8 *vHHH9HuH;L  f*Hm+Ht$ T$K T$t$ fDH@`H5HH%HIHH I9Gu'DLp2I/AmL `LH5gIHuf.HDHH9HuH;T H@`HHHHIHH3 I9Gu'DL1I/AJL# =LH5IHuXf* HH H5i|H8 h HH H5@|H8 @AWH' AVAUIATIUSHHHD$(HD$0HD$8HHL4H HuoH6LAHt$(MH HFH9t H; ^LUHH9H(HHHH[]A\A]A^A_fHH Hh|H5QATL zAH {H81Xz$ZH J{H=uXh;1HH[]A\A]A^A_HuH6Ht$(#DSOfDLy1H M'HL9t'H;LuI4Ht$(H MGDHA0E1HD$@JtH9H H9AH9Fy k~ HQH;VHFHyH9AHAt HDY DV DD@@8A ~HyHA@HE|$A VL^0HHA@IEDA~ADDE9u;H $H LL$1HLL$H $fDIM9fDH! H9uuH9uuHϺLL$H $ HHtgH; H $H;= LL$H9LL$HL$H<$ LL$HL$H<$H/Ny*HD$( Hj$IfK4$H uxH=U81&@HL$(HT$0MLL #yHHt$(5LL$H $ZLL$H $6@HLL$Ht$H $2H $Ht$LL$i HLL$HL$H4$H4$HL$LL$;HvHHyHHHH H5lxH_xH81 $DDDDxo$ff.AWAVAUATUSHH L= HHAIL~HEHHE HCA?HE AC$HDHC8HC0HC@HEHC HC1AHC(HEH{H/HkL91H[]A\A]A^A_L5 LoPM9H I9MI9N„A} A~ IUI;VIEIvH9@H@t HEE A~ D@@8A Iu0IHA@LE@ MF0IvH@IEA}DA91Ht#LH|H  DA2H5# H= 'UH=NRH t 5H{HvH/NHCZ@HE('HmHC,E0C$HE8HC0HE@HC8DfDM9L5 M9tvMI9NNLLIHXH; L;-q M9LImAEEHM9uLLcIH7H;` H AH;֋ DM9LImH A{EEf.LmPL5] M9?I9MI9N„NFA} A~ %IUI;VIEINH9@H@t HA} Av 8@ IM0IH@IDH@ IN0IH@IDHȃDA9@HQHR=DH H5JJH8*H[]A\A]A^A_fDImELH * qDM9uM9\ODfDLH ي MfDLxH (ImD;LI%@IvHMmHXA}DxL -LA}D9IvH?I}HDDD8fHGt{HGHPHvHtOHt14@HtHcWHHcHHE@GWHH f.GWHH HUHH@`HHHHHH@H;ň uHHEHPHveHHtuHeDHmt)H]HH5nt$HHtH@fDHHD$cHD$@HtHcUHHcHHEEUHH fEUHH HkH7HXH@`HHHHHHH H9GuXHGHGHPHvWHt}HthH|$AH|$H/HD$hHD$H5HJHX1@HH9CH;lu#LeM$L9MuH;-u E11LHcIFIHuHs H50&H8.HHs H5&H8`LuMv1 HI9t L;duIE1JtI98LL(IM9u.fDHWHBpHtH@Ht HBhHtHxtAVAUATIUSHHGH5Τ HHvHHHEHXpHt[HSHtRLHHHmtH[]A\A]A^DHHD$;HD$H[]A\A]A^fHPhH HRHH s I9L$Ml$IMHMH;It H;$r Ht H{LH7Hr HH2t+ID$L`H.s H5-LH81RfHm0H YH=e8H1[]A\A]A^fHH뱐IcD$IHcHEII~HEH;Ls trH;+q =HXpL`hHH{LQIH5HHSI,$LHD$tHD$f.MHEJ(H9HEHHDHE1Ht$t$LH Mt;IT$Ht1M*I$HHHlIT$ILXIHHXH HqH( 1fHH9 H;TuH|$(HD$(A$MHHx$$$$$$$$$$$$$$$$$$$$$$$$$$$`HIH H;h H5 HuLA A:@fLLL$8LL$8IA9AHmI)DDE1H NH=OH|$(tH|$(HHD$HHMt I/HL[]A\A]A^A_HcCIHcHEIIHD$LLh@HMIHg T$$H5 H86IAC;A2DDH MAH=m,A DA9dHf I9Ad MaID$H MI)L@Hf I9A MyIGH Mt IcAIHcHEIIjI)LKfDHf I9AMiIEH Mt IcAIHcHEII.I)LfDHe T$$H5n H85pIA=Au`fL9J\IHDI9H1AE1L; d LL)HIHcT$HԀLHHHǃ|$ H@ HcD$ HD$L$ MIȃD$L$ fML$8$IcAIHcHEIILL$8>LL$8H I@HAc T$$LT$XH5 LL$PH8LD$HHL$@L\$83L\$8HL$@LD$HLL$PLT$X91L;c 211MM9JHIL; xc WM MIIMfM9HHAMOIZIA+:AuHHHH@HHD$HI4HLL$VLL$M6I),L6L(^BfDLLD$8LD$8fLLD$@LL$8LD$@LL$8-cHHD$ILLh@H'IMM9MOM)HLL$HLD$@HD$8YLL$HLD$@HD$8DIMIA9AHmHLL$8AT$dH=4 1H rH8H=IE1IA:As@3ItIA:A=@HIHHTImIL.fKH$LL8H$LfIn~fIUIA):A@IIHILH .G9H=bHG I`IA?:A(IAL:ALD$8IfIAY:ALL$@LD$8LL$8LL$8HIIrDcCII M3MbIHH9 HuH;S_ A$11M$$$$$$$$$$$$$$$$$$$$$$$$$$$tHIHKH;^ H5 HLAA:PfLLL$8LL$8HHLL$@HD$8CH|$8LL$@IH/%LL$8LL$8E1AAn9Ld$01E1L; ^] CMLHM)LL$8ULL$8H=IHD$(fInH\$`LLL$8LL$8HIHLL$8hI/LL$8IL>LL$8IIoEaAAII ALLL$8LL$8HHLL$@HD$8H|$8LL$@IH/aLL$8LL$8MDcCII IHI3IEyAAII MԾLHHII9LHL)MԸLH(IIEiAAII IA9AMH BIߺ8Aľ};H=!ADAf:LLL$8LL$8IEaAAII IHIMILLL$8qLL$8IEyAAII IHALLL$82LL$8IEiAAII IIA:AA A:HB[ HBE1MH56 H81 H YA:H=BwIA:AWAp9AE1QIA/:A/AA:3HmJMA9AM)I"fDAWIAVAUATIUSHXHHD$8HD$@HxHFH>HE HD$HH9t/HXHtKHqH~b1fDHH9tOH;TuHGI$LI<$HHX[]A\A]A^A_ÐHH9tHuH; Y tfDHX HD$H fDHHhH9t HHPHuL(LpMtIEHtHEMtIA@f@ϘHcHD$8HAJHSX HHD$@HD$HIHHD$8I$MgIG HD$@HD$8IG(L  HD$@IAHHIH=HL$LL$LL$HL$1LLIMKL|$@H|$HH/I,$H\$@HD$HHD$@Mt ImHtHmtzMtI.t_H;I@LHD$HD$HX[]A\A]A^A_HV HL(LpMJOL@fDH0yL ]L41LLHD$@HA)A)HD$8H|$@Ht H/HD$@H|$HHt H/HD$L  HD$HHxXI9HIAHHW4@'A@HXHHJH21HH9L;LuH <DH=vH|$HL$8HT$HHt$@6H|$8HH/HD$8H|$@H/HD$@H|$HH/HD$fInfHnHD$HflHH8L@LxLpHt H/Mt I(Mt I/I$HxH^HI9HuL; T HD$fInfHnflHH8L@HXLpHt H/hMt I(Ht H+H|$8Ht H/H|$@Ht H/H|$HHt H/*H=H :DI$Hx1}L,A)H|$8HH/ )THuHQ H5AH8HD$@A) yo A*LD$PLD$-L>/L1I$HxHLD$T$LD$T$|T$T$LljT$T$dH߉T$T$^T$T$`T$T$bIQH1 @HH9t I;|u1ItH9HT$(HL$ LL$H|$nHL$ HT$(H|$LL$HH9u_AWHg AVfHnAUATIUHH@HhSfHnHflHxL H#N HD$`H HD$hLL$0HD$8HT$@)D$PHL,H{HH|LLuLL$0MH LHkHHD$8IMhLML M1HI9KL;DuIDHgHD$@I+HVHFLLuHD$@HFLL$0HD$8MLL$0HD$8LT$@L=)P HI$It$H=9P AHEHG{ HAWjR5 j5 PjRL IHEHPMHHEtvHxL[]A\A]A^A_@H,HHL=O MLLL$0IfHuZLVL=_O LT$@HFHD$8HfDLuMkLT$@L=O f.H 7AHHPN H|9H5 SL 77H81HXuZH ]6cH=E1L=N MxHFHLuHD$8HT$0HH n6Hp6IHII?IA[fDLL$0#fDE1I@0JtHD$ I9IfDHN I9@H9F3+Ax ~ >IPH;VHFIHH9@H@t HAx D^ D8@ .IHH@HHE|$ A HN0HHA@HEȃ #DA9uELL$LD$HtPLT$E1HLT$LD$LL$AfDIM9JtI9KDTL=L M9uuL9uuLǺLT$LL$LD$HHH;L LD$H;=)L LL$LT$L9 LT$(LL$LD$H|$JLT$(LL$LD$H|$AH/ E E22Ht}u2HHEH ~3/vH=25L=K MgH{ LH>IHtWHD$0IHL$0HT$PILL 6H1*uDjHTufH訾1LT$LL$LD$茾LT$LL$LD$LLT$(Ht$LL$LD$TLD$LL$Ht$LT$(HLT$(LL$LD$Ht$Ht$LD$LL$LT$(\HvHIxHkHugDDAWH} AVfHnAUATIUHH@HhSfHnHflHxL  HF HD$`H HD$hLL$0HD$8HT$@)D$PHL,H{HH|LLuLL$0MH6} LHHHD$8IMhLMLm} M1HI9KL;DuIDHgHD$@I+HVHFLLuHD$@HFLL$0HD$8MLL$0HD$8HT$@L=H HI$It$H=G AHEHAWj5s 5~ j5C| Pj5zx  IHEHPMHHEtvHxL[]A\A]A^A_@H,HHL=H LLLL$0IfHuZHVL=G HT$@HFHD$8H@}LuMkHT$@L=G f.H /AHHF H0H52SL /H81X?ZH . H= E1L=)G LxHFHLuHD$8HT$0HH .H.IHII?IA[fDLL$0#fDE1I@0JtHD$ I9IfDHYG I9@H9F3+Ax ~ >IPH;VHFIHH9@H@t HAx D^ D8@ .IHH@HHE|$ A HN0HHA@HEȃ #DA9uELL$LD$HtPLT$E1H!LT$LD$LL$AfDIM9JtI9KDTL=QE M9uuL9uuLǺLT$LL$LD$3HHH;0E LD$H;=D LL$LT$L9 LT$(LL$LD$H|$ʽLT$(LL$LD$H|$AH/ E E2貼Ht}&2HHEH + uH= L=ID LgHIt LHIHtWHD$0IHL$0HT$PILL ,H豪*+DHTfH(1LT$LL$LD$ LT$LL$LD$LLT$(Ht$LL$LD$ԴLD$LL$Ht$LT$(HLT$(LL$LD$Ht$蔴Ht$LD$LL$LT$(\HvHIxHHgDDAWHgv AVfHnAUATIUHH@HhSfHnHflHxL x H#? HD$`Hx HD$hLL$0HD$8HT$@)D$PHL,H{HH|LLuLL$0MHu LHkHHD$8IMhLMLu M1HI9KL;DuIDHgHD$@I+HVHFLLuHD$@HFLL$0HD$8MLL$0HD$8HT$@L=)A HI$It$H=A AHEHAWj5Al 5w j5t Pj5p z IHEHPMHHEtvHxL[]A\A]A^A_@H,HHL=@ LLLL$0IfHuZHVL=_@ HT$@HFHD$8HfDLuMkHT$@L=@ f.H (AHHP? H(H5SL 7(H81HXZH ]'* H=vE1L=? LxHFHLuHD$8HT$0HH n'Hp'IHII?IA[fDLL$0#fDE1I@0JtHD$ I9IfDH? I9@H9F3+Ax ~ >IPH;VHFIHH9@H@t HAx D^ D8@ .IHH@HHE|$ A HN0HHA@HEȃ #DA9uELL$LD$HtPLT$E1H衴LT$LD$LL$AfDIM9JtI9KDTL== M9uuL9uuLǺLT$LL$LD$賱HHH;= LD$H;=)= LL$LT$L9 LT$(LL$LD$H|$JLT$(LL$LD$H|$AH/ E E22Ht}h2HHEH ~$ H=5L=< LgHl LH>IHtWHD$0IHL$0HT$PILL &%H1*mDjHTZfH訯1LT$LL$LD$茯LT$LL$LD$LLT$(Ht$LL$LD$TLD$LL$Ht$LT$(HLT$(LL$LD$Ht$Ht$LD$LL$LT$(\HvHIxHkHagDDAWH?o AVfHnAUATIUHHPHSfHnHflHxL q H7 HD$`Hp HD$hLL$0HD$8HT$@)D$PHL,H{HH|LLuLL$0MHn LHHHD$8IMhLMLmn M1HI9KL;DuIDHgHD$@I+HVHFLLuHD$@HFLL$0HD$8MLL$0HD$8HT$@L=9 HI$It$H=: AHEHAWj5d 5o j5m Pj5i s IHEHPMHHEtvHxL[]A\A]A^A_@H,HHL=9 LLLL$0IfHuZHVL=8 HT$@HFHD$8H@}LuMkHT$@L=8 f.H AHH7 H%!H52SL H81ȳXZH  H=&E1L=)8 LxHFHLuHD$8HT$0HH HIHII?IA[fDLL$0#fDE1I@0JtHD$ I9IfDHY8 I9@H9F3+Ax ~ >IPH;VHFIHH9@H@t HAx D^ D8@ .IHH@HHE|$ A HN0HHA@HEȃ #DA9uELL$LD$HtPLT$E1H!LT$LD$LL$AfDIM9JtI9KDTL=Q6 M9uuL9uuLǺLT$LL$LD$3HHH;06 LD$H;=5 LL$LT$L9 LT$(LL$LD$H|$ʮLT$(LL$LD$H|$AH/ E E2貭Ht}2HHEH \ 3H=BL=I5 LgHe LHIHtWHD$0IHL$0HT$PILL H豛*DHTցfH(1LT$LL$LD$ LT$LL$LD$LLT$(Ht$LL$LD$ԥLD$LL$Ht$LT$(HLT$(LL$LD$Ht$蔥Ht$LD$LL$LT$(\HvHIxHH݁gDDAWHgg AVfHnAUATIUHH@HhSfHnHflHxL i H#0 HD$`Hi HD$hLL$0HD$8HT$@)D$PHL,H{HH|LLuLL$0MHf LHkHHD$8IMhLMLf M1HI9KL;DuIDHgHD$@I+HVHFLLuHD$@HFLL$0HD$8MLL$0HD$8HT$@L=)2 HI$It$H=0 AHEHAWj5A] 5h j5e Pj5a k IHEHPMHHEtvHxL[]A\A]A^A_@H,HHL=1 LLLL$0IfHuZHVL=_1 HT$@HFHD$8HfDLuMkHT$@L=1 f.H AHHP0 HH5SL 7H81HXZH ]H=E1L=0 LxHFHLuHD$8HT$0HH nHpIHII?IA[fDLL$0#fDE1I@0JtHD$ I9IfDH0 I9@H9F3+Ax ~ >IPH;VHFIHH9@H@t HAx D^ D8@ .IHH@HHE|$ A HN0HHA@HEȃ #DA9uELL$LD$HtPLT$E1H补LT$LD$LL$AfDIM9JtI9KDTL=. M9uuL9uuLǺLT$LL$LD$賢HHH;. LD$H;=). LL$LT$L9 LT$(LL$LD$H|$JLT$(LL$LD$H|$AH/ E E22Ht}2HHEH ~% H=5L=- LgH] LH>IHtWHD$0IHL$0HT$PILL 7H1*DjHTfH訠1LT$LL$LD$茠LT$LL$LD$LLT$(Ht$LL$LD$TLD$LL$Ht$LT$(HLT$(LL$LD$Ht$Ht$LD$LL$LT$(\HvHIxHkHgDDAWH'] AVAUIATUSHHHHD$(HD$0HD$8HHL$HHKH>LAH|$(M> HG HWHBHH) Ho 躣HcЉH9 7 1̜IH I}H5_ HGHH IM Hc苡HHH) I9FnM~MaI^IHI.fInfHnͿAflHt$0)D$0HC'H@8HHL1HHMt I/HmwHv H+|HBH;I+ t H;()  HD$HIH$HHWE1H|$2IFH* I9^;H $H9HIFHHH $HMt I/kIEHImHx( H9EVHD$0H5v* H\$8H}H9פHt$8E1HE,H@8HDH1HHMt I/HHm]ID$I;D$ oHIL$HHID$H*}H|$IHD$LHHHtH_) H2H9 vI. MtqI/ukL aHH' H4H5/SL AH H81踣X:\ZH H=vE1HHL[]A\A]A^A_@HuH>H|$(GDHtcGHEtLy1H X M fHL9H;LuIL\$HL\$L\$HHD$H H5L\$H8IL\$HT$;HH$NH$HIH@HHD$HHH$HFLL$H $LL$H $HLL$Ht$H $迎H $Ht$LL$eHLL$HL$H4$莎H4$HL$LL$4HvHHyH1DD1=DD1LHL$ؗL$HH@`HHHHHH H9Eu&@HXHmHÏHH5OnHHuf6\L$-L$HHD$H H5 H8eHT$L$/\A\HjMt11LA\kA\諓HVH H5H8;AWH'O AVAUATIUSHHhL nQ L-7 HD$@HhHD$HHD$PLL$0Ll$8HHLHH2HQHHIH HHIHH I?SIH5xH8L A1 XZH a H=E1HhL[]A\A]A^A_HHLHZMHI$It$H=H AHEH^E HH,P AUjRPjRLPj5M S IHEHPM%HHEVHGIfoLvLY)D$0MnLL$0\@LYMHHTM LHL\$L$L$L\$HIIHD$0M~~HML5zM H1DHH9L;tuM4MLt$8IRLvLt$8LLL$0f.LLYLL$0MLt$8DMHHEH 6 H=IF0L\$E1HD$ L$Ld$IHH\$LMDO|L9H H9CI9G{ KA XHSI;WIGHsH9@H@t H{ E_ D@@8@ HsH@HHE|$ A Iw0IHA@IDDAADD>E9u*HHčfDIL9LL$H\$Ld$DL9uuM9uuLHIHtH; L;=u M9L豏I/oLL\$L$MH\$Ld$y;L$虎L$Ht8fDLL\$L$MH\$Ld$O4&fDHL$0HT$@ILL H|x%LL$0<H耉Q?RfDLD$,TD$,$H@L(xIwHH{HLT$L$葍L$LT$HDD>DD>ff.AWHD AVAUATIUSHHhL HD$@HhHD$HH'K HD$PHD$0LT$8HHL,HH0HOHHIH HqHIHH I?SIH5FH8L A1ُXCZH Z H=E1觻HhL[]A\A]A^A_DHHLH\LI$HIt$E1H=% HEL1? H J jAPQjAPAQHj 5C PpM IHEHPM$HHEWHJoHVLI)D$0MvHD$0\@LIMHH$C LHLL$ԩLL$L8 HIHD$0MHML5JG H1DHH9L;tuITHHT$8IQHVHT$8HHD$0f.HLIHD$0M~HT$8LHHEH  yH=轹IF0LL$E1HD$ Ld$IHH\$LMfO|L9H H9CI9G%{ [A pHSI;WIGHsH9@H@t H{ E_ D@@8@ ?HsH@HHE|$ A Iw0IHA@IDDA9A<DD>E9u2HH蔇L  IL9LH\$Ld$fL9uuM9uuLH辄IHtH; L L;=6 M9LrLk I/aLLL$H\$MLd$y-[Ht6-@LLL$H\$MLd$KT"fHL$0HT$@ILL Hvx%HD$08HHIM2LfDLD$,D$,L +@HLy @LLY ya@IwHH{HLL$ELL$L H&DD>DD>ff.AWHB AVAUATIUSHHhL D L- HD$@HhHD$HHD$PLL$0Ll$8HHLHH2HQHHZIH GHHIHH I?SIH5H8L {A1苉X._ZH H=E1YHhL[]A\A]A^A_HHLHZMHI$It$H=` AHEH8 HHC AUjRPjRLPj5OA )G IHEHPM%HHEVHǀIfoLvLY)D$0MnLL$0\@LYMHH@ LHL\$L$耣L$L\$HIIHD$0M~~HML5@ H1DHH9L;tuM4MLt$8IRLvLt$8LLL$0f.LLYLL$0MLt$8DMHHEH d_H=mIF0L\$E1HD$ L$Ld$IHH\$LMDO|L9Hs H9CI9G{ KA XHSI;WIGHsH9@H@t H{ E_ D@@8@ HsH@HHE|$ A Iw0IHA@IDDAADD>E9u*HHDfDIL9LL$H\$Ld$DL9uuM9uuLHv~IHtH;w L;= M9L1I/oLL\$L$MH\$Ld$y;L$L$Ht8_fDLL\$L$MH\$Ld$O4&fDHL$0HT$@ILL MHYpx%LL$0<H}Q?_RfDLD$,|D$,$HzLzxIwHH{HLT$L$L$LT$H_DD>DD>ff.AWAVIAUATUSHHIH@L-C H5< HL91L{HHtEHEH5z7 HL9z1H[{IHyHmuH{~HL[]A\A]A^A_f Ht~茁HHH5. E11HLـHmIuH'{DLHHH1yIH I}XH(H9HNHEHHWd@WL@?HXHHJH1HH9H;lu111LbfHHIML;- L;-= u L;- u5u{HmuHyImTLyGLHHH9ZHuH;-r HE1;HtImXHmt!I,$L^yfHHywIHG MwXL(M9MIEHIVA@A@IXHt;HJH1HH9L;lu111L`MM9tMuL;-9 tf. I$H;yfDLLyu@LxH]Hv1 HH9t2H;|uI]HA1 HH9tBM;tu+E1JtH9ZH|$HIH|$L9u1H9ItI9LHT$HT$HAWAVAUIATIUSHxH=8 HD$8HD$@HD$HHD$8HHIuXLvHD$8IHzuH S HH HLpI9t M+HPHuHH@HL$HD$Ht HD$HMtIHD$HtHHEH58 HHHHD$@HOI}hzHD$HHLT$@H5[ I9rMzMIBIHH|$@HD$@H/<HD$HLT$@Ht$PfHnfInLd$`fl)D$PIBBH@8IH11LHD$8Mt I/H|$HH/H|$8H|$@HD$HH/I}hL|$8HD$@HD$8uHILHHt$fIn~D$H:HZflLjHrHt H/fHt H+oMt Im/HmI,$AMt I/Hx[]A\A]A^A_H0H@Ht$HD$HHT$(Ht$ LT$,xIH}Ht$ HT$(LT$HHHICHFHHFHIC uHFHHFIC(IBHH-H=bHL$(L\$ LT$rLT$L\$ HL$(L\$ 1LLHD$xHD$L\$ HI+LHD$tsHD$f.LHD$SsHD$fA.,AHE1E1H|$@Ht H/H|$HHt H/H DDHD$H=jŦHHD$t-HEHP1HUHuHHD$rHD$MLHD$rHD$Hx[]A\A]A^A_srfDcrfDIGH; H; LhpMtEI}t>1tHHD$HLAULT$I*u5LHD$qHD$!H@hH#H@H1LHD$8HA,AI@qfDLqLHD${qHD$HD$fqHD$@HHD$KqHD$zHD$DT$1qHD$DT$ fHD$DT$qDT$HD$fA:,AAV,LL$8MI)H|$@HD$8Ht H/HD$@H|$HHt H/HCXfHHD$8HC`CXHD$@HChHChH5+ HD$HHEHHhIMIH|$8L9TI/HD$8H{XLS`L{hHCXHD$@HC`HD$HHChHt H/Mt I*wMt I/SHD$8HD$@HD$HH VDH=qHL$8HT$@HHt$HUTA,AE1HHL$fIn~D$H8LXflHXHHHt H/Mt I+Ht H+H|$8HHHPHHHDT$Hl$nDT$HD$AE1O]w\AX,LT$nT$eHt$XE1Am,Ht$XIIGHHHD$8L\$DT$nL\$DT$HDT$nDT$LDT$mDT$LmH|$@m/m1epIHLHLnImLHD$mHD$LT$pmT$L׉T$[mT$tLT$ T$DmLT$ T$IIoIGHH5$ H=2 A,E1cAA,AuILu1812L1LL\$ZtL\$L\$6qL\$HuH H5L\$ HD$H:lmL\$ HD$HD$8A,AHff.HHxHtHHt&HÐHui@f.Q@H H=賟1Hff.AWH% AVIAUATIUSHL HD$PHHD$XHHD$`HHD$0HD$8HD$@HD$hHD$pLT$HH=LHCHxHJcH@HFHD$HHFHD$@HFLEHD$8HHD$0II5MMIH$ M1HL9KH;\uIHD$8HHUIL-( H1fDHCH9HL;luIHD$@HIMH* LHL\$LD$.L\$L HLD$HD$HIM~VHL$0HT$PMLL <H]uLL$0HL$8HD$@HT$HL4 &fIuMgLL$0HL$8HD$@HT$HIHIvH= AHEARj5i' Pj5h# QHj5l# ~/ IHEHPMBHHEHĈL[]A\A]A^A_H&HIH [H]AHMEIHH HH5ATL H81pX|yZH H=|E1d[HphGHVHT$HHFoHNLHD$@)D$0HLAHD$0@LAH5" LHLD$L\$HD$0HLD$L}L\$Le I @LqIE0LD$1L\$HD$ HLLd$IIHM|L9H H9EI9G} KA `HUI;WIGHuH9@H@t H} E_ D@@8@ OH}HA Iw0IHA@IDDAADD>E9uFHt HiL u)fLD$L\$HLLd$IfHCI9HL9uuM9uuLHfIHt^H; L L;=> u M9FI/tLD$L\$HLLd$_f.HD$@bjHiHH H H5jL lAHH81pmY^\y@LHC0LD$1HD$ L\$Ld$ILIHf.MlM9HS I9GI9E]UA FA} WIWI;UIEIwH9@H@t HA EM D@@8u{@  IHA )Iu0IHA@IDDA!A1DD.E9u0H.H2gL DHH9HD$8hHHH AH5$jL H >H8H1k_RyAXfDM9uuM9uzLLdIHkH; L L;- u M9Imx LLD$L\$HLd$fLLD$L\$HLd$IRfHHEtH yH=詖@L8hL1 @HuH@HHE|$ LhL 1IwH@HHE|$ H_bthyZyPy@LD$,,bL D$,#@H`L ,@L_Li  @IwHLD$,aD$,L1 lL_L L_L iL\$ fL\$HfcyIuHDD>DD.DD>gDD.eH {AH(HyQAWAVAUATUSHH(HGH5" HHHHvH}H;= 5L}M(LeII$HmL|$L5 I|$L9t L2ht~IT$BtrHt$HjE1 H=Ht$ _LHt$I#eMI/:L_SfDH_cID$H@8IHHt$1ɺLII/tMf.LHmuH~_Y@HD$L5 L9tKL#gu?HEHP8LDM Ht$11HAIIofHUBtLbE1 .H=o]UL1AIIcMVI,$H=\ H5 HGHHIMH- $ H\$HD$H}L9tL5fDHUBHt$HZE1 %H=Ht$]u@Ht$LHcH-bHuH H5H8^DIEYHIEu L]Mt I,$eH E1H=xHEt3H@8HDHt%Ht$1ɺHHHs&aIHZHD$HHD$IGHEHHH=[p1LHHaH2I/H I9D$Il$HM|$HEII,$ofHnfHn˿flLt$)D$IG|H@8IHkL1LIHt Hm>H+MKI/LL[IIEMHIEI.H(L[]A\A]A^A_@L[Lm_IHrHD$HHD$IAID$HHH=LL$JZLL$LL$1LLIV`MLL$wI)L&[xMl$fDL}HD$H\$I|$L9tLbIT$BL|$Lr1 uIl$H=-YLHAI_MNH+MNfHhZ/LXZ2LHZI.PL6ZCL(ZM1Lt$HYHT$]IHOIHT$HIID$HuIFHIFID$ IGLMH=oX1LLAI^MI,$LXYLHYYfDaHdLL- MH=WL1HAII]Mq]H8H H5ZH8YDIEYHIE@3aIHIEQI.3YfD\HuHg H5ؕH80YI/LXf1LH_I/HLWfMIE/YHIELWSN\HuH H5;H8XI/L~Wf \HH H5H8LXE1[HuHO H5H8XH+)HVfE1}L1LLL$~^LL$I\[LL$HIkH H5=H8WLL$SE151LL&^I [IHmH~ H5H8GWL1H]IHI[ILVff. ff.ff.AWAVLcAUIATUSHHHGHEIISIHAJ41M~'H HIT$H  H HH9uL;- IEI}HPIUImE1Lt$D$MMIHED$@H H9EH?VIVMJ"IIH9IVH=(HxHH޸H 2HEH H5HH81K@H =(H5H81K@|(f(AWH? AVAUATIUSHHHL- HD$0HD$8Ll$(HHL4HBHHHIHT$(HI$HIt$E1H=x HEH HL  AUjPAQjPAQjP IHEHPMHHEHBfDHHHHH HIHHH?L @HLIL@HH- SHԷH5H81,JX{ZH AH=E1uHHL[]A\A]A^A_LyMLHHT$(L 1L;DHL9uI@0E1HD$JtI9ZH I9@H9FAx ~ IPH;VHFIxH9AHAt HEX DV DD@@8A IxHA@HE|$A mL^0HHA@IEDAhAkDDE9VL$H`LL$HCLL$L$ 0EHHT$0HL$(ILL ʵH{3HT$( }{@HHEt&H "{H=ƕs@H?fDM9uL9uuzLǺLL$L$D@HH@H;A L$H;= LL$uwL9trLL$LD$H<$DLL$LD$H<$H/tSIM9fDKHHT$(IODIfD$LL$L$>D$LL$L$LLL$Ht$L$HHM-?Ig-bA>-j?HPIAi-@-dIHl$E1}A~-a11'L=IH2I/G-IHl$%L% L9HHH HհIH5Q-H81=H (-E1H=ŋi711LLW=L$H6:L$HHtH H5sH8p6L$H H5rH8Q6MB-L<5 AAG-IA fHHIHHtLЅt1HZ HHÐLHHt8H(u4@H PH=Њsh1H@@ff.AWHo fAVfHnIHxAUHATIUSHxHD$`H~ )D$0fHnflHD$@HD$h)D$PHlHLHHH HLyHD$0LL- H1HCH9HL;luIHD$8HI_HLL$0HT$@H NH>HFLyHD$@HFHD$8HHD$0MLL$0HD$8HT$@H IHIvH=S AHEQHj5 5 j5 Pj5  IHEHPMcHHE5HxL[]A\A]A^A_HHHVH  HT$@oHFL)T$0FLHLT$LyHb UULT$HHD$0HUIRDH AHH HiH5B{ATL ƦH819XxZH sH=EE1e HH 'H)AHMEI@H  H fHx1LML- M1HI9L;luIHHD$@L{HFHHYHD$8HT$0{fDE1IE0JtHD$ I94fDH I9EH9F#A} P~ ~IUH;VHFIMH9@H@t HA} D^ D8@ vI}HA HHN0HHA@HEȃ5DA9u9HtQLL$HLT$2LT$LL$DIAL9IJtI9K fH  I9uuH9uuLHL$LL$LT$/HHtMH; LT$H;=u LL$uHL$H9;H/NdHD$83H_HH̺ H _H5.xjL AH8H816Y^xf.IE0E1HD$(@N|M9"Hû I9EI9G A} A IUI;WIGIMH9@H@t HA} Aw 8@ IMH@HHE|$(@ IO0IH@IDHȃD>A9ufLL$Ht2L\$HLT$0LT$L\$LL$u2fK/H ٹ I9uu I9utIM9DLLLT$HL$ L\$LL$-LT$HItwH; LL$L;= L\$1HL$ I9#LL\$LL$LT$42L\$LL$LT$I/LDLT$1LT$HtDxf.HHEH ^xH=`{HL$0HT$PMLL HQxLL$LT$H|$d1LL$LT$H|$IMH@HHE|$ yH+\fDxfDLL$D$LT$}+LL$D$LT$Df.LLL$Ht$LT$I)LT$Ht$LL$DHLL$LT$Ht$)Ht$LT$LL$TDHvHDLD$ L\$LL$LT$*D$ L\$LL$LT$ LL\$LL$LT$(LT$LL$L\$LL\$LL$LT$^(LT$LL$L\$IwHmI}HHD.Hu*H AD>JD>>xfDAWH fAVfHnIHAUHxATIUSHxHD$`H )D$0fHnflHD$@HD$h)D$PHiHLHHH HLyHD$0LL-y H1@HCH9HL;luIHD$8HI_HLL$0HT$@H a NH>HFLyHD$@HFHD$8HHD$0MLL$0HD$8HT$@H  IHIvH= AHEQHj5, 5 j5 Pj5  IHEHPMcHHE5HxL[]A\A]A^A_HHHVH q HT$@oHFL)T$0FLHLT$LyH JLT$HHD$0HUIUDH AHHP H#H5pATL 6H81G/X|ZH \XH=}E1[ HH HAHMEI@H H fH&LML- M1HI9L;luIHHD$@L{HFHHYHD$8HT$0{fDE1IE0JtHD$ I94fDH I9EH9F#A} P~ ~IUH;VHFIMH9@H@t HA} D^ D8@ vI}HA HHN0HHA@HEȃ5DA9u9HtQLL$HLT$](LT$LL$DIAL9IJtI9K fH I9uuH9uuLHL$LL$LT$k%HHtMH;l LT$H;= LL$uHL$H9;H/NdHD$8)H_HH< H ϘH5mjL "AHH81&,Y^|f.IE0E1HD$(@N|M9"H3 I9EI9G A} A IUI;WIGIMH9@H@t HA} Aw 8@ IMH@HHE|$(@ IO0IH@IDHȃD>A9ufLL$Ht2L\$HLT$%LT$L\$LL$u2fK/H I I9uu I9utIM9DLLLT$HL$ L\$LL$ #LT$HItwH; LL$L;= L\$1HL$ I9#LL\$LL$LT$'L\$LL$LT$I/LDLT$<$HtD|f.HHEH Ε.}H=JxU{HL$0HT$PMLL ;H|LL$LT$H|$&LL$LT$H|$IMH@HHE|$ yH#!\fD|fDLL$D$LT$ LL$D$LT$Df.LLL$Ht$LT$LT$Ht$LL$DHLL$LT$Ht$Ht$LT$LL$TDHvHDLD$ L\$LL$LT$0 D$ L\$LL$LT$ LL\$LL$LT$LT$LL$L\$LL\$LL$LT$LT$LL$L\$IwHmI}HHD/$Hu*H AD>JD>>|fDAWH fAVfHnIHAUHhATIUSHxHD$`H] )D$0fHnflHD$@HD$h)D$PHkHLHHH HLyHD$0LL- H1fDHCH9HL;luIHD$8HI_HLL$0HT$@H Ѫ NH>HFLyHD$@HFHD$8HHD$0MLL$0HD$8HT$@H IHIvH=ê AHEQHj5 5n j5 Pj5  IHEHPMcHHE5HxL[]A\A]A^A_HHHVH HT$@oHFL)T$0FLHLT$LyH" 5@LT$HHD$0HUISDH tAHH HH5"fATL H81$XkZH ̐ H=}sE1P HH H AHMEI@H H fHXLML- M1HI9L;luIHHD$@L{HFHHYHD$8HT$0{fDE1IE0JtHD$ I94fDH I9EH9F#A} P~ ~IUH;VHFIMH9@H@t HA} D^ D8@ vI}HA HHN0HHA@HEȃ5DA9u9HtQLL$HLT$LT$LL$DIAL9IJtI9K fH I9uuH9uuLHL$LL$LT$HHtMH;ܦ LT$H;=U LL$uHL$H9;H/NdHD$8H_HH H ?H5cjL AHkH81!Y^Mf.IE0E1HD$(@N|M9"H I9EI9G A} A IUI;WIGIMH9@H@t HA} Aw 8@ IMH@HHE|$(@ IO0IH@IDHȃD>A9ufLL$Ht2L\$HLT$lLT$L\$LL$u2fK/H I9uu I9utIM9DLLLT$HL$ L\$LL$|LT$HItwH;x LL$L;= L\$1HL$ I9#LL\$LL$LT$L\$LL$LT$I/LDLT$LT$HtDTf.HHEH > H=mJ{HL$0HT$PMLL H1 YLL$LT$H|$DLL$LT$H|$IMH@HHE|$ yH\fDKfDLL$D$LT$]LL$D$LT$Df.LLL$Ht$LT$)LT$Ht$LL$DHLL$LT$Ht$Ht$LT$LL$TDHvHDLD$ L\$LL$LT$D$ L\$LL$LT$ LL\$LL$LT$qLT$LL$L\$LL\$LL$LT$>LT$LL$L\$IwHmI}HHDHu*H eAD>JD>>CfDAWH fAVfHnIHAUHATIUSHxHD$`H˝ )D$0fHnflHD$@HD$h)D$PHiHLHHH HLyHD$0LL- H1@HCH9HL;luIHD$8HI_HLL$0HT$@H A NH>HFLyHD$@HFHD$8HHD$0MLL$0HD$8HT$@H IHIvH=; AHEQHj5 5 j5> Pj5- _ IHEHPMcHHE5HxL[]A\A]A^A_HHHVH Q HT$@oHFL)T$0FLHLT$LyH 5LT$HHD$0HUIUDH AHH0 HH5[ATL H81'XzZH <]H=iE1E HH wHyAHMEI@H a H fHLML-m M1HI9L;luIHHD$@L{HFHHYHD$8HT$0{fDE1IE0JtHD$ I94fDHa I9EH9F#A} P~ ~IUH;VHFIMH9@H@t HA} D^ D8@ vI}HA HHN0HHA@HEȃ5DA9u9HtQLL$HLT$=LT$LL$DIAL9IJtI9K fH i I9uuH9uuLHL$LL$LT$KHHtMH;L LT$H;=ś LL$uHL$H9;H/NdHD$8H_HH H H5~XjL AHH81Y^zf.IE0E1HD$(@N|M9"H I9EI9G A} A IUI;WIGIMH9@H@t HA} Aw 8@ IMH@HHE|$(@ IO0IH@IDHȃD>A9ufLL$Ht2L\$HLT$LT$L\$LL$u2fK/H ) I9uu I9utIM9DLLLT$HL$ L\$LL$ LT$HItwH; LL$L;=a L\$1HL$ I9#LL\$LL$LT$L\$LL$LT$I/LDLT$nLT$HtDzf.HHEH {H=ce@{HL$0HT$PMLL )HzLL$LT$H|$LL$LT$H|$IMH@HHE|$ yH \fDzfDLL$D$LT$ LL$D$LT$Df.LLL$Ht$LT$ LT$Ht$LL$DHLL$LT$Ht$a Ht$LT$LL$TDHvHDLD$ L\$LL$LT$ D$ L\$LL$LT$ LL\$LL$LT$LT$LL$L\$LL\$LL$LT$LT$LL$L\$IwHmI}HHDHu*H ~AD>JD>>zfDAWH fAVfHnIH8AUHATIUSHxHD$`H; )D$0fHnflHD$@HD$h)D$PHiHLHHH HLyHD$0LL-I H1@HCH9HL;luIHD$8HI_HLL$0HT$@H NH>HFLyHD$@HFHD$8HHD$0MLL$0HD$8HT$@H a IHIvH= AHEQHj5| 5N j5n Pj5  IHEHPMcHHE5HxL[]A\A]A^A_HHHVH HT$@oHFL)T$0FLHLT$LyH +LT$HHD$0HUIUDH T|AHH H}H5QATL |H81X~^ZH {jH=^E1e; HH {H{AHMEI@H ѓ H fH8LML- M1HI9L;luIHHD$@L{HFHHYHD$8HT$0{fDE1IE0JtHD$ I94fDHѓ I9EH9F#A} P~ ~IUH;VHFIMH9@H@t HA} D^ D8@ vI}HA HHN0HHA@HEȃ5DA9u9HtQLL$HLT$LT$LL$DIAL9IJtI9K fH ّ I9uuH9uuLHL$LL$LT$HHtMH; LT$H;=5 LL$uHL$H9;H/NdHD$8h H_HH H yH5MjL ryAHezH81v Y^`^f.IE0E1HD$(@N|M9"H I9EI9G A} A IUI;WIGIMH9@H@t HA} Aw 8@ IMH@HHE|$(@ IO0IH@IDHȃD>A9ufLL$Ht2L\$HLT$LLT$L\$LL$u2fK/H I9uu I9utIM9DLLLT$HL$ L\$LL$\LT$HItwH;X LL$L;=ю L\$1HL$ I9#LL\$LL$LT$L\$LL$LT$I/LDLT$LT$HtDg^f.HHEH v^H=*Y5{HL$0HT$PMLL wHl^LL$LT$H|$$LL$LT$H|$IMH@HHE|$ yHs\fD^^fDLL$D$LT$=LL$D$LT$Df.LLL$Ht$LT$ LT$Ht$LL$DHLL$LT$Ht$Ht$LT$LL$TDHvHDLD$ L\$LL$LT$D$ L\$LL$LT$ LL\$LL$LT$QLT$LL$L\$LL\$LL$LT$LT$LL$L\$IwHmI}HHDHu*H EtAD>JD>>V^fDAWH fAVfHnAUATIUHHHHSHh)D$ fHnflHD$PHD$0HD$X)D$@HL4HH$HRHH]HD$ IL= M1HL9kL;|uIHD$(HHCL}HD$HF M1fHL9H;\uIHD$0HH\$H/HHFH]HD$0HFHD$(HHD$ HG Ld$ H|$(&HVHFoL&H~HD$0)T$ HG LwIFHI III LLl$0HHH= HÅb Hm'/H=ر H5A HGHH HHTH H9E6LuM)L}IIHmfInfInƿAflHl$@)D$@IG H@8IH L1HLIMt I.M5I/kL;- t2IEH;  LLJHH H(PI$LI$HLHD$?HD$Hh[]A\A]A^A_McHcGIHcHEI>@H LHH]HD$ H LmHHH HqH5DATL {pAH noH81X^NZH 2oH=RP/1Hh[]A\A]A^A_HP.HHHS HHEHD HL-* =IH H5z E1HHLI,$I HEHMW HEH H5ޱ LIHM H8 I/ LvIHW H= HKHIHD HIs HLANHmJ H mDH=uQ-I,$LHC0E1HD$@JtH9H H9CH9FUM{ ~ HCH;FHVH{H9AHAt HDS DN DD@@8utA H{HA LV0HHA@IEDAXADDE9u)HHDIM9HD$0eHHH H lH5AjL omAHgnH81sY^JNL L9uuL9usHߺLL$HHbH;΄ H;=L LL$L9H|$H|$H/ fKODwGII DDwGII IfHFHD$(HHD$ HEHD$IfDIG0E1HD$@JtI9H I9GH9FmeA ~ IWH;VHFIH9AHAt HEW DN DD@@8A SIHA@HE|$A LV0HHA@IEDAADDE9u2H(LD$HWLD$@IM9HD$(HHH AH5L?jL jH iH8Hk1_@NAXNfDL I M9uuL9usLLL$LD$,HH]H;) LD$H;= uLL$L9H/K_L(HHD$@H5H Ld$HH}H9t }HUBnLt$HHZE1 QH=+2LLIIMH@I//ANE1LPH gDH=K(Mf.Le HuH H5}gH8fD{HI fDHHHEHHEHCIuHEHHEHC IGHHH=0I51HLI_M H+H4rANAHmt%H fDDH=YJ&HfDD$D$fDHHt$Ht$fH{HA@HE|$GDLD$H|$LD$H|$IHLeIHl$HE1ANIHE1HN>NHHt$Ht$MHL$ HT$@MLL gHON7HvHHCH;HLpD$LD$ZD$LD$@L@`LLD$Ht$)Ht$LD$HLD$Ht$Ht$LD$HLHvH1DDN H YdH=G|$I$HP14DD DDeANAFDDI/ANHe6NANHIWH cNH=KG#H@`HHHHHH@H| H9uTfD?LuIFHvTIItaH5IHmH_HH55hHH_H@MtHcEIHcHEIDuEII HmGDuEII IyYNYMhI.^LQII1HL\I^HHHqz H5QcHDcH81qNHy H5 ,H8aH@`HHHHIHH9XuRIEMuIFHviIItvLIImqLdH5fHgIHuHmHMtIcEIHcHEIEuAEII EuAEII ImH|x H5*H8EH@`HtaHHtULIHtHH9Xu"L`I/ILH5eHIHuIqHuHx H5M`H8ANLH N`NH=Cg H ,`NH=CE HH#x H5_H8IHtH;?t L;-s 2M9)LImFtILT$HLd$H$yNHD$0H [AL `ZH:~$DILT$HLd$H$O 3HHEH Zk~H=R>IG0L$E1HD$ Ll$MLd$IHH\$LDO|L9Hs H9CI9G { A HSI;WIGHsH9@H@t H{ E_ D@@8@ HsH@HHE|$ A UIw0IHA@IDDA]AmDD>E9uTHtHu>@MLL$Ll$H\$Ld$OfDL9uu M9u*t&IL9LL$H\$Ld$~fDLHIHtH;q L;=q M9L[I/tMLL$Ll$H\$Ld$GfDL$?L$HtA~@HL$0HT$@ILL _ZHx-LL$0HHY]F~5fDLD$ D$ L8 L+IuHI|$HzfDLD$,D$,HEZL8BIwHH{HDD>DD>DD$DD>ff.AWH AVAUATIUSHHhL5~o HD$@HHD$0HD$HHD$PLt$8HHLHHHZHHWH WAHOL UEHTWIHLOHHAn HXXSH5+H81@X:|ZH UVH=9E1HhL[]A\A]A^A_@HHZL^L\$8LLL$0 oL^Li)D$0MLL$0HI$It$H=In AHEHo HHe AVjRPjRLPj5  IHEHPM&HHE2HX%LyL-= 1MfHL9L;luM LL$0MqMoM2L\$8&MLLiLL$0M~HML=| H1HH9L;|uMML\$8IIE0LT$E1HD$Ld$MH$HLDLlM9H{m I9D$I9E A|$ A} IT$I;UIEIt$H9@H@t HE\$ EM DD@@8u}A I|$HA@HE|$A bIu0IHA@IDDAADDE9u'HHIHL9H$fM9uuM9uuLLIHtH;k L;- k 2M9)LIImFtILT$HLd$H$yNHD$04H RAL QH|$DILT$HLd$H$O 3HHEH FRRp|H=5IG0L$E1HD$ Ll$MLd$IHH\$LDO|L9Hk H9CI9G { A HSI;WIGHsH9@H@t H{ E_ D@@8@ HsH@HHE|$ A UIw0IHA@IDDA]AmDD>E9uTHtHu>@MLL$Ll$H\$Ld$OfDL9uu M9u*t&IL9LL$H\$Ld$~fDLHIHtH;h L;=oh M9LI/tMLL$Ll$H\$Ld$GfDL$L$Ht%|@HL$0HT$@ILL QHx-LL$0HY]*|5fDLD$ lD$ LX8 L@+IuHI|$HzfDLD$,D$,HEZL8BIwHH{HDD>DD>DD$DD>ff.AWH? AVAUATIUSHHhL-f HD$@HHD$0HD$HHD$PLl$8HHLHHHZHHkNH [NAHOL MEHNIHLOHHe HOSH5"H81X+ZH M H=f1E1^ HhL[]A\A]A^A_@HHZHVHT$8HHD$0 oHVLq)D$0MHD$0I$HIt$E1H=d HEL H jAPQjAPAQHj5 P IHEHPM%HHE1H$fLyL5m 1MfHL9L;tuIHD$0HpMwM2HT$8&LHLqHD$0M~HML=̘ H1HH9L;|uIHHT$8IIF0LT$E1HD$Ld$MH$HLDLtM9Hd I9D$I9F A|$ A~ IT$I;VIFIt$H9@H@t HE\$ EN DD@@8u}A I|$HA@HE|$A bIv0IHA@IDDAADDE9u'HHHL9H$fM9uuM9uuLLIHtH;b L;5]b 2M9)LI.GtILT$HLd$H$yOHD$0H PJAL IH%fDILT$HLd$H$K3HHEH IaH=R-M IG0L$E1HD$ Lt$MLd$IHH\$LDO|L9HSb H9CI9G { A HSI;WIGHsH9@H@t H{ E_ D@@8@ HsH@HHE|$ A UIw0IHA@IDDA]AmDD>E9uTHtH(u>@MLL$Lt$H\$Ld$KfDL9uu M9u*t&IL9LL$H\$Ld$~fDLH@IHtH;A` L;=_ M9LI/tMLL$Lt$H\$Ld$GfDL$L$Ht@HL$0HT$@ILL IHIx-HD$0HY]5fDLD$ D$ L8 L+IvHI|$HzfDLD$,TD$,H@EZL(8BIwHH{HDD>DD>DD$DD>ff.AWH AVAUATIUSHHhL5^ HD$@HHD$0HD$HHD$PLt$8HHLHHHZHHEH EAHOL ZDEHEIHLOHH\ H GSH5BH81XZH DpH=(E1HhL[]A\A]A^A_@HHZL^L\$8LLL$0 oL^Li)D$0MLL$0HI$It$H=a\ AHEH HHݒ AVjRPjRLPj5( Z IHEHPM&HHE2H%LyL-݇ 1MfHL9L;luM LL$0MqMoM2L\$8&MLLiLL$0M~HML= H1HH9L;|uMML\$8IIE0LT$E1HD$Ld$MH$HLDLlM9H\ I9D$I9E A|$ A} IT$I;UIEIt$H9@H@t HE\$ EM DD@@8u}A I|$HA@HE|$A bIu0IHA@IDDAADDE9u'HHHL9H$fM9uuM9uuLL.IHtH;/Z L;-Y 2M9)LImFtILT$HLd$H$yNHD$0H AAL P@H~$DILT$HLd$H$O 3HHEH @;H=$IG0L$E1HD$ Ll$MLd$IHH\$LDO|L9HY H9CI9G { A HSI;WIGHsH9@H@t H{ E_ D@@8@ HsH@HHE|$ A UIw0IHA@IDDA]AmDD>E9uTHtHxu>@MLL$Ll$H\$Ld$OfDL9uu M9u*t&IL9LL$H\$Ld$~fDLHIHtH;W L;=W M9LKI/tMLL$Ll$H\$Ld$GfDL$/L$Ht~@HL$0HT$@ILL l@H虽x-LL$0H8Y]~5fDLD$ D$ L8 L+IuHI|$HzfDLD$,D$,HEZLx8BIwHH{HDD>DD>DD$DD>ff.AWH AVAUATIUSHHhL5nU HD$@HHD$0HD$HHD$PLt$8HHLHHHZHH =H <AHOL ;EHD=IHLOHH1T Hc>SH5H810X}ZH E<H=^ E1HhL[]A\A]A^A_@HHZL^L\$8LLL$0 oL^Li)D$0MLL$0HI$It$H=!T AHEH_ HH- AVjRPjRLPj5x  IHEHPM&HHE2HH%LyL-- 1MfHL9L;luM LL$0MqMoM2L\$8&MLLiLL$0M~HML=l H1HH9L;|uMML\$8IIE0LT$E1HD$Ld$MH$HLDLlM9HkS I9D$I9E A|$ A} IT$I;UIEIt$H9@H@t HE\$ EM DD@@8u}A I|$HA@HE|$A bIu0IHA@IDDAADDE9u'HH9HL9H$fM9uuM9uuLL~IHtH;Q L;-P 2M9)L9ImFtILT$HLd$H$yNHD$0$H 8AL 7H}$DILT$HLd$H$O 3HHEH 68}H=JIG0L$E1HD$ Ll$MLd$IHH\$LDO|L9HP H9CI9G { A HSI;WIGHsH9@H@t H{ E_ D@@8@ HsH@HHE|$ A UIw0IHA@IDDA]AmDD>E9uTHtHu>@MLL$Ll$H\$Ld$OfDL9uu M9u*t&IL9LL$H\$Ld$~fDLHIHtH;N L;=_N M9LI/tMLL$Ll$H\$Ld$GfDL$L$Ht}@HL$0HT$@ILL 7Hx-LL$0HY]}5fDLD$ \D$ LH8 L0+IuHI|$HzfDLD$,D$,HEZLȾ8BIwHH{HDD>DD>DD$DD>ff.AWHOz AVAUATIUSHHhL5L HD$@HHD$0HD$HHD$PLt$8HHLHHHZHH[4H K4AHOL 2EH4IHLOHHK Hm5SH5H81X+zZH 3H=E1NHhL[]A\A]A^A_@HHZL^L\$8LLL$0 oL^Li)D$0MLL$0HI$It$H=K AHEHv HH} AVjRPjRLPj5x  IHEHPM&HHE2H蘾%LyL-}x 1MfHL9L;luM LL$0MqMoM2L\$8&MLLiLL$0M~HML=~ H1HH9L;|uMML\$8IIE0LT$E1HD$Ld$MH$HLDLlM9HJ I9D$I9E A|$ A} IT$I;UIEIt$H9@H@t HE\$ EM DD@@8u}A I|$HA@HE|$A bIu0IHA@IDDAADDE9u'HH艿HL9H$fM9uuM9uuLLμIHtH;H L;-MH 2M9)LImFtILT$HLd$H$yNHD$0tH ?0AL .Hz$DILT$HLd$H$O 3HHEH /XazH==IG0L$E1HD$ Ll$MLd$IHH\$LDO|L9HCH H9CI9G { A HSI;WIGHsH9@H@t H{ E_ D@@8@ HsH@HHE|$ A UIw0IHA@IDDA]AmDD>E9uTHtHu>@MLL$Ll$H\$Ld$OfDL9uu M9u*t&IL9LL$H\$Ld$~fDLH0IHtH;1F L;=E M9LI/tMLL$Ll$H\$Ld$GfDL$ϽL$Htz@HL$0HT$@ILL .H9x-LL$0HظY]z5fDLD$ 謸D$ L蘶8 L耶+IuHI|$HzfDLD$,DD$,H0EZL8BIwHH{HDD>DD>DD$DD>ff.AWHv AVAUATIUSHHhL-D HD$@HHD$0HD$HHD$PLl$8HHLHHHZHH+H +AHOL J*EH+IHLOHHB HD-SH52H81оXZH * H=^E1HhL[]A\A]A^A_@HHZHVHT$8HHD$0 oHVLq)D$0MHD$0I$HIt$E1H=C HELn H x jAPQjAPAQHj5t PA| IHEHPM%HHE1H$fLyL5t 1MfHL9L;tuIHD$0HpMwM2HT$8&LHLqHD$0M~HML= v H1HH9L;|uIHHT$8IIF0LT$E1HD$Ld$MH$HLDLtM9H B I9D$I9F A|$ A~ IT$I;VIFIt$H9@H@t HE\$ EN DD@@8u}A I|$HA@HE|$A bIv0IHA@IDDAADDE9u'HHٶHL9H$fM9uuM9uuLLIHtH;@ L;5? 2M9)LٸI.GtILT$HLd$H$yOHD$0ŷH 'AL A&H%fDILT$HLd$H$K3HHEH &) ׎H=J IG0L$E1HD$ Lt$MLd$IHH\$LDO|L9H? H9CI9G { A HSI;WIGHsH9@H@t H{ E_ D@@8@ HsH@HHE|$ A UIw0IHA@IDDA]AmDD>E9uTHtHhu>@MLL$Lt$H\$Ld$KfDL9uu M9u*t&IL9LL$H\$Ld$~fDLH耱IHtH;= L;=< M9L;I/tMLL$Lt$H\$Ld$GfDL$L$Ht@HL$0HT$@ILL &H艣x-HD$0H(Y]5fDLD$ D$ L8 LЭ+IvHI|$HzfDLD$,蔯D$,H耭EZLh8BIwHH{HDD>DD>DD$DD>ff.AWHf AVAUATIUSHHhL-^; HD$@HHD$0HD$HHD$PLl$8HHLHHHZHH"H "AHOL !EH4#IHLOHH!: HZ$SH5H81 XZH 5" H=E1HhL[]A\A]A^A_@HHZHVHT$8HHD$0 oHVLq)D$0MHD$0I$HIt$E1H=: HELRe H #p jAPQjAPAQHj5he Ps IHEHPM%HHE1H7$fLyL5e 1MfHL9L;tuIHD$0HpMwM2HT$8&LHLqHD$0M~HML=\m H1HH9L;|uIHHT$8IIF0LT$E1HD$Ld$MH$HLDLtM9H[9 I9D$I9F A|$ A~ IT$I;VIFIt$H9@H@t HE\$ EN DD@@8u}A I|$HA@HE|$A bIv0IHA@IDDAADDE9u'HH)HL9H$fM9uuM9uuLLnIHtH;o7 L;56 2M9)L)I.GtILT$HLd$H$yOHD$0H AL H֍%fDILT$HLd$H$K3HHEH & (H=IG0L$E1HD$ Lt$MLd$IHH\$LDO|L9H6 H9CI9G { A HSI;WIGHsH9@H@t H{ E_ D@@8@ HsH@HHE|$ A UIw0IHA@IDDA]AmDD>E9uTHtH踫u>@MLL$Lt$H\$Ld$KfDL9uu M9u*t&IL9LL$H\$Ld$~fDLHШIHtH;4 L;=O4 M9L苭I/tMLL$Lt$H\$Ld$GfDL$oL$Htݍ@HL$0HT$@ILL Hٚx-HD$0HxY]5fDLD$ LD$ L88 L +IvHI|$HzfDLD$,D$,HФEZL踤8BIwHH{HDD>DD>DD$DD>ff.AWHf AVfHnAUATIHx0HhUfHnSflHHxL=2 HD$`Hh HD$0HD$hHD$8L|$@)D$PHHLHHZHLLiLL$0MHD$8HT$@HI$It$H=1 AHEHAWj51] 5h j5e Pj5e k IHEHPMHHEHxL[]A\A]A^A_HHFLLiHD$@HFLL$0HD$8MLL$02DHfHHHH#H AHOL EH\LOODx@HpALiL5d 1MHL9L;tuM LL$0MIMzkH AL HH/ HH53SH81ЫXwZH %H=E1fHc LHL$L$HHD$8IMHML5(d H1HH9L;tuIHHD$@IILLLL$0HVHT$@HFHD$8@HFHLiHD$8HT$0jfDLL$0HT$@@fIF0L$E1HD$ Ll$MLd$IHH\$LDOtL9H/ H9CI9F { A~ HSI;VIFHsH9@H@t H{ E^ D@@8@ HsH@HHE|$ A Iv0IHA@IDDA9AIDD6E9uTHtH蘤u>@MLL$Ll$H\$Ld$K&fDL9uu M9u*t&IL9LL$H\$Ld$~fDLH谡IHtH;- L;5/- DM9;LkI.QtMLL$Ll$H\$Ld$GfDL$OL$HwHHEH n'xH=ZE6LAIF0E1L$MHD$ILLd$MMtM9 HK- I9D$I9FA|$ A~ IT$I;VIFIt$H9@H@t HE\$ EN DD@@8A I|$HA@HE|$A Iv0IHA@IDDAADDE9u3HLT$HLT$DHL9fDM9uuM9uuLLLT$IIHtdH;J+ LT$L;5* M9LLT$LT$I.CkILd$LML$yOHD$0ߢH AL [Hw?ILd$LML$O DHL$0HT$PILL Hw3H蘝LD$,脝D$,HpLXIvHrH{HHLD$ LT$D$ LT$fL$藡L$HowLLT$ӚLT$tLLT$賚LT$TIvHII|$HDD6DDrfHLL$H$?H$LL$fDH+uH>I.A%L4$4$fHHHH H5 AH8近A>DH H5JH8蚑mDHCHHD$fHxImH=U HA3H+>dH߉4$94$QIxHA}L $rL $HI>HIH'H@HH$H|HA<$L$L $HI>(H H52H8肐H+>ImAL4$W4$oL@5HLL$H$'H$LL$@'AHCHHD$8fINHLߎr>AHŽEH g'E1H=*}11>A11JH蚖Hݾ''1ff.@HGHH;^ u 1AVAUATUSHHtIMt%HL[]A\A]A^D苖IfDkHH H{XH(H9HtHEHHW@@HXHHJHN1HH96H;luHkhHChfLk`CXH/t`MtImt[HHmHތHH{XfLk`HkhHChCXHu行L藌LmM1 HI9t6H;|uKHHH98HuH;- &PE1JtH9kH|$ZH|$TIM9uff.@AVAUIATUSHH=r? HGHH; u.1LwIHHL[]A\A]A^LH<IMu-IH I|$XH(H90HHEHSHW@@HXH3HJH~d1 HH9tWH;luIl$hfMt$`ID$hAD$XH/Mt I.HtHmuH覊fD;IHt E1H LH5H81] IH;tI|$XfMt$`Il$hID$hAD$XHINDLFLuMS1 HI9t6H;|uHHH9HuH;- 1HtH9YH|$ƑH|$BHI9uff.AUIHATUHSHHHWH=< :IH< H@IEL#MtI$HL[]A\A]D賍HuHH[]A\A]ff.AWAVAUATUSHHHHM裌IHHCHHCID$H5B HF>HCHH; 1HHH[L- L9e!IHHEHLHhQIHI/3I,$Hy; H5: H9pH9 HHL=9 M蚋IHHCHHCID$HJ HHJ Ml$(ID$ IERIHfInfInfl@ILp(I. Hm/HL[]A\A]A^A_HL t111LHo蛋HL-k IEHkL9HR: H@H98 H8 HHL58 MsIHHCHHCIGHkI HH`I IG I$Mg(.IHfInfInfl@I,$MLH@HMLDLLЅHH E1E1RL HH8H sH51耍XZRfHyH5RHwfHHH׃IH= MwXL(M9M IEH2IVA@A@IXH2HJH1DHH9L;lu111LlfHHHHIHW MnXH(L9!M.HEHnIUA@@IXHtZHJH1@HH9H;luH Jp#H=pcE1DML9UMuH;-' CT@H=B HJ5 H5K5 IafD #fDH H=E1I/ #L4$ ق4$@H=iB I@I,$I/ #u#H 8H=hAUI,$P@D#I/L4$MM;4$MIm L4$4$H=A H3 H53 IHfDH #AH=襵I,$xDH=IA I@I.t_$E1MH ,H=\Of. $H1#MM$LL#nH #H=迴I,$QE1IUH~1 HH9t\M;tuL}M1 HI9twL;lunLHI9HuL;-- O1H9SItI9LHL$H$`HL$H$H1HtI9LH$-H$HI9u #LMMff.AWH7 AVAUIATUSHH H$HhH|$(HDŽ$H$HDŽ$H$HILHHH6MHH AHOL 6EHIMLOHH HAUH5H81軆XZH H=E1色HL[]A\A]A^A_@H HVHFHD$H$L>L$0fDHFo.LqHD$)$MfL$HD$xLHDŽ$HDŽ$EHD$ H.HD L(hLE1AHƹAHD$xIHH$HH|$xH/- H1 L$HD$xHDŽ$H*. H9PH. H0HH-- Hl$xHHEH55 HHH9IL$H|$xMH/ Hm0 H- HD$xH9PHt- HKHL`- MI@LD$LH5$9 HHLD$IMI( H I9EnH? H$LHDŽ$L$H$MHD$xHHI)H H$H9 H9GHD$xH$HDŽ$H$褬H$H|$xH/ H$HD$xHCH$H/ H$H;= HDŽ$H;=  H9 ÀAŅH$H/ HDŽ$EMgH9\$ yHD$H HLpI9t M HPHuHLhHT$Ht HD$HMtIMtIEH. H /+ H9HH+ HHH=+ H$HqHGH55 HHHD$xL$HhI(\H|$x1HDŽ$H = H$H9OfHnD$)$贪H$H$HtH/H$H|$xHDŽ$HH/THD$xH|$ !|HD$xH09}H$HH;~$HL$HDŽ$HDŽ$D$xHD$x@HtHHD$HHMt I.Mt ImTHM, H V) H9H\H=) HHL )) LL$xMIAH5; LHHIL$H|$xMH/ H+ H( HD$xH9PH( HHL ( LL$xMIAH52 LHHIH|$xMVH/+H$1HD$xH  H$H9OfHnfHnL$fl)$WH|$xH$Ht H/HD$xImL$MH$H/H$HDŽ$HL$HD$IEAuHDŽ$I} HD$H= H|$ HD$0< IGH53 LHHIL$MH I9F7MFM*IFIHH$H$H/H$H$L$LD$LD$H$I(L$M)H$H/H58 1H$HDŽ$YvH$IH~H$H/8H$H;=4 HDŽ$H;= H9zAƅH$H/HDŽ$E H( H % H9HH|% H_HL5h% L$MIFH5\/ LHHIMaH$H/H H$1HDŽ$I9NfHnfInLfl)$GH$H$IHtH/$L$HDŽ$MI.SL$I9HD$ I^fHDŽ$HHD$AXHsff/HD$(H5}. HbIH1HD$8HD$(H5,. HbLL$8HIHDŽ$H I9@BI@H$HAMPHII(H$H$LLL$@LT$8H$LT$8LL$@H$H$HtH/H$HDŽ$HI*H$H/uLL$8HDŽ$yH|$0LL$8HD$H HD$ HT$L|$hHHD$8LIHLl$PLl$HD$@HD$(LL$(HLt$XHl$`IHHI6 fHnMtgE1f.IM9tOCLBLT$uT$ff(YBL 5 fC.\\YzuHT$ HL$HT$8HD$8Hl$@TH9D$0^LL$(Ll$PLt$XHl$`L|$hH|$HLL$&pLL$H5"5 1LNLL$II)BMI( HD$H\$HI/bL|$fDHiL=5) 1H)fHH93M;|uMLqL$M~IL$H-0 H1 1HH9+I;luIHD$H H$IofDLodofDLoo%fDopfDIG0LT$E1HD$Ll$MILMfDOtL9H H9EI9F } [A~ hHUI;VIFHuH9@H@t HDU EN DD@@8u{A 1H}HA@HE|$A  Iv0IHA@IDDAADDE9u&HH`qfIM9Ll$fH9uuI9uuLHnIHtH; L;5 Z I9Q LYsI.wLLT$MMLl$ySHDŽ$?rH AL HlLLT$MLl$MO<@H|$ oH$IHqH$HH~H$HDŽ$HDŽ$HEH0LhHt$H#fDH|$xҦE1E1A5E11E1HD$E1E1Ht H/ H$Ht H/"H$Ht H/;Mt I(\Mt I)uMt I+~H :DH=+Mt I/gE1MtImtHMtI.tMHtHmtQHL$H*HHD$HHHkLkfDLkfDHkfDL\$ LL$LD$lkL\$ LL$H$LD$L\$ LL$LD$H5C LHD$H'HD$HIHMH@0ID$H&HPHF#H#AD$AT$HH HD$I,$"HD$HL;- 1'IEE1H|$HD$(^ H|$HIE1H1fHIH9! HIL)H9~fD EfDDfDIDfDLDD@fDHE0HL$E1HD$ H\$LO|L9H H9EI9GUM} (A 2HUI;WIGHuH9@H@t HDU EO DD@@8usA H}HA Iw0IHA@IDDAA/DDE9u(HHF@II9HD$hHH\HH) H5L jAH HmH81KA['[fDH;- uuL;=| urLHrCIHcH;o L;= u L;=7 . I/dHL$H\$HL$H\$Ot@L`B;LPBJH@B*L LpMHE0HL$E1HD$ H\$LM@N|L9*H# H9EI9G} 3A  HUI;WIGHuH9@H@t HDU EO DD@@8u{A H}HA@HE|$ A Iw0IHA@IDDAA:DDE9u&Ht@HCvfDIM9IH\$kfDIHL$H\$KDRL@@fDH5 H= 1 HD$@IHp1H@7H|$@H/H|$H1E1HD$@ArE1Ht H/H|$PHt H/uH|$XHt H/yHt H+H DʉH=sMtI,$E1Mt I.MuImjL?]IH5V H*%t Iɚ;LH5 Hf*tHI9L9|$  HD$H; qH H H9H H H HL% Ld$HM H5 L,HD$XIHm H|$HH/"H|$X1HD$HH H$H9O!fHnD$)$7oH|$HHD$@HHtH/H\$@HD$HHI!H|$XH/HD$XH|$@H;= H;= H;=d YCÅ#H|$@H/FHD$@HD$H  H9H['HHD$XH|$=HD$@IH'KAHD$HIHg#HD$@H|$XLHD$@ID$H= ֩H٠AvRL,;I,$tqAq1E1E1ML:@HM0LEHIDHH}HA@HE|$ gL:L75L*5#5Az@I*HD$PH5 LaHD$PIH=H5 H\5HD$@HH|$PH/J HD$PH|$@H;=: H;=  H;= 9AŅ<H|$@H/7 HD$@EH H@H9u H` HHLL LT$PMH5 LgHD$HIHGH|$PH/H5 LHD$P/HD$PIH[H|$H1HD$XH Ҿ H$H9O=fHnfInHg flH$)$6dH|$XHD$@Ht H/)HD$XH|$PH/!HD$PH|$@H|$HH/THD$HH|$@H;= AH;= D H;=N v C8AŅH|$@H/HD$@EH H H9HH HHL LT$HMH5 LHD$PIHmH|$HH/H5 1LHD$H2HD$HIH7H4HD$XIHHL\2IHH|$XH/gH|$HLLT$(HD$X5LT$(HHD$XhH|$HH/HD$HI*H|$PH H9GHD$XH$HDŽ$H$bHD$@H|$XH/HD$XH|$@H|$PH/HD$PH|$@H;=s AH;= DuH;=9 t26H|$@AH/^HD$@E0*Ls0Hf0LY0LL0B080q.0OL!0S1۽)Aj5%fDL0xL/}/ZHD$@HGHD$HHHWHHH|$PHT$PH/SHD$HH|$PH$1۽:Ay;Ay1E1E14/*/ /H/! /H5x H= 1 HD$HIH1H%H|$HH/ JAz1E1HD$H Aq1E1E1\H,DD 1۽\A{LU,LD$(4.D$(H#,L,It$H1E1^A{IwHLD$(-D$(D`A{1E1E1vL+H+HL$2HL$H. H:0HD$PIHH= H 6HD$HIHH|$PH/? HD$HH= H$HD$PHDŽ$H$[HD$PIHH|$HH/HD$HH|$P1#H|$PH/uA|1E1HD$PE19IwH5H}H0HA}1E1E1H=` Hq H5r 譢IH|$@MｪAfHt H/{H|$XHD$@Ht H/HD$XMt I*H|$HHt H/ HD$HH|$PHt H/HD$L- HD$PHxXI9H=IEHxHWJ@=2A@$HXHHJH1fHH9L;luH DʉH= ^H|$HL$XHT$PHt$@ \H|$@Ht H/ HD$@H|$PHt H/HD$PH|$XHt H/HD$LHLHD$XH#H-HD$XIHxH= H2HD$PIH@H|$XH/2 HD$PH=g H$HD$XHDŽ$H$XHD$XIH H|$PH/uHD$PH|$X1X H|$XH/GMA1HD$XE1E1HI9YHuL;- GHD$LHLDL$M1E1HE1!DL$LDL$)DL$DL$LT$(DL$LT$LDL$(DL$DL$(DL$DL$(DL$DL$LT$g(H|$XDL$LT$gD/ADD}H=S IH|$XMｬAE10HGHD$HHHWHHH|$@HT$@H/HD$HH|$@H$MAL'r~'t'j'`'0I)H|$@ϡA9DD''''i1E1MAHD$HAD$HD$H= H H5 KIcL -HD$H|$@Ld$HtDlDD1E1M A) /I4EH=r =IIVH1@HH9I;|u*H mAHmH;3 yL׺X&IHH;U AH;ұ DL; LLT$(+LT$(AI*vEx%LT$PI*t2HD$PEPH|$@ѡAE10L(%1E1M A<%4H|$H1E1MADDIUH1HH9 I;|uH= H H5 IMA1E1E141E1MALJ$1E1FA1۽DAwH=@ I*H=, H H5 yIH|$@(AE1H|$@KAH|$@IAH= 蓑I'H= H H5 Id]Z;1۽mA|HGHD$XHHWHHH|$HHT$HH/5HD$XLT$PH$H|$Hp1E1pA|E1E1A[H|$@NAHGHD$HH0HWHHH|$XHT$XH/pHD$HH|$XH$]H|$XA@>H1'H|$@QA H|$@OA4Aj1E1MA|1E1MAd1E1MۢAL}AH|$H1۽A!H=z EIH=f H H5 賑IcH|$@SAH|$H1۽A1۽AH|$@nAE1LoMmHGIEHH|$PHD$PH/HD$XH|$PH$L$H$KKHD$@Im@LS3_A1E1E11E1AqoH|$H1E1A1۽AA1۽AH= ÍIH@`H.HHLIH Hd I9D$u%L}?I,$HD$LULH5+IHuE1AAE1 TAT@A1E1E11۽AH|$H1E1+Al1۽)A+A1E1E1HD$pH-=HD$xHT$PH9Py9HPHT$xHg9H@HHH|$pHD$pH//9HD$xH|$pH$H)Hj*H|$xH$Ht H/9H$HD$x:H|$pH/8H$HD$pH/8HDŽ$KHD$`MKHD$HL\$XE1Hl$XLd$hLMHH@HHD$JMHL$HHD$PHL$@H|$LIH8LL$HH0HH H0H0H0KHC 1H0/@H(H0HH@(H;{lHH@HHtȀ84H(HI8HcI H0HL|$p]fDfDHLLHHHLHpH`HP%H@4DT$@.DT$@@DT$HLD$@DT$HLD$@fLDT$@DT$@|fDT$@DT$@s@DT$@DT$@r@LEL%] M 1HI9 L;duIH H$HfDHFHMHD$H$HH$UID$0HL$E1HD$ H\$LMMN|M9 H3 I9EI9GUMA} A IUI;WIGIuH9@H@t HEU EO DD@@8urA I}HA Iw0IHA@IDDAA\DDE9u'H%HII9HDŽ$HHH H5>L ijAH #iHkH81AZ.A[fL M9u|M9uoLLLL$IH[H; L;=e uLL$M96 I/OHL$H\$M @HL$H\$MKHD$DHD$H;L :aH$H$HH$HH Hܢ H9PHâ HHH= H$HHGH5 HHHD$xHH$H/ H|$x1HDŽ$H :~ H$H9OfHnD$)$#H$HD$pHtH/uHD$pHDŽ$AaH H|$xH/` HD$xL%HD$xH=HD$H$HQ ~D$pH$HD$pHDŽ$D$xHD$x@Ht H/H$HDŽ$Ht H/H$HDŽ$Ht H/HDŽ$H* H H9PHʠ HHL% Ld$pMID$H5 LHH'ILd$xMH|$pH/HD$pHD$pIHHL$HHD$pHH$H$IHHY H H9P8H H2HL ՟ MH5e LLL$LL$HII)H5 H$LLD$LD$YI(H$Ht$pH|$xIH H|$xH/THD$xH|$pH/2H$HD$pH/ Hֶ At$HDŽ$I|$ I$I\$H|$ HD$HD$0HfH= H*D$0ݵ Lt$HH5 IHD$(H$HfIH5ȩ [H$HHHD$pHGz H9GHGHD$pH, HWHHH$H$H/HD$pH$H$H$~H|$pIHt H/HD$pM_H$H/HDŽ$I.xHD$(HD$HIHD$H~wHD$HJI1HT$ LH@HHl$8LL|$HIL|$0LLd$0IHL$@HIMLLIHl$ L9t$uHl$8L|$HLd$0H|$(~H$HtkH5r 1#H$H$H/ H$HDŽ$HL$(H HHD$HHHDŽ$I$ME11Ld$ HD$8HD$0HD$HD$(Hy HHn HD$@ID$0HL$E1HD$ H\$HLN|M9 Hy I9D$I9G A|$  A  IT$I;WIGIt$H9@H@t HET$ EO DD@@8A  I|$HA@HE|$ A  Iw0IHA@IDDA A2DDE9uTHtHu>DHHL$H\$Kf.L w M9uu M9utIL9HH\$pLLLL$IHtH;w L;=Jw LL$M9LI/N tHHL$H\$M{H5HD$ E111HD$E1E1AHD$8AHD$0HD$HD$(@HD$ E1E11HD$E1AAHD$8HD$0HD$HD$(fDHAAL E`ILHH$H$ M:fAAH5 H|$HH5t HHD$ LL$ HII)L M9I9~L;u qLLD$ LD$ A_I(# ELH5y H|$_IHNHD$pHD$PI9D$ID$HD$pHML$HII,$$HD$pH$LLL$H$XH|$pLL$IHt H/~HD$pMI)iH5 1LLD$LD$HIfI(}M9I9L; tt xLLL$aLL$ I)) IHGH3 HH# IAHD$H;t HDk P H@utEHPIA LϾHڟ LL$HHHß IA(LL$HII) LLjI}HA@HE|$ nLLL$ ELL$ AAmAHD$ E1E11HD$E1HD$8HD$0HD$(MI)LDT$HLD$@LDT$HLD$@D/+ !LLAAAgH$Ht H/ H$HDŽ$Ht H/ H|$pHDŽ$Ht H/ HD$pH|$xHt H/F H YDHD$xH=?5HL$pHT$xHH$HD$Hp H9P]HH$LIHHD$LL$HILHH$HHD$4LD$HHD$"H$H/ HDŽ$I( H$Ht H/H|$xHDŽ$Ht H/'HD$xH|$pHt H/HH$HD$pH$H$RH=, WIb,DLD$ LD$ LD$D$LL$(LD$ LL$(LD$ LL4H$IHFHD$HHD$pHH$HD$pHDŽ$HAyL"H"L > HD$ E1E11HD$AAHD$8HD$0HD$HD$(!IwH^LLL$ LL$ LL|r>HD$(cLL$(LD$ *HHD$ E1E11HD$AșAHD$8HD$0HD$HD$(g}HH0H;0 HHH0HH0H0eDDD}LD$D$L %LwIwHI|$H_LHD$JLD$;L.L!HD$ E1E11HD$AOAHD$8HD$0HD$(FDDHD$ E11E1HD$AAHD$8HD$0HD$(H= H= H5> VI(H(H TA<H=` +TIIHD$ E11E1HD$AQAHD$8HD$0HD$(@DDHD$ E11A HD$AHD$8HD$0HD$(A=AvHD$ E11ATHD$AHD$8HD$0HD$(~LD$ IET/ ILl$PM9Hl$XLd$hH|$`H$HtkH5| 1-H$H$H/H$HDŽ$HT$H HHD$@HHHDŽ$HD$ E1HD$HI/ HLHD$ LD$ HD$ E11E1HD$AiAHD$8HD$0HD$(H=ћ HR H5S TIHD$ E11E1HD$AFAHD$8HD$0HD$HD$(2I@HD$xHIXHHI( HD$xLd$pIH$nLHD$ E1E11HD$8AΞAHD$0HD$HD$(H= H H5 SIy3HF(HJ(H)0HLcJ4LN(L;(}INL(HJ(H0H=/ OI,HD$ E11AHHD$AHD$8HD$0HD$HD$(QLD$IDDLu#HD$ E1E11HD$8AОAHD$0HD$HD$(IHD$ E11E1HD$ASAHD$8HD$0HD$HD$(>H= NI(AJH=D HՉ H5։ QHHD$ E1E11HD$8AӞAHD$0HD$HD$(.$F_uHH5{ HH\$p] MRE1E1H >H=<>ApE1AHD$pHD$ HD$HD$θYLLHD$ E1E1AHD$AHD$酸HD$ E1E1A HD$AHD$SHD$ E1E1A HD$AHD$!HD$ E1E1AHD$AHD$HD$ E1E1A1HD$AƷA/E1E1E1HD$ AHD$隷HD$ E1E1AHD$AHD$hHD$ E1E1A HD$A?HD$ E1E1A(HD$AHD$ E1E1A#HD$AAAHD$ E1E1E1HD$HD$鸶H=q Ht H5t ;IHD$ E1E1AHD$AmH=& 8IWHD$ E1E1AHD$AHD$'HD$pIHH{ HL$HHD$pH{ HPHAH;Q HIAD$ A@u<<DAHD$pIT$HHDŽ$L` H LjCHH HD$pHP(H5t _H$IHH@H;Q I$L$Ld$xMH$H/mHt$xHDŽ$F @u<@<EHD$pHVHD$xHp0H{ LHH|$pA9Hz ACHHG8HD$xIHH|$pH/HD$xH= H$HD$pHDŽ$H$HD$pIH4H|$xH/HD$xH|$p1qH|$pH/oHD$pAAHGH$HHWHHH|$xHT$xH/(H$H|$x1ɺHD$ E1E1A,HD$AH= 5I H= H'q H5(q S8IE1E1E1A*HD$ AHD$ALBu kaH5-u H]H\$x RE1E1H 7H=7AΛE1AHD$xHD$ HD$HD$8HD$HD$(>E1E1A^A'&wHJ ;T$yHcT$1H|$A}AIHHD$DT$@E1E1H$H$HH$DT$@E1HD$ HD$HD$ZAqA׿dͿ!HD$ E1E1AHD$AHD$AT膿HD$ E1E1AHD$AHD$鿰JIHD$ E1E1AHD$AHD$郰AE1E11HD$ AE1HD$HD$BAH$H/tAHD$AE1E1HDŽ$HD$HL$HHD$ HxAЛAE1HD$ HD$HD$8铯E1E1AA頯+HD$ E1E1AϜHD$AHD$dH;J u@LPXI HD$ E1E1A͜HD$AHD$H;H tH5Cq LIH;lJ uXH|$PXIL$MHD$ E1E1AHD$AHD$餮H;{H tH5p H|$耻IHHD$A`E1E1ACAnE1E1AlA!AWHov fAVfHnAUATUHHSHHL-~ L%~ H|$H0H-)$fHnfHnHflHHDŽ$fHn)$HH fHnflL$H$H~ )$fHnflHD$`H$L$)$H L4HH#@HcHf.HF H$HFH$HFH$L~HLmL$H$HH?HcHHLmH$ML%t M1f.HL9L;duM u\HL߲HH<H;> H;-Z> u H;->  Hm0HtY@HtbH% LvL$Ho.L~HD$P)$HujHF HD$`H$LnL$L5 > LmHmn LHzH$H)LEI@H %AHH= H'H5jSL %H81XZH %H= 1HH[]A\A]A^A_f.H;I= uOL;%8= u>LH.IH/H;+= L;%< u L;%< - I,$LH\$Ll$ݴHq I f.H$LHHIH$H$H$L$L$HD$PH$L$HD$`HLT$諯LT$HLD$蓯LD$fI(# Hb HM^ H9XU%H4^ Hm&HL ^ M$IBLT$LH5HD$01E1E1HD$(E1AAHD$8HD$ HD$HD$HD$HD$@H5U 脌ILHD$PML|$XAXHD$HHD$PL|$X1E1HD$0E1E11HD$(E1AAHD$8HD$ HD$HD$HD$HD$@HD$HKH]H;LUHIHm[fHnL׺LT$D$PH$)$H+LT$HD$HHLT$诠LT$DL|$X1E1E1HD$0E1E11HD$(AAHD$8HD$ HD$HD$HD$HD$@+fH=Y^ H*O H5+O IfDL|$X1E1E1HD$0E1E1AHD$(AHD$8HD$ HD$HD$HD$HD$@@H=] IE@+LT$HefDLEMvH]IHHmfInfInHflH$LD$)$LD$HD$XI(LL?L|$X1E1E1HD$0E1E11HD$(E1AAHD$8HD$ HD$HD$HD$HD$@Lp|L` 8HH H=a\ H"M H5#M HfDHD$01E11HD$(E1E1E1HD$8A̓AHD$ HD$HD$HD$HD$@L蘝HuHHLD$sLD$f IHD$01E11HD$(E1E1E1HD$8AΓAHD$ HD$HD$HD$HD$@H= [ Hk@LD$(輜D$(TLLD$補LD$EfLD$(脜D$((HW LT$H[fDHD$01E1E1HD$(E1E1AѓHD$8AHD$ HD$HD$HD$HD$@Hؙ~hLrPH訙eL萙MIt$HfDH{HM1E1E1HD$0E1E11HD$(AAHD$8HD$ HD$HD$HD$HD$@@IZH MzHII*jHN fHnLfHnflH$H$)$sH+IHLD$yLD$It$H%fDH{HH5Z H|$XwH111HHD$+LD$HHUI(H5yZ H|$X_wH11ҾHHD$LD$HII(eLֺHLT$0LT$HI) H+I*L;& L;% oL;% bLLD$ŞLD$jI( H5Y H|$HvH 111HHD$LD$HII(RH5UY H|$XLT$6vLT$H111HLT$HD$谓LD$LT$HH.I(L׺HLT$LT$HII*BH+!L;$ L;]$  L;$  LLD$萝LD$bI(aHE111jL#[ 1H聇Y^IH8H4% I9A,I9"H5!X H|$HLL$uLL$HHa111H胒LL$HIH+IQ IAHHH9H9IIQLHIAI(H5X H|$LL$ttLL$HHD$@H-H'" H9CLsMLSIIHHD$HHfInfInL׺flH$LL$LT$)$ZI.LT$LL$HHI*H5YV HLL$sLL$HI,H+HH5V H|$HLL$LT$vsLT$LL$HH111HLL$LT$LT$LL$HHD$H+H I9B\MrMOIZIHI*[HX HLL$H$L$H$HD$H$$I.LL$HD$@dHL$HHD$HHH|$@: H+H5M H|$XLL$ZrLL$HIg HRH HC H9Xy!HC HA!HL~C M H5N LLL$ LT$L\$qL\$LT$HHD$LL$ K I+ H I9B'MrMIZIHI*9fInƺHLL$D$H$)$I.LL$HD$PIHL$HHD$HHH|$P|!H+H\$XHHD$HHH53U LLL$~LL$ TLL$HI)HT LLL$LD$HI@HT HH=Q 1{LD$LL$HI)I(< H5T LLL$LT$ƛLT$LL$HHD$ %H8I*HD$H HH9X+H\$HD$PH$LL$HH$HDŽ$HLL$IIMo*I(8IBH; 1)IRH,IBHD$IB HD$IB(HD$ HD$HHD$HHD$ HI*? HD$0HD$(HD$8H5YM LLL$X|LL$X'H5J L|LL$X}$H5S L|LL$X0$t'H5Q Lf|LL$X}0,H5R LLL$X:|LL$XBHD H@!H;? CH? HBHH? H9H5I HLL$X'nLL$XHI8H+$%HD HN? H9XAH5? H6HL!? M6H5J LL\$pLL$hLT$XmLT$XLL$hHL\$pIf6I*16H|$ LD$pL\$h5H5XG H|$ LL$XamLL$XL\$hHLD$pIj5H|$LD$xL\$pLL$h4Ht$HHD$X LT$XLL$hHL\$pLD$xI4I*BGH I9@FHD$ LǺH$L\$pLL$hLD$XHDŽ$L$H$ LD$XLL$hL\$pHLI.EHEH)EL\$hLL$XÒLL$XL\$hHIDEHXHD$PL\$pHI@ LL$hLD$XؔLD$XLL$hHL\$pHDLt$`H5N HLD$pL\$hLLL$XǕLL$XL\$hLD$pDH5F LHLD$hL\$`蔕LL$XL\$`LD$h6DLLHLL$hLD$`L\$XkL\$XLD$`HLL$hICI+CI(CH+sCL;5` L;5 OCL;5$ BCLLL$XLL$XC H5F LLL$XxLL$X0"H|$0X*HD$0HIH5D LLL$XjLL$XH *H|$@HLL$`HD$X?LD$XLL$`HI6I(5)H|$HLLL$`L\$X8L\$XLL$`HH ,I+(HL$@HHD$XHHF)LLL$@LL$@HB)H5L HHLL$XHD$@iLD$@LL$X(I((HD$PHH\$@HD$XdHD$01E1E1HD$(E1E1AHD$8AHD$ HD$HD$HD$HD$@@L谋1葉HHHD$01E1E1HD$(E1E1ALHD$8AHD$ HD$HD$HD$HD$@'fDD|@諏Hb苏HܒDD.DDHD$PML|$XA^HD$HHLT$蔊LT$LHD$}LT$DHD$01E11HD$(E1E1E1HD$8AAHD$ HD$HD$HD$HD$@H='H H8 H58 tIHD$01E1E1HD$(E1E1AHD$8AHD$ HD$HD$HD$HD$@n ILLT$[LT$LT$H=HD$01E11HD$(E1E1E1HD$8AAHD$ HD$HD$HD$HD$@H=F IDDAAHD$01E11HD$(E1E1E1HD$8E1HD$ HD$HD$HD$HD$@HLD$AHD$X)HD$`1E1E1H%HH5A=AH81bHD$PLT$`1LL$hL\$pHD$XLD$x̶HD$P11E1E1A;AHD$X駶H1E1E1HH5LL$`A:H81AaHD$P1E1LL$`L\$hHD$XLD$pLLL\$hLL$XHD$pYLD$pL\$hLL$XHD$P1E1E1A7AHD$XHD$P1E1E1A5AHD$XtH= L\$hLL$XeLL$XL\$hIHHT$`LL$XAYHT$`LL$XH1E1E1HH5LL$`AH81A`HD$P1E1LL$`LD$hE1HD$X9HD$P1E1E1E1AAHD$XHD$P1E1E1E1E1AAHD$XHD$P1E1E1E1E1AAHD$XyHD$P1E1E1E1AAHD$X4H=d LL$X*LL$XHH=F H LL$XH5 LL$XHHD$P1E1E1E1A2AHD$XHD$P1E1E1E1A0AHD$X鞢HLL$XWLL$XHD$PE1E1E1AAHD$XcHD$PE1E11IE1E1AHD$XA鞳LHL$hHT$`LL$X'WHL$hHT$`LL$XMxMoIHIHI(fInfInǺHflH$LL$`HL$X)$蛇I/HL$XLL$`HPLHL$hHT$`LL$XVHL$hHT$`LL$X%HqVLD$`LL$XLHL$`LL$XPVLL$XHL$`QHLD$LL$/VLL$LD$HD$P1E11AAHD$X^LLL$`E1E1UHD$P1E1LL$`AAHD$X鿠HD$P1E1E1AAHD$X霠HD$P1E1E1HD$0E1E1AHD$8AHD$ HD$HD$HD$HD$X\HD$P1AAHD$X LL\$`LL$XUL\$`LL$XHD$PM1E11E1AAHD$X>MhMM`IEI$I(fInźLLL$XD$H$)$mImLL$XILL\$`LL$XhTL\$`LL$XLD$h1E1AqHLL$`H H5AH81\HD$P1E1LL$`LD$hE1HD$X^LLL$XSLL$X.HLL$XHD$`SLD$`LL$XHD$PE1E1AnAHD$X鞞HD$PE1E1AlAHD$X}H= LL$XsLL$XH$H= H LL$XH5 LL$XHHHLL$`E1H5AkAH81ZHD$P1E1LL$`HD$XHLL$XLD$RH\$LL$XHD$0HD$(HD$8HD$PA)1E1AE1HD$X鈝H= H  LL$XH5 LL$XITHH)LL$`E1H5A3AH81 ZHD$P1E1LL$`HD$XLLL$XHD$`RL\$`LL$X)HD$P1E11E1A6AHD$X1HD$P1E1E1A4AHD$X駜H= LL$XLL$XIHD$PE1ASAHD$XkLHT$`LL$X`QHT$`LL$X-HD$PME1AOAHD$X)LHT$`LL$XQHT$`LL$XM{M|McII$I+fInfInǺLflH$LL$X)$蛁I/LL$XHfLHT$`LL$XPHT$`LL$XEHL\$`LL$XuWHD$x WLL$XL\$`IMHD$P1A:AHD$X1LLL$X+PLL$X6H|$QLL$XL\$`HItHXeH|$L\$`LL$X8PL\$`LL$XIxH?HL\$hH54LL$`E1A9AH81WHD$PLL$`1L\$hHD$X|H= H-L\$hH5)LL$XL\$hLL$XILLL$X@OLL$XHD$P1E1E1HD$0AܖAHD$8HD$ HD$HD$HD$XߙLpHM2LXIIHHD$HHfInLߺLL$D$PH$L\$)$dI.L\$HD$LL$ LL\$LL$YNL\$LL$H=s LL$X9LL$XHXHD$PA&1E1AE1E1HD$XHJHHHH L\$hHEHH5"LL$`H81UHD$PLL$`1E1HD$0L\$hE1AtHD$XAHD$(HD$ HD$HD$HD$QH= HLL$XH5LL$XHXHL\$LL$MLL$L\$VHD$PAt1E1HD$0AE1HD$XHD$(HD$ HD$HD$HD$髗HsL\$hH5LL$`H81{THD$P1E1E11AҗAHD$XHLL$XHD$`OLLD$`LL$XTHD$PE1E1AǗAHD$XHD$PE1E1AŗAHD$XH=W LL$XLL$XHH=9 HjLL$XH5fQLL$XHH5 H=6 1LL$X*)LL$XHI1H_BImLL$XtFHD$PA1E1AE1HD$XIHD$PA1E1AE1HD$X&LLL$`AE1KHD$P1E1LL$`AHD$XHD$P1E1AAHD$XѕHD$P1E1E1HD$0AIAHD$(HD$ HD$HD$HD$HD$XxHD$PA1E1AE1HD$XUмHLL$XGJLL$XvLLL$X0JLL$XULLL$XJLD$`LL$X/HD$P1E1E1AeAHD$XGHD$PAdHD$XA1E1E1E1!HD$PAcHD$XHD$P1E1E1E1AaAHD$XHD$P1E1E1E1AYAHD$X{HL\$hLL$XQIL\$hLL$XKHD$P1E1IE1E1AUAHD$XyLHL$pL\$hLL$XIHL$pL\$hLL$XMxMsIHIHI(HD$ fInfInHflǺL\$pH$LL$hHL$XH$)$dyI/HL$XLL$hL\$pHTLHL$pL\$hLL$XQHHL$pL\$hLL$X)LLD$pL\$hLL$X&HLD$pL\$hLL$X铸LHL$pL\$hLL$XGLL$XL\$hHL$pAWH AVAUATUSHHHD$PH0HD$XHHD$`HHD$hHH|$HD$0HD$8HD$@HD$pHD$HHL,H HHHcHfHFHD$HHFHD$@HFLEHD$8HHD$0HH%HMHL% M1HL9{L;duIDHD$8HL}IL% M& 1DHL9 L;duIDHD$@H IML}L%  M11@HI93L;duIDHHD$HIM~@HL$0HT$PILL FH19yZHuMuHD$HLl$0L|$8Hl$@HD$H L(hE111HALAIHH8Hk L(hE111HALAIHH8EH& H(hE111HAHHH;H8 AFA;D$HSH <H9HH#HHL-MIEH5LHH0HH2ImO f(L$GIHHLDIH2Im-HVH9EZHt$XHLD$XLD$ HD$PtLD$ III(MI)L;=XL;=L;=LIŅD$ E11D$Ӑf.H.HHH HAHMEIHHHeH5YSL ޷H81JXnZH . H=͝E1vHĈL[]A\A]A^A_HBAHFHD$HD$HHnoL~L.Hl$@)\$0@HLAHD$0`LAH= LHLD$]eHD$0HLD$L}I>DHD$|fDLBLLL$ ALL$ LHD$ ALD$ fI/KH4H H9HHHqHH-HZHEH5HHHIMHmD$CHHHLAIHHmHCI9GHt$XLHD$PLl$XqMHImH\I(}H;-NAH;-DGH;-:HFAŅpHmE HH H9HHHHL=xMIGH5LHHIIIHMIHHaH H9H}HHHH-HAHEH5)HHHrHHHmHH=H9x*H~HcHLjMICHL$ LL\$H5QHH{L\$HL$ IMNI+.H(I9@wLHt$XHL$ LD$HD$PLd$XLt$`oLD$HL$ ILMHmHH9AHHt$XL\$XL\$ HL$HD$PH\$`+oHL$L\$ HII+HI/HWI9EHt$XLHD$PHl$XnMIHmMI)L;=bL;= L;=& LCŅI/E+HD$HH=MLHpILL 8j5Sj5AVjHT$PH HH@HII/LHD$ =HT$L<,H<;CL@IHZL @IHpH?IHfI*T$f/fI*f/D$KD=I9[HD$LLD$ HHHL$?HL$HILHD$(>HL$L\$(HHLD$ L>HL$L\$(HIHt$HE1H=jA5HPj5UUj5|ASHT$`L\$hHL$X HPHL$L\$HHH) I+ Hm Im I,$tDI.ItifH+9H;,fH: 1LHT$:HT$IMtI.tHu@L:fDID$0LD$1HD$ H\$LMI̐NtM9HI9GI9FUMA j A~ w IWI;VIFIwH@H9@t HEW EN DD@@8urA `IHA " Iv0IHA@IDDA AM DDE9u'HH<II9HD$@>H1HH)H H5jL AHzH81AY^NL;=uuL;5|urLLr9IHcH;oL;5u L;57I.LD$H\$LDLD$H\$LIDfMID$0LD$1HD$ H\$LMI̐NtM9HSI9GI9FUMA A~ $IWI;VIFIwH9@H@t HEW EN DD@@8urA %IHA JIv0IHA@IDDA A DDE9u'HH1:II9HD$8;HHHAH5,jL H FH8H1>_DAXfDL;=)uuL;5urLL7IHcH;L;5u L;5I.