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                   (                   0                   8                   @                   H                   P                   X                   `                   h                   p                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           HH HtH     5 % @ % h    % h   % h   % h   % h   % h   % h   % h   p% h   `% h	   P%z h
   @%r h   0%j h    %b h   %Z h    %R h   %J h   %B h   %: h   %2 h   %* h   %" h   % h   % h   p%
 h   `% h   P%~ h   @%~ h   0%~ h    %~ h   %~ h    %~ h   %~ h    %~ h!   %~ h"   %~ h#   %~ h$   %~ h%   %~ h&   %~ h'   p%~ h(   `%~ h)   P%z~ h*   @%r~ h+   0%j~ h,    %b~ h-   %Z~ h.    %R~ h/   %J~ h0   %B~ h1   %:~ h2   %2~ h3   %*~ h4   %"~ h5   %~ h6   %~ h7   p%
~ h8   `%~ h9   P%} h:   @%} h;   0%} h<    %} h=   %} h>    %} h?   %} h@   %} hA   %} hB   %} hC   %} hD   %} hE   %} hF   %} hG   p%} hH   `%} hI   P%z} hJ   @%r} hK   0%j} hL    %b} hM   %Z} hN    %R} hO   %J} hP   %B} hQ   %:} hR   %2} hS   %*} hT   %"} hU   %} hV   %} hW   p%
} hX   `%} hY   P%| hZ   @%| h[   0%| h\    %| h]   %| h^    %| h_   %| h`   %| ha   %| hb   %| hc   %| hd   %| he   %| hf   %| hg   p%| hh   `%| hi   P%z| hj   @%r| hk   0%j| hl    %b| hm   %Z| hn    %R| ho   %J| hp   %B| hq   %:| hr   %2| hs   %*| ht   %"| hu   %| hv   %| hw   p%
| hx   `%| hy   P%{ hz   @%{ h{   0%{ h|    %{ h}   %{ h~    %{ h   %{ h   %{ h   %{ h   %{ h   %{ h   %{ h   %{ h   %{ h   p%{ h   `%{ h   P%z{ h   @%r{ h   0%j{ h    %b{ h   %Z{ h    %R{ h   %J{ h   %B{ h   %:{ h   %2{ h   %*{ h   %"{ h   %{ h   %{ h   p%
{ h   `%{ h   P%z h   @%z h   0%z h    %z h   %z h    %z h   %z h   %z h   %z h   %z h   %z h   %z h   %z h   %z h   p%z h   `%z h   P%zz h   @%rz h   0%jz h    %bz h   %Zz h    %Rz h   %Jz h   %Bz h   %:z h   %2z h   %*z h   %"z h   %z h   %z h   p%
z h   `%z h   P%y h   @%y h   0%y h    %y h   %y h    %y h   %y h   %y h   %y h   %y h   %y h   %y h   %y h   %y h   p%y h   `%y h   P%zy h   @%ry h   0%jy h    %by h   %Zy h                                    QHG   uH#r HH5d H81w(1Ht$H;W tHq HH5d H81MZAWIAVAAUAMATDAAULLSH(H4$HT$D$8HH,  H4$1L9}HHHTHHHHRH$Hu1   MuL- E1FIE1HhHHHHl$IHtHHH   HL$1HH-ą DMEMH DLDD\$DUA	DAUQA  AWDAWt$@PPt$@PPAPE1H`HMtIuLHtH
HH(H[]A\A]A^A_AWIAVAUIATIH5:R UHSHLD$Hu  LHIHHu0LHL$MH5c HH'p H81E   H HHu@HLIIMH5c HPHo AWHT$H81ZY=HHIIHQHt#IHuLHt16HIuLHHHH[]A\A]A^A_AVEAUIATIHUSMHt3H;in Hu1AtHLLHu'HWH>n H8stJ1[]A\A]A^ATUHSaHxHtJHz Hu	Hz ;H9t6Hn H5b H8H5Z HIHu1   H HtH   HI$HuLHtHIHuHuHrA   HO HHHO xA   HO LHHO xA   HO LHHO exE1HO LHHO EdH[]A\AWIAVIAUIATIULSSH=j H   E1E1E1LpD   HLP(H@LXpMtI$1E1Lc H{@H{HIL{PLCXLC8Lk`IE HtHE AFW11Hkh%  HKxH         tOtQHO tP=   t@Hړ =  t9Hl H5N H8Hu,H"HGg 1H HS0H1ZH[]A\A]A^A_HX   HT$0Ht$(HL$8LD$@LL$HH|$`HT$ D$   H|$HT$Ht:LHIй   1҃/w
΃LHHH6HI4HH   uHXAVIHAUEATIUHSH   HH@   u H@k HLH5Sb H81qLK(HC Mt   I9LLIM9s#H?j MHLH57b H81M-Au7I9s2RL1MPIHb 11TY^yHuHA1H[]A\A]A^AUWIATI1UHSHH(HG`Ht$HD$HGhG`HD$HGpHWpHT$H|$HD$H{`    Ht$HuHT$HtHH|$3yiH|$HtHHD$HtH I} I$HU HSxHHHt
HunH|$Ht
HuZHtHuHH1QH|$1IE I$HE Ht
Hu"H|$Ht
HuH|$HuHuH([]A\A]SHHh HH8H9tHuH@HuHGH:HHH =H[AWAVAUIATIUSHL>.   HT$LHtLxLHHC  H=uI VHH   H HH$H   HHIHuzHt%   H IcT$LH-      HT$LHPIH   MtHxIE LhHuHtwH<$LHIHtSIE M9It^HIuLIcT$LLMt HuH[LHM uHJIuL;E1HHIuL!HH[]A\A]A^A_UHHSHAPH?HHt
HuHtHM uHHtHuZH[]X[]H9  AUATUSHAPHu1u  HFHH      Lf1I9~H;\u
   A  HE1M9~JtH9tHC         @tzHFH   sY   @tPHX  HtHJ1H9~1H;ttHHH   H9uHuH;56f cIms
H肉 Hxt:HW   tf   @t]sW   @tNHX  HtHJ1H9H;lHH   H9Hu1H;-e YHH[]A\A]Z[]A\A]ø   AU1ATUSHHH4$Ht$Ht$Ht$Ht$ Ht$(HL$HT$HHxxIH=H IHHuGHd H8uHOe H5` H8x   H=H HHtH5H H+HM HuHZHuH>d H5H H8xHd H9Ct%Hyd H5_ H8HuPHF1HHH uHH=  H<$5  H$d H5$H H8Hc I|$`  H-u_ L-H H0   H  L  a HL$(HT$ LHt$7tZ1Ht$8H      HD$0H	z HD$8Hc H8% HHt111H HuH  I|$xHL$HT$H4$H|$Ht
HuH|$ Ht
HuH|$(Ht
HuHL FHt
HuH|$1H$Ht
Hu}H|$1HT$Ht
Hub1HH[]A\A]AU1ATUSHHH4$Ht$Ht$Ht$Ht$ Ht$('HL$HT$HHxxI&H=F HHu4Ha H8q  H=E RHHT  H5DF HwHM HuHH+  Hna H9Ct,Ha H5] H8ZH   Hi   1HZHHH uHFH7 H$HuHa H5E H8    H    v#   H5B] HAa H81s  H!a    H5]] H81GH   uH` H5^ H8r5  H` H5^ H8RH` I|$`  H-"\ L-D H0   H  L   HL$(HT$ LHt$tZ1Ht$8H      HD$0Hv HD$8H` H8Ғ HHt111H HuH  I|$xHL$HT$H4$H|$Ht
HuH|$ Ht
HuyH|$(Ht
HueHL8 IHtHuHAH|$1H$Ht
Hu'H|$1HT$Ht
Hu1HH[]A\A]ATIHUHSHHWH=s Hs HRI$HE HuH[]A\F H []A\AWAVAUATUSH(
  H~ Ht)1H9%  H^ H5@] H8P  HH=F Hbs H   H H=0C :HtH HCs H   H=C HtH H's H|   Hs H= H5B Z   H^ H 0HH  u1Hr Hul$   HHH$  APH   HA   LI    RH\ PHzB P1H 1   H  HM 1H.HWr H  1HHEr H  H$  H5%   H=B H$  HIL  HA H?IH   LHIHtv   w  H=? *HHuIuxLun1HL1HIuHTIuLGIM uL9IuSL,IH\    HH5|[ H81MtIM uLIl  L_  MV  ID$ 1E1H$L5Kr Hc1D  H$A  J<8LH$  HtH
vH$  H$  HtAIHMH  uHcD  H$A  J<8LM:IHuI$  L  HH  uI$uL 1I<Hj  HH  uH 1L%~ H$  Ǆ$  	
H| /IH   HHuH5Z    1HHuH#  /1HH5h H} HuHIH=}  tH  H=} 1H5f tH} Ht=9n  u2`H  Hw H5x H=   HHu  L%F HLHt}~#Z Hu fHnH   (fHnH  flfHnH8  )-o (fHnflBo (flflo )Qo HH  H LH  dHhr IHL3| Hs Ho  H$  Hu H$  H:q H$  Ho H$  6Ho H  Hu IHH{ L{ Hy  H$  H`x H$  Hq H$  H2o H$  Hp H$  Hw H$  Hn H$  Ht H$  H$  HZn Hb  Hy IHLz Hs Hn A H$  Ht H$  .Hn H  Hx IHLz Hp HDn !H$  Hm H   Hkx IHHVq Hn LXz 0H$  H$q H$  Hq H$  H~y H$  yHHgm HQHtWHHuHH-; H?HHtj  H; HHA   HHk HQHuHu5Hz+HHuHhH-; HHH   L%;       H=  t@H=:k  ttLH=`B  H= Ht51HH u' MHuHV H5"B H8H= b  A       HHH: Hj HA   H
  HHH: eHj HA   0  HHH: 8Hj HA      HHHx: Hxj HA      HHHS: HSj H[A      HHH.: H.j H.A      HHH: H	j HA      HHH9 WHi HA      HHH9 *Hi HA      HHHm= Hi HzA      HHHk9 Hui HMA      HHH79 HPi H A      HHH9 vH+i HA      HHH8 IHi H   H7 HHA   HHh HQHHHuH	L58 LzHHH$  H5OZ F  L%v H$  H$Ml$ I   MHHt[LE8 LLHuHM >H1LHLMdLx LhtMHM uHELHHH-ru H 1L,$H$  L$  H$  Le H?MMM Mt`L: LLHHLL$LL$@H$  HIIPLHlCLx L`tMHuHH=>7 HHH-t H 1L,$H$  L$  H$  Le H?MMM Mt`L: LLHHLL$!LL${H$  HIILHl~Lx L`tMHuHH=6 3HHZHx 1L,$H~F fHnHK H-s fHnHP H$  L$  flH$  Le H  )$  M~fF fl)$  MM MtpL8 LLHHL$L$tHHH$  HIIpLHlcLx L`tMHLHuG  s  Ld E111H=p 1* IH  H5Wp H=`d HIHȅ  IHuL(L1d E111H=p 1 IHh  H5o H=d HiIHȅa  IHuLLc E111H=ln 1l IH  H59n H=c H
IHȅ  IHuLj
   0IH  Hq H5o H  Hq H5p L~  Hyq H5n L`  Hcq H5o LdB  HMq H5nk LF$  H7q H5@m L(  H!q H5Jf L
  Hq H5d L  Hp H5^m L  Hp H50k L  H5qn H=*b LIHȅ  IHuLIH  H*p H5h HKx8Hp H5ao L1d  Hp H5km LyL%G    r  H'h H5o LxHo H5o LxHm H5o LxH5qm H=2a LIHȅ  IHuLLSb H` H=U\ Hl H5f IH  H5f H=` H0IHȅ}  IHuLLa H` H=[ Hl H5l IH3  H5l H=^` HIHȅ$  IHuL&H-a L-0l L%d IH  H5i LH>yI  L  H5k LLxH  H5^c HLx  L%E 
   }  L%E    l  L%E    [  L%E    J  L%wE    9  L%fE    (  L%UE      L%DE       L%3E R   
  ~g E1~%j ~-k ~5k ~=k gi %Hk ~k -k 5k )\$~` =k )d$ ~%` k )l$0~` ~-` )t$@%` ~5a )|$P-` ~=c 5gc )T$`={c )\$p)$   )$   )$   )$   ~c ~^c ~d ~%d (c ~-d ~5d c c %d ~=d )$   -d ~d 5d )$   =d ~d )$   d ~d )$   d ~%d d )$   %d )$  )$   )$0  )$@  )$P  )$`  ~-d ~5d ~=d ~e -d 5d ~he ~pe =d Be ~%e )$p  )$  ;e ~-se ~5{e )$  De ~=te %Ee )$  -Fe ~ve 5Ge =`e )$  	g )$  )$  )$  )$  )$   )$  ~f ~f ~%f ~-g f f ~5g ~=[g %f -f ~Ug )$   )$0  5&g ~Fg ~Vg )$@  =g ~%?i g )$P  g ~-ai Bg %Ki )$`  -Ti )$p  )$  )$  )$  )$  )$  ~5i ~=^ ~^ ~a 5eg =Vh ~a ~%^b _a ha ~-Xb )$  )$  )b ~5h ~=a )$  %b ~c -[h )$   5a ~] =g \ )$  \ )$   )$0  )$@  )$P  )$`  )$p  _ ~(] D~5] D~-_ D~%_ e D~] D~] D5t_ D~] D~e )$  D-Z_ ~=] ~5] D%"_ Db] ~-:g ~%c Db] DJ] ~^ D] ~^ =] ~g 5f -\ %a W^ a f D~=a D=pa D)$  D~=\ D=^ D)$  D(|$D)$  D(|$ D)$  D(|$0D)$  D(|$@D)$  D(|$PD)$   D(|$`D)$  D(|$pD)$   D($   D)$0  D($   D)$@  D($   D)$P  D($   D)$`  D($   D)$p  D($   D)$  D($   D)$  D($   D)$  D($   D)$  D($  D)$  D($   D)$  D($0  D)$  D($@  D)$  D($P  D)$   D($`  D)$  D($p  D)$   D($  D)$0  D($  D)$@  D($  D)$P  D($  D)$`  D($  D)$p  D($  D)$  D($  D)$  D($  D)$  D($   D)$  D($  D)$  D($   D)$  D($0  D)$  D($@  D)$  D($P  D)$   D($`  D)$  D($p  D)$   D($  D)$0  D($  D)$@  D($  D)$P  D($  D)$`  D($  D)$p  D($  D)$  D($  )$0  ($  D)$  D($  )$@  D)$  D($   D)$P  D)$  D($  D)$`  D)$  D($   D)$p  D)$  D($0  D)$  D)$  D($@  D)$  D)$  D($P  D)$  D)$   D($`  D)$  D)$  D($p  )$  D)$   )$  )$  )$   ($  H\$ )$  )$  )$   )$0  H$LN$IGH   LH  HH;  H9? H8q  H? LH5Z+ E1H81LL%# 3  IuLHu
   HuH   L%j=       L%T=       qL%9       [L%9       EL%9       /L%9 
      L%v9       L%`9        L%J9 R      L%49       LfT HR H=N H^ H5bW HHt8H5~Y L%?> M9guHNHL6HL&1L%8    vL%R"    13   HM uHYLS H[R H=TM HU^ H5V VHHt1H5BV M9guHNHL7HLM'1L%8    HL%8       HM uHL4S HQ H=L H] H5V HHt1H5V M9guHNHL7HL'1L%y7    ;HL%e7    '  HM uHHU 1H=< H$  H$  H      H$  HQ L$  H$  n HHʽ  H5,U H=P H-  HM uHIuLHCV 5E^    5B^ 5X 5U 5U 5U 5X 5Z 5S 5] 5] 5T 5xT 5bT 5TT 5S 5T 5S 5S 5S 5S 5U 5U 5U 5U 5U 5lS 5[ 5R 5U P53R 5mR 5/R 5X 5\ 5V 5V 5y] 5k] 5W 5W 5W 5V 5V 5V 5U 5U 5R 5\ 5R 5[ 5M] 57] 5)] 5\ 5[ 5Z 5Z 5Z 5Z 5Z 5Z 5Z 5uZ 5'Z 5Z 5Z 5Y 5Y 5Y 5Y 5Y 5Y 5Y 5W 5W 5W 5W 5W 5uW 5gW 5YW 5KW 5=W 5W 5	W 5V 5V 5wV 5iV 5V 5V 5U 5U 5U 5U 5U 5yU 5[U 5MU 5?U 51U 5#U 5U 5T 5T 5T 5=T 5T 5	T 5S 5S P15lS 5&S 5S 5R 5R 5nP 5P 5
P 5O 5O 5O 5O 5T 5Q 5Y 5zS 5\[ 5.[ 5Z 5Z 5Z 5~Z 50Z 5
Z 5Y 5Y 5Y 5"Y 5Y 5X 5X 5rX 5dX 5VX 5HX 5:X 5X 5W 5W 5jW 5\W 5.W 5 W 5W 5W 5V 5V 5V 5V 5V 5U 5U 5U 5U 5U 52U 5|T 5nT 5PT 5BT 54S 5&S 5R 5R 5R 5~R 58R 5*R 5R 5R 5 R 5Q 5Q 5Q 5Q 5bQ 5Q 5P 5P 5P 5P 5P 5P 5P 5P 5P 5P 5rP 5dP 5VP 5HP 5
P 5O 5O 5O 5O 5O 5O 5O 5N 5N 5N 5N 5N 5N 5N 5xN 5RN 5DN 56N 5(N 5M 5M 5M 5M 5jM L[M LLM H=M H.M H5L _H0  IH  H5L H=J HQIHȅ  IHuL豻~+ H- H5 A   HF H7 A   H5ʣ + H- ~+ H= ) H )$H H/ H Hj H H QfHn   HU PflH H j )I PIH H  H5_L H=I HPIHȅ  IHuL谺(<$HM H-~ H5 H0 A   ~* A   )= H H5[ H= Hm HN Hg Hj Hc H\ QfHnʹ   H
 PflHF H j ) PIH H  H5|K H=H HeIHȅ%  IHuLŹ($$HR H-3 H5 H5 A   ~) A   )%Z H H5 H=I H" Hm H Hj H H QfHn   H PflH H j ) PIH H3  H5J H=H HzIHȅK  IHuLڸ(4$HW H- H6 H: A   ~) A   )5 H H5ş H= Hן H Hџ Hj H͟ HƟ QfHn   Ht PflH H1 j )h PIH H^  H5I H='G H菵IHȅq  IHuL($H\ H- H>6 H? A   ~)( A   )Ğ H H5z H= H H H Hj H H{ QfHnҹ   H) PflHe HF j ) PIH H  H5I H=<F H褴IHȅ  IHuL($Ha H-R Hc6 HD A   ~F' A   )y H H5/ H=h HA H H; Hj H7 H0 QfHn   Hޜ PflH H[ j )Ҝ PIH H  H5 H H=QE H蹳IHȅ  IHuL(,$Hf H- H6 HI A   ~c& A   )-. H H5 H= H H H Hj H H QfHn   H PflHϛ Hp j ) PIH H߽  H5=G H=fD HβIHȅ  IHuL.(<$Hk H- H6 HN A   ~% A   )= H H5 H=Қ H H H Hj H H QfHnʹ   HH PflH H j )< PIH H
  H5zF H={C HIHȅ	  IHuLC($Hp H-q H6 HS A   ~$ A   ) H H5N H= H` H- HZ Hj HV HO QfHnڹ   H PflH9 H j ) PIH H5  H5E H=B HIHȅ/  IHuLXHq H ~# H#7 ~# HD A   A   # H" -w H5 H H H=  )\$@fHnH j flQ   PH H j - ) ) PH IHX  H5E H=A HIHȅM  IHuLeH H ~" H7 (t$@j A   A   QH5͖    H= Hʖ HӖ H̖ PfHnH H flH H֟ j -v )5 )p PH IH  H5>D H=@ H'IHȅ  IHuL臱H  HIb j ~" fHnH  H H5$ flHڕ Hu A   H H A   H5B ) ( fHnH= Ha HJH H HS H HR8 )Ӕ ~! Q   PflH H H# H j ) PIH Hq  H5AC H=? HIHȅ\  IHuLRH3 H ~  (\$@H  L-7 A   A   j    H5 H= H Hړ AUfHnH PflH H H j -j ) )l PH IH  H5D H=> HIHȅ  IHuLs~%3  L% H%7 A   f-X Hq A   H5 %  L%n HG H= ~ f-Y )% H )d$`Hk Hv He Hj Ha HZ QfHn   H PflHD H j ) PIH H  H5C H== HIHȅ  IHuLc(<$L5h H	7 A   H\ HM A   H5  L5	 H=R ~ )=C H H H H Hj H H QfHnʹ   H PflH H j ) PIH HҶ  H5B H=< HIHȅ  IHuLq(T$`Hm L%ޏ H6 f-؏ HI A   A   ) H ~ H5 H= HƏ H H Hj H H QfHnڹ   Hc PflH H j )W PIH H  H5B H=; HIHȅ̩  IHuL~(d$`Hj L% H6 f- HF A   A   )% H ~( H5a H= Hs H Hm Hj Hi Hb QfHn   H PflHL H͙ j ) PIH H  H5"A H=: H+IHȅ  IHuL苫(4$Hh L59 H6 HK A   ~U A   )5` H H5 H=O H( H H" Hj H H QfHn   HŌ PflH H j ) PIH HC  H5?@ H=9 H@IHȅ  IHuL蠪($Hm L5 H6 HP A   ~r A   ) H H5ˋ H= H݋ H H׋ Hj HӋ H̋ QfHnҹ   Hz PflH H j )n PIH Hn  H5\? H=8 HUIHȅ6  IHuL赩H^ H
 ~-  ~ H A   A   - H    H5p H H H= )l$fHnH: j flAUHs PH j f- )-c ) PH IH  H5> H=7 HcIHȅU  IHuLè(,$H- Hy5 A   Hl H] A   H5@ H-) H=r ~ )-c H H9 HR	 H3 Hj H/ H( QfHn   Hֈ PflH H j )ʈ PIH H  H5= H=	7 HqIHȅt  IHuLѧ(<$H~ H- H5 Ha A   ~ A   )=& H H5܇ H= H Hu H Hj H H݇ QfHnʹ   H PflHǇ H( j ) PIH H  H5< H=6 H膤IHȅ  IHuL(T$@H H j ~ AUA   A   PD5Wk    H5 H H=Ɇ H H fHnH HX H HZ flj D5= ) )? PH IH  H5= H=>5 H覣IHȅˣ  IHuLH_ H ~( H- (d$@j A   A   QH5^    H= Hk Ht Hm PfHnH  HQ flHV Hw j D5 )%G )  PH IHN  H5>< H=_4 HǢIHȅ  IHuL'H H8 ~Q H, (t$@j A   A   QH5    H=S H, H5 H. PfHnH H flH H j D5 )5 ) PH IH  H5w; H=3 HIHȅ/  IHuLHHn Hb ~z H+ (L$@j A   A   QH5    H= H H H PfHnH Hӂ flH؂ H j D5 )ɂ ) PH IH  H5: H=2 H	IHȅa  IHuLi($H H- H 2 H A   ~ A   )ށ H H5 H=́ H HP H Hj H H QfHn   HC PflH H j )7 PIH H  H59 H=1 HIHȅ  IHuL~(,$H H-l Hm2 H A   ~ A   )- H H5I H= H[ Hq HU Hj HQ HJ QfHn   H PflH4 HՏ j ) PIH H  H58 H=0 H3IHȅ  IHuL蓡(<$H H-! H2 H A   ~ A   )=H H H5~ H=7 H H H
 Hj H H~ QfHnʹ   H~ PflH~ H j )~ PIH H=  H58 H=/ HHIHȅӞ  IHuL訠($H H-} H3 H A   ~ A   )} H H5} H=} H} H H} Hj H} H} QfHnڹ   Hb} PflH} H j )V} PIH Hh  H547 H=. H]IHȅ  IHuL轟($$H H-| HT3 H A   ~ A   )%| H H5h| H=| Hz| H  Ht| Hj Hp| Hi| QfHn   H| PflHS| H j )| PIH H  H5Q6 H=
. HrIHȅ  IHuLҞHn H@  ~4 H]& (t$@j A   A   QH5*{    H=^{ H7{ H@{ H9{ PfHnHz H{ flH"{ HC j D5z )5{ )z PH IHʨ  H5z5 H=+- H蓛IHȅQ  IHuL($L- H2 A   H, H A   H5y L-y H="z ~* )z H Hy H Hy Hj Hy Hy QfHnҹ   Hy PflHy HC j )zy PIH H  H55 H=9, H衚IHȅp  IHuL($H> L-x H2 H! A   ~[ A   )x H H5x H=x Hx H7 Hx Hj Hx Hx QfHn   H;x PflHwx HX j )/x PIH H  H54 H=N+ H趙IHȅ  IHuL~5 H? H3 A   H# D5` A   H5Ow 5 f- ~a H=rw )5kw H )t$PH<w HA H6w Hj H2w H+w QfHn   Hv PflHw HV j D5v f-v )v PH IH  H53 H=>* H覘IHȅ  IHuL(|$PH" H2 D5u H f-u A   A   )=v H ~` H5u H=v Hu HX Hu Hj Hu Hu QfHnʹ   Hxu PflHu HU j )lu PIH HB  H52 H=K) H賗IHȅ  IHuL($H  L-t H2 H A   ~ A   )t H H5~t H=t Ht Hz Ht Hj Ht Ht QfHnڹ   H-t PflHit Hj j )!t PIH Hm  H51 H=`( HȖIHȅۗ  IHuL(($$H% L-Vs H3 H A   ~