<LD$H\$LDLD$H\$LIDJfID$0LD$1HD$ H\$HLMIfDNtM9HI9GI9F A A~ IWI;VIFIwH@H9@t HEW EN DD@@8uzA fIHA@HE|$ A EIv0IHA@IDDAd Ax DDE9u%HH7IL9HH\$fDL;=uuL;5 uuLL5IHtH;L;5L;5L9I.lkHLD$H\$Ly/8HUHLD$H\$LIDfDD$ 1E1E1D$E11E1E1Ht HmMt ImMtI/tgMt I+MtI(t=T$t$H qH=?2gMpI,$NE1]fDL(3fDLL\$ LD$3L\$ LD$xLLD$2LD$iHL\$ LD$2L\$ LD$LL\$ LD$2L\$ LD$D$ 1E1E1D$̏1D$%5IHx H=BH*;IH'I/P H=Ht$XLl$XHD$P5aHHWImN 1H(Hm, D$ E1E11D$@L1D$ E1E11D$ۏL7IHA@HE|$ DL6IHA@HE|$ EL01vL)BD$ 1D$HLD$(0D$(GL.`L.yHIvHH=HH5IfDD$ E11D$fDHX0 8HD$ E1D$pH=IIe@LD$(/D$(L/JL-L-LHT$/HT$^HHT$/HT$_ImLL$ LD$(IjLLL$(LD$ 4.LL$(LD$ ID$ E1LD$ϐRL,`BL+V-H-gIvHIHLLD$ HL$-LD$ HL$DDGHL\$ HL$-L\$ HL$Lj-4DD1HD$ E1E11D$u1HD$ E1E11D$JHD$1LD$HbD$ E1E11D$DD$}/IHPH=H5IHImH=Ht$XL\$XL\$HD$P[L\$HH&I+[1H"#Hm9D$ E1E11D$>bL,HLL$,LL$L+ H5H=k1d IH1H"ImUD$ E1E11D$^DDD$ E1E1D${1H)AHL\$ LD$N+LD$L\$ L7+DDD$ E1E1D$ڐRH=3HTH5U耡H`D$E1D$ I+KE1E1MX/H #AHx:D$ E11D$+H=HH5I,3ID$ E1D$ܐD$D$ MH=KHD$-1D$ I/zE11LHL$)HL$H E1E1E1@k2IH=觝IoD$ߐD$ D$D$ DDD$ E1D$0H=|H}H5~ɟH|D$D$ 1HH=8HFD$ E1D$2+MOMMGIII/fInfInLǺflHt$PLL$(LD$ )D$PqYLL$(LD$ HI)LLD$ m(LD$ D$MD$ OD$ E1D$5H=\HMHL$H5I褞HL$IID$ E11D$2H=HL$ٛHL$IHLL$(LD$ 'LD$ LL$(D$ D$7#A0HL$ L\$I}D$ ID$LMxM|IhIHEI(fInfInHt$PHflǺHL$Lt$`)D$PWI/HL$IcLL\$ HL$&L\$ HL$BD$ E11D$LIM@LyIIH)"fInfInHt$PLflǺLL$ L\$H\$`)D$PPWLL$ L\$HI)LL\$L&L\$D$ LD$cbD$ M1D$zXMEMMMIIImfInfHnLϺflHt$PLD$ LL$)D$PVLD$ LL$II(LLL$%LL$LHD$%L\$D$ E11D$~LV%H5bH=1IH1HIm\D$ E1E11D$FH$L$L$D$ E11D$H$L$LLD$(LL$ $LL$ LD$(HL\$ LL$p$LL$L\$ D$ E11D$,LHL$:$HL$D$9MD$ LLL$ LD$$LD$LL$ LD$ E1E1D$6fD$ E11D$ZL#D$MD$ D$ E11D$ME1E1E1E1AWH/fAVfHnAUATIUHHHSHhHD$PHk)D$ fHnflH<$HD$XHD$0)D$@H L4HH(HHL}HD$ LL-H 1HH9L;luM,Ll$(M IOH5Hl$ L|$0IfHHFL}HD$0HFHD$(HHD$ M/ Hl$ Ll$(L|$0H L(hE111HALAIHu H8SH El$L(hHE11HA1AHHs H8H=Eu MHHH59L H= Lc*IHqLH*HHIm H~H H9HHHHLMI@LD$LH5HHLD$IMI( H«I9EHt$HLHD$@Hl$H8QMIMQI( IVH;H= IFHHHHIcVHHcHHEHIHHMHHWHmI9A)LHt$XLL$HD$PLd$XLl$`3LL$ILMH)HHI9GKHt$XLLHD$PLt$X3II.IߺE A]MH+L;L;L;֎ LLT$LT$+I*)HD$HH=MLHpIL LjAQAUjAQUjHT$PLT$HH@LT$HI1I*LDH&HHH uHuAHMEIHH?HHxH5JSL &vH817 X8ZH Lu H=\E15HĈL[]A\A]A^A_H0HFHD$HD$HLvo&H^L>Lt$@)d$0@HLAHD$0PLAHLHLD$#HD$0HLD$L}I.DHD$|fDL`HLL$KLL$H8GAA H+6HLL$T$ LL$T$LːMt I/ Ht H+H sDH=)[3I,$A+Ht HmM}ImrLef.HxA;E*"Lf.f(BLL$ f.~L$ D$YHL$ ~f.VL$ f(ff/f/T$4f.L$Lt$f(T$ IHHL$pHL$HI=T$ HD$(f(KHL$LL$(HID$LL$ %HL$LL$ HHHHL5jHAPH='SjPAWjPHT$`LL$hHL$XAHPHL$LL$HIH) I)z I/ H+ I,$t0HmDHHILID$0LD$1HD$ H\$LMI̐NtM9HI9GI9FUMA A~ IWI;VIFIwH@H9@t HEW EN DD@@8urA IHA Iv0IHA@IDDA A2 DDE9u'HHaII9HD$@HHHH pH5[EjL pAHrH81Y^L;=YuuL;5LurLLBIHcH;?L;5u L;5I.LD$H\$LDLD$H\$LIDbfH߉T$$T$9MID$0LD$1HD$ H\$LMI̐NtM9HI9GI9FUMA A~ IWI;VIFIwH9@H@t HEW EN DD@@8urA uIHA Iv0IHA@IDDA< A DDE9u'HHII9HD$8UH8HHyAH5BjL `nH mH8Hbp1c_AX&fDL;=مuuL;5̅urLLIHcH;L;5=u L;51I.LD$H\$LDLD$H\$LIDfID$0LD$1HD$ H\$HLMIfDNtM9HI9GI9F A  A~ IWI;VIFIwH@H9@t HEW EN DD@@8uzA IHA@HE|$ A Iv0IHA@IDDAA DDE9u%HHIL9HH\$fDL;=ɃuuL;5uuLLIHtH;L;55L;5{LmI.kHLD$H\$Ly/bHIoHLD$H\$LIDfDLLT${LT$E1A. {DHLT$KLT$A/ NH I)XLHL$T$T$HL$9fDH=LL$aLL$HC AمLL$ HL$ILKMFMI^IHI.ofInfHnHt$PHflƺLL$ LD$Ll$`)D$PLD$LL$ II(LLL$LL$AV? DD MqMIYIHI)fInfInHt$PHflź)D$P<I.ILLT$BLT$A`< aH5!H=1IH1HAI/D LHL$HL$H=HH5BbIA*E LLD$LD$s.LL$IE A,H=U_IUE A/1@H=d/_HA1E IE AFIYHIIHHI)fInfHnHϺflHt$PHL$Ll$`)D$PH+HL$IHHL$HL$MOMI_IHI/&fInfInHt$PHflźLL$)D$PLL$II)|LLT$LT$eE AapH5H={1tIH1HApI/F LLD$ LL$LL$LD$ pH AL{AB A7 tA9 dA!; TLLL$)LL$LHL$HL$1AD AlF LAWHWAVIAUATUSHH>uHD$PH8HD$XH-hHD$`HpHD$hHӫH|$HD$0HD$pH\$8HD$@H\$HHLI9MTIMH|$HLl$8HD$@H<$DIuTMAHML%vH1fHH9L;duIHHD$HIMHL$HLd$0Ll$8HD$@H $<HF HHH$LnLl$8L&Ld$0L=ؚHD$XHD$PIH;=OttH5FtIWBHt$XHjE1 MH=6$Ht$u@Ht$LHHE(HuHqH5$H8mDH tZvE1H=A(bHHFH$HD$HHFHD$@IGt3H@8IHt&Ht$X1ɺLHHt@IHZHD$XHHD$XI@IGHH< H=#LD$kLD$ LD$1LLHwHLD$ I( HH jH9H8HQHHL5=MIFH5LHHNIIHMaIHLHMIH I/L;5@qL;5p+I9"LADž I.EH\$HMH=oALHsIHLHæt$jRPjRLPj5>IHPH I.HmHĈL[]A\A]A^A_@L&LALd$0LAH%LHL$HD$0IH L$IH$IE@H WAL !XHHoH-ZH5{,AVH81XvZH ,WH=>E1HLHL$L$HIZ HD$8IMHML% H^1 HH9SL;duIH9HD$@ILd$0fDMwI.DLJEHH SH9HyH:HHL=&M=IGH5LHHIIHMIHLHFIHI.L;=9nL;=mI9LAƅI/E HD$MH=>mLLHpILL 4$jGY^IHV I/Lf.LHLDOID$0LD$E1HD$ L<$ILMLt$IfOlL9HmH9EI9E } 3A} @HUI;UIEHuH9@H@t HD] EU DD@@8A ]H}HA@HE|$ A 5Iu0IHA@IDDA?A$DDE9u*HHtfDIM9LLt$L<$zDH9uuI9uuLHIHtH;kL;--ku I9eImtLLD$Lt$ML<$yWfHSHL$0HT$PMLL UH)vl@LLD$Lt$ML<$KMHRH RAHOL {QEHSLOOD@fAAv@DDE1H #RH=9H=!HH5nTIfDLH|$HLd$0HD$@H<$KIH=QIg@AvAI.BLZ5DID$0L$E1HD$ L|$ILMLt$IfOlL9HCjH9EI9E} A} HUI;UIEHuH9@H@t HD] EU DD@@8A H}HA@HE|$ A Iu0IHA@IDDAADDE9u*HHfDIM9LL$Lt$L|$DH9uuI9uuLHFIHtH;GhL;-gI9 LImNnLL$Lt$ML|$y:L$L$HvfDLL$Lt$ML|$K{L=H$AAwI/LDLAwA;L5LAA8w놾v@1LLLD$LD$HI(RL4ELD$,D$,,HLAwAcAA1wH=ٗHH5&PIfDIuHH}HIyH=LMI6@AA3wKLD$,D$,A6wAHLI(YLLIuH^H}H;L$9L$HgI(tL$L$Hv@DDH=܏H9HEt H;geHIH H=Ht$XLt$XHD$PIHI.1LA#AmwI/AANwEH LAL JHLHFIH* I.L;=9]L;=\I9LAƅ`I/E H$LH=w]MLHpILtIH I/LfLL4HFHLIHD$8HT$0fDDOMH DH!DMHII?IALd$0Ll$@9fID$0LL$E1HD$ L|$ILMLl$IOtL9Hc\H9EI9F } A~ HUI;VIFHuH9@H@t HD] EV DD@@8A H}HA@HE|$ A Iv0IHA@IDDAADDE9u*HH4fDIM9LLl$L|$H9uuI9uuLHnIHtH;oZL;5YI9L)I.wLLL$Ll$ML|$y3HxtfDLLL$Ll$ML|$KfA\Au@DDE1H 3AH=(H=1HzH5z~CIfDLAuA\I.uL@[IH=Ɋ@Io@LISH!LHLL$iLL$HIQHD$0If.A\AuI/LDL[HL$0HT$PMLL BHt1HLcI.HLfID$0LL$E1HD$ L|$ILMLl$IOtL9HXH9EI9F5-} A~ kHUI;VIFHuH9@H@t HD] EV DD@@8A 3H}HA@HE|$ A Iv0IHA@IDDAA'DDE9u|HHTu\f.LLL$Ll$ML|$ytLL$LL$HBtUDH9uu I9uztvIM9LLL$Ll$L|$DLLL$Ll$ML|$Kf.AuA\LLHIH{H;UL;5sUI9LI.*_A^AGuLL$LL$Ht%DkHuHSH5XH8I.LfYLD$,tD$,A)uA]A^A@uH=aH"uH5#u>IfDHLIvHjH}H@H=;I@SIA^ABucAEuA^LD$,cD$,5HR'dH=~H9HEt H;YTHIH H=Ht$XLt$XHD$PIHI.1LAaAtu蜽I/LDDHJLL.Ll$0}DHH^H\$@LvLt$8f.H舿Lf.D$ Lf. \D$HrH"lD$H9P HlHRHL=kMIGH5zLHHPIIHM#IH'D$LD$ oLD$ HIHII9@LHt$XLL$XLL$(LD$ HD$PCLD$ LL$(IMI) MI/ L;-JL;-MJu L;-JDIm ESLt$D$MIEIHD$IHH{uLMLH5 JHH==IjAHP5#j5xASL\$HjPL\$XIHPHTIm I/ I+AALLL$LL$@HKHIHH\$@fH T1AHHHH3H5ATL 1H81XrZH 0H=E1eHxL[]A\A]A^A_HH$@HXLL\$CL\$ fL(HE1LLL$LL$MHf.LvHHILt$8HD$0fDLLD$賻LD$zfL蘻MH /H/MHII?IALl$0kfD1IE0HtHD$ I9:HiHI9EH9F#A}  ~ F IUH;VHFI}HAH9At HE] DF DD@@8A k I}HA@HE|$ A C L^0HHA@IEDAV ALDDE9u0HtEHL$H9HL$fDHI9HtI9Id@LqFM9uuL9uuLLD$HL$XHHtbH;YFHL$H;=ELD$L9HL$H|$HL$H|$H/fFYHrfDE1E11E1E1rE1Mt I/MtI)tCMtI(tXH -H=MI,$E1LLD$t$诸LD$t$@Lljt$蔸t$fDLLD$LL$t$rLD$LL$t$QE1E1E1E1rDLL\$+L\$HDo@HtLHHL$ HL$HIHD$0Hf.HL$0HT$PMLL .HZrLLD$ 苷LD$ LHL$sHL$qfLLL$L\$NLL$L\$IF01HD$ DHtI9jHKDI9FH9FA~ ~  IVH;VHFI~H9AHAt HE^ DF DD@@8A  I~HA@HE|$ A c L^0HHA@IEDA+ AS DDE9usHt|HL$HHL$uM@yTHL$蚺HL$HrBfLYBM9uuL9HI9M4LtE1^fDLAƅXQsE1Im1 Lt$E1E1;t$E1E1@LHL$LD$衵HL$HHH;AH;=ALD$L9HL$H|$GHL$H|$H/fD .%H E1E1sE1E1AD$D$HE1E1 sE1E1DH=IrH`H5`*IfDH=!rL\$'L\$IHL$pHL$HrL訳ZH蘳L舳MLD$tD$H=qH2`H53`)IfDE1E1E1ɻ sLE1E1M sE1I+ALLD$LL$t$Բt$LL$LD$H=p&I5@SIPLHD$苲LL$GMhMUMxIEII($fHnfInHt$PLflúLd$`)D$PImI;L.E1E1ɻ s3E1E1sH=pH^H5^N(I=fDE1s~fDLLL$L\$膱LL$L\$6LHD$cLL$L\$ @H=yoD%I@LL$IfDE1sfDD$HL$D$HL$~@LHt$HL$֮HL$Ht$aHHL$Ht$覮Ht$HL$1H=nH2]L\$H5.]&L\$I_@sLfHvHI}HE1E1E1ɻ3s諸L\$LD$I,fsI(E1@H=m#I@E1E1M5s;IMWMMGIII/fInfInLǺflHt$PL\$ LT$LD$)D$P LT$LD$L\$ II*LLL$ LD$L\$LL$ LD$L\$ftE1I˻tE1E1Mǻ8sMCMWIKIHI+fInfInHϺflHt$PLD$ LL$HL$)D$P)LD$ HL$LL$II(+LLL$HL$LL$HL$ @D$HL$D$HL$9LHt$HL$ګHL$Ht$HHL$Ht$豫Ht$HL$E1E1ɻMseMpMMxIII(fInfInHt$PLflǺLL$ )D$PI.LL$ ILLL$ LL$ DDHvHI~HH5pH=Zr1kIH1H襣I/K/tE1E1H5pH=r1!IHQ1H[I.E1E1asE1E16Lt'~sL0sDDDDME1E1sDDLLD$ LT$L\$ƫL\$LT$LD$ ULLL$ HL$LD$蛫LD$HL$LL$ LLL$ zLL$ LE1`/tE13LKE1ɻ+tE1E1E1]sE1E1E1E1LL\$t$t$L\$E1fAWHWgAVAUIATIUSHHHD$(HD$0HD$8HeHL4H}HH>LAH|$(M HW7H9GLIGHM"HcGIHcHEII2LIoHHIHHIEH5eLHHIMIHH~HHH5sjHLHmH]HoTH9Xu HVTH HH-BTHy HEH5FkHHH IM HmjH5scLLxImUIFH-zlHHH=c辧 LHLIӭM I.I,$IEH52aLHH HHi ImH3H9]LuMLeII$HmHjHt$0LLt$0HD$8I.IMGI,$TIEH5iLHH& IIEHIEMHI9^aMnMTMfIEI$I.Ht$0LLl$0MImH'HI,$HEHXpHH{LשIHH=3HHI,$IM~LHSImFHUHJH]HMHunHH$踦H$\fHH}2Hr!H5ATL AH VH81gXdZH |H=81HH[]A\A]A^A_HuH>H|$(D fDHY1H bHHH9H;LuIfHt$8HIHD$0H0bHD$8&I6fDL0Ae1$fDH=9^HJH5JHfDE1A eDHL$(HT$0MLL HH|$()LH$茟H$Ae~H=]dH@I Ht$81LMHD$0 HDLA'e4AeE11蓧HYsHH1AeD[ILL$H $蒞LL$H $/@AUeDHLL$Ht$H $ZH $Ht$LL$QHLL$HL$H4$"H4$HL$LL$#HvHHyHodmDDDDdIH(H5KAeH8蘞AWHXAVfHnAUIH`H-ATfHnH@fHnUflHSHHH$H))D$`fHnHD$8flHD$@HI`H|$HD$HD$HH+)HD$0HDŽ$HD$P)D$pMsL4H H!HcHDHF HD$PHFHD$HHFHD$@LfH.M}Ld$8Hl$0HHHg!HcHfDM}H%YLLbHD$0HH=IM HWLL2IHHD$8IHl$0MH\LLH HD$@IMIMH-VH1f.HH9I;luIHHD$HIM~TIMH-VH1fHH9c I;luIHHD$PIMHl$0Ld$8HD$HH\$@HD$HD$PHD$HEI$L;%y'L5NHD$HD$`HD$hI~H;=&(tH5(萢IVBHt$hLjE1 H=Ht$ \Ht$ u;LAIuMHuHs%H5H8<@H Dfa1H=n@IFH@8IHHt$h1ɺLIMtHNMH DH9H H~DH5HL5jDM!IFH5NULHHKIIHMIHLLڙIH>I/L;%L;K%L;%LLT$ ~LT$ A.I*EH|$H;=o%AH;=$DH;=1%&AHD$H1LHHLLHIARLT$ _Y^HLT$II* H;$ILImI.Ht HmI,$QHĘH[]A\A]A^A_@ƛIHHD$hHHD$hIGIFLMH=-舖1LLAI蝜M[I/LrDHWH[HcHfDH#HEH #HHD$ HHtbpH \H=Im L%;L1LL裏I/IlD^LHD$ ÇLT$ M3boE1qaf.DLxLLT$cLT$1fLHdLHD$3LT$tċHuH@H5H8 fI/LfL؆nLD$,ĆD$,L谄L蘄 H:H 1H9H} H1H HL=0MJ H5BLcIH` I/LֺLLT$ 袆LT$ HIw I*L;5L;5L;5TLFADžm I.EHL$H; <H; H; |HAg HD$H1HLHLLHIAWKAYAZIHUtb&@LIt$HfDIHD$DD$H7bnrf,boaH=BHZ/H5[/&IfDbn)fH|$fbLD$,TD$,yIYo.b+H=IBI@HLsHcaL踃1boQH=AH-H5-IfDcfIt$HfDH{HH=pA;IoDc(ƋHvLDDL[M|L{IIH+fInfInHt$`LflúL\$)D$`至L\$II+PLLT$舂LT$9)LT$Iqd HP\aDDd6DedDD(蟆H jAL HUa3LЁLT$cgDDH#5H=,,H9xqH,HiHL5+M>H5_CL^IHI.LLɁIHI/L; L;: HL; ;LLT$ mLT$ AI*xE2H|$H;=^ H;= EH;=" 8H|$AǃHD$HE1HHLLLHIARLT$ G_AXHLT$IbvH=Y>H*H5*IXbqpAbMZbE1q膈IH==I$dLHHMYLxIIHHD$HHfInfInHt$`LflĺLL$)D$`0LL$HI)$L6LHD$ $LT$ Lq]bD_bqE1L~%HL\$~L\$DLT$cRcH2H= )H9xH(HqHL=(MH5E@L[IH3I/LֺLLT$ ~LT$ HIEI*L;= L;= L;=d LVAƅI/EH|$H;=L H;= H;= H|$AƃbHD$E1LHLLHIRHAW DY^IHexb6@D$迁DD$HjbrbsH=;H}'H5~'iI|sbH=:IYL|XLHD$ |LT$ gbs+HLL$n|LL$DLS|{MbsE1FDebuH=J:H&H5&ID$薀DD$HbtHR/H=;&H9xH"&HHL5&MH5~=LXIHkI.LL{IHI/L;L;iL; LLT$ 蜀LT$ AI*EjHL$H; H; H; QH|$AAǃHD$E1HLHLLHIASARLT$ AYAZIHY|Ic*D DYwb H=(6ILwbwE1E1bwjLw5LHD$ wLT$ DH+H=!H9xH!HHL5!MH5;0LTIHI.LLwIHXI/7L;L;&L;lLLT$ Y|LT$ AI*EIHL$H; JH; H; H|${AǃHD$LHEHLLHIQ1ARLT$ <^_HLT$Iuc~DUM cE1ycyH=4I9H=4H9 H5: UI{6c4c{OH=3I/H=3HH5I zHFc|DL;u~;c{E11cyE1yHbxyH2czy cE19c{gLHD$ tLT$ rLt.yHrc~&DH5v0LQIHH;H;iL;=LyÅI/H=n+H;=wIEt H;ulL|IMH=@9Ht$hL|$hHD$`ȢIHI/1LhjI.icLwIH56H=81PIHtU1HjI.t.cLs cE1LrccDLHD$ rLT$ }ecLrpMbcE1}@`c}H=0uI H=0HH5I,cL,rhgc}E1L rcLq_ccAWH2AVAUATUHSHHL%;4H $HD$PH-hHD$XHHD$`HHD$hHH|$HD$0H4HD$pHD$8Ld$@HL$HHuL4Hl H LHcHHFHD$HHFHD$@HFL.LEHD$8Ll$0HtTHHSHMH+LHLD$ƓLD$HHD$8ILl$0ML}L%-M$1fHI9# L;duIH IHD$@M~TL}L%.M[1fHI9L;duIH-HD$HIM)Ll$0HD$8Ld$@L|$HH-#HD$XHD$PH}H;=tH5{wHUBHt$XHZE1 5H=Ht$Lnu@Ht$LHftHsHuHdH5լH8-pDH 4'`E1H=HEH@8HDHmHHt$X1ɺHHtH="H H9H HH HHHX HCH5m)HHH IHHM HHQLHnHH I.KH;H;:wH;jHrsAƅ H+[EcHM!H=H9x HH HHHh HCH5u(HHH IHHM HHLHmHH I.H;H;JH;HrAƅ H+ME L5m/M9HI9D$I9FA|$ gA~ ;IT$I;VID$INH9@H@t HED$ A~ D8sA %IL$0IHA@LE@ IN0IvH@HEȃ A $>9Ht!LHnf.HD$H=4MLHHpHH1IHwA`AfFoIH2HD$XHHD$XIFHEHH H=j 1HLHpH I.7Lj%fDHMHH HcHfDL.LELl$0LEL- MH5+LHLD$}LD$HI HD$0IxfDLuL=LfLd$@HFHD$8L.Ll$09fL=L=yL=iML;%Y HD$H=MLLHpIL/IH I. HmHĈL[]A\A]A^A_L;=uGL;-u6LLiIH'H;L;-9u L;-=Im?LD$H\$LmmHDHL$0HT$PILL H[_H+DHzhEH5*L}S HL$MHHqH;HHWHL\H=o.IH H+Hht@HgHg^LgHH<IH )HHIHHyI?SIH5ڰH8L ]A1moX_ZH H=E1;fDDPID$0LD$1HD$ H\$LMI̐NlM9"HCI9GI9EA rA} IWI;UIEIwH9@H@t HEW EM DD@@8uzA `IHA@HE|$ A 8Iu0IHA@IDDAADDE9u%Ht7Hi&DIL9H\$LD$H\$LIf.HejL;59uLL/fIHGH;,L;%L;%{LjI,$tuL8eAA3`@DDE1H #H=wH=!#HH5nHEfDH=+IHIAAm`Hd;mIH="tH@A5`AH+2HJd%DID$0LD$1HD$ H\$LMI̐NlM9HCI9GI9E A A} IWI;UIEIwH9@H@t HEW EM DD@@8~A ZIHA@HE|$ A 9Iu0IHA@IDDAADDE9u)HHfDIL9LD$H\$@L;=YuuL;-LuuLLFcIHtH;GL;-L;- LgIm jLD$H\$Ly6LD$fLD$H_LD$H\$LIf.AA8`I.LaDA:`A{L~L|$HfL8g+1HLCiI.H_fHuHH5H8VbfDI.L>afAA`H=AH" H5# HUfDH=H;@A`AkkiI>LD$,`D$,AA`Lx`Lh^~`LP^qHA`AIuHIHH=H;=zHEt H;HhHHH=?%Ht$XH\$XHD$PǎIHH+1LA A`[VI.Qr@LD$,\_D$,LH]^HL0]Q0IuHIHLD$cLD$Hh_yI,$L^AAE`DDDD{A A`DDYLD$!cLD$H_DD.LT\AA`L3\AR`AIvHMd$HH]gA $>A $>H&bHHA A`A`A LH  `E1H= hAWHAVfHnAUIATUSHhHpfHnflHxHHD$`HZ H<$HD$hH\$0HD$8H\$@)D$PHHLLHWIH* I.L;=L;=gI9L\Aƅ`I/E H$LH=MLHpIL$IH I/LVfLVLV4HFHLIHD$8HT$0fDDOMH HMHII?IALd$0Ll$@9fID$0LL$E1HD$ L|$ILMLl$IOtL9HH9EI9F } A~ HUI;VIFHuH9@H@t HD] EV DD@@8A H}HA@HE|$ A Iv0IHA@IDDAADDE9u*HHWfDIM9LLl$L|$H9uuI9uuLHUIHtH;L;5I9LYI.wLLL$Ll$ML|$y3XHxG]fDLLL$Ll$ML|$KfAcA]@DDE1H H=複H=HH5.IfDLSA]AcI.uLfS@ \IH=yDIo@L0SISHLHLL$vLL$HIQHD$0If.AcA]I/LRDLR[HL$0HT$PMLL HEL]1HLZI.HLNRfID$0LL$E1HD$ L|$ILMLl$IOtL9H3H9EI9F5-} A~ kHUI;VIFHuH9@H@t HD] EV DD@@8A 3H}HA@HE|$ A Iv0IHA@IDDAA'DDE9u|HHTu\f.LLL$Ll$ML|$ytLL$mULL$HB@]UDH9uu I9uztvIM9LLL$Ll$L|$DLLL$Ll$ML|$Kf.A]AcL0PLHPIH{H;L;5#I9L_UI.*_AeA]LL$=TLL$H9]%DTHuHH5H8`PI.LNOfYLD$,$OD$,A]AdAeA]H= HH5^IfDHLLLIvHjH}H@H= dI@WIAeA]cA]AeLD$,ND$,5HL'dH=fH9HEt H; HVIH H=0Ht$XLt$XHD$P|IHI.1LAhA]LDI/LUKDDLyC(@LejH=HqH5rݹIMl$O$MLd$(IDM$fKHYWA]AH=˶IM}MMuIIImdfInfInHt$0Lfl)D$0ZsI/HLeBsFHuHwH5H8@CIm;L-B.D$HL$BD$HL$HHL$Ht$?Ht$HL$$HHt$HL$?HL$Ht$HvHsLIHP1LHHIImIDADSFHuHH5~H8SBImL@AL3AAD1LLHImI HH5~H8Aff.AWAVAUIATUHSH 10IM H AD$Pf)D$0ID$HHD$@LuHHHPfHnHHD$PfHnfHnHH-flH$H)D$`fHnflHD$HHDŽ$)D$pMIHJcHf.HE8HD$PHE0HD$HHE(HD$@HE LHD$8HEHD$0=HI HJcHfDHELHD$0=HH5}LHV1DHD$8HHH5 LHV DHD$@HHHH\$0H|$8H-H9oLIGHMt HcGIHcHEII HD$@H|$PHD$HD$HHD$H} H;=&AH;=Du H;=AƉD$HCH;t H;HD$H;HH;AHCHAD$0M|$H1MPHD$H@H;cHD$HI|$XH/ HD$ID$XHD$Ic|$0H HID$(>IcT$0ID$8HIT$@HKHH{HPHr E1L|$(M\fAVHHcHcHDHP IHIHHIT$8JIL9{ NtEIHAII9n9 IvHFHg HvHIHL$u LZYH AH=djI,$ E1HĘL[]A\A]A^A_ÐHE8HD$PHE0HD$HHE(omH} H]HD$@)l$07fDH5iLHV;H HD$HHHH5;LHV:H HD$PHH1HL$0HT$`ML 9L(v ;D$ :HL3HH5LHV2:HD$0Hg HHH5H|$H HH H7H9G LWM LOIIH/HkLHt$`LT$`LT$(LL$ HD$h}eLT$(LL$ II*M I)HL$HHD$ HHIEH;ֿIEI|$XLl$H/u+4HD$H;ID$XaHH5FH84yHmHD$#Lt$v8LL$HI)uL3HfDL@MIMII(IEH5tLHHIMM9paMhMTMpIEII(fInfInHt$0Lflĺ)D$0P>ImIMdI./ I/ I$HPI$I$H HmH @HH9DHuH;2fDHaH H9H8HHHLM<I@L$LH5"HHL$IMI(L5M9wHt$8LHD$0H\$8=MIMI*HH H9HLHͽHHLMID$L$LH5HHL$IMM9pLHt$8LD$HD$0Hl$8L|$@_9HmLT$I MI*5I,$7HH,$IHPHoHnHI)\$ HN H\$ @HiHU1H?HH9CI;\uIH\$ H!HMHHl$(|LLx:LhtLX/I( HHظH9XHHHLMI@LD$LH5gHHLD$IIHMIH/ ID$LT$LH5-HHXLT$IM1IPHBpHE H@H8 LT$LH4$LD$LD$LT$HIHHIHMLT$ LT$HH-HX7 LT$HIXHoHxH9XH_H5HHKHHCLT$HLD$H5HHLD$LT$IM H+H5LLLT$LD$ LD$LT$I/LLHLD$LT$LT$LD$HIQI* HmI(IEL\$LH5hHHL\$IMM9pKIhH>MpHEII(TfInfHnHt$0LflƺL\$)D$0=5HmL\$IPMPI.dI/CH5LL\$L\$HI1L\$HI0H.LLL\$LD$HI@HH? LD$L\$HIBI(I/H4$LLL\$aL\$!LL\$HI"HLL\$HD$FLD$L\$HII(I,$H,$:I+H,$MQfDImLHHIH\$ H.ML$HwM1fHI9I;\uI,H}Hl$(HE1HC0KtHD$H91fDHH9CH9F{  ~  HSH;VHFH{H9AHAt HDS DF DD@@8~A  H{HA@HE|$A  LV0HHA@IEDA A DDE9u)Ht>L $HcL $II9KtH9Kt@LL9uuL9uuHߺLD$L $HHt_H;L $H;=aLD$L9SLL$H<$5LL$H<$H/ J]HD$ $H tAL sH2DLPLLT$;LT$L(LHC01HD$DItH9H#H9CH9F{ W ~ ~ HSH;VHFH{H9AHAt HD[ DF DD@@8A U H{HA@HE|$A 4 L^0HHA@IEDA A{ DDE9u;L $HHL$HHL$L $DHI9fDL1L9uuL9uuHߺLD$LL$H $HHtjH;H $H;=LL$LD$L9LL$HL$H<$LL$HL$H<$H/dFyHt`9fDI,WLHL&LIHL$ HT$0MLL wLH\$ L`LHt$8L$HD$0Ld$8.L$IMMXMoMPIII(l fInfHnL׺flHt$0L\$LT$L|$@)D$0-L\$LT$H$I+CLLT$LT$,LGLLT$LT$HLLD$[LD$NLI1Ax@RHBhHHxH4$LLT$LD$6&LD$LT$H>f.E1LL$ML$f.MtI+uLMsH=HbH5crIfDE1E1E1E1Af1MtI(tSHtH+thMtI/t}H 9oDH=LbL$.ML$FI,$E13LL\$$$L\$fDHL\$$L\$${LL\$$L\$$fE1E1E1E1A$@H=HJH5KpIfDH=qHt$I$L`HHD$pHp HD$xIHHH5ҠH HT$xHt$pH H$IHHmBH|$pH/)HD$pH|$xH/H$HD$xH/HDŽ$M9PHH=H9xHӗH_HL5L$M HOH H9H HH{HH-kHNHEH5OHHHIMHmqHqI9FH$LHDŽ$L$ MHD$pHHNI*TH$HHD$H^$H|$xH/HHt$lLHD$xXHD$xIHi%L9?%HD$xLWHH$H5LHD$xHH$H5HH$HH%H|$xH/H$H;=oHD$xH;=nL9>Åx%H$H/HD$8H5VHDŽ$HHH'HD$8H5HHD$xHC'HD$pH5tmH9p$%HPHT$pH%H@HH$HH|$xHD$xH/$HD$pH|$xH$H|$pH$HtH/"H$HD$pH)H|$xH/#H$HD$xH/"HDŽ$H$H$HH$HD$(IF I9F:HD$Ht$H\$HHL$8Ld$8MHHHHD$@HL$ Ht$0I$0HD$ISH\$0HHD$@IHx_Ld$PH|$ LICHL$LHHD$L$LHLLHLHH+\$IuLd$PADHH!HbID$HHIcD$IL$<I$(ID$(I$0I9L$  MH\$HLd$8H$Ht H/:+H$HDŽ$Ht H/!+H$HDŽ$Ht H/-'H5f1HHDŽ$H$H+9(H$H(H+'HDŽ$H7I$I.!H|$H!HMHD$HHH|$HHjH3YH5(t$8L QAH RH81XZH RH=EE1sHL[]A\A]A^A_fDHC0E1L|$MHD$(ILLt$IfDIlI9HskI9D$H9E4,A|$ } IT$H;UgHEIt$H9@H@t HAET$ DM DD@@8A I|$HA@HE|$(A Hu0HHA@DHDAAIDDE9HH:@MLt$L|$IمHJM9uuWL9uuNHL^HHtCH;_iH;-hu^L9tYH!HmtTjfHI93MLt$L|$aMLt$L|$IHD$JfHmuHD$@:D$@@L(x} f.HxDHuHA}DDfI|$H5fDH|$0LMML$XI\$H- 1HfDHH9oI;luH|$LL$ML{M<:L/@LD$ LD$DDL)LLD$LD$LD$H\$pLD$H|$H5`HGHHHH\$pH&HHHQH52H H5H|$pHHD$xHHH|$pH/ HD$pHm ImLd$xx HD$xHE0E1HD$OtL9HgH9EI9F} u A~  HUI;VIFHMH9@H@t Hu EF D8uw@  H}H@HE|$A  IN0IvHA@HEȃDA9u'HHt{II9iL9uuM9uuLH?IHt?H;@eL;5dM9LI.ty(HDŽ$H^٪@HD$N-H=QHLD$H5NLD$H4LD$1E1A5AH|$pE1HtH/,H|$xHt H/Ht HmH$Ht H/Mt I*H KDDH=>L Mt I.teE1HtH+tMH|$tHt$HHD$HH/MI$HI$HL sHLE1L]HLT$LT$ LT$LT$#LT$LT$LT$H|$xLT$LD$E111A7AH|$pHH=LD$NJLD$HyLD$IIFHD$xHInHHEI.HD$xIH$LD$1E1LALAE1 L(4H'AE11E1AE1LAAHAA11E1E1XH5H|$)H$IHH5nH!HD$xHHH$H/H|$xH;=`HDŽ$@H;=s_@ L9 ŅH|$xH/zHD$x3M9|AD$@8H 1LhHD$xHH L9,H5JH|$8HD$xH$IHH5\HHD$pHHHHH+H5 H{H5ՅH|$pHIHGH|$pH/.HD$pHm H$H2]H9GHoHHGHEHH$H$H/fInH$fHnH$flú)$dHD$xHm4I.Hl$xE1A[A HgH$H/H|$xHDŽ$H/HHHD$xp Hh] u 'I$MA$8I$(H@8Hc@ I$0LD$D$3H5<H=%1HD$pHH_1HSH|$pH/< HD$pE111H|$xAAkH6{L!qHH|$xE11AӫAH=CHzH=HH5NFHXE11E1AիA+IvHnH}HKLt$0IHD$@HxVLd$XH\$Ld$ L|$PILLIHHD$H0HuI6H0HEII)IuL|$PLd$X~ADHkHVGT$OT$H BAH=D+}1AAH|$xE1AثAL{H^{@LLD$IfHD$xLD$H$AhE11E1A}$:a#"HHHD$8H5rHHD$xHHDŽ$H XH9HHPH$HH@HH$HH|$xHD$xH/H$H|$xH$'H$HD$pHtH/qHD$pHDŽ$H?H|$xH/\HD$xH|$pH/:HD$p|H$H$HH$HD$(HD$0IF I9FOHL$8H|$H\$PHD$Ld$HHIHHL$ HHHD$@HL$8I0HD$IH\$8HHD$@HxhLt$XIH|$ LIHt$LHILLLD$0LD$HLLHLHL)IuLt$X,D$c|$HH D$@|$HH IFHHIcFINI(IF(I0I9N Ld$HH\$PH|$0H$Ht H/xH$HDŽ$Ht H/_H$HDŽ$Ht H/H51HHDŽ$XH$H+{H$HTH+=HDŽ$Kf.A8I(H@8Hc@ I0HT$8HHD$@Hx`HHl$ L|$ILt$XMILHIIHD$H0H3I4$H0HI$M)IuML|$Lt$XH@D$w|$H+HVGT$t$ T$t$H =H=knIV0I0I;0 HI0IV0I0D.@H=RHyH5y?I(IT$0I$0I;$0 HI$0IT$0I$0E111AACH=ކHoyH5py+?HH=AI(IL膿4I(Ll1E1AAkHA`A11E1E1#fH|$xE11AA0I$(ID$(I+$0ID$0I$0I(I+0IF0IF(I0PVI蜾#1AA#H5%H=ރ1HD$xHH1H4H|$xH/1AHD$xA!CH5qH*Lt$x11AkA E11AA#kؽν:H$1Y赽諽衽HT$(Ht$ 荽HT$(Ht$ MNLLT$iLT$$LW*1E1A]AVAA#11E1Ht$(HT$ Ht$(HT$ H$1 1E1AAE111AAWVIH5C}H|$8H$IHH5^|LIHgHD$LT$HH6HpH5 {HLT$H5oLH躙LT$HHD$pH>I*'Hm?H$H0GH9GrHoHeHGHEHH$H$H/HD$pH$H$H$H$cHD$xHmH|$pH/xHD$pH\$xHY1E11AAbDAA11E1E1):AH+t(A%E111qE11AA%[HA%11軺E1A论~褺H\$pL|$x萾LAHHL蹢HDŽ$HD$xHD$pHD$(A%11H$H$HH$E1A 1E11A۬A~Hڹbйƹ1E1A0AE11A=A #H5nmH薹H\$xHD$pH$HDŽ$H$)HD$xAA1E11E1AA11E1AAE111AAqL۸H|$xAAH踸A2A11E1E1&蓸Aȭ~4AA!cHVE11AA.H3x)pH$HDŽ$L$HD$xHE1ADA WACA E1E1@E1E1AAA )H|$xE1A?A H5[kL胷mA A11E1E1HHE11A8A%H%A\H+t(A.E111E11AZA.zHA.11ڶE1`ApH=#|11E1AvA苭E11蛶GH$A4E111AǬAfV\7RLEH8AmA11E1E1V iAٮHD$(A.11H$H$HH$葮E1GLLD$謵LD$ HHD$蕵LD$H$L|$xyLAHHL袝HD$pHD$xHDŽ$K:*Aծ6ALLD$LD$(HHD$LD$A A LӴbAЮA̮賴zL覴y蜴蒴舴~%fAWHvAVAUIATUSHHL5wH$H- HDŽ$H$HDŽ$L$HILH;=#>H;=i>^AŅP H|$PfoLvHI)$HH$mfDLqH-s1MLfHL9+I;luI,H$H&INH"L$H.HIH$H~MD$H-iMx1HI9kI;luM4MPL$H"fDMMHXHHqH1HH9H;TuH5=qHHD$PIHH5-sH9,H@H;9=y1E1I}AIm*HD$PE %HcH TaH9H3H;aH3HL-'aLl$`M3H5qLBHD$XIHY3H|$`H/,H:H|$XHD$`H$HD$ H1H9OG4fHnfHnH3rL$flH$)$*H|$`HD$PIHtH/.Ll$PHD$`M8H|$XH/,HD$XLd$PHmx,HhbH `HD$PH9H6H_H8HL-_Ll$XM3H5iLHD$`IH}8H|$XH/l.H5'sLHD$X^HD$XIH8H|$`HL$ 1HD$HAH9O<fHnfInH$flHtL)$H|$HHD$PHt H/:0HD$HH|$XH/-HD$XLl$PM%8H|$`H/-HH5ShHD$`Ll$PHD$P觜IH;HH5gHD$胜L\$HHD$`HV2HD$XHD$ H9Gh<HGHD$XH<HWHHH|$`HT$`H/T0HD$XH|$`HL\$H$H|$XL\$HD$PHtH/C1HD$PHD$XAH1H|$`H//HD$`H|$PH//L\$HD$PHL$xHT$pHHt$hHD$蚥LrL\$HH+;HHkL\$HCL|$IHL臲IH9/H蓮HD$PH6諯HD$`HHv;HD$PH8LHD$PHFH^ HHD$PH%;H|$`H//HT$PHLHD$`;:H|$PH/4HD$PHHD$PHy:HD$`HH;HD$PH^ LHHFHD$PHD$PH!=H|$`H/4HD$`LjHD$`H ;肮HD$XHH:HD$`HT$PH^ LHHFHD$`JQ<H|$XH/8HD$XH|$PH/8HD$PHڬHD$PH}<HD$XHH.<HD$PH^ LLHHFHD$P輧;H|$XH/~8HD$XHL|$L\$H|$hHt H/u=HD$hH|$pHt H/<HD$pH|$xHt H/<H5+m1LL\$HD$xˆL\$HD$xI+H=L\$xM&=I+=HD$xL55LHH9THuH;5BfDHA\H YH9H[#HYH,$HL-YLl$`M#LH茩AŃ$H|$`H/HD$`EH[H QYH9H+'H8YHHL-$YLl$`Mz'H5WjLoHD$PIH'H|$`H/ HD$`謫HD$`IH9(H4jHH)jHD$`HPH}H5=eHD$XIH}(H@H;4*IEHD$XHD$HH*H|$XH/!HD$HHD$XP @utEHt$`HPHD$HHF HeHHH|$`H}eHG(蜈HD$HH=)H|$`H/1"HD$`|HD$`IH)HD$HIEHkHHT$`HD$HHB 萬HD$HHH[*HiH5)g蜭T%HT$HHt$`H|$P调HD$XIH20H|$PH/%HD$PH|$`H/$HD$`H|$HH/#HD$HH|$XH/$HD$XH5phI9tIGH;2h'IHH59`褔IHTHH5_腔HD$HHH@#HD$`Ht0H9G(HGHD$`HD)HWHHH|$HHT$HH/!HD$`H|$HH$H$H|$`HD$XHtH/:"HD$XHD$`AMH"H|$HH/ HD$HH|$XH/ HD$XIHHL$hHT$pHHt$xHD$衝MvLH轪11HHI+HD$XH11LHHD$HH!HEH;]1HT$X8HHpHHyHL$LHT$`HT$HL$H!HD$HHQLD$I(\!i!H|$XH/HEH;0HD$XHT$HHHpHHyHL$ LHT$ХHT$HL$H+!HD$HHQLD$AI(m"E!H|$HH/HD$HIH|$xHt H/3HD$xH|$pHt H/l4HD$pH|$hHt H/Y4H5Ef1LHD$hHD$hIm3Ll$hMb5Im%3HD$hL5.I DH/2HD$PEHiUH bSH9HHISH2HH5SHD$HHH(UH SH9HHRHHL-RLl$`MIEH5#_LHH<IMH|$`H/Hl,H$HD$`HD$ H1I9M4fHnfHnLfl)$H|$`HD$XHtH/HD$XHD$`HImH|$HHD$ H9GIHD$XH$HDŽ$L$H$BHD$PH|$XH/Ll$PH|$HHD$XMH/%HD$HL|$PI.H}HSHD$PH9+HH5]HHpILl$PMGH5bL9PIEH;,IEH.E1HfIm HD$PEH5`H|HD$PIH,H;+L;-e+ L;-+ L蝤AƅLl$PImHD$PEL5i+L9HEH55`HD$HEHHHILl$PM111L訙HD$HHH|$PH/ HD$PH|$HHD$HxH|$HH/ HEH5XHHD$HHH}HH|$HHTHGH55ZHHILl$PH|$HMH/ HD$HH|$P@HD$H$H|$PH/b HQH NHD$PH9HHNHHL-NLl$PMIEH5WLHHWHD$HLD$PHLI( HD$PH|$踟HD$PIH͠HD$XIHHD$PHD$PIEHD$PIHH-PH MH9HBHMHYHLMM ICL\$(LH55XHHGL\$(ILl$`MI+" HT$`H5wVH|$P}H|$`H/ HT$PHt$XHD$`H|$HyyHD$`IH:H|$HH/YHD$HH|$XH/7HD$XH|$PH/HD$PLl$`HD$`M9UIEH5UHD$(HEHHHIL\$`MICH5VLHHHD$PHpH|$`H/HD$`H|$PH;='H;= ' L9 JH|$PH/HD$PH5cUH+ 迉IH HH5 UHD$0蛉L\$0HHD$`HHD$XHD$ H9G!HGHD$XH!HWHHH|$`HT$`H/HD$XH|$`H$L\$ H$H|$XL\$ HD$PHtH/[HD$PHD$XH6#H|$`H/HD$`H|$PH/L\$ HD$PHL$xHT$pHHt$hHD$0賒HH{Lt$0LL$ LD$(HL$Ɲ_AXHL\$  H|$hHt H/HD$hH|$pHt H/HD$pH|$xHt H/H5\1LL\$HD$x8vL\$HD$xI+L\$xM&I+HD$xIImYHD$PH/LH}H9{DE1L|$MHE0H\$LIIlHD$ I9.H9%I9D$H9E*"A|$  }  IT$H;UHEIt$H9@H@t HET$ DM DD@@8u|A  I|$HA@HE|$ A v Hu0HHA@HDDAADDE9u&Ht;H fDHL9IlI9IMH\$L|$K,l@L 9#M9uuL9uuHLLL$"HHt]H;##H;-"LL$L9H؛Hm MIMH\$L|$`HDŽ$輚H AL 8 HM~oDMAyE1E1AݯH|$HLD$PHtH/LD$PMt I(H|$XHt H/H|$`Ht H/Mt I+DDE1H z H=;MtImt/HtHmt3MI/L(LfDHfDL\$L\$f@LdL\$ΔLD$PL\$LL\$諔L\$L\$薔L\$@HE0HL$E1HD$(H\$HLl$MM@KlH9H!H9CH9E { + }  HSH;UHEHsH9@H@t HD[ DU DD@@8u|A S H{HA@HE|$(A 2 Hu0HHA@HDDAL AIDDE9u'HHYIM9MH\$Ll$fLL9uuL9uuHHLT$ 肓HHtH;H;--LT$ L9H8Hm[ ]MHL$H\$Ll$y)*HtuMHL$H\$Ll$O4uDS4fDHDHH9HuH;YfL k MLLH$H$+H$fDˑfD`賑YH<L葑 DvMA~E1E1AH=S]I9H|$HA1A@E1HhE1A}AE1A7A%ffA.Gz fA/GaH5UH=*V1cnHD$XIHt91H蜇H|$XH/\HD$XA$E1E1AE1A AfkfD[ fDKsfD;fDL(^L H5CH A}AE1E1H~IH|$HAApL訏螏KLD$PAAE1E1xmn~IHHH5IHD$0p~L\$0HHD$`HHD$PHD$ H9GHGHD$PHHWHHH|$`HT$`H/!HD$PH|$`H$L\$ H$藿H|$PL\$ HD$XHtH/_HD$XHD$PHH|$`H/ HD$`H|$XH/ L\$0HD$XHL$hHT$pHHt$xHD$8與SHLH{HD$(t$0LL$ LD$(HL$QA艒DH>Y^HLT$ L\$0LL\$茌H|$xL\$Ht H/HD$xH|$pHt H/4HD$pH|$hHt H/+H5:Q1LL\$HD$hjL\$HD$hI+L\$hMI+HD$hLAvH|$HHt H/ HD$HH|$PHt H/W HD$PH|$XHt H/D HD$XH|$`Ht H/1 H DHD$`H=DH|$HL$`HT$XHt$Hr Ht$HHL$`1HT$X蘕HD$PHH1LiImIP H|$PH/7 HD$PML;%wL;%L;%;L-I,$Ld$HMt I,$HD$HH|$XHt H/HD$XH|$`Ht H/HD$HL$hHD$`HT$pHt$xHL5IH@hH H@(H LHa|HzAAE1E1LD$PAAQH{HD$荊D$7ukImHD$PLEg H0\H@hHZ H@(HM LHA 褒IAAHuHI|$HmMLD$PAA~'H=GH:H5:%I'(HAAE1E1H|$HAAHD$ FD$ 81ޑIMA~AH DH莑AA@H=FIND$0諈D$0HEJH;#  LHIHUH;E AH; DL;- LImAEA3AE1E1pL\$A~L\$SL/~H;{ L~IH?H; H; L;-a LSImAEAAE1E1}L}pL}LD$PAٳAH;L 1LPXLD$PAͳAE1bAfA.EADEH$11(L}WE1AA L\$|L\$gL\$|L\$;L|8|K|^L\$|HD$XH|$`HL\$AAE1ATAyE1ARAeH=i:4I=H=U:HV-H5W-IH|HD$PLD$PAAV{`H$1AI+AE1{~A{I+V AE1AyAL\$d{HD$PL\$H$1}H$11lHGHD$`HHWHHH|$XHT$XH/ HD$`H|$XH$kAI+ LE1ALE1AwAzyH|$HL\$Ht H/ HD$HH|$PHt H/ HD$PH|$XHt H/M HD$XH|$`Ht H/D H AL\$HD$`H=H|$8HL$PHT$`Ht$XV`L\$ Ht$XHL$P1HT$`L\$9HD$HHH L\$1L9WL\$II+? H|$HH/& HD$HM L;%L;%uM9lL~I,$e Ld$X Mt I,$ HD$XH|$`Ht H/ HD$`H|$PHt H/ HD$8HL$hHD$PHT$pHt$xHqnJ4n5*nH nnL|$L\$*AmL|$L\$?AL|$L\$7AL|$L\$AL|$L\$5AmL\$L\$lmL\$]mLPmAֱHD$8HL$hAHT$pHt$xHeE1~OtOwHH|$H\ORO.LEOH=i HH5IZH|$@E1A AEH=. I-A ADI/tH|$@E1 DLE1NH|$@^WIDDrLD$ ND$ WHLAH8NHD$HH|$HHD$HHH|$@A yH|$/NL"LbDH|$@E1A A7H= HH5mI;jRH-H|$@E1E1A ADLKIt$HwIHS#VIJH= _I A AfQHH|$@E1E1A A(\H|$@E1E1A A2@LEHH|$PLLgMHGI$HH|$@HD$@H/HD$HfInH|$@fInflH$H$)$V}I,$IL`LH|$@E1E1A A;H|$@A ApTHNLH5HLLl$HDDLT$HA ArILK\PHnH AHLAA H8KH|$@LqKDDsH= HH5IKHFA6H8XKHD$PIm!H|$@E1A ALJH|$@E1A A>H$1HDŽ${HD$@LJH=蝾IE1A A,SIH|$@E1A AH$11H=sHH5I#JkLJOH|$HH$1LIH=ItH|$@E1A AnRIDDHGHD$HHHWHHH|$@HT$@H/HD$HH|$@H$rE1A ABIL5I+IA H|$@[H$A A4H80IH|$@6H|$@A A H&HHHHH|$@A A'H=HRH5SIuH5GHwH=Ll$@H=~II@A)I/LA E1 HH|$@VP4H|$@E1A A,3LA E1GH|$@PI.LGLGI,$tA A0fLA0A |G"P5MA.$H=SIH=tHH5IH|$@A ASLwMHGIHH|$HHD$HH/{HD$PfInH|$HfInflH$H$)$wHD$@I.LFH|$@E1A AOrFH|$HHt H/SHD$HH|$PHt H/@H H |HD$PH=ۭyH|$ HL$PHT$HHt$@],QHL$PHT$H1Ht$@JOH1HLHD$(O#I/L\$(II+MbL;3L;L;T$LLT$JLT$AI*pEHt$@ENHt H.HD$@H|$HHt H/zHD$HH|$PHt H/gHD$ HL$XHD$PHT$`Ht$hH=AeI/t>H|$@E1E1A H$1H$11pAQLE1E1A hDH|$@H|$@E1A A҉MH|$@A AebH|$@E1E1A AFDCI*DLCLLT$(CLT$(LHD$0CLT$0L\$(AHD$ HL$XE1A HT$`Ht$hHEMt I.?Ht$0HtHHD$HH0H$Ht H/)HT$XHtHHD$HHHL$hHtHHD$HH Ht$@HtHHD$HHHT$8HtHHD$HHHL$HHtHHD$HHHt$PHtHHD$HHHT$`HtHHD$HHHL$(HtHHD$HHHt$HHD$HHMt I,$Ht H+HD$xHĈ[]A\A]A^A_ÐH22ifD2pfD{2fDk2fD[2fDK2fDL82H(2<L2<H2;H1L1H11fDH1H1H1H1Hx1Hh1$HX13HH1BL81H(1H1H.RHDŽ$H;\$ H'6HD$HDHQH :H9HSIH!HKHL- L$MHH5mL H$H$IH9JH/' HH5HDŽ$H9pJHH HL-xL$MJH5Lp H$IH LH$H/*HSH5HDŽ$H9pWMHHOHL-L$MMMH5sL H$IHNH$H/-+HH$HDŽ$H$8HD$8H1H9OOH$0H$H$8_H$H$Ht H/ BH$HDŽ$H/*L$HDŽ$MOH$H/@H$H5)HDŽ$ H$H$IHPH/AH$HL$81HDŽ$H$8H9ORH$0H$H$8^H$H$Ht H/FH$HDŽ$H/~@L$HDŽ$MQH$H/@H{H5dHDŽ$L$HDŽ$HH5H9pdHpH4gHH\HD$H$HcH5'Ho HD$H$H\fH$H/NH5 HHDŽ$, HD$H$HuH$Ht$81HDŽ$AH9w?vfHnHD$H$@H$0H4LHD$@)$0]H$H$Ht H/ZH$HDŽ$H/NH$HDŽ$HD$HwH$H/PHdH$HDŽ$H9H$H;=÷FH;|$ E1H$…{H/XHDŽ$HH rH9H[HYH5HHEHD$H$HH5HhHD$H$H)H$H/wHIH5HDŽ$H9p?HHHHHD$H$HnH5LHH$HD$H$HH/T|H5HHDŽ$HD$H$HH$Ht$81HDŽ$AH9wyfHnHD$@D$H4L)$0ZH$H$Ht H/%H$HDŽ$H/H$HDŽ$HD$HʝH$H/>H5H$HDŽ$HD$H$H̰H$H/H$HL$81HDŽ$AH9O]Ht$@H$0H$HLH$8YH$H$Ht H/ H$HDŽ$H/H$HDŽ$HD$HH$H/HDŽ$LIEH$L$(HD$H$H?HH$H9H;5 tHD$ H9tH|$?-…8H$HD$Ht$HHD$0HHHDŽ$sH$HH$H$H$H/H$HDŽ$H/H$H$HH$H/őH$HDŽ$ImHD$HDŽ$Ll$H L(LT$hLT$E11HA1HAHD$H$HXH$HH$H/AH+H$HDŽ$H$@HDŽ$H\$ H9$WZH$H5H_vHD$H$HYH5HH9JH@H;_HQHH?HH1H)Hu HJH\$HHD$HHuH%HDŽ$H5H=1HD$H$HH1*H$H/H$D$x\iE1HDŽ$H$HDŽ$DŽ$3HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$fHx$ik$8fD[$ fDK$fDHE1E1E1Hl$H$HDŽ$D$xfDŽ$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$HD$ fDH=H"H5#IL$Mf.HɯE1E1HDŽ$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$Hl$D$xfDŽ$HD$ fK+IYH E1E1HDŽ$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$Hl$D$xfDŽ$HD$ QfH= ԕI^@HAE1E1HDŽ$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$Hl$D$xfDŽ$HD$ \6H$HHD$ HH8H +HiE1E1HDŽ$HD$(H$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$Hl$D$xfDŽ$HD$ H٬E1H$L;d$ kHDHDŽ$HH$H9%$I$H^H5H9pLHHMHHHD$H$H8LH5HHD$H$HLH$H/4HDŽ$/#HD$H$HsMI$L`[%HD$H$HNHH5H9pOHHQHHHD$H$HPH5H-HD$H$HQH$H/X;H$H$HDŽ$H5%H$~OH/=H$H$HDŽ$H$HD$H$H6VH$H/>H$HDŽ$H/>H$HDŽ$H/>I,$H$HDŽ$H$K>HLd$pHDŽ$HD$L;$L;5L;t$ L"e=*H;\$ 2H5HHD$H$H RHKHDŽ$HD$8HHD$H9prRHH@H$H{UHVHHH$H$H/<H$H$Ht$H$0H|$H$0VMH$HD$H$HtH/>H$HD$H|$HDŽ$QH$H/y:L$1ɺHHDŽ$HDŽ$LH$IHjSLHfH$H$IHTH/=H$HDŽ$I,$HD$f=H5-H|$(HDŽ$H$IH;\HDŽ$HD$8I9FdIFH$HmIVHHH$H$H/FHH$L$H$0fHnLD$p)$0KH$H$IHtH/~IL$HDŽ$H$MdH/k?H5H|$HDŽ$L$HDŽ$HD$0H$H@lHD$0H$HlIH$Lp! HD$0H$HlHH5mH%!PH$H$H$0HD$0H$HeH$H/OH$HDŽ$H/OH$HDŽ$H/rOHL$HDŽ$HDŽ$H H9HHHوHHHD$XH$HH5DH4HD$XH$HH$H/LXHDŽ$fHD$XH$HfI$H$L`HD$XH$HHeH5HHH H9HݐHHHHHD$XH$HАH5H>HD$XH$HH$H/yH$H5HDŽ$H$AH$H/o|H$H$HDŽ$H$HD$XH$HH$H/{}H$HDŽ$H/S}H$HDŽ$H/+}H$HDŽ$I,$HD$05{HDŽ$HDŽ$HD$`HD$PHD$HHD$8HD$@HD$hHD$X$dL\$0H5!I{GH5QLHD$(H$HHDŽ$H58H9psHH@H$H[HQHL$0HH$H$H/~$H$LP)$0[FH$H$Ht H/H$HDŽ$HD$(HH$H/yHT$0L$HDŽ$HHD$(HHyHDŽ$Ld$0H5H|$HHD$(H$HFH5H9t$(^H HH@H$H9rE1HzHAHH$HHeHDŽ$E^$SPH5H|$0HD$(H$HYH5HL$(H9jHAH;$E1HyAH$H.iHDŽ$EOH>H5ǾH9p'HHHHHD$(H$H߭H5HHD$(H$HH$H/ʐHDŽ$dHD$(H$H1H5gH|$}HD$(H$HHT$(H5;H$>`H$H/H$H5HDŽ$H$,HD$(H$HH$H/H$HDŽ$H/hH$Ht$0HDŽ$H|$HDŽ$HD$("*H$HHH5H|$(`H$H/HD$(L$HDŽ$HD$xH@H$HDŽ$DŽ$HHD$H!HHHD$pHBHH7I,$H$LLLL$…HD$xgE1E1H$HDŽ$DŽ$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$LxHHDŽ$HD$ =S fDCfD3fD#KH=GIH;[FIH1H;H;o@L;l$ d@L8Im]@D$xhE1E1H$HDŽ$DŽ$"HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$mH=.IefDWfDHIE1E1HDŽ$HD$(H$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xfDŽ$HD$ fDI: fD }fD &fD fDH;! LFIH<H;CAH;DH HD$ I9LI/AED$xfE1E1H$HDŽ$E1DŽ$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$  fDLT$ T$6{ kfDk #fD[ fDK fDD$xfH$Ht H/ H$HDŽ$Ht H/H$HDŽ$Ht H/H$HDŽ$Ht H/H$HDŽ$Ht H/I}XH5 HDŽ$y$DŽ$t$xH nH=?s*?H$H$LH$ZH$HH}L$HGH;7;HHuH$HT;H=DH$H;H$H/&H$H=2H$8HDŽ$HDŽ$0H$89H$HZ=H$H/ 'L$HDŽ$MyI@:,A@LL$',1 IHLL$1HLI/LL$IYMIH@?tMMMtYL;t$ AIFHtA@T@SILLLD$LL$OLD$LL$LLLD$u LD$Mt I(E7H$H/%HDŽ$D$xJgDŽ$H$HDŽ$HDŽ$IHDŽ$HDŽ$Ht H/>&H$HDŽ$Ht H/%&IH$LHDŽ$LLPHH$HPH@LL$HHH$H$H$LT$LT$LL$7I. IH$LLH$H$LH$ HDŽ$HDŽ$HDŽ$HDŽ$IE1E1H$H$H$E1@H$HDŽ$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$SHD$(E1E1H$HDŽ$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xgDŽ$!f.H=HʲH5˲|H_fDfDfDfD&fD9fDH=qyH@HD$(E1E1H$HDŽ$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xgDŽ$!zfD$xffDfDT$T$tfDD$x!gDŽ$D$xfH$kfDI/ELr DH$811D$xfH$ 3ofD#fDH$LHD$H$HCHH$H9H;5EHL$ H97H4 AH$HD$EvOHt$HHD$0HHp'HDŽ$EPH5-H$1HD$H$HTHH$H9H; P/HD$ H9!HH$D$HHL$$WHL$HHD$0HH1HDŽ$L$HXH;\$ (DH*H CH9HlH*HkHHHD$H$H3kH5!HHD$H$HjH$H/ 9H5HߺHDŽ$HD$H$HhnH4H$HDŽ$AHD$8H1H9wufHnH$0D$H4LHD$@)$0v2H$H$Ht H/QH$HDŽ$H/AH$H$HDŽ$HD$H4tH/IH$1H$HDŽ$HD$H$HmH$H/LH$H;$HDŽ$H;=܌I0H;|$ >0H$Aą2xH/*PHDŽ$EuH(HHHH5H$HD$H$HuHDŽ$Ht$8H9psHH@H$HsHQHALd$@HH$H$H/cH$H$LLH$00H$H$Ht H/jH$HDŽ$HD$HH$H/bH$HDŽ$H+H$bHHHDŽ$H9XfHH@HHqHD$H$HH5TH4H$HD$H$HH/zbHDŽ$fHD$H$HH\$pHH$HXHD$H$H HHH9XgHHڈHHHD$H$H)H5HXHD$H$H H$H/qH$H5HDŽ$H$ۖH$H/SxH$H$HDŽ$H$HD$H$HH$H/wH$HDŽ$H/wH$HDŽ$H/wH$H5HDŽ$HDŽ$HHD$X-HD$H$HHD$H\$8HDŽ$H9X~H\$HCH$H~HSHAHH$H$H/sH$H\$@IcH$H$0H)H4,H$H$Ht H/H$HDŽ$HD$HH$H/H$1E11HDŽ$E1HDŽ$Ll$HHD$h1L|$0IHl$`HH$H$1H$IH]H;$L;bnL;D$ nLAŅȇH$H/HDŽ$EH5H|$(IH$H H$H$H$HixH$IHH$H$HDŽ$I@HD$8H9GHGH$HHWHHH$H$H/ÈH$P~$H)HD$@Hc$H4)$0*H$H$Ht H/fH$HDŽ$H/-L$HDŽ$MH$H/sHDŽ$L$Mt I,$H5 H$HDŽ$H$IHH;$AH;$D,~L;D$ !~L]AąH$H/HDŽ$EfH$H5 H9p HHHLL$M)H5@LH$HpH$H/YH$HD$8HDŽ$H9G1H$H$H$8H)H$0PHD$@HcH4(H$H$Ht H/σL$HDŽ$M H$H/DHDŽ$L$Ht HmV1ɺHLHDŽ$SH$HHLH$HH$H/HDŽ$H$I,$H5>HHDŽ$:H$HH$H#IEH$LhH$HطHH5 H8H$H$H$H$HH$H/tH$HDŽ$H/LH$HDŽ$H/$HDŽ$L$Mt I/H3H5 HDŽ$H9pHH$HLӠL$MH5LH$HH$H/ЮHDŽ$H$H/I$H$L`+H$HH$H5H3H$H$H$>H$H5H$H/ڲH$HDŽ$H/H$HDŽ$H/įH$HDŽ$HGH;ܮHWHHGH$HG H$H$HH$HH$H/3HDŽ$H$H$Ht H+HDŽ$H$Mt I.H5EHHDŽ$H$IHeHDŽ$HD$8I9@BI@H$H-IPHAHH$H$H/H$HL$@IcH$H$0H)H4#H$H$Ht H/L$H$HDŽ$M H/H$HDŽ$H/ΧH5LHDŽ$H$IHHDŽ$HD$8I9@3I@H$HIPHAHH$H$H/H$Ht$@AWH$8H$HcH$0L)H4|"H$H$Ht H/L$H$HDŽ$MH/HDŽ$L$I,$aH5LHDŽ$H$HH$HcH$HH$H/HD$hHDŽ$H@L`pM I|$HT$ H$H$HSHD$H|$hLHAT$LD$AI(H$EH/xH5LHDŽ$H$HʵH$H1H$HļH$H/H$H$HDŽ$H$H/_IMH$HDŽ$H;zLIHDH;|H;{ L;l$  LIm D$xgE1E1H$HDŽ$DŽ$"HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$HGH$H$HWHHH$H$H/H$H$H$0ܳD$xfH$81-ffDHDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xgDŽ$齷DKofD;xfD+ܾfDE1ffA.GADEHyHD$ qDT$T$EHDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xgDŽ$"闶H=XHH5bI郭D$xAhE1E1H$HDŽ$DŽ$'HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$׵HDŽ$E1HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xgDŽ$"SmH=^I4vrH=,18E1H.HDŽ$鋹DH5MH|$(HD$H$H8?+HD$H$H KHHHH$HPIH$Lx 2HD$H$HOHT$pH5H8$KHIH5rH9pQHYHXHHEHD$H$H&QH5HHHD$H$HXH$H/)H$H5HDŽ$H$OH$H/z5H$H$HDŽ$H$uHD$H$H:bH$H/8H$HDŽ$H/a8H$HDŽ$H/98H$HDŽ$HDŽ$HD$0HDŽ$HD$`HD$PE1HD$HHD$8HD$@HD$hHD$XHD$HDŽ$E1HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xKhDŽ$)H=HǓH5ȓ]I馶FeLLT$LL$/LT$LL$HDŽ$E1HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xhDŽ$"HGH$HhHWHHH$H$H/#H$H$H$0 HDŽ$E1HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xMhDŽ$)H=ƣYIH=HˑH5̑[I?HWMHDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xPhDŽ$)HDŽ$E1HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xgDŽ$鑮_H=9HH5ZIb‰D$HHDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xRhDŽ$)鯭B8. HDŽ$E1HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xgDŽ$ImLT$|T$EndH=HH5XI颲HDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xUhDŽ$) }HDŽ$E1HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xgDŽ$|HGH$HܨHWHHH$H$H/H$H$H$0锨KH=ǞTIHDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xWhDŽ$)W;HDŽ$E1H$D$xjL$DŽ$IHD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$鼩LLB;8m.EHGH$HHWHHH$H$H/[ H$H$H$0鳯HDŽ$E1HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xmhDŽ$)鰨H1HDŽ$&?L_1ffA.GEHiH5 H8loHDŽ$E1HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xqhDŽ$)鉧H;hh'IH`H;$H; iL;l$ LDImD$xgE1E1H$HDŽ$DŽ$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$yH HGH$H׭HWHHH$H$H/(H$H$H$0鏭HDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xhDŽ$)t7HD$x6Ht$HHD$0HHHDŽ$H5jH$HD$H$HHǺLHD$H$HH$H/HfH$HDŽ$H9H$H;=OfH;|$ H$r&H/|HDŽ$'HHt$(HIH҅D$H9X)HH-HHHD$H$H*H5HHD$H$H,H$H/6D$HDŽ$HD$H$HU;H$H\$81HDŽ$AH9_=fHnH$0D$H4LHD$@)$0 H$H$Ht H/]H$HDŽ$H/L H$HDŽ$HD$HK<H$H/' H$H;$HDŽ$H;=SdH;|$ H$Å=H/t HDŽ$ACHYH҃H9X BHH&FHHHD$H$HUAH58HHD$H$HIH$H/J H5AH$HDŽ$谴HD$H$HGH$H/ H5ٙ1H$HDŽ$HD$H$HOH$HD$8HDŽ$H9GK:HGH$H6:HWHHH$H$H/I+Ht$@H$~$$)$02H$H$Ht H/a8H$HDŽ$H/&H$HDŽ$HD$HPH$H/'H$H;$HDŽ$H;=aG H;|$ < ÅQH$H/+HDŽ$MVD$\fTڙHD$H$HUHǺLHD$H$Hv[H$H/:H$H;$HDŽ$H;= aH;|$ F…]H$H/L>HDŽ$H$`H5?H=1 HD$H$H.H|$17H$H/H$D$x/jE1HDŽ$H$HDŽ$DŽ$<HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$fD{D$mD$rH_Ld$pE1HDŽ$H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xljDŽ$CHD$;H=H~H5~IIHD$鰷T$T$/H^Ld$pE1HDŽ$H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xnjDŽ$CHD$jH=+EHD$?LHHDŽ$̠H]Ld$pE1HDŽ$H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xqjDŽ$CHD$靛H-T#xH]E1E1HDŽ$HD$(H$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xfDŽ$HD$ ȚDIGXfH$IG`AGXH$IGhIGhH$ H>\Ld$pE1HDŽ$H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xvjDŽ$CHD$D$x0gDŽ$tH;U\dQPXHkImLT$BT$鎿4*H=NHzH5zEHD$$D$x:gDŽ$ٗH[Ld$pE1HDŽ$D$x}jDŽ$CHD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$鵘HnZLd$pE1HDŽ$H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xxjDŽ$CHD$$HDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$x2iDŽ$.钗%H=IAHD$-D$x=gDŽ$HYLd$pE1HDŽ$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xzjDŽ$CHD$H$E1HDŽ$HD$(H$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xKiDŽ$2/H5H$H$E1HDŽ$D$xAiH$DŽ$0HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$pHDŽ$E1H$HD$(L$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xjDŽ$K{H$811ݭHDŽ$E1L$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xjDŽ$K\1ff.GEf鄰\4D$xkH$HDŽ$L$DŽ$NHD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0鏓"HDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xhDŽ$+H=HtH5t?HD$HLd$L$HDŽ$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xjDŽ$L\1mHSLd$pE1HDŽ$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xjDŽ$CHD$̑H$81龪AIm0LT$"T$bELd$L$HDŽ$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xjDŽ$LHDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xhDŽ$+cH=$9HD$ƘH;6Q:H|$YHD$HSHL$H; ORH; Q:)HD$ H9,)HHL$HHD$0HH%)x4H$H/HDŽ$麟fH$E1HDŽ$D$xMiH$DŽ$2HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$H$E1HDŽ$HD$(H$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xniDŽ$4[H5H|$RHD$(H$H_UHEwH nH9H#UHnHvHHnHD$(HD$(H$HTH5{H|$(ݠHD$(H$HH$H/THDŽ$HD$(H$HHL$0HH$HH/HD$(H$HCHbvH5mH9pHmHcHHmHD$(HD$(H$HH5|~HH$HD$(H$HВH/SH$H5|HDŽ$H$ϑH$H/KSH$H$HDŽ$H$艟HD$(H$HVH$H/RH$HDŽ$H/RH$HDŽ$H/RHDŽ$_HD$(H$HH$HT$(HDŽ$HBwHD$(H$H|HT$xH5yH|$({-H$H$H$膞HD$(H$HҏH$H/H$HDŽ$H/mH$HDŽ$H/lH$L$HDŽ$HDŽ$HD$xHD$(hK骧HDŽ$E1H$HD$(L$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xkDŽ$T&蹿d诿QH$E1HDŽ$HD$(H$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xpiDŽ$4xHDŽ$L$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xjDŽ$M 莾H$HD$PHNLIHND$E1H(HHHD$`I'#H|$P HD$H$HRLHD$H$H?RHt$`HH$HD$H$HYH/ SH$H$HDŽ$HD$H$HhH$H/RH$HDŽ$H/ QH$H;$HDŽ$H;=FIC=H;|$ 8=H$Aƅ[H/jFHDŽ$EHʃfɿI*fHDŽ$HD$0HqHD$0LpMepHD$(H52wH薫HD$H$HoHD$(H5vHhH$HoH5`GHDŽ$Ht$8H9pSHPH$HSH@HHH$H$H/RH$H$H$0Ht$@H$0H)H4oH$H$Ht H/DH$HDŽ$[H$H/iRH$HDŽ$H/ARHDŽ$费H$H$HH$HD$KLH+T$PLHHD$XH|$(LHNHALDILD$XML[[H$Ht H/lQH$HDŽ$Ht H/QH$HDŽ$Ht H/QHDŽ$H$HtpH5}1藗H$H$H/PH$HDŽ$HD$HkhHL$HHD$(HHPHDŽ$H$LHD$H$HgH$ARE1E1jH|$@11HD$H$A[A\HUH$H/OH$H5rHDŽ$胖H$HD$H$HGhH/~LH$HD$8HDŽ$H9GuGHGH$Ht6HWHHH$H$H/ROD$HH$H$HcT$HHL$@H$0H)H4:H$H$Ht H/3H$HDŽ$HD$HH$H/IHt$0L$HDŽ$HHD$HHBHDŽ$Ld$0HDŽ$HT$pH50xH|$0WD$x#qE1H$DŽ$L$HD$(HD$PHD$HHD$8HD$@HD$hHD$XHD$铁#bHDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xhDŽ$+uXHABH5LD$H8ULD$ H$81_HGH$HHWHHH$H$H/3H$H$AH$HT$1\Ht$(HHD$xHH95HDŽ$HD$0L$HD$(HHD$x陀HDŽ$L$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xkDŽ$Ms1ff.GE}1LLD$LL$ܹLL$LD$HHU遫HDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xhDŽ$+~*KHDŽ$E1H$D$xkL$DŽ$THD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$}菳|H$E1HDŽ$D$xriH$DŽ$4HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$O} -вH5vH=Mx1FHD$H$HJH|$1tH$H/$*HDŽ$E1H$D$xkL$HDŽ$DŽ$UHD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$M|H5~uH=gw1`HD$H$HH;H|$1莨H$H/(.H$D$xiE1HDŽ$H$HDŽ$DŽ$5HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$U{HDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xhDŽ$#zM̯C9/mLHD$LD$LL$; H=-nH[H5[z&HD$Nۯ_HDŽ$E1H$D$xhDŽ$+HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$yHDŽ$E1H$HD$(L$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xkDŽ$WyH諮1n4n*mHDŽ$H$HD$(L$HD$`HD$PHD$HHD$8HD$@HD$hHD$XD$x kDŽ$N_褔H5@XH=!Z1rHD$H$HH|$1HH$H/4H$D$xiE1HDŽ$H$HDŽ$DŽ$8HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$^HT$(蝓HT$(}HDŽ$E1H$HD$(L$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xkDŽ$[s]HDŽ$E1L$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xkDŽ$[]Ld$0H$D$x;kL$HDŽ$DŽ$PHD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$Xr\Ld$0H$HDŽ$L$HD$(HD$`HD$PHD$HHD$8HD$@HD$hD$x4kDŽ$P[H=OHD$ԹD$xmqH$DŽ$L$[HDŽ$E1H$HD$(L$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xlkDŽ$R4[H=NHD$HDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xhDŽ$"ZH=DNHD$X!wLd$0H$HDŽ$L$HD$(HD$`HD$PHD$HHD$8HD$@HD$hD$x1kDŽ$PYH$E1HDŽ$HD$(H$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xiDŽ$9[YH=MHD$cH=MH:H5:SHD$cHDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xhDŽ$,XHDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xhDŽ$,WH$E1HDŽ$HD$(H$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xiDŽ$9cWHDŽ$E1L$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xkDŽ$[VL$8vHROHHGOHD$`D3L$8E1p/jHGH$HTHWHHH$H$H/RH$H$1AH$Ht$HD$1Of.@E=蜋_fHDŽ$E1HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xhDŽ$,UHDŽ$E1H$HD$(L$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$x%lDŽ$^TH5NNH=P1hHD$H$HL]1H0H$H/HDŽ$E1L$HDŽ$D$x lDŽ$\HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$ THDŽ$E1HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xhDŽ$,SH;pH|$(蓉HD$(H8%Ht$(H$H9AH;5D+HD$ H9H8Ht$(AHH$HHE5D$xoqH$DŽ$L$HD$(RYHDŽ$E1L$D$xkDŽ$[HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$3RH$E1HDŽ$HD$(H$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xiDŽ$9QH=ZEH2H52HD$XoLd$0H$HDŽ$L$HD$(HD$`HD$PHD$HHD$8HD$@HD$hD$xkDŽ$PKH.AHDŽ$lHwHDŽ$Ld$0H$HDŽ$L$HD$(HD$`HD$PHD$HHD$8HD$@HD$hD$xCkDŽ$PVJmfm mD H$E1HDŽ$HD$(H$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xjDŽ$;IH5BH=D1\HD$H$HPQH|$1uH$H/ H$D$x jE1HDŽ$H$HDŽ$DŽ$:HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$HD$xVqH$DŽ$L$kHH;T H51Z|HrH= <HD$XeE1郁H$E1HDŽ$HD$(L$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xIlDŽ$_GH$E1HDŽ$HD$(L$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xGlDŽ$_+GH=:HD$}H=:H(H5(HD$}HGH$HSHWHHH$H$H/OH$H$1AKS|HDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$D$xgDŽ$EHDŽ$E1H$D$xiDŽ$,HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$JEzzz~EH$E1HDŽ$HD$(L$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xLlDŽ$_DH$E1HDŽ$HD$(H$HD$`L$HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xQlDŽ$_ DH$E1HDŽ$HD$(H$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xjDŽ$;qCD$xBqH$DŽ$L$ICHDŽ$E1L$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$x9lDŽ$^B\xf|RxjfHDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xhDŽ$,#BHDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xiDŽ$,AH$E1HDŽ$D$x jH$DŽ$;HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pHD$@v wv錹H$E1HDŽ$HD$(H$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$x}iDŽ$5@@uH$E1HDŽ$HD$(H$HD$`L$HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xSlDŽ$_?H=g32HD$ w#uHu8H$E1HDŽ$HD$(H$HD$`L$HD$PHD$HHD$8HD$@HD$hHD$0D$xilDŽ$`>H$E1HDŽ$HD$(H$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xiDŽ$8X>ss'|s{H$E1HDŽ$HD$(L$HD$`HD$PHD$HHD$8HD$@HD$hHD$0D$x}lDŽ$`=NsyHl$Ll$HL|$8Hl$`H\$HL|$0Lt$PE1H$Ld$@H$D$xlL$HDŽ$DŽ$aHD$(HD$`HD$0/=H$E1HDŽ$HD$(H$HD$`L$HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xUlDŽ$_u=lt3lHDŽ$E1H$HD$(L$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xkDŽ$X6HDŽ$E1L$HD$(HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$x9nDŽ$v5HDŽ$E1H$HD$(L$HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$x7nDŽ$v5jDjH=(HD$(VH=(HH5HD$(VH;H|$(jHD$(HHL$(H$H9H; FbHD$ H9TH}oHL$(AHH$HHMEUD$xqH$DŽ$L$HD$( 4Ht$(EHH$HHH|$(xiHD$(E1fHf.@ADETHi>iD$HH$餰$iHia ii銮T$hHcT$&1h鵭h鍭huD$xqH$DŽ$L$3D$xqH$DŽ$L$2D$xqH$DŽ$L$HD$(2D$xqH$DŽ$L$2HDŽ$E1H$HD$(L$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xkDŽ$U1D$xqH$DŽ$L$1D$xqH$DŽ$L$1H$E1HDŽ$HD$(H$HD$`L$HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xZlDŽ$_1H$E1HDŽ$D$xXlH$DŽ$_L$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$0fH$1AH$H$HL$ UH$L$HT$("YHT$(LLHO=D$xpHDŽ$HDŽ$HDŽ$HD$H$E1H$H$HMH$DŽ$HD$(L$HD$PHD$HHD$8HD$@HD$hHD$XHD$D$xp_I,$DPL+T:D$xp6T TD$xpD$xpLSSSSSS7SPSSޒH$HD$(H>XHIHDŽ$E1H$D$xoL$DŽ$HD$(HD$PHD$HHD$8HD$@HD$hHD$XHD$THDŽ$E1L$HD$(HD$PHD$HHD$8HD$@HD$hHD$XD$xoDŽ$HDŽ$E1L$HD$(HD$PHD$HHD$8HD$@HD$hHD$XD$xoDŽ$H=9HD$H=#HH5pHD$HDŽ$E1H$HD$(L$HD$PHD$HHD$8HD$@HD$hHD$XD$x oDŽ$~HDŽ$E1H$HD$(L$HD$PHD$HHD$8HD$@HD$hHD$XD$x oDŽ$zRPPP/PHPaPzHDŽ$E1L$HD$(HD$PHD$HHD$8HD$@HD$hHD$XD$x%oDŽ$~HDŽ$E1L$HD$(HD$PHD$HHD$8HD$@HD$hHD$XD$xoDŽ$IH= HH5HHD$雪HDŽ$E1H$HD$(L$HD$PHD$HHD$8HD$@HD$hHD$XD$xoDŽ$3OjHDŽ$E1H$HD$(L$HD$PHD$HHD$8HD$@HD$hHD$XD$xoDŽ$ HDŽ$E1H$HD$(L$HD$PHD$HHD$8HD$@HD$hHD$XD$xoDŽ$H=k 6HD$Hl$H$Ll$@Hl$`L|$8Ll$HLt$PL|$0E1H\$HL$H$HDŽ$D$xlDŽ$cHD$(HD$`HD$0MHl$H$Ll$@Hl$`L|$8Ll$HLt$PL|$0E1H\$HL$H$HDŽ$D$xlDŽ$dHD$(HD$`HD$0Hl$H$Ll$@Hl$`L|$8Ll$HLt$PL|$0MH\$HL$H$HDŽ$HD$(HD$`HD$0D$xlDŽ$dD$xgnHDŽ$E1H$HD$(L$HD$PHD$HHD$8HD$@HD$hHD$XD$xenDŽ$zPHHDŽ$H$HD$(L$HD$PHD$HHD$8HD$@HD$hHD$XHD$D$xZnDŽ$yHDŽ$E1L$HD$(HD$PHD$HHD$8HD$@HD$hHD$XHD$D$xNnDŽ$xIHl$L|$0H$Hl$`Ll$@H\$PLl$HLd$8H$HD$HL$HDŽ$HD$(HD$`HD$0D$xmDŽ$j J(XJXH$Hl$ML|$0Hl$`Ll$@H\$PLl$HLd$8H$HD$HL$HDŽ$HD$(HD$`HD$0D$xmDŽ$ihE1VIHl$L|$0H$Hl$`Ll$@H\$PLl$HLd$8H$HD$HL$HDŽ$HD$(HD$`HD$0D$x|mDŽ$iqIkVgIWHH9tHuH;IH=vQ$AHdVHD$E1铧IgHDŽ$E1H$HD$(L$HD$PHD$HHD$8HD$@HD$hHD$XD$xoDŽ$H鳤wH鋤mHcHl$L|$0Ll$@Hl$`Lt$PILl$HLd$8H$H\$HL$H$HDŽ$HD$(HD$`HD$0D$x=mDŽ$hNHl$L|$0Ll$@Hl$`Lt$PE1Ll$HLd$8H$H\$HL$H$HDŽ$D$x2;Ll$@Ll$HH\$HL|$0Hl$Hl$`Lt$PAH$H/=HDŽ$ Ld$8H$E1D$xmmH$HDŽ$L$DŽ$hHD$(HD$`HD$0 Hl$L|$0Ll$@Hl$`Lt$PLl$HE1H\$HKCIH˷LH H5=HEHE1H81JLd$8H$D$xmmH$HDŽ$L$DŽ$hHD$(HD$`HD$0 lBHl$L|$0Ll$@Hl$`Lt$PILl$HLd$8H$H\$HL$H$HDŽ$HD$(HD$`HD$0D$x]mDŽ$hM HWHu>HGHH@H$H$MADMAMAMHl$L|$0Ll$@Hl$`Ll$HLt$PH\$HH HHH1H HEHH5E1H81&ILd$8H$D$xHmH$HDŽ$L$DŽ$hHD$(HD$`HD$0B L@AM@NLd$8H$E1D$xHmH$HDŽ$L$DŽ$hHD$(HD$`HD$0 H%H5E1H814HLd$8H$D$xHmH$HDŽ$L$DŽ$hHD$(HD$`HD$0P H=H2H53^IKJH? L?I?I?IHl$L$Ll$@Hl$`L|$8Ll$HLt$PL|$0IH\$HH$HDŽ$HD$(HD$`HD$0D$x!mDŽ$g Hl$H$Ll$@Hl$`L|$8Ll$HLt$PL|$0E1H\$HL$H$HDŽ$D$x mDŽ$gHD$(HD$`HD$0 Hl$H$Ll$@Hl$`L|$8Ll$HLt$PL|$0IH\$HL$H$HDŽ$HD$(HD$`HD$0D$xmDŽ$gLl$@Hl$`L|$8Ll$HLt$PIL|$0H\$HH$Ld$H$HDŽ$L$HD$(HD$`HD$0D$x mDŽ$fLl$@Hl$`L|$8Ll$HLt$PIL|$0H\$HH$Ld$H$HDŽ$L$HD$(HD$`HD$0D$xmDŽ$fL=RGHDŽ$E1L$HD$(HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$x>nDŽ$v  L$Hl$H$Ll$@Hl$`L|$8Ll$HLt$PL|$0IH\$HL$H$HDŽ$HD$(HD$`HD$0D$xmDŽ$gaHl$H$Ll$@Hl$`L|$8Ll$HLt$PL|$0IH\$HL$H$HDŽ$HD$(HD$`HD$0D$xmDŽ$gHl$Ll$HL|$8Hl$`H\$HL|$0Lt$PMH$Ld$@H$HDŽ$L$HD$(HD$`HD$0D$xlDŽ$b]Hl$H$Ll$@Hl$`L|$8Ll$HLt$PL|$0IH\$HL$H$HDŽ$HD$(HD$`HD$0D$xlDŽ$cH=HH5IAL:fIH$Hl$Ll$@Hl$`L|$8Ll$HH\$PL|$0H$HD$HHDŽ$L$HD$(HD$`HD$0D$xmDŽ$l<9~IH$Hl$E1Ll$@Hl$`L|$8Ll$HH\$PL|$0H$HD$HD$xmL$HDŽ$DŽ$kHD$(HD$`HD$0L19HIH$Hl$Ll$@Hl$`L|$8Ll$HH\$PL|$0H$HD$HHDŽ$H$D$xmL$HD$(HD$`HD$0DŽ$k LHPHl$HHLl$@Hl$`H HDHHL|$8E1H5Ll$HL|$0H81=@H$H\$PD$xmH$HD$HH$HDŽ$L$DŽ$kHD$(HD$`HD$0L7 GIH$Hl$Ll$@Hl$`L|$8Ll$HH\$PL|$0H$HD$HHDŽ$L$HD$(HD$`HD$0D$xmDŽ$kIH$Hl$Ll$@Hl$`L|$8Ll$HH\$PL|$0H$HD$HHDŽ$H$D$xmL$HD$(HD$`HD$0DŽ$k6L6E6iEH$Hl$ML|$0Hl$`Ll$@H\$PLl$HLd$8H$HD$HL$HDŽ$HD$(HD$`HD$0D$xmDŽ$jHDŽ$E1H$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$x+jDŽ$< HDŽ$E1H$HD$(L$HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xXoDŽ$H=MHNH5O蚫HD$HDŽ$E1L$HD$(HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$x]oDŽ$HDŽ$E1H$HD$(L$HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xUoDŽ$rHDŽ$E1H$HD$(L$HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xSoDŽ$H=HD$魊H=HH5HD$鉊L3CHhHD$!13NCIH$Hl$Ll$@Hl$`L|$8Ll$HH\$PL|$0H$HD$HHDŽ$H$D$xmL$HD$(HD$`HD$0DŽ$l Hl$Ll$HL|$8Hl$`H\$HL|$0Lt$PIH$Ld$@H$HDŽ$L$HD$(HD$`HD$0D$xlDŽ$bHD$XLl$HHl$L|$8Hl$`H\$HL|$0Lt$PE1H$HLd$@HD$0HDŽ$HD$`iH$TT$1T$TlD$xqH$DŽ$L$D$xqH$DŽ$L$D$xqH$DŽ$L$H=W"HD$(m1@pD$xrH$DŽ$L$ND$xrH$DŽ$L$HD$(D$xqH$DŽ$L$D$xqH$DŽ$L$D$xqH$DŽ$L$HD$(HDŽ$E1L$HD$(HD$PHD$HHD$8HD$@HD$hHD$XD$x:oDŽ$~=D$xqH$DŽ$L$D$xqL$DŽ$D$xqL$DŽ$H=RHD$(lH=qH"H5#辥HD$(slHGH$H6HWHHH$H$H/H$6Hl$H$Ll$@Hl$`L|$8Ll$HLt$PL|$0IH\$HL$H$HDŽ$HD$(HD$`HD$0D$xlDŽ$eP.H$.6Hl$H$Ll$@Hl$`L|$8Ll$HLt$PL|$0MH\$HL$H$HDŽ$HD$(HD$`HD$0D$xlDŽ$e$H=谡I05H$E1HDŽ$HD$(H$HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$HD$pD$xjDŽ$:vHDŽ$E1L$HD$(HD$`HD$PHD$HHD$8HD$@HD$hHD$XHD$0D$xlDŽ$\Hl$H$Ll$@Hl$`L|$8Ll$HLt$PL|$0MH\$HL$H$HDŽ$HD$(HD$`HD$0D$xlDŽ$etH,4HGH$HPHWHHH$H$H/tH$+鉇+H$HDŽ$E1L$D$xAnDŽ$vHD$(HD$PHD$HHD$8HD$@HD$hHD$XHD$0HD$}H +CP+rH$*9E19ff.@AWHAVIH@fHnAUfHnHATflUHHPH-SfHnHHfHnHL%H)D$`fHnL flHD$0)D$pfHnflLd$8HD$XHDŽ$HD$@Ld$HLL$P)$HLHH]HcH@HF(HD$XHF HD$PHFHD$HHFHD$@L~L.LML|$8Ll$0H H"HcHDH9LHLL$L$}LL$LL$HIj HD$8IMNHGLHLL$L$;LL$LL$H HD$@IMlHLHLL$L$KL$LL$H HD$HIM-HML-uHf1 HH9KL;luIHAHD$PIMHML-H1DHH9L;luIE9\HtH@'BLLL$L$MH\$Lt$KE9u8LT$HH%LT$f.IL9L $LT$H\$M9uuM9uuLLLT$I"IHtH;JLT$L;=íuM9tLLT$'LT$I/cL $LT$MH\$yGLT$L $%L $LT$HeL $LT$MH\$KffDH|$XLl$0HL$@Hl$HLL$P]f.H i1LM@H Q1L1LfD1nfL%@HsHHEt$ HeeDLD$,, D$,eH "L IwHnLD$,LT$D$,LT$VLT$L $R$L $LT$HeLLT$LT$~LLT$cLT$o^IwHIzHLT$L $#L $LT$HeyDD>DD>LT$L $#L $LT$He0DD>WDD>h@#H AL He@HHH?Pf*Y*Hff.HGH?H~CAUIATIUHS1HfDH}UADHI9uH[]A\A]fDH~SAUIATIUHS1HfDI}AUf*YE*AHH9uH[]A\A]AUIATL%UH- SHH(I}AUfHH HH*YLH9IEI}AL$HcAT$\$L$D$f(fW%)f(2T$L$f($YD$Xf/KH(f([]A\A]f.fWV) i)H([]\A\A]f(fDH~CAUIATIUHS1HfDLADHH9uH[]A\A]DAVAUIATL%UH-SHHI}AUfɉ *YL9IEI}AL$HcAT$ \D$L$A(W-S(A(7T$ L$(fA*Y'YD$X/HH([]A\A]A^@f*Y'W' 'H[]\A\A]A^(H~CAUIATIUHS1HfDL ADHH9uH[]A\A]DH~[AUIATIUHS1HfDI}AUfW0'fW#'AHH9uH[]A\A]fff.@H~sAUIATE1UHSHHDI}AUf*Y&W&ZZW&BDIL9uH[]A\A]AWAVIAUL-0ATL%'UHSHH(IFI>L$HcT$\$L$%,&D$Yf(YmT$L$f($YD$Xf/wAI>AVfII LH!H*AYLtfW %I94?H(f([]A\A]A^A_@IFI>fWO% j%I>Y $AVfW*% $fW%f(XYf/vX .%AzfW $m@H~CAUIATIUHS1HfDLADHH9uH[]A\A]DAWAVIAUATL%NUH-FSH>HDIFI> HcL$ \D$%_$fAnfZAYAf(YL$ f(fA*Y#YD$XZf/wDI>AVfAA A*AYfA~t W#fA~D9l/HfAn[]A\A]A^A_IFI>f*Y,#We#@ #I>YL$AVf*Y"W-#L$W#(XY/vX "AfA~RW "fA~AH~CAUIATIUHS1HfDLADHH9uH[]A\A]DUHH0f.D$d|$ff.8=f/|$@H}UHD$ {t$T$\f/r5 ]D$f(^\$f/rH0]D$"L$ \^D$|$L$ D$f(Y\f( ^T$\$\f/(H0]f.|$\=!!Y|$(ff.2Q5v^t$@Hff(D$YXFf/sf(L$H}YYD$UL$ !f(YYY\f/wbL$ D$D$%\d$f(L$ f(X YD$(YYXf/D$'D$(YD$H0]DH0f]H0]fDUHH .D$ud$f.R=/|$%md$H}UfH*YT$T$  Bt$T$ \/r- %D$ (^\$ /rH ]fD$L$\^D$-|$L$D$ (Y\( ^,T$ \$\/#H ]Dt$\5~fvYt$.;Q=Od$^|$Hpf(D$YX/s(L$H}YYD$ UL$f(*YYD$YY\/w_L$D$D$ =\|$ (L$(XYD$YYX/D$D$YD$ H ]@H f]H ]K%ff.HHH?PHHff.HHH?PHff.HHH?PHHff.HGH?f.E„f.f(D„USH(-f/Kf1X \$^T$YYX Y\ YX Y\ YX Y\ YX Y\ Yf(L$L$X tT$f(5\$^f(\f/YX DX\vHH~CH@\L$Hf(T$_L$H9T$\uH(f([]f(f\H,H*Dff(ff.@H$L$YD$X$Hff.HD$QYD$HfDHHH?$L$PYD$X$HHL$a YD$HfDHL$ aYD$ HfDUHH0pD$ f/L$(f/f(f/vf/@H}UH}D$U ^L$ D$D$ ^L$(D$D$XD$f/rL$XL$ff/vf/L$H0]^f(fDD$ H2 HD$D$( L$X^H0f(]H?U\$ HCf(D$(XYfHnf/wfD$ f(D$^L$ L$ L$f(^T$(T$ f(_\\$f(L$ \$T$ D$\f( XD$Y L$H0]\f( HYt HXfDUHH $D$8 $Hf(Yf($\$$H]Y^f(ff.fUHHHD$L$H]^f(ÐHD$ ^D$Hff(ff.z uHT$  T$H^ ff.HD$ ~ fWP~ fW ,^L$H ff.fSHH$L$ ff/wFH;Sf/r \\f( L$Y$H[\@X_ YD$X$H[ff.AVfI~SHHL$H;SZf(N\f/v fW L$H[YfInA^\SHH$L$DH;Sff/v \^ YD$X$H[fHHff.HD$fXf.wQYD$Hff.fUHHD$L$HY <$f(L$L$ff(f.w!QY $f.w1Q^H]f(D$f(tT$ff(f( $V $f(ff.AWf(AVATUSHH@f/D$f.azuE1H@L[]A\A^A_f.D$fWE1z BD$f.IL$H;SL$Yf/L$wH@L[]A\A^A_fDff.-Qf(D$L$L$Y ;X ;D$05Yf(L$ \ /\-f(#\% ^ 'f(d$8XfI~XfI~^\fH~f.H;SH;f(\T$ST$ D$f(fTB\fIn^L$XD$ YXD$X2 L$f/ |L,\$rfHnf/M_5Wf/v f/Gf(L$((D$fInL$(t$8D$D$ Y^X|$ID$X|$f(f(\fI*YL$0\L$D$fH*L$c L$\f/L$H@L[]A\A^A_D$B f(fUH\^f(H]f.AWfAVH*AUIATIUSHH$t H9r ,Me$AEf(\A}|$Pf/t$H# L$PT$Yf(fD$HAEX\$AM(f(L$% \$Y\$HH,fL$T$f.Im0f(\$h Qf(YD\$HY>%-6\f(fTf.050d$PXf(t$(fD(D$AE8ffA(H*XXXf(Am@$A\f(\$xA]PY|$8^f(A}H\XfD(\$@A]Xf(\^f(YXYf(Yl$H\\$`^A]`Yf(XYfA(AXXL$pAMhAYf(D$AEpfA(^D^Xf(D$XAExfA(XD$ AMl$LH)H$fH;Sd$ H;Yd$Sd$f/d$f(Vf/d$"t$l$@fH*e\YT$0f(^XXD$8\X\$(fT^\f/L$[L$T$0L,MI)LH?HL1H)H~#D$hYD$(fH*\f/fd$P^d$HI*YI94f(jf/$M)f/L$(MGH[]LA\A]A^A_Df.8 ADEf/d$Xwcd$0D$^D$`XD$8L,MSEJd$0\d$L$YYL$`d$0D$\$x^D$p\f(&L,M9EL$d$0\d$XYYL$pqfDHEI9IVf(ff(H*H^\YH9uIFH9HUff(H*H^\^H9uWf(^ t$hHX HHf(XYX ^^XT$(YfH*^f(T$0\$D\$T$0f(f(\f/Xd$0f/IFfEfEL*HEfEL*LfL*$L)HH*fE(D$EYfA(fA(D$A^fE(D$AYEYfD(l$DYD$$D$D$ND$$D$fA(^D$!T$HD$$t$Yt$PAYf(^=B 5B L$-6 H)f(f(D$D$^d$0D$DY$D$D$D$D$\f(^\ fD(^D\D^ f(A\fEL*DX\$(DY$A^D EXfEM*AYDXf(A^A^AXfD(D\f(E^A\fD(A^D\f(E^A\fD(A^A^Xf(A^A^D\f(E^\A^A\fD(A^\A^D\f(E^\A^A\A^\^L$A^A^XXf/f($YT$\XL,~fDH,ffUH*f(fT\fVf(f(t$P\l$Hf( f.Bhf/B]J8rz Hj0L$J@Yt$P5a$JH|$HL$8JPYt$(L$xJXL$@J`L$`Jh\$hL$pJpL$JxL$XL$ D$hT$L$[T$L$Ff.AUIATIUSHH8D$t H9rWd$-yfMeI*AE\AeAm f($l$$Ybd$$L$f(AEfYYAeXX f.Q-f(YXf/aH,Im0$H;S$1f/f(vp@HH9})$H;S$f/1f(HH9|Lf\H)HH*YT$YfH*YT$^f/wH8[]A\A]Ðf.Bf/Bz ZHj0|$9H81[]A\A]f(d$(\$ T$ $cd$(T$-׻ $\$ YXf/f(l$ d$$$d$l$ f(YXH,ff.Hf.Eur*fUHH*f/rY[f/rM]\4Yf/f(r&IH]L)fD1D]rfkIH]L)UHH$f(L$dL$ff.`$f/v]f(HL$\f(+H$L$ff(f.~QX$H]YXY Hf(TfHHH*X$H]fDH]fB$HH]D$f(T$f(hf.UHH $f(D$$$Hf(Yf($&\$$H]Y^f(ff(f(SHXf(H ^L$\$l$}\$L$Y )f(YYYf(YXff.w\Q\YT$\$H;XT$S\$T$f(f(X^f/s Y^f(H f([f(\$T$\$T$f(UHH@D$8f(L$Sf/D$Gf/D$s;|$f/ -ft$Yl$YXf.Qf(XL$f(Xf.JQ\T$f(f(X^f(YXXL$^L$0&f(^XD$L$ \f/D$sH}UYT7\$0H}f(YXXL$f(L$^\d$(YL$ UL$ f(\Y\f/D$\H}UD$D$(f(Xf/D$vfWXT$8 f(fT~T$X;t$T$\of/vfWH@]H}UX\ݵY=H@]f^D$f.QD$H:YD$ XD$8f/vXf/q\dD=Pf(|$|$^Xf|$D$0(D$qf(L$ L$ f(f(|l$f(hff.fSHH0D$ fWZD$(H;Sf/D$ D$H;SYD$(T$f(fWYf/~f(T$\$\$D$f(L$^*XL,MaT$ff.E„EH0L[f/ArA@HijHH?D$\$PL$$f(f/vf(fDYHXf/wHÐHD$~T$$fWf(Q~ $f(fW f(^df(fTf.v3H,ff(%fUH*fTXfVf(f/HsH,HDf/r1ff.AVSHH(\~f(D$tD$H;SH;D$S%F\d$fI~ S^L$f(=f(fTf.v;H,f=H*f(fT\ gfUf(fVf/ ]5f/Kf(L$T$^X>T$l$f(fInYf(\i^Yf(\U^f/H(H,[A^f.f(f(H8H\\T$H?L$D$(f(d$^l$ 4$P4$d$L$T$f/r;l$ \$(Yf(Yff.wPQXH8f(f(\ \fYYf.w*Q\H8f(f($$f(f($$f(1HATIIUHI SHLHI LHL IIL III LH I ĸH9wfDH;SD!H9r[]A\DH;SL!H9sH;SL!H9rf.ff.@AWAVAUATIUSHHttHHH?IIH9wqHEAEDjAME9v,D1AAA9sH}UAME9wI IHL[]A\A]A^A_@HEHEuQLbIHHI9v+L1HIIH9sfDH}UIHI9wHL$DHEH}L!I9rL$oDHEH}D!D9wL$ODЉI>@I0fDAWAVAUATAUSHteHGIH?AEu`JL$ Dl$ AME9v%1AAA9sI>AVAME9wI AHD[]A\A]A^A_@IFI>D!9rD$f.AfAWAVAUATUSHt$H\$PfA։IAMfAAEEF-DD$ H?AUDD$ A$3EAfA9v^AAƙAAf9r&ID3A$xA<$3AfA9v%uI}AUA$3AfA9wD$H[]A\A]A^A_+A$PA$D!f9s!uI}AUA$D!f9rfD$H[]A\A]A^A_fuDH?AUA$D$fH[]A\A]A^A_@+AxA9+A)ff.@AWAVAUATUSHt$ H\$PA։IAMAAEE~H?AUA$3D@A8v^AEAƙAA8r#Ff3A$xDA<$3@A8v%uI}AUDA$3@A8wD$ fH[]A\A]A^A_f+A$PA$D!@8s!uI}AUA$D!@8rD$ H[]A\A]A^A_uDH?AUA$D$ H[]A\A]A^A_D+AxA9+A)ff.@USHHl$ tAHL˅tmA)EH[]fDH?QEAWAVAUATIULSH(HL$HujH~OHHHfInLHHLHH9uHt$HHtLdH([]A\A]A^A_IHH9EH|$~DrE1Dt$D$fI}AUt$I9s$D$19s@I}AUI9wH LJLIL9|$uLf.HEE1HLrH|$H\$fI}AUIHHL9s-HD$1IHH9sI}AUIHH9wHLJDIL9|$ufH|$1fI}AULHDHH9\$ufDH|$n1f.I}AULHDHH9\$uBIII LHI LHI LHI LHI LH I H|$E1fDI}AUL!H9rLJDIL9|$uIII LHI LHI LHI LHI H|$E1I}AUD!9wLJDIL9|$u[1OfAWAVAUATMUHSHt$H~pHAHHfnLHfpHLHH9uHH@t,t$HHHA4H9~HAtH9~AtH[]A\A]A^A_@IӃEDrE1Dt$\$ H~f.I}AUt$I9v$D$ 19s@I}AUI9wH L$C IL9uH[]A\A]A^A_fIII LHI LHI LHI LHA HE1I}AUD!9rD$CIL9uH[]A\A]A^A_ÐH1DI}AUD$AHH9uH[]A\A]A^A_1zAWAVAUATUSLHfHHAHCHfnLHfaHfpLʐHH9uHHt\Hxf4CHH9~KHxftH9~=HxftH9~/HxftH9~!HxftH9~Hft H9}ft H[]A\A]A^A_DIAfHEH~DrII1H$A1D$ ufI?AWfD9s@D$ Af9s1t1fA9vI?AWȉfA9wۿHDfKH;$2t1뒐AHHH HHH HHH HH HM4I11t@1!fA9sI?AW!fA9rDHfSL9uH[]A\A]A^A_@HI,IHDfCH9mI?AWATfHSH9uP1DAWAVIAUATUSH@t$ uVH~>> from numpy.random import Generator, PCG64 >>> rng = Generator(PCG64()) >>> rng.standard_normal() -0.203 # random See Also -------- default_rng : Recommended constructor for `Generator`. Gets the bit generator instance used by the generator Returns ------- bit_generator : BitGenerator The bit generator instance used by the generator __pyx_capi__name__loader__loader__file__origin__package__parent__path__submodule_search_locationsMissing type objectcannot import name %Sendunparsable format string'complex double''signed char''unsigned char''short''unsigned short''int''unsigned int''long''unsigned long''long long''unsigned long long''double''complex long double''bool''char''complex float''float'a structPython objecta pointera string'long double'an integer is required%s (%s:%d)View.MemoryView._errexactlyis_f_contigis_c_contigView.MemoryView.Enum.__init__numpy/random/_generator.pyxView.MemoryView._err_dimView.MemoryView._err_extents__getstate__at leastat most__cinit__BitGenerator__setstate_cython____reduce__tupleExpected %s, got %.200s__setstate____reduce_cython__View.MemoryView.memview_slicememviewsliceobjlogisticgumbellognormallaplacespawnrayleighpoissonnoncentral_fView.MemoryView._unellipsifystandard_cauchy'NoneType' is not iterablevonmiseswaldnoncentral_chisquarebeta__pyx_unpickle_Enumweibullstandard_tlogseriespowerparetozipfname '%U' is not defineddirichletmultivariate_hypergeometricmultinomialnumpy/__init__.cython-30.pxdnumpy.PyArray_MultiIterNew2numpy.PyArray_MultiIterNew3multivariate_normalvhunegative_binomialtriangularstandard_gammastandard_normaluniformintegersstandard_exponentialrandombuiltinscython_runtime__builtins__%d.%d4294967296complexnumpyflatiterbroadcastndarraygenericnumberunsignedintegerinexactcomplexfloatingflexiblecharacterufuncnumpy.random.bit_generatorSeedSequenceSeedlessSequencenumpy.random._commondoubleLEGACY_POISSON_LAM_MAXuint64_tMAXSIZE_rand_uint64_rand_uint32_rand_uint16_rand_uint8_rand_bool_rand_int64_rand_int32_rand_int16_rand_int8check_constraintcheck_array_constraintdouble (double *, npy_intp)kahan_sumdouble_fillfloat_fillvalidate_output_shapecontdisccont_fcont_broadcast_3discrete_broadcast_iiiView.MemoryViewnumpy.core._multiarray_umath_ARRAY_API_ARRAY_API not found_ARRAY_API is NULL pointernumpy.import_arrayinit numpy.random._generatordefault_rngformatcopy_fortrancopypermutationpermutedoutshuffleassignmentdeletionbuffer dtypeBuffer not C contiguous.choiceTbasestridessuboffsetsndimitemsizenbytes__repr__numpy.random._generator.Enumnumpy.random._generator.arraymemview__getattr___bit_generatorspspsspspspspspss`spspsPspspsPsPsPspspspspspspspspspspspspspspspspsssPsps`sss`spspsPspspspssPspss, D  fr ~ P ʑ8N Z = =fBNZ֎rʎv*d6d||||||||l||l||\\\||||||||||||||||||l||l|||\|; ԎԎԎԎԎԎԎ|ԎԎlԎԎlllԎԎԎԎԎԎԎԎԎԎԎԎԎԎԎԎԎ|ԎԎlԎԎԎlԎv`````````F``F``````````````````F[````````````````````````O[O`````````````”`````.```O``````````````````x44^'U'L'PGW8864-4$4zzpppt(yp5LtdL4 \ET;;;;:OEP;u;;DSTPPPPPSS%QdQQQiTYYYY5T,T__pyx_fatalerror00010203040506070809101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899default_rng(seed=None) Construct a new Generator with the default BitGenerator (PCG64). Parameters ---------- seed : {None, int, array_like[ints], SeedSequence, BitGenerator, Generator}, optional A seed to initialize the `BitGenerator`. If None, then fresh, unpredictable entropy will be pulled from the OS. If an ``int`` or ``array_like[ints]`` is passed, then it will be passed to `SeedSequence` to derive the initial `BitGenerator` state. One may also pass in a `SeedSequence` instance. Additionally, when passed a `BitGenerator`, it will be wrapped by `Generator`. If passed a `Generator`, it will be returned unaltered. Returns ------- Generator The initialized generator object. Notes ----- If ``seed`` is not a `BitGenerator` or a `Generator`, a new `BitGenerator` is instantiated. This function does not manage a default global instance. See :ref:`seeding_and_entropy` for more information about seeding. Examples -------- ``default_rng`` is the recommended constructor for the random number class ``Generator``. Here are several ways we can construct a random number generator using ``default_rng`` and the ``Generator`` class. Here we use ``default_rng`` to generate a random float: >>> import numpy as np >>> rng = np.random.default_rng(12345) >>> print(rng) Generator(PCG64) >>> rfloat = rng.random() >>> rfloat 0.22733602246716966 >>> type(rfloat) Here we use ``default_rng`` to generate 3 random integers between 0 (inclusive) and 10 (exclusive): >>> import numpy as np >>> rng = np.random.default_rng(12345) >>> rints = rng.integers(low=0, high=10, size=3) >>> rints array([6, 2, 7]) >>> type(rints[0]) Here we specify a seed so that we have reproducible results: >>> import numpy as np >>> rng = np.random.default_rng(seed=42) >>> print(rng) Generator(PCG64) >>> arr1 = rng.random((3, 3)) >>> arr1 array([[0.77395605, 0.43887844, 0.85859792], [0.69736803, 0.09417735, 0.97562235], [0.7611397 , 0.78606431, 0.12811363]]) If we exit and restart our Python interpreter, we'll see that we generate the same random numbers again: >>> import numpy as np >>> rng = np.random.default_rng(seed=42) >>> arr2 = rng.random((3, 3)) >>> arr2 array([[0.77395605, 0.43887844, 0.85859792], [0.69736803, 0.09417735, 0.97562235], [0.7611397 , 0.78606431, 0.12811363]]) permutation(x, axis=0) Randomly permute a sequence, or return a permuted range. Parameters ---------- x : int or array_like If `x` is an integer, randomly permute ``np.arange(x)``. If `x` is an array, make a copy and shuffle the elements randomly. axis : int, optional The axis which `x` is shuffled along. Default is 0. Returns ------- out : ndarray Permuted sequence or array range. Examples -------- >>> rng = np.random.default_rng() >>> rng.permutation(10) array([1, 7, 4, 3, 0, 9, 2, 5, 8, 6]) # random >>> rng.permutation([1, 4, 9, 12, 15]) array([15, 1, 9, 4, 12]) # random >>> arr = np.arange(9).reshape((3, 3)) >>> rng.permutation(arr) array([[6, 7, 8], # random [0, 1, 2], [3, 4, 5]]) >>> rng.permutation("abc") Traceback (most recent call last): ... numpy.exceptions.AxisError: axis 0 is out of bounds for array of dimension 0 >>> arr = np.arange(9).reshape((3, 3)) >>> rng.permutation(arr, axis=1) array([[0, 2, 1], # random [3, 5, 4], [6, 8, 7]]) shuffle(x, axis=0) Modify an array or sequence in-place by shuffling its contents. The order of sub-arrays is changed but their contents remains the same. Parameters ---------- x : ndarray or MutableSequence The array, list or mutable sequence to be shuffled. axis : int, optional The axis which `x` is shuffled along. Default is 0. It is only supported on `ndarray` objects. Returns ------- None See Also -------- permuted permutation Notes ----- An important distinction between methods ``shuffle`` and ``permuted`` is how they both treat the ``axis`` parameter which can be found at :ref:`generator-handling-axis-parameter`. Examples -------- >>> rng = np.random.default_rng() >>> arr = np.arange(10) >>> arr array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> rng.shuffle(arr) >>> arr array([2, 0, 7, 5, 1, 4, 8, 9, 3, 6]) # random >>> arr = np.arange(9).reshape((3, 3)) >>> arr array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> rng.shuffle(arr) >>> arr array([[3, 4, 5], # random [6, 7, 8], [0, 1, 2]]) >>> arr = np.arange(9).reshape((3, 3)) >>> arr array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> rng.shuffle(arr, axis=1) >>> arr array([[2, 0, 1], # random [5, 3, 4], [8, 6, 7]]) permuted(x, axis=None, out=None) Randomly permute `x` along axis `axis`. Unlike `shuffle`, each slice along the given axis is shuffled independently of the others. Parameters ---------- x : array_like, at least one-dimensional Array to be shuffled. axis : int, optional Slices of `x` in this axis are shuffled. Each slice is shuffled independently of the others. If `axis` is None, the flattened array is shuffled. out : ndarray, optional If given, this is the destination of the shuffled array. If `out` is None, a shuffled copy of the array is returned. Returns ------- ndarray If `out` is None, a shuffled copy of `x` is returned. Otherwise, the shuffled array is stored in `out`, and `out` is returned See Also -------- shuffle permutation Notes ----- An important distinction between methods ``shuffle`` and ``permuted`` is how they both treat the ``axis`` parameter which can be found at :ref:`generator-handling-axis-parameter`. Examples -------- Create a `numpy.random.Generator` instance: >>> rng = np.random.default_rng() Create a test array: >>> x = np.arange(24).reshape(3, 8) >>> x array([[ 0, 1, 2, 3, 4, 5, 6, 7], [ 8, 9, 10, 11, 12, 13, 14, 15], [16, 17, 18, 19, 20, 21, 22, 23]]) Shuffle the rows of `x`: >>> y = rng.permuted(x, axis=1) >>> y array([[ 4, 3, 6, 7, 1, 2, 5, 0], # random [15, 10, 14, 9, 12, 11, 8, 13], [17, 16, 20, 21, 18, 22, 23, 19]]) `x` has not been modified: >>> x array([[ 0, 1, 2, 3, 4, 5, 6, 7], [ 8, 9, 10, 11, 12, 13, 14, 15], [16, 17, 18, 19, 20, 21, 22, 23]]) To shuffle the rows of `x` in-place, pass `x` as the `out` parameter: >>> y = rng.permuted(x, axis=1, out=x) >>> x array([[ 3, 0, 4, 7, 1, 6, 2, 5], # random [ 8, 14, 13, 9, 12, 11, 15, 10], [17, 18, 16, 22, 19, 23, 20, 21]]) Note that when the ``out`` parameter is given, the return value is ``out``: >>> y is x True dirichlet(alpha, size=None) Draw samples from the Dirichlet distribution. Draw `size` samples of dimension k from a Dirichlet distribution. A Dirichlet-distributed random variable can be seen as a multivariate generalization of a Beta distribution. The Dirichlet distribution is a conjugate prior of a multinomial distribution in Bayesian inference. Parameters ---------- alpha : sequence of floats, length k Parameter of the distribution (length ``k`` for sample of length ``k``). size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n)``, then ``m * n * k`` samples are drawn. Default is None, in which case a vector of length ``k`` is returned. Returns ------- samples : ndarray, The drawn samples, of shape ``(size, k)``. Raises ------ ValueError If any value in ``alpha`` is less than zero Notes ----- The Dirichlet distribution is a distribution over vectors :math:`x` that fulfil the conditions :math:`x_i>0` and :math:`\sum_{i=1}^k x_i = 1`. The probability density function :math:`p` of a Dirichlet-distributed random vector :math:`X` is proportional to .. math:: p(x) \propto \prod_{i=1}^{k}{x^{\alpha_i-1}_i}, where :math:`\alpha` is a vector containing the positive concentration parameters. The method uses the following property for computation: let :math:`Y` be a random vector which has components that follow a standard gamma distribution, then :math:`X = \frac{1}{\sum_{i=1}^k{Y_i}} Y` is Dirichlet-distributed References ---------- .. [1] David McKay, "Information Theory, Inference and Learning Algorithms," chapter 23, http://www.inference.org.uk/mackay/itila/ .. [2] Wikipedia, "Dirichlet distribution", https://en.wikipedia.org/wiki/Dirichlet_distribution Examples -------- Taking an example cited in Wikipedia, this distribution can be used if one wanted to cut strings (each of initial length 1.0) into K pieces with different lengths, where each piece had, on average, a designated average length, but allowing some variation in the relative sizes of the pieces. >>> s = np.random.default_rng().dirichlet((10, 5, 3), 20).transpose() >>> import matplotlib.pyplot as plt >>> plt.barh(range(20), s[0]) >>> plt.barh(range(20), s[1], left=s[0], color='g') >>> plt.barh(range(20), s[2], left=s[0]+s[1], color='r') >>> plt.title("Lengths of Strings") multivariate_hypergeometric(colors, nsample, size=None, method='marginals') Generate variates from a multivariate hypergeometric distribution. The multivariate hypergeometric distribution is a generalization of the hypergeometric distribution. Choose ``nsample`` items at random without replacement from a collection with ``N`` distinct types. ``N`` is the length of ``colors``, and the values in ``colors`` are the number of occurrences of that type in the collection. The total number of items in the collection is ``sum(colors)``. Each random variate generated by this function is a vector of length ``N`` holding the counts of the different types that occurred in the ``nsample`` items. The name ``colors`` comes from a common description of the distribution: it is the probability distribution of the number of marbles of each color selected without replacement from an urn containing marbles of different colors; ``colors[i]`` is the number of marbles in the urn with color ``i``. Parameters ---------- colors : sequence of integers The number of each type of item in the collection from which a sample is drawn. The values in ``colors`` must be nonnegative. To avoid loss of precision in the algorithm, ``sum(colors)`` must be less than ``10**9`` when `method` is "marginals". nsample : int The number of items selected. ``nsample`` must not be greater than ``sum(colors)``. size : int or tuple of ints, optional The number of variates to generate, either an integer or a tuple holding the shape of the array of variates. If the given size is, e.g., ``(k, m)``, then ``k * m`` variates are drawn, where one variate is a vector of length ``len(colors)``, and the return value has shape ``(k, m, len(colors))``. If `size` is an integer, the output has shape ``(size, len(colors))``. Default is None, in which case a single variate is returned as an array with shape ``(len(colors),)``. method : string, optional Specify the algorithm that is used to generate the variates. Must be 'count' or 'marginals' (the default). See the Notes for a description of the methods. Returns ------- variates : ndarray Array of variates drawn from the multivariate hypergeometric distribution. See Also -------- hypergeometric : Draw samples from the (univariate) hypergeometric distribution. Notes ----- The two methods do not return the same sequence of variates. The "count" algorithm is roughly equivalent to the following numpy code:: choices = np.repeat(np.arange(len(colors)), colors) selection = np.random.choice(choices, nsample, replace=False) variate = np.bincount(selection, minlength=len(colors)) The "count" algorithm uses a temporary array of integers with length ``sum(colors)``. The "marginals" algorithm generates a variate by using repeated calls to the univariate hypergeometric sampler. It is roughly equivalent to:: variate = np.zeros(len(colors), dtype=np.int64) # `remaining` is the cumulative sum of `colors` from the last # element to the first; e.g. if `colors` is [3, 1, 5], then # `remaining` is [9, 6, 5]. remaining = np.cumsum(colors[::-1])[::-1] for i in range(len(colors)-1): if nsample < 1: break variate[i] = hypergeometric(colors[i], remaining[i+1], nsample) nsample -= variate[i] variate[-1] = nsample The default method is "marginals". For some cases (e.g. when `colors` contains relatively small integers), the "count" method can be significantly faster than the "marginals" method. If performance of the algorithm is important, test the two methods with typical inputs to decide which works best. .. versionadded:: 1.18.0 Examples -------- >>> colors = [16, 8, 4] >>> seed = 4861946401452 >>> gen = np.random.Generator(np.random.PCG64(seed)) >>> gen.multivariate_hypergeometric(colors, 6) array([5, 0, 1]) >>> gen.multivariate_hypergeometric(colors, 6, size=3) array([[5, 0, 1], [2, 2, 2], [3, 3, 0]]) >>> gen.multivariate_hypergeometric(colors, 6, size=(2, 2)) array([[[3, 2, 1], [3, 2, 1]], [[4, 1, 1], [3, 2, 1]]]) multinomial(n, pvals, size=None) Draw samples from a multinomial distribution. The multinomial distribution is a multivariate generalization of the binomial distribution. Take an experiment with one of ``p`` possible outcomes. An example of such an experiment is throwing a dice, where the outcome can be 1 through 6. Each sample drawn from the distribution represents `n` such experiments. Its values, ``X_i = [X_0, X_1, ..., X_p]``, represent the number of times the outcome was ``i``. Parameters ---------- n : int or array-like of ints Number of experiments. pvals : array-like of floats Probabilities of each of the ``p`` different outcomes with shape ``(k0, k1, ..., kn, p)``. Each element ``pvals[i,j,...,:]`` must sum to 1 (however, the last element is always assumed to account for the remaining probability, as long as ``sum(pvals[..., :-1], axis=-1) <= 1.0``. Must have at least 1 dimension where pvals.shape[-1] > 0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn each with ``p`` elements. Default is None where the output size is determined by the broadcast shape of ``n`` and all by the final dimension of ``pvals``, which is denoted as ``b=(b0, b1, ..., bq)``. If size is not None, then it must be compatible with the broadcast shape ``b``. Specifically, size must have ``q`` or more elements and size[-(q-j):] must equal ``bj``. Returns ------- out : ndarray The drawn samples, of shape size, if provided. When size is provided, the output shape is size + (p,) If not specified, the shape is determined by the broadcast shape of ``n`` and ``pvals``, ``(b0, b1, ..., bq)`` augmented with the dimension of the multinomial, ``p``, so that that output shape is ``(b0, b1, ..., bq, p)``. Each entry ``out[i,j,...,:]`` is a ``p``-dimensional value drawn from the distribution. .. versionchanged:: 1.22.0 Added support for broadcasting `pvals` against `n` Examples -------- Throw a dice 20 times: >>> rng = np.random.default_rng() >>> rng.multinomial(20, [1/6.]*6, size=1) array([[4, 1, 7, 5, 2, 1]]) # random It landed 4 times on 1, once on 2, etc. Now, throw the dice 20 times, and 20 times again: >>> rng.multinomial(20, [1/6.]*6, size=2) array([[3, 4, 3, 3, 4, 3], [2, 4, 3, 4, 0, 7]]) # random For the first run, we threw 3 times 1, 4 times 2, etc. For the second, we threw 2 times 1, 4 times 2, etc. Now, do one experiment throwing the dice 10 time, and 10 times again, and another throwing the dice 20 times, and 20 times again: >>> rng.multinomial([[10], [20]], [1/6.]*6, size=(2, 2)) array([[[2, 4, 0, 1, 2, 1], [1, 3, 0, 3, 1, 2]], [[1, 4, 4, 4, 4, 3], [3, 3, 2, 5, 5, 2]]]) # random The first array shows the outcomes of throwing the dice 10 times, and the second shows the outcomes from throwing the dice 20 times. A loaded die is more likely to land on number 6: >>> rng.multinomial(100, [1/7.]*5 + [2/7.]) array([11, 16, 14, 17, 16, 26]) # random Simulate 10 throws of a 4-sided die and 20 throws of a 6-sided die >>> rng.multinomial([10, 20],[[1/4]*4 + [0]*2, [1/6]*6]) array([[2, 1, 4, 3, 0, 0], [3, 3, 3, 6, 1, 4]], dtype=int64) # random Generate categorical random variates from two categories where the first has 3 outcomes and the second has 2. >>> rng.multinomial(1, [[.1, .5, .4 ], [.3, .7, .0]]) array([[0, 0, 1], [0, 1, 0]], dtype=int64) # random ``argmax(axis=-1)`` is then used to return the categories. >>> pvals = [[.1, .5, .4 ], [.3, .7, .0]] >>> rvs = rng.multinomial(1, pvals, size=(4,2)) >>> rvs.argmax(axis=-1) array([[0, 1], [2, 0], [2, 1], [2, 0]], dtype=int64) # random The same output dimension can be produced using broadcasting. >>> rvs = rng.multinomial([[1]] * 4, pvals) >>> rvs.argmax(axis=-1) array([[0, 1], [2, 0], [2, 1], [2, 0]], dtype=int64) # random The probability inputs should be normalized. As an implementation detail, the value of the last entry is ignored and assumed to take up any leftover probability mass, but this should not be relied on. A biased coin which has twice as much weight on one side as on the other should be sampled like so: >>> rng.multinomial(100, [1.0 / 3, 2.0 / 3]) # RIGHT array([38, 62]) # random not like: >>> rng.multinomial(100, [1.0, 2.0]) # WRONG Traceback (most recent call last): ValueError: pvals < 0, pvals > 1 or pvals contains NaNs multivariate_normal(mean, cov, size=None, check_valid='warn', tol=1e-8, *, method='svd') Draw random samples from a multivariate normal distribution. The multivariate normal, multinormal or Gaussian distribution is a generalization of the one-dimensional normal distribution to higher dimensions. Such a distribution is specified by its mean and covariance matrix. These parameters are analogous to the mean (average or "center") and variance (the squared standard deviation, or "width") of the one-dimensional normal distribution. Parameters ---------- mean : 1-D array_like, of length N Mean of the N-dimensional distribution. cov : 2-D array_like, of shape (N, N) Covariance matrix of the distribution. It must be symmetric and positive-semidefinite for proper sampling. size : int or tuple of ints, optional Given a shape of, for example, ``(m,n,k)``, ``m*n*k`` samples are generated, and packed in an `m`-by-`n`-by-`k` arrangement. Because each sample is `N`-dimensional, the output shape is ``(m,n,k,N)``. If no shape is specified, a single (`N`-D) sample is returned. check_valid : { 'warn', 'raise', 'ignore' }, optional Behavior when the covariance matrix is not positive semidefinite. tol : float, optional Tolerance when checking the singular values in covariance matrix. cov is cast to double before the check. method : { 'svd', 'eigh', 'cholesky'}, optional The cov input is used to compute a factor matrix A such that ``A @ A.T = cov``. This argument is used to select the method used to compute the factor matrix A. The default method 'svd' is the slowest, while 'cholesky' is the fastest but less robust than the slowest method. The method `eigh` uses eigen decomposition to compute A and is faster than svd but slower than cholesky. .. versionadded:: 1.18.0 Returns ------- out : ndarray The drawn samples, of shape *size*, if that was provided. If not, the shape is ``(N,)``. In other words, each entry ``out[i,j,...,:]`` is an N-dimensional value drawn from the distribution. Notes ----- The mean is a coordinate in N-dimensional space, which represents the location where samples are most likely to be generated. This is analogous to the peak of the bell curve for the one-dimensional or univariate normal distribution. Covariance indicates the level to which two variables vary together. From the multivariate normal distribution, we draw N-dimensional samples, :math:`X = [x_1, x_2, ... x_N]`. The covariance matrix element :math:`C_{ij}` is the covariance of :math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance of :math:`x_i` (i.e. its "spread"). Instead of specifying the full covariance matrix, popular approximations include: - Spherical covariance (`cov` is a multiple of the identity matrix) - Diagonal covariance (`cov` has non-negative elements, and only on the diagonal) This geometrical property can be seen in two dimensions by plotting generated data-points: >>> mean = [0, 0] >>> cov = [[1, 0], [0, 100]] # diagonal covariance Diagonal covariance means that points are oriented along x or y-axis: >>> import matplotlib.pyplot as plt >>> x, y = np.random.default_rng().multivariate_normal(mean, cov, 5000).T >>> plt.plot(x, y, 'x') >>> plt.axis('equal') >>> plt.show() Note that the covariance matrix must be positive semidefinite (a.k.a. nonnegative-definite). Otherwise, the behavior of this method is undefined and backwards compatibility is not guaranteed. This function internally uses linear algebra routines, and thus results may not be identical (even up to precision) across architectures, OSes, or even builds. For example, this is likely if ``cov`` has multiple equal singular values and ``method`` is ``'svd'`` (default). In this case, ``method='cholesky'`` may be more robust. References ---------- .. [1] Papoulis, A., "Probability, Random Variables, and Stochastic Processes," 3rd ed., New York: McGraw-Hill, 1991. .. [2] Duda, R. O., Hart, P. E., and Stork, D. G., "Pattern Classification," 2nd ed., New York: Wiley, 2001. Examples -------- >>> mean = (1, 2) >>> cov = [[1, 0], [0, 1]] >>> rng = np.random.default_rng() >>> x = rng.multivariate_normal(mean, cov, (3, 3)) >>> x.shape (3, 3, 2) We can use a different method other than the default to factorize cov: >>> y = rng.multivariate_normal(mean, cov, (3, 3), method='cholesky') >>> y.shape (3, 3, 2) Here we generate 800 samples from the bivariate normal distribution with mean [0, 0] and covariance matrix [[6, -3], [-3, 3.5]]. The expected variances of the first and second components of the sample are 6 and 3.5, respectively, and the expected correlation coefficient is -3/sqrt(6*3.5) ≈ -0.65465. >>> cov = np.array([[6, -3], [-3, 3.5]]) >>> pts = rng.multivariate_normal([0, 0], cov, size=800) Check that the mean, covariance, and correlation coefficient of the sample are close to the expected values: >>> pts.mean(axis=0) array([ 0.0326911 , -0.01280782]) # may vary >>> np.cov(pts.T) array([[ 5.96202397, -2.85602287], [-2.85602287, 3.47613949]]) # may vary >>> np.corrcoef(pts.T)[0, 1] -0.6273591314603949 # may vary We can visualize this data with a scatter plot. The orientation of the point cloud illustrates the negative correlation of the components of this sample. >>> import matplotlib.pyplot as plt >>> plt.plot(pts[:, 0], pts[:, 1], '.', alpha=0.5) >>> plt.axis('equal') >>> plt.grid() >>> plt.show() logseries(p, size=None) Draw samples from a logarithmic series distribution. Samples are drawn from a log series distribution with specified shape parameter, 0 <= ``p`` < 1. Parameters ---------- p : float or array_like of floats Shape parameter for the distribution. Must be in the range [0, 1). size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``p`` is a scalar. Otherwise, ``np.array(p).