 A   )%}s H H53s H=ls HEs H H?s Hj H;s H4s QfHn   Hr PflHs H j )r PIH H  H50 H=u' HݕIHȅ  IHuL=(4$H* L-r H43 H A   ~	 A   )52r H H5q H=!r Hq H Hq Hj Hq Hq QfHn   Hq PflHq H j )q PIH Hâ  H5	0 H=& HIHȅ'  IHuLR(L$PH. H_3 f-p H D5[ A   A   )p H ~ H5p D5~p H=p Hp H Hp Hj Hp Hp QfHnҹ   H=p PflHyp H j )1p PIH Hߡ  H5/ H=% HIHȅ>  IHuLX(\$PH$ HM3 D5^o H f-To A   A   )o H ~ H5;o H=to HMo H HGo Hj HCo H<o QfHn   Hn PflH&o H j )n PIH H  H5,. H=$ HIHȅ\  IHuLe(l$`L5y f-n H;3 H H A   A   L5m H5m ~ H=$n )-n H Hm H Hm Hj Hm Hm QfHn   Hm PflHm H j )m PIH H  H5:- H=# HIHȅs  IHuLk(<$H L-l H23 H A   ~ A   )=l H H5l H=l Hl H  Hl Hj Hl Hl QfHnʹ   HEl PflHl H j )9l PIH HI  H5W, H=" H IHȅ  IHuL耓($H H3 A   H A   ~3 H5\k HEk H~ H=k )k H HVk HC HPk Hj HLk HEk QfHnڹ   Hj PflH/k HЀ j )j PIH Hm  H5m+ H=! H.IHȅ  IHuL莒(d$`H~ L5j H2 f-j H} A   A   )%Cj H ~0 H5i H=*j Hj HZ Hi Hj Hi Hi QfHn   Hi PflHi H j )i PIH H  H5* H=  H;IHȅ֐  IHuL蛑(t$`fD- L5h H2 H} H| A   A   fD-h H5h ~? H=h )5h H Hh Hg Hh Hj Hh Hh QfHn   HDh PflHh H~ j )8h PIH H  H5) H= H?IHȅ  IHuL蟐($H- H2 A   H{ H{ A   H5\g H-Eg H=g ~N )g H HUg H} HOg Hj HKg HDg QfHnҹ   Hf PflH.g H} j )f PIH HΛ  H5( H= HMIHȅ
  IHuL譏($H
{ H-f H2 Hz A   ~ A   )Bf H H5e H=1f H
f H Hf Hj H f He QfHn   He PflHe H} j )e PIH H  H5' H= HbIHȅ0  IHuL(,$Hz H-d HQ2 Hy A   ~  A   )-d H H5d H=d Hd H Hd Hj Hd Hd QfHn   H\d PflHd H| j )Pd PIH H$  H5' H= HwIHȅV  IHuL׍(|$PHy Ht2 fD-c Hx D5^R A   A   )=c H ~ H5Yc D5Bc H=c Hdc H H^c Hj HZc HSc QfHnʹ   Hc PflH=c H{ j )b PIH H?  H5& H= H|IHȅl  IHuL܌(T$PHx Ha2 D5"b Hw fD-b A   A   )Pb H ~ H5a H=7b Hb H H
b Hj Hb Ha QfHnڹ   Ha PflHa H*z j )a PIH Ha  H5'% H=  H舉IHȅ  IHuL($$Hw H-` H72 Hv A   ~ A   )%` H H5` H=` H` H H` Hj H` H` QfHn   Hb` PflH` H?y j )V` PIH H  H5D$ H=5 H蝈IHȅ  IHuL(4$H
v H-_ HT2 Hu A   ~ A   )5_ H H5h_ H=_ Hz_ H/ Ht_ Hj Hp_ Hi_ QfHn   H_ PflHS_ HTx j )_ PIH H  H5a# H=J H貇IHȅՉ  IHuL(L$PHu Ho2 fD-;^ Ht D5N A   A   )f^ H ~ H5^ D5] H=F^ H^ H< H^ Hj H^ H^ QfHnҹ   H] PflH] HYw j )] PIH Hҕ  H5n" H=O H跆IHȅ  IHuL(\$PHt HL2 D5\ Hs fD-\ A   A   )] H ~ H5\ H=\ H\ HV H\ Hj H\ H\ QfHn   Hh\ PflH\ Hev j )\\ PIH H  H5! H=[ HÅIHȅ  IHuL#(,$H s H-[ H*2 Hr A   ~5 A   )-[ H H5n[ H=[ H[ Hy Hz[ Hj Hv[ Ho[ QfHn   H[ PflHY[ Hzu j )[ PIH H  H5  H=p H؄IHȅ.  IHuL8(<$Hr H-FZ H/2 Hq A   ~R A   )=mZ H H5#Z H=\Z H5Z H H/Z Hj H+Z H$Z QfHnʹ   HY PflHZ Ht j )Y PIH HJ  H5 H= HIHȅT  IHuLM($HR HC2 A   Hp A   ~p H5X HX Hp H=Y )Y H HX H HX Hj HX HX QfHnڹ   HX PflHX Hs j )tX PIH Hn  H5 H= HIHȅs  IHuL[H  HW j A   HW H  A   HW HW H H5W HW H H=W Q   PHW Hr j fW PIH H  H5  H= H7IHȅ  IHuL藄(d$`L- Ht1 A   f- H(o A   H5V L-V Ho H=V ~ f-V )%V H HV H* HV Hj HV HV QfHn   H;V PflHwV Hq j )/V PIH HՐ  H5M H= H6IHȅЃ  IHuL薃(t$`H2n L-cU H1 f-]U Hn A   A   )5U H ~ H59U H=rU HKU HE HEU Hj HAU H:U QfHn   HT PflH$U Hp j )T PIH H  H5b H= HCIHȅ  IHuL裂(L$`H/m L-T H1 f-T Hm A   A   )8T H ~ H5S H=T HS H` HS Hj HS HS QfHnҹ   HS PflHS Ho j )S PIH H  H5w H= HPIHȅ  IHuL谁HIF HBV ~=
 L-  HR A   ~ A   HiR H: =k H5lR HR HR H=R HJ)|$0fHnH*R H[R HQ flH9R H1 j HAR Q   PHCR HLR Hn j L-TR Q )=6R )Q PH IH  H5e H= H&~IHȅ  IHuL膀HE (l$0j HT H*Q A   ~ A   HP Hx H5P H=Q HQ HP HJHP HQ fHnHP H flHtP Q   PHP HP HP Hm j L-P IP )-P )KP PH IH	  H5Y H= H}IHȅ  IHuLrHD (|$0j HR HO A   ~ A   H;O H H5=O H=O HoO HXO HJH=O HH fHnHO H/ flHN Q   PHO HO H$O Hl j L-,O N )=O )N PH IH  H5U H= H{IHȅ~  IHuL^~(T$Hh H f-M ~ D-B A   A   )N HH5M H=N D-M HM HH HM Hj HM HM QfHnڹ   HxM PflHM Hk j )dM PIH H.  H5 H= H{IHȅ~  IHuLk}HĿ HL j L%  HL H>. D5 A   QA      HL HL Hw H5L PH=L HL Hj j L%L D5cL `L PH IHt  H5 H= H;zIHȅL}  IHuL|Ht HK j A   HK H. A   HK QH5K    H=K HK H PHK H)j j L%K D5qK nK PH IHȉ  H5` H= HyyIHȅ|  IHuL{H"  j HJ A   HJ HEK A   HJ HJ H- H5J HJ H H=J Q   PHJ HYi j }J zJ PH IH  H5 H=E
 HxIHȅ{  IHuL{Hv  H ~ (d$HI H- A   A   j H5I H=I HI HI QfHn   HI PflHI HI H~h j D-]I f-ZI )%I )PI PH IHB  H5F H=_	 HwIHȅ{  IHuL'zH O H) H"  ~ fHnHH H> H-  flHH H~H ~~ )T$ fHnA   A   j flH5#H H=lH HEH HJHG HG H HH H>2 Q   PHH HH HH HKg j H-"H G )H )G PH IH"  H5H
 H=) HvIHȅy  IHuLxHR H# H= H-%G HF (T$ A   A   HF HF ~W H5F j fHnH=F HF HJflHTF HMF H HgF Hp5 Q   PHjF HsF H|F H-f j F )jF )F PH IH!  H59	 H= HzuIHȅx  IHuLwHN H| Hm< H-E HGE (d$ A   A   HOE H8E ~H H5D j fHnH=;E HE HJflHD HD H HD H8 Q   PHD HD HD He j D )%D )|D PH IH   H5* H= HctIHȅw  IHuLv~[ H$ H ~e HC H; H- A    HC HC A   )\$ fHnH5nC HWC j flH=C Q   PHtC H}C Hd j H-%C )nC )'C PH IHA  H5= H= HnsIHȅv  IHuLuHg H ~ (L$ H|B H@ A   A   j H5@B H=yB HbB H[B QfHnҹ   H	B PflH5B H>B H?c j H-A )/B )A PH IHx  H5f H=' HrIHȅ(v  IHuLt($Hd_ H-A HE HG_ A   ~ A   )DA H H5@ H=3A HA H9 HA Hj HA H@ QfHn   H@ PflH@ HFb j )@ PIH H  H5 H=< HqIHȅNu  IHuLt(,$Hi^ H-? HP HL^ A   ~ A   )-? H H5? H=? H? HV H? Hj H? H? QfHn   H^? PflH? H[a j )R? PIH H΁  H5 H=Q HpIHȅtt  IHuLs(<$Hn] H-> HW HQ] A   ~ A   )=> H H5d> H=> Hv> Ht Hp> Hj Hl> He> QfHnʹ   H> PflHO> Hp` j )> PIH H  H5 H=f HoIHȅs  IHuL.r($Hs\ H-<= H5\ HV\ A   ~ A   )c= H H5= H=R= H+= H H%= Hj H!= H= QfHnڹ   H< PflH= H_ j )< PIH H$  H5 H={  HnIHȅr  IHuLCqH0 H ~ (d$H< HZ` D-5 A   j A   H5; H=< H; H; QfHn   H; PflH; H; H^ j D-t; fo; )%; )m; PH IHK  H5k H= HmIHȅq  IHuLTpH}1 H ~6 (t$H: H{b A   A   j H5: H=: H: H: QfHn   HO: PflH{: H: H] j D-,: f': )5l: )%: PH IHy~  H5 H= HmIHȅq  IHuLlo($HY H-Z9 Hd HY A   ~> A   )9 H H579 H=p9 HI9 H HC9 Hj H?9 H89 QfHnҹ   H8 PflH"9 H\ j )8 PIH H}  H5  H= H!lIHȅ1p  IHuLn($HX H-8 H8i HX A   ~[ A   )68 H H57 H=%8 H7 H H7 Hj H7 H7 QfHn   H7 PflH7 H[ j )7 PIH H|  H5 H= H6kIHȅWo  IHuLmHs Hd ~ Hm (l$D-2 j A   Qf-e A      PH56 H=6 H6 H6 H6 fHnH6 H[6 H6 HZ flj D-@6 f-=6 )-6 );6 PH IH{  H5 H= HBjIHȅtn  IHuLlH+_ Hv ~ Hq (|$j A   A   QH5Z5    H=5 Hg5 Hp5 Hi5 PfHnH5 HM5 flHR5 HZ j D-4 f-4 )=<5 )4 PH IH!{  H5 H= H\iIHȅm  IHuLkH%} H ~ Hu (T$D-C0 j A   QA      H54 H!4 H=:4 H#4 H4 PfHnH3 H 4 flH4 H&Y j D-3 f-3 )3 )3 PH IHJz  H5. H= HohIHȅl  IHuLj(d$PHT Hw D-2 HT f-2 A   A   )%3 H ~ H52 H=2 H2 H] H2 Hj H2 H2 QfHn   Ha2 PflH2 HX j )U2 PIH Hmy  H5C H= H|gIHȅk  IHuLi(4$H- Hzz A   HS HS A   H5y1 H-b1 H=1 ~ )51 H Hr1 Hs Hl1 Hj Hh1 Ha1 QfHn   H1 PflHK1 H,W j )1 PIH Hx  H5Y H=" HfIHȅ k  IHuLh($HR H-80 H HR A   ~ A   )_0 H H50 H=N0 H'0 H H!0 Hj H0 H0 QfHnҹ   H/ PflH 0 HAV j )/ PIH Hw  H5v H=7 HeIHȅ&j  IHuLg($HQ H-. H HQ A   ~ A   )/ H H5. H=/ H. H H. Hj H. H. QfHn   Hy. PflH. HVU j )m. PIH Hv  H5 H=L HdIHȅLi  IHuLg(,$HP H-- H+ HP A   ~. A   )-- H H5- H=- H- H H- Hj H- H- QfHn   H>- PflHj- HkT j )2- PIH Hv  H5 H=a HcIHȅrh  IHuL)f~q H  (|$#, HO fHnH* A   fl)=w, A   H5
, )s, H=\, ~ H+ HH, H H+ HH, H+ HUO H
H+ H+ HHb j H+ H+ fHnH Q   flfHnPHR+ )k+ ~ H+ fl)a+ j HS PIH Ht  H5 H= HobIHȅ)g  IHuLd~%/ H  (=ɢ A   fHnHgN ~ A   fl)=) H5* H=p* )d$p(d$ (t$p)%Z* )5c* HH	* Hv H* HH	* H) HM H
H* H) HH` j H) H) fHnH Q   flfHnPHX) )q) ~Q H) fl)g) j HQ PIH Hs  H5 H= HaIHȅe  IHuLuc(\$ (d$pA   A   (-h HM H5:( H=( ~ )( )%( )-' HH,( HA H&( HH,( H( HL H
H$( H( HHc j H( H' fHnH Q   flfHnPH{' )' ~$ j flH' )' HqP PH IHcr  H5o H=p H_IHȅd  IHuL8b(L$ (T$pA   A   (+ HK H5]& H=& ~ )& )& )& HHO& H HI& HHO& H@& HQK H
HG& H8& HH j H5& H& fHnH Q   flfHnPH% )% ~ j flH% )% H4O PH IH<q  H5: H=3 H^IHȅc  IHuL`~ H  L-e  HnJ fHnfInZ$ A   fl- A   )$ (Ş H5N$ H=$ )-$ )	$ H~& )$   H?$ H H9$ HH?$ H0$ HI H
H7$ H($ HH j H%$ H# fHnH Q   flfHnPH~# )# ~ H# fl)# j HM PIH Ho  H5 H= H+]IHȅ)b  IHuL_H  H^ ~- (\$@H" Hb - $ A   j A   H5w" H=" H" H" QfHn   H@" PflHl" Hu" HL j -" )g" ) " PH IHo  H5 H= HG\IHȅVa  IHuL^H\ H ~Q H (l$@j A   A   QH5?!    H=s! HL! HU! HN! PfHnH! H2! flH7! HL j -  )-)! )  PH IHLn  H58 H= Hi[IHȅ`  IHuL]~ H:G Hk -%  HG A   A   H5  $ H=5  ).  H ~C H H H Hj H H QfHn   H PflH HK j ) PIH Hmm  H5[ H= HtZIHȅ_  IHuL\HM Hփ  ~ (L$0H H  L%D  A   H H fInA   fHnH H*! H flfHnH^ 5g )  H5 ~! H= H Hy  HE HJflH H H[ H H )t$pH j H Q   PH H H ) )5 )t J fE @ j HI PIH Hk  H5 H= HXIHȅ*^  IHuLH[HA HJ  ~ (l$0HV H  (t$pA   H] H& A   H5 fHnH j H=W flHl H fHn) ~ Hr H  H flH HJHN H H Hq H Q   PH H H H H )- )5 )  f  j HH PIH Hj  H5 H= HoWIHȅ\  IHuLYHh  Hр  ~ (T$0H H  (\$pA   H H A   H5p fHnH j H= flH H fHn)@ ~H H Hu  Hs flH HJH HF Hz H HQ Q   PH+ H4 H= HF HO )` )i )  f  j HF PIH H1i  H5% H= HUIHȅZ[  IHuLVXH/  HX  ~H (t$0H H-  (|$pA   H Ht A   H5 fHnH j H= flH H fHn) ~ H Hq  H flH/ HJH H H H H Q   PH H H H H )5 )= )i ? f: 5 j HE PIH Hg  H5 H= H}TIHȅY  IHuLVH  H  ~ ~= HH H{  ~ A   HL H =. (- fHnH )$    flHT H A   ) H5y ~q H=
 H H HJ)= fHnH H~ flH HL Hu )$   H^ j He Q   Hh Hq Hz ) )- )  PHC j PIH HWf  H5/ H= HRIHȅvX  IHuLPUH9  H  ~r ($   H H4z  ($   A   H H (1 A   fHnH j H5 flH HG  fHnHK H= H] HJH H H̯ H Hf ) ~ Q   PflH H H H H HBB j V ) ) )1 )j PH IHd  H5 H= HQIHȅW  IHuLSH*  j H fD5 H H H-ă  A   Hw Hp A   H[ QH5[    H=o PH_ H`A j H-W fD5' " PH IHBd  H5 H=G HPIHȅWV  IHuLSHh  H j A   H H A   Hv Hw H H5i QH=    PHl H@ j H-d fD54 / PH IHc  H5C H= HOIHȅU  IHuLLR~ H  fIn~ HY H H  L5t  flHY H" ~%J )$   (+ A   A   )H fHn% H fl)$   H5 H= )w ~ HH Hq  H H HJ)% fHnH Hu flH HC H j H[ Q   H^ Hg Hp Hy ) ) L5  PH> j PIH Hb  H5 H= HRNIHȅT  IHuLPH[  Hw  ~ (l$0H H  (t$pA   H H A   H53 fHnH j H= flH H fHn) ~ H
 Hm  H6 flHK HJH
 H	 H H
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 j Hr= PIH H`  H5@ H=q HLIHȅR  IHuL9OHb  H;v  ~ (T$0Hg	 H   (\$pA   Hn	 H7	 A   H5 fHnH j H=h	 flH}	 H~ fHn) ~2 H H  H flH HJH_ H H& H H Q   PH H H H H ) ) ),  f  j H; PIH HK_  H5 H= H`KIHȅLQ  IHuLMH  Ht  ~2 (t$0H H7  (|$pA   H H A   H5 fHnH j H= flH$ H fHn)Q ~ H* Hj  H flH HJH HW H H) H Q   PH< HE HN HW H` )5q )=z )  f  j H: PIH H]  H5^ H= HIIHȅO  IHuLGLH0  H  ~ (\$0H (d$pH)s  A   H H L- A   fHnH j H5 flfHnH H  ) H= ~Y H2 HK HJflH H HX H H Q   PH H H H H ) )%( ) L-R P fK F j H9 PIH H\  H5 H= HnHIHȅ|N  IHuLJH  H ~` H  HZ ($   A   A   H_ H( ($   H5 fHnH j ( flfHnH Hp ) H=2 ~ H H HJflH= H H Hx H Q   PH H H H H )= ) )  ) L5   j H7 PIH H([  H5 H= HFIHȅM  IHuL[IH  H  ~ (l$0H (t$pH=p  A   H H A   H5\ fHnH j H= flfHnH H ), ~ Hm H HJflH H@ H H H Q   P)-} j )5 ) L-  f  H H H H H H"6 PH IHY  H5 H=! HEIHȅK  IHuLGHy  (T$0j H H Hf A   A   H H5| ~l H= HV H H H HJHf Hh fHnHC Ht flH Q   PH; HD HM H5 j  )> ) PH IHX  H5M H= HnDIHȅJ  IHuLF($$L-ӄ H A   H0 H0 A   H5 L- H== ~U )%. H H H H Hj H H QfHn   H PflH H4 j ) PIH HW  H5s H= H|CIHȅI  IHuLE(4$H1/ L- H+ H/ A   ~ A   )5 H H5 H= H H H Hj H H QfHn   HV PflH H33 j )J PIH HW  H5 H=) HBIHȅH  IHuLD($H6. L- HH& H. A   ~ A   ) H H5\ H= Hn H Hh Hj Hd H] QfHnҹ   H PflHG HH2 j ) PIH HAV  H5 H=> HAIHȅH  IHuLDH2 H ~ظ (\$ HT H0 A   A   j H5 H=Q H: H3 QfHn   H PflH H Hw1 j L- ) ) PH IHxU  H5 H=_ H@IHȅLG  IHuL'CHF H ~ H4 (l$ j A   A   QH5    H= H H H PfHnH H flH H0 j L- )- ) PH IHT  H5G H= H?IHȅ~F  IHuLHBH!5 HC ~* HA (|$ j A   A   QH5    H= H H H PfHnHb H flH H/ j L-@ )= )B PH IHS  H5p H= H	?IHȅE  IHuLiAH2S Hj ~S H4N (T$ j A   A   QH5a    H= Hn Hw Hp PfHnH# HT flHY H. j L- )J ) PH IHS  H5 H= H*>IHȅD  IHuL@Hs4 H ~| HT (d$ j A   A   QH5"    H=V H/ H8 H1 PfHnH H flH H- j L- )% ) PH IHTR  H5 H= HK=IHȅD  IHuL?H$R H ~ H^\ (t$ j A   A   QH5    H= H H H PfHnH H flH H- j L- )5 ) PH IHQ  H5 H= Hl<IHȅFC  IHuL>HZ  H ~γ (L$H Hc D5L A   j fD-| A   H5 H H H= QfHnҹ   Hh PflH H H., j D5E fD-A )v )? PH IHP  H55 H= Hv;IHȅaB  IHuL=~֮ fInj Hd  fHnA   H.  Ho flH\ H A   )x H5 ~ H=b HK H$ flfHnH H )I Hf ~Z fHnH H flH Hm ) ~. Q   PflH H H H H* j D )e PH IHgO  H5 H= H:IHȅA  IHuL|<~ H}a  H% A   fHnHt A   H57 ` H= ) ~j fl) (hz ) H~6 H H H H H H	H H fHnH j flH H=r fHn) H ~Ұ Q   PflH H Hj) j )q PIH H)N  H5 H=` H8IHȅ?  IHuL(;H  H ~R (\$ H Hx H-y A   j A   H5s H= H H QfHn   H< PflHh Hq H( j H- )b ) PH IHYM  H5 H=z H7IHȅ ?  IHuLB:H[  H_ ~t (l$Hp H| A   A   j H54 H=m HV HO QfHn   H PflH) H2 H' j D5 fD- )- ) PH IHL  H5J H= H6IHȅ*>  IHuL[9H  H ~ (|$H) H:~ A   A   j H5 H=& H H QfHnʹ   H PflH H H& j D5 fD- )= ) PH IHK  H5k H= H6IHȅT=  IHuLt8H H ~ (T$H H A   A   j H5 H= H H QfHnڹ   H PflH H H% j D5d fD-` ) )V PH IHJ  H5 H= H-5IHȅ~<  IHuL7Hh  (d$0j H
 H H