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized logarithmic series distribution. See Also -------- scipy.stats.logser : probability density function, distribution or cumulative density function, etc. Notes ----- The probability mass function for the Log Series distribution is .. math:: P(k) = \frac{-p^k}{k \ln(1-p)}, where p = probability. The log series distribution is frequently used to represent species richness and occurrence, first proposed by Fisher, Corbet, and Williams in 1943 [2]. It may also be used to model the numbers of occupants seen in cars [3]. References ---------- .. [1] Buzas, Martin A.; Culver, Stephen J., Understanding regional species diversity through the log series distribution of occurrences: BIODIVERSITY RESEARCH Diversity & Distributions, Volume 5, Number 5, September 1999 , pp. 187-195(9). .. [2] Fisher, R.A,, A.S. Corbet, and C.B. Williams. 1943. The relation between the number of species and the number of individuals in a random sample of an animal population. Journal of Animal Ecology, 12:42-58. .. [3] D. J. Hand, F. Daly, D. Lunn, E. Ostrowski, A Handbook of Small Data Sets, CRC Press, 1994. .. [4] Wikipedia, "Logarithmic distribution", https://en.wikipedia.org/wiki/Logarithmic_distribution Examples -------- Draw samples from the distribution: >>> a = .6 >>> s = np.random.default_rng().logseries(a, 10000) >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s) # plot against distribution >>> def logseries(k, p): ... return -p**k/(k*np.log(1-p)) >>> plt.plot(bins, logseries(bins, a) * count.max()/ ... logseries(bins, a).max(), 'r') >>> plt.show() hypergeometric(ngood, nbad, nsample, size=None) Draw samples from a Hypergeometric distribution. Samples are drawn from a hypergeometric distribution with specified parameters, `ngood` (ways to make a good selection), `nbad` (ways to make a bad selection), and `nsample` (number of items sampled, which is less than or equal to the sum ``ngood + nbad``). Parameters ---------- ngood : int or array_like of ints Number of ways to make a good selection. Must be nonnegative and less than 10**9. nbad : int or array_like of ints Number of ways to make a bad selection. Must be nonnegative and less than 10**9. nsample : int or array_like of ints Number of items sampled. Must be nonnegative and less than ``ngood + nbad``. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if `ngood`, `nbad`, and `nsample` are all scalars. Otherwise, ``np.broadcast(ngood, nbad, nsample).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized hypergeometric distribution. Each sample is the number of good items within a randomly selected subset of size `nsample` taken from a set of `ngood` good items and `nbad` bad items. See Also -------- multivariate_hypergeometric : Draw samples from the multivariate hypergeometric distribution. scipy.stats.hypergeom : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Hypergeometric distribution is .. math:: P(x) = \frac{\binom{g}{x}\binom{b}{n-x}}{\binom{g+b}{n}}, where :math:`0 \le x \le n` and :math:`n-b \le x \le g` for P(x) the probability of ``x`` good results in the drawn sample, g = `ngood`, b = `nbad`, and n = `nsample`. Consider an urn with black and white marbles in it, `ngood` of them are black and `nbad` are white. If you draw `nsample` balls without replacement, then the hypergeometric distribution describes the distribution of black balls in the drawn sample. Note that this distribution is very similar to the binomial distribution, except that in this case, samples are drawn without replacement, whereas in the Binomial case samples are drawn with replacement (or the sample space is infinite). As the sample space becomes large, this distribution approaches the binomial. The arguments `ngood` and `nbad` each must be less than `10**9`. For extremely large arguments, the algorithm that is used to compute the samples [4]_ breaks down because of loss of precision in floating point calculations. For such large values, if `nsample` is not also large, the distribution can be approximated with the binomial distribution, `binomial(n=nsample, p=ngood/(ngood + nbad))`. References ---------- .. [1] Lentner, Marvin, "Elementary Applied Statistics", Bogden and Quigley, 1972. .. [2] Weisstein, Eric W. "Hypergeometric Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/HypergeometricDistribution.html .. [3] Wikipedia, "Hypergeometric distribution", https://en.wikipedia.org/wiki/Hypergeometric_distribution .. [4] Stadlober, Ernst, "The ratio of uniforms approach for generating discrete random variates", Journal of Computational and Applied Mathematics, 31, pp. 181-189 (1990). Examples -------- Draw samples from the distribution: >>> rng = np.random.default_rng() >>> ngood, nbad, nsamp = 100, 2, 10 # number of good, number of bad, and number of samples >>> s = rng.hypergeometric(ngood, nbad, nsamp, 1000) >>> from matplotlib.pyplot import hist >>> hist(s) # note that it is very unlikely to grab both bad items Suppose you have an urn with 15 white and 15 black marbles. If you pull 15 marbles at random, how likely is it that 12 or more of them are one color? >>> s = rng.hypergeometric(15, 15, 15, 100000) >>> sum(s>=12)/100000. + sum(s<=3)/100000. # answer = 0.003 ... pretty unlikely! geometric(p, size=None) Draw samples from the geometric distribution. Bernoulli trials are experiments with one of two outcomes: success or failure (an example of such an experiment is flipping a coin). The geometric distribution models the number of trials that must be run in order to achieve success. It is therefore supported on the positive integers, ``k = 1, 2, ...``. The probability mass function of the geometric distribution is .. math:: f(k) = (1 - p)^{k - 1} p where `p` is the probability of success of an individual trial. Parameters ---------- p : float or array_like of floats The probability of success of an individual trial. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``p`` is a scalar. Otherwise, ``np.array(p).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized geometric distribution. Examples -------- Draw ten thousand values from the geometric distribution, with the probability of an individual success equal to 0.35: >>> z = np.random.default_rng().geometric(p=0.35, size=10000) How many trials succeeded after a single run? >>> (z == 1).sum() / 10000. 0.34889999999999999 # random zipf(a, size=None) Draw samples from a Zipf distribution. Samples are drawn from a Zipf distribution with specified parameter `a` > 1. The Zipf distribution (also known as the zeta distribution) is a discrete probability distribution that satisfies Zipf's law: the frequency of an item is inversely proportional to its rank in a frequency table. Parameters ---------- a : float or array_like of floats Distribution parameter. Must be greater than 1. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``a`` is a scalar. Otherwise, ``np.array(a).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Zipf distribution. See Also -------- scipy.stats.zipf : probability density function, distribution, or cumulative density function, etc. Notes ----- The probability density for the Zipf distribution is .. math:: p(k) = \frac{k^{-a}}{\zeta(a)}, for integers :math:`k \geq 1`, where :math:`\zeta` is the Riemann Zeta function. It is named for the American linguist George Kingsley Zipf, who noted that the frequency of any word in a sample of a language is inversely proportional to its rank in the frequency table. References ---------- .. [1] Zipf, G. K., "Selected Studies of the Principle of Relative Frequency in Language," Cambridge, MA: Harvard Univ. Press, 1932. Examples -------- Draw samples from the distribution: >>> a = 4.0 >>> n = 20000 >>> s = np.random.default_rng().zipf(a, size=n) Display the histogram of the samples, along with the expected histogram based on the probability density function: >>> import matplotlib.pyplot as plt >>> from scipy.special import zeta # doctest: +SKIP `bincount` provides a fast histogram for small integers. >>> count = np.bincount(s) >>> k = np.arange(1, s.max() + 1) >>> plt.bar(k, count[1:], alpha=0.5, label='sample count') >>> plt.plot(k, n*(k**-a)/zeta(a), 'k.-', alpha=0.5, ... label='expected count') # doctest: +SKIP >>> plt.semilogy() >>> plt.grid(alpha=0.4) >>> plt.legend() >>> plt.title(f'Zipf sample, a={a}, size={n}') >>> plt.show() poisson(lam=1.0, size=None) Draw samples from a Poisson distribution. The Poisson distribution is the limit of the binomial distribution for large N. Parameters ---------- lam : float or array_like of floats Expected number of events occurring in a fixed-time interval, must be >= 0. A sequence must be broadcastable over the requested size. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``lam`` is a scalar. Otherwise, ``np.array(lam).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Poisson distribution. Notes ----- The Poisson distribution .. math:: f(k; \lambda)=\frac{\lambda^k e^{-\lambda}}{k!} For events with an expected separation :math:`\lambda` the Poisson distribution :math:`f(k; \lambda)` describes the probability of :math:`k` events occurring within the observed interval :math:`\lambda`. Because the output is limited to the range of the C int64 type, a ValueError is raised when `lam` is within 10 sigma of the maximum representable value. References ---------- .. [1] Weisstein, Eric W. "Poisson Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PoissonDistribution.html .. [2] Wikipedia, "Poisson distribution", https://en.wikipedia.org/wiki/Poisson_distribution Examples -------- Draw samples from the distribution: >>> import numpy as np >>> rng = np.random.default_rng() >>> s = rng.poisson(5, 10000) Display histogram of the sample: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 14, density=True) >>> plt.show() Draw each 100 values for lambda 100 and 500: >>> s = rng.poisson(lam=(100., 500.), size=(100, 2)) negative_binomial(n, p, size=None) Draw samples from a negative binomial distribution. Samples are drawn from a negative binomial distribution with specified parameters, `n` successes and `p` probability of success where `n` is > 0 and `p` is in the interval (0, 1]. Parameters ---------- n : float or array_like of floats Parameter of the distribution, > 0. p : float or array_like of floats Parameter of the distribution. Must satisfy 0 < p <= 1. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``n`` and ``p`` are both scalars. Otherwise, ``np.broadcast(n, p).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized negative binomial distribution, where each sample is equal to N, the number of failures that occurred before a total of n successes was reached. Notes ----- The probability mass function of the negative binomial distribution is .. math:: P(N;n,p) = \frac{\Gamma(N+n)}{N!\Gamma(n)}p^{n}(1-p)^{N}, where :math:`n` is the number of successes, :math:`p` is the probability of success, :math:`N+n` is the number of trials, and :math:`\Gamma` is the gamma function. When :math:`n` is an integer, :math:`\frac{\Gamma(N+n)}{N!\Gamma(n)} = \binom{N+n-1}{N}`, which is the more common form of this term in the pmf. The negative binomial distribution gives the probability of N failures given n successes, with a success on the last trial. If one throws a die repeatedly until the third time a "1" appears, then the probability distribution of the number of non-"1"s that appear before the third "1" is a negative binomial distribution. Because this method internally calls ``Generator.poisson`` with an intermediate random value, a ValueError is raised when the choice of :math:`n` and :math:`p` would result in the mean + 10 sigma of the sampled intermediate distribution exceeding the max acceptable value of the ``Generator.poisson`` method. This happens when :math:`p` is too low (a lot of failures happen for every success) and :math:`n` is too big ( a lot of successes are allowed). Therefore, the :math:`n` and :math:`p` values must satisfy the constraint: .. math:: n\frac{1-p}{p}+10n\sqrt{n}\frac{1-p}{p}<2^{63}-1-10\sqrt{2^{63}-1}, Where the left side of the equation is the derived mean + 10 sigma of a sample from the gamma distribution internally used as the :math:`lam` parameter of a poisson sample, and the right side of the equation is the constraint for maximum value of :math:`lam` in ``Generator.poisson``. References ---------- .. [1] Weisstein, Eric W. "Negative Binomial Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NegativeBinomialDistribution.html .. [2] Wikipedia, "Negative binomial distribution", https://en.wikipedia.org/wiki/Negative_binomial_distribution Examples -------- Draw samples from the distribution: A real world example. A company drills wild-cat oil exploration wells, each with an estimated probability of success of 0.1. What is the probability of having one success for each successive well, that is what is the probability of a single success after drilling 5 wells, after 6 wells, etc.? >>> s = np.random.default_rng().negative_binomial(1, 0.1, 100000) >>> for i in range(1, 11): # doctest: +SKIP ... probability = sum(s>> rng = np.random.default_rng() >>> n, p = 10, .5 # number of trials, probability of each trial >>> s = rng.binomial(n, p, 1000) # result of flipping a coin 10 times, tested 1000 times. A real world example. A company drills 9 wild-cat oil exploration wells, each with an estimated probability of success of 0.1. All nine wells fail. What is the probability of that happening? Let's do 20,000 trials of the model, and count the number that generate zero positive results. >>> sum(rng.binomial(9, 0.1, 20000) == 0)/20000. # answer = 0.38885, or 39%. triangular(left, mode, right, size=None) Draw samples from the triangular distribution over the interval ``[left, right]``. The triangular distribution is a continuous probability distribution with lower limit left, peak at mode, and upper limit right. Unlike the other distributions, these parameters directly define the shape of the pdf. Parameters ---------- left : float or array_like of floats Lower limit. mode : float or array_like of floats The value where the peak of the distribution occurs. The value must fulfill the condition ``left <= mode <= right``. right : float or array_like of floats Upper limit, must be larger than `left`. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``left``, ``mode``, and ``right`` are all scalars. Otherwise, ``np.broadcast(left, mode, right).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized triangular distribution. Notes ----- The probability density function for the triangular distribution is .. math:: P(x;l, m, r) = \begin{cases} \frac{2(x-l)}{(r-l)(m-l)}& \text{for $l \leq x \leq m$},\\ \frac{2(r-x)}{(r-l)(r-m)}& \text{for $m \leq x \leq r$},\\ 0& \text{otherwise}. \end{cases} The triangular distribution is often used in ill-defined problems where the underlying distribution is not known, but some knowledge of the limits and mode exists. Often it is used in simulations. References ---------- .. [1] Wikipedia, "Triangular distribution" https://en.wikipedia.org/wiki/Triangular_distribution Examples -------- Draw values from the distribution and plot the histogram: >>> import matplotlib.pyplot as plt >>> h = plt.hist(np.random.default_rng().triangular(-3, 0, 8, 100000), bins=200, ... density=True) >>> plt.show() wald(mean, scale, size=None) Draw samples from a Wald, or inverse Gaussian, distribution. As the scale approaches infinity, the distribution becomes more like a Gaussian. Some references claim that the Wald is an inverse Gaussian with mean equal to 1, but this is by no means universal. The inverse Gaussian distribution was first studied in relationship to Brownian motion. In 1956 M.C.K. Tweedie used the name inverse Gaussian because there is an inverse relationship between the time to cover a unit distance and distance covered in unit time. Parameters ---------- mean : float or array_like of floats Distribution mean, must be > 0. scale : float or array_like of floats Scale parameter, must be > 0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``mean`` and ``scale`` are both scalars. Otherwise, ``np.broadcast(mean, scale).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Wald distribution. Notes ----- The probability density function for the Wald distribution is .. math:: P(x;mean,scale) = \sqrt{\frac{scale}{2\pi x^3}}e^ \frac{-scale(x-mean)^2}{2\cdotp mean^2x} As noted above the inverse Gaussian distribution first arise from attempts to model Brownian motion. It is also a competitor to the Weibull for use in reliability modeling and modeling stock returns and interest rate processes. References ---------- .. [1] Brighton Webs Ltd., Wald Distribution, https://web.archive.org/web/20090423014010/http://www.brighton-webs.co.uk:80/distributions/wald.asp .. [2] Chhikara, Raj S., and Folks, J. Leroy, "The Inverse Gaussian Distribution: Theory : Methodology, and Applications", CRC Press, 1988. .. [3] Wikipedia, "Inverse Gaussian distribution" https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution Examples -------- Draw values from the distribution and plot the histogram: >>> import matplotlib.pyplot as plt >>> h = plt.hist(np.random.default_rng().wald(3, 2, 100000), bins=200, density=True) >>> plt.show() rayleigh(scale=1.0, size=None) Draw samples from a Rayleigh distribution. The :math:`\chi` and Weibull distributions are generalizations of the Rayleigh. Parameters ---------- scale : float or array_like of floats, optional Scale, also equals the mode. Must be non-negative. Default is 1. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``scale`` is a scalar. Otherwise, ``np.array(scale).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Rayleigh distribution. Notes ----- The probability density function for the Rayleigh distribution is .. math:: P(x;scale) = \frac{x}{scale^2}e^{\frac{-x^2}{2 \cdotp scale^2}} The Rayleigh distribution would arise, for example, if the East and North components of the wind velocity had identical zero-mean Gaussian distributions. Then the wind speed would have a Rayleigh distribution. References ---------- .. [1] Brighton Webs Ltd., "Rayleigh Distribution," https://web.archive.org/web/20090514091424/http://brighton-webs.co.uk:80/distributions/rayleigh.asp .. [2] Wikipedia, "Rayleigh distribution" https://en.wikipedia.org/wiki/Rayleigh_distribution Examples -------- Draw values from the distribution and plot the histogram >>> from matplotlib.pyplot import hist >>> rng = np.random.default_rng() >>> values = hist(rng.rayleigh(3, 100000), bins=200, density=True) Wave heights tend to follow a Rayleigh distribution. If the mean wave height is 1 meter, what fraction of waves are likely to be larger than 3 meters? >>> meanvalue = 1 >>> modevalue = np.sqrt(2 / np.pi) * meanvalue >>> s = rng.rayleigh(modevalue, 1000000) The percentage of waves larger than 3 meters is: >>> 100.*sum(s>3)/1000000. 0.087300000000000003 # random lognormal(mean=0.0, sigma=1.0, size=None) Draw samples from a log-normal distribution. Draw samples from a log-normal distribution with specified mean, standard deviation, and array shape. Note that the mean and standard deviation are not the values for the distribution itself, but of the underlying normal distribution it is derived from. Parameters ---------- mean : float or array_like of floats, optional Mean value of the underlying normal distribution. Default is 0. sigma : float or array_like of floats, optional Standard deviation of the underlying normal distribution. Must be non-negative. Default is 1. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``mean`` and ``sigma`` are both scalars. Otherwise, ``np.broadcast(mean, sigma).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized log-normal distribution. See Also -------- scipy.stats.lognorm : probability density function, distribution, cumulative density function, etc. Notes ----- A variable `x` has a log-normal distribution if `log(x)` is normally distributed. The probability density function for the log-normal distribution is: .. math:: p(x) = \frac{1}{\sigma x \sqrt{2\pi}} e^{(-\frac{(ln(x)-\mu)^2}{2\sigma^2})} where :math:`\mu` is the mean and :math:`\sigma` is the standard deviation of the normally distributed logarithm of the variable. A log-normal distribution results if a random variable is the *product* of a large number of independent, identically-distributed variables in the same way that a normal distribution results if the variable is the *sum* of a large number of independent, identically-distributed variables. References ---------- .. [1] Limpert, E., Stahel, W. A., and Abbt, M., "Log-normal Distributions across the Sciences: Keys and Clues," BioScience, Vol. 51, No. 5, May, 2001. https://stat.ethz.ch/~stahel/lognormal/bioscience.pdf .. [2] Reiss, R.D. and Thomas, M., "Statistical Analysis of Extreme Values," Basel: Birkhauser Verlag, 2001, pp. 31-32. Examples -------- Draw samples from the distribution: >>> rng = np.random.default_rng() >>> mu, sigma = 3., 1. # mean and standard deviation >>> s = rng.lognormal(mu, sigma, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 100, density=True, align='mid') >>> x = np.linspace(min(bins), max(bins), 10000) >>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2)) ... / (x * sigma * np.sqrt(2 * np.pi))) >>> plt.plot(x, pdf, linewidth=2, color='r') >>> plt.axis('tight') >>> plt.show() Demonstrate that taking the products of random samples from a uniform distribution can be fit well by a log-normal probability density function. >>> # Generate a thousand samples: each is the product of 100 random >>> # values, drawn from a normal distribution. >>> rng = rng >>> b = [] >>> for i in range(1000): ... a = 10. + rng.standard_normal(100) ... b.append(np.prod(a)) >>> b = np.array(b) / np.min(b) # scale values to be positive >>> count, bins, ignored = plt.hist(b, 100, density=True, align='mid') >>> sigma = np.std(np.log(b)) >>> mu = np.mean(np.log(b)) >>> x = np.linspace(min(bins), max(bins), 10000) >>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2)) ... / (x * sigma * np.sqrt(2 * np.pi))) >>> plt.plot(x, pdf, color='r', linewidth=2) >>> plt.show() logistic(loc=0.0, scale=1.0, size=None) Draw samples from a logistic distribution. Samples are drawn from a logistic distribution with specified parameters, loc (location or mean, also median), and scale (>0). Parameters ---------- loc : float or array_like of floats, optional Parameter of the distribution. Default is 0. scale : float or array_like of floats, optional Parameter of the distribution. Must be non-negative. Default is 1. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``loc`` and ``scale`` are both scalars. Otherwise, ``np.broadcast(loc, scale).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized logistic distribution. See Also -------- scipy.stats.logistic : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Logistic distribution is .. math:: P(x) = P(x) = \frac{e^{-(x-\mu)/s}}{s(1+e^{-(x-\mu)/s})^2}, where :math:`\mu` = location and :math:`s` = scale. The Logistic distribution is used in Extreme Value problems where it can act as a mixture of Gumbel distributions, in Epidemiology, and by the World Chess Federation (FIDE) where it is used in the Elo ranking system, assuming the performance of each player is a logistically distributed random variable. References ---------- .. [1] Reiss, R.-D. and Thomas M. (2001), "Statistical Analysis of Extreme Values, from Insurance, Finance, Hydrology and Other Fields," Birkhauser Verlag, Basel, pp 132-133. .. [2] Weisstein, Eric W. "Logistic Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LogisticDistribution.html .. [3] Wikipedia, "Logistic-distribution", https://en.wikipedia.org/wiki/Logistic_distribution Examples -------- Draw samples from the distribution: >>> loc, scale = 10, 1 >>> s = np.random.default_rng().logistic(loc, scale, 10000) >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, bins=50) # plot against distribution >>> def logist(x, loc, scale): ... return np.exp((loc-x)/scale)/(scale*(1+np.exp((loc-x)/scale))**2) >>> lgst_val = logist(bins, loc, scale) >>> plt.plot(bins, lgst_val * count.max() / lgst_val.max()) >>> plt.show() gumbel(loc=0.0, scale=1.0, size=None) Draw samples from a Gumbel distribution. Draw samples from a Gumbel distribution with specified location and scale. For more information on the Gumbel distribution, see Notes and References below. Parameters ---------- loc : float or array_like of floats, optional The location of the mode of the distribution. Default is 0. scale : float or array_like of floats, optional The scale parameter of the distribution. Default is 1. Must be non- negative. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``loc`` and ``scale`` are both scalars. Otherwise, ``np.broadcast(loc, scale).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Gumbel distribution. See Also -------- scipy.stats.gumbel_l scipy.stats.gumbel_r scipy.stats.genextreme weibull Notes ----- The Gumbel (or Smallest Extreme Value (SEV) or the Smallest Extreme Value Type I) distribution is one of a class of Generalized Extreme Value (GEV) distributions used in modeling extreme value problems. The Gumbel is a special case of the Extreme Value Type I distribution for maximums from distributions with "exponential-like" tails. The probability density for the Gumbel distribution is .. math:: p(x) = \frac{e^{-(x - \mu)/ \beta}}{\beta} e^{ -e^{-(x - \mu)/ \beta}}, where :math:`\mu` is the mode, a location parameter, and :math:`\beta` is the scale parameter. The Gumbel (named for German mathematician Emil Julius Gumbel) was used very early in the hydrology literature, for modeling the occurrence of flood events. It is also used for modeling maximum wind speed and rainfall rates. It is a "fat-tailed" distribution - the probability of an event in the tail of the distribution is larger than if one used a Gaussian, hence the surprisingly frequent occurrence of 100-year floods. Floods were initially modeled as a Gaussian process, which underestimated the frequency of extreme events. It is one of a class of extreme value distributions, the Generalized Extreme Value (GEV) distributions, which also includes the Weibull and Frechet. The function has a mean of :math:`\mu + 0.57721\beta` and a variance of :math:`\frac{\pi^2}{6}\beta^2`. References ---------- .. [1] Gumbel, E. J., "Statistics of Extremes," New York: Columbia University Press, 1958. .. [2] Reiss, R.-D. and Thomas, M., "Statistical Analysis of Extreme Values from Insurance, Finance, Hydrology and Other Fields," Basel: Birkhauser Verlag, 2001. Examples -------- Draw samples from the distribution: >>> rng = np.random.default_rng() >>> mu, beta = 0, 0.1 # location and scale >>> s = rng.gumbel(mu, beta, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 30, density=True) >>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta) ... * np.exp( -np.exp( -(bins - mu) /beta) ), ... linewidth=2, color='r') >>> plt.show() Show how an extreme value distribution can arise from a Gaussian process and compare to a Gaussian: >>> means = [] >>> maxima = [] >>> for i in range(0,1000) : ... a = rng.normal(mu, beta, 1000) ... means.append(a.mean()) ... maxima.append(a.max()) >>> count, bins, ignored = plt.hist(maxima, 30, density=True) >>> beta = np.std(maxima) * np.sqrt(6) / np.pi >>> mu = np.mean(maxima) - 0.57721*beta >>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta) ... * np.exp(-np.exp(-(bins - mu)/beta)), ... linewidth=2, color='r') >>> plt.plot(bins, 1/(beta * np.sqrt(2 * np.pi)) ... * np.exp(-(bins - mu)**2 / (2 * beta**2)), ... linewidth=2, color='g') >>> plt.show() laplace(loc=0.0, scale=1.0, size=None) Draw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay). The Laplace distribution is similar to the Gaussian/normal distribution, but is sharper at the peak and has fatter tails. It represents the difference between two independent, identically distributed exponential random variables. Parameters ---------- loc : float or array_like of floats, optional The position, :math:`\mu`, of the distribution peak. Default is 0. scale : float or array_like of floats, optional :math:`\lambda`, the exponential decay. Default is 1. Must be non- negative. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``loc`` and ``scale`` are both scalars. Otherwise, ``np.broadcast(loc, scale).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Laplace distribution. Notes ----- It has the probability density function .. math:: f(x; \mu, \lambda) = \frac{1}{2\lambda} \exp\left(-\frac{|x - \mu|}{\lambda}\right). The first law of Laplace, from 1774, states that the frequency of an error can be expressed as an exponential function of the absolute magnitude of the error, which leads to the Laplace distribution. For many problems in economics and health sciences, this distribution seems to model the data better than the standard Gaussian distribution. References ---------- .. [1] Abramowitz, M. and Stegun, I. A. (Eds.). "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing," New York: Dover, 1972. .. [2] Kotz, Samuel, et. al. "The Laplace Distribution and Generalizations, " Birkhauser, 2001. .. [3] Weisstein, Eric W. "Laplace Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LaplaceDistribution.html .. [4] Wikipedia, "Laplace distribution", https://en.wikipedia.org/wiki/Laplace_distribution Examples -------- Draw samples from the distribution >>> loc, scale = 0., 1. >>> s = np.random.default_rng().laplace(loc, scale, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 30, density=True) >>> x = np.arange(-8., 8., .01) >>> pdf = np.exp(-abs(x-loc)/scale)/(2.*scale) >>> plt.plot(x, pdf) Plot Gaussian for comparison: >>> g = (1/(scale * np.sqrt(2 * np.pi)) * ... np.exp(-(x - loc)**2 / (2 * scale**2))) >>> plt.plot(x,g) power(a, size=None) Draws samples in [0, 1] from a power distribution with positive exponent a - 1. Also known as the power function distribution. Parameters ---------- a : float or array_like of floats Parameter of the distribution. Must be non-negative. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``a`` is a scalar. Otherwise, ``np.array(a).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized power distribution. Raises ------ ValueError If a <= 0. Notes ----- The probability density function is .. math:: P(x; a) = ax^{a-1}, 0 \le x \le 1, a>0. The power function distribution is just the inverse of the Pareto distribution. It may also be seen as a special case of the Beta distribution. It is used, for example, in modeling the over-reporting of insurance claims. References ---------- .. [1] Christian Kleiber, Samuel Kotz, "Statistical size distributions in economics and actuarial sciences", Wiley, 2003. .. [2] Heckert, N. A. and Filliben, James J. "NIST Handbook 148: Dataplot Reference Manual, Volume 2: Let Subcommands and Library Functions", National Institute of Standards and Technology Handbook Series, June 2003. https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/powpdf.pdf Examples -------- Draw samples from the distribution: >>> rng = np.random.default_rng() >>> a = 5. # shape >>> samples = 1000 >>> s = rng.power(a, samples) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, bins=30) >>> x = np.linspace(0, 1, 100) >>> y = a*x**(a-1.) >>> normed_y = samples*np.diff(bins)[0]*y >>> plt.plot(x, normed_y) >>> plt.show() Compare the power function distribution to the inverse of the Pareto. >>> from scipy import stats # doctest: +SKIP >>> rvs = rng.power(5, 1000000) >>> rvsp = rng.pareto(5, 1000000) >>> xx = np.linspace(0,1,100) >>> powpdf = stats.powerlaw.pdf(xx,5) # doctest: +SKIP >>> plt.figure() >>> plt.hist(rvs, bins=50, density=True) >>> plt.plot(xx,powpdf,'r-') # doctest: +SKIP >>> plt.title('power(5)') >>> plt.figure() >>> plt.hist(1./(1.+rvsp), bins=50, density=True) >>> plt.plot(xx,powpdf,'r-') # doctest: +SKIP >>> plt.title('inverse of 1 + Generator.pareto(5)') >>> plt.figure() >>> plt.hist(1./(1.+rvsp), bins=50, density=True) >>> plt.plot(xx,powpdf,'r-') # doctest: +SKIP >>> plt.title('inverse of stats.pareto(5)') weibull(a, size=None) Draw samples from a Weibull distribution. Draw samples from a 1-parameter Weibull distribution with the given shape parameter `a`. .. math:: X = (-ln(U))^{1/a} Here, U is drawn from the uniform distribution over (0,1]. The more common 2-parameter Weibull, including a scale parameter :math:`\lambda` is just :math:`X = \lambda(-ln(U))^{1/a}`. Parameters ---------- a : float or array_like of floats Shape parameter of the distribution. Must be nonnegative. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``a`` is a scalar. Otherwise, ``np.array(a).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Weibull distribution. See Also -------- scipy.stats.weibull_max scipy.stats.weibull_min scipy.stats.genextreme gumbel Notes ----- The Weibull (or Type III asymptotic extreme value distribution for smallest values, SEV Type III, or Rosin-Rammler distribution) is one of a class of Generalized Extreme Value (GEV) distributions used in modeling extreme value problems. This class includes the Gumbel and Frechet distributions. The probability density for the Weibull distribution is .. math:: p(x) = \frac{a} {\lambda}(\frac{x}{\lambda})^{a-1}e^{-(x/\lambda)^a}, where :math:`a` is the shape and :math:`\lambda` the scale. The function has its peak (the mode) at :math:`\lambda(\frac{a-1}{a})^{1/a}`. When ``a = 1``, the Weibull distribution reduces to the exponential distribution. References ---------- .. [1] Waloddi Weibull, Royal Technical University, Stockholm, 1939 "A Statistical Theory Of The Strength Of Materials", Ingeniorsvetenskapsakademiens Handlingar Nr 151, 1939, Generalstabens Litografiska Anstalts Forlag, Stockholm. .. [2] Waloddi Weibull, "A Statistical Distribution Function of Wide Applicability", Journal Of Applied Mechanics ASME Paper 1951. .. [3] Wikipedia, "Weibull distribution", https://en.wikipedia.org/wiki/Weibull_distribution Examples -------- Draw samples from the distribution: >>> rng = np.random.default_rng() >>> a = 5. # shape >>> s = rng.weibull(a, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> x = np.arange(1,100.)/50. >>> def weib(x,n,a): ... return (a / n) * (x / n)**(a - 1) * np.exp(-(x / n)**a) >>> count, bins, ignored = plt.hist(rng.weibull(5.,1000)) >>> x = np.arange(1,100.)/50. >>> scale = count.max()/weib(x, 1., 5.).max() >>> plt.plot(x, weib(x, 1., 5.)*scale) >>> plt.show() pareto(a, size=None) Draw samples from a Pareto II or Lomax distribution with specified shape. The Lomax or Pareto II distribution is a shifted Pareto distribution. The classical Pareto distribution can be obtained from the Lomax distribution by adding 1 and multiplying by the scale parameter ``m`` (see Notes). The smallest value of the Lomax distribution is zero while for the classical Pareto distribution it is ``mu``, where the standard Pareto distribution has location ``mu = 1``. Lomax can also be considered as a simplified version of the Generalized Pareto distribution (available in SciPy), with the scale set to one and the location set to zero. The Pareto distribution must be greater than zero, and is unbounded above. It is also known as the "80-20 rule". In this distribution, 80 percent of the weights are in the lowest 20 percent of the range, while the other 20 percent fill the remaining 80 percent of the range. Parameters ---------- a : float or array_like of floats Shape of the distribution. Must be positive. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``a`` is a scalar. Otherwise, ``np.array(a).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Pareto distribution. See Also -------- scipy.stats.lomax : probability density function, distribution or cumulative density function, etc. scipy.stats.genpareto : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Pareto distribution is .. math:: p(x) = \frac{am^a}{x^{a+1}} where :math:`a` is the shape and :math:`m` the scale. The Pareto distribution, named after the Italian economist Vilfredo Pareto, is a power law probability distribution useful in many real world problems. Outside the field of economics it is generally referred to as the Bradford distribution. Pareto developed the distribution to describe the distribution of wealth in an economy. It has also found use in insurance, web page access statistics, oil field sizes, and many other problems, including the download frequency for projects in Sourceforge [1]_. It is one of the so-called "fat-tailed" distributions. References ---------- .. [1] Francis Hunt and Paul Johnson, On the Pareto Distribution of Sourceforge projects. .. [2] Pareto, V. (1896). Course of Political Economy. Lausanne. .. [3] Reiss, R.D., Thomas, M.(2001), Statistical Analysis of Extreme Values, Birkhauser Verlag, Basel, pp 23-30. .. [4] Wikipedia, "Pareto distribution", https://en.wikipedia.org/wiki/Pareto_distribution Examples -------- Draw samples from the distribution: >>> a, m = 3., 2. # shape and mode >>> s = (np.random.default_rng().pareto(a, 1000) + 1) * m Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, _ = plt.hist(s, 100, density=True) >>> fit = a*m**a / bins**(a+1) >>> plt.plot(bins, max(count)*fit/max(fit), linewidth=2, color='r') >>> plt.show() vonmises(mu, kappa, size=None) Draw samples from a von Mises distribution. Samples are drawn from a von Mises distribution with specified mode (mu) and dispersion (kappa), on the interval [-pi, pi]. The von Mises distribution (also known as the circular normal distribution) is a continuous probability distribution on the unit circle. It may be thought of as the circular analogue of the normal distribution. Parameters ---------- mu : float or array_like of floats Mode ("center") of the distribution. kappa : float or array_like of floats Dispersion of the distribution, has to be >=0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``mu`` and ``kappa`` are both scalars. Otherwise, ``np.broadcast(mu, kappa).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized von Mises distribution. See Also -------- scipy.stats.vonmises : probability density function, distribution, or cumulative density function, etc. Notes ----- The probability density for the von Mises distribution is .. math:: p(x) = \frac{e^{\kappa cos(x-\mu)}}{2\pi I_0(\kappa)}, where :math:`\mu` is the mode and :math:`\kappa` the dispersion, and :math:`I_0(\kappa)` is the modified Bessel function of order 0. The von Mises is named for Richard Edler von Mises, who was born in Austria-Hungary, in what is now the Ukraine. He fled to the United States in 1939 and became a professor at Harvard. He worked in probability theory, aerodynamics, fluid mechanics, and philosophy of science. References ---------- .. [1] Abramowitz, M. and Stegun, I. A. (Eds.). "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing," New York: Dover, 1972. .. [2] von Mises, R., "Mathematical Theory of Probability and Statistics", New York: Academic Press, 1964. Examples -------- Draw samples from the distribution: >>> mu, kappa = 0.0, 4.0 # mean and dispersion >>> s = np.random.default_rng().vonmises(mu, kappa, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> from scipy.special import i0 # doctest: +SKIP >>> plt.hist(s, 50, density=True) >>> x = np.linspace(-np.pi, np.pi, num=51) >>> y = np.exp(kappa*np.cos(x-mu))/(2*np.pi*i0(kappa)) # doctest: +SKIP >>> plt.plot(x, y, linewidth=2, color='r') # doctest: +SKIP >>> plt.show() standard_t(df, size=None) Draw samples from a standard Student's t distribution with `df` degrees of freedom. A special case of the hyperbolic distribution. As `df` gets large, the result resembles that of the standard normal distribution (`standard_normal`). Parameters ---------- df : float or array_like of floats Degrees of freedom, must be > 0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``df`` is a scalar. Otherwise, ``np.array(df).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized standard Student's t distribution. Notes ----- The probability density function for the t distribution is .. math:: P(x, df) = \frac{\Gamma(\frac{df+1}{2})}{\sqrt{\pi df} \Gamma(\frac{df}{2})}\Bigl( 1+\frac{x^2}{df} \Bigr)^{-(df+1)/2} The t test is based on an assumption that the data come from a Normal distribution. The t test provides a way to test whether the sample mean (that is the mean calculated from the data) is a good estimate of the true mean. The derivation of the t-distribution was first published in 1908 by William Gosset while working for the Guinness Brewery in Dublin. Due to proprietary issues, he had to publish under a pseudonym, and so he used the name Student. References ---------- .. [1] Dalgaard, Peter, "Introductory Statistics With R", Springer, 2002. .. [2] Wikipedia, "Student's t-distribution" https://en.wikipedia.org/wiki/Student's_t-distribution Examples -------- From Dalgaard page 83 [1]_, suppose the daily energy intake for 11 women in kilojoules (kJ) is: >>> intake = np.array([5260., 5470, 5640, 6180, 6390, 6515, 6805, 7515, \ ... 7515, 8230, 8770]) Does their energy intake deviate systematically from the recommended value of 7725 kJ? Our null hypothesis will be the absence of deviation, and the alternate hypothesis will be the presence of an effect that could be either positive or negative, hence making our test 2-tailed. Because we are estimating the mean and we have N=11 values in our sample, we have N-1=10 degrees of freedom. We set our significance level to 95% and compute the t statistic using the empirical mean and empirical standard deviation of our intake. We use a ddof of 1 to base the computation of our empirical standard deviation on an unbiased estimate of the variance (note: the final estimate is not unbiased due to the concave nature of the square root). >>> np.mean(intake) 6753.636363636364 >>> intake.std(ddof=1) 1142.1232221373727 >>> t = (np.mean(intake)-7725)/(intake.std(ddof=1)/np.sqrt(len(intake))) >>> t -2.8207540608310198 We draw 1000000 samples from Student's t distribution with the adequate degrees of freedom. >>> import matplotlib.pyplot as plt >>> s = np.random.default_rng().standard_t(10, size=1000000) >>> h = plt.hist(s, bins=100, density=True) Does our t statistic land in one of the two critical regions found at both tails of the distribution? >>> np.sum(np.abs(t) < np.abs(s)) / float(len(s)) 0.018318 #random < 0.05, statistic is in critical region The probability value for this 2-tailed test is about 1.83%, which is lower than the 5% pre-determined significance threshold. Therefore, the probability of observing values as extreme as our intake conditionally on the null hypothesis being true is too low, and we reject the null hypothesis of no deviation. standard_cauchy(size=None) Draw samples from a standard Cauchy distribution with mode = 0. Also known as the Lorentz distribution. Parameters ---------- size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Default is None, in which case a single value is returned. Returns ------- samples : ndarray or scalar The drawn samples. Notes ----- The probability density function for the full Cauchy distribution is .. math:: P(x; x_0, \gamma) = \frac{1}{\pi \gamma \bigl[ 1+ (\frac{x-x_0}{\gamma})^2 \bigr] } and the Standard Cauchy distribution just sets :math:`x_0=0` and :math:`\gamma=1` The Cauchy distribution arises in the solution to the driven harmonic oscillator problem, and also describes spectral line broadening. It also describes the distribution of values at which a line tilted at a random angle will cut the x axis. When studying hypothesis tests that assume normality, seeing how the tests perform on data from a Cauchy distribution is a good indicator of their sensitivity to a heavy-tailed distribution, since the Cauchy looks very much like a Gaussian distribution, but with heavier tails. References ---------- .. [1] NIST/SEMATECH e-Handbook of Statistical Methods, "Cauchy Distribution", https://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm .. [2] Weisstein, Eric W. "Cauchy Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CauchyDistribution.html .. [3] Wikipedia, "Cauchy distribution" https://en.wikipedia.org/wiki/Cauchy_distribution Examples -------- Draw samples and plot the distribution: >>> import matplotlib.pyplot as plt >>> s = np.random.default_rng().standard_cauchy(1000000) >>> s = s[(s>-25) & (s<25)] # truncate distribution so it plots well >>> plt.hist(s, bins=100) >>> plt.show() noncentral_chisquare(df, nonc, size=None) Draw samples from a noncentral chi-square distribution. The noncentral :math:`\chi^2` distribution is a generalization of the :math:`\chi^2` distribution. Parameters ---------- df : float or array_like of floats Degrees of freedom, must be > 0. .. versionchanged:: 1.10.0 Earlier NumPy versions required dfnum > 1. nonc : float or array_like of floats Non-centrality, must be non-negative. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``df`` and ``nonc`` are both scalars. Otherwise, ``np.broadcast(df, nonc).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized noncentral chi-square distribution. Notes ----- The probability density function for the noncentral Chi-square distribution is .. math:: P(x;df,nonc) = \sum^{\infty}_{i=0} \frac{e^{-nonc/2}(nonc/2)^{i}}{i!} P_{Y_{df+2i}}(x), where :math:`Y_{q}` is the Chi-square with q degrees of freedom. References ---------- .. [1] Wikipedia, "Noncentral chi-squared distribution" https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution Examples -------- Draw values from the distribution and plot the histogram >>> rng = np.random.default_rng() >>> import matplotlib.pyplot as plt >>> values = plt.hist(rng.noncentral_chisquare(3, 20, 100000), ... bins=200, density=True) >>> plt.show() Draw values from a noncentral chisquare with very small noncentrality, and compare to a chisquare. >>> plt.figure() >>> values = plt.hist(rng.noncentral_chisquare(3, .0000001, 100000), ... bins=np.arange(0., 25, .1), density=True) >>> values2 = plt.hist(rng.chisquare(3, 100000), ... bins=np.arange(0., 25, .1), density=True) >>> plt.plot(values[1][0:-1], values[0]-values2[0], 'ob') >>> plt.show() Demonstrate how large values of non-centrality lead to a more symmetric distribution. >>> plt.figure() >>> values = plt.hist(rng.noncentral_chisquare(3, 20, 100000), ... bins=200, density=True) >>> plt.show() chisquare(df, size=None) Draw samples from a chi-square distribution. When `df` independent random variables, each with standard normal distributions (mean 0, variance 1), are squared and summed, the resulting distribution is chi-square (see Notes). This distribution is often used in hypothesis testing. Parameters ---------- df : float or array_like of floats Number of degrees of freedom, must be > 0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``df`` is a scalar. Otherwise, ``np.array(df).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized chi-square distribution. Raises ------ ValueError When `df` <= 0 or when an inappropriate `size` (e.g. ``size=-1``) is given. Notes ----- The variable obtained by summing the squares of `df` independent, standard normally distributed random variables: .. math:: Q = \sum_{i=0}^{\mathtt{df}} X^2_i is chi-square distributed, denoted .. math:: Q \sim \chi^2_k. The probability density function of the chi-squared distribution is .. math:: p(x) = \frac{(1/2)^{k/2}}{\Gamma(k/2)} x^{k/2 - 1} e^{-x/2}, where :math:`\Gamma` is the gamma function, .. math:: \Gamma(x) = \int_0^{-\infty} t^{x - 1} e^{-t} dt. References ---------- .. [1] NIST "Engineering Statistics Handbook" https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm Examples -------- >>> np.random.default_rng().chisquare(2,4) array([ 1.89920014, 9.00867716, 3.13710533, 5.62318272]) # random noncentral_f(dfnum, dfden, nonc, size=None) Draw samples from the noncentral F distribution. Samples are drawn from an F distribution with specified parameters, `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of freedom in denominator), where both parameters > 1. `nonc` is the non-centrality parameter. Parameters ---------- dfnum : float or array_like of floats Numerator degrees of freedom, must be > 0. .. versionchanged:: 1.14.0 Earlier NumPy versions required dfnum > 1. dfden : float or array_like of floats Denominator degrees of freedom, must be > 0. nonc : float or array_like of floats Non-centrality parameter, the sum of the squares of the numerator means, must be >= 0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``dfnum``, ``dfden``, and ``nonc`` are all scalars. Otherwise, ``np.broadcast(dfnum, dfden, nonc).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized noncentral Fisher distribution. Notes ----- When calculating the power of an experiment (power = probability of rejecting the null hypothesis when a specific alternative is true) the non-central F statistic becomes important. When the null hypothesis is true, the F statistic follows a central F distribution. When the null hypothesis is not true, then it follows a non-central F statistic. References ---------- .. [1] Weisstein, Eric W. "Noncentral F-Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NoncentralF-Distribution.html .. [2] Wikipedia, "Noncentral F-distribution", https://en.wikipedia.org/wiki/Noncentral_F-distribution Examples -------- In a study, testing for a specific alternative to the null hypothesis requires use of the Noncentral F distribution. We need to calculate the area in the tail of the distribution that exceeds the value of the F distribution for the null hypothesis. We'll plot the two probability distributions for comparison. >>> rng = np.random.default_rng() >>> dfnum = 3 # between group deg of freedom >>> dfden = 20 # within groups degrees of freedom >>> nonc = 3.0 >>> nc_vals = rng.noncentral_f(dfnum, dfden, nonc, 1000000) >>> NF = np.histogram(nc_vals, bins=50, density=True) >>> c_vals = rng.f(dfnum, dfden, 1000000) >>> F = np.histogram(c_vals, bins=50, density=True) >>> import matplotlib.pyplot as plt >>> plt.plot(F[1][1:], F[0]) >>> plt.plot(NF[1][1:], NF[0]) >>> plt.show() f(dfnum, dfden, size=None) Draw samples from an F distribution. Samples are drawn from an F distribution with specified parameters, `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of freedom in denominator), where both parameters must be greater than zero. The random variate of the F distribution (also known as the Fisher distribution) is a continuous probability distribution that arises in ANOVA tests, and is the ratio of two chi-square variates. Parameters ---------- dfnum : float or array_like of floats Degrees of freedom in numerator, must be > 0. dfden : float or array_like of float Degrees of freedom in denominator, must be > 0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``dfnum`` and ``dfden`` are both scalars. Otherwise, ``np.broadcast(dfnum, dfden).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Fisher distribution. See Also -------- scipy.stats.f : probability density function, distribution or cumulative density function, etc. Notes ----- The F statistic is used to compare in-group variances to between-group variances. Calculating the distribution depends on the sampling, and so it is a function of the respective degrees of freedom in the problem. The variable `dfnum` is the number of samples minus one, the between-groups degrees of freedom, while `dfden` is the within-groups degrees of freedom, the sum of the number of samples in each group minus the number of groups. References ---------- .. [1] Glantz, Stanton A. "Primer of Biostatistics.", McGraw-Hill, Fifth Edition, 2002. .. [2] Wikipedia, "F-distribution", https://en.wikipedia.org/wiki/F-distribution Examples -------- An example from Glantz[1], pp 47-40: Two groups, children of diabetics (25 people) and children from people without diabetes (25 controls). Fasting blood glucose was measured, case group had a mean value of 86.1, controls had a mean value of 82.2. Standard deviations were 2.09 and 2.49 respectively. Are these data consistent with the null hypothesis that the parents diabetic status does not affect their children's blood glucose levels? Calculating the F statistic from the data gives a value of 36.01. Draw samples from the distribution: >>> dfnum = 1. # between group degrees of freedom >>> dfden = 48. # within groups degrees of freedom >>> s = np.random.default_rng().f(dfnum, dfden, 1000) The lower bound for the top 1% of the samples is : >>> np.sort(s)[-10] 7.61988120985 # random So there is about a 1% chance that the F statistic will exceed 7.62, the measured value is 36, so the null hypothesis is rejected at the 1% level. gamma(shape, scale=1.0, size=None) Draw samples from a Gamma distribution. Samples are drawn from a Gamma distribution with specified parameters, `shape` (sometimes designated "k") and `scale` (sometimes designated "theta"), where both parameters are > 0. Parameters ---------- shape : float or array_like of floats The shape of the gamma distribution. Must be non-negative. scale : float or array_like of floats, optional The scale of the gamma distribution. Must be non-negative. Default is equal to 1. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``shape`` and ``scale`` are both scalars. Otherwise, ``np.broadcast(shape, scale).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized gamma distribution. See Also -------- scipy.stats.gamma : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Gamma distribution is .. math:: p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)}, where :math:`k` is the shape and :math:`\theta` the scale, and :math:`\Gamma` is the Gamma function. The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant. References ---------- .. [1] Weisstein, Eric W. "Gamma Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/GammaDistribution.html .. [2] Wikipedia, "Gamma distribution", https://en.wikipedia.org/wiki/Gamma_distribution Examples -------- Draw samples from the distribution: >>> shape, scale = 2., 2. # mean=4, std=2*sqrt(2) >>> s = np.random.default_rng().gamma(shape, scale, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> import scipy.special as sps # doctest: +SKIP >>> count, bins, ignored = plt.hist(s, 50, density=True) >>> y = bins**(shape-1)*(np.exp(-bins/scale) / # doctest: +SKIP ... (sps.gamma(shape)*scale**shape)) >>> plt.plot(bins, y, linewidth=2, color='r') # doctest: +SKIP >>> plt.show() standard_gamma(shape, size=None, dtype=np.float64, out=None) Draw samples from a standard Gamma distribution. Samples are drawn from a Gamma distribution with specified parameters, shape (sometimes designated "k") and scale=1. Parameters ---------- shape : float or array_like of floats Parameter, must be non-negative. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``shape`` is a scalar. Otherwise, ``np.array(shape).size`` samples are drawn. dtype : dtype, optional Desired dtype of the result, only `float64` and `float32` are supported. Byteorder must be native. The default value is np.float64. out : ndarray, optional Alternative output array in which to place the result. If size is not None, it must have the same shape as the provided size and must match the type of the output values. Returns ------- out : ndarray or scalar Drawn samples from the parameterized standard gamma distribution. See Also -------- scipy.stats.gamma : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Gamma distribution is .. math:: p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)}, where :math:`k` is the shape and :math:`\theta` the scale, and :math:`\Gamma` is the Gamma function. The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant. References ---------- .. [1] Weisstein, Eric W. "Gamma Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/GammaDistribution.html .. [2] Wikipedia, "Gamma distribution", https://en.wikipedia.org/wiki/Gamma_distribution Examples -------- Draw samples from the distribution: >>> shape, scale = 2., 1. # mean and width >>> s = np.random.default_rng().standard_gamma(shape, 1000000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> import scipy.special as sps # doctest: +SKIP >>> count, bins, ignored = plt.hist(s, 50, density=True) >>> y = bins**(shape-1) * ((np.exp(-bins/scale))/ # doctest: +SKIP ... (sps.gamma(shape) * scale**shape)) >>> plt.plot(bins, y, linewidth=2, color='r') # doctest: +SKIP >>> plt.show() normal(loc=0.0, scale=1.0, size=None) Draw random samples from a normal (Gaussian) distribution. The probability density function of the normal distribution, first derived by De Moivre and 200 years later by both Gauss and Laplace independently [2]_, is often called the bell curve because of its characteristic shape (see the example below). The normal distributions occurs often in nature. For example, it describes the commonly occurring distribution of samples influenced by a large number of tiny, random disturbances, each with its own unique distribution [2]_. Parameters ---------- loc : float or array_like of floats Mean ("centre") of the distribution. scale : float or array_like of floats Standard deviation (spread or "width") of the distribution. Must be non-negative. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``loc`` and ``scale`` are both scalars. Otherwise, ``np.broadcast(loc, scale).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized normal distribution. See Also -------- scipy.stats.norm : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Gaussian distribution is .. math:: p(x) = \frac{1}{\sqrt{ 2 \pi \sigma^2 }} e^{ - \frac{ (x - \mu)^2 } {2 \sigma^2} }, where :math:`\mu` is the mean and :math:`\sigma` the standard deviation. The square of the standard deviation, :math:`\sigma^2`, is called the variance. The function has its peak at the mean, and its "spread" increases with the standard deviation (the function reaches 0.607 times its maximum at :math:`x + \sigma` and :math:`x - \sigma` [2]_). This implies that :meth:`normal` is more likely to return samples lying close to the mean, rather than those far away. References ---------- .. [1] Wikipedia, "Normal distribution", https://en.wikipedia.org/wiki/Normal_distribution .. [2] P. R. Peebles Jr., "Central Limit Theorem" in "Probability, Random Variables and Random Signal Principles", 4th ed., 2001, pp. 51, 51, 125. Examples -------- Draw samples from the distribution: >>> mu, sigma = 0, 0.1 # mean and standard deviation >>> s = np.random.default_rng().normal(mu, sigma, 1000) Verify the mean and the variance: >>> abs(mu - np.mean(s)) 0.0 # may vary >>> abs(sigma - np.std(s, ddof=1)) 0.0 # may vary Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 30, density=True) >>> plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) * ... np.exp( - (bins - mu)**2 / (2 * sigma**2) ), ... linewidth=2, color='r') >>> plt.show() Two-by-four array of samples from the normal distribution with mean 3 and standard deviation 2.5: >>> np.random.default_rng().normal(3, 2.5, size=(2, 4)) array([[-4.49401501, 4.00950034, -1.81814867, 7.29718677], # random [ 0.39924804, 4.68456316, 4.99394529, 4.84057254]]) # random standard_normal(size=None, dtype=np.float64, out=None) Draw samples from a standard Normal distribution (mean=0, stdev=1). Parameters ---------- size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Default is None, in which case a single value is returned. dtype : dtype, optional Desired dtype of the result, only `float64` and `float32` are supported. Byteorder must be native. The default value is np.float64. out : ndarray, optional Alternative output array in which to place the result. If size is not None, it must have the same shape as the provided size and must match the type of the output values. Returns ------- out : float or ndarray A floating-point array of shape ``size`` of drawn samples, or a single sample if ``size`` was not specified. See Also -------- normal : Equivalent function with additional ``loc`` and ``scale`` arguments for setting the mean and standard deviation. Notes ----- For random samples from the normal distribution with mean ``mu`` and standard deviation ``sigma``, use one of:: mu + sigma * rng.standard_normal(size=...) rng.normal(mu, sigma, size=...) Examples -------- >>> rng = np.random.default_rng() >>> rng.standard_normal() 2.1923875335537315 # random >>> s = rng.standard_normal(8000) >>> s array([ 0.6888893 , 0.78096262, -0.89086505, ..., 0.49876311, # random -0.38672696, -0.4685006 ]) # random >>> s.shape (8000,) >>> s = rng.standard_normal(size=(3, 4, 2)) >>> s.shape (3, 4, 2) Two-by-four array of samples from the normal distribution with mean 3 and standard deviation 2.5: >>> 3 + 2.5 * rng.standard_normal(size=(2, 4)) array([[-4.49401501, 4.00950034, -1.81814867, 7.29718677], # random [ 0.39924804, 4.68456316, 4.99394529, 4.84057254]]) # random uniform(low=0.0, high=1.0, size=None) Draw samples from a uniform distribution. Samples are uniformly distributed over the half-open interval ``[low, high)`` (includes low, but excludes high). In other words, any value within the given interval is equally likely to be drawn by `uniform`. Parameters ---------- low : float or array_like of floats, optional Lower boundary of the output interval. All values generated will be greater than or equal to low. The default value is 0. high : float or array_like of floats Upper boundary of the output interval. All values generated will be less than high. The high limit may be included in the returned array of floats due to floating-point rounding in the equation ``low + (high-low) * random_sample()``. high - low must be non-negative. The default value is 1.0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``low`` and ``high`` are both scalars. Otherwise, ``np.broadcast(low, high).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized uniform distribution. See Also -------- integers : Discrete uniform distribution, yielding integers. random : Floats uniformly distributed over ``[0, 1)``. Notes ----- The probability density function of the uniform distribution is .. math:: p(x) = \frac{1}{b - a} anywhere within the interval ``[a, b)``, and zero elsewhere. When ``high`` == ``low``, values of ``low`` will be returned. Examples -------- Draw samples from the distribution: >>> s = np.random.default_rng().uniform(-1,0,1000) All values are within the given interval: >>> np.all(s >= -1) True >>> np.all(s < 0) True Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 15, density=True) >>> plt.plot(bins, np.ones_like(bins), linewidth=2, color='r') >>> plt.show() choice(a, size=None, replace=True, p=None, axis=0, shuffle=True) Generates a random sample from a given array Parameters ---------- a : {array_like, int} If an ndarray, a random sample is generated from its elements. If an int, the random sample is generated from np.arange(a). size : {int, tuple[int]}, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn from the 1-d `a`. If `a` has more than one dimension, the `size` shape will be inserted into the `axis` dimension, so the output ``ndim`` will be ``a.ndim - 1 + len(size)``. Default is None, in which case a single value is returned. replace : bool, optional Whether the sample is with or without replacement. Default is True, meaning that a value of ``a`` can be selected multiple times. p : 1-D array_like, optional The probabilities associated with each entry in a. If not given, the sample assumes a uniform distribution over all entries in ``a``. axis : int, optional The axis along which the selection is performed. The default, 0, selects by row. shuffle : bool, optional Whether the sample is shuffled when sampling without replacement. Default is True, False provides a speedup. Returns ------- samples : single item or ndarray The generated random samples Raises ------ ValueError If a is an int and less than zero, if p is not 1-dimensional, if a is array-like with a size 0, if p is not a vector of probabilities, if a and p have different lengths, or if replace=False and the sample size is greater than the population size. See Also -------- integers, shuffle, permutation Notes ----- Setting user-specified probabilities through ``p`` uses a more general but less efficient sampler than the default. The general sampler produces a different sample than the optimized sampler even if each element of ``p`` is 1 / len(a). Examples -------- Generate a uniform random sample from np.arange(5) of size 3: >>> rng = np.random.default_rng() >>> rng.choice(5, 3) array([0, 3, 4]) # random >>> #This is equivalent to rng.integers(0,5,3) Generate a non-uniform random sample from np.arange(5) of size 3: >>> rng.choice(5, 3, p=[0.1, 0, 0.3, 0.6, 0]) array([3, 3, 0]) # random Generate a uniform random sample from np.arange(5) of size 3 without replacement: >>> rng.choice(5, 3, replace=False) array([3,1,0]) # random >>> #This is equivalent to rng.permutation(np.arange(5))[:3] Generate a uniform random sample from a 2-D array along the first axis (the default), without replacement: >>> rng.choice([[0, 1, 2], [3, 4, 5], [6, 7, 8]], 2, replace=False) array([[3, 4, 5], # random [0, 1, 2]]) Generate a non-uniform random sample from np.arange(5) of size 3 without replacement: >>> rng.choice(5, 3, replace=False, p=[0.1, 0, 0.3, 0.6, 0]) array([2, 3, 0]) # random Any of the above can be repeated with an arbitrary array-like instead of just integers. For instance: >>> aa_milne_arr = ['pooh', 'rabbit', 'piglet', 'Christopher'] >>> rng.choice(aa_milne_arr, 5, p=[0.5, 0.1, 0.1, 0.3]) array(['pooh', 'pooh', 'pooh', 'Christopher', 'piglet'], # random dtype='>> np.random.default_rng().bytes(10) b'\xfeC\x9b\x86\x17\xf2\xa1\xafcp' # random integers(low, high=None, size=None, dtype=np.int64, endpoint=False) Return random integers from `low` (inclusive) to `high` (exclusive), or if endpoint=True, `low` (inclusive) to `high` (inclusive). Replaces `RandomState.randint` (with endpoint=False) and `RandomState.random_integers` (with endpoint=True) Return random integers from the "discrete uniform" distribution of the specified dtype. If `high` is None (the default), then results are from 0 to `low`. Parameters ---------- low : int or array-like of ints Lowest (signed) integers to be drawn from the distribution (unless ``high=None``, in which case this parameter is 0 and this value is used for `high`). high : int or array-like of ints, optional If provided, one above the largest (signed) integer to be drawn from the distribution (see above for behavior if ``high=None``). If array-like, must contain integer values size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Default is None, in which case a single value is returned. dtype : dtype, optional Desired dtype of the result. Byteorder must be native. The default value is np.int64. endpoint : bool, optional If true, sample from the interval [low, high] instead of the default [low, high) Defaults to False Returns ------- out : int or ndarray of ints `size`-shaped array of random integers from the appropriate distribution, or a single such random int if `size` not provided. Notes ----- When using broadcasting with uint64 dtypes, the maximum value (2**64) cannot be represented as a standard integer type. The high array (or low if high is None) must have object dtype, e.g., array([2**64]). Examples -------- >>> rng = np.random.default_rng() >>> rng.integers(2, size=10) array([1, 0, 0, 0, 1, 1, 0, 0, 1, 0]) # random >>> rng.integers(1, size=10) array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) Generate a 2 x 4 array of ints between 0 and 4, inclusive: >>> rng.integers(5, size=(2, 4)) array([[4, 0, 2, 1], [3, 2, 2, 0]]) # random Generate a 1 x 3 array with 3 different upper bounds >>> rng.integers(1, [3, 5, 10]) array([2, 2, 9]) # random Generate a 1 by 3 array with 3 different lower bounds >>> rng.integers([1, 5, 7], 10) array([9, 8, 7]) # random Generate a 2 by 4 array using broadcasting with dtype of uint8 >>> rng.integers([1, 3, 5, 7], [[10], [20]], dtype=np.uint8) array([[ 8, 6, 9, 7], [ 1, 16, 9, 12]], dtype=uint8) # random References ---------- .. [1] Daniel Lemire., "Fast Random Integer Generation in an Interval", ACM Transactions on Modeling and Computer Simulation 29 (1), 2019, http://arxiv.org/abs/1805.10941. standard_exponential(size=None, dtype=np.float64, method='zig', out=None) Draw samples from the standard exponential distribution. `standard_exponential` is identical to the exponential distribution with a scale parameter of 1. Parameters ---------- size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Default is None, in which case a single value is returned. dtype : dtype, optional Desired dtype of the result, only `float64` and `float32` are supported. Byteorder must be native. The default value is np.float64. method : str, optional Either 'inv' or 'zig'. 'inv' uses the default inverse CDF method. 'zig' uses the much faster Ziggurat method of Marsaglia and Tsang. out : ndarray, optional Alternative output array in which to place the result. If size is not None, it must have the same shape as the provided size and must match the type of the output values. Returns ------- out : float or ndarray Drawn samples. Examples -------- Output a 3x8000 array: >>> n = np.random.default_rng().standard_exponential((3, 8000)) exponential(scale=1.0, size=None) Draw samples from an exponential distribution. Its probability density function is .. math:: f(x; \frac{1}{\beta}) = \frac{1}{\beta} \exp(-\frac{x}{\beta}), for ``x > 0`` and 0 elsewhere. :math:`\beta` is the scale parameter, which is the inverse of the rate parameter :math:`\lambda = 1/\beta`. The rate parameter is an alternative, widely used parameterization of the exponential distribution [3]_. The exponential distribution is a continuous analogue of the geometric distribution. It describes many common situations, such as the size of raindrops measured over many rainstorms [1]_, or the time between page requests to Wikipedia [2]_. Parameters ---------- scale : float or array_like of floats The scale parameter, :math:`\beta = 1/\lambda`. Must be non-negative. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``scale`` is a scalar. Otherwise, ``np.array(scale).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized exponential distribution. Examples -------- A real world example: Assume a company has 10000 customer support agents and the average time between customer calls is 4 minutes. >>> n = 10000 >>> time_between_calls = np.random.default_rng().exponential(scale=4, size=n) What is the probability that a customer will call in the next 4 to 5 minutes? >>> x = ((time_between_calls < 5).sum())/n >>> y = ((time_between_calls < 4).sum())/n >>> x-y 0.08 # may vary References ---------- .. [1] Peyton Z. Peebles Jr., "Probability, Random Variables and Random Signal Principles", 4th ed, 2001, p. 57. .. [2] Wikipedia, "Poisson process", https://en.wikipedia.org/wiki/Poisson_process .. [3] Wikipedia, "Exponential distribution", https://en.wikipedia.org/wiki/Exponential_distribution beta(a, b, size=None) Draw samples from a Beta distribution. The Beta distribution is a special case of the Dirichlet distribution, and is related to the Gamma distribution. It has the probability distribution function .. math:: f(x; a,b) = \frac{1}{B(\alpha, \beta)} x^{\alpha - 1} (1 - x)^{\beta - 1}, where the normalization, B, is the beta function, .. math:: B(\alpha, \beta) = \int_0^1 t^{\alpha - 1} (1 - t)^{\beta - 1} dt. It is often seen in Bayesian inference and order statistics. Parameters ---------- a : float or array_like of floats Alpha, positive (>0). b : float or array_like of floats Beta, positive (>0). size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``a`` and ``b`` are both scalars. Otherwise, ``np.broadcast(a, b).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized beta distribution. random(size=None, dtype=np.float64, out=None) Return random floats in the half-open interval [0.0, 1.0). Results are from the "continuous uniform" distribution over the stated interval. To sample :math:`Unif[a, b), b > a` use `uniform` or multiply the output of `random` by ``(b - a)`` and add ``a``:: (b - a) * random() + a Parameters ---------- size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Default is None, in which case a single value is returned. dtype : dtype, optional Desired dtype of the result, only `float64` and `float32` are supported. Byteorder must be native. The default value is np.float64. out : ndarray, optional Alternative output array in which to place the result. If size is not None, it must have the same shape as the provided size and must match the type of the output values. Returns ------- out : float or ndarray of floats Array of random floats of shape `size` (unless ``size=None``, in which case a single float is returned). See Also -------- uniform : Draw samples from the parameterized uniform distribution. Examples -------- >>> rng = np.random.default_rng() >>> rng.random() 0.47108547995356098 # random >>> type(rng.random()) >>> rng.random((5,)) array([ 0.30220482, 0.86820401, 0.1654503 , 0.11659149, 0.54323428]) # random Three-by-two array of random numbers from [-5, 0): >>> 5 * rng.random((3, 2)) - 5 array([[-3.99149989, -0.52338984], # random [-2.99091858, -0.79479508], [-1.23204345, -1.75224494]]) spawn(n_children) Create new independent child generators. See :ref:`seedsequence-spawn` for additional notes on spawning children. .. versionadded:: 1.25.0 Parameters ---------- n_children : int Returns ------- child_generators : list of Generators Raises ------ TypeError When the underlying SeedSequence does not implement spawning. See Also -------- random.BitGenerator.spawn, random.SeedSequence.spawn : Equivalent method on the bit generator and seed sequence. bit_generator : The bit generator instance used by the generator. Examples -------- Starting from a seeded default generator: >>> # High quality entropy created with: f"0x{secrets.randbits(128):x}" >>> entropy = 0x3034c61a9ae04ff8cb62ab8ec2c4b501 >>> rng = np.random.default_rng(entropy) Create two new generators for example for parallel execution: >>> child_rng1, child_rng2 = rng.spawn(2) Drawn numbers from each are independent but derived from the initial seeding entropy: >>> rng.uniform(), child_rng1.uniform(), child_rng2.uniform() (0.19029263503854454, 0.9475673279178444, 0.4702687338396767) It is safe to spawn additional children from the original ``rng`` or the children: >>> more_child_rngs = rng.spawn(20) >>> nested_spawn = child_rng1.spawn(20) Unsupported dtype %r for standard_gammaUnsupported dtype %r for standard_normalunable to allocate shape and strides.sum(colors) must not exceed the maximum value of a 64 bit signed integer (%d)pvals must have at least 1 dimension and the last dimension of pvals must be greater than 0.probabilities are not non-negativenumpy.core.umath failed to importno default __reduce__ due to non-trivial __cinit__negative dimensions are not allowedn too large or p too small, see Generator.negative_binomial Notesmethod must be one of {'eigh', 'svd', 'cholesky'}method must be "count" or "marginals".memory allocation failed in permutedmean and cov must not be complexmean and cov must have same lengthhigh - low range exceeds valid boundsgot differing extents in dimension covariance is not symmetric positive-semidefinite.cov must be 2 dimensional and squarecolors must be a one-dimensional sequence of nonnegative integers not exceeding %d.check_valid must equal 'warn', 'raise', or 'ignore'both ngood and nbad must be less than %da must be a sequence or an integer, not a must be a positive integer unless no samples are takena cannot be empty unless no samples are takenWhen method is "marginals", sum(colors) must be less than 1000000000.Unsupported dtype %r for standard_exponentialUnsupported dtype %r for integersUnable to convert item to objectProviding a dtype with a non-native byteorder is not supported. If you require platform-independent byteorder, call byteswap when required.Out of bounds on buffer access (axis Invalid mode, expected 'c' or 'fortran', got Invalid bit generator. The bit generator must be instantiated.Insufficient memory for multivariate_hypergeometric with method='count' and sum(colors)=%dIndirect dimensions not supportedIncompatible checksums (0x%x vs (0x82a3537, 0x6ae9995, 0xb068931) = (name))Generator.standard_normal (line 1051)Generator.standard_gamma (line 1226)Generator.standard_exponential (line 473)Generator.standard_cauchy (line 1709)Generator.noncentral_f (line 1483)Generator.noncentral_chisquare (line 1629)Generator.negative_binomial (line 3038)Generator.multivariate_normal (line 3598)Generator.multivariate_hypergeometric (line 4084)Generator.hypergeometric (line 3374)Fewer non-zero entries in p than sizeEmpty shape tuple for cython.arrayConstruct a new Generator with the default BitGenerator (PCG64). Parameters ---------- seed : {None, int, array_like[ints], SeedSequence, BitGenerator, Generator}, optional A seed to initialize the `BitGenerator`. If None, then fresh, unpredictable entropy will be pulled from the OS. If an ``int`` or ``array_like[ints]`` is passed, then it will be passed to `SeedSequence` to derive the initial `BitGenerator` state. One may also pass in a `SeedSequence` instance. Additionally, when passed a `BitGenerator`, it will be wrapped by `Generator`. If passed a `Generator`, it will be returned unaltered. Returns ------- Generator The initialized generator object. Notes ----- If ``seed`` is not a `BitGenerator` or a `Generator`, a new `BitGenerator` is instantiated. This function does not manage a default global instance. See :ref:`seeding_and_entropy` for more information about seeding. Examples -------- ``default_rng`` is the recommended constructor for the random number class ``Generator``. Here are several ways we can construct a random number generator using ``default_rng`` and the ``Generator`` class. Here we use ``default_rng`` to generate a random float: >>> import numpy as np >>> rng = np.random.default_rng(12345) >>> print(rng) Generator(PCG64) >>> rfloat = rng.random() >>> rfloat 0.22733602246716966 >>> type(rfloat) Here we use ``default_rng`` to generate 3 random integers between 0 (inclusive) and 10 (exclusive): >>> import numpy as np >>> rng = np.random.default_rng(12345) >>> rints = rng.integers(low=0, high=10, size=3) >>> rints array([6, 2, 7]) >>> type(rints[0]) Here we specify a seed so that we have reproducible results: >>> import numpy as np >>> rng = np.random.default_rng(seed=42) >>> print(rng) Generator(PCG64) >>> arr1 = rng.random((3, 3)) >>> arr1 array([[0.77395605, 0.43887844, 0.85859792], [0.69736803, 0.09417735, 0.97562235], [0.7611397 , 0.78606431, 0.12811363]]) If we exit and restart our Python interpreter, we'll see that we generate the same random numbers again: >>> import numpy as np >>> rng = np.random.default_rng(seed=42) >>> arr2 = rng.random((3, 3)) >>> arr2 array([[0.77395605, 0.43887844, 0.85859792], [0.69736803, 0.09417735, 0.97562235], [0.7611397 , 0.78606431, 0.12811363]]) Cannot transpose memoryview with indirect dimensionsCannot take a larger sample than population when replace is FalseCannot create writable memory view from read-only memoryviewCannot assign to read-only memoryviewCan only create a buffer that is contiguous in memory.Buffer view does not expose stridesAll dimensions preceding dimension %d must be indexed and not sliced zipf(a, size=None) Draw samples from a Zipf distribution. Samples are drawn from a Zipf distribution with specified parameter `a` > 1. The Zipf distribution (also known as the zeta distribution) is a discrete probability distribution that satisfies Zipf's law: the frequency of an item is inversely proportional to its rank in a frequency table. Parameters ---------- a : float or array_like of floats Distribution parameter. Must be greater than 1. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``a`` is a scalar. Otherwise, ``np.array(a).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Zipf distribution. See Also -------- scipy.stats.zipf : probability density function, distribution, or cumulative density function, etc. Notes ----- The probability density for the Zipf distribution is .. math:: p(k) = \frac{k^{-a}}{\zeta(a)}, for integers :math:`k \geq 1`, where :math:`\zeta` is the Riemann Zeta function. It is named for the American linguist George Kingsley Zipf, who noted that the frequency of any word in a sample of a language is inversely proportional to its rank in the frequency table. References ---------- .. [1] Zipf, G. K., "Selected Studies of the Principle of Relative Frequency in Language," Cambridge, MA: Harvard Univ. Press, 1932. Examples -------- Draw samples from the distribution: >>> a = 4.0 >>> n = 20000 >>> s = np.random.default_rng().zipf(a, size=n) Display the histogram of the samples, along with the expected histogram based on the probability density function: >>> import matplotlib.pyplot as plt >>> from scipy.special import zeta # doctest: +SKIP `bincount` provides a fast histogram for small integers. >>> count = np.bincount(s) >>> k = np.arange(1, s.max() + 1) >>> plt.bar(k, count[1:], alpha=0.5, label='sample count') >>> plt.plot(k, n*(k**-a)/zeta(a), 'k.-', alpha=0.5, ... label='expected count') # doctest: +SKIP >>> plt.semilogy() >>> plt.grid(alpha=0.4) >>> plt.legend() >>> plt.title(f'Zipf sample, a={a}, size={n}') >>> plt.show() weibull(a, size=None) Draw samples from a Weibull distribution. Draw samples from a 1-parameter Weibull distribution with the given shape parameter `a`. .. math:: X = (-ln(U))^{1/a} Here, U is drawn from the uniform distribution over (0,1]. The more common 2-parameter Weibull, including a scale parameter :math:`\lambda` is just :math:`X = \lambda(-ln(U))^{1/a}`. Parameters ---------- a : float or array_like of floats Shape parameter of the distribution. Must be nonnegative. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``a`` is a scalar. Otherwise, ``np.array(a).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Weibull distribution. See Also -------- scipy.stats.weibull_max scipy.stats.weibull_min scipy.stats.genextreme gumbel Notes ----- The Weibull (or Type III asymptotic extreme value distribution for smallest values, SEV Type III, or Rosin-Rammler distribution) is one of a class of Generalized Extreme Value (GEV) distributions used in modeling extreme value problems. This class includes the Gumbel and Frechet distributions. The probability density for the Weibull distribution is .. math:: p(x) = \frac{a} {\lambda}(\frac{x}{\lambda})^{a-1}e^{-(x/\lambda)^a}, where :math:`a` is the shape and :math:`\lambda` the scale. The function has its peak (the mode) at :math:`\lambda(\frac{a-1}{a})^{1/a}`. When ``a = 1``, the Weibull distribution reduces to the exponential distribution. References ---------- .. [1] Waloddi Weibull, Royal Technical University, Stockholm, 1939 "A Statistical Theory Of The Strength Of Materials", Ingeniorsvetenskapsakademiens Handlingar Nr 151, 1939, Generalstabens Litografiska Anstalts Forlag, Stockholm. .. [2] Waloddi Weibull, "A Statistical Distribution Function of Wide Applicability", Journal Of Applied Mechanics ASME Paper 1951. .. [3] Wikipedia, "Weibull distribution", https://en.wikipedia.org/wiki/Weibull_distribution Examples -------- Draw samples from the distribution: >>> rng = np.random.default_rng() >>> a = 5. # shape >>> s = rng.weibull(a, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> x = np.arange(1,100.)/50. >>> def weib(x,n,a): ... return (a / n) * (x / n)**(a - 1) * np.exp(-(x / n)**a) >>> count, bins, ignored = plt.hist(rng.weibull(5.,1000)) >>> x = np.arange(1,100.)/50. >>> scale = count.max()/weib(x, 1., 5.).max() >>> plt.plot(x, weib(x, 1., 5.)*scale) >>> plt.show() vonmises(mu, kappa, size=None) Draw samples from a von Mises distribution. Samples are drawn from a von Mises distribution with specified mode (mu) and dispersion (kappa), on the interval [-pi, pi]. The von Mises distribution (also known as the circular normal distribution) is a continuous probability distribution on the unit circle. It may be thought of as the circular analogue of the normal distribution. Parameters ---------- mu : float or array_like of floats Mode ("center") of the distribution. kappa : float or array_like of floats Dispersion of the distribution, has to be >=0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``mu`` and ``kappa`` are both scalars. Otherwise, ``np.broadcast(mu, kappa).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized von Mises distribution. See Also -------- scipy.stats.vonmises : probability density function, distribution, or cumulative density function, etc. Notes ----- The probability density for the von Mises distribution is .. math:: p(x) = \frac{e^{\kappa cos(x-\mu)}}{2\pi I_0(\kappa)}, where :math:`\mu` is the mode and :math:`\kappa` the dispersion, and :math:`I_0(\kappa)` is the modified Bessel function of order 0. The von Mises is named for Richard Edler von Mises, who was born in Austria-Hungary, in what is now the Ukraine. He fled to the United States in 1939 and became a professor at Harvard. He worked in probability theory, aerodynamics, fluid mechanics, and philosophy of science. References ---------- .. [1] Abramowitz, M. and Stegun, I. A. (Eds.). "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing," New York: Dover, 1972. .. [2] von Mises, R., "Mathematical Theory of Probability and Statistics", New York: Academic Press, 1964. Examples -------- Draw samples from the distribution: >>> mu, kappa = 0.0, 4.0 # mean and dispersion >>> s = np.random.default_rng().vonmises(mu, kappa, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> from scipy.special import i0 # doctest: +SKIP >>> plt.hist(s, 50, density=True) >>> x = np.linspace(-np.pi, np.pi, num=51) >>> y = np.exp(kappa*np.cos(x-mu))/(2*np.pi*i0(kappa)) # doctest: +SKIP >>> plt.plot(x, y, linewidth=2, color='r') # doctest: +SKIP >>> plt.show() uniform(low=0.0, high=1.0, size=None) Draw samples from a uniform distribution. Samples are uniformly distributed over the half-open interval ``[low, high)`` (includes low, but excludes high). In other words, any value within the given interval is equally likely to be drawn by `uniform`. Parameters ---------- low : float or array_like of floats, optional Lower boundary of the output interval. All values generated will be greater than or equal to low. The default value is 0. high : float or array_like of floats Upper boundary of the output interval. All values generated will be less than high. The high limit may be included in the returned array of floats due to floating-point rounding in the equation ``low + (high-low) * random_sample()``. high - low must be non-negative. The default value is 1.0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``low`` and ``high`` are both scalars. Otherwise, ``np.broadcast(low, high).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized uniform distribution. See Also -------- integers : Discrete uniform distribution, yielding integers. random : Floats uniformly distributed over ``[0, 1)``. Notes ----- The probability density function of the uniform distribution is .. math:: p(x) = \frac{1}{b - a} anywhere within the interval ``[a, b)``, and zero elsewhere. When ``high`` == ``low``, values of ``low`` will be returned. Examples -------- Draw samples from the distribution: >>> s = np.random.default_rng().uniform(-1,0,1000) All values are within the given interval: >>> np.all(s >= -1) True >>> np.all(s < 0) True Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 15, density=True) >>> plt.plot(bins, np.ones_like(bins), linewidth=2, color='r') >>> plt.show() triangular(left, mode, right, size=None) Draw samples from the triangular distribution over the interval ``[left, right]``. The triangular distribution is a continuous probability distribution with lower limit left, peak at mode, and upper limit right. Unlike the other distributions, these parameters directly define the shape of the pdf. Parameters ---------- left : float or array_like of floats Lower limit. mode : float or array_like of floats The value where the peak of the distribution occurs. The value must fulfill the condition ``left <= mode <= right``. right : float or array_like of floats Upper limit, must be larger than `left`. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``left``, ``mode``, and ``right`` are all scalars. Otherwise, ``np.broadcast(left, mode, right).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized triangular distribution. Notes ----- The probability density function for the triangular distribution is .. math:: P(x;l, m, r) = \begin{cases} \frac{2(x-l)}{(r-l)(m-l)}& \text{for $l \leq x \leq m$},\\ \frac{2(r-x)}{(r-l)(r-m)}& \text{for $m \leq x \leq r$},\\ 0& \text{otherwise}. \end{cases} The triangular distribution is often used in ill-defined problems where the underlying distribution is not known, but some knowledge of the limits and mode exists. Often it is used in simulations. References ---------- .. [1] Wikipedia, "Triangular distribution" https://en.wikipedia.org/wiki/Triangular_distribution Examples -------- Draw values from the distribution and plot the histogram: >>> import matplotlib.pyplot as plt >>> h = plt.hist(np.random.default_rng().triangular(-3, 0, 8, 100000), bins=200, ... density=True) >>> plt.show() standard_t(df, size=None) Draw samples from a standard Student's t distribution with `df` degrees of freedom. A special case of the hyperbolic distribution. As `df` gets large, the result resembles that of the standard normal distribution (`standard_normal`). Parameters ---------- df : float or array_like of floats Degrees of freedom, must be > 0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``df`` is a scalar. Otherwise, ``np.array(df).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized standard Student's t distribution. Notes ----- The probability density function for the t distribution is .. math:: P(x, df) = \frac{\Gamma(\frac{df+1}{2})}{\sqrt{\pi df} \Gamma(\frac{df}{2})}\Bigl( 1+\frac{x^2}{df} \Bigr)^{-(df+1)/2} The t test is based on an assumption that the data come from a Normal distribution. The t test provides a way to test whether the sample mean (that is the mean calculated from the data) is a good estimate of the true mean. The derivation of the t-distribution was first published in 1908 by William Gosset while working for the Guinness Brewery in Dublin. Due to proprietary issues, he had to publish under a pseudonym, and so he used the name Student. References ---------- .. [1] Dalgaard, Peter, "Introductory Statistics With R", Springer, 2002. .. [2] Wikipedia, "Student's t-distribution" https://en.wikipedia.org/wiki/Student's_t-distribution Examples -------- From Dalgaard page 83 [1]_, suppose the daily energy intake for 11 women in kilojoules (kJ) is: >>> intake = np.array([5260., 5470, 5640, 6180, 6390, 6515, 6805, 7515, \ ... 7515, 8230, 8770]) Does their energy intake deviate systematically from the recommended value of 7725 kJ? Our null hypothesis will be the absence of deviation, and the alternate hypothesis will be the presence of an effect that could be either positive or negative, hence making our test 2-tailed. Because we are estimating the mean and we have N=11 values in our sample, we have N-1=10 degrees of freedom. We set our significance level to 95% and compute the t statistic using the empirical mean and empirical standard deviation of our intake. We use a ddof of 1 to base the computation of our empirical standard deviation on an unbiased estimate of the variance (note: the final estimate is not unbiased due to the concave nature of the square root). >>> np.mean(intake) 6753.636363636364 >>> intake.std(ddof=1) 1142.1232221373727 >>> t = (np.mean(intake)-7725)/(intake.std(ddof=1)/np.sqrt(len(intake))) >>> t -2.8207540608310198 We draw 1000000 samples from Student's t distribution with the adequate degrees of freedom. >>> import matplotlib.pyplot as plt >>> s = np.random.default_rng().standard_t(10, size=1000000) >>> h = plt.hist(s, bins=100, density=True) Does our t statistic land in one of the two critical regions found at both tails of the distribution? >>> np.sum(np.abs(t) < np.abs(s)) / float(len(s)) 0.018318 #random < 0.05, statistic is in critical region The probability value for this 2-tailed test is about 1.83%, which is lower than the 5% pre-determined significance threshold. Therefore, the probability of observing values as extreme as our intake conditionally on the null hypothesis being true is too low, and we reject the null hypothesis of no deviation. standard_normal(size=None, dtype=np.float64, out=None) Draw samples from a standard Normal distribution (mean=0, stdev=1). Parameters ---------- size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Default is None, in which case a single value is returned. dtype : dtype, optional Desired dtype of the result, only `float64` and `float32` are supported. Byteorder must be native. The default value is np.float64. out : ndarray, optional Alternative output array in which to place the result. If size is not None, it must have the same shape as the provided size and must match the type of the output values. Returns ------- out : float or ndarray A floating-point array of shape ``size`` of drawn samples, or a single sample if ``size`` was not specified. See Also -------- normal : Equivalent function with additional ``loc`` and ``scale`` arguments for setting the mean and standard deviation. Notes ----- For random samples from the normal distribution with mean ``mu`` and standard deviation ``sigma``, use one of:: mu + sigma * rng.standard_normal(size=...) rng.normal(mu, sigma, size=...) Examples -------- >>> rng = np.random.default_rng() >>> rng.standard_normal() 2.1923875335537315 # random >>> s = rng.standard_normal(8000) >>> s array([ 0.6888893 , 0.78096262, -0.89086505, ..., 0.49876311, # random -0.38672696, -0.4685006 ]) # random >>> s.shape (8000,) >>> s = rng.standard_normal(size=(3, 4, 2)) >>> s.shape (3, 4, 2) Two-by-four array of samples from the normal distribution with mean 3 and standard deviation 2.5: >>> 3 + 2.5 * rng.standard_normal(size=(2, 4)) array([[-4.49401501, 4.00950034, -1.81814867, 7.29718677], # random [ 0.39924804, 4.68456316, 4.99394529, 4.84057254]]) # random spawn(n_children) Create new independent child generators. See :ref:`seedsequence-spawn` for additional notes on spawning children. .. versionadded:: 1.25.0 Parameters ---------- n_children : int Returns ------- child_generators : list of Generators Raises ------ TypeError When the underlying SeedSequence does not implement spawning. See Also -------- random.BitGenerator.spawn, random.SeedSequence.spawn : Equivalent method on the bit generator and seed sequence. bit_generator : The bit generator instance used by the generator. Examples -------- Starting from a seeded default generator: >>> # High quality entropy created with: f"0x{secrets.randbits(128):x}" >>> entropy = 0x3034c61a9ae04ff8cb62ab8ec2c4b501 >>> rng = np.random.default_rng(entropy) Create two new generators for example for parallel execution: >>> child_rng1, child_rng2 = rng.spawn(2) Drawn numbers from each are independent but derived from the initial seeding entropy: >>> rng.uniform(), child_rng1.uniform(), child_rng2.uniform() (0.19029263503854454, 0.9475673279178444, 0.4702687338396767) It is safe to spawn additional children from the original ``rng`` or the children: >>> more_child_rngs = rng.spawn(20) >>> nested_spawn = child_rng1.spawn(20) shuffle(x, axis=0) Modify an array or sequence in-place by shuffling its contents. The order of sub-arrays is changed but their contents remains the same. Parameters ---------- x : ndarray or MutableSequence The array, list or mutable sequence to be shuffled. axis : int, optional The axis which `x` is shuffled along. Default is 0. It is only supported on `ndarray` objects. Returns ------- None See Also -------- permuted permutation Notes ----- An important distinction between methods ``shuffle`` and ``permuted`` is how they both treat the ``axis`` parameter which can be found at :ref:`generator-handling-axis-parameter`. Examples -------- >>> rng = np.random.default_rng() >>> arr = np.arange(10) >>> arr array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> rng.shuffle(arr) >>> arr array([2, 0, 7, 5, 1, 4, 8, 9, 3, 6]) # random >>> arr = np.arange(9).reshape((3, 3)) >>> arr array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> rng.shuffle(arr) >>> arr array([[3, 4, 5], # random [6, 7, 8], [0, 1, 2]]) >>> arr = np.arange(9).reshape((3, 3)) >>> arr array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> rng.shuffle(arr, axis=1) >>> arr array([[2, 0, 1], # random [5, 3, 4], [8, 6, 7]]) rayleigh(scale=1.0, size=None) Draw samples from a Rayleigh distribution. The :math:`\chi` and Weibull distributions are generalizations of the Rayleigh. Parameters ---------- scale : float or array_like of floats, optional Scale, also equals the mode. Must be non-negative. Default is 1. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``scale`` is a scalar. Otherwise, ``np.array(scale).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Rayleigh distribution. Notes ----- The probability density function for the Rayleigh distribution is .. math:: P(x;scale) = \frac{x}{scale^2}e^{\frac{-x^2}{2 \cdotp scale^2}} The Rayleigh distribution would arise, for example, if the East and North components of the wind velocity had identical zero-mean Gaussian distributions. Then the wind speed would have a Rayleigh distribution. References ---------- .. [1] Brighton Webs Ltd., "Rayleigh Distribution," https://web.archive.org/web/20090514091424/http://brighton-webs.co.uk:80/distributions/rayleigh.asp .. [2] Wikipedia, "Rayleigh distribution" https://en.wikipedia.org/wiki/Rayleigh_distribution Examples -------- Draw values from the distribution and plot the histogram >>> from matplotlib.pyplot import hist >>> rng = np.random.default_rng() >>> values = hist(rng.rayleigh(3, 100000), bins=200, density=True) Wave heights tend to follow a Rayleigh distribution. If the mean wave height is 1 meter, what fraction of waves are likely to be larger than 3 meters? >>> meanvalue = 1 >>> modevalue = np.sqrt(2 / np.pi) * meanvalue >>> s = rng.rayleigh(modevalue, 1000000) The percentage of waves larger than 3 meters is: >>> 100.*sum(s>3)/1000000. 0.087300000000000003 # random random(size=None, dtype=np.float64, out=None) Return random floats in the half-open interval [0.0, 1.0). Results are from the "continuous uniform" distribution over the stated interval. To sample :math:`Unif[a, b), b > a` use `uniform` or multiply the output of `random` by ``(b - a)`` and add ``a``:: (b - a) * random() + a Parameters ---------- size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Default is None, in which case a single value is returned. dtype : dtype, optional Desired dtype of the result, only `float64` and `float32` are supported. Byteorder must be native. The default value is np.float64. out : ndarray, optional Alternative output array in which to place the result. If size is not None, it must have the same shape as the provided size and must match the type of the output values. Returns ------- out : float or ndarray of floats Array of random floats of shape `size` (unless ``size=None``, in which case a single float is returned). See Also -------- uniform : Draw samples from the parameterized uniform distribution. Examples -------- >>> rng = np.random.default_rng() >>> rng.random() 0.47108547995356098 # random >>> type(rng.random()) >>> rng.random((5,)) array([ 0.30220482, 0.86820401, 0.1654503 , 0.11659149, 0.54323428]) # random Three-by-two array of random numbers from [-5, 0): >>> 5 * rng.random((3, 2)) - 5 array([[-3.99149989, -0.52338984], # random [-2.99091858, -0.79479508], [-1.23204345, -1.75224494]]) power(a, size=None) Draws samples in [0, 1] from a power distribution with positive exponent a - 1. Also known as the power function distribution. Parameters ---------- a : float or array_like of floats Parameter of the distribution. Must be non-negative. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``a`` is a scalar. Otherwise, ``np.array(a).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized power distribution. Raises ------ ValueError If a <= 0. Notes ----- The probability density function is .. math:: P(x; a) = ax^{a-1}, 0 \le x \le 1, a>0. The power function distribution is just the inverse of the Pareto distribution. It may also be seen as a special case of the Beta distribution. It is used, for example, in modeling the over-reporting of insurance claims. References ---------- .. [1] Christian Kleiber, Samuel Kotz, "Statistical size distributions in economics and actuarial sciences", Wiley, 2003. .. [2] Heckert, N. A. and Filliben, James J. "NIST Handbook 148: Dataplot Reference Manual, Volume 2: Let Subcommands and Library Functions", National Institute of Standards and Technology Handbook Series, June 2003. https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/powpdf.pdf Examples -------- Draw samples from the distribution: >>> rng = np.random.default_rng() >>> a = 5. # shape >>> samples = 1000 >>> s = rng.power(a, samples) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, bins=30) >>> x = np.linspace(0, 1, 100) >>> y = a*x**(a-1.) >>> normed_y = samples*np.diff(bins)[0]*y >>> plt.plot(x, normed_y) >>> plt.show() Compare the power function distribution to the inverse of the Pareto. >>> from scipy import stats # doctest: +SKIP >>> rvs = rng.power(5, 1000000) >>> rvsp = rng.pareto(5, 1000000) >>> xx = np.linspace(0,1,100) >>> powpdf = stats.powerlaw.pdf(xx,5) # doctest: +SKIP >>> plt.figure() >>> plt.hist(rvs, bins=50, density=True) >>> plt.plot(xx,powpdf,'r-') # doctest: +SKIP >>> plt.title('power(5)') >>> plt.figure() >>> plt.hist(1./(1.+rvsp), bins=50, density=True) >>> plt.plot(xx,powpdf,'r-') # doctest: +SKIP >>> plt.title('inverse of 1 + Generator.pareto(5)') >>> plt.figure() >>> plt.hist(1./(1.+rvsp), bins=50, density=True) >>> plt.plot(xx,powpdf,'r-') # doctest: +SKIP >>> plt.title('inverse of stats.pareto(5)') permuted(x, axis=None, out=None) Randomly permute `x` along axis `axis`. Unlike `shuffle`, each slice along the given axis is shuffled independently of the others. Parameters ---------- x : array_like, at least one-dimensional Array to be shuffled. axis : int, optional Slices of `x` in this axis are shuffled. Each slice is shuffled independently of the others. If `axis` is None, the flattened array is shuffled. out : ndarray, optional If given, this is the destination of the shuffled array. If `out` is None, a shuffled copy of the array is returned. Returns ------- ndarray If `out` is None, a shuffled copy of `x` is returned. Otherwise, the shuffled array is stored in `out`, and `out` is returned See Also -------- shuffle permutation Notes ----- An important distinction between methods ``shuffle`` and ``permuted`` is how they both treat the ``axis`` parameter which can be found at :ref:`generator-handling-axis-parameter`. Examples -------- Create a `numpy.random.Generator` instance: >>> rng = np.random.default_rng() Create a test array: >>> x = np.arange(24).reshape(3, 8) >>> x array([[ 0, 1, 2, 3, 4, 5, 6, 7], [ 8, 9, 10, 11, 12, 13, 14, 15], [16, 17, 18, 19, 20, 21, 22, 23]]) Shuffle the rows of `x`: >>> y = rng.permuted(x, axis=1) >>> y array([[ 4, 3, 6, 7, 1, 2, 5, 0], # random [15, 10, 14, 9, 12, 11, 8, 13], [17, 16, 20, 21, 18, 22, 23, 19]]) `x` has not been modified: >>> x array([[ 0, 1, 2, 3, 4, 5, 6, 7], [ 8, 9, 10, 11, 12, 13, 14, 15], [16, 17, 18, 19, 20, 21, 22, 23]]) To shuffle the rows of `x` in-place, pass `x` as the `out` parameter: >>> y = rng.permuted(x, axis=1, out=x) >>> x array([[ 3, 0, 4, 7, 1, 6, 2, 5], # random [ 8, 14, 13, 9, 12, 11, 15, 10], [17, 18, 16, 22, 19, 23, 20, 21]]) Note that when the ``out`` parameter is given, the return value is ``out``: >>> y is x True permutation(x, axis=0) Randomly permute a sequence, or return a permuted range. Parameters ---------- x : int or array_like If `x` is an integer, randomly permute ``np.arange(x)``. If `x` is an array, make a copy and shuffle the elements randomly. axis : int, optional The axis which `x` is shuffled along. Default is 0. Returns ------- out : ndarray Permuted sequence or array range. Examples -------- >>> rng = np.random.default_rng() >>> rng.permutation(10) array([1, 7, 4, 3, 0, 9, 2, 5, 8, 6]) # random >>> rng.permutation([1, 4, 9, 12, 15]) array([15, 1, 9, 4, 12]) # random >>> arr = np.arange(9).reshape((3, 3)) >>> rng.permutation(arr) array([[6, 7, 8], # random [0, 1, 2], [3, 4, 5]]) >>> rng.permutation("abc") Traceback (most recent call last): ... numpy.exceptions.AxisError: axis 0 is out of bounds for array of dimension 0 >>> arr = np.arange(9).reshape((3, 3)) >>> rng.permutation(arr, axis=1) array([[0, 2, 1], # random [3, 5, 4], [6, 8, 7]]) pareto(a, size=None) Draw samples from a Pareto II or Lomax distribution with specified shape. The Lomax or Pareto II distribution is a shifted Pareto distribution. The classical Pareto distribution can be obtained from the Lomax distribution by adding 1 and multiplying by the scale parameter ``m`` (see Notes). The smallest value of the Lomax distribution is zero while for the classical Pareto distribution it is ``mu``, where the standard Pareto distribution has location ``mu = 1``. Lomax can also be considered as a simplified version of the Generalized Pareto distribution (available in SciPy), with the scale set to one and the location set to zero. The Pareto distribution must be greater than zero, and is unbounded above. It is also known as the "80-20 rule". In this distribution, 80 percent of the weights are in the lowest 20 percent of the range, while the other 20 percent fill the remaining 80 percent of the range. Parameters ---------- a : float or array_like of floats Shape of the distribution. Must be positive. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``a`` is a scalar. Otherwise, ``np.array(a).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Pareto distribution. See Also -------- scipy.stats.lomax : probability density function, distribution or cumulative density function, etc. scipy.stats.genpareto : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Pareto distribution is .. math:: p(x) = \frac{am^a}{x^{a+1}} where :math:`a` is the shape and :math:`m` the scale. The Pareto distribution, named after the Italian economist Vilfredo Pareto, is a power law probability distribution useful in many real world problems. Outside the field of economics it is generally referred to as the Bradford distribution. Pareto developed the distribution to describe the distribution of wealth in an economy. It has also found use in insurance, web page access statistics, oil field sizes, and many other problems, including the download frequency for projects in Sourceforge [1]_. It is one of the so-called "fat-tailed" distributions. References ---------- .. [1] Francis Hunt and Paul Johnson, On the Pareto Distribution of Sourceforge projects. .. [2] Pareto, V. (1896). Course of Political Economy. Lausanne. .. [3] Reiss, R.D., Thomas, M.(2001), Statistical Analysis of Extreme Values, Birkhauser Verlag, Basel, pp 23-30. .. [4] Wikipedia, "Pareto distribution", https://en.wikipedia.org/wiki/Pareto_distribution Examples -------- Draw samples from the distribution: >>> a, m = 3., 2. # shape and mode >>> s = (np.random.default_rng().pareto(a, 1000) + 1) * m Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, _ = plt.hist(s, 100, density=True) >>> fit = a*m**a / bins**(a+1) >>> plt.plot(bins, max(count)*fit/max(fit), linewidth=2, color='r') >>> plt.show() out must have the same shape as xnumpy.core.multiarray failed to import normal(loc=0.0, scale=1.0, size=None) Draw random samples from a normal (Gaussian) distribution. The probability density function of the normal distribution, first derived by De Moivre and 200 years later by both Gauss and Laplace independently [2]_, is often called the bell curve because of its characteristic shape (see the example below). The normal distributions occurs often in nature. For example, it describes the commonly occurring distribution of samples influenced by a large number of tiny, random disturbances, each with its own unique distribution [2]_. Parameters ---------- loc : float or array_like of floats Mean ("centre") of the distribution. scale : float or array_like of floats Standard deviation (spread or "width") of the distribution. Must be non-negative. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``loc`` and ``scale`` are both scalars. Otherwise, ``np.broadcast(loc, scale).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized normal distribution. See Also -------- scipy.stats.norm : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Gaussian distribution is .. math:: p(x) = \frac{1}{\sqrt{ 2 \pi \sigma^2 }} e^{ - \frac{ (x - \mu)^2 } {2 \sigma^2} }, where :math:`\mu` is the mean and :math:`\sigma` the standard deviation. The square of the standard deviation, :math:`\sigma^2`, is called the variance. The function has its peak at the mean, and its "spread" increases with the standard deviation (the function reaches 0.607 times its maximum at :math:`x + \sigma` and :math:`x - \sigma` [2]_). This implies that :meth:`normal` is more likely to return samples lying close to the mean, rather than those far away. References ---------- .. [1] Wikipedia, "Normal distribution", https://en.wikipedia.org/wiki/Normal_distribution .. [2] P. R. Peebles Jr., "Central Limit Theorem" in "Probability, Random Variables and Random Signal Principles", 4th ed., 2001, pp. 51, 51, 125. Examples -------- Draw samples from the distribution: >>> mu, sigma = 0, 0.1 # mean and standard deviation >>> s = np.random.default_rng().normal(mu, sigma, 1000) Verify the mean and the variance: >>> abs(mu - np.mean(s)) 0.0 # may vary >>> abs(sigma - np.std(s, ddof=1)) 0.0 # may vary Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 30, density=True) >>> plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) * ... np.exp( - (bins - mu)**2 / (2 * sigma**2) ), ... linewidth=2, color='r') >>> plt.show() Two-by-four array of samples from the normal distribution with mean 3 and standard deviation 2.5: >>> np.random.default_rng().normal(3, 2.5, size=(2, 4)) array([[-4.49401501, 4.00950034, -1.81814867, 7.29718677], # random [ 0.39924804, 4.68456316, 4.99394529, 4.84057254]]) # random noncentral_f(dfnum, dfden, nonc, size=None) Draw samples from the noncentral F distribution. Samples are drawn from an F distribution with specified parameters, `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of freedom in denominator), where both parameters > 1. `nonc` is the non-centrality parameter. Parameters ---------- dfnum : float or array_like of floats Numerator degrees of freedom, must be > 0. .. versionchanged:: 1.14.0 Earlier NumPy versions required dfnum > 1. dfden : float or array_like of floats Denominator degrees of freedom, must be > 0. nonc : float or array_like of floats Non-centrality parameter, the sum of the squares of the numerator means, must be >= 0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``dfnum``, ``dfden``, and ``nonc`` are all scalars. Otherwise, ``np.broadcast(dfnum, dfden, nonc).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized noncentral Fisher distribution. Notes ----- When calculating the power of an experiment (power = probability of rejecting the null hypothesis when a specific alternative is true) the non-central F statistic becomes important. When the null hypothesis is true, the F statistic follows a central F distribution. When the null hypothesis is not true, then it follows a non-central F statistic. References ---------- .. [1] Weisstein, Eric W. "Noncentral F-Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NoncentralF-Distribution.html .. [2] Wikipedia, "Noncentral F-distribution", https://en.wikipedia.org/wiki/Noncentral_F-distribution Examples -------- In a study, testing for a specific alternative to the null hypothesis requires use of the Noncentral F distribution. We need to calculate the area in the tail of the distribution that exceeds the value of the F distribution for the null hypothesis. We'll plot the two probability distributions for comparison. >>> rng = np.random.default_rng() >>> dfnum = 3 # between group deg of freedom >>> dfden = 20 # within groups degrees of freedom >>> nonc = 3.0 >>> nc_vals = rng.noncentral_f(dfnum, dfden, nonc, 1000000) >>> NF = np.histogram(nc_vals, bins=50, density=True) >>> c_vals = rng.f(dfnum, dfden, 1000000) >>> F = np.histogram(c_vals, bins=50, density=True) >>> import matplotlib.pyplot as plt >>> plt.plot(F[1][1:], F[0]) >>> plt.plot(NF[1][1:], NF[0]) >>> plt.show() noncentral_chisquare(df, nonc, size=None) Draw samples from a noncentral chi-square distribution. The noncentral :math:`\chi^2` distribution is a generalization of the :math:`\chi^2` distribution. Parameters ---------- df : float or array_like of floats Degrees of freedom, must be > 0. .. versionchanged:: 1.10.0 Earlier NumPy versions required dfnum > 1. nonc : float or array_like of floats Non-centrality, must be non-negative. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``df`` and ``nonc`` are both scalars. Otherwise, ``np.broadcast(df, nonc).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized noncentral chi-square distribution. Notes ----- The probability density function for the noncentral Chi-square distribution is .. math:: P(x;df,nonc) = \sum^{\infty}_{i=0} \frac{e^{-nonc/2}(nonc/2)^{i}}{i!} P_{Y_{df+2i}}(x), where :math:`Y_{q}` is the Chi-square with q degrees of freedom. References ---------- .. [1] Wikipedia, "Noncentral chi-squared distribution" https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution Examples -------- Draw values from the distribution and plot the histogram >>> rng = np.random.default_rng() >>> import matplotlib.pyplot as plt >>> values = plt.hist(rng.noncentral_chisquare(3, 20, 100000), ... bins=200, density=True) >>> plt.show() Draw values from a noncentral chisquare with very small noncentrality, and compare to a chisquare. >>> plt.figure() >>> values = plt.hist(rng.noncentral_chisquare(3, .0000001, 100000), ... bins=np.arange(0., 25, .1), density=True) >>> values2 = plt.hist(rng.chisquare(3, 100000), ... bins=np.arange(0., 25, .1), density=True) >>> plt.plot(values[1][0:-1], values[0]-values2[0], 'ob') >>> plt.show() Demonstrate how large values of non-centrality lead to a more symmetric distribution. >>> plt.figure() >>> values = plt.hist(rng.noncentral_chisquare(3, 20, 100000), ... bins=200, density=True) >>> plt.show() negative_binomial(n, p, size=None) Draw samples from a negative binomial distribution. Samples are drawn from a negative binomial distribution with specified parameters, `n` successes and `p` probability of success where `n` is > 0 and `p` is in the interval (0, 1]. Parameters ---------- n : float or array_like of floats Parameter of the distribution, > 0. p : float or array_like of floats Parameter of the distribution. Must satisfy 0 < p <= 1. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``n`` and ``p`` are both scalars. Otherwise, ``np.broadcast(n, p).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized negative binomial distribution, where each sample is equal to N, the number of failures that occurred before a total of n successes was reached. Notes ----- The probability mass function of the negative binomial distribution is .. math:: P(N;n,p) = \frac{\Gamma(N+n)}{N!