 A   A   H H5` ~ H= H: Hy H| He HJHJ He fHnH' H flH Q   PH H( H1 H$ j  )%" ) PH IHI  H5y H= H4IHȅt;  IHuLr6H H ~ī Hu (t$@D% j A   QA      H5 H H= H H PfHnH H flH H# j D% )5 ) PH IHI  H5 H= H,3IHȅ:  IHuL5H HК ~ H (L$@j A   A   QH5    H= H H H PfHnHf H flH H" j D%D ) )F PH IHHH  H5 H= HM2IHȅ9  IHuL4Hֽ H ~ Hp (\$ j A   A   QH5u    H= Hr H{ Ht PfHnH? HX flH] H" j H- )N ) PH IHG  H5 H= Hn1IHȅ9  IHuL3H  H ~-8 L-Qj  Hj L%s A   A   H` HI -" ~ HJ)l$pfHn-rq j flH H5 H H H= H H Q   PH H H H  j L- L%t -v )- )x PH IHfF  H5 H= H?0IHȅ7  IHuL2H  (|$pj A   H H A   H5 H H ~ H= HJHx H fHnHU H. flH Q   PHM HV H_ H j L-g L% - )=C ) PH IHpE  H5 H= H3/IHȅ6  IHuL1H  (T$pj A   H H1 A   H5 H- H ~ H=' HJH H fHnH Hʸ flH Q   PH H H H j L- L%d -f ) )` PH IHzD  H5 H= H'.IHȅ5  IHuL0H( Hm ~ (d$ H Hn H-gn A   j A   H5r H= H H QfHn   H; PflHg Hp H j H- )%a ) PH IHC  H5 H=پ HA-IHȅ5  IHuL/H: HW ~3 (t$ Ho HX A   A   j H53 H=l HU HN QfHn   H PflH( H1 H j H- )5" ) PH IHB  H5A H= Hb,IHȅL4  IHuL.(L$`L-l H A   fD%l H A   H5 L- H H=( ~  ) fD% H H HƓ H Hj H H QfHnҹ   H PflH H j )x PIH HA  H5 H= H_+IHȅZ3  IHuL-(\$`H L- H fD% H A   A   ) H ~0 H5 H= H Hْ H Hj H H QfHn   H0 PflHl H j )$ PIH HA  H5 H= Hk*IHȅw2  IHuL,H$# H ~u ($   Hv Hg A   A   j H5: H=s H\ HU QfHn   H PflH/ H8 H9 j L- fD% )-! ) PH IHB@  H5 H= H)IHȅ1  IHuL+H  H ~ ($   H, H A   A   j H5 H=) H H QfHnʹ   H PflH H HO j L- fD% )= ) PH IHn?  H5 H=/ H(IHȅ0  IHuL*H H ~ ($   H H A   A   j H5 H= H H QfHnڹ   Ho PflH H He j L-L fD%L ) )F PH IH>  H54 H=E H'IHȅ/  IHuL*($$H H-{ H< H A   ~ A   )% H H5X H= Hj H8 Hd Hj H` HY QfHn   H PflHC Hd j ) PIH H=  H5 H=Z H&IHȅ/  IHuL")H HΆ ~ (t$ HP H A   A   j H5 H=M H6 H/ QfHn   H PflH	 H H j H- )5 ) PH IH<  H5 H={ H%IHȅD.  IHuLC(H, H ~ (L$ H Hj A   A   j H5 H= H H QfHnҹ   H PflH H H j H-{ ) )} PH IH3<  H5 H= H%IHȅv-  IHuLd'($Ha H- H HD A   ~& A   ) H H5 H= H H H Hj H H QfHn   H> PflHz H j )2 PIH H^;  H5 H= H$IHȅ,  IHuLy&H H  ~[ H\ (l$@- j A   QA      H5F H_ H=x Ha HZ PfHnH H> flHC H j - )-5 ) PH IH:  H5< H=ʹ H5#IHȅ+  IHuL%H~  H" ~ (|$@HC HD A   A   j H5 H=@ H) H" QfHnʹ   H PflH H H j - )= ) PH IH9  H5f H= HW"IHȅ*  IHuL$H HP ~ (T$ H H H-b A   j A   H5 H= H H QfHnڹ   H PflH H H! j H-h ) )j PH IH8  H5 H=	 Hq!IHȅ'*  IHuL#H H] ~˙ (d$ H H A   A   j H5 H= H H QfHn   HL PflHx H HB j H-) )%r )+ PH IH/8  H5Ѽ H=* H IHȅY)  IHuL"H[ H ~ H (t$D%y j A   Qf-` A      PH56 H=o HH HQ HJ fHnH6 H H8 HY flj D% f- )5 ) PH IHQ7  H5E H=6 HIHȅv(  IHuL!H' H ~ H! (L$j A   A   QH5    H=* H H H PfHnH H flH Ho j D% f- ) ) PH IH6  H5 H=P HIHȅ'  IHuL!H) H ~* H3 (\$j A   A   QH5    H= H H H PfHnH H flH H j D%h f-e ) )[ PH IH5  H5 H=j HIHȅ&  IHuL2 HK  (l$0j L5=Q  H0 H A   A   H H ~ H5V HJHk H fHnHH H  L-Z flQH    H=b PH2 H; HD Hu j L5L L-  )-' ) PH IH4  H5 H=O HIHȅ%  IHuL(|$PH H# D% H f- A   A   )=, H ~	 H5 H= H Hs H Hj H H QfHnʹ   H PflH Hf j )} PIH H3  H5 H=\ HIHȅ$  IHuL$H-_ Hۃ ~N H& (T$j A   A   QH5    H= H H H PfHnH^ H flH H j D%< f-9 )~ )7 PH IH2  H5ŷ H=v HIHȅ$  IHuL>(d$PH H) D%d H f-Z A   A   )% H ~@ H5A H=z HS H HM Hj HI HB QfHn   H PflH, H
 j ) PIH H"2  H5 H= HIHȅ)#  IHuLKHT  H ~ (t$H9 H. A   A   j H5 H=6 H H QfHn   Hƿ PflH H H	 j D% f- )5 ) PH IHR1  H5D H= HIHȅT"  IHuLeH  H4 ~ (L$H HT? A   A   j H5 H= Hپ HҾ QfHnҹ   H PflH H H j D%] f-Z ) )X PH IH0  H5 H= HIHȅ!  IHuLH HW ~ɐ HC (\$@j A   A   QH5    H= H H H PfHnHI Hj flHo H j $ )] )& PH IH/  H5 H=ը H=IHȅ   IHuLHF H_:  ~5 HD fHnH8  ~ ~=ԏ flH) L% A   H% H> A   H5 )t$ fHn-e] H H flH= H Hڻ fHnH )<$(|$ fl($j fHn) H[ ~C Q   flPH H H H )= ) )G L% - j Ha PIH HW.  H5 H=` HIHȅJ  IHuL(H~ (d$ (,$HiO HZ j A   A   QH5 ~t    H H=I H H PH H H fHnH j flfHnHҹ H ) ~ HŹ Hι flHӹ HT L%U -W )% )-ɹ )b PH IH>-  H5 H=1 HIHȅ,  IHuLH  (L$0j A   H~ H A   H5Z H H| ~L H= HJHR H| fHnH/ HZ flH Q   PH' H0 H9 HJ j L5A L-· ÷ ) )ŷ PH IHG,  H5ñ H=$ HIHȅ0  IHuLH  (\$0j A   HѤ H
 A   H5 H H ~G H=  HJHŶ H{ fHnH Hg flH` Q   PH H H H= j L5 L-- . ) )( PH IHP+  H5ΰ H= HIHȅ4  IHuLH8 HA3  ~y Hjl fHnHz ~V (t$@H2 L%s A   A   H( Ha flH5 H H=8 H! H fHnH )$flj ) ~ Q   PH´ H˴ HԴ Hݴ H j ) fHnHY flL%N )5 )` PH IH*  H5 H=Ϣ H7IHȅ  IHuL(\$PHc Ht A   HG D-  A   H5s ) H ~ H= f-KQ D-< He H>y H_ Hj H[ HT QfHn   H PflH> H  j f- ) PH IH3)  H5 H=Ρ H6IHȅ  IHuLH  Hp ~H (l$HD H-~ A   A   j H5 H=A H* H# QfHn   Hѱ PflH H H  j D- f- )- ) PH IHc(  H5 H= HPIHȅ8  IHuL(|$PHl H D-ְ HO f-̰ A   A   )= H ~: H5 H= HŰ Hdw H Hj H H QfHnʹ   Hb PflH H j )V PIH H'  H5$ H= H]IHȅV  IHuLH Hv ~ Hh (T$j A   A   QH5    H= H H H PfHnHG Hh flHm H. j D-% f-" )W )  PH IH&  H5~ H= HwIHȅ  IHuL(d$@(,$L% A   Hj A   ~ H5 )%n H=g )-p HH Hu H HH H H H
H H HH j H Hխ fHnH Q   flPfHnHm )~ ~ Hǭ H j fl)k PIH H%  H5 H=ڝ HBIHȅ]  IHuLH?  (L$0j H-  H֬ H A   A   H H5E ~M H= H Hh Hq HZ HJH? Hv fHnH H՞ flHҫ Q   PH H H& H j  ) ) PH IH$  H5 H= H'IHȅS  IHuLH A   H$  Hc H$  H| H$  H H$  H6 H$  H H$  H H$  H H$  H H$  H H$  H̨ H$   HŨ H$  HΨ H$  HǨ H$  H H$   H H$(  Hڝ H H$0  H̝ H$  H} H$8  H H$  Hg H$@  H H$  HQ H$H  Hҝ H$  HS H$P  H H$  H$X  H H$`  H H$h  H H$p  HP H$x  Hi H$  H H$  H{ H$  Ht H$  Hm H$  Hn H$  Hg H$  H` H$  HY H$  HR H$  HK H$  HD H$   H= H$  HN H$  HG H$  H` H$   HY H$(  HR H$0  HK H$8  HD H$@  H H$H  H~ H$P  Hס H$X  Hء H$`  Hѡ H$h  Hʡ H$p  Hۡ H$x  Hԡ H$  H͡ H$  Hơ H$  H H$  H H$  H H$  H H$  H H$  H H$  HM H$  HF H$  H? H$  H8 H$  H1 H$  H* H$  H# H$  HD H$   H= H$  H6 H$  Ho H$  Hh H$   Ha H$(  HZ H$0  HS H$8  HL H$@  HE H$H  HF H$P  H_ H$X  H( H$`  HQ H$h  HJ H$p  HK H$x  H4 H$  H H$  H H$  Ho H$  H H$  Hq H$  Hj H$  Hc H$  H\ H$  H% H$  H H$  H H$  H H$  HI H$  HB H$  H H$  H H$   H} H$  H> H$  H H$  H H$   Hi H$(     H$0  H H$8  H H$@  H H$H  H@ H$P  HA H$X  HJ H$`  H+ H$h  H$ H$p  H H$x  H H$  H H$  H H$  H H$  H
 H$  H H$  H H$  H H$  H H$  H H$  H H$  HQ H$  HR H$  H; H$  H H$  H H$  H H$   H H$  H H$  H H$  H H$   H H$(  H| H$0  H] L H H$8  H$  H= H$H IH4L%c 3     m( HC?LHHJ?.HH9?H5 HHHtFLHIHt#HIHD$tLt$
L'HuHLHM uHH>  1L%y    >HL%y    >L%b    >L%b w  >L%b   >L%ob   >L%^b   q>L%Mb   `>L%<b 9  O>L%+b `  >>L%b   ->L%	b   >L%a   >L%a   =L%a &  =L%a :  =L%a a  =L%a   =L%a   =L%a   =L%pa   =L%_a   r=L%Na .  a=L%=a U  P=L%,a z  ?=L%a   .=L%
a   =L%`   =L%`   <L%`   <L%`   <L%` ?  <L%` f  <L%`   <L%`   <L%q`   <L%``   s<L%O` 	  b<L%>` 5	  Q<L%-` \	  @<L%` 	  /<L%` 	  <L%_ 	  <L%_ 	  ;L%_ 
  ;L%_ :
  ;L%_ ]
  ;L%_ 
  ;L%_ 
  ;L%_ 
  ;L%r_ 
  ;L%a_   t;L%P_ ;  c;L%?_ ^  R;L%._   A;L%_   0;L%_   ;L%^   ;L%^   :L%^ <  :L%^ a  :L%^ o  :L%^   :L%^   :L%^   :L%s^   :L%b^ +  u:L%Q^ I  d:L%@^ _  S:L%/^ x  B:L%^   1:L%^    :L%]   :L%] >  9L%]   9L%]   9L%]   9L%] f  9L%]   9L%] D  9L%t]   9L%c]   v9L%R] '  e9L%A] b  T9L%0]   C9L%]   29L%] D  !9L%\   9L%\   8L%\   8L%\ o  8L%\   8L%\ 	  8L%\ W  8L%\   8L%u\ h  8L%d\   w8L%S\ v  f8L%B\   U8L%1\ ^  D8L% \   38L%\   "8L%[ b  8L%[    8L%[ "  7L%[ y  7L%[   7L%[ 8  7L%[ p  7L%[   7L%v[   7L%e[ h  x7L%T[   g7L%C[ :  V7L%2[   E7L%![   47L%[ E  #7L%Z   7L%Z $  7L%Z   6L%Z   6L%Z V  6L%Z   6L%Z j   6L%Z    6L%wZ !!  6L%fZ z!  y6L%UZ !  h6L%DZ X"  W6L%3Z "  F6L%"Z #  56L%Z V#  $6L% Z #  6L%Y #  6L%Y +$  5L%Y e$  5L%Y $  5L%Y %  5L%Y %  5L%Y J&  5L%xY &  5L%gY L'  z5L%VY '  i5L%EY (  X5L%4Y s(  G5L%#Y (  65L%Y )  %5L%Y \)  5L%X )  5L%X )  4L%X 4*  4L%X *  4L%X *  4L%X +  4L%X V+  4L%yX +  4L%hX +  {4L%WX ,  j4L%FX `,  Y4L%5X ,  H4L%$X ,  74L%X <-  &4L%X -  4L%W %.  4L%W q.  3L%W .  3L%W ./  3L%W /  3L%W O0  3L%W 0  3L%zW 1  3L%iW 1  |3L%XW 1  k3L%GW H2  Z3L%6W 2  I3L%%W ?3  83L%W 3  '3HL%Qm    3L%V       L%V w     L%V      L%V      L%V      uL%V      _L%kV 9     IL%UV `     3L%?V      L%)V      L%V      L%U      L%U &     L%U :     L%U a     L%U      L%U      mL%yU      WL%cU      AL%MU      +L%7U .     L%!U U     L%U z     L%T      L%T      L%T      L%T      L%T      {L%T      eL%qT ?     OL%[T f     9L%ET      #L%/T      L%T      L%T      L%S 	     L%S 5	     L%S \	     L%S 	     L%S 	     sL%S 	     ]L%iS 	     GL%SS 
     1L%=S :
     L%'S ]
     L%S 
     L%R 
     L%R 
     L%R 
     L%R      L%R ;     L%R ^     kL%wR      UL%aR      ?L%KR      )L%5R      L%R      L%	R <     L%Q a     L%Q o     L%Q      L%Q      L%Q      yL%Q      cL%oQ +     ML%YQ I     7L%CQ _     !L%-Q x     L%Q      L%Q      L%P      L%P >     L%P      L%P      L%P      qL%}P f     [L%gP      EL%QP D     /L%;P      L%%P      L%P '     L%O b     L%O      L%O      L%O D     L%O      L%O      iL%uO      SL%_O o     =L%IO      'L%3O 	     L%O W     L%O      L%N h     L%N      L%N v     L%N      L%N ^     wL%N      aL%mN      KL%WN b     5L%AN      L%+N "     	L%N y     L%M      L%M 8     L%M p     L%M      L%M      L%M h     oL%{M      YL%eM :     CL%OM      -L%9M      L%#M E     L%M      L%L $     L%L      L%L      L%L V     L%L      }L%L j      gL%sL       QL%]L !!     ;L%GL z!     %L%1L !     L%L X"     L%L "     L%K #     L%K V#     L%K #     L%K #     L%K +$     uL%K e$     _L%kK $     IL%UK %     3L%?K %     L%)K J&     L%K &     L%J L'     L%J '     L%J (     L%J s(     L%J (     L%J )     mL%yJ \)     WL%cJ )     AL%MJ )     +L%7J 4*     L%!J *     L%J *     L%I +     L%I V+     L%I +     L%I +     L%I ,     {L%I `,     eL%qI ,     OL%[I ,     9L%EI <-     #L%/I -     L%I %.     L%I q.     L%H .     L%H ./     L%H /     L%H O0     L%H 0     sL%H 1     ]L%iH 1     GL%SH 1     1L%=H H2     L%'H 2     L%H ?3     L%G 3     HH=x HL  HuHII   [#IH\$ uLHw Hw H9Hu"L=w MtI7H= (  IH=~ H]w H5^w zIM   H5~ H=ow LIHȅ   IHuL7IH   Hx H5x HxHx H5x LvyL%F    "H5J H=v LKIHȅxIHLL%vF 3  "L%eF 3     CL%OF       -IF"H(
  []A\A]A^A_H=xp {& ( LHLHLHLHLHqLHaf() ) f() ) f() ) f() ) f() ) f() ) f() ) f() ) f() ) f() ) f() ) f() ) f() ) f() ) f() ) f() )  f() ) f(( ) f(( ) f(( ) f(( ) f(( ) f(( ) f(( ) f(( ) f(( ) f(( ) f(( ) f(( ) f(( ) f(( ) f(( ) f(( )  f(( ) H=r Hr H9tHN_ Ht	        H=r H5r H)HH?HHHtH-_ HtfD      =er  u+UH=*^  HtH=.T d=r ]     w    ff/w>f(fT  f/rĦ YY  Y\Y  ff.     @ HX fHHH1HBff.     ff.     ff.     ff.     ff.         f(f(f(HYf(\H9u\ Yff.      % Hݥ fHYHH1HXff.         f(f(f(HY\H9u\YXf(ff(Hq fHX\n  HH1XH&ff.     ff.          f(f(f(HY\H9u\Y fD  HGPH     HG`H     H[ H @ HGhHtH fH[ H @ H   HtH     HH|$ZHtH|$H   H HAWAVAUIATUS1HHAH.L!L?HD$LwH~-fAAOHAM} foflAMuH9uH|$H[]A\A]A^A_]) ff.     fAWAVAUE1ATIUSHHAHH)L?HD$LwH~1AZf(fIM<$foflfZAMt$L9uH|$H[]A\A]A^A_(      AWIAVE1AUATUSHHHQHL)HL$ HLgHoHT$HT$0H$HT$HL$H~ED  KIHt$H|$Af(D$ IA$f(D$0MgE IoL94$uH|$6( HH[]A\A]A^A_    AWIAVE1AUATUSHHHQHL)HL$ HLgHoHT$HT$0H$HT$HL$H~GD  ZHt$f(IH|$fAfZD$ IA$fZD$0MgE IoL94$uH|$' HH[]A\A]A^A_D  AWE1AVAUATUSHH8HQHL1HL$ H/LoLgHT$HT$(H$HT$HL$H~DD  E Ht$IH|$AD$ H+AE D$(LkA$LcL9<$uH|$& H8[]A\A]A^A_     AWE1AVAUATUSHH8HQHL1HL$ H/LoLgHT$HT$(H$HT$HL$H~PD  fHt$H|$IZE AfH+ZD$ AE fLkZD$(A$LcL9<$uH|$& H8[]A\A]A^A_ff.     AWAVAUATU1SHH(HHL7LoLLgHT$HQHD$HT$H~3AIu HI>HD$L3LkA$L{LcH9l$uH|$H([]A\A]A^A_u% D  AWAVE1AUATUSHH(HHLgH7HoLoHT$HQL HD$HT$H~_ff.     A$H4$IA] AeU HD$H4$LcfoH3HkflLkA/L{ L9t$uH|$H([]A\A]A^A_$ @ AWAVE1AUATUSHH(HHLgH7HoLoHT$HQL HD$HT$H~pff.     fffH4$AZe AZ$Zf(ZU HD$fIH4$LcfoH3HkflLkfZAL{ L9t$uH|$H([]A\A]A^A_#  AWAVAUATU1SHH(HHLwH7LoLHT$HQLg HD$HT$H~Rff.     AH>H4$HAAM HD$H4$LsA$H3LkL{Lc H9l$uH|$H([]A\A]A^A_2# fAWAVE1AUATUSHH(HHHqL'HoLoHD$HT$LHt$H~Sff.     @ A$M IAU A]HD$L#HkfoLkflA'L{L9t$uH|$H([]A\A]A^A_" @ AWAVE1AUIATUSH(HHHqH/H_LgHD$HT$LHt$H~_ff.     @ ffAZ$HD$ZZE f(fIIm I]foMeflfZAM}L9t$uH|$H([]A\A]A^A_!      AWAVAUATU1SHH(HHHqL7LoLHD$HT$LgHt$H~5AE I>HAHD$L3LkA$L{LcH9l$uH|$H([]A\A]A^A_3!  AWAVE1AUATUSHHHHQL!H/LoLH$HT$H~>f     E AM IAUAH+LkfoflAL{L94$uH|$H[]A\A]A^A_   AWAVE1AUIATUSHHHQH)HLgLH$HT$H~Ff     fAZ$f(fZII] foMeflfZAM}L94$uH|$H[]A\A]A^A_  ff.     AWIAVAUATUS1HHAL.L1L'HD$HoM~ fA$HAM'E IoI9uH|$H[]A\A]A^A_ f.     AWIAVAUATUSHH(HHqH9IIhMxHt$MpMh H   H|$E1HD$LLIMHIfAE AH$AMu }A'AoA^HD$H$L+foLsL{flHkHA$Lc H9L$uH|$H([]A\A]A^A_ fAWIAVAUATUSHH(HHqH9IIhMxHt$MpMh H   H|$E1HD$LLIMHIfZ} AZ/AZAZM f(f(H$ff(f(HD$fffH$L+foLsL{flHkHfZA$Lc H9L$uH|$H([]A\A]A^A_ f     AWAVE1AUATUSHH(HHLgH7HoLoHT$HQL HD$HT$H~fff.     fffH4$fZAZ] ZU AZ$HD$IH4$LcZH3AHkLkL{ L9t$uH|$H([]A\A]A^A_ ff.     fAWAVE1AUIATUSH(HHHqH/H_LgHD$HT$LHt$H~]ff.     @ E MIA$$Al$[HD$Im I]foMeflA7M}L9t$uH|$H([]A\A]A^A_: f.     AWAVE1AUIATUSH(HHHqH/H_LgHD$HT$LHt$H~eff.     @ AZ,$ZZM f(f(f(fHD$ffIIm I]foMeflfZAM}L9t$uH|$H([]A\A]A^A_r fAWAVE1AUIATUSHHHQH)HLgLH$HT$H~Cf     KIA$A\$I] MefoflA'M}L94$uH|$H[]A\A]A^A_ ff.      AWAVE1AUIATUSHHHQH)HLgLH$HT$H~If     AZ$Zf(f(ffII] MefoflfZAM}L94$uH|$H[]A\A]A^A_8      AWAVAUATU1SHH(HHHqL7LoLHD$HT$LgHt$H~5I} AHAHD$L3LkA$L{LcH9l$uH|$H([]A\A]A^A_  AWAVE1AUATUSHH(HHHqL'HoLoHD$HT$LHt$H~Vff.     @ fffIAZ$AZU ZM HD$L#HkZLkAL{L9t$uH|$H([]A\A]A^A_ AWAVAUATU1SHHHHH1HIHD$8LLwLgHT$LoL Ht$HL$(HD$ H~UfLL$I<$HAAHt$ HD$LL$LsAE D$8LLcLkAL{ 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 tf.`f(Vf(|$T$d$wT$-j: f(d$|$Yf(Yf(Yf(Xff.wOQf(f(L$|$d$;wL$f-9 |$d$f(Rf(L$|$\$v\$|$fL$-9 f(f(ff.      SHHG      HWH       t"HtpHu"GWHH	HH u4H[fD  s{HH tHu{HuPf.     H9 H5 H8w.     GH[    H	 H5: H8w|H@`Ht`H   HtTHHtJHJ H9Cu+@ HH+:H߉D$uD$%HQHHuzHuH H5A H87whfAWAVAUATIUHSHHhLG0M      tHwHhHL[]A\A]A^A_HVL   opIH   1LY|HHtiHHLcIm HtAHhH[]A\A]A^A_    HVHvHu[HhH1[]A\A]A^A_AD  LptfD  Im :  H HSPH5 H81t1D  LMMtI<LD$HHT$LL$3tIH.  HT$LL$LD$HtmHBH  ID$ I9  H1HHff.     ff.     D  AoDAHH9uHHt	ILILLD$HT$LL$oqLL$HT$HLD$H  H|$PE1HD$XL|$0H|$H|$HM$A   H\$8ILIHD$H    H|$HT$LD$ LL$(+HD$PHT$XH HHHL#   IDIHHT$Ht$LHArttHD$PHT$XHT$LD$ LLL$(L|$0H\$8M   LL$HLLt$ALL$HL$HH)tK1MM%D  HI9tI<H/u8rfD  L(ojLrHLL$	rLL$1ff.     D  ILIHH9uS$p1L1nH H5 LL$1Lt$H8|sLL$HL$&ff.     fHH;5] tHtHF    tAH 1H   H   HtH(t1HfD  H(qfD  H H5 H8r UHSHHtbH;5 HufH    H5 H8{nH   HH   HtH/t1H[]D  pf     Hq     HF    uH H5m H8=rfD  UHSHHtbH;5# HufHg    H5 H8mH   HH   HtH/t1H[]D  of     H     HF   uH$ H5U H8qfD  HHt?HF   t2HGPHHwPHtH(t1H@ H`ofD  H H5z H8"qH     HHt?HF   t2HGHHHwHHtH(t1H@ HnfD  HI H5: H8pH     ff.z   f(~T -<2 Yf(fTf/   H%"2 f/wd\ L$^Xf(fT fW)kL$~ $fTf(	kX$L$H^vf($u$H^uff.     @ ff.z   f(Hh1 Yf/v&f($u$H^pfD  x L$^Xf(fT. fWEjL$$f(fT% f(%jX$L$H^=pff.     fATUHSHHH H9F1  HvH  HGH;    H; tzHXpHtAH{ t:HhIH  HHSI,$u[LHD$lHD$GfHXhHtwHCHtnH  HH[]A\     HEHH9s4HDH H[]A\fHG1H9s%HEHH H[]A\Hff.     fHXgHH,  HHoH+uHHD$kHD$    HiIHt&HpI,$H   f.     HuZpH|   HEH;Q    H;< HHHEH4 H   HcsHEH; h  H}  HEH0f     H HH2rt*HCHXkH H5 HH81jf1~f     LHD$jHt$	f     Hn@ HHHt$HHt$HxHHCHu<sHcHZ Ht$H8mje@kHCHt$Ht0Hu?SCHH	HGH; HHGsCHH	H7HnH'H; HQHIHEHcff.     ff.   %, f(fT" f.   f.   HhHe ~C -3 fHnHP H|$flf(\)\$0fHn\~ H  flHD$P)\$@f(f(f(v D$D$    