\Gamma(n)}p^{n}(1-p)^{N}, where :math:`n` is the number of successes, :math:`p` is the probability of success, :math:`N+n` is the number of trials, and :math:`\Gamma` is the gamma function. When :math:`n` is an integer, :math:`\frac{\Gamma(N+n)}{N!\Gamma(n)} = \binom{N+n-1}{N}`, which is the more common form of this term in the pmf. The negative binomial distribution gives the probability of N failures given n successes, with a success on the last trial. If one throws a die repeatedly until the third time a "1" appears, then the probability distribution of the number of non-"1"s that appear before the third "1" is a negative binomial distribution. Because this method internally calls ``Generator.poisson`` with an intermediate random value, a ValueError is raised when the choice of :math:`n` and :math:`p` would result in the mean + 10 sigma of the sampled intermediate distribution exceeding the max acceptable value of the ``Generator.poisson`` method. This happens when :math:`p` is too low (a lot of failures happen for every success) and :math:`n` is too big ( a lot of successes are allowed). Therefore, the :math:`n` and :math:`p` values must satisfy the constraint: .. math:: n\frac{1-p}{p}+10n\sqrt{n}\frac{1-p}{p}<2^{63}-1-10\sqrt{2^{63}-1}, Where the left side of the equation is the derived mean + 10 sigma of a sample from the gamma distribution internally used as the :math:`lam` parameter of a poisson sample, and the right side of the equation is the constraint for maximum value of :math:`lam` in ``Generator.poisson``. References ---------- .. [1] Weisstein, Eric W. "Negative Binomial Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NegativeBinomialDistribution.html .. [2] Wikipedia, "Negative binomial distribution", https://en.wikipedia.org/wiki/Negative_binomial_distribution Examples -------- Draw samples from the distribution: A real world example. A company drills wild-cat oil exploration wells, each with an estimated probability of success of 0.1. What is the probability of having one success for each successive well, that is what is the probability of a single success after drilling 5 wells, after 6 wells, etc.? >>> s = np.random.default_rng().negative_binomial(1, 0.1, 100000) >>> for i in range(1, 11): # doctest: +SKIP ... probability = sum(s>> mean = [0, 0] >>> cov = [[1, 0], [0, 100]] # diagonal covariance Diagonal covariance means that points are oriented along x or y-axis: >>> import matplotlib.pyplot as plt >>> x, y = np.random.default_rng().multivariate_normal(mean, cov, 5000).T >>> plt.plot(x, y, 'x') >>> plt.axis('equal') >>> plt.show() Note that the covariance matrix must be positive semidefinite (a.k.a. nonnegative-definite). Otherwise, the behavior of this method is undefined and backwards compatibility is not guaranteed. This function internally uses linear algebra routines, and thus results may not be identical (even up to precision) across architectures, OSes, or even builds. For example, this is likely if ``cov`` has multiple equal singular values and ``method`` is ``'svd'`` (default). In this case, ``method='cholesky'`` may be more robust. References ---------- .. [1] Papoulis, A., "Probability, Random Variables, and Stochastic Processes," 3rd ed., New York: McGraw-Hill, 1991. .. [2] Duda, R. O., Hart, P. E., and Stork, D. G., "Pattern Classification," 2nd ed., New York: Wiley, 2001. Examples -------- >>> mean = (1, 2) >>> cov = [[1, 0], [0, 1]] >>> rng = np.random.default_rng() >>> x = rng.multivariate_normal(mean, cov, (3, 3)) >>> x.shape (3, 3, 2) We can use a different method other than the default to factorize cov: >>> y = rng.multivariate_normal(mean, cov, (3, 3), method='cholesky') >>> y.shape (3, 3, 2) Here we generate 800 samples from the bivariate normal distribution with mean [0, 0] and covariance matrix [[6, -3], [-3, 3.5]]. The expected variances of the first and second components of the sample are 6 and 3.5, respectively, and the expected correlation coefficient is -3/sqrt(6*3.5) ≈ -0.65465. >>> cov = np.array([[6, -3], [-3, 3.5]]) >>> pts = rng.multivariate_normal([0, 0], cov, size=800) Check that the mean, covariance, and correlation coefficient of the sample are close to the expected values: >>> pts.mean(axis=0) array([ 0.0326911 , -0.01280782]) # may vary >>> np.cov(pts.T) array([[ 5.96202397, -2.85602287], [-2.85602287, 3.47613949]]) # may vary >>> np.corrcoef(pts.T)[0, 1] -0.6273591314603949 # may vary We can visualize this data with a scatter plot. The orientation of the point cloud illustrates the negative correlation of the components of this sample. >>> import matplotlib.pyplot as plt >>> plt.plot(pts[:, 0], pts[:, 1], '.', alpha=0.5) >>> plt.axis('equal') >>> plt.grid() >>> plt.show() multivariate_hypergeometric(colors, nsample, size=None, method='marginals') Generate variates from a multivariate hypergeometric distribution. The multivariate hypergeometric distribution is a generalization of the hypergeometric distribution. Choose ``nsample`` items at random without replacement from a collection with ``N`` distinct types. ``N`` is the length of ``colors``, and the values in ``colors`` are the number of occurrences of that type in the collection. The total number of items in the collection is ``sum(colors)``. Each random variate generated by this function is a vector of length ``N`` holding the counts of the different types that occurred in the ``nsample`` items. The name ``colors`` comes from a common description of the distribution: it is the probability distribution of the number of marbles of each color selected without replacement from an urn containing marbles of different colors; ``colors[i]`` is the number of marbles in the urn with color ``i``. Parameters ---------- colors : sequence of integers The number of each type of item in the collection from which a sample is drawn. The values in ``colors`` must be nonnegative. To avoid loss of precision in the algorithm, ``sum(colors)`` must be less than ``10**9`` when `method` is "marginals". nsample : int The number of items selected. ``nsample`` must not be greater than ``sum(colors)``. size : int or tuple of ints, optional The number of variates to generate, either an integer or a tuple holding the shape of the array of variates. If the given size is, e.g., ``(k, m)``, then ``k * m`` variates are drawn, where one variate is a vector of length ``len(colors)``, and the return value has shape ``(k, m, len(colors))``. If `size` is an integer, the output has shape ``(size, len(colors))``. Default is None, in which case a single variate is returned as an array with shape ``(len(colors),)``. method : string, optional Specify the algorithm that is used to generate the variates. Must be 'count' or 'marginals' (the default). See the Notes for a description of the methods. Returns ------- variates : ndarray Array of variates drawn from the multivariate hypergeometric distribution. See Also -------- hypergeometric : Draw samples from the (univariate) hypergeometric distribution. Notes ----- The two methods do not return the same sequence of variates. The "count" algorithm is roughly equivalent to the following numpy code:: choices = np.repeat(np.arange(len(colors)), colors) selection = np.random.choice(choices, nsample, replace=False) variate = np.bincount(selection, minlength=len(colors)) The "count" algorithm uses a temporary array of integers with length ``sum(colors)``. The "marginals" algorithm generates a variate by using repeated calls to the univariate hypergeometric sampler. It is roughly equivalent to:: variate = np.zeros(len(colors), dtype=np.int64) # `remaining` is the cumulative sum of `colors` from the last # element to the first; e.g. if `colors` is [3, 1, 5], then # `remaining` is [9, 6, 5]. remaining = np.cumsum(colors[::-1])[::-1] for i in range(len(colors)-1): if nsample < 1: break variate[i] = hypergeometric(colors[i], remaining[i+1], nsample) nsample -= variate[i] variate[-1] = nsample The default method is "marginals". For some cases (e.g. when `colors` contains relatively small integers), the "count" method can be significantly faster than the "marginals" method. If performance of the algorithm is important, test the two methods with typical inputs to decide which works best. .. versionadded:: 1.18.0 Examples -------- >>> colors = [16, 8, 4] >>> seed = 4861946401452 >>> gen = np.random.Generator(np.random.PCG64(seed)) >>> gen.multivariate_hypergeometric(colors, 6) array([5, 0, 1]) >>> gen.multivariate_hypergeometric(colors, 6, size=3) array([[5, 0, 1], [2, 2, 2], [3, 3, 0]]) >>> gen.multivariate_hypergeometric(colors, 6, size=(2, 2)) array([[[3, 2, 1], [3, 2, 1]], [[4, 1, 1], [3, 2, 1]]]) multinomial(n, pvals, size=None) Draw samples from a multinomial distribution. The multinomial distribution is a multivariate generalization of the binomial distribution. Take an experiment with one of ``p`` possible outcomes. An example of such an experiment is throwing a dice, where the outcome can be 1 through 6. Each sample drawn from the distribution represents `n` such experiments. Its values, ``X_i = [X_0, X_1, ..., X_p]``, represent the number of times the outcome was ``i``. Parameters ---------- n : int or array-like of ints Number of experiments. pvals : array-like of floats Probabilities of each of the ``p`` different outcomes with shape ``(k0, k1, ..., kn, p)``. Each element ``pvals[i,j,...,:]`` must sum to 1 (however, the last element is always assumed to account for the remaining probability, as long as ``sum(pvals[..., :-1], axis=-1) <= 1.0``. Must have at least 1 dimension where pvals.shape[-1] > 0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn each with ``p`` elements. Default is None where the output size is determined by the broadcast shape of ``n`` and all by the final dimension of ``pvals``, which is denoted as ``b=(b0, b1, ..., bq)``. If size is not None, then it must be compatible with the broadcast shape ``b``. Specifically, size must have ``q`` or more elements and size[-(q-j):] must equal ``bj``. Returns ------- out : ndarray The drawn samples, of shape size, if provided. When size is provided, the output shape is size + (p,) If not specified, the shape is determined by the broadcast shape of ``n`` and ``pvals``, ``(b0, b1, ..., bq)`` augmented with the dimension of the multinomial, ``p``, so that that output shape is ``(b0, b1, ..., bq, p)``. Each entry ``out[i,j,...,:]`` is a ``p``-dimensional value drawn from the distribution. .. versionchanged:: 1.22.0 Added support for broadcasting `pvals` against `n` Examples -------- Throw a dice 20 times: >>> rng = np.random.default_rng() >>> rng.multinomial(20, [1/6.]*6, size=1) array([[4, 1, 7, 5, 2, 1]]) # random It landed 4 times on 1, once on 2, etc. Now, throw the dice 20 times, and 20 times again: >>> rng.multinomial(20, [1/6.]*6, size=2) array([[3, 4, 3, 3, 4, 3], [2, 4, 3, 4, 0, 7]]) # random For the first run, we threw 3 times 1, 4 times 2, etc. For the second, we threw 2 times 1, 4 times 2, etc. Now, do one experiment throwing the dice 10 time, and 10 times again, and another throwing the dice 20 times, and 20 times again: >>> rng.multinomial([[10], [20]], [1/6.]*6, size=(2, 2)) array([[[2, 4, 0, 1, 2, 1], [1, 3, 0, 3, 1, 2]], [[1, 4, 4, 4, 4, 3], [3, 3, 2, 5, 5, 2]]]) # random The first array shows the outcomes of throwing the dice 10 times, and the second shows the outcomes from throwing the dice 20 times. A loaded die is more likely to land on number 6: >>> rng.multinomial(100, [1/7.]*5 + [2/7.]) array([11, 16, 14, 17, 16, 26]) # random Simulate 10 throws of a 4-sided die and 20 throws of a 6-sided die >>> rng.multinomial([10, 20],[[1/4]*4 + [0]*2, [1/6]*6]) array([[2, 1, 4, 3, 0, 0], [3, 3, 3, 6, 1, 4]], dtype=int64) # random Generate categorical random variates from two categories where the first has 3 outcomes and the second has 2. >>> rng.multinomial(1, [[.1, .5, .4 ], [.3, .7, .0]]) array([[0, 0, 1], [0, 1, 0]], dtype=int64) # random ``argmax(axis=-1)`` is then used to return the categories. >>> pvals = [[.1, .5, .4 ], [.3, .7, .0]] >>> rvs = rng.multinomial(1, pvals, size=(4,2)) >>> rvs.argmax(axis=-1) array([[0, 1], [2, 0], [2, 1], [2, 0]], dtype=int64) # random The same output dimension can be produced using broadcasting. >>> rvs = rng.multinomial([[1]] * 4, pvals) >>> rvs.argmax(axis=-1) array([[0, 1], [2, 0], [2, 1], [2, 0]], dtype=int64) # random The probability inputs should be normalized. As an implementation detail, the value of the last entry is ignored and assumed to take up any leftover probability mass, but this should not be relied on. A biased coin which has twice as much weight on one side as on the other should be sampled like so: >>> rng.multinomial(100, [1.0 / 3, 2.0 / 3]) # RIGHT array([38, 62]) # random not like: >>> rng.multinomial(100, [1.0, 2.0]) # WRONG Traceback (most recent call last): ValueError: pvals < 0, pvals > 1 or pvals contains NaNs logseries(p, size=None) Draw samples from a logarithmic series distribution. Samples are drawn from a log series distribution with specified shape parameter, 0 <= ``p`` < 1. Parameters ---------- p : float or array_like of floats Shape parameter for the distribution. Must be in the range [0, 1). size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``p`` is a scalar. Otherwise, ``np.array(p).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized logarithmic series distribution. See Also -------- scipy.stats.logser : probability density function, distribution or cumulative density function, etc. Notes ----- The probability mass function for the Log Series distribution is .. math:: P(k) = \frac{-p^k}{k \ln(1-p)}, where p = probability. The log series distribution is frequently used to represent species richness and occurrence, first proposed by Fisher, Corbet, and Williams in 1943 [2]. It may also be used to model the numbers of occupants seen in cars [3]. References ---------- .. [1] Buzas, Martin A.; Culver, Stephen J., Understanding regional species diversity through the log series distribution of occurrences: BIODIVERSITY RESEARCH Diversity & Distributions, Volume 5, Number 5, September 1999 , pp. 187-195(9). .. [2] Fisher, R.A,, A.S. Corbet, and C.B. Williams. 1943. The relation between the number of species and the number of individuals in a random sample of an animal population. Journal of Animal Ecology, 12:42-58. .. [3] D. J. Hand, F. Daly, D. Lunn, E. Ostrowski, A Handbook of Small Data Sets, CRC Press, 1994. .. [4] Wikipedia, "Logarithmic distribution", https://en.wikipedia.org/wiki/Logarithmic_distribution Examples -------- Draw samples from the distribution: >>> a = .6 >>> s = np.random.default_rng().logseries(a, 10000) >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s) # plot against distribution >>> def logseries(k, p): ... return -p**k/(k*np.log(1-p)) >>> plt.plot(bins, logseries(bins, a) * count.max()/ ... logseries(bins, a).max(), 'r') >>> plt.show() lognormal(mean=0.0, sigma=1.0, size=None) Draw samples from a log-normal distribution. Draw samples from a log-normal distribution with specified mean, standard deviation, and array shape. Note that the mean and standard deviation are not the values for the distribution itself, but of the underlying normal distribution it is derived from. Parameters ---------- mean : float or array_like of floats, optional Mean value of the underlying normal distribution. Default is 0. sigma : float or array_like of floats, optional Standard deviation of the underlying normal distribution. Must be non-negative. Default is 1. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``mean`` and ``sigma`` are both scalars. Otherwise, ``np.broadcast(mean, sigma).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized log-normal distribution. See Also -------- scipy.stats.lognorm : probability density function, distribution, cumulative density function, etc. Notes ----- A variable `x` has a log-normal distribution if `log(x)` is normally distributed. The probability density function for the log-normal distribution is: .. math:: p(x) = \frac{1}{\sigma x \sqrt{2\pi}} e^{(-\frac{(ln(x)-\mu)^2}{2\sigma^2})} where :math:`\mu` is the mean and :math:`\sigma` is the standard deviation of the normally distributed logarithm of the variable. A log-normal distribution results if a random variable is the *product* of a large number of independent, identically-distributed variables in the same way that a normal distribution results if the variable is the *sum* of a large number of independent, identically-distributed variables. References ---------- .. [1] Limpert, E., Stahel, W. A., and Abbt, M., "Log-normal Distributions across the Sciences: Keys and Clues," BioScience, Vol. 51, No. 5, May, 2001. https://stat.ethz.ch/~stahel/lognormal/bioscience.pdf .. [2] Reiss, R.D. and Thomas, M., "Statistical Analysis of Extreme Values," Basel: Birkhauser Verlag, 2001, pp. 31-32. Examples -------- Draw samples from the distribution: >>> rng = np.random.default_rng() >>> mu, sigma = 3., 1. # mean and standard deviation >>> s = rng.lognormal(mu, sigma, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 100, density=True, align='mid') >>> x = np.linspace(min(bins), max(bins), 10000) >>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2)) ... / (x * sigma * np.sqrt(2 * np.pi))) >>> plt.plot(x, pdf, linewidth=2, color='r') >>> plt.axis('tight') >>> plt.show() Demonstrate that taking the products of random samples from a uniform distribution can be fit well by a log-normal probability density function. >>> # Generate a thousand samples: each is the product of 100 random >>> # values, drawn from a normal distribution. >>> rng = rng >>> b = [] >>> for i in range(1000): ... a = 10. + rng.standard_normal(100) ... b.append(np.prod(a)) >>> b = np.array(b) / np.min(b) # scale values to be positive >>> count, bins, ignored = plt.hist(b, 100, density=True, align='mid') >>> sigma = np.std(np.log(b)) >>> mu = np.mean(np.log(b)) >>> x = np.linspace(min(bins), max(bins), 10000) >>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2)) ... / (x * sigma * np.sqrt(2 * np.pi))) >>> plt.plot(x, pdf, color='r', linewidth=2) >>> plt.show() logistic(loc=0.0, scale=1.0, size=None) Draw samples from a logistic distribution. Samples are drawn from a logistic distribution with specified parameters, loc (location or mean, also median), and scale (>0). Parameters ---------- loc : float or array_like of floats, optional Parameter of the distribution. Default is 0. scale : float or array_like of floats, optional Parameter of the distribution. Must be non-negative. Default is 1. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``loc`` and ``scale`` are both scalars. Otherwise, ``np.broadcast(loc, scale).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized logistic distribution. See Also -------- scipy.stats.logistic : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Logistic distribution is .. math:: P(x) = P(x) = \frac{e^{-(x-\mu)/s}}{s(1+e^{-(x-\mu)/s})^2}, where :math:`\mu` = location and :math:`s` = scale. The Logistic distribution is used in Extreme Value problems where it can act as a mixture of Gumbel distributions, in Epidemiology, and by the World Chess Federation (FIDE) where it is used in the Elo ranking system, assuming the performance of each player is a logistically distributed random variable. References ---------- .. [1] Reiss, R.-D. and Thomas M. (2001), "Statistical Analysis of Extreme Values, from Insurance, Finance, Hydrology and Other Fields," Birkhauser Verlag, Basel, pp 132-133. .. [2] Weisstein, Eric W. "Logistic Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LogisticDistribution.html .. [3] Wikipedia, "Logistic-distribution", https://en.wikipedia.org/wiki/Logistic_distribution Examples -------- Draw samples from the distribution: >>> loc, scale = 10, 1 >>> s = np.random.default_rng().logistic(loc, scale, 10000) >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, bins=50) # plot against distribution >>> def logist(x, loc, scale): ... return np.exp((loc-x)/scale)/(scale*(1+np.exp((loc-x)/scale))**2) >>> lgst_val = logist(bins, loc, scale) >>> plt.plot(bins, lgst_val * count.max() / lgst_val.max()) >>> plt.show() is not compatible with broadcast dimensions of inputs integers(low, high=None, size=None, dtype=np.int64, endpoint=False) Return random integers from `low` (inclusive) to `high` (exclusive), or if endpoint=True, `low` (inclusive) to `high` (inclusive). Replaces `RandomState.randint` (with endpoint=False) and `RandomState.random_integers` (with endpoint=True) Return random integers from the "discrete uniform" distribution of the specified dtype. If `high` is None (the default), then results are from 0 to `low`. Parameters ---------- low : int or array-like of ints Lowest (signed) integers to be drawn from the distribution (unless ``high=None``, in which case this parameter is 0 and this value is used for `high`). high : int or array-like of ints, optional If provided, one above the largest (signed) integer to be drawn from the distribution (see above for behavior if ``high=None``). If array-like, must contain integer values size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Default is None, in which case a single value is returned. dtype : dtype, optional Desired dtype of the result. Byteorder must be native. The default value is np.int64. endpoint : bool, optional If true, sample from the interval [low, high] instead of the default [low, high) Defaults to False Returns ------- out : int or ndarray of ints `size`-shaped array of random integers from the appropriate distribution, or a single such random int if `size` not provided. Notes ----- When using broadcasting with uint64 dtypes, the maximum value (2**64) cannot be represented as a standard integer type. The high array (or low if high is None) must have object dtype, e.g., array([2**64]). Examples -------- >>> rng = np.random.default_rng() >>> rng.integers(2, size=10) array([1, 0, 0, 0, 1, 1, 0, 0, 1, 0]) # random >>> rng.integers(1, size=10) array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) Generate a 2 x 4 array of ints between 0 and 4, inclusive: >>> rng.integers(5, size=(2, 4)) array([[4, 0, 2, 1], [3, 2, 2, 0]]) # random Generate a 1 x 3 array with 3 different upper bounds >>> rng.integers(1, [3, 5, 10]) array([2, 2, 9]) # random Generate a 1 by 3 array with 3 different lower bounds >>> rng.integers([1, 5, 7], 10) array([9, 8, 7]) # random Generate a 2 by 4 array using broadcasting with dtype of uint8 >>> rng.integers([1, 3, 5, 7], [[10], [20]], dtype=np.uint8) array([[ 8, 6, 9, 7], [ 1, 16, 9, 12]], dtype=uint8) # random References ---------- .. [1] Daniel Lemire., "Fast Random Integer Generation in an Interval", ACM Transactions on Modeling and Computer Simulation 29 (1), 2019, http://arxiv.org/abs/1805.10941. hypergeometric(ngood, nbad, nsample, size=None) Draw samples from a Hypergeometric distribution. Samples are drawn from a hypergeometric distribution with specified parameters, `ngood` (ways to make a good selection), `nbad` (ways to make a bad selection), and `nsample` (number of items sampled, which is less than or equal to the sum ``ngood + nbad``). Parameters ---------- ngood : int or array_like of ints Number of ways to make a good selection. Must be nonnegative and less than 10**9. nbad : int or array_like of ints Number of ways to make a bad selection. Must be nonnegative and less than 10**9. nsample : int or array_like of ints Number of items sampled. Must be nonnegative and less than ``ngood + nbad``. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if `ngood`, `nbad`, and `nsample` are all scalars. Otherwise, ``np.broadcast(ngood, nbad, nsample).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized hypergeometric distribution. Each sample is the number of good items within a randomly selected subset of size `nsample` taken from a set of `ngood` good items and `nbad` bad items. See Also -------- multivariate_hypergeometric : Draw samples from the multivariate hypergeometric distribution. scipy.stats.hypergeom : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Hypergeometric distribution is .. math:: P(x) = \frac{\binom{g}{x}\binom{b}{n-x}}{\binom{g+b}{n}}, where :math:`0 \le x \le n` and :math:`n-b \le x \le g` for P(x) the probability of ``x`` good results in the drawn sample, g = `ngood`, b = `nbad`, and n = `nsample`. Consider an urn with black and white marbles in it, `ngood` of them are black and `nbad` are white. If you draw `nsample` balls without replacement, then the hypergeometric distribution describes the distribution of black balls in the drawn sample. Note that this distribution is very similar to the binomial distribution, except that in this case, samples are drawn without replacement, whereas in the Binomial case samples are drawn with replacement (or the sample space is infinite). As the sample space becomes large, this distribution approaches the binomial. The arguments `ngood` and `nbad` each must be less than `10**9`. For extremely large arguments, the algorithm that is used to compute the samples [4]_ breaks down because of loss of precision in floating point calculations. For such large values, if `nsample` is not also large, the distribution can be approximated with the binomial distribution, `binomial(n=nsample, p=ngood/(ngood + nbad))`. References ---------- .. [1] Lentner, Marvin, "Elementary Applied Statistics", Bogden and Quigley, 1972. .. [2] Weisstein, Eric W. "Hypergeometric Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/HypergeometricDistribution.html .. [3] Wikipedia, "Hypergeometric distribution", https://en.wikipedia.org/wiki/Hypergeometric_distribution .. [4] Stadlober, Ernst, "The ratio of uniforms approach for generating discrete random variates", Journal of Computational and Applied Mathematics, 31, pp. 181-189 (1990). Examples -------- Draw samples from the distribution: >>> rng = np.random.default_rng() >>> ngood, nbad, nsamp = 100, 2, 10 # number of good, number of bad, and number of samples >>> s = rng.hypergeometric(ngood, nbad, nsamp, 1000) >>> from matplotlib.pyplot import hist >>> hist(s) # note that it is very unlikely to grab both bad items Suppose you have an urn with 15 white and 15 black marbles. If you pull 15 marbles at random, how likely is it that 12 or more of them are one color? >>> s = rng.hypergeometric(15, 15, 15, 100000) >>> sum(s>=12)/100000. + sum(s<=3)/100000. # answer = 0.003 ... pretty unlikely! gumbel(loc=0.0, scale=1.0, size=None) Draw samples from a Gumbel distribution. Draw samples from a Gumbel distribution with specified location and scale. For more information on the Gumbel distribution, see Notes and References below. Parameters ---------- loc : float or array_like of floats, optional The location of the mode of the distribution. Default is 0. scale : float or array_like of floats, optional The scale parameter of the distribution. Default is 1. Must be non- negative. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``loc`` and ``scale`` are both scalars. Otherwise, ``np.broadcast(loc, scale).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Gumbel distribution. See Also -------- scipy.stats.gumbel_l scipy.stats.gumbel_r scipy.stats.genextreme weibull Notes ----- The Gumbel (or Smallest Extreme Value (SEV) or the Smallest Extreme Value Type I) distribution is one of a class of Generalized Extreme Value (GEV) distributions used in modeling extreme value problems. The Gumbel is a special case of the Extreme Value Type I distribution for maximums from distributions with "exponential-like" tails. The probability density for the Gumbel distribution is .. math:: p(x) = \frac{e^{-(x - \mu)/ \beta}}{\beta} e^{ -e^{-(x - \mu)/ \beta}}, where :math:`\mu` is the mode, a location parameter, and :math:`\beta` is the scale parameter. The Gumbel (named for German mathematician Emil Julius Gumbel) was used very early in the hydrology literature, for modeling the occurrence of flood events. It is also used for modeling maximum wind speed and rainfall rates. It is a "fat-tailed" distribution - the probability of an event in the tail of the distribution is larger than if one used a Gaussian, hence the surprisingly frequent occurrence of 100-year floods. Floods were initially modeled as a Gaussian process, which underestimated the frequency of extreme events. It is one of a class of extreme value distributions, the Generalized Extreme Value (GEV) distributions, which also includes the Weibull and Frechet. The function has a mean of :math:`\mu + 0.57721\beta` and a variance of :math:`\frac{\pi^2}{6}\beta^2`. References ---------- .. [1] Gumbel, E. J., "Statistics of Extremes," New York: Columbia University Press, 1958. .. [2] Reiss, R.-D. and Thomas, M., "Statistical Analysis of Extreme Values from Insurance, Finance, Hydrology and Other Fields," Basel: Birkhauser Verlag, 2001. Examples -------- Draw samples from the distribution: >>> rng = np.random.default_rng() >>> mu, beta = 0, 0.1 # location and scale >>> s = rng.gumbel(mu, beta, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 30, density=True) >>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta) ... * np.exp( -np.exp( -(bins - mu) /beta) ), ... linewidth=2, color='r') >>> plt.show() Show how an extreme value distribution can arise from a Gaussian process and compare to a Gaussian: >>> means = [] >>> maxima = [] >>> for i in range(0,1000) : ... a = rng.normal(mu, beta, 1000) ... means.append(a.mean()) ... maxima.append(a.max()) >>> count, bins, ignored = plt.hist(maxima, 30, density=True) >>> beta = np.std(maxima) * np.sqrt(6) / np.pi >>> mu = np.mean(maxima) - 0.57721*beta >>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta) ... * np.exp(-np.exp(-(bins - mu)/beta)), ... linewidth=2, color='r') >>> plt.plot(bins, 1/(beta * np.sqrt(2 * np.pi)) ... * np.exp(-(bins - mu)**2 / (2 * beta**2)), ... linewidth=2, color='g') >>> plt.show() geometric(p, size=None) Draw samples from the geometric distribution. Bernoulli trials are experiments with one of two outcomes: success or failure (an example of such an experiment is flipping a coin). The geometric distribution models the number of trials that must be run in order to achieve success. It is therefore supported on the positive integers, ``k = 1, 2, ...``. The probability mass function of the geometric distribution is .. math:: f(k) = (1 - p)^{k - 1} p where `p` is the probability of success of an individual trial. Parameters ---------- p : float or array_like of floats The probability of success of an individual trial. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``p`` is a scalar. Otherwise, ``np.array(p).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized geometric distribution. Examples -------- Draw ten thousand values from the geometric distribution, with the probability of an individual success equal to 0.35: >>> z = np.random.default_rng().geometric(p=0.35, size=10000) How many trials succeeded after a single run? >>> (z == 1).sum() / 10000. 0.34889999999999999 # random gamma(shape, scale=1.0, size=None) Draw samples from a Gamma distribution. Samples are drawn from a Gamma distribution with specified parameters, `shape` (sometimes designated "k") and `scale` (sometimes designated "theta"), where both parameters are > 0. Parameters ---------- shape : float or array_like of floats The shape of the gamma distribution. Must be non-negative. scale : float or array_like of floats, optional The scale of the gamma distribution. Must be non-negative. Default is equal to 1. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``shape`` and ``scale`` are both scalars. Otherwise, ``np.broadcast(shape, scale).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized gamma distribution. See Also -------- scipy.stats.gamma : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Gamma distribution is .. math:: p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)}, where :math:`k` is the shape and :math:`\theta` the scale, and :math:`\Gamma` is the Gamma function. The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant. References ---------- .. [1] Weisstein, Eric W. "Gamma Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/GammaDistribution.html .. [2] Wikipedia, "Gamma distribution", https://en.wikipedia.org/wiki/Gamma_distribution Examples -------- Draw samples from the distribution: >>> shape, scale = 2., 2. # mean=4, std=2*sqrt(2) >>> s = np.random.default_rng().gamma(shape, scale, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> import scipy.special as sps # doctest: +SKIP >>> count, bins, ignored = plt.hist(s, 50, density=True) >>> y = bins**(shape-1)*(np.exp(-bins/scale) / # doctest: +SKIP ... (sps.gamma(shape)*scale**shape)) >>> plt.plot(bins, y, linewidth=2, color='r') # doctest: +SKIP >>> plt.show() f(dfnum, dfden, size=None) Draw samples from an F distribution. Samples are drawn from an F distribution with specified parameters, `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of freedom in denominator), where both parameters must be greater than zero. The random variate of the F distribution (also known as the Fisher distribution) is a continuous probability distribution that arises in ANOVA tests, and is the ratio of two chi-square variates. Parameters ---------- dfnum : float or array_like of floats Degrees of freedom in numerator, must be > 0. dfden : float or array_like of float Degrees of freedom in denominator, must be > 0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``dfnum`` and ``dfden`` are both scalars. Otherwise, ``np.broadcast(dfnum, dfden).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Fisher distribution. See Also -------- scipy.stats.f : probability density function, distribution or cumulative density function, etc. Notes ----- The F statistic is used to compare in-group variances to between-group variances. Calculating the distribution depends on the sampling, and so it is a function of the respective degrees of freedom in the problem. The variable `dfnum` is the number of samples minus one, the between-groups degrees of freedom, while `dfden` is the within-groups degrees of freedom, the sum of the number of samples in each group minus the number of groups. References ---------- .. [1] Glantz, Stanton A. "Primer of Biostatistics.", McGraw-Hill, Fifth Edition, 2002. .. [2] Wikipedia, "F-distribution", https://en.wikipedia.org/wiki/F-distribution Examples -------- An example from Glantz[1], pp 47-40: Two groups, children of diabetics (25 people) and children from people without diabetes (25 controls). Fasting blood glucose was measured, case group had a mean value of 86.1, controls had a mean value of 82.2. Standard deviations were 2.09 and 2.49 respectively. Are these data consistent with the null hypothesis that the parents diabetic status does not affect their children's blood glucose levels? Calculating the F statistic from the data gives a value of 36.01. Draw samples from the distribution: >>> dfnum = 1. # between group degrees of freedom >>> dfden = 48. # within groups degrees of freedom >>> s = np.random.default_rng().f(dfnum, dfden, 1000) The lower bound for the top 1% of the samples is : >>> np.sort(s)[-10] 7.61988120985 # random So there is about a 1% chance that the F statistic will exceed 7.62, the measured value is 36, so the null hypothesis is rejected at the 1% level. exponential(scale=1.0, size=None) Draw samples from an exponential distribution. Its probability density function is .. math:: f(x; \frac{1}{\beta}) = \frac{1}{\beta} \exp(-\frac{x}{\beta}), for ``x > 0`` and 0 elsewhere. :math:`\beta` is the scale parameter, which is the inverse of the rate parameter :math:`\lambda = 1/\beta`. The rate parameter is an alternative, widely used parameterization of the exponential distribution [3]_. The exponential distribution is a continuous analogue of the geometric distribution. It describes many common situations, such as the size of raindrops measured over many rainstorms [1]_, or the time between page requests to Wikipedia [2]_. Parameters ---------- scale : float or array_like of floats The scale parameter, :math:`\beta = 1/\lambda`. Must be non-negative. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``scale`` is a scalar. Otherwise, ``np.array(scale).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized exponential distribution. Examples -------- A real world example: Assume a company has 10000 customer support agents and the average time between customer calls is 4 minutes. >>> n = 10000 >>> time_between_calls = np.random.default_rng().exponential(scale=4, size=n) What is the probability that a customer will call in the next 4 to 5 minutes? >>> x = ((time_between_calls < 5).sum())/n >>> y = ((time_between_calls < 4).sum())/n >>> x-y 0.08 # may vary References ---------- .. [1] Peyton Z. Peebles Jr., "Probability, Random Variables and Random Signal Principles", 4th ed, 2001, p. 57. .. [2] Wikipedia, "Poisson process", https://en.wikipedia.org/wiki/Poisson_process .. [3] Wikipedia, "Exponential distribution", https://en.wikipedia.org/wiki/Exponential_distribution choice(a, size=None, replace=True, p=None, axis=0, shuffle=True) Generates a random sample from a given array Parameters ---------- a : {array_like, int} If an ndarray, a random sample is generated from its elements. If an int, the random sample is generated from np.arange(a). size : {int, tuple[int]}, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn from the 1-d `a`. If `a` has more than one dimension, the `size` shape will be inserted into the `axis` dimension, so the output ``ndim`` will be ``a.ndim - 1 + len(size)``. Default is None, in which case a single value is returned. replace : bool, optional Whether the sample is with or without replacement. Default is True, meaning that a value of ``a`` can be selected multiple times. p : 1-D array_like, optional The probabilities associated with each entry in a. If not given, the sample assumes a uniform distribution over all entries in ``a``. axis : int, optional The axis along which the selection is performed. The default, 0, selects by row. shuffle : bool, optional Whether the sample is shuffled when sampling without replacement. Default is True, False provides a speedup. Returns ------- samples : single item or ndarray The generated random samples Raises ------ ValueError If a is an int and less than zero, if p is not 1-dimensional, if a is array-like with a size 0, if p is not a vector of probabilities, if a and p have different lengths, or if replace=False and the sample size is greater than the population size. See Also -------- integers, shuffle, permutation Notes ----- Setting user-specified probabilities through ``p`` uses a more general but less efficient sampler than the default. The general sampler produces a different sample than the optimized sampler even if each element of ``p`` is 1 / len(a). Examples -------- Generate a uniform random sample from np.arange(5) of size 3: >>> rng = np.random.default_rng() >>> rng.choice(5, 3) array([0, 3, 4]) # random >>> #This is equivalent to rng.integers(0,5,3) Generate a non-uniform random sample from np.arange(5) of size 3: >>> rng.choice(5, 3, p=[0.1, 0, 0.3, 0.6, 0]) array([3, 3, 0]) # random Generate a uniform random sample from np.arange(5) of size 3 without replacement: >>> rng.choice(5, 3, replace=False) array([3,1,0]) # random >>> #This is equivalent to rng.permutation(np.arange(5))[:3] Generate a uniform random sample from a 2-D array along the first axis (the default), without replacement: >>> rng.choice([[0, 1, 2], [3, 4, 5], [6, 7, 8]], 2, replace=False) array([[3, 4, 5], # random [0, 1, 2]]) Generate a non-uniform random sample from np.arange(5) of size 3 without replacement: >>> rng.choice(5, 3, replace=False, p=[0.1, 0, 0.3, 0.6, 0]) array([2, 3, 0]) # random Any of the above can be repeated with an arbitrary array-like instead of just integers. For instance: >>> aa_milne_arr = ['pooh', 'rabbit', 'piglet', 'Christopher'] >>> rng.choice(aa_milne_arr, 5, p=[0.5, 0.1, 0.1, 0.3]) array(['pooh', 'pooh', 'pooh', 'Christopher', 'piglet'], # random dtype=' 0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``df`` is a scalar. Otherwise, ``np.array(df).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized chi-square distribution. Raises ------ ValueError When `df` <= 0 or when an inappropriate `size` (e.g. ``size=-1``) is given. Notes ----- The variable obtained by summing the squares of `df` independent, standard normally distributed random variables: .. math:: Q = \sum_{i=0}^{\mathtt{df}} X^2_i is chi-square distributed, denoted .. math:: Q \sim \chi^2_k. The probability density function of the chi-squared distribution is .. math:: p(x) = \frac{(1/2)^{k/2}}{\Gamma(k/2)} x^{k/2 - 1} e^{-x/2}, where :math:`\Gamma` is the gamma function, .. math:: \Gamma(x) = \int_0^{-\infty} t^{x - 1} e^{-t} dt. References ---------- .. [1] NIST "Engineering Statistics Handbook" https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm Examples -------- >>> np.random.default_rng().chisquare(2,4) array([ 1.89920014, 9.00867716, 3.13710533, 5.62318272]) # random bytes(length) Return random bytes. Parameters ---------- length : int Number of random bytes. Returns ------- out : bytes String of length `length`. Examples -------- >>> np.random.default_rng().bytes(10) b'\xfeC\x9b\x86\x17\xf2\xa1\xafcp' # random binomial(n, p, size=None) Draw samples from a binomial distribution. Samples are drawn from a binomial distribution with specified parameters, n trials and p probability of success where n an integer >= 0 and p is in the interval [0,1]. (n may be input as a float, but it is truncated to an integer in use) Parameters ---------- n : int or array_like of ints Parameter of the distribution, >= 0. Floats are also accepted, but they will be truncated to integers. p : float or array_like of floats Parameter of the distribution, >= 0 and <=1. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``n`` and ``p`` are both scalars. Otherwise, ``np.broadcast(n, p).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized binomial distribution, where each sample is equal to the number of successes over the n trials. See Also -------- scipy.stats.binom : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the binomial distribution is .. math:: P(N) = \binom{n}{N}p^N(1-p)^{n-N}, where :math:`n` is the number of trials, :math:`p` is the probability of success, and :math:`N` is the number of successes. When estimating the standard error of a proportion in a population by using a random sample, the normal distribution works well unless the product p*n <=5, where p = population proportion estimate, and n = number of samples, in which case the binomial distribution is used instead. For example, a sample of 15 people shows 4 who are left handed, and 11 who are right handed. Then p = 4/15 = 27%. 0.27*15 = 4, so the binomial distribution should be used in this case. References ---------- .. [1] Dalgaard, Peter, "Introductory Statistics with R", Springer-Verlag, 2002. .. [2] Glantz, Stanton A. "Primer of Biostatistics.", McGraw-Hill, Fifth Edition, 2002. .. [3] Lentner, Marvin, "Elementary Applied Statistics", Bogden and Quigley, 1972. .. [4] Weisstein, Eric W. "Binomial Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/BinomialDistribution.html .. [5] Wikipedia, "Binomial distribution", https://en.wikipedia.org/wiki/Binomial_distribution Examples -------- Draw samples from the distribution: >>> rng = np.random.default_rng() >>> n, p = 10, .5 # number of trials, probability of each trial >>> s = rng.binomial(n, p, 1000) # result of flipping a coin 10 times, tested 1000 times. A real world example. A company drills 9 wild-cat oil exploration wells, each with an estimated probability of success of 0.1. All nine wells fail. What is the probability of that happening? Let's do 20,000 trials of the model, and count the number that generate zero positive results. >>> sum(rng.binomial(9, 0.1, 20000) == 0)/20000. # answer = 0.38885, or 39%. .astype(np.float64)) > 1.0. The pvals array is cast to 64-bit floating point prior to checking the sum. Precision changes when casting may cause problems even if the sum of the original pvals is valid.When method is 'count', sum(colors) must not exceed %dGenerator.permutation (line 4797)Generator.multinomial (line 3838)Axis argument is only supported on ndarray objects wald(mean, scale, size=None) Draw samples from a Wald, or inverse Gaussian, distribution. As the scale approaches infinity, the distribution becomes more like a Gaussian. Some references claim that the Wald is an inverse Gaussian with mean equal to 1, but this is by no means universal. The inverse Gaussian distribution was first studied in relationship to Brownian motion. In 1956 M.C.K. Tweedie used the name inverse Gaussian because there is an inverse relationship between the time to cover a unit distance and distance covered in unit time. Parameters ---------- mean : float or array_like of floats Distribution mean, must be > 0. scale : float or array_like of floats Scale parameter, must be > 0. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``mean`` and ``scale`` are both scalars. Otherwise, ``np.broadcast(mean, scale).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Wald distribution. Notes ----- The probability density function for the Wald distribution is .. math:: P(x;mean,scale) = \sqrt{\frac{scale}{2\pi x^3}}e^ \frac{-scale(x-mean)^2}{2\cdotp mean^2x} As noted above the inverse Gaussian distribution first arise from attempts to model Brownian motion. It is also a competitor to the Weibull for use in reliability modeling and modeling stock returns and interest rate processes. References ---------- .. [1] Brighton Webs Ltd., Wald Distribution, https://web.archive.org/web/20090423014010/http://www.brighton-webs.co.uk:80/distributions/wald.asp .. [2] Chhikara, Raj S., and Folks, J. Leroy, "The Inverse Gaussian Distribution: Theory : Methodology, and Applications", CRC Press, 1988. .. [3] Wikipedia, "Inverse Gaussian distribution" https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution Examples -------- Draw values from the distribution and plot the histogram: >>> import matplotlib.pyplot as plt >>> h = plt.hist(np.random.default_rng().wald(3, 2, 100000), bins=200, density=True) >>> plt.show() standard_gamma(shape, size=None, dtype=np.float64, out=None) Draw samples from a standard Gamma distribution. Samples are drawn from a Gamma distribution with specified parameters, shape (sometimes designated "k") and scale=1. Parameters ---------- shape : float or array_like of floats Parameter, must be non-negative. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``shape`` is a scalar. Otherwise, ``np.array(shape).size`` samples are drawn. dtype : dtype, optional Desired dtype of the result, only `float64` and `float32` are supported. Byteorder must be native. The default value is np.float64. out : ndarray, optional Alternative output array in which to place the result. If size is not None, it must have the same shape as the provided size and must match the type of the output values. Returns ------- out : ndarray or scalar Drawn samples from the parameterized standard gamma distribution. See Also -------- scipy.stats.gamma : probability density function, distribution or cumulative density function, etc. Notes ----- The probability density for the Gamma distribution is .. math:: p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)}, where :math:`k` is the shape and :math:`\theta` the scale, and :math:`\Gamma` is the Gamma function. The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant. References ---------- .. [1] Weisstein, Eric W. "Gamma Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/GammaDistribution.html .. [2] Wikipedia, "Gamma distribution", https://en.wikipedia.org/wiki/Gamma_distribution Examples -------- Draw samples from the distribution: >>> shape, scale = 2., 1. # mean and width >>> s = np.random.default_rng().standard_gamma(shape, 1000000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> import scipy.special as sps # doctest: +SKIP >>> count, bins, ignored = plt.hist(s, 50, density=True) >>> y = bins**(shape-1) * ((np.exp(-bins/scale))/ # doctest: +SKIP ... (sps.gamma(shape) * scale**shape)) >>> plt.plot(bins, y, linewidth=2, color='r') # doctest: +SKIP >>> plt.show() standard_exponential(size=None, dtype=np.float64, method='zig', out=None) Draw samples from the standard exponential distribution. `standard_exponential` is identical to the exponential distribution with a scale parameter of 1. Parameters ---------- size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Default is None, in which case a single value is returned. dtype : dtype, optional Desired dtype of the result, only `float64` and `float32` are supported. Byteorder must be native. The default value is np.float64. method : str, optional Either 'inv' or 'zig'. 'inv' uses the default inverse CDF method. 'zig' uses the much faster Ziggurat method of Marsaglia and Tsang. out : ndarray, optional Alternative output array in which to place the result. If size is not None, it must have the same shape as the provided size and must match the type of the output values. Returns ------- out : float or ndarray Drawn samples. Examples -------- Output a 3x8000 array: >>> n = np.random.default_rng().standard_exponential((3, 8000)) standard_cauchy(size=None) Draw samples from a standard Cauchy distribution with mode = 0. Also known as the Lorentz distribution. Parameters ---------- size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. Default is None, in which case a single value is returned. Returns ------- samples : ndarray or scalar The drawn samples. Notes ----- The probability density function for the full Cauchy distribution is .. math:: P(x; x_0, \gamma) = \frac{1}{\pi \gamma \bigl[ 1+ (\frac{x-x_0}{\gamma})^2 \bigr] } and the Standard Cauchy distribution just sets :math:`x_0=0` and :math:`\gamma=1` The Cauchy distribution arises in the solution to the driven harmonic oscillator problem, and also describes spectral line broadening. It also describes the distribution of values at which a line tilted at a random angle will cut the x axis. When studying hypothesis tests that assume normality, seeing how the tests perform on data from a Cauchy distribution is a good indicator of their sensitivity to a heavy-tailed distribution, since the Cauchy looks very much like a Gaussian distribution, but with heavier tails. References ---------- .. [1] NIST/SEMATECH e-Handbook of Statistical Methods, "Cauchy Distribution", https://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm .. [2] Weisstein, Eric W. "Cauchy Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CauchyDistribution.html .. [3] Wikipedia, "Cauchy distribution" https://en.wikipedia.org/wiki/Cauchy_distribution Examples -------- Draw samples and plot the distribution: >>> import matplotlib.pyplot as plt >>> s = np.random.default_rng().standard_cauchy(1000000) >>> s = s[(s>-25) & (s<25)] # truncate distribution so it plots well >>> plt.hist(s, bins=100) >>> plt.show() poisson(lam=1.0, size=None) Draw samples from a Poisson distribution. The Poisson distribution is the limit of the binomial distribution for large N. Parameters ---------- lam : float or array_like of floats Expected number of events occurring in a fixed-time interval, must be >= 0. A sequence must be broadcastable over the requested size. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``lam`` is a scalar. Otherwise, ``np.array(lam).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Poisson distribution. Notes ----- The Poisson distribution .. math:: f(k; \lambda)=\frac{\lambda^k e^{-\lambda}}{k!} For events with an expected separation :math:`\lambda` the Poisson distribution :math:`f(k; \lambda)` describes the probability of :math:`k` events occurring within the observed interval :math:`\lambda`. Because the output is limited to the range of the C int64 type, a ValueError is raised when `lam` is within 10 sigma of the maximum representable value. References ---------- .. [1] Weisstein, Eric W. "Poisson Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PoissonDistribution.html .. [2] Wikipedia, "Poisson distribution", https://en.wikipedia.org/wiki/Poisson_distribution Examples -------- Draw samples from the distribution: >>> import numpy as np >>> rng = np.random.default_rng() >>> s = rng.poisson(5, 10000) Display histogram of the sample: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 14, density=True) >>> plt.show() Draw each 100 values for lambda 100 and 500: >>> s = rng.poisson(lam=(100., 500.), size=(100, 2)) ' object which is not a subclass of 'Sequence'; `shuffle` is not guaranteed to behave correctly. E.g., non-numpy array/tensor objects with view semantics may contain duplicates after shuffling. laplace(loc=0.0, scale=1.0, size=None) Draw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay). The Laplace distribution is similar to the Gaussian/normal distribution, but is sharper at the peak and has fatter tails. It represents the difference between two independent, identically distributed exponential random variables. Parameters ---------- loc : float or array_like of floats, optional The position, :math:`\mu`, of the distribution peak. Default is 0. scale : float or array_like of floats, optional :math:`\lambda`, the exponential decay. Default is 1. Must be non- negative. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n, k)``, then ``m * n * k`` samples are drawn. If size is ``None`` (default), a single value is returned if ``loc`` and ``scale`` are both scalars. Otherwise, ``np.broadcast(loc, scale).size`` samples are drawn. Returns ------- out : ndarray or scalar Drawn samples from the parameterized Laplace distribution. Notes ----- It has the probability density function .. math:: f(x; \mu, \lambda) = \frac{1}{2\lambda} \exp\left(-\frac{|x - \mu|}{\lambda}\right). The first law of Laplace, from 1774, states that the frequency of an error can be expressed as an exponential function of the absolute magnitude of the error, which leads to the Laplace distribution. For many problems in economics and health sciences, this distribution seems to model the data better than the standard Gaussian distribution. References ---------- .. [1] Abramowitz, M. and Stegun, I. A. (Eds.). "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing," New York: Dover, 1972. .. [2] Kotz, Samuel, et. al. "The Laplace Distribution and Generalizations, " Birkhauser, 2001. .. [3] Weisstein, Eric W. "Laplace Distribution." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LaplaceDistribution.html .. [4] Wikipedia, "Laplace distribution", https://en.wikipedia.org/wiki/Laplace_distribution Examples -------- Draw samples from the distribution >>> loc, scale = 0., 1. >>> s = np.random.default_rng().laplace(loc, scale, 1000) Display the histogram of the samples, along with the probability density function: >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, 30, density=True) >>> x = np.arange(-8., 8., .01) >>> pdf = np.exp(-abs(x-loc)/scale)/(2.*scale) >>> plt.plot(x, pdf) Plot Gaussian for comparison: >>> g = (1/(scale * np.sqrt(2 * np.pi)) * ... np.exp(-(x - loc)**2 / (2 * scale**2))) >>> plt.plot(x,g) dirichlet(alpha, size=None) Draw samples from the Dirichlet distribution. Draw `size` samples of dimension k from a Dirichlet distribution. A Dirichlet-distributed random variable can be seen as a multivariate generalization of a Beta distribution. The Dirichlet distribution is a conjugate prior of a multinomial distribution in Bayesian inference. Parameters ---------- alpha : sequence of floats, length k Parameter of the distribution (length ``k`` for sample of length ``k``). size : int or tuple of ints, optional Output shape. If the given shape is, e.g., ``(m, n)``, then ``m * n * k`` samples are drawn. Default is None, in which case a vector of length ``k`` is returned. Returns ------- samples : ndarray, The drawn samples, of shape ``(size, k)``. Raises ------ ValueError If any value in ``alpha`` is less than zero Notes ----- The Dirichlet distribution is a distribution over vectors :math:`x` that fulfil the conditions :math:`x_i>0` and :math:`\sum_{i=1}^k x_i = 1`. The probability density function :math:`p` of a Dirichlet-distributed random vector :math:`X` is proportional to .. math:: p(x) \propto \prod_{i=1}^{k}{x^{\alpha_i-1}_i}, where :math:`\alpha` is a vector containing the positive concentration parameters. The method uses the following property for computation: let :math:`Y` be a random vector which has components that follow a standard gamma distribution, then :math:`X = \frac{1}{\sum_{i=1}^k{Y_i}} Y` is Dirichlet-distributed References ---------- .. [1] David McKay, "Information Theory, Inference and Learning Algorithms," chapter 23, http://www.inference.org.uk/mackay/itila/ .. [2] Wikipedia, "Dirichlet distribution", https://en.wikipedia.org/wiki/Dirichlet_distribution Examples -------- Taking an example cited in Wikipedia, this distribution can be used if one wanted to cut strings (each of initial length 1.0) into K pieces with different lengths, where each piece had, on average, a designated average length, but allowing some variation in the relative sizes of the pieces. >>> s = np.random.default_rng().dirichlet((10, 5, 3), 20).transpose() >>> import matplotlib.pyplot as plt >>> plt.barh(range(20), s[0]) >>> plt.barh(range(20), s[1], left=s[0], color='g') >>> plt.barh(range(20), s[2], left=s[0]+s[1], color='r') >>> plt.title("Lengths of Strings") Unsupported dtype %r for randomGenerator.triangular (line 2794)Generator.standard_t (line 1774)Generator.exponential (line 405)unable to allocate array data.probabilities do not sum to 1Generator.logseries (line 3517)Generator.lognormal (line 2545)Generator.geometric (line 3323)Generator.dirichlet (line 4300)Generator.chisquare (line 1561)Generator.vonmises (line 1880)Generator.rayleigh (line 2657)Generator.permuted (line 4505)Generator.logistic (line 2465)Generator.binomial (line 2894)numpy/random/_generator.pyxnsample must be nonnegative.itemsize <= 0 for cython.arraya and p must have same sizeStep may not be zero (axis %d)Generator.weibull (line 2061)Generator.shuffle (line 4665)Generator.poisson (line 3162)Generator.laplace (line 2261)Generator.integers (line 526)nsample must be an integermean must be 1 dimensionalRange exceeds valid boundsIndex out of bounds (axis %d)Generator.uniform (line 945)Generator.pareto (line 1963)Generator.normal (line 1123)Generator.gumbel (line 2346)probabilities contain NaNout must be a numpy arraynsample must not exceed %dGenerator.random (line 299)Generator.power (line 2160)Generator.gamma (line 1317)Generator.choice (line 681)Dimension %d is not directGenerator.zipf (line 3235)Generator.wald (line 2726)Generator.spawn (line 241)Generator.bytes (line 653)p must be 1-dimensionalnumpy.random._generatorCannot index with type 'numpy.core.multiarraydefault_rng (line 4869)Invalid shape in axis Generator.f (line 1395)normalize_axis_indexyou are shuffling a 'NotImplementedErrornsample > sum(colors)ngood + nbad < nsamplecline_in_tracebackarray is read-only__pyx_unpickle_Enumascontiguousarraymay_share_memorystandard_normal__setstate_cython____pyx_PickleError_poisson_lam_maxdtype_is_objectcollections.abcallocate_bufferView.MemoryView__generator_ctorRuntimeWarningAssertionError__reduce_cython__count_nonzero__class_getitem__bit_generatorOverflowErrorversion_infosearchsortedreturn_index__pyx_checksumnumpy.linalg_initializingdefault_rngcollectionscheck_validUserWarningPickleErrorOutput size MemoryErrorImportErrorstacklevel__pyx_vtable____pyx_resultn_childrenmode > rightlogical_orleft == rightissubdtypeempty_likeValueErrorIndexErrorwriteablesum(pvals__reduce_ex____pyx_statemarginalsleft > modeisenabledhasobjectenumerateTypeErrorGeneratorwarningsswapaxessubtract__setstate__reversedregisterreduce__pyx_type_pickleoperatoritemsizeisscalarisnativeisfiniteintegershigh - low__getstate__endpointcholeskyallcloseSequenceEllipsistobytesstridesshuffle__rmatmul__reshapereplacensamplememview__imatmul__greaterfortranfloat64float32disablecastingcapsule at 0x{:X}asarrayalpha < 0updateunpackuniqueuint64uint32uint16struct__reduce__randompickle__name__method__matmul__length__import__ignoreformatencodeenabledoublecumsumcopytocolorsastypearangezerosuint8statestartspawnsigmashapescalerightravelrangeraisepvals_pcg64ordernumpyngoodkappaisnanint64int32int16indexflagsfinfoerrorequal__enter__emptydtypedfnumdfdencount__class__arrayalphaPCG64ASCIIwarn__test__takestopstepsqrt__spec__sortsizesideseedsafertolprodpacknoncndimnbadnamemodemean__main__locklessleftitemintpint8highfull__exit__eigh__dict__copybool_baseaxisatolNonezigtolsyssvdsum__str__outobj__new__maxlowloclam (got epsdotcovany and alladdabc?([...,:-1]) > 1.0qh?333333?C?/*p?3f?(_?xY?յS?N?J?F?DB?Qt??u+ ?A?Į?"?ʝ?G??i>l>7>>*J>>>^>>F>>7P>>K{>>>u>;->>>|>eO>4(>8>L>N>ȿ>>>>·>ε>߳>>>0>U>~>|>ަ>Y>IP>w>ҟ>B>e>)>~>_>>C>{>>J>﷍>X(>'>N>Í>x >b>x>>!>^}>;z>Хw>@t>wr>byl>i>g>Sd>3a>^>]\>&Y>z)W>T>P R>O>L>5~J>3H>E>nC>@>VK>>;>9>07>4>2>>0>p->+>s)>7'>%>"> >s>L>*>= >T>T>4>>y >ϣ > >>L>>l>=+==0 =C==8==hp==0== =n==|===;=ں=Z=o,=ް=ߗ=.W===%==r=W= C=4=M,=4*=D.=y8=H=~=x=3E3lM3FT3/[3b3i34p3fw3&~3[3B3ψ3g37!3>3T3d3n3r3Fq3j3_31P3r<3$3k 33ȸ3q3|{3P3#3C333dY3"3+3®3r35333x37333p3-33731b33l44(44h4C44 4` 4M 47 44?4nB44L4 i4a4T044542`44p. 4!4"4i$4%4@'4t(4>*4+4,4j.4/4'P1424):4454&)7484c:4;4$=4+>4@4A4KC4vD4B(F4G4:I4J4rTL4M4GuO4Q4R44T4U4EiW4Y4 Z4G\4]4_4:a4b4d4Bf4\g4ji4bk4m4n4p4\r4}"t4Yu4Hw4[y4X{46.}4 4q4a4]S4F4N<434,4+(4{%4$4o&4,*4'04m84 C4P4_4q474{4w4>ԕ44s4<4d444$4 (4a44lߢ4$4l44x 4_444{4 4EP4±4{:4귴4);4nķ4S444<*4տ44A4.44ע44f4RW4R4*Y4Fk44δ444444g44k4<444y44u4_45555@5ó 5 5]5^555q5v 5!5%5V*5s/5;S55:<5D5NO5^5Nv5QHqoMֻanjDotTrotou$w'xx,jyy7\z׻z{W{S{{.|3|]|ȃ|||I||}C0}F}Z}m}}S}(}}-}}"}}|}M}~i ~~~B(~o0~C8~?~F~M~T~Z~a~f~l~r~]w~v|~`~ ~~$~m~~~w~:~ަ~f~ѭ~#~Z~y~~q~K~~~^~~a~~~`~~~~~~~~f~*~~~-~~J~~=~~~\~~~$~U~}~~~~~pH`  i   6  H  A!B+m 5XttW3 `wK\ L   s   G {V~~~d~~x~~K~~~~~~~~~)~~~a~~~{~;~~A~~~m~~z~~~"~k~]~~~ԃ~|~s~j~Ua~W~K~?~2~$~~~ }}} }}i}A}}|Q|D|{3N{zeyww7ms?7E?P?'{{?*!?bv?mU?9U1T?/v?x]?&1$-?~ n?cK[!?I?\Omg?f?uLi=?sڂl?x?Qf?ij?%ᨯC?+?Dܻ?z?cE#;?^E#?$O?2m?P"K?>?{s?%;?omo?3;?J9?++?*T[?};1s?HeC?$`?vE!=?ſ-r?MBц?K=?Q}6Ei?7u? !?z}k? ~?@?`x?*?8? Qi?oTC?_(4?ָ?@je?!u v?7Zi?{ ?I?]T?9]??}?8aD:?Yζi?Ɲҷ?r^sSw?ꍰ07?d>[?%۹? Ə{?'HB>?vX#?l1&?:l?磽!O?ލ?&?ڋ?ﾀ+ j?A1?N0Z?0H?}G?(V?5$1!?pB9 ?b"FS?)vEW(?vG}rO?~ /? {^?Z? ?ބS?i"?lR?3Sn?>N?Ґ]b?,|y2?jG>?TLҫ?~>\O??@YH?/֎@?9O"H?>?1 7?8?Ox?]4?5D9g?r|?>ܸ$8? [B/?I䠟?O?y%d?bPޱ?c?PR?j?F}?9(Q1?c?(ڦ^w?0U^Q?1j?T ξ?x.BTv?Imb.??6YJ?)ِ?\C}?%d?w?SN?эv?pa?,Q&?@oű?SuFe?PV?;?I?viׯ?4D?.g?X1Iα?Jy?!dJ?پz?j»?8G;?L|{ʎ?mwn?k9:9??Ry?A&E?U?Ŗ<?k&_?G??~#? V#?_?S?Q| z? Y&?$?htQz? 3Tݜ?pXP?N梚?H*g?gS(u?1c?w@rT?Q=I?QA?]1%? RD?lj?W'n?-BU؊?h?t4? n?boQ?qvi?_)N?]tQW}?6H#z? 67w?"Ηs?C@Wi=q?ḰXl?f?$ka?%> T+Y? O?K 2=?]d<A]X`<+M[Ij<[5q&<.8eG< h#ឪV <;LC%K<ꆭh NVeΙVn6nvK zicp%E tQ)2U1WQ9Lin?23F:L"3\LQ V f[_rWDdx h+*k2=Ko:qr Mu\x?A{FS~8;b=ZV`bBtu9=JE>XدGwdO 8cx AFẙi&zqVYםΡag6 X83:뇡koɣj_ۤ| Mg^ݧt|Ψ_ΓXp2X^ttH蟿W;ޭl~$\z[߁İPp:J+N!X ɦ֬ ᆴX7(. Ɉ?5}h.G{tr&oya=cA/˺DH0⤮<)9O@ᣩTrVj֋@?˷dsI^i@(0߾ta&⊂l1EA1T[n&mi#d)B}QJwt}B < EOvpc/F<Ң"Ae އ0~ Rfq(*QtH3D@M`P}hwx%ƿ8*JG+[EliPIw+ E>ҙ02yΩ4A (Nt.Ȱ--̕^&܌z#;ޖu~g6X .pmF 3n bH޵LaEZvpR(-x_b˿ӰdyQӶVg<7܆ut7$MH𯋉ld"rqտH)݄ /0 wپ}2}K D5z&R cM,}uc?Ѡp5.bJ3ʸT[vv+\[U@ضBi"7oLeiFγ>SR(D2Z> B0$y1gWr-ެ @樫(afoeW-|&aY +M?V#z?u?q?}n?k?Lh?e?Rc?`?Zw^?*+\?Y?RW?U?_S?XQ?߱O?M?3K?J?GH?F?jD?`C?(`A?j??>?x,>N>>q>>>j>>k>>Π>>F>>>'>\>#>u>J>*>_F>d>+>$>w>>>JK>y>|>iݿ>>I>;>ʾ>t>5<> ~>>>O>>>~3>T>ե>(>g~>ՠ>G/>>>F>J> >:n>bԓ>Q<>>x>~>>>^>Ј>D>l>1>>%>\D>@|>?y>Bv>Hs>Qp>#^m>mj>|g>md>a>^>$[> Y>=3V>[S>P>M>J>~H>UE>B>?>=>S:>7>"4>=22>T/>d,>m+*>m'>c$>N?">,>>m>t>F>>1*> > >Y>>ʗ>>I=_={==^==&=_=g=='0===P6=˙=\= s==d= =yo=/=6=.=fЍ=x=i'=܀=a1y=p=xIh=_==W=TO=G=>=N6=.=&===-H==<א<̀<<<.4V?4=3@4A4A4qB4C4D4udE4-CF4K"G4H4H41I4J4vK4\fL4HM4+N4aO4O4bP4ٽQ4R4ԊS4crT4ZU4CV4-W4ZX4Y4UY4Z4[4(\4_]4^4_4C`4va4alb40cc47[d4~Te4Of4Jg42Hh4Fi4Fj4Hk4Kl4MPm4Vn4^o48hp4sq4r4s4 t4u4v4Cw4x4 z42{40S|4u}4~44v4@ 4L4>4ق4v444lV44R4F44p4 I44"4_44Ќ4l4L4`4ԏ4坐4y4ݖ4%44r&4k44(4444.4Q4N4t44\۶4H94̻4p44~X4w4p_4~444wE`mru\zw8xky5zz/ {ԃ{{7|3}|&|H|}C}g}ۇ}}a}g}]}~~4%~5~C~Q~g^~ij~u~>~2~~r~դ~Ƭ~N~u~C~~~~k~~~~~~t~~~6 < :#%](*.-z/13579;=?EABD:FGNIJ8LMNLPQR T=UdVWXYZ[\]^~__`;abbcod.eefLggh~~7~~/~7~~ ~ ~w~G]~>~Y~,}6}b}|O|06{x?yjD?l[T?w'??o?Wp?xI?-3?x^j??N?R:e?4:>?l?*?%z?PՋt?4?e;?$"?zaWF}?Gz‘B?Oq1? OU?ߺH?7a?nV,? K?Xhw?հ<?Vp\?m?)?zP?ZcX?*;Q^?#*'g? U7?e&$ ?jJo?\Ȭ)?L&?FS?leZ&?g ?NIO??xRr!?P_hy?y6IJO?_5%?[X~?1>?bU?+À?PX?5:pɗ0?8d?;U?J?͓?)m?ېZ]G?/|!? ?iT??Wq?PF9 ?ߓ^??ۮY?3???i?Z8o? O5?ٸ?P?R9?igP?La;?L?!ވ?%o?{7=8?Ҁt?DvC?6?=p\?;So&?mj?W?j?$O?z5Ѽ?Ҏ?C|P?yh|?%H?/ZM?f!w;??>ǭ?MAz?G?y?.?P9կ?TT}?g4K?#$O? Y?BM?6C;?B"_U?~t$?œ߉?52?Ҙl'?DɤT?<(i?qE8 ? Uī?OQM?o^?Sq͒?Gط5?zx?1zd}?:R!?Wg?~& ~k?=~-2?ZҿҶ?'|j_]?it?[?8R?uqb?#h?z|J?G~`?\!>?GF?vJ?l󈬚?5hȩmE?㭍?-l ?uG?1i%?調?M?e*|?zè?^V?4<%F?B}u?c-@c?n? R=?Kr?*}T#?,"k>?R) ?K{o?vaӽ?命8? t;I_? h?3xk?3Ӻ?b3?vZ9S?LJisk?M$a.?ftW?+ ?"@|?&#?p>_?1fҲ? DE?} ?/?%,?0?5nl+,&?QG?b. ?,*(>?p_8?cU)?h*?'wާ?dИۦ?ԭ<ڥ?]']ۤ?ݣ?=|?j?.?ĥׁ?u? ̓0?"NR? y? ڥ?d֔?^8 ?0`4I?IrO*?O'?x A?B?/)?7h`|?] ٨v?p?gC_e?T?yx;I< <[,L< Ŀk<4xV<=A[<'?}y<NG<~;[xo6xu{fUY>9>{ppCBwS(:5^dܓAN}8) YfHqն&|s f2,2Ztզޗ .n ZR'ӯB)[l@u Pҍ'TȈt(5wI'L/$;nXMØT`OArW,+jtȳRfARnqӊ<KZW$eKs) 4<=>)G'QA@Y.(5bX jz>lq{2Xx{~JH҄Cc`Qz%~ )Q\HsrUb'Bkq-hnק Ψ;3Kd)P^٨Tv$Hx"$ 5..&$ŗ: Aޓ=?~)@ lѿ3 ; @UUUUUU?"@m{??@@5gG8?SˆB?AAz?<ٰj_?$+K?88C?J?llf?UUUUUU?dg?̶e*= ףp=@n?[ m?h|?5?333333 @r?$~?B>٬ @r鷯?Q?Q?9v?(\@ffffff@0C.@4@x&?@?UUUUUU?a@X@`@|@@MA>@@-DT! @h㈵>.A-DT! -DT!@3?r?q?0@9B.? * ?,|l @yD@:5/?@@R2B@96SC@wz*E@r4dF@OOfq]@Ob^@+NT_@ݭC#`@~{`@kbba@YSȐa@n b@1Ib@5ca c@c@ͦ3 d@\>d@nz e@s9Je@FGGʪ f@yyuf@IJC g@Y&g@oFh@·h@aQL i@ai@ F~x*j@&Pj@7k@!+k@VFl@ l@tVm@pZNm@k9ihn@HQOUn@a,~|o@b4nʼnp@+e Ip@cp@)Vp@*q@6Gaq@q@>m#FJq@FK.5r@b)C|r@Wrr@V] s@rRs@GIqs@ >6qs@jB*t@ A=rt@fIw|t@d'-u@X+{ Mu@# u@ZGDu@;#(v@b%rv@iv{Իv@w@Ow@\&әw@}6-#w@h͙.x@k?7yx@–'x@_*y@Yy@1*y@^TTy@,{L@@$IfO@0 PD `X pl  0 @ @ \ px ` 8 P\ @ 0 h `, d `(`@tpdP|8T`L` 0P00(Px@P (x00(plPH@!0)0)P*0P336H7x89:X?@BP0DF`G pIJx !@!t!!("pt"`" D###@L$0$ $p%4%x%`%p&&pd&& &H' '(`\())\** +X++0+ 4,`H, , -(H./.7`/>/Fx0M1@^d1pd1jt2p2uH33`304 404@4D5556 66@7(8`8`99P: $;;`<<$<,T=p5= >l>F>P?^? a@c@0dApmxAA@lBp0B@tCLDD@EPXFP'F@BpGOGP{HHIPJPJ@0K0TLLL`MDMpM8NNNPtOOP$P@`PPP$Q@|QQQ4RR`R SpDSSSS T0$T@8TlT@T`TTTTU0UPPUpUUU@UU@ V,VDV`VVVW`WWW$X@DX0hXXXXXY ,Y0PYY@YZZP[@[ [ $\0\]8]]^@P^`^zRx $P FJ w?;*3$"DX l 4EBDD d GBI AAB, (4 40\AA ABDF THDi C pPDp D \BED D(D0| (D ABBH Q (D DBBC D (A ABBE 4X[BBA A(H0F(A ABB LA@ G h H ,pAG0 AE  AA H\BHB B(F0A8F`  8D0A(B BBBH xAx O o4 @eBGD m DBH L DBF 4DxQADD ^ CAE M CAG |AU J O,;lN4TwAAG O CAD I CAC LBID D(GP (C ABBI | (F ABBI 4@,BKH { ABE D DBN XxBED A(F0s (D ABBB L (D ABBK D(D DBB4AAG  CAH I CAK $ pBIC ^ABD4XBEL E(A0A8E@8D0A(B BBBD| BEL E(A0A8E@8D0A(B BBB8~BEH A(A0b(D BBB8`BBE A(A0J(D BBB4<0eBDD E GBH AABthcLTBEA A(D@8 (A ABBE m (A ABBE ,ID `ABp XQ t7Bk C P$@ BHE A(D0JGfA\0D(A BBBxDDbH|BBE D(D0h (J BBBG I (D BBBE lBBB A(D0D@r 0A(A BBBG \ 0D(A BBBI ` 0D(D BBBB LpAGHh$BBD A(G@Z (A ABBH U(F ABBdBEF E(A0A8G 8F0A(B BBBG # 8C0A(B BBBA h BBD  EBH T BBP F EBK f BBF Q EBH t BBH ( z}AOG^}CA$ 5gcBDA XABH pg:BBB B(D0A8F`8A0A(B BBB4( BKH y ABG D DBN ` ,ct 'BBB B(D0D8Dp^xM_xApK 8A0A(B BBBD | 8A0A(B BBBB N8K0A(B BBB 0 P ,BAD D0  AABD `  DABI k  AABI 4d heBGD m DBH L DBF  4 luBDD ` ABC AAB, AG0 DK V AI  $DE G \ D L< QBEE B(A0A8G 8A0A(B BBBE  H l:BBB E(A0D8D@^ 8D0A(B BBBA ( `AAG  CAD  d, QBB B(A0D8DP`HPt 8D0A(B BBBG H BBB B(H0D8GP  8D0A(B BBBA X LSTAD D0  AABK M  CABE D  DABM hL<P=BBB B(A0A8G 8A0A(B BBBH ,@cAG0 AG  AA |BBB B(A0A8DPz 8A0A(B BBBF C 8A0A(B BBBK { 8A0A(B BBBK @<8BAD | DBG D ABI P AEJ .D F AA @BAD G DBD ] AEE _ DBK ptBBD A(G@ (A ABBC x (A ABBB _ (G ABBE h (A ABBB 4\[BAG S DBE n DBD LBBB D(G0o (D BBBF _ (I GBBE p(BJE D(D0 (D EBBF F (D BBBH B (J DBBL a(I BBBHX.a%BBB B(D0A8G`8D0A(B BBB8cHBBA A(GP1(D ABB`,,BBB E(D0D8F` 8A0A(B BBBD N 8A0A(B BBBE D DD P D k0d(3IA z GBD P(4B] A J F F J 0AJ0 AD R AE nA,d|AQ N DR `AC F 0(AJ` AD R AE nA,\@|AQ N DR `AC F XBIA A(GPp (C ABBD DXW`_XFP\ (F ABBI DD O E k`BEF B(A0D8D` 8A0A(B BBBI 8C0A(B BBB`l`LBBB B(A0A8DP 8D0A(B BBBI p 8C0A(B BBBD HL!BBB E(A0A8DPY 8D0A(B BBBI D":BID h BBE L BBH @ BBD Td#BBB A(A0G@ 0A(A BBBE x 0C(A BBBF 8%BBA A(D@ (A ABBD 8'ZBBA A(I@ (A ABBD l48(BBE A(C0J@ 0D(A BBBD Q 0D(A BBBD d 0D(A BBBA <)CBEB B(D0 (G BBBF *>BBB B(A0C8Il 8A0A(B BBBE  EZBvDNBn BzDnB}AkB{A8iBAA  ABG O FBA PDjBBA D0  ABBE v  ABBE e  CBBD 4kBDG x ABH q CBJ 0THl#BEA G0Q  DBBH PDm)BBA D0b  DBBE L  DBBD q  DBBG \ nBBA A(L@ (D ABBK Q (D ABBF d (D ABBC H<oAD { AG V AA l AC D(R0`(A F AB `pBBB A(G0 (D BBBD l (D BBBB  (D BBBD htBMS A(Gp (A ABBH xWRxFp\ (F ABBI xW_xFp8XzBEA a BBC K EBF HX{BBB B(A0A8D`k 8D0A(B BBBJ | \D d(Q0F8F@FHFPFXF`FhFpCxCCCCCCCCCCCCCCBO I H cT`BAG DBI O DBK S DBG  DBA LBEA D(D0 (A ABBA K (D DBBI $LD R J k(TLD R J k@HBDD0i ABJ V ABG v CBE p`BBB E(A0DP 0C(B BBBE  0A(B BBBH ^ 0A(B BBBA lhL(dBBB E(D0D8J( 8A0A(B BBBA Xx BIA A(G`D (D ABBG DhWp_hF`b (D ABBE (ȗBAA Q ABH X,tBIB B(A0A8GzV_F\ 8C0A(B BBBK X\PtBIB B(A0A8GzV_F\ 8C0A(B BBBK XttBIB B(A0A8GzV_F\ 8C0A(B BBBK X BBB B(A0A8Dp+ 8D0A(B BBBJ xMgxAp p BBB E(D0D8GTGGGGGGGGGGGGGGGGGGGGGGGGGGGG G G G G G G G G G G G G G G G G G G G G G G LW 8A0A(B BBBF p 2BIB E(D0A8D 8D0A(B BBBJ DW_F^ 8A0A(B BBBH d!ĿBBB B(A0A8D@ 8A0A(B BBBD j 8F0A(B BBBG p!D ~ AA !BIB B(D0A8G 8A0A(B BBBF DV_F\ 8C0A(B BBBA  8C0A(B BBBJ D$"BBA  DBD ,(R0`(C A BBB Dl"pBBA  DBD ,(R0`(C A BBB D"BBA  DBD ,(R0`(C A BBB H"@BBB B(A0A8DP1 8D0A(B BBBD H#=l\#BBB D(A0D@[ 0A(A BBBF V 0A(A BBBJ  0C(A BBBJ $#@ BIB B(D0D8GGGGGGGGGGGGGGGGGGGGGGGGGGS 8D0A(B BBBA AGGGGGGGGGGGGGGGGGGGGGGGGGSd$(BEB B(D0A8D 8A0A(B BBBB  8A0A(B BBBH \%BIG B(D0O8PDkBAFBFABATW 8D0A(B BBBE VRF%BIG B(D0O8PDdBFFBFABFQW 8D0A(B BBBE VRFt&BIG B(D0O8PDdBFFBFABFQW 8D0A(B BBBE VRF'BIG B(D0O8PDdBFFBFABFQW 8D0A(B BBBE VRF'BIG B(D0O8PDdBFFBFABFQW 8D0A(B BBBE VRF\(tBIB E(A0A8GV_F_ 8D0A(B BBBE x(,%BIB B(D0A8GL`F_ 8D0A(B BBBH drBAABADBFQ)|2DBIB B(D0A8GL`F_ 8D0A(B BBBF ldBABBGEFAQ)D8%BIB B(D0A8GL`F_ 8D0A(B BBBH drBAABADBFQH*=BBE B(A0A8DP 8D0A(B BBBJ d\*B BBB E(D0A8D 8A0A(B BBBD  8A0A(B BBBH *8MdDZ B C*M BIE B(D0A8G!XBFABFAEFQ^ 8D0A(B BBBH zWRFW_AV`GH+W BBB B(A0A8G` 8D0A(B BBBE +Lb+HbL,DbBBE E(A0A8Dn 8D0A(B BBBA HX,j BBB E(A0A8DP 8D0A(B BBBE `,xqIBB A(D0 (D BBBB H (D BBBF I (D BBBE -s]BIB B(D0A8G^gBABBABBAQvHYF_ 8D0A(B BBBI H-hx' BBE B(D0A8Gp 8D0A(B BBBC -LDj B C E . BMN H(D0A8D,WEFFBFABFQ[ 8D0A(B BBBD WRFW_A. BMQ H(D0A8D)WEFFBFABFQ[ 8D0A(B BBBD WRFW_A 8A0A(B BBBD dW_F^ 8A0A(B BBBH W_AiV`G1BIB B(D0A8GORF_ 8D0A(B BBBE KrBAABADBFQ82BIB B(D0A8GORF_ 8D0A(B BBBE KrBAABADBFQ2BIB B(D0A8GORF_ 8D0A(B BBBE SdBABBGEFAQP3BIB B(D0A8GORF_ 8D0A(B BBBE KrBAABADBFQ3@BIB B(D0A8GORF_ 8D0A(B BBBE KrBAABADBFQh4dBIB B(D0A8GORF_ 8D0A(B BBBE KrBAABADBFQ4BIB B(D0A8GORF_ 8D0A(B BBBE SdBABBGEFAQ5BIB B(D0A8GORF_ 8D0A(B BBBE SdBABBGEFAQ 6 BIG B(L0F8KdBFFBFABFQ[ 8D0A(B BBBI VKFL6DBEB E(A0A8D 8D0A(B BBBG @6!bBB A(A0D@S 0D(A BBBF $,7?WBDA LABHT7?BBE B(A0A8DP8D0A(B BBB@7 BBE A(A0D@z 0D(A BBBD H7"tBHA D(G0s (D ABBF N(D ABBX08 #4 BBB B(A0A8DP 8D0A(B BBBA aXN`gXAPX8+*BIB E(A0A8GPRFb 8D0A(B BBBE 84V/CBIB B(A0A8Jz VRFb 8D0A(B BBBF W`F GIB!GNA9̘/UBMG B(A0Q8J}VRFb 8D0A(B BBBB H^A+W`G:xtBMG B(A0K8JK VRFa 8D0A(B BBBK  V`GIRA:ay$BIB B(A0A8JVRFb 8D0A(B BBBI MeFABFBBRgLLEBFABFBY!W_A)V`G`;lBMG B(D0Q8DWRF_ 8D0A(B BBBD gFFBFBBFAO_W_F;`"BIB B(A0A8J eBBBBABTgVRFb 8D0A(B BBBA IBKHBABBAYW_AIV`G<|BIE B(A0A8GrtBAABADBFMe 8D0A(B BBBE WKFBGA\l=BIG E(A0A8ZWRF_ 8D0A(B BBBD =BIG B(D0A8ZrBAFBFBBAMFMJFBFBGARWRF_ 8D0A(B BBBD t>M BIB E(D0A8DW_F^ 8A0A(B BBBH  8C0A(B BBBD >+BIG R(O0L8J\LAf 8D0A(B BBBE \JAORF\MB\HB_LBEGABMD4EHBDLA\?`2MBIB B(A0D8J< 8D0A(B BBBI L`F\\@PFBIG E(A0A8ZWRF_ 8D0A(B BBBD @t9BCBBB B(A0A8GBFFAAAAACNREFFAAAAACN38A0A(B BBB\dAHV BIB B(A0A8GHYF_ 8D0A(B BBBA |AaBBB E(A0D8G WRFm 8D0A(B BBBB  W_FVaG DB{BLB B(D0A8Jq 8A0A(B BBBA GGGGGGGGGGGGGGGGGGGGGGGGGFFFFFFFFFFCCCCCCCCCCCCCCCBS@hCԂWAJvLKA AF d CA ,C|AQ N DR `AC F HC@IBAJvLKA ABH l CBA ,(DD|AQ N DR `AC F XXD#BIE E(A0A8DPRF_ 8D0A(B BBBD \DȲ78BIG B(Q0F8K Y_Fb 8D0A(B BBBG |EHBIB E(A0A8JPRFb 8D0A(B BBBG K_B UmAlE(3(BMG E(A0A8TWRFb 8D0A(B BBBA ` V`GF[BBE B(D0D8J 8A0A(B BBBB ;yH]BKG^AP^SBlFr\ BIQ N(E0Q8ZEJIAG 8A0A(B BBBD MORFFzv  G~%G]$G~ 88G~IGED D(F0a(A ABBG8tG~YGED D(F0t(A ABBDHG~BEH H(KP (E ABBK [(A AFB8GIGED D(F0b(A ABBFT8H-BBE H(H0K@ 0D(A BBBE m0A(A FBB8HIGED D(F0b(A ABBF8HЀaGED D(F0v(A ABBJ<IyGED D(G0O(A ABBHHHIDBBE I(H0K8K` 8E0A(B BBBE 8IIGED D(F0b(A ABBFHIBBE B(H0H8KP 8F0A(B BBBD 8JIGED D(F0b(A ABBFHXJ$AG@ AI t AK 1 AF J EI J AE HJxAG0 AC q AF B AE J EA J AE JGJKGJ KGJ8K 0LKvAD@O EAH `K$D _KD UK(D cKԊD UK܊D U0KAG@ AO t EA A,LDQDLSAG }AdL/AG ]ALD ULB\ ]LHCD z(LAG V AI XA$LiBFG0IAK M,NAG DA@M\DIXMd3D g A tMAG _ AE lMBFB A(A0Gpg 0D(A BBBK V 0D(A BBBG / 0D(A BBBA N&IXL$Nȑ BFG E(D0A8J 8A0A(E BBBF LtN8RBED A(G`e (A ABBB t (C ABBA 0NHka L nJHA G L<NĞ&AG  AL l AK L AC O DE 8OWAG AA XOIO0 EA ,|OCAGP# AD _ AH OAG@ DD O_D ZOD P(PVBAG@CFB @P L@ M r E 0dPاMGG T ABF hHPTZBBB B(D0A8D@} 8D0A(B BBBE HPhBBB B(D0A8DPm 8D0A(B BBBE x0QܩBDB B(A0A8DP 8A0A(B BBBD C 8A0A(B BBBC a 8A0A(B BBBE xQBDB B(A0A8DP 8A0A(B BBBC B 8A0A(B BBBD ` 8A0A(B BBBF ((R4IACD g AAG HTRXBBB B(D0D8D`b 8A0A(B BBBH R,BBB B(D0D8DP 8A0A(B BBBE  8A0A(B BBBC d 8A0A(B BBBB m 8A0A(B BBBA d8S{BBB B(A0A8GP 8A0A(B BBBF I 8A0A(B BBBE xS`BBE B(A0A8DPR 8K0A(B BBBI _ 8A0A(B BBBG L 8A0A(B BBBJ ,TwKHE }ABH\LTдBIB B(A0D8D`n 8A0A(B BBBA S8A0A(B BBBdT 2BBB B(D0A8Du 8A0A(B BBBH  8C0A(B BBBE LU:BBB B(A0A8Gb 8A0A(B BBBC LdUBBB F(D0D8G 8D0A(B BBBB U` jLPL  p X  o`8   `W6p oH6oo4o  6pFpVpfpvpppppppppqq&q6qFqVqfqvqqqqqqqqqrr&r6rFrVrfrvrrrrrrrrrss&s6sFsVsfsvssssssssstt&t6tFtVtftvtttttttttuu&u6uFuVufuvuuuuuuuuuvv&v6vFvVvfvvvvvvvvvvvww&w6wFwVwfwvwwwwwwwwwxx&x6xFxVxfxvxxxxxxxxxyy&y6yFyVyfyvyyyyyyyyyzz&z6zFzVzfzvzzzzzzzzz{{&{6{F{V{f{v{{{{{{{{{||&|6|F|V|f|@%X@pDppp|3d~NQ:  ` D\[ ` #Lp,`%L o+,-`2:pE4J4S0NpZ:Di]aZdEc VLDpM Xp0OZMDdip `1 oL LV  5Hd0JpWDM`X`?O{`MmWZD@Wx.S @ UPh    @ T $G   ` s |0 > v K `n @]c .Z v`@J 2H@> p@/ n@" ` ` ``    ;0S` h@g _ V O   к` *q f =е`M `@8 p$ ` Ѕ  @b &@ZrUGCC: (GNU) 10.2.1 20210130 (Red Hat 10.2.1-11) L L  L 0 LI Li ME `M  pM M * M= 0OHO&j OP O O P P[ Q> QZ`8} 8@ PT Vx Ve WQ pWU X;i `Xw X Z P[ [ p|p | }6 ~~P X`c@yx9 \e 0]c ]T ` `7 $ aQ a|{ 0b d @ d e `i/ Áz}S 6 \ 6 f h6 r X6 ~ 6  4  `! E x.  3 ! $' 7P &y ` = `+  B  5 ` Q < * ^ 2 o  #  & 81  &  *   @& ?  * a  &  @% !  ,   )   &   ) 7   %`  (   (   &   %  %   @ "A  ` 2j   *   (   +  ` #  ) 1  ( T  "|  &   '   )   )   & .  ' R  * s   &   *   %  ` & % !> $ !e (  `&  `*  '  @*  / '  LP 0 c (   " ` [  ?  .* + H 6 R / f +  @+  5  ,  6   & /  . + 4 9 / M  v (  h.  p2  '  6  (1   !*  "S $ z @ . ` )  ( /  x0  @. 8 7`  F T6  S6  6  6  6  6  Q6  6  `'   .0 ` 9Y  ) M6  I6  E6  `2  0.  4  83  ?6  ;6  4  4 " - = 03 M `- g 4 v  3  5  5  6  5   .  5 * )S @ { 6  3  3  /  4   2 P2 C 4 Q . g -  x/  .  3  @ T +  + $ 5 1 3 @ 4 N . d 76 p % 3 3  h/  +  6  4  4 * 5 7 ` $ ^ 3 n 36 z 3  4  .  5  4  h0  3  3  @2  4  1 , /6 8 4 F 4 T 5 a R    4  4  3  2  3  2   5  A }6 L P. c K 02  (6  $ 2  z )  1  5 ( 2 9 @ &b @h  z6  3  2  3  4  X/  4  4  4  5  2 . `[ V 5 c [ 8 0  2  ~4  1  1  X0  5  1  @' 3 x4 A $6 M t 5  0  H0  3  5  6  5  80  O d  > > 3 f 6 r x5  0  3  6  -  r5  # !$  `( G  %p  2   3   @ '  2  m5   (0 ! w6  !  4! \! I! 6 ! 0 ! B! h5 ! 3 ! c5 ! ^5 " @ '(" ` $Q" 6 ]" r4 k" , " 3" Y5 " " @ = # ` 4# @, Q# t6 \# 2 l# @( # ' # ) # , # l4 # + $ 'D$ "m$ H/ $ * $ ' $ 6 $ $ 1 % f4 % 6 $% `) F% "n% 6 x% * % T5 % % _4 % "& +& 3 :& 1 K&  r& - & & #& @) & % #' O5 0' Y4 >' @ ]g' - ' 8/ ' 0 ' 0 ' 1 ' @- ' / ' S4 ( 3 ( @ <( M4 J( G4 X(   ( x3 ( 1 ( . ( 0 ( 1 ( 2 ( 2 ( (/ ) 1 ) A4 -) 2 =) J5 J) E5 W) ;4 e) / z) @5 ) x1 ) - ) 54 ) 2 ) x ) ;5 * /4 * 65 * 15 +* )4 9* `r a* (5 n* 5 {* / * * @ t* ` + - + @i  C+ X Ok+ #4 y+ 4 + 5 + 5 + 6 + , + !+ ,  , 2 , / 1, l3 @, h1 Q, 5 ],  N, 0 , 5 , X1 , 5 , 5 , 5 , 2 , 5 , O Y - p6 *- e3 9- ^3 H- W3 W- 4 e- p% -  &- E - P3 - I3 - B3  . . . 9 F. D m. 5 z. H1 . , . 0 . 6 . `, . 4 . 5 / ! -/ =cD/ :W/ Pkt/ kc/ Pl'/ m / m0 oe/0 oV0 ppuy0 p0 r0 PsQ0 z0 `{: 1 |*1 ~E1 c1 |1 S1 =1 c1 2 82 Й.-2 @2 X2 @[v2 2 `2 %2 H2 `,3p3h63P9G3 Dk3 33 3 3 |4 0b4 |4 p4 D4 p4 L5 p55 0:[5 p5 585 `Z5 5 C6 >76 `F6 a6 `z6 P6 #6 )6 P6 @&7 _7 777 #7h97 @$7`98 @+\68 ,W8 3u8 4L8 4L8 58 @6!98F9 :29 :`9 :9 ? 9 C9 Et:8: JtI: Nt}: S : _ : i2; o*; uA; x; ~; 0; < "< =9< Q< ` e< p< `<8< = `Q= = `= = %:> Dt>8> %> P> 0 $? PdQ?  ?  ? ? @ %@7<@ `% ^@ p,{@ .]@ P4' @ =A > HA H A 0S A ] B Ph 8B rlB B `B C WC pC C кD ?D 0 wD 0D7D P!D GWD E E t2E 4 `E$wE$E$Ex$E *F9F@#%F8#AF0#XF(#tF #F#F#F#F#F" G"$G"@G p/CG"G"G"G"G" H"'H">H"ZH"qHx"Hp"Hh"H`"HX"H" I"&I"=I"YI7sI `/UI8I8JP")JH"EJ@"\J8"xJ0"J("J "J"J"J"K"(K!DK![K!wK!K!K!K!K!K!L!'L!CL8tL еtL!L!L!M! M!7Mx!SMp!jMh!M`!MX!MP!MH!M@!N8!N!6N!RN0!iN(!N !N!N!N N *y$,O CO _O vO O O O O O P +P8bP OP P P P  Q #Qx ?Q9pQ @g`"Q Q Q QR*RFR]RyRRRRR8S QShSSSS8S  T7TST8TTxT8T U`,UXGUP]UHxU@U8UpUhU7U M .V`DVX_V +VPVHV9W@W83W 9jWWW0W(W9X X4X9jXXXH9XXY@9Z(9tZ MZZZ[[ S[h[[[x[ BC[7[7\7&\7?\7Y\@\8\8\8,x8\p8\h8\%\ \p9 ](]%@@] \]`%@z] ]8]8]82^%@@^ v^$^$^$^$^$^$_$&_$B_$Y_$u_ _ & _$_$` 1!` KB` TW` Z|` p[I` a|a @b#Dap$[ah$wa`$aX$aP$aH$a@$a8$b0$'b($Cb $Zb$vb$b$b Ѕ78b#bx#cp#.ch#Jc`#acX#}cP#cH#c Hc#d#d#4d#Pd#gd#d#d#d$d#d#e#e#3e#Oe#fe#e (ep eh e` fX #f0 :f( Vf mf fP fH f@ f8 f 0(g0>g(Ygogg gggghh3hNhdhhhhhhhip(ihCi`YiXtiPiHi@i8iij j8jNjijjjjjjj0k(-kCk^ktkxkkxkpkhkl"l8lSlillllhl G\ m`hm@% 'm0=m`\m P|m m m m` mmPn3nLn`n`Ptn` nxn  o @ Oo @o R o tp @ Jp p p p  ;q uq q q  %r v = er `n r c r Z -s @J Oks @> s @/ s @" t ` Ut  t ` )t d u Cu  u ` D u Y u 1v 'vv v v ` K&w q hw f w `M Iw @8 +x $ zx ` $ x  x .y  "my @h y Ky Ly PLy@y y L z (z C 2z K