w#H< HcH      H 	   H= 1F ^ Hhf     Hy 	   H= 1 @ D$H 	   H=c     D$D  D$     D$H 뾐H- 	   H= 1覯 [H?    HH= HL01} 2     AVfI~SH$T$n   H5 H H87epj$f.zf(fT L$f.* v! H[A^f     ,HfIn[A^HcA      fof(HHXL$8f(flD$ )<$XT$0f(L$( D$D$ X  \$T$0^f(\$ \$~% =i) f\$$^l$8L$(fX-H) D$ fYfW f(f(f(ff)t$谜 ff(fff(L$HHfYfYf(fXf\f(fD  HGPH     AVfI~SH$T$l   H5  H H8gch$f.zf(fTI L$f.( vQ H[A^f     ,HfIn[A^Hc8:      AVfI~SH$T$Tl   H5` Hg H8b h$f.zf(fT L$f.;( v H[A^f     ,HfIn[A^Hc;      f(fH(XL$f(\$J \$fW= T$_ D$f(  YD$H(D  f(Ht^|d%, ' XHf1ff.     f     f(f(HY\f(H9uYfD  f & HH)Hf(D  Htr|x% & x& H1fYX ff.     ff.     fD  f(f(HY\f(H9uYfD  f & HH)Hf(zfH% f(f( fW% YXl$\& Xf(Y% I2 YD$Hff.      Xf(f(H fW%P % \X\% l$Y>% Xf(1 YD$Hff.      LVM   1ff.     @ HI9tH9|u   f.     E1ff.     fJTHB   t~   @tuH9tHX  Ht,LAM~[1    HI9tGH;TufD  HD  H   H9pHuH; ^ff.      IM9c1Sf(ffH~Xf(H T$d$F d$\$fHnfW%̞  f(ff(),$ ff(fffY$H fY[f(f\fXff(f    f.   f(fH      H   Hf(HW1-_ fW5' ff(f(\    fH*HXf(XX^Yf(^YXXH9fd$H*XzE d$HY               \X  HH   " Yf.ztH   Htej Hf%ff.     ff.     ff.     f(ff(H*YHYf(\HuY\fI" T$H*Y! _T$HYf.     H    H= 1v  Hf      fD     H?LOIЃtHIALf     HtIH>IAHL    HH IH H5 H81]1H    H?IHHWtHGH8LJHHHA HtHHHfD  HH- HHl H5w H81z]1H HH- f(XL$8\D$(\|$f(f(\\$f(|$0Xf(T$ B L$T$ - |$0D$Xd$(f(\\$XY f(d$fW5 Xf(f(`, d$T$t$8- Yf(f(XXT$\#B T$HH^f(ff(f(HYf(X=\ XYf(fD(\X\\f(D\ f(YYfA(Yf(XDYfWЙ \f(AXn fHf(f(YY\Xf(f     HG         @   HFH      |      @tsH9t.HX  Ht2HJH~I1D  HH9t7H;tu   f.     H   H9tHu1H;5 f1D  b    t@ ff(f(HYXX-ܘ Y\f(X\\ \f(YYf(YYf(fW5d \f(f(X Hf.     f(ff(H@ Yf(YYY\-8 X\f(\f(Yf(YYYf(fW5ԗ \f(f(Xo fHf(fffYfXf(fXf\f(ff.     H   LOH?t%IHumHMu4IA1H     Ht{H   H>LBf     H IHl H5M H81Y1H    Hy tH IH H5Դ H81XD  Ha IH H5 H81X@ Hy [ff.     f(XHX= L$8T$@Xf(\$$$l$ \= $$fE\$f(=R T$@f(f(XXAYf)t$t$8AY\\Xt$Hf(\L$0l$f(f(\,$l$ Xf(l$@f(T$8Y= fE T$8f(fA(\d$0t$Hfl$@fW-_ )|$ = fD(EYf(\D$Yf(Y$AYXf(XXA\Xf(趍 ff(fffYD$ fYf(f\fXff^L$HXf(f     ff(f(HD Yf(ǔ Yf(AYXAYl$\f(X\\ f(AYf(YYf(X5 AYfW=1 \f(Xf(̌ l$fHf(fYYfYff(fXf\ff(fff.     ff(f(HYXXYf(ԓ f(X\f(X l$\\\f(YYf(YYf(X5 fW=J f(\ Xf(݋ l$fHf(fYYfYff(fXf\ff(fff.     fH8f(fD(HHO  !  fD(5 $ EX\XDXXDYH   D^HO1fE(DXfffA(H*HXfD(XDXXAYfA(XAXf(fD(XDXYAYAYAYYAYXf(AXXXXYY^DXfD(H9_fD$H*Xf(s9 D$H8AY ȑ H8 AXY H8fD  ff(L$ H*D$T$(Xf(d$f(l$8 d l$DD$ T$($|$f(d$AX\Y f(fW% XXf(" Y$H8@ AUIIHATI?USHHH HM!  ItCH9       HG8HH  HHH1[L]A\A]D  H9  L L9  LX  M  IkH~1fL9tHH9|ILH9uHKAcM)La1 uHkH= (WuDLHAHSRH   UWHu 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H+  H=I H  D51 D  HcHD;d   2  1    ~qS9~_)HcHDA9}߉ Hm HH[]A\A]A^A_$    H H$ A9A9~}LcIIE;g|  r A9tmD9}4DIc)HPHHHHHHtHHH)AEgI/D5 HE 1D;gË	 A9   Dp@IcHHHLcD5 D5 IH IS@ H<$HtH/tOH|$HtH/tFMI/L#L#H###볿   #HH H3 H$ D`H(HE D HcHL<II?I/HE H/&#D;gt֋ t"I1A   R   \1D  AUIATIUHSH(HD$    o$H   HD$    HHý HD$H   HEH   M  I  H֜ HH8ATH L 1A   H H5) "XZH|$HtH/u%"H+[  H<    H=X H(1[H]A\A] IqIM HHL$HAH5 HHH   H$  Ѕ   H H HH|$HtH/u!H+   H(H[]A\A] IU HHT$HU      HT$HMHH~ jKt QHPLD$( H H|$HH/M&H` HH8j f.     H H(H[]A\A]f.     H Hԕ    H= 1yHL$Ht$MHL} H: DD  f.H^     Etff.E  AVfS   Hx-^ ^ $\fT$f(\f(l$(YYf(d$0Y\f(XL$@D$H#fD  H\$T$ H     ff(fHH|$(t$0f(f(H*HCYHYY|$YfH*HCH\H*Xf(\$f(T$ ^^^^,$^^X,$X|$Jm $D$D$4m Y< f/D$|$H\$@f@ 8 f($$l$YYYYt$`\f(X\$hf(YYYYf(\L$0fH~$\IXt$P5\ \t$(l$XfH~\5[ Hf(t$]l $t$ff/^    f.    Etf.E  ~s[ f(f f(   f(fWfW|$ t$8   D  f(f(fTZ fTZ f/F  f(f(fD(51[ ^YX^f(YYD\XDYYfL~fH~fHnfHn$$l$T$\$Ck %K l$f/$$  \$T$  |$8t$ f(f(f(YYYY\Xf*f(^Xf(^ff.Xf(^fH~f(^fH~" 11HfHnfHn    f(f(5Y ^YX^f(YY\XYYfH~fH~D  fHnfInQj f(f(fD\$@Dd$HY f( A\Dl$0= A\f(YfD(DYYfA(YYD\ XD$(AYfE(YYfD(DYYDY\DYfA(Xq YDX\$XAY\L$`XD$hE\XXXAXXL$PAXAXXX f.XAXzt~~%6W f(fTfTf/r|f(f(^YXHX ^f(YY\XYYfH~fH~HHxfHnfHn[A^f.     ^^fH~fH~@ f(^YXW ^f(Y\YXYYfH~fH~@ ff( f.{
bW ÐHXHv ~u fHnH|$0H flHD$ )T$f(BW \iP D$8D$@   
wHǵ HcHfHQv 	   H=v 1` V HXf     H 	   H=nv 1` @ D$H 	   H=Hv    ]` D$D  D$0     D$H 뾐Hu 	   H=u 1` [H    HH=u HL1_ 2     f.zf(f(f.{U  HXHu ~ fHnHu H|$flfHn)L$0~އ fl)L$@U \N D$D$    
wHf HcHD  Ht 	   H=u 1&_ >U HXf     HY 	   H=t 1^ @ D$H 	   H=t    ^ D$D  D$     D$Hs 뾐Ht 	   H=wt 1^ [H    HH=St HL01]^ 2     f.zf.{\T  HXHs ~m fHnHt H|$flfHn)\$0~V fl)\$@f()T \L D$D$    
wH HcHf     H1s 	   H=s 1] S HXf     HɈ 	   H=ds 1f] @ D$Hc 	   H=>s    =] D$D  D$     D$H 뾐H}r 	   H=r 1\ [H    HH=r HL01\ 2     f.zf(f(f.{R  HXHq ~Մ fHnH*u H|$flfHn)L$0~Ƅ fl)L$@R \,Q D$D$    
wH HcHD  Hq 	   H=r 1\ R HXf     H9 	   H=q 1[ @ D$Hӆ 	   H=q    [ D$D  D$     D$HS 뾐Hp 	   H=mq 1f[ [H    HH=Iq HL01=[ 2     f.zf.{<Q  HXHop ~M fHnH} H|$flfHn)\$0~> fl)\$@f(	Q \M D$D$    
wH> HcHf     Hp 	   H=p 1vZ P HXf     H 	   H=Wp 1FZ @ D$HC 	   H=1p    Z D$D  D$     D$HÄ 뾐H]o 	   H=o 1Y [Ho    HH=o HL01Y 2     f.zf(f(f.{O  HXHn ~ fHnHo H|$flfHn)L$0~ fl)L$@uO \* D$D$    
wH֮ HcHD  Hn 	   H=(o 1X N HXf     H 	   H=n 1X @ D$H 	   H=n    X D$D  D$     D$H3 뾐Hm 	   H=n 1FX [H߂    HH=dn HL01X 2     f.zf(f(f.{N  HhHGm f(~! fHnH6m H|$flfHnHm )L$0~ HD$Pfl)L$@M f(\\f(? D$D$    
wHV HcHf     Hl 	   H=Qm 16W NM Hhf     Hi 	   H=!m 1W @ D$H 	   H=l    V D$D  D$     D$H 뾐Hl 	   H=l 1V [H/    HH=l HL01mV 2     f.zf(f(f.{dL  HhHk f(~q~ fHnHk H|$flfHnHok )L$0~k~ HD$Pfl)L$@%L f(\\f(! D$D$    
wHҫ HcHf     H!k 	   H=k 1U K Hhf     H 	   H=yk 1VU @ D$HS 	   H=Sk    -U D$D  D$     D$H 뾐Hmj 	   H=	k 1T [H    HH=j HL01T 2     f.f(f.t
f.f({J     HhHi f(~| fHnJ H|$Hj flfHnHj )\$0\~| HD$Pfl)\$@f(f(3 D$D$    
wHB HcHD  Hii 	   H=i 1S I HhÐH	 	   H=i 1S @ D$H~ 	   H=i    }S D$D  D$     D$H#~ 뾐Hh 	   H=ai 16S cH}    HH==i HL01S :     f.f(f.t
f.f({H     HhH'h ~{ fHnHh H|$flfHnHxu )\$0~z HD$Pfl)\$@f(H \( D$D$    
wHƨ HcHD  Hg 	   H=[h 1&R >H Hhf     HY} 	   H=+h 1Q @ D$H| 	   H=h    Q D$D  D$     D$Hs| 뾐Hg 	   H=g 1Q [H|    HH=g HL01]Q 2     f.f(f(f.t
f.f({DG  Hhf(Hsf ~Qy fHnH2g H|$flfHnf()L$0Hs ~?y HD$Pfl)L$@G \h+ D$D$    
wH> HcHHf 	   H=f 1vP F Hhf     H{ 	   H=f 1FP @ D$HC{ 	   H=`f    P D$D  D$     D$Hz 뾐H]e 	   H=f 1O [Hoz    HH=e HL01O 2     f.   %. f(fTD f.   f.   HhHd ~w -E fHnHd H|$flf(\)\$0fHn\~pw Hd flHD$P)\$@f(f(f(1 D$D$    
w#H HcH D     HAd 	   H=d 1N D Hhf     Hy 	   H=d 1vN @ D$Hsy 	   H=d    MN D$D  D$     D$Hx 뾐Hc 	   H=Qd 1N [Hx    HH=-d HL01M 2     USHxD$`L$XiT - f/  L$Xfd$`    f.@Ef.Et	@  -C    % HD$    HD$    fHD$    f(H$    l$hd$ fHH  Q  |$`t$Xf(HHfl$f(f(YYH*YY<$\Xf(f(\$H^f(T$P^f*X<$^Xl$f(T$^d$Xt$0d$Xl$@T$R L$D$($R YD$ l$@f/D$(t$0\$HT$Pf(f(T$0\$@R L$D$(D$R YD$ \$@f/D$(T$0|$`\|$hL$Xf(|$(MR f/] |$()  f    f.E  @  ff(ff.     fd$|$f(f(YYYY\ \$Xf(XfH~f\D$XfH~}  f%(A f\L$Xf(\D$`d$hyQ d$hf/)  DD$`L$XD\fA(DD$\f(4$9Q f/I 4$DD$/  f    f.Etf(l$Xf.E<  |$X~->@ f    E f(DD$HfWfW)l$0f(L$ |$(t$@   ff(f(fT> fT> f/N  f(f(t$hfD(^YX^f(YYD\XDYYfL~fH~fHnfHn,$d$\$T$O |$ ,$d$f/  T$\$  |$@t$(f(f(f(YYYY\Xf*f(^Xf(^ff.Xf(^fH~f(^fH~$    D$`L$XofH~fH~HHxfHnfHn[]fT$X~b> f   %q f(f(fWfWT$P|$X   f(f(fT= fT= f/.  f(f(T$hfD(^YX^f(YYD\XDYYfL~fH~fHnfHnl$@t$(\$Hd$0<N l$ t$(f/l$@ d$0\$H|$XT$Pf(f(f(YYYY\Xf*f(^Xf(^ff.Xf(^fH~f(^fH~"D  f(f(T$h^YX^f(YY\XYYfH~fH~    HQ 1ff(f(t$h^YX^f(YY\XYYfH~fH~    DD$Hf(f(1 YYYl$XX\ff.f(YYYY% \X\$$z   ~: l$XfA(fTfTf/   f(f(T$h|$`A^YYDXX\A^f(YYfH~fH~HfHnfHn%fWL$0\$f( \\D$fH~fH~D  ~%; H$    HD$    )d$0f(A^fH~|$`A^fH~y    fA(D$hf(f(^DYYDXl$`Y\A^XYYfH~fH~D  D$`L$X?K f(f(fL$XfA(D$K ~52: D$f(f()t$0f.     AUATUHSHH< H  Hܙ LKHl$H$    L9  H=v I9  IX  H   LFM~)1    HTH9   H9   HI9uA   "  IA8HH  HHt$1H      HHH[]A\A]f.     Lff.     ff.         H   H9t4HuHu H9t#LH   H9tHuH9VfD  HSBALjE1 uLcH=[n uBHLAH!H@# HuHWu H5@n H8     1f     Ht$H1ɺ   HHH[]A\A] HSBXL9HC0    H) H= H0HGH   H   IMI|$H!t H9t@HX  H   HqH   1ff.     HH9   H9TuID$(HP@H  H HuL% LR`IbI,$:LeH^ &HfD  H   H9HuH;s rH5's H9t]uID$@ fID$HXH;r K11H= L IHDI,$tML AUATUSHHHr H{`H(H9   H   HEH         HW         @            @   HX  H   HJH~X1D  HH9tFH;luH{`fLchHkpHCp    C`HtH/tQMtI,$t5HtHm tH[]A\A]fD  HH[]A\A]fD  LfD  먐H8tH{`o LeM~1ff.     HI9tWH;|u; HD  H   H9 HuH;-lq MfLchHkpHCp    C`E1JtH9HG   tW   @tNHFH      te   @t\HX  Ht^HJ1H1D  HH9t#H;tu{H|$1H|$dIM9j   tHH   H91HuH;5}p uff.      AUATUSHHG     H   IHH;ip H5:       1HH   He LKLd$H$    L9  H=o I9  IX  H   LFM~"1HTH9   H9   HI9uA   B  IA8HH1  Ht$1HH      H    H~  HH=D@ HEHPHDo H5Em 1H81HH[]A\A] LD  H   H9t4HuHn H9t#LH   H9tHuH9&fD  HSBLj1 uHkH=g W   HLAH~HtjH+VHHH[]A\A]f     Ht$1ɺ   HH    HSBpL9xHC0Hu%HNn H57g H8ff.     @ 1`dHzff.     SHH=} HGH   H;m u1ҹ   H"Ht[ HHt@Hut@ {Ht1[fH!m HH5Q H811ݐf     AWAVAUIATIUHSHHHE HHE H   H   HCHL   AHH  HAIH   HAH5  `Hx`IHH}  H+tI,$1Mu H[]A\A]A^A_fD  H fD  Hh HtrH[]A\A]A^A_    Hx`IH&  A   H\ Hgk LH5e H81{H+uHHtHm uHf{Hx`IHM  Hk 1H(M H5 H81H+=H80 H(   Hj    H5 H81H+   Hm uHI.Lf     H)k H2H9  IGpIGp    fIWhAG`H/tNHtH*tcH=H(3Hx& Hhd HX- HD$H$BHD$H$    HH$$H$E1Htj H0H9g  Mt$pfM|$hID$p    AD$`H/	  Mt
I/  Mt
I.   HK IA   HW         @   HVH           @  HX  Ht0HJHA1fD  HH9*H;tujH   H9ZHuH;5ci fIWhIGpIGp    AG`HE:fD  LLoI`̒I|$`fM|$hMt$pAD$`ID$p    Hy@    tBfD  AWHW AVAUATUSHH(HD$    HD$HD$    H   LAHM   H  H  HFh HH8SH2T LX 1A   HBK H5b }XZH|$HtH/uHb    H= E1[u  fD  HuL&I$Ld$H=f| H| H9Ge  H-{ H5  HE ID$H5< LH   H  HHs  L-f L9  H=lg H9{/  H;t!HTIH
  H+  LHEL={ L   M  H=	`   HLHAIM  Hm   H+  ID$H5N LLH   H  IHQ   IH[  IE H|$HtH/uH(L[]A\A]A^A_    HH HD$HG     HT$HH4IHR j 1PAPLD$(z H H|$IH(HHe HH8j     He H5* H8*Hm   II.t&HW`    H=3 E1 fD  LfD  H=9 HHfD  HH+tHgLH\ LWH\$HD$    L9  Ld M9  IX  H  LNM~(1fD  HTH9,  L9#  HI9uA   -  IB8HH  Ht$1H      IMD  H+:     H% H HSH}HHx H-tx H@Hqx HsH+H Hm OH}B     KHWLH   H9t.HuHc H9tLH   L9tHuI9HWBLrE1 uLH=q\ u:HLAI7M9HuHmc H5V\ H8Hm tHgHLHIHff.     Hm tjH+9Hg,m"HuHb H5[ H8Ht$HT$HHj LN  Y^qHHt$1ɺ   IHWBL9HG0ff.     AVfHAUATUSHH{ fHnHx  fHnHP)$)D$~y^ HD$@    fl)D$ ~g^ fl)D$0Ht)LAHM~H  HЛ HcH Hq  HHPHH$HHT$HPH@HHT$H HD$H=u Hu H9G  L-u M$  IE HCH5 HH   H  HH  H-|` H9  H=a H9{  H;t!HIH   H+F  LIEL5pu L   M`  H=Y <  HLLAI`M  Im D  H+L  I,$T  HE H<$Ht
H/  H|$Ht
H/  H|$Ht
H/  H|$Ht
H/  HPH[]A\A]A^ HVHHT$HPHHT$HPHHT$HHH$HW     HT$ H4HIHK j 1PAPLD$  H    H:H< tFHCHt)H< t2HCHtH< t!HHtH< tH$    HH_ HHK Li@ A   HB H5pY H8S1MXZH<$Ht
H/   H|$HtH/thH|$HtH/tHH|$HtH/t0HYY    H=e~ 1HPH[]A\A]A^fD  ɐf     f     nfD  Hy LWH\$(HD$     L9^  L] M9N  IX  H  LNM~%1 HTH9B  L99  HI9uA   :  IB8HH)  Ht$(1H      IM   H+     H ;fD  fD  HPH[]A\A]A^ fD  LH+HI,$LfD  HuH] H5U H8@Im    H+uHGHhW    H=t| 1F     H-Y} HUHIHq L-p H@Hp MHkI=fD  Im uLu@ H H=| ,IMD H[ H5R{ H8RIm L_f.     HWBB  LbE1 uLwH=T 6HLAI]M_HH[ H5xT H8{ HLLIHYf     Ht$ HHHj LG Z Y^{Lff.     ff.     fH   H9t4HuHZ H9t#LH   L9tHuI9fD  HWB@ Ht$(1ɺ   'IL9HG0ff.     fAWAVAUATUSHXHD$0    HD$8    kHB  H=n IHD$(    Hm H9G>  Hm H~  HH\$0H;VY   HY H9C  HH; HD$uH<HD$0    E1E1HD$8    H|H9D$  HL$HHT$@HHt$(z2  Ll$@Hl$HIE Ll$8HE Hl$0Mt
I.u  HD$8    Mt
I/m  HD$0    HE     HEH  A    t>HD  H:  EUHH	HH B  Aff.     fH  D# H=3m AHYl H9G7  L@l M  I LD$0DLD$iLD$HHD$8I  IPHBpH
  H@H
  LD$LLLD$HH_  I(
  I/HD$0    	  LLHT$HD$8    HT$  H*

  IM    3Hx`HHtgHW H0H9  LmpHEp    fHUhE`H/  Ht
H*  MtIm uLff.     @ H+f	  I$Lff.     @ I$HtOMtI.t4MtI/tHXH[]A\A]A^A_    L`fD  LPfD  L@fD  H+  IMN   I(tEH|$81HtH/tSHtH*t8HQ H=fB 1ɴI$H<@ LfD  HfD  HT$HT$    H+  H|$8MIM   Ht1һM   dD  HP K   H=A 16H-v HUHHHCj Hti H@Hqi H#HHfD  H=Iv HH\$0HnHP L   H=FA 諳I,$?L2 HT H5A H5u H81aIE1E1L   [fD  H=yp HH  Ht$H1H\$HH      mHHtHT H@HL$H9  H;S   HHm I
  Ll$8MjH+  HS LHD$fHCHL$E1E1HD$0    HD$8    H9  H;S   H!HH]HG     HWH  LoHo IE HE H/  Ll$8Hl$0Mt
I.  HD$8    Mt
I/  HD$0    HE     HEH  A    t,H   H  HHH y  A)H DX H=g AHf H9G%  Lf M  I LD$0DLD$LD$HHD$8I)IPHBpHp  H@Hc  LD$LLLD$HHI(  I.HD$0      LLHT$HD$8    oHT$xNH*  HCHL$IMH9HD$(H9CH|HPHT$(H	fD  H+   H|$8H   MIN   _HLD$cLD$+f     LH~ L8 HHHAH Hj	  HQ H5 K H8AD  HHT$H|$8HT$HHMIN        H@`H  H   H  HIH  H@L5Q L9u  ff.         =	  IGH  A    t>H  H  AGAWHH	HH   Aff.     I/Lf     HD$(H9CHPHT$(HSH<H"    LfD  Lj LB LHT$sHT$af     LHT$SHT$.f     UEHH	HH UH/O H58I H8A7D  H Du    HBhLLH  Hx   LD$gLD$H} H  LD$0H+
  M
  L   ZD  L=o IWLIHkc Lb H@Hb MKLILD$0MH+MI  H߻N   H|$81HHM H5G H8D  HT$0Ht$8Hl$0
  Ll$8Zf.     H=n $I\@ LHT${HT$LHT$cHT$f     HH H8 Du    H;=M ,  HL LD$0H8LD$H  H= H. HDH5l 1LD$1 H% HBhLLH  Hx   LD$peLD$H H+l  HfD  HL H5l H82H+K  H|$81һL   H"L   )f     HILD$LD$HLJIHH@|@ L=m IWLuIH` L_ H@H_ ML#ILD$0M`D  HK H5ZE H8BeD  H(H+ H=yl I뗺   H5j 1LD$pHHH@`H  H   H  HIHq  H@L5GK L9ucf     IGH   A    t(H   HtNLHH Y  AI/LTLIIH+H@D  AWAGHH	HH tH!J H5*D H8AEwHHHJ H5j H8-LD$LD$HHI H5C H8LHAH H|  HI H5C H8EAZEwQH3HI H5, H8H1I H5
C H8HaHHHT$HT$-HH%I H5+ H8H@`H  H   H  LIH  L9pusI@     I@H  A    t6H   HtVLLD$RLD$H¸H9o  AI(LHFIHyAPA@HH	¸H9sHG H5A LD$H8LD$AEpHH|$8N   H~1һN   aqH}`fHUhLmpE`HEp    HN?HDG H5A LD$H8 LD$fH@`H!  H   H  LHD$H  L9p   HD$H@   @  HD$H@H   tqH   HufHL$AQHH	кH9rkAHL$HHD$HHiHa\H$EHD$HjE1H|$RAH9sH   H$F H5-@ H8AyHD$DpkHE H5? H81HH)F H5( H8HLD$LD$HH@`HtYH   HtMH|$HHt>L9pu&H|$rH|$AH/;DHHuHHwE H5' H8VHCHuH;E H5' H8ZH@`HtH   HtsLLD$LD$HHt\L9pu:LD$H|$~H|$LD$AH/NLD$]LD$:LD$CLD$HHuLD$LD$HoHD H5& H8LD$OZHvHHLD$LD$8H|$8H1һL   IfD  AWAVAUATUSH   Hv  HE  Hy R  4  HA   S  H<HoHH#  H=LX HHW H9GW  H-W H
  HE H{C H9E  fHt$xHH       )D$puHm HD$  H|$ m
  HX HU  X V  1HHHC  H5Y HtAHE HPHU E  H	  AY  H5ZY 1HHH  HD$H
  H=2W HV HD$X    H9G  L%V M0  I$L;%A V  H_B I9D$$  L,I<$ HD$`<  Ll$E1Lt$`LI9
  HL$pHT$hLHt$X  Lt$hIMt
I/W  HLL	  M@ H@j HH    E1HĘ   L[]A\A]A^A_     HD$    HE1E1HD$    HHL$ 1HD$X    -HL$ 1H\$0HD$`IHD$pHLHD$(L|$8IHH9  HL$(H|$ HT$hHt$X  Ld$hLt$pI$IMtI/uLHMtIm uL4H==U HT H9G,  HT H  HHSHBpH  H@H  LHIM  H+L	  I.R	  H=T H4T H9G  L5T M  IIVHBpHU  H@HH  LLIMl  I.
  HtHm 
  IG   I  IGH<      tUH  H
  A_AGHH	HH t)H? H59 H8ff.      +H  IE     IEH  A    t<H:  H@
  AmAEHH	HH F
  Af     HH/  D	 IG   d  IGH  D$@    t=H  H	
  AGAOHH	HH 
  D$@f     ;IH  IE     IEHA      t:HX  H	  AuAEHH	HH 	       HH  |$@ H=\R HQ H9G;  L5Q M  IIFH5^ LH   H  HH  I.  HEH5^ HH   H  IMa  Hm   IHt$(1H      H=] Lt$pL|$xL$   觿HIHPIH9  HI  H~  Hm P  H=YQ HP H9G  L5P M/  IIFH5] LH   H  HHx  I.  HEH5V HH   H*  IMB  Hm '	  IHt$(1H      H=\ Lt$pL|$xL$   褾HIHPIH  HI  H  Hm   IG   	  IGHM  A    t7H  H  AGAWHH	HH   A@ KHH  IE     IEH      t:H  H  A]AEHH	HH   f.     H`  DLM H\$`H|$ f     11HH +Hx`IHHt\Hu: H2H9e  MupIEp    fIEhAE`H/  Ht
H(  MtI.uLĿ@ I,$  MtI/uL袿HE1Ll$pHD$`    HHl$ LHD$XI1HLl$IL9   HL$HT$hHt$`HþK  L|$hLd$pII$HtHm   MtIm   H|$LLx  Lt$XHML=L9zH9 H5^Y IMHl$ H8H+  L|$IMID$    1E1i  f     Hx H=iS HHFHy3    H=$  H+  E1 H+	Hf     Hq8 HH H52 L E1H8R1H$ 諽Y^@ L%R IT$LlHHL H-SL H@HPL H袾LH!fH7 H5
X MH8GMt
I.8  H|$HHD$HH  I,$  ID$    I1HD$    E1E1HD$       fD  LeLmI$IE Hm tG    Ht$p   LLd$pHD$x    iI,$HD$t$LHm YH蘼fD  L舼fD  Hx Lh HHIE1E1E1HD$    HD$    D$    f.     t$ H=1 H=" I.   E1HL$HHD$ HH   MtIm uLλHL$HtHHD$HH   MtI/tlHt$HtHHD$HHuH聻MtI,$uLmH4Hm )HQ@ L@< L0fD  H 9 H\ HHT$Ht$HL$HL$Ht$HT$D  HG  D$    IE11HD$    E1E1HD$    zf.     L舺) L蘿HǉH Hf躿HXi@ L`HAH H  H/4 H5) H8AD  LHÉD$@H H&  H3 H5- H8觻D$@f.     LȾHÉH )H  H3 H5( H8Y    L`ID$    I1HD$    E1E1HD$     +fD  L L L HBhLHH/  Hx $  KID  L踸 L訸B L蘸I"H舸 Hx Hh     v  H5oG 1HHH@`Hf  H   HV  LHHE  H2 HD$HH9E  HE   s  HEH  A    t2H  H^  EMHH	ȹH9f  AHm H艷@ Lx HE1e0LXK HH+ H8 HBhLLHB  Hx 7  IID  A_'    L H)1 H5jQ H\$0ML|$8H8蝸HL$ H)  D$    I~fD  HL$ MH\$0L|$8H)  HD$H H)  Lt$c    Eu    L@ L0I     HY AGD$@# H L-1Q IUL荸HHD HTD H@HQD HöL;I     M  HL$ LH\$0MD$    E1E11L|$8Iff.     @ H)   Ht,H.u&HLD$8LL$0HT$(4LD$8LL$0HT$(MtI)tBMtI(uLHT$(HT$(HH*HD  LLD$0HT$(ƴHT$(LD$0f.     HHt$@LD$8LL$0HT$(蔴Ht$@LD$8LL$0HT$(% IE1E1E1HD$    HD$    D$    -D  Am    H=yO I@ HL$ IMH\$0D$    E111L|$8I@ H+IMHl$   HD$H H+  L|$HL$MI HN HSHMIHB L5B H@HB M胴HI     M  HL$ LH\$0E1D$    L|$8E11ID  L-qN IULŵIHB L%A H@HA MLsIMH|$HHD$HH  IIE11HD$    HD$    D$    s Hy, H H5L H81AH|$HHD$HH  I,$LIIE1;1E1D$    HD$    HD$        H=YM 蔾I@ HL$ MLH\$0D$    L|$8E11InfD  H=M LI@ HD$`    H=hH H-  Ht$p1Ld$pH      蜮IH  H@L--+ L9  H;%+   LI.I<  M  I,$  ML-* ID$E1L9tMH;* tnL~IHMtI/tH|$HLWmID$ML9uHD$XI9D$MtHPHT$XIfD  HD$XI9D$HPHT$XIT$L4I{D  L`t Hl$ Ld$IHD$    E1E11I11E1f     HL$ LH\$0E1HD$    E11L|$8I1H) H5# H8躱D  H) H5
 H8蚱D  HL$ LHH\$0HD$    E11L|$8E1I HL$ LHMHD$    E11H\$0L|$8IHL$ LMH\$0HD$    E11L|$81IH)) H5# H8>D  H-I HUH蝱IH= L5D= H@HA= MӯHKI     MHL$ LMH\$0HD$    E11L|$81I     Hy( H5 H8:D  HL$ LHH\$0HL|$8LE1D$    E1I    H L HAH  H  H' H5! H8谯AD  H踭HL$  fD  H蠭2 HHL$ 苭HL$ EwH=qH IHL$ LHMHD$    E11H\$0L|$8IIYL?HǉH H  H' H5p H8ЮfA]]HL$ LH\$0L|$8H)g  D$    IH虶IH-G HUH>IH; L5: H@H: MAtHHH  HL$ LHH\$0HD$    E11L|$8E1IHjH>HH=F }HçHƵIaɫI,$^mI,$  M聧IHL$ LH\$0L|$8H)^  D$    IHJL"I HL$ LIL|$8HD$    E11H\$01IH#HH#BHL$ LHH\$0HD$    E11L|$8E1IH$ H5 H8謬H$ H5 H8葬H|$HHD$HH  ILD$    1IE1E11HD$    E1E1HD$    	HHt$(HL$ HHL$ Ht$(xL1L$qHHt$(HL$ HL$ Ht$(LH@`Hz  H   Hj  LHHY  HK$ H@H\$HH9uuff.     f   B  HEH      t/H   HuT]EHH	HH u[f     Hm uH=hH "HHAH@{H3HǉH tHb	  H# H5 H8Ȫ듋]fD  H@`H  H   H   LHH  H3# HD$HH9Eur     HE     HEH  A    t,H   HuIEHHEH	HH uNAHm H+H HHuH)HAH tH
  H! H5] H8轩ADu듐H@`H1  H   H!  LHH  H+" HD$HH9CuiHC     HCH  D$@    t*H   HuFCKHH	HH uOD$@H+TH,GHHHuKH*HǉD$@H tH?	  H  H5 H8轨D$@땋CD$@ŦH@`H  H   H  LHH  H! HD$HH9CudHC   :  HCHQ      t(H   HuDsCHH	HH uKH+H!HHHuHHǉH tH  H H5T H8货뜋k111HH貥H H5 H8wH H5 H8\H H5Y H8AHtAH9Hr  HB H5K H8A~DuuH H5K H8ۦ"H@`H  H   H
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  f( T f/  f/nV   DR  1f(f(~55 -W YfD(fD(f(f(Y YXY^X^^X^DXfD(E^DXfDTfD/wD%sW DrW EYEY   Y= f(EXDNW A^iQ EYf(E$A^fD(DX Y^X^XY^X^XDXfD(E^fDTfD/wAYEY˅tAXAY} HH[]A\A]D  f(A\ҐfA(A\AE # f(f(L$DQ QXDD$YT$A^f($$$$    f(5T T$f(^%iT Qf(XYYYX%QT X5T YYX%AT X5qT YYX%1T X5aT YYX%!T X5QT YYX%T X5AT YYX%T X51T YYXX^5-Q Y^=ET YX=AT YX==T YX=9T YX=5T YX=1T YAe %S YX%S YX%S YX%S YX%S YX%S YX%S X=S L$f/S DD$YYXX^=S Y^Y#[S Yf(\%S =S YXS YX%S Y\=S Y\hS Y\%|S YX=S YXLS YX%`S Y\=S Y\PS Y\%LS YX=S YY^XY^YA$f(\:S YX6S Y\2S YX.S Y\2S ^XY|~- f(5 H|$8YL Ht$0DN fW%O DN Q`O YQ^M ^d$(D^f(YDYXD\N YX#O YDYXN D\N YXO YDYXN D\cN YXN YDYXN D\EN YXN DL$ YDYXaN D\ N YYDYXKN D\
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f/ v$H\$]\$HYfD   %  f(Y- YXX YYX% X YYYX% X YYX% X YYX% Xt YYX% X Y^YXXY AWflf(f(AVf(f(AUffATfI~USfH~fHnHH)|$f(fff.)<$z,u*fIn    f.Ef.tf.f{u~' ` f(fTf.srX%:* f(f(}f(f(f(fffYd$fY4$f(fXf\f(ff.  HHf(f[f(]A\A]A^A_ÐfTf.rff.    ) f/@  f(f(\$0d$(l$ 1 l$ d$(\$0f/f(5, ~' f(YfWY\f(fTfUfV^f/t  ff(f(t$0f(d$ l$(@Xl$(ffI~fH~f(f(f(Xd$ ffI~ fI~f(f(WfInfInfD(fD(fInfHnYfA(fA(Yh(  f(d$ l$(Xt$0f/   ff.     L$8t$0l$(d$ d$ l$(t$0L$8f(c  ff(f(d$(l$  l$ d$(f/wff/S  5+ f('  X^XYf(Xf/=f/5 / f(D Y) YDXXm DYDX YX[ YDYDXy YXE DYDXg YX3 DYDXU YX! DYYX@ Y=< AX^YXXYXf(T$ T$ f(@f     X&  Xf/   f/
    d  f(Y|( YXXD YYXd X4 YYYXP X  YYX@ X YYX0 X  YYX( X Y^YXXfB f(D  % f(fHnfInf(f?ff.     f(ff(HfW# fTfUfV f/   %M( f(Y\%Ũ d$Hg d$ f(fH   ff.     f(f(f(HY\XPH9uf(\Y' HYD  f(T$T$-˷ H$f L fH   ^\- Cff.     ff.     ff.     ff.     ff.     @ f(f(f(HY\XHH9u\Y' HQY^Ðf(ff(fW! fTfUfV+ f/r}%& H&f f(b H   Y\' %ff.     ff.         f(f(f(HY\X@H9u\YD  %p Hd  fH   ^\% (ff.     ff.     f.     f(f(f(HY\XHH9u\% QY^D  H(f(f( fT% f/   -% Hc S fH   Y\- 2ff.     ff.     ff.     f     f(f(f(HY\XHH9uf(\$L$T$$$^L$$$T$f(\$f(\Y$ YYff(fW H(fTfUfVD  f(\$$$$$5 H a 0 \$fH   ^\5ۤ ff.     fD  f(f(f(HY\XPH9u\Y$ QY^6f(f(fT% @ f/   5# f(fHOa  H   Y\-4 2ff.     ff.     ff.     f     f(f(f(HY\XPH9uf(\YYff(fWN fTfUfV@ -H H_  fH   ^\- @ff.     ff.     ff.     ff.     ff.     f(f(f(HY\XHH9uf(Q\Y" ^3f(ff(5ģ fWo fTfUfVf/f(Yr- f/+  Y+  \fD  HH%D t = H|$8Ht$0* ^ YXXF YYYX YX X& YYX YXr X
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  H(ff.      Sf(fH f/z    q f/  f(- d$Y\f(f(YX Y\X f(Y\X-u f(Y\Xi f(Y\X] f(Y\X-Q f(Y\XE f(Y\X9 Y\\1 \ Y YfH~f(\$m \$d$$\f(\$!H"W d$\$D$fL H   ff.          f(f(f(HY\XHH9uf(L$T$T$L$f(fHn\Y( YL$Y$H [\Y    1Ҿ   H=< 1#
  H [D  0 HQ  H   ^\f<ff.     ff.     ff.     ff.          f(f(f(HY\X@H9u\YR H Q[^@ 1Ҿ   H=; 1[
  H [ff.     ff(fH8f/z      5r f/   f(fW $*$- HO  fH   ^\- ff.     f.     f(f(f(HY\XHH9u\YR H8QY^Ð1Ҿ   H=: 1[
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 f     HH f(f/&  ff/z>    f( ܗ T$YXY\ʗ YX YX YX֗ Y\ YXƗ YX YX Y\ YX YX YX ^f(Y$x T$D$f(+ T$YD$^\Y X$HHD  ^$ 5L H|$8w -ו Ht$0T$f(\$(YYXX YYYX- YX. Xƕ YYX- YX X YYX-j YX X YYX-N YXڕ Xr YYX-2 YX YY$Q Xl$ L$YX= YX9 YX5 YX1 YX- f(Yt$f(\5K f(r l$ t$X5. XX$L$X \$(T$^f(Q^Yl$8YYD$0XY ^HHfD  1Ҿ   H=/ 1
 ; HHfD  1Ҿ   H=/ 1c
  f     Sf(؉H@   uK=[ f/Y  ff/      1Ҿ   H=D/ 1
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 $Y  f(f(d  \$YYX\J YYXr X: YYXb \* YYXR X YYXB \
 YYX2 X YYX* \ ^$f(萺5ȉ \$Yf(t$ YD$X$    1Ҿ   H=' 1C
  fD  ff/   f.z    ffH*f(fT XM Y f/   f.   Uf(f(ھ   S   H(L fW Hl$HL$L$fTfUH) fVL$f~ \$uVCD$v(f(H(f([]f      f( H	 4u t    HH=L& #D$@ f(ff/   f.z@ uD  f(fT fX Y f/wf.   Uf(f(ھ   S   H(  fWK Hl$HL$D$fTfUH fVD$f(fA \$uICL$vf(H([]     H 4uZ t    HH=% \"L$@ f.&  f.fD(  AVfD(fɺ    ATfD(f(UDSHXfD.fWS fATfDUfDVEfD.щEt=t91Ҿ   H=$ 14
 - fI~f( fIn  fD  fA(fA(DD$DT$DL$< f/  DD$fAXf/   DL$DT$f/(  f/  D fE/  f/    S  | ׃ f/  f% fD/>  5 - Ld$@fI~f(f   f(LfA/f(b T$Hf(fA(fA(      fA(DT$FfA(Lt$@^ DT$  |$@T$HfI~U  f     @ ff(f f/  F f/v`11   DT$H=" D
 DT$ffD/r*   f(HXf[f(f]A\A^       f1fA/  ~ fA(-5 HL$@      fA(% fTfAT  DT$Y f/- fA(D$@" D$HfA(  T |$@T$HDT$fI~T  f(  1Ҿ   H=l! 1T$ 
 D$f     h f     f/vD fE/  f/   z L$0f/   f/
  YR D\$(\$ DL$DT$DD$[L$0fW- % DD$YDT$DL$\$ D\$(f/ffD/=    Ld$@-F fI~f(T$HL   fA(fA(fA(Lt$@DT$W   t$@T$HfI~M |$@T$HDT$fI~"fD  fA/   Fg1Ҿ   H= 1T$5	 T$fInf(f %` fD/         1Ҿ   H= 1	 6 Ld$@fA(fA(D - % L   D$@&       D\$8D$HfA(l$0d$(\$ DD$DT$DL$ DL$DT$DD$\$ d$(l$0D\$8|$@   T$HffI~)uDfA/1Ҿ   H= 1	 DT$HfD/ujf.     !fD  f(ff/wf.z uÐ      f.fzUf(f(¾   S   H(fW Hl$HL$fTfUHfV D$ D$f(f( \$uGCL$w)H 4u0 uH([]    f(f.        HH= L$@ f.&  f.fD(  AVfD(fɺ    ATfD(f(UDSHXfD.fW fATfDUfDVEfD.щEt=t91Ҿ   H=> 1	 - fI~f( fIn  fD  fA(fA(DD$DT$DL$蜸} f/  DD$fAXf/  } DL$DT$f/(  f/  DE} fE/  f/z    S  _t w{ f/  f%A| fD/>  5 -.| Ld$@fI~f(f   f(LfA/f(| T$Hf(fA(fA(      fA(DT$FfA(Lt$@ DT$  |$@T$HfI~U  f      ff(f f/   f/v`11   DT$H=L 	 DT$ffD/r*  z f(HXf[f(f]A\A^       f1fA/  ~R fA(-z HL$@      fA(%z fTfATy DT$Y{ f/ fA(D$@ D$HfA(   |$@T$HDT$fI~T  f(  1Ҿ   H=$ 1T$	 D$f      f    ` f/vDz fE/  f/   q L$0f/  x f/
  Y D\$(\$ DL$DT$DD$L$0fW %=y DD$YDT$DL$\$ D\$(f/ffD/=P    Ld$@-x fI~f(T$HL   fA(fA(fA(Lt$@DT$O   t$@T$HfI~M{ |$@T$HDT$fI~"fD  fA/   Fg1Ҿ   H=E 1T$	 T$fInf(f(w % x fD/         1Ҿ   H= 1k	 v Ld$@fA(fA( -w %w L   D$@       D\$8D$HfA(l$0d$(\$ DD$DT$DL$F DL$DT$DD$\$ d$(l$0D\$8|$@   T$HffI~)uDfA/1Ҿ   H= 1b	 DT$HfD/ujf.     !fD  f.f(   USH8Hx_ff.zU uH8[]@ ~ f(fTf.0n vNf.& zftV H8[]    1Ҿ   H= 1	 3 H8[]@  f^f.wSf/H  ff(fH*X QfTX Y f/vYYH8[]fD  L$H<$(L$ff(f/  H<$fH*X ff.     f.f   f(f(HL$   HT$    $$fWd fTfUfV D$ 
 D$(f(f(_ L$ \$$$uICwH ,um f(@ %  1Ҿ   H=0 1d$$	 $d$v 11҉$$H= L$	 E$$vL$Z0 M Uf(f(SHHf.zCHH   $D$P$d$f(ff.z'u% fHHf(f([]f.     ~ `k f(fTf.wRfTf.vxff.zut ffD  1Ҿ   H= 1	 S fyfff.]Wf.% zf(f(KffH*X f.  ff(f(¾   HL$,HT$0   fW d$$fTfUfV D$0 D$8f( l$0\$,t$8$d$   CwAH ,   u*ff/r f.Ⱥ    Et- f( f(f(fl$4$蜥ǩl$4$f(f(f(YYY\f(YXf.f(f(͢f(f(1Ҿ   H=- 1L$d$t$,$	 ,$t$d$L$	11҉L$H= $$t$l$	 E$$L$vl$t$5 f( f(f(f}訨5 f(    ATf(USH0Hu_f.  ff.z
 t2f(fT f.=h    / f.z
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 f/    f/   H( f/   w %ر \$^Y^T$f(d$Y-k f(,$`fd$f.f(      D$X$-\$f(\   f.      f( a \$YYb $胟$\$f(Yf(Y\f(YXYYf(\Yf(\Yff(H(ffTfUfV]f(fD  f(T$IAb $$$Z T$f(XYYD$YXYXYD  f.   ff/f(    f/   H( f/   u ^YL$ί ^f(L$Y-i f(l$ifL$f.f(      D$XD$5]          f( _ YY` D$蘝T$
 f(Yf(Y\f(YXYYf(\Yf(\f(Y\ff(H(ffTfUfV]f(     f(\$QI` D$d$` \$f(XYYD$YXYXYiff.     f.  ATf(fUSHPf/  % f(\f/  f/  f(~5< \\fTf/ b  f.z
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 k	 c HfD  ff** ff/w>a f/wy,H1Ҿ   1H=B
 j	 kc HfD  ff\Ѓ**f(x      f.   ff/w%` f/v.H1Ҿ   1H=͆
 Ej	 b H     ] -  f(fTf.wbff/wf*f/wf.z~   f(\\ff.zpunf(f(!f     pb     H,ffUH*f(fT\f(ffVf/off( Xf(K ff.     f.  f(fHf/w_ f/v&1Ҿ   H=
 1i	 a H@ ~5\ = f(f(fTf(f.   f*f/wff/*  f.z.  f\f.      & f/  ~\] d$fWf(i'd$~5+\ ~3] ^ Y fTf.   f.f  fWfTfUfVf(D  H,ffUH*f(fT\fVf(f*f/fD  h`     Xf(f(H  f(~    fn    f(\f(?] \f(Af.      ` f/wsf/%` wif(< D YYX, YX0 YYX( XYX0 Y\^XfWf( ] ~[ \fWfWf(ff.     f.  f(fH(f/w
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  f/%B4    \%$\ l$f($l$~wY f( ^fTf.)  f.f  [ f(fWBZ fTfUfVH,f5[ fUH*f(fT\fVff(f/f.     X[ f(^f(?[ \fD  ([ ^ d$l$Xf(f(\$ f/e^ l$\$d$   Z f(f(H(\p  ] f/   f/^    f(T YYXL YXxZ Y< YX8 YX4 YX@ \^XfWX     f(f(f( f(Z \efP\ f(\Y fW^X <fWQX f(+     f(ff(5L f/~W   f(-Y f(f(fTf.   f.      f(fTf/ wff.zlujf(f(fD(fTf.  f.z)u'\ Yf/vff/v\	D  f(ff/N  ff.      HH7 f(XYf/rrff/  f(f(^\Xf($ $HH^f(H,ffUH*f(fT\f(fVf(|$fT\$Y )$f/rf(l$8T$ t$0 f($T$ t$0fT^L$($f(μ T$ 4$\$d$(f(XYY^f(Xf(4$4$X |$\$YT$ l$8,^f*f.4$zu\%W uf(\d$Yf(,Y$d$HHY     ~xT f(f(fTf(f.v3H,f-V fUH*f(fT\f(fVf.Y fD   f/,ԅ   f(f(Ÿ   Da5 ff.     ff.      ff(*XY\Yf(fTfA/v^f(9u^ÐH,ffDUH*f(fT\f(fAVfD  f(f(t$X\ t$$f(I$fWT HH\f([f(fD  AVUSHpD$f($t$$f(U4 ^f/   f(L$4$ f4$L$f.zM  %U f(  - f(f("ff.     ff.         t(XfD(D^AYXfD(DYfD/rYHp[]A^^\f(f.     %xT f(ffWR -x    fD(@ =  tHff(*^XDYf(fA(^XfTQ f(fTxQ Yf/rf(|$t$l$$$~t$$$=;W l$YfI~f(fT Q f/|$x  ff.z5  fD( fDWQ    |$HYDT$(DT$@t$Pl$ d$T$8D  t$(Yt$@1d$fD(t$(f*f(t$0fWQ D  d$L$j  Xd$D$L$f(d$GD$t$ f(DXA^fTP f/vL$(l$8D$ AY^L$0XfTO l$8fT-O Yf/w*fIn|$HHl$l\D$8t$Pd$@   fD(l$-U D\fA(fTsO D$f/  f(d$ |$t$xD$ft$|$d$ fD.l$zfD(\  D    |$HD$PEYt$XfDWO l$ DT$(DT$@d$DL$8D  |$(Y|$@1d$f(|$(f*f(|$0fWO fD  d$L$  Xd$$L$f(d$X$|$ f(X^fT)N f/vY\$(l$8L$ f(^D$0XfTM l$8fT-M Yf/w*|$HD$PDL$8t$Xd$f(fInHl$lAX\Df(Hl$l$$XH|$t$ |$t$f(fIn$$\ f(fTGM f.   f.   ff(fW3N fTfUfVfH~Hf(<$| f(fIn\J<$fHnHp[]YA^\f(fIn^ f(fTL f.   fInHl$lfWM fH~    xQ f/w
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XI@E9   YDHXIPE9   YDHXI`E9   YDHXIpE9   YDHX   E9}uYDHX   E9}`YDHX   E9}KYDHX   E9}6YDHX   E9}!YDHX   E9}YX   3YA^XfD(fAW]D  ff/R  f.  	  1Ҿ   H=
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   pxD$  $  fD(f(fD(YEYEYD\f(YAXfA.$  EXDXIuf`hD$  $  fD(f(fD(YEYEYD\f(YAXfA.]  EXDXH$  T$Pf/$DXDXXDDXvQfDT fA(fT{ DXfA/v/E$   fE(I$    D$     1f     'YAX4Dd$   wAA   ffE1LR f(f(L$@  HH$8  H$(  $   H$  $   D$0  D$  D$  D$   D$   $   $   HH$  La $   $   fD(LY^ H9X$   D$   $   H$(  D$   D$  H$8  L$@  D$  D$0  2zfA(f(L$  L$  H$   D$  D)$   D)$   D)$   |$xt$pDD$Xl$@d$0T$ =L$  L$  H=P fD(|$xD$  f(H$   t$pfD($   DD$XfD($   l$@fD($   d$0T$ \$0T$ fA(fA(ĉ$8  L$0  H$(  H$  $   $  D$  D$   D$   D$   D)$   D$   <L$0  Lk\ H$(  f($   f($  D$  L_ H$  D$   D$   D$   fD($   D$   T$`fA(IfA(fA(މ$(  L$  H$  H$   H$   $   $  $   $   D$   FHo_ H$  Ht$pfD(fD(fD(H$   fD(f(BH$   fAI9$   $   f$(  L$  Lx^ fYL[ $  $   )D$   If(f(fA(؉$8  fA(L$0  H$(  H$  $   $  D$  D$   D$   D)$   $   $   $8  L$0  L?Z H$(  $   L] $  D$  H$  D$   D$   fD($   $   $   f(f芾f(fD$ fA($$$   _$$$   f(ff(f(ĉ$)l$ /f(l$ $yf(f(fA(̉$f()l$0|$ DL$@d$@f(l$0|$ $f(f($f(f(܉D$ fA(Dd$pt$XD)L$@)l$0衽Dd$pD$ fD(t$XfD(L$@f(l$0fDff(f(D)$   $   f($   DfD($   $   $   f(ffA(L$H  H$0  H$(  $   $@  $8  D$  D$  $  $   D$   D$   D$   蜼L$H  D$  LW $@  H$0  L[ D$  AX$8  H$(  Hc$   $  AX$   D$   fD(D$   D$   fD(3fA(L$H  H$0  H$(  $   $@  $8  $  $  D$  D$   D$   D$   D$   耻L$H  $@  LV $8  H$0  fD(LY H$(  Hc$   $  $  D$  D$   D$   D$   D$   L$8  H$   H$  $  $0  $(  $  $   D$   D$   D$   茺L$8  $0  LU $(  H$   fD(fD(H$  LX Hc$  $  $   D$   D$   D$   ZfA(f(f(ffA(L$H  H$0  H$(  $   $@  $8  D$  D$  $  $   D$   D$   D$   sL$H  $@  LT fD(H$0  $8  f(H$(  Hc$   LW D$  D$  $  $   D$   D$   D$   fL$H  H$0  H$(  $  $@  $8  D$   D$  $  $   D$   D$   D$   gL$H  $@  LS $8  fD(H$0  fD(H$(  Hc$  LV D$   D$  $  $   D$   D$   D$   fA(L$H  H$0  H$(  $   $@  $8  D$  D$  $  $   D$   D$   D$   UL$H  $@  L}R fD(H$0  $8  f(H$(  Hc$   LU D$  D$  $  $   D$   D$   D$   jL$H  H$0  H$(  $  $@  $8  D$   D$  $  $   D$   D$   D$   IL$H  $@  LqQ $8  fD(H$0  fD(H$(  Hc$  LT D$   D$  $  $   D$   D$   D$   fA(L$H  H$0  H$(  $   $@  $8  D$  D$  $  $   D$   D$   D$   7L$H  $@  L_P fD(H$0  $8  f(H$(  Hc$   LS D$  D$  $  $   D$   D$   D$   uL$H  H$0  H$(  $   $@  $8  D$  D$  $  $   D$   D$   D$   +L$H  $@  LSO $8  H$0  fD(fD(H$(  Hc$   LR D$  D$  $  $   D$   D$   D$   fA(L$H  H$0  H$(  $   $@  $8  D$  D$  $  $   D$   D$   D$   L$H  $@  LAN fD(H$0  $8  f(H$(  Hc$   LxQ D$  D$  $  $   D$   D$   D$   L$H  H$0  H$(  $   $@  $8  D$  $  $  D$   D$   D$   D$   L$H  $@  L5M $8  H$0  fD(fD(H$(  LsP Hc$   D$  $  $  D$   D$   D$   D$   fA(L$H  H$0  H$(  $   $@  $8  D$  D$  $  $   D$   D$   D$   L$H  $@  L#L fD(H$0  $8  f(H$(  Hc$   LZO D$  D$  $  $   D$   D$   D$   ZfA(L$0  H$  H$  $  $(  $   D$   D$   $   $   D$   D|$L$0  $(  LK fD(H$  $   f(H$  Hc$  LVN $   D|$D$   D$   $   D$   L$0D$ f(fd$`Sd$`f(fTf(f(l$0$(l$0\$ $f(;fA(L$0  H$  H$  $  $(  $   D$   D$   $   $   D$   D|$蜮L$0  $(  LI fD(H$  $   f(H$  Hc$  LL $   D|$D$   D$   $   D$   L$0  H$  H$  $  $(  $   $   $   D$   D$   D$   D|$読L$0  $(  LH $   H$  fD(fD(H$  D|$L	L Hc$  $   $   D$   D$   D$   fA(L$0  H$  H$  $  $(  $   D$   D$   $   $   D$   D|$責L$0  $(  LG fD(H$  $   f(H$  Hc$  LK $   D|$D$   D$   $   D$   L$0  H$  H$  $  $(  $   D$   D$   $   $   D$   D|$L$0  $(  LF $   H$  fD(fD(H$  Hc$  LJ $   D|$D$   D$   $   D$   fA(L$0  H$  H$  $  $(  $   D$   D$   $   $   D$   D|$ȪL$0  $(  LE fD(H$  $   f(H$  Hc$  L'I $   D|$D$   D$   $   D$   \L$0  H$  H$  $  $(  $   D$   D$   $   $   D$   D|$֩L$0  $(  LD $   H$  fD(fD(H$  Hc$  L4H $   D|$D$   D$   $   D$   fA(L$0  H$  H$  $  $(  $   D$   D$   $   $   D$   D|$ިL$0  $(  LD fD(H$  $   f(H$  Hc$  L=G $   D|$D$   D$   $   D$   L$0  H$  H$  $   $(  $   D$  D$   $   $   D$   D|$L$0  $(  LC $   fD(H$  fD(H$  D$  LHF Hc$   D|$D$   $   $   D$   <fA(L$0  H$  H$  $  $(  $   D$   D$   $   $   D$   D|$D|$D$   LE $   LB D$   AXHc$  D$   AXH$  $   H$  L$0  $   fD($(  fD(L$0  H$  H$  $  $(  $   $   $   D$   D$   D$   Dd$L$0  $(  LA $   H$  fD(fD(H$  Dd$LVD Hc$  $   $   D$   D$   D$   pfA(L$0  H$  H$  $  $(  $   $   $   D$   D$   D$   DL$L$0  $(  L'@ fD(H$  $   f(H$  DL$L_C Hc$  $   $   D$   D$   D$   $   fA($   L$(  H$  H$  $   $   $  $   $   D$   D|$
L$(  $   L2? $  H$  fD(fD(H$  D|$LiB Hc$   $   $   D$   f.     f.     @ AWfD(f(AVAUATUSHh  H $H   $   H$`  ^É$  H$X  `   H$  $   $   f(ቔ$   HǄ$      HǄ$      HǄ$(      $$P  L$`$   $   $0  ^5q $P  f)$  )$  )$  )$  )$  )$  r H$@  1f(h H|$pH^Hh HǄ$8      HǄ$H      YHǄ$X      H$P  HǄ$8      $`  f(fffA/)$@  +  D|$P$   l@  t$`fH$  L$X  H$8  H$  ~= A   YH$@  H$  L=+ YD$PH$   H$`  A   Ǆ$       Ǆ$      Ǆ$      $  ~5 H$0  D$   MM$  )$   )t$AD$f$   T$P*\$`   X$   )HD$p   Hc)f(I퉼$   fID$0)t$ 5 I^Yt$\$  YX$  f.K  f(f(YY\f(YXf.L$@]L  X L$@$   $   fH~详$   $   $   f(h $   XF衡f$   $   f(f(fffYfYd$ f(fXf\f(ff.rK  |$0fHH$8  YHf$   f()YY\fYX$   f.J  ff(f(HH$@  Hf$   )v at$fYfD(DYYfA(\ffD(Y|$ DXfD.:J  f(fA(D$   1\$@fHnӻ   ffA)    ԠfHI}fD(fHL$p~5s YHfD(HAY)4D D$   fE۸   fE(fD(D\XfA(fD(fD(v  fD  fA(fA(fA(YDCYY\fA(YXf.@  IcA,X`  fA(fA(fA(YDKYY\fA(YXf.B  IcA,X  fA(fA(fA(YDCYY\fA(YXf.AA  IcA,X  fA(fA(fA(YDKYY\fA(YXf.I  IcA,X  fA(fA(fA(YDCYY\fA(YXf.C  IcA,X   fA(fA(fA(YDK	YY\fA(YXf.yF  IcA,X	M  fA(fA(fA(YDC
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  fA(fA(fA(YDKYY\fA(YXf.N  IcA,X  fA(fA(fA(YDCYY\fA(YXf.D  IcA,X   fA(fA(fA(YDKYY\fA(YXf.)C  IcAXf(`  fA(fA(؍SYAYY\f(AYXf.G  McCXf(  fA(f(fA(YAYY\f(AYXf.8s  HcA,Xf|$ fA(AYf(AYAY\fA(AYXf.@<  f(f(f(YYY\f(YXf..:  DYL$$NfA/vf(\$fTfTXf/   H   fD(fD(fE.S8  LcfA(CAXfA(fA(fA(YDCYY\fA(YXf._:  HcAX,փfA(fA(fA(YDKYY\fA(YXf.?  IcA,Xf(zf.        8  LfH f(f(fD($   Hf     +Kf(f(fD(YYDY\f(YAXf.6  HXXfAWfAWH9uf(H$   5 HHfH$0  $   )ffAY   M   )4D      XT$PD$0fDL$@$   X\$`)t$ |$ݙt$0ffY|$DL$@Yf(YY\f(f(t$ Xf.o  $   D\\f(T$fATf($   f/B  H胼$   f   E$   Hf/$P  D`  $     D$   _fInHf(Y ,  fD(EYYYD\f(AYXfA.V  f(L$@HcH$(  H$   D$   D$   讘D$   $   $(  fA(T$ t$<HT$ \$HL$@D$   Y   YYf(f(AYf(YY\f(AYXf.U  $   &	  H$   0  8  f(f(f(HYH  Y  Y\f(YXf.n  $   AAOt'Ǆ$      AID9$   fD  D$   \$`2[ fT$P$   $   $  HL$@A9d
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  ff% *|$Pt$`X$   f($   ^f(YYYd$Y\Xf.td  f(f(YY\f(YXf.fH~id  XN fHn$   T$fH~PT$$   f( L$d$ XKf$   l$f(d$ Yf(YYY\f(X$  $8  f.c  $   ff(YYf(YYf(f(\X$   $@  f.c  I f(ff((t$ff(Yf(YYYf(fD(\DX|$ fD.]e  D$ fA(Dl$$  Dl$f(fх)$P  '/  fHnf fHnD$   H$X  A      nfE~ Dh f(f(~ H$P  )T$fED$   fE()$`  f(L= AYD$   IHDYD$   fD(E\DXfA(fE(fD(Q  f(f(f(YˍMYY\f(YXf.[  HA,XI5  f(f(f(Y̍EYY\f(YXf.W\  HcA,XIp  f(f(f(YˍMYY\f(YXf.\  HA,XI  f(f(f(Y̍EYY\f(YXf.h]  HcA,XI  f(f(f(YˍMYY\f(YXf.]  HA,XI  f(f(f(Y̍E	YY\f(YXf.y^  HcA,XI	B  f(f(f(YˍM
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  5Q $  y=^ $  $   fH$(  H$   H$  ,H$  *É$  \$  $  Y$   D$(  D$   Tʃ)ʃu~=" fDWfDW$   ET$](  LcD9H$X  ~= L¹   $  L$p  HAH- Ǆ$       HǄ$      Ǆ$       D$  D$  D$  I)|$D$   D$   $   fD)*$  X$   D$@  H$p  9  $     HD$p   A   HE)	  $@  $h  $  $8  $0  $H  $   $   $  IcfHHf(Hff.      hHXXf(f(H9uރ$     D$@fl$ $  $   X\$`d$XT$P藉t$@fd$f(l$ Yf(YYY\Xf.J  \$   f(\$0  f(T$fTf/$   J  $      E$   f/$P   Dy Y   $   DY      fA(|$$   l$@$   DD$0L$ fQ|$f(t$XfTf/$     $   L$ DD$0l$@$   $     $   XD$  ffA(YYfA(Y\fA(AYXf. <  f(fD(f(YDYYD\f(YXfD.9I  H$  f(H$  L$@D$   |$0輇|$0$   $(  f(T$ t$OHcT$ \$HL$@D$   HY   YYf(AYf(f(YAY\f(YXf.H  $   f(f(  H8  0  f(T$YYfD(fD(΋$   DỸHH    D\f(YDXfE.QF  El$Ed$$   ~= fE(Dl$0fE(Dd$   fA(fA($  $  $   D$0  D$  D$  D$   認D$   D$  $   fA(fA(DL$@D$   mfD$0     D$  DL$@fD(fD.fE(D$   $   $   fE($  $  E  fD.E  ~= f(fA()$   $0  D$  D$   DD$@D$   l$0d$ .d$ f/$`  l$0D$   $0  DD$@D$   D$  f($   w$   fEfE(fE(fE($   $   f(f(AYAYAYAY\f(Xf.ID  AXAXAT$$   AD$ffWf.$   $   fW$   
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YY\f(YXf.z1  Hcl XA
  f(f(f(YA~YY\f(YXf.1  Hcl XA  f(f(f(YAvYY\f(YXf.82  Hcl XA   f(f(f(YA~YY\f(YXf..  HcXT f(A  f(f(f(YAFYY\f(YXf.E9  HcXT f(A  f(f(f(YYY\f(YXf.9  Hl Xff.      T$ \$0EfD(fD(fDf(fD(fDAYAYEYAYfD(D\DXfE.h&  fA(fA(fffAYfAYf(fXf\f(ff.&  DY$   $A)$fA/v$f(d$f(ffTfTXf/&  AIAW  fE(fE(fD.d$AF'  Ic\$T AXf(f(f(YAvYY\f(YXf.y'  HXl Af(f(f(YAFYY\f(YXf.'  Hcl XAf(Jf.     $      Ǆ$      5f(ff/  $   ff(f(ݍXHcH8  0  Y|$f(fD(f     L$  A   LD  ~5 fWfDWd$`D|$PD  $   $  \$   \$0  DD$   D$   )$   D$   A)T$fD(f(fDf)|$0Hcۋ$  $  @  $  D$D$  D$  $   f*d$ EjD$   A  Hc$  H$X  <$f(Hc$   $   f(HHf(fE(fE($  X$fEfE$   fD$   fD$   YY$  Yf(Yf(Y\f(YXf.s:  AXAXf(f(fffYT$0fAYf(fXf\$\v fD(ff.D$_9  fA(]fE(ffD(Uf(ffDYf(ffAYfA(fXfA\fD(ff.D3  f($   fEXD)$   fDWfDWDe  Al$fD(fD(<$$   D9$  H$X  fD(D)HcHHHfD(fD(fA(fA(fD(f(fD($  $   XYY$  DYYDYD\f(YDXfE.1  EXEXT$fD(fD(\= f(EYAYEYAYD\DXfE.0  S[fA(fA(fE(YYDY\fA(YAXf.n/  DXDXЃHfEWfEWDDSD9<ff.    ff(|$d$@$   f(fTl$0fTf(|$ f(t$$   Ust$f/$`  L$ l$0$   |$@$   Y	  D$0f(l$@$   \$ |$v4$T$0|$\$ ^l$@$   f/  $   o f1f(l$fD(fD(̓HH  C   uH$`  A   |$0Hc$   IcD$   HH$X  UD$  D$  DYHcHD$  Y$  H@  HD$   D0  D8  $   f($  fA(f(fA(YAYAY\f(YXf.8  AXAXfA(fE(fE(DX$   X$  YDYDYD\fA(YDXfE.7  D#Dk  DD$   A9   H$X  HcD$   D$  ff(fD(f(f(f(f(f(YAYAY\f(YXf.g6  XAXfA(fA(fA(EXAXYYY\fA(YXf.J5  HHHLDA9R$  $   $H  $8  $8  $h  Hc$  H$X  Dt$0Lc$   |$@D$   D$   HH\H,$   AGHH)h  f.     f(|$fTfTf(f(Usf/$   	  $d$ Et$B@  $   $   t$f(YYf(YYf(\Xf.)  LfD(f(HfD(     DYYDYD\f(YDXfE.-)  $   $   f(f(YYYY\f(Xf.(  I$B$0  L$ B$8  Mc$   t$HH9  $  X\$@$   <$t$ Yf(Y$  f(YYYY\f(Xf.)  T$@fA(\Q fA(XXd$T$@f($   $   YYf($   YYf(f(\X$   f.$   Y(  mMf(L$p$   $   $   Uuf   $   L$pf(f.f(f(Eo  f.E]  $   d$p$   $   $   td$pf(opf/$`  $   $   8  fAf(f(f($   d$0f(f(YYYY\Xf.&  $   XXf($   fW$   |$0EfWe|$0AF$   H$   D$DT$ 4$|$ H9mD$   f(DL$@$  D$   $   d$0Dt$ D$   D$0  uit$P~=G f(Dt$ d$0f($   DL$@D$   fW\$  X$P  fWf/  D$0  d$@D$   $  fA(fA(D$  D$  $   D$   )$  [j|$P\\|$`\\mD$0L$ rD\$ DT$0D$   d$@f($   D$  D$  $  f($  Ufһ   Ǆ$      f/Ǆ$      1fEf(4$1HD$    AYDYZ$   f(t$|$f(fAT$   fATf(D$   f(DT$@D$   d$0DD$ D$   D$0  m|$f/$   DD$ d$0$   DT$@D$   D$   $   
  fA(fA(ҍE@  AYfA(D$0  D$   $   YY\fA(AYXf.   HHD   D  fA(fA(fE(YYDY\fA(YDXfD.!  fA(fA(fA(AYAYAY\fA(AYXf.2!  HD,0  D,8  HcAD9$   fD(fE(Hf(fD(t$Pf(t$|$@f(fATl$pfATf(d$`f(D$   Dt$ D$   D$   !kDt$ f/$   D$   |$@t$Pd$`fD($   l$p7  @  Dk$   $   D$   $   f(D$   Yf(YYY\Xf.y  HHD   D  fA(fA(fA(YYY\fA(YXf.  f(fA(fA(AYfA(AYAY\fA(AYXf.  HfD(0  fA(fA)T$00  $   8  IcT$AE9<fD(fD(Hf(f($   D$$   DT$ <$t$ 2ff.      fǄ$   L$  $   $   f($  \$    ~5 E1Y)t$YfH~fH~ff(eD$   D$   fEf(1HD$    AYDYJf(l$p$   b|$Pf($   f(f(fW\X$P  fWf/   $   l$pf(d|$P\\|$`\\`g$   L$p,l\$p$   f(f(fEfE(fA(ff(f($   )$   D$   D$   D9T$fD()Af(fDf)|$0	$   A   Ǆ$       A   Ǆ$      t$0ef(|$@HH$   D)$p  $h  \$ T$`|$@fD($p  $h  \$ T$H$   XXfAWfAWH9LǄ$       ffA(fA(H$  f(H$  $  $h  D$  D$  D$  D$  D$  D$p  D$   Dl$@`LcH$  D$  CH$  f(ً$  D$  XD$  D$  $h  D$  D$p  Dl$@D$   Ef(f(f(H$  f(t$@H$  $  D$  D$  D$  D$  D$p  D$h  $   _H$  D$  D$  H$  D$  t$@D$  $  D$p  D$h  $   fA(fA(H$  H$  $  $p  D$h  D$  D$  D$  D$  D$  D$  D$   Dl$@$^H$  D$  D$  f(H$  f(ዄ$  D$  $p  D$h  D$  D$  D$  Dl$@D$   D$ fA(fA(fA(H$  H$  $  D$  D$  D$  D$  D$p  $h  $   Dd$@(]H$  D$  H$  f(f(D$  $  D$  $h  Dd$@D$  D$p  $   fA(fA(f(H$  H$  $  D$p  D$h  D$  D$  D$  D$  D$  D$  D$   Dl$@2\H$  D$  D$  f(H$  $  D$  D$p  D$h  D$  D$  D$  Dl$@D$   fA(fA(f(H$  H$  $  D$p  D$h  D$  D$  D$  D$  D$  D$  D$   Dl$@.[H$  D$  D$  f(H$  $  D$  D$p  D$h  D$  D$  D$  Dl$@D$   黽fA(f(f(H$  fA(H$  $  D$p  D$h  D$  D$  D$  D$  D$  D$  D$   Dl$@&ZH$  D$  D$  f(H$  $  D$  D$p  D$h  D$  D$  D$  Dl$@D$   cfA(f(f(H$  fA(H$  $  D$p  D$h  D$  D$  D$  D$  D$  D$  D$   Dl$@YH$  D$  D$  f(H$  $  D$  D$p  D$h  D$  D$  D$  Dl$@D$   fA(fA(f(H$  H$  $  D$p  D$h  D$  D$  D$  D$  D$  D$  D$   Dl$@XH$  D$  D$  f(H$  $  D$  D$p  D$h  D$  D$  D$  Dl$@D$   GfA(fA(f(H$  f(H$  $  D$p  D$h  D$  D$  D$  D$  D$  D$  D$   Dl$@WH$  D$  f(H$  D$  f($  D$  D$p  D$h  D$  D$  D$  Dl$@D$   ˻fA(fA(f(H$  H$  $  D$p  D$h  D$  D$  D$  D$  D$  D$  D$   Dl$@
VH$  D$  D$  f(H$  $  D$  D$p  D$h  D$  D$  D$  Dl$@D$   wfA(f(f(H$  fA(H$  $  D$p  D$h  D$  D$  D$  D$  D$  D$  D$   Dl$@UH$  D$  D$  f(H$  $  D$  D$p  D$h  D$  D$  D$  Dl$@D$   L$`D$Pff(lTf(f(T$fPTD$ fD(鰵T$0f(f(f$   l$ Tl$ $   $   T$0fl$ Sl$ $   f(f]f(f($   $   S$   $   L$@gfA(f(f(H$  fA(H$  $  D$p  D$h  D$  D$  D$  D$  D$  D$  D$   Dl$@SH$  D$  D$  f(H$  $  D$  D$p  D$h  D$  D$  D$  Dl$@D$   f(fA(fA(H$  f(H$  $  D$p  $h  D$  D$  D$  D$  D$  D$  D$   Dl$@QH$  D$  D$  f(H$  f(ً$  D$  D$p  $h  D$  D$  D$  Dl$@D$   L$ D$0fA(fA($  $  D$  D$   $  D)$  D)$  $  Q$  $  D$  fD(D$   fD($  fD($  fD($  $  fA(fA(f($  $   f(D$  D$  D$  D$  mP$  $   D$  f(D$  D$  fD$  ~ff(f(ǉ$  D$  f(D$  D$   D$  $  $  OIc$  $  T f($  D$  D$   D$  XD$  Qf(f(ǉ$  $  D$  D$  D$  D$   $  $  $O$  D$  $  f(f(D$  D$  D$   $  $  f(f(f(ǉ$  f(Չ$  D$  D$  D$  D$   $  $  rN$  D$  D$  $  f(D$  D$   $  $  wf(f(f(Չ$  $  D$  D$  D$  D$   $  $  M$  D$  D$  $  f(D$  D$   $  $  f(f(f(ǉ$  f(Չ$  D$  D$  D$  D$   $  $  M$  D$  D$  $  f(D$  D$   $  $  sfA(f(f(H$  fA(H$  $  D$p  D$h  D$  D$  D$  D$  D$  D$  D$   Dl$@>LH$  D$  D$  f(H$  $  D$  D$p  D$h  D$  D$  D$  Dl$@D$   [fA(fA(f(H$  H$  $  D$p  D$h  D$  D$  D$  D$  D$  D$  D$   Dl$@:KH$  D$  D$  f(H$  $  D$  D$p  D$h  D$  D$  D$  Dl$@D$   f(f(f(Չ$  $  D$  D$  D$  D$   $  $  dJ$  D$  D$  $  f(D$  D$   $  $  
f(f(f(Չ$  f(܉$  D$  D$  D$  D$   $  $  I$  D$  f(f(D$  D$  $  $  D$   $  qfA(ffA($   l$0d$ |$3Il$0$   d$ |$f(f(f(f(f(ǉ$  f(Չ$  D$  D$  D$  D$   $  $  H$  D$  D$  $  f(D$  D$   $  $  9f(f(f(Չ$  $  D$  D$  D$  D$   $  $  H$  D$  D$  $  f(D$  D$   $  $  f(f(f(ǉ$  f(Չ$  D$  D$  D$  D$   $  $  VG$  D$  D$  $  f(D$  D$   $  $  {f(f(f(Չ$  $  D$  D$  D$  D$   $  $  F$  D$  D$  $  f(D$  D$   $  $  fA(f(fA(ˉD$fA(DL$@$   Dl$0Dd$ !FDL$@Dl$0Dd$ D$f(f($   |fA(fA(fA($   fA(|$0D|$ Dt$EDt$D|$ |$0f(f($   fA(fA(D|$PDt$@D$   DL$0D\$ DD$VEDD$D\$ DL$0Dt$@f(D$   D|$Pf(f($   $   D$   Dt$0DT$ DL$DDL$DT$ Dt$0f(f(D$   fA(fA(fA(ۉD$fA(DL$@$   DD$0|$ |DDL$@DD$0|$ D$f(f($   ffA(fA(D$0D$   $   Dl$@D$   D\$ DT$	DDl$@D$0D\$ f(D$   fD($   DT$D$   f(f(D$$   $   DT$CDT$D$f(f(l$$$oCl$$$fD(fD(\$$f($   8Cf(f(%$   D$0$   t$pCt$p$   f($   \$f($   B$   $   oL$ $D$   DL$pBDL$pD$   fA(fA(D)$   $   Hl$pd$`|$PD\$@D$   DL$0DD$ D|$D4$BD\$@D$   fD($   D|$AXAXD4$DD$ DL$0|$PfEWd$`l$pfEW$   KD9 \$fA(fA(f(D)d$pl$`d$PD|$@$   Dt$0t$ DD$D$JAfD(d$pl$`d$PD|$@fD(fD($   Dt$0t$ DD$D$f(f(D)d$pt$`D\$PDT$@D$   |$0Dt$ l$$$@t$`fD(d$pD\$PDT$@fD(fD(D$   |$0Dt$ l$$$fA(fA($   $   D)$   $   |$pD)D$`DD$PDL$@D$   Dt$ @|$p$   fD(fD(D$`$   fD($   DT$PfD$   DL$@D$   Dt$ ?fA(?f(f( fA(f(f(l$ DL$u?l$ DL$fD(f(f(f(ǉ$  f(Չ$  D$  D$  D$  D$   $  $  ?$  D$  $  f(f(D$  D$  D$   $  $  	f(f(f(Չ$  D$  D$  D$   D$  $  $  Z>$  D$  D$  f(D$   D$  $  $  T$@f(f(fl$0d$ =l$0d$ $   $  $   f=D$0L$ L$f(f(f($   d$0t$ {=d$0$   t$ fD(fD(_fA(fA($   $   )$  $   DD$@D$   l$0d$ =DD$@f($  f(l$0d$ f($   D$   ,T$@f<l$ d$f(f(͵L$`ff(f(<f(f(f(f(\$0T$ g<\$0T$ L$T$@fl$0d$ 5<l$0d$ $   $0  f(f(t$ |$;t$ |$fD(阶fA(HD$;HD$f(f(>f(f(f(ǉ$  f(Չ$  D$  D$  D$  D$   $  $  e;$  D$  D$  $  f(D$  D$   $  $  Wf(f(f(Չ$  $  D$  D$  D$  D$   $  $  :$  D$  D$  $  f(D$  D$   $  $  f(f(D)d$P$   $   D|$pD)$   $   $   Dt$`D)l$@$   d$ :D|$pfD($   fD(Dt$`$   $   fD(d$PfDfD(l$@d$ $   f(f(D)$   D$   D$   DL$pDt$`D)d$PD)l$@$   |$ ^9DL$pfD($   Dt$`f(f(D$   D$   fD(d$PfD(l$@|$ $   fA(fA(D$   D$   D$   $   t$@$   \$0T$ D\$DT$8HHDT$HA9D\$T$ \$0t$@D$   L$   D$   D$   D$   Yf(fA(f(D$   f(d$0D$   D$   D$   DD$@$   DL$ t$l$7DD$@D$   D$   d$0f(f(D$   DL$ D$   t$$   l$fA(fA(f(D$   f(|$@$   D$   $   l$0D\$ DT$7|$@D$   l$0fD(fD($   $   D\$ D$   DT$fA(f(f(D$   fA(Dl$@D$   D$   $   DL$0DD$ |$p6Dl$@D$   DL$0f(f(D$   D$   DD$ $   |$f(f(f(ǉ$p  f(Չ$h  D$  D$  D$  D$  D$  D$  $   $0  5$p  D$  D$  f(D$  D$  $h  D$  D$  $   $0  f(f(f(Չ$p  $h  D$  D$  D$  D$  D$  D$  $   $0  4$p  D$  D$  f(D$  D$  $h  D$  D$  $   $0  ^f(f(f(ǉ$p  f(Չ$h  D$  D$  D$  D$  D$  D$  $   $0  4$p  D$  D$  f(D$  D$  $h  D$  D$  $   $0  Ӣf(f(f(Չ$p  $h  D$  D$  D$  D$  D$  D$  $   $0  63$p  D$  D$  f(D$  D$  $h  D$  D$  $   $0  Mf(f(f(ǉ$p  f(Չ$h  D$  D$  D$  D$  D$  D$  $   $0  `2$p  D$  D$  f(D$  D$  $h  D$  D$  $   $0  ¡f(f(f(Չ$p  $h  D$  D$  D$  D$  D$  D$  $   $0  1$p  D$  D$  f(D$  D$  $h  D$  D$  $   $0  <f(f(f(ǉ$p  f(Չ$h  D$  D$  D$  D$  D$  D$  $   $0  0$p  D$  D$  f(D$  D$  $h  D$  D$  $   $0  鱠f(f(f(Չ$p  $h  D$  D$  D$  D$  D$  D$  $   $0  /$p  D$  D$  f(D$  D$  $h  D$  D$  $   $0  +L$`ff(f(j/f(f(hf(f(\$ T$D/\$ T$fH~h$   fl$ d$/l$ d$$  $8  ۛf(f(f$   l$ d$.l$ d$$   $@  ff(f(ǉ$h  D$  f(D$  D$  D$  D$  D$p  $   $0  :.$h  $0  $   f(D$p  f(D$  D$  D$  D$  D$  f(f(ǉ$p  $h  D$  D$  D$  D$  D$  D$  $   $0  o-$p  D$  D$  f(D$  f(D$  $h  D$  D$  $   $0  _T$f,D$ fD(鄚$   f,f(xf(f(f(ǉ$p  f(Չ$h  D$  D$  D$  D$  D$  D$  $   $0  [,$p  D$  D$  f(D$  f(D$  $h  D$  D$  $   $0  ʝf(f(f(Չ$h  D$  D$  D$  D$  D$  D$p  $   $0  +$h  D$  D$  f(D$  D$  D$  D$p  $   $0  ND$ fA(fA(fA($  $  D$  D$  D$p  $h  $   D$0  *$  $  D$  fD(D$  fD(D$p  $h  $   D$0  ޜfA(fA(f($  $  f(D$  D$  D$p  D$h  D$   D$0  *$  $  D$  D$  D$p  D$h  D$   D$0  \f(f(f(ǉ$p  f(Չ$h  D$  D$  D$  D$  D$  D$  $   $0  D)$p  D$  D$  f(D$  D$  $h  D$  D$  $   $0  ԙf(f(f(Չ$p  $h  D$  D$  D$  D$  D$  D$  $   $0  r($p  D$  D$  f(D$  D$  $h  D$  D$  $   $0  NT$0fD$   'f(t$ D$   |$f(f(鿐f(f(f(Չ$p  f(܉$h  D$  D$  D$  D$  D$  D$  $   $0  `'$p  D$  f(f(D$  D$  D$  $h  D$  D$  $   $0  郘fA(fA(f(H$  H$  $  $h  D$  D$  D$  D$  D$  D$p  D$   Dl$@y&H$  D$  D$  f(H$  $  D$  $h  Dl$@D$  D$  D$p  D$   ֋f(f(%f.     f     AWf(AAVf(IAUATUSH  $   ~f \$p)$  f(jh $   f()$  ~]h L$h)$  f(Wh $   )$   g $  ^T$@d$8$p  HǄ$x      g $  fHg )$  )$  )$  )$  )$  )$  )$  )$   )$  )$   )$0  )$@  )$P  )$`  g H$  ^H$  H
 $  $  f(HǄ$      HǄ$      HǄ$      HǄ$      HǄ$      H$  Xf $   ^f)$p  ffW5d fWd $   f/t$P\$Hw$   l$H\$h|$P$   fYYl$hXd$H\l$Pf.P  ,$l$@fH$  H$  d$,H$   H$   *É$  \$   Y-g f(%g $  
 ,$$`  Y$  $p  Yăd$)f(fW5c f(fD(YD\f(Y\fA.O  HfA(H    Yf(f(YY\f(AYXf.N  ff/D$H	  \$H\$hf(f)$   EeG  $   M  H$  ~%a D$        H$   H$  A      H$   H$  H$   H$  H$   H$  H$   H$0  D$0   H$   L$  D$   A)d$t$X|$`    D   fH)H$      f($   HcD)|$HIAԍUI*f(J0H$   ff(J0H$   Xf(J40H$   J<0f(WH$   1$   N0H$   |$N0?\$xD$fB4  BX4  $   t$`BX4   f("|$fA[f(A^Yf(YYY\f(Xf.MF  l$xf(t$|$8\fTf/f(b
  A   HED$0HD$0H  Hf/$   t$x  
  $X  Dw
 zd 
 YYY\Zd YXf.BK  f(f(H$     H$  H$8  $P  $@  $0  $   貰H$8     $0  $   H$  $  $  f(f(謢c 
 D
 $  $  Y$@  $P  YDY\^c YAXf.J  HH0  8  fD(fD(fD(DYDYDYE\fD(DYEXfE.=J  Hf(H    YfD(fD(DYDYD\f(YDXfE.H  H|$Xt$`EX  EX  f(f(YYYY\f(Xf..H  f(f(f(AYAYAY\f(AYXf.G  D$xMcH$   $  H$   $0  $   \~$   $  $  $  f(|$x#L$  $  $0  HYp  YYD$xf(f(Yf(YY\f(YXf.F  f(݃|$0f  ff/D$HrfW%-] If(AGfB(4  fHHP  fYX  f(f(ffYf(fXf\f(ff.H  t$Xl$`A] \ \ YYX\f.H  A  D$   L$  
 \$HfA_T$P$X  D$XL$`9  ]A9  AGfl$@1*D$  b H$0  H$   H$  f($   $  E$   @Hf($8  Xf`b $H  f($   $0  $@  $P  $X  $`  $h  f($p  f(H$h  P$   L$`  L$P  l$ 8$@  $H  $   $P  $   $X  $   $   AYAZ$   d*  d$PXt$hfD$Xf(f(l$ff(Yf(YY\f(YXf.nV  T$x\~-CY t$8f()l$fTf/	  D$P  $  $8  $   $  D$  D$X  $(  $   D$  D$`  $   D$   D$h  $   D$0  D$   $   fD/  ,$DL$XLc퉬$  L$0ID$P  DYMD$X  $`  Yl$`ALLcD$h  HHHD  D  f(p  $  f(fA(f(AYYY\fA(AYXf.=  AXAXDXL$XXd$`fD(f(fD(AYEYEYD\f(AYDXfE.Y>  De DmA   $  A9  Dd$XDl$`Hc   f.     XAXEXAXf(f(f(AYAYAY\f(AYXf.G  HHHALADA9  f(fD(f(f(f(fA(fA(YYY\f(YXf.Pf(fA(f(D$  f(t$D$  D$  D$P  D$@  $8  $   DL$0,$t$,$D$  f(D$  f($8  DL$0D$  D$P  D$@  $   ff/j&  f/$   [&  fl$Xt$`kV AE ^V YY\Xf.E;  D$ tffA.Uz<u:fA.Uz2u0D$ A   L$`D$XI9$   rfA   AUD$ L$`D$XfD    $8  $0  $  $  $  $  fI~f(f($   $  $  fInefI~$  R
 $0  $  $   $8  YfIn\\
 X$X  f(fTD$f/D$8~   ff/$  f/$   $  d$XfT AE t$`f(YXYf(\f..:V L$`f(KfD  A.$  D$0Dpf     DHǄ$       HǄ$0      HǄ$      HǄ$      HǄ$       HǄ$       HD$x    HǄ$       HǄ$       HǄ$       HǄ$       HǄ$       $    #  5#V 
 ff/L$H-iS sf(f(Y$   $  t$H$   H$   ,$B\8,$D$  t$$  )ЃufDW=R fW%R $`  $p  fWR f(Yf(YY\f(YXf.N  )HH    fWqR f(f(Yf(YY\f(YXf.N  DUE6  A9$  $   1"  IcA   1~=P HD$     A   HD$  LD$  E܉$  HL$  I)|$D<$d$0$   $8  ,$d$0DD)ff䉄$  )$p  f*)$`  Xl$@A+  DE9  $     $   X\$hf(f$   XT$P$@  }f$@  f(Yf(YY\f(Yf(Xf.vM  \d$xf(l$fTf/l$8  ff/|   Cf(f(Љ$  HH    $P  f($@  f(ff/D$HrfW%LP f(f($P  AE$@  Hf(f(HYX  P  YYYf(\X$  $  f.8  ]M$  $  $  f($  $  $     $  $  $  f(f$  f.E  f.E  $  $  $  $  $  6$  f(f/$   $  $  3  D$ ff(f(f($p  fYf($`  fYf(f\fXf(ff.b@  fX<$fW=uN mN eN <$$   ut$0fW5EN Yt$0$8  YX\f.?  ff.N  H  f.>  8  A   AIHE92  $8  $   #fD  f(f($   fI~$   $@  fInfI~$@  Y
 $8  f(d$t$8YfIn\\?
 XfTf/ff/  f/$     1fff.     ff.     @ HHHAD9rD|$ D$ H  []A\A]A^A_L$`A   D$Xf     f(|$)$  $  f(fTd$xfTf($8  $0  f(Hd$xf/$   $  f($  $   $0  $8  f(d$x$   ^T$p$  f/f($  $X  ff/  f/$     l$XfK AE d$`f(YXYf(\f.9H  D$ /D$ A   D$0   L$`D$X:@ fW%8K  $  AHH  H    $     $     $     t$x  $     $     $     $   0     $  )8  $  $  $   $0  f.     H$  ~-I D$0      H$   H$  A   H$   H$  H$   H$  H$   H$  H$   H$0  D$x   D$     H$   D$   L$  )l$t$X|$`       ff/B  f/$   3  d$XfII AE |$`f(YXYf(\f.1  D$ t(ffA.U    fA.U    D$ D$x   L$`D$XI9$   =   A   D1D)fDT$@AԍU)H*HcH$   f($   IIf(J0H$   fXf(f(J0H$   T$J40H$   LPH$   $   N0H$   N0y%f(l$ B4  I   B\4   H^_|$8HHfTf/f(Ei|$xDE|$0f/$   $  jD|$0fI~B4  T  B4  $   $0  $  r$  $0  fI~f(f($8  E$  fIn"fI~$  
 $   YfIn\\
 X$X  fTD$f/D$8Z	  D$0|$x$0  $8  Dp  u
 ]J UJ YYY\M
 YXf.3  f(f(H$     H$  $P  H$@  $8  $0  螖H$@     $8  $0  H$  $   $  f(f(蘈I 
 -
 D$  $   Y$P  YY\TI YXf.2  HH0  8  fD(f(fD(YDYDYD\f(YDXfE.2  HH    f(f(f(AYYY\f(AYXf.2  H|$XAXDt$`  AX  f(fA(YYY\fA(YXf.0  f(fD(f(YDYYD\f(YXfA.1  fInMc\$  H$   H$   D$8  $0  $   v$  $  $  $   $  f( 	L$  D$8  $0  HYp  YY$  f(f(AYf(YY\f(AYXf.U0  f(݃|$0fx  ff/D$HP  f(ID$xf(fB(4  fɃfYHHX  P  f(f(ffYf(fXf\f(ff./  d$Xl$`A] B f(YXYf(\f.-  |$xD$x   L$`D$XfAUD$ D$x   L$`D$XYf     $X  D$0Dpf.     A   HDf/$     C$  $   H$  $   H$     H$  $  $  $   $(  "H$     H$  $P  $   $@  $(  $$   $0  D$@  D$P  f(f(YYYYf($  X$  \f.:  $  $  f(f(AYAYAYAY\f(Xf.:  $   X$8  XD$   D$   f(f(AYAYAYAY\f(Xf.=  f(fD(fD(YDYDYD\f(YDXfE.M=  H$   \$   D$  H$   D$  $  f(R$  $  $  $P  f($@  Hc$  $P  $@  D$  D$  HHYp  YYf(AYf(f(AYAY\f(AYXf.;  f(f(ԃ  H  $P    $@  rffW%> f(    f(t$)$   $  $  f(fTfTf($8  $@  f(]f/$   $  $  f($   $0  
$8  $@  f($0  ^T$p$  $  f/f($   $X  ff/  f/$     d$Xf= AE t$`f(YXYf(\f.4  D$ fD$ D$0   D$x   L$`D$X$X  ff/  f/$     d$Xf= AE l$`f(YXYf(\f.> L$`D$XD  $   $   $  $  $   $P  $   $@  $P  $P  $@  q9
 $P  $  f(l$$  Y\f(\
 XfTf/l$8  ff/  Cf(f(ى$  Hf(H    $P  f($@  If     H$  $  f$  fHnfHnf$  ff.     $  f(t$$  $P  f(fTfTf($@  $  f($  f/$   $@  $P  $  $  $    $  $  $  $  f(rl$p$  ^f/  $P  ff(f(f(HǄ$@      Ǆ$      $  99$  f($   f(1H$   H$0  H$  Hf(f($   f$  f($   $   $   $   $(  $   $0  $   $8  $   $@  $   $H  $  $P  $  $X  $(  $`  $8  $h  $p  H$h  P$   L$`  L$P  $P  a$   $X  $`  $   $(  $   $p  $   $0  $  $x  $   $8  $@  $   $@  $0  $   $H  $   $P  $   $h  $   XZ$@  f     $X  fD$0   A   f/VD$0   E1F d$0f(d$$   f(fAT$  fATf($  f(D$D$P  D$@  D$8  D$  D$  D$f/$  $   d$0D$8  D$@  D$P  $  $    fA(f(fA(Bp  AYAMD$  D$  $  AYAY\f(AYXf.1  f(f(fD(LHD4p  D4x  AYAYEY\f(AYDXfA.0  fA(fA(fA(AYAYAY\fA(AYXf.U)  IF,  F,  LcA9  fD(fE(Hf(fD(fD  AtA       $  D<$ED$@  d$0D$P  L$  D9$X  E)$  HcfED$P  D$X  $`  $h  Dp  D*E:D$   A	  Hc$  $   HLfD  $   T$Xf(AXYY\$`f(YfD(YDY\f(YDXfA.  AXEXD\5 fD(fA(fE(AYEYEYD\f(AYDXfE.&  DuEf(fA(YfA(AYY\fA(YXf.-  AXAXfDW=3 fW%3 UMf  Al$A9$  D)HcHLf.     f(fA(fA(fE(T$XfA(fD($   AXYY\$`fD(YDYDYD\f(AYDXfE.  DXDXfA(fA(fA(D\4 AYAYAY\fA(AYXf.#  DsKfA(f(fA(AYYAY\f(YXf."  XXHfDW=2 fW%2 3kA9    l$8f(l$t$@f(fATDD$xfATf(|$pf(DT$hd$PD|$HDL$0D$D$   D$   D$f/$   DL$0l$8t$@D|$Hd$PDT$h|$pDD$x  f(f(f(p  AYDkD$   D$   $   AYAY\f(AYXf.*  Hf(f(HDp  Dx  AYfA(YAY\fA(YXf.)  fA(fA(fE(AYAYEY\fA(AYDXfA.#  HD  D  IcAE9fD(fD(Hf(fA(    5
 3  T$x\$   @ ff.    f D$ E fD$0   A   f/ZD$0   E1J@ McA   Dd$01LLt$hM~=. HD$  A   L$  E)|$HfA(DfD))|$ f(f$  )<$A  DE9  $   {  D$   f(|$D\L$xfATf/|$8k  A   HDf/$   	  $   $   $  $p  $`  D$P  D$@  $   $8  $   $   $8  $8  $   c
 $8  D$@  f(t$D$P  Y$`  $p  \f(\*
 AXfTf/t$8$  j  KAr  fɹ      f/Z     1N   9$  t9$  c  fD$0PHcH  H  H$   $     $   $     |$x$     $   $     $  $  0     )$   (T$0$0  vf     ffD/KfD(fD(Hcf(f(HD  D  ff/D$HrfDWl, fA(fA(fA(fA(fA(AYAUAYHcAYHP  X  \fA(AYXf.$  U]ff(fD(ffDfY$fDYd$ f(fAXfA\fD(ff.D"  + fDX+ fDW=+ fW%+ YYDeX\f."  ffD.z9u7fD.z0u.A   AIHE92  f(f(fD  At
A   fED$     Lt$h Hc$  Dl$ D\$8$   Hl$@IlN$0D$   AGt$hHD<$H)d$0D$   b  ff(d$L$ D$pfTfTQf/$     t$h|$@Dsp  $   $   f($   YYf(YYf(\Xf.  HfD(f(HfD(p  x  DYYDYD\f(YDXfE.%  t$p|$ f(f(YYYY\f(Xf.%  HD$@  L$h  Ic$   $   IL9  $   X\$8T$Xd$@|$hYf(Y\$`f(YYYY\f(Xf.  l$8fA(\-T* fA(XX$   l$8f($   $   YYf($   YYf(f(\X\$ f.d$p0  A\$AL$f(L$x$   $   $   Wf   $   L$xf(f.f(f(E  ff.Ek  L$pD$ $   $   T$xT$xf(sf/$   $   $   *  fAf(f(f($L$0f(f(YYYY\f(Xf.  XX,$d$0fW-' fW%' AT$AD$,$d$0P$   I$   Dd$@Dl$hd$@l$hL9wDl$ D  $   Dd$@$   Dl$hl$@d$h*    ff.z&u$f t$p|$     f(\$x$   Hf($   \D$PX$   fW & f/C  $   \$xf(d$Pt$H\\\\$   L$xl$x$   f(K$   H$  $   H$     $  $  $  $p  D$`  D$P  H$@  $   $(  uH$@     H$  $8  $   $   $(  g$  $   $0  D$   D$8  fD(D$P  Yf(D$`  $  YDYYfD($  DX$p  D\fE.  $  $  f(fD(AYAYEYD\f(f(AYXfA.  $   AXEX$   f(fD(YDYYYD\f(XfA.  f(fE(fA(YEYYD\f(AYXfA.0  $   H$   $  \$   H$   $  $  D$p  D$P  $@  $  D$`  D$`  $  $  $8  fA($   Hc$  $8  $   D$P  $@  HHD$p  $  H$  Y4p  $  YYfD(fD(EYf(YDYD\f(AYDXfE.]  fA(fA(ЃK  HD  D  r Afɻ   Ǆ$     f/Ǆ$         ff(f(ff/lKfD(fD(Hcf(f(HD  D  $8  ff($   H$0  $@  *$  H$  f(f($P  $   fH$   $   D$   f(H$   $(  $  $   $   $   $   $0  $   $8  $   $@  $  $H  $  $P  $(  $X  $8  $`  $h  $p  H$h  WXT$P1$   L$`  L$P  a$   $(  $0  $   $8  $   $@  $   $H  $   $P  $   $X  $   $`  $   $h  $   $p  $  $x  $   $@  $0  Y^$P  $@  $8  D$   $P  $  $  HǄ$@      $  Ǆ$      $  D$  f($  $  $  $  $  f($   \D$PX$   fW= f/W  $  $  f(d$Pl$H\\\\G$  $  $  $  f($  f(t$$p  $  f(fATfATf(D$`  D$P  f(D$@  D$8  D$   $  $  5f/$   D$   D$8  D$`  $  $p  fA($  $  fA(V  D$  $  $P  $@  $8  fA(D$   D$  D$  D$p  D$`  PDT$pfE$  D$   $8  $@  A^$P  f/   D$`  1$p  fA(fD($  gt$pHǄ$@      Ǆ$      $P  |HǄ$      HǄ$      d$@   D$     A   D$0   $$%DT$pfE1 fE(fE(1fA(fA(D$     $  D<$ED$@  d$0D$P  L$  E)D9$X  ;ED$     Lt$h  f(f($ff(f(阹fA(f(f(D$  fA(<$D$  D$P  D$@  $8  D$   DD$0TDD$0<$D$  f(D$  f(D$P  D$@  $8  D$   UfA(fA(f(D$  f(D$$  $P  D$@  $8  $   D\$0D\$0D$  $  D$fD(fD($P  D$@  $8  $   fA(f(DT$pd$hD|$Pt$Hl$@DL$8D\$0DD$<$d$h<$DT$pD|$PfD(fD(t$Hl$@DL$8D\$0DD$f(fA(fA(D$   $   DT$xt$pl$hDL$PD\$HDl$@Dd$8D|$0$$^t$pD$   $   DT$xf(l$hDL$PD\$HDl$@Dd$8D|$0$$fA(fA(fA(d$xf(D|$pt$hl$PD\$HDD$@|$8DL$0D$d$xD|$pt$hl$PfD(fD(D\$HDD$@|$8DL$0D$?f(f(DT$xDl$pDd$hd$PD|$HDL$@D\$8t$0,$$d$P,$DT$xDl$pf(fD(Dd$hD|$HDL$@D\$8t$0_$@  f(f($P  $  $  $  $  $  $  f(f(f(pf(f(fA(fA($  $  B$  $  f(f(L$`D$XD$0  D$   $  $  D$0  D$   $  $  pf(f(D$0  D$   $  $  D$0  D$   $  fD(fD($  鮶1 L$`D$X@fA(d$,$&d$,$f(f(ű
  f(f($  $  $  $  f(f(p$0  $   $  $  $0  $   $  fD(fD($  gd
 L $0  $   $  $  +$0  $   $  f(f($  駴  f(f(_f(f(f(ff(f(f: f(ΉD$ D$ d$,$fD(L$h f$   df(f(ԮL$`D$X$0  $   $  +$  $   $0  f(f($  $  fD(f(f(f(fA(f(f(f(f(f(ff(f(f
  f(f($  s$  f(f(*]
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    AYfEfA(fD(D\XfE(fD(  f.     f(f(f(AYˍMAYAY\f(AYXf.  Hc,XHa  f(f(f(AYˍUAYAY\f(AYXf.  Hc,XH  f(f(f(AYˍMAYAY\f(AYXf.   Hc,XH  f(f(f(AYˍUAYAY\f(AYXf.]  Hc,XH*  f(f(f(AYˍMAYAY\f(AYXf.  Hc,XH%  f(f(f(AYDE	AYAY\f(AYXf.  Hc,XH	  f(f(f(AYˍU
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  fA(f(fA(Y̍MAYY\f(AYXf.  Hc,XH  fA(fA(fA(YˍUYY\fA(YXf.  Hc,XH   fA(fA(fA(Y̍MYY\fA(YXf.  Hc,XH
  fA(fA(fA(YэUYY\fA(YXf.h  Hc,XH  fA(fA(fA(YYY\fA(YXf.R  Hc,X    f(T$(fD(ffD)4$t$ fD(EYf(AYAYf(f(AYD\XfD.f  f(fA(fffY$fAYf(fXf\f(ff.
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  fA(fA(Hcf(XAYÍMf(f(AYAY\f(AYXf.  HcX,Hf(f(f(AYˍUAYAY\f(AYXf.  Hc,XHf(Aff   X$  X$  X$  X$  X$  X$  4  X$   X$    X$  X$     X$   X$(     X$0  X$8     X$@  X$H     X$P  X$X  	   X$`  X$h  
t{X$p  X$x  tdX$  X$  tMX$  X$  t6X$  X$  uX$  X$  ff.     fD
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 f/D$p?  I   DDf/$     An|$HfA(fE(fA(YDYYD\fA(YXfA.n  f(L$ HcH$H  H$@  DD$(|$8 $H  $@  <$|$8T$f(负T$$YP  DD$(L$ YYf(f(AYf(YY\f(AYXf.  Am  p  LIH  Y  YIEA   A'AG9$   =$   L$   4$  \$@
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 ,$f(\$(L$8H,$d$f/$   D$ ;\$(L$8f(T$ ,$^T$0f/d$$   |$Hff/TH$   H$   fL$   D0A2d$p|$|H$   \$0   $   D$hL$@
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 fA(YfA(YSD9`v\f(fA(f(H$   f(D$$D$   D$  D$  D$  $   $   脒H$   D$   f(D$$D$  D$  fD$  $   $   ffA(fA(H$  f(D$$   $   D$0  D$(  D$   $  D$  D$   D$D$   $   f(Ћ$   f(H$  D$  $  D$   D$(  D$0  QL$ f(fA(fA(H$  D$0  D$(  D$   D$  $  $   $   D)$   H$  D$0  D$(  fD(D$   f(D$  $  $   $   fD($   fA(f(f(H$  fA($  $   $   D$8  D$0  D$(  $   D$  D$   D$H$  D$8  D$0  D$f($   $  $   $   D$(  D$  D$   1fA(fA(H$  $  $   $   D$8  D$0  D$(  $   D$  D$   D$DH$  D$8  D$0  D$f(f($   $  $   $   D$(  D$  D$   fA(fA(f(H$  $  $   $   D$8  D$0  D$(  $   D$  D$   D$hH$  D$8  D$0  D$f($   $  $   $   D$(  D$  D$   fA(fA(f(H$  $  $   $   D$8  D$0  D$(  $   D$  D$   D$萍H$  D$8  D$0  D$f($   $  $   $   D$(  D$  D$   fA(f(f(H$  fA($  $   $   D$8  D$0  D$(  $   D$  D$   D$贌H$  D$8  D$0  D$f($   $  $   $   D$(  D$  D$   fA(f(f(H$  fA($  $   $   D$8  D$0  D$(  $   D$  D$   D$؋H$  D$8  D$0  D$f($   $  $   $   D$(  D$  D$   fA(f(f(H$  fA($  D$   $   D$8  D$0  D$(  $   D$  D$   D$H$  D$8  D$0  D$f($   $  D$   $   D$(  D$  D$   fA(fA(f(H$  $  $   $   D$8  D$0  D$(  $   D$  D$   D$"H$  D$8  D$0  D$f($   $  $   $   D$(  D$  D$   `fA(fA(f(H$  D$  $   $   D$8  D$0  D$(  $   D$  D$   D$IH$  D$8  D$0  D$f($   D$  $   $   D$(  D$  D$   %fA(fA(f(H$  $   $   D$0  D$(  D$   $  D$  D$   D$wH$  D$0  D$(  D$f($  $   D$   D$  $   D$   f(fA(fA(H$  f(Չ$  $   $   D$8  D$0  D$(  $   D$  D$   D$袇H$  D$8  D$0  D$f($   $  $   $   D$(  D$  D$   fA(fA(f(H$  f(Չ$  $   $   D$8  D$0  D$(  $   D$  D$   D$ƆH$  D$8  D$0  D$$   $  $   $   D$(  D$  D$   fA(fA(f(H$  $  $   $   D$8  D$0  D$(  $   D$  D$   D$H$  D$8  D$0  D$f($   $  $   $   D$(  D$  D$   nfA(f(f(H$  fA($  $   $   D$8  D$0  D$(  $   D$  D$   D$H$  D$8  D$0  D$f($   $  $   $   D$(  D$  D$   Cf(f(DL$8ADD$0H|$(t$ d$,$u|$(DD$0t$ DL$8XfA(D\
 ,$Xd$YfA(YSD9f(f(DL$8D\$0DD$(DT$ t$<$DL$8D\$0f(t$<$f(DD$(DT$ fD  f(f(\$(T$ 菃\$(T$ $T$L$@fD$h^f(f(Sf(fۉt$|$(t$ $$/|$(t$ t$$$f(7f(f(t$(d$ \$$t$(d$ \$$bD  T$8f(f(fl$(d$ 譂l$(d$ D$HL$XT$8fl$(d$ ul$(d$ D$PL$`.fA(Nf(f(JfA(f(f(|$fA(4$|$4$fD([f(f(L$@D$ht$$$t$$$f(f(5f(ff(ωt$ f(l$$$讁t$ l$$$f(f(fT$f聁D$(L$ AWfD(f(AVAUAATULSH  $P  ~
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 $H  $   f(
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 \f(f(fA*Y$A$f*YD$H[]A\A]fD   1Ҿ   A$HH=z 1[]A\A]      H,f5 fUH*f(fT\fVf(     AuA   f( Ht$HfW/ \f(f(>
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  AIE       L$YA,	  f(LfHJ*tIEAEH9tff.     @H @H9u@tHAL f= fEAWA*D*t$fD(D\DY  fA(fE(LDT$A   fHfAnfEnfo5 fEfELD fDoD|$fDp fEp fEfD  fAoH fEfofpfXfXfADfpfEXfAXfXfAXfD\f\f\f\fAYfYfAXfAXfA\fA\H@H9tD|$@  fA\$H*E)fHcA*L    XX\A\A\YAX\AȍH9  ffɃ*D)*XX\A\A\YAX\CD9=  fɉf*D)*XX\A\A\YAX\CDE_fA(fo5 fD A   HfEnHffEp H foH fAfXfpfXfD(f\fDXfD\fAYHf(f\fXf\fY@H9uA   AfACMcA*J    Xf(A\XA\YBA9}XfA*Xf(A\XA\YL9~(f*Xf(A\XA\YLA   L$D)^څ  97  D~ fHDΣ f(f.     xAf*XXYL XfD(f(fET\EYfATfD/wf(H9}YA$f     D)A   9  D~ LcENfED* f.     E   f(Ǹ   ff.     ff.          EfA)A*Yf*ȃ^D9~fA*XXBYL YDXfA(fA(fAT\AYfATf/wfA(IAD9ODYăGII9A$1^A$ff.     ATALYYAD\\\^^\ADHH9uMcHcC̰   ff.     ff.     ff.     fD  YDf(AD\ADHHLD$oLD$L1`LXH8[]A\A]A^A_E_    1A   ] A\A\YfD  9p  D~ fEHD fA(f.     xUf*XXtf(\YtXYL \f(f(fATA\AYfATf/wfD(H9}YA$r     A   DD)9  HD$LcEsfD~ AD, ff.     EE   f(ǿ   ff.     ff.     D  Df)*Yf*σ^D9~fA*XXEtfD(D\FY\DYAXBYL Y\f(f(fATA\AYfATf/wfD(IAD93HD$DYC4II9AE_u,D$fc 3 *\\YAA$^A$HLD$LD$I   ~   ff(/fE)fEfA(
f5H5Y@ @  HD$LD$HHtEHzH1LHH2H)H8  @  HMtZH   D  Mu   Mt%L^HLD$LD$LHf.     f.         UHAWAVAUATSH   EfT[ Mv uf/ȉULpLhxr,D E1A AHeD[A\A]A^A_]D  L%	? A@  ILHHt.HxHH     Hǀ8      H1H)@  HL@  HEH  HxH     E1LHǀ8      HH)HL@  H@  7IH  HxHH     Hǀ8      HLH)@  HH  D}HMLDED踄HHEUPxLMMELDDʮ^_  }HUHMDELEDf(`Rd  HUUHDxEu%Aǃ4  E}fD)ǃf.H4  .  f*XE,Ѓ?  Hu- fHHH6ff.     ff.     ff.     ff.     HH9t.f(X f(\f(fT fT Yf/vH}M8 ^`HYHpYЅ  YHhLXPH}GL=H}4A   H&f}fɉx*Y A*XEY ,f(YXL r@8x@PЃD؉(C  H}    HEfH0L AXfHEE`*MlxX\ Yx`Xf(Xf(\^fT f/vH}	  HEHEA9pH0L f(⋕XHEfEx*X`rxYP@f(Yf*(YE^8Y0(J  H`X  HUH@   fHEH Hf(ftEX*`XY\  xYx`XHXf(\^fTK f/vH}	wHEH@HEH9^H YPHEUMLMLEEuLDX(xE謿]LU\g  Hpf(Y^8YYEX0HhXYXx H}OHhLfH}]*H0L f(ދHE@HUfHH@   H HEf(fX*`Xf(\L \< YDxE謾Yx`XHXf(\^fTd f/vH}	.HEH@HEH9Rf(ffY*Exxf(fY*(YE^8Y0(f?PfYL@  HHtFHxHE1HL H)L8  HE@  HHt=H肿IH}tH7A   )LXH}OHEIL8H}/H'Lf.     D  AWAVMAUAATAU@  SHHH55 HL$ LD$(D$L$T$H<  L$HD$DHdAǃ   Aun\$f/h D$<
      L$   MHىT$L$DD$AH8HHD[]A\A]A^A_fD  LL$(LD$ HDL$D$tA[    A        HHٺMHD$DDPL$   L$ D$ZYtD$<JA   BHHoH'    USHcHH=4 YH    ,H[]f     SHcH=3 0H    [D  AW	   AVAUIATIUHSHcH  HCH=3 H    D4Et^HH% HDMtA<$ uZHG HL$      LHn% L1V
Hte莼H  []A\A]A^A_@ LLH   IH   HG L$   LH$ L1@ H=$ 费HHt!AtFA   H(H-     t\HH=  E     HH5$ 葵HHm H= tPHtAtL荺        LCfD  HH5f$ 9H@ HhH= ff.     @ H   HL$8LD$@LL$Ht7)D$P)L$`)T$p)$   )$   )$   )$   )$   H$   HL$D$   HD$HD$ D$0   HD$H   fD  UHSHèuu2uHu^H[]fD  1HS    H*t1Hi#    Ht1Hf#    HtHHH_# 1[   ] H   HL$8LD$@LL$Ht7)D$P)L$`)T$p)$   )$   )$   )$   )$   H$   HL$D$   HD$HD$ D$0   HD$^H   fD  fff.     ff.     @ WNf(Xd$d$\d$d$\\$\$d$\\$f(DD$|$Xd$A\\$\$X\\$\$\L$L$\$\L$t$l$L$\Xf(XL$L$\L$d$f(\$X\Xf(XD$D$\D$T$D$\    HHgnf(L$Y\$$$l$D$(T$(f(fW \$L$Y\$T$(Y$XXf(Xf(D$0D$0\D$8T$8D$0HH\fH  '._~f(f(d$(^\$H|$0l$Yf(t$ $p  f($p  fW B|$0t$ D$p  D$f(f(f(t$@Y|$8DD$$x  $x  fWy DD$$x  d$(XXD$fA(f(X$  $  A\$  $  \$  \fW $  $  \$  $  \$   $  $  \$(  D$(  \$HD$   l$f(A\$  \fWs $0  $0  \$8  $8  \$@  $0  $8  \$H  f(D$H  D$@  $0  AXA\Xf(AXX$P  $P  \$X  $X  $P  \Xf(X$`  $`  \$h  $h  $`  f(\f(d$(^\$0Y$   f($   fW3 L$l$ 蒮|$8L$D$   D$f(f(YDD$$   $   fW DDD$$   d$(\$0XXD$fA(f(X$   $   A\$  $  \$   \fW_ $   $   \$   $   \$   $   $   \f(\$   D$   D$   $   $   $   A\\AX$   $   l$ fW t$@L$\$   $   $   \$   D$   $   $   A\Xf(XX$   $   \$   $   $   \XX$   $   \$   $   f($   X^D$PD$P\D$Xd$XD$P\f(X\$`\$`\\$h\$h\T$pT$`\$h\T$xl$x\$pT$`\XXf(X$   $   \$   $   $   HĘ  \fD  HfH)$  H    H   gf. z6u4ff.zJuHff(fH~fH~H   HfHnfHnffr f/f(sf.     f(d$(\$k~=C H< H$   D$ fWH$   $     \$~= f(L$f(f(l$Y$   f($   fW;l$d$(\$Y\$Yt$ $   XXf(X$   $   \f($   $   \$   XL$hL$h\L$pL$p\D$xD$hL$p\f$   f(D$   DD$xXd$hA\$   $   $   $   \$   $   $   \$   f($   $   $   AX\Xf(XX$   $   \$   $   $   \f(Xf(X$   $   \$   $   $   f(\ \D$8D$8\D$@m \$@\D$HD$8\$@\D$Pt$Pl$H\$8\f(f(XXXL$XL$X\L$`L$`\L$XD  f.     ܼ f/r11fHnfHn    f/ H      HsUfSH(  f.    f.GzH      ?      = |$X% f( m ^Xl f(D$PfTf.v3H,fl$XfUH*f(fT\fVD$P|$PH|$(H 1\$ f(f(Y$h  f($h  fW b|$P-\ $h  $f(f(f(Yd$$p  $p  fW d$\$ $p  H|$(XX$f(WX$x  $x  \f($  $  \$x  \fW, $  $  \$  $  \$  $  $  \$   f(D$   $  $  \A\$(  $(  X\$0  f($0  fWw \$8  $(  $0  \$@  $@  $8  $(  \Xf(X$H  $H  \$P  f($P  $H  X\f(XX$X  $X  \$`  $`  $X  \Z YYf(D$Hf(f(Y<$$   f($   fWY ģ<$DT$H$   Oi f(f(XAYXfA(AYXf(X$   $   \$   $   $   \h Yt$ Yf(X$   $   \$   $   \$   $   $   \$   fA(D$   $   $   X$   $   A\$   $   \$   $   $   \$   f($   $   $   A\XfA(\Xf(XX$   $   \$   $   $   \Xf(X$   $   \$   $   $   \f(l$(Yd$0D$xT$xf(fW L$mL$t$ YL$HT$xY4$h XXf(X$   $   \$   $   $   \f(L$ Yt$D$`T$`f(fWg ҠL$  ܒ Y\$Yt$`l$(d$0XXf(XD$hD$h\D$pD$p\$h\f(ŃHX$  $  \$  $  \$  $  $  \$  f(D$  D$  $  XA\$  $  \$  $  \$  $  $  \$  f($  $  $  AX\Xf(XX$  $  \$   $   $  \Xf(X$  $  \$  $  \d$@$  <$L$ f(l$8Y$  f($  fW. 虞L$ \$YL$H3$  Y$t$ X[\$0Xf(X$  $  \$  $  \f(L$$  YL$($  f($  fW} \$0L$(t$ Yt$Yl$8$  d$@f(XXf(X$  $  \$  $  $  \f(fT f/ v	f(û	   X$  $  \$   $   \$(  $  $   \$0  f(D$0  D$(  $  XA\$8  $8  \$@  $@  \$H  $8  $@  \$P  f($P  $H  $8  AX\Xf(X$X  $X  \f(X$`  $`  $X  \Xf(X$h  $h  \$p  $p  $h  \f(\$Y$$  f($  fW 舛$\$$  f(Xf(YXf(YXXf(X$  $  \f($  $  \$  X$x  $x  \$  $  \$  $x  $  \$  f(D$  $  $x  XA\$  $  X\$  $  \$  $  $  \$  $  $  $  \Xf(XX$  $  \$  $  $  \f(XX$  $  \$  $  $  \؃|$X,l$Pf(X$  $  \$  $  \$   $  $  \$  $  $   $  \f(f(XXX$  $  \$  $  $  \,$fH~$fHnf(f)<$H$HT$H(  fHnfHn[]D  = f.|$X60ff.G!H> H? f.     f.     f.          f(f(ff(\f/vf(\ff/zV      % Y\ YX% YX YX% YX YX% Y\ YX% Y\| YXx ^ff/   \\^YD   5  f/YX YX5 YX YX5D Y\ YX YX Y\ Y\ Y\| ^vY^D  f Y XXY UHSHH(   =   W     Z     x  =   2  d     f1ҋ   f/       E@ǅ          \MPEp        f     =   -    =      =      =   .  EpEH   ǅ      E`H([]@ 
      O@G`f/  Wf/  Ǉ      Ǉ   
   GH      O`뎐GpO@1fW f/        f/  ǅ         ǅ      ǅ         t     Ep   f   MKM8      C         =        
  _  S0fCXf/A  f/  H( C(ǃ      H   KC8ǃ   P   fCfs0K8~% f(fD(f(ffDTf(f(f(fTfD/     fTK\$Y   T$l$r\$T$5 f(~%r Xl$Yf(Y   f(\fC`f(fTf/  ǃ      CK8   ff/  f/C0  ǃ       ǃ     @ G O(1fGHf/G   I  f/E  f/E  HǇ      D  G ff.   z6  ǅ   d   @ O1G f         f/1f/   u
f/   f/щ   ǅ          EPYEXUpǅ       EPX˒      EH   ǅ      E`H([]fD  ǅ       EHH([]ǅ         ǅ      ǅ      D   1E#   iD   1EEHǅ       EE`   I@ f/f/ǃ   1f/ǃ            EH    E`    ;f.zt{ {({@fCf(   f(f(k8f(s(f=   =     G FX f/f/ȉ   ǅ       UPYUX   ǅ       \UPʔD  G GH   Ǉ      G(GG`H([]@ EHH([]ff/@   Eǅ      MpXMPp f/rRf/	     EH   M E`fT7 YE0ǅ   Z   EPVf     H H   :f/K0f/ǃ      ǃ        H    H   ǅ     EH   U`   CXH f(C0fH      HK H   HǇ       |D   s(fA(f   ff/K  fTf(Ë      A\YCp   ǃ       f(\fcxf/+  r  ff.    f(   XH s@H   f(f{ S   ǃ   1f/ǃ          eGH    Ǉ      \c@fD(fDfDffA\fDK fEfE\fA^YfD(cHfYDYCpA\~ %Q fD(fDUf(fTfDVfA(~- fWfWCpcxt1f(Yf/f(Yf/f(^XCp   E@EHǅ         E`Fcx뎃P=   u^CXfC0YC8f/r)CC(C81   f        f.Chztً   =   aǃ   f.     H(L$D$[T$L$D$f( t$%* f(6 D5 f(f(fD(^D^fD(DXA^EYA^f(fD(YDXfD(fD(f(DXEYDY DXDX^EYDXDXAYDY- XXYAYXX^YAYXAYAXf(x AYDYYAXYAYAXf(AXY\Z AYDD YAXXYf(Yf(\/ H(Yf(AX^Xff.     ff(tV f/J  SH UW f/   =C^ { |$^! L$YY\ YX Y\ YX ^D$f(TL$f(f(\-^ f(YXD$\XD$H [\,؅M 1f(ff.         f*XY9uf(\$L$ćD] L$\$\f*T$XD   f/   > f(f\Yf/wJ \n Yf(\ X^ YYX XN YXJ YXF YXB YX> YX: YYXB XB ^Y齆D   p f/f(@f.     ^Xf/w#ff.     f= f(f(fT( f/sJH(L f/   f/   fL f/w H( f(̽ % Y Y\ YX YX| YX YXl YYXd XX^Y 5H f(~%T T$L$^fWYf(<$Yt$tt$<$f(  ~% T$YL$X YfWX] YX YXM YXq YX= YX YX- Y^E \ Y^f\X H(fWfTfUfVf( ~0 f(T$$fWYdT$-N f( $X~ YX YX-! YXݻ YX- YXͻ YX- YX YX- YX YX- YX YYX XŻ ^ Y\q H(XffWfTfUfVf(ff.     f(f(fT  f/   f/nO   ff(X  XYX YX YX YX YX YX Y^ f(\Xff/wH f(f(f(fTf(@ H84 f/    T$ 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D$   AYD|$`AYXd$H$   T$@X: XL$XxD$8fHnxDT$8DL$ DY$   \$0D\D\T$xY\$pfA(AXDL$8XpT$@-5 D$ f(Xf(+xd$H=9 D$0Xd$Pf(x\$0$   T$pDL$8\t$8Yf(\D$xAXXt$8$   D$   D|$`fD(D$0f(fD(|$HDl$ XfE(DD$@D\$hL$X|$fE(D|$8DD$(-4  f(EXEX:9 ^$$fD(XDXXX8 XDYf(^fA(DYfA(AYAYXf(\AYXfT1 AYA^DYf(^f(XDY Yf/Fd$P$Dt$(D|$8f(DD$@|$HXDd$hDl$XfD(X8 DXY\$0DYT$ f(\AYAY^D^nf.     f(D$fT0 XDXf(X7 XfE(EYD\EYA^A^Y# Yf/DYs^f(E\D\57 A^fA(DY7 X\A^f/AYYfA(YXX>F7 Yf(f-2 f(f(f($\f$ff/L$f(f),$wf(f),$H$HD$H   fHnfHn[A^fD  H,ffUH*fVf(4f     H      ?1ff/D$wH1랐fA(fW#0 H   [A^l@ D$H   [A^ff.     AUf(1   ATUSHH  f(6 H$  Hl$0$  H)$      HHf(5 Hڵ )$0  ff/H$X    DS1 fD/fA(  f/  fD/  f/f(  f/fD(  fD/  f/d  fD/  f(~- L$- X#5 t$fT\\f/C  fA(DT$ Xd$fT\\f/+  YHL$   l$(L$`  W$H  D$`  D$  l$(   |$t$D 0 d$f/DT$   fA/  fHLd$ \D$  DT$l$|$D$`  Ǆ$H     $   V$H  D$`  D$  |$l$DT$Ds/ d$ _  1ffD  ffEɸCHDkH  []A\A]@ ffEɸ     f(fA(f(l$(A\AXfA(d$DT$t$DL$ t$HLDL$ D$  Ǆ$H     \D$`  $   U$H  D$`  D$  t$DT$d$DM. l$(fA/.fA(HLD$  \d$ DT$l$t$D$`  Ǆ$H     $   U$H  D$`  D$  t$l$D- DT$d$ ^3ffA(fEɸB@ fEɸfA(*@ ffEɸD  fA(ff.     f(fA(fA(l$(A\AXf(d$DT$|$DL$ |$HLDL$ D$  Ǆ$H     \D$`  $   S$H  D$`  D$  |$DT$d$D}, l$(ifEɸ   fA(fEɸ   fA(   E   fAUf(1   ATfD(USHH  f(X0 X H$  Hl$0H)$      HHH f(.0 $X  )$0  ff/H$@  H H$    5+ f/  f/$  f/  fD/  f/fD(  f/  f/  f/z  f(L$D~'( ( Xc/ DD$l$fAT\\f/,  fA(DL$(Xd$ fAT\\f/  L$   H$`  LQ$H  D$`  D$     |$l$5h* d$ f/DL$(DD$  ffE/  fHLd$ \D$  DL$DD$|$D$`  Ǆ$H     $   "Q$H  D$`  D$  |$DD$DL$d$ 5) ^1fu)E  5     ffEҸCHDsH  []A\A]@ ffEҸ     ffEҸfA(fA(f(DD$ A\XfA(d$DL$l$DT$(l$HLDT$(D$  Ǆ$H     \D$`  $   O$H  D$`  D$  l$DL$d$5m( DD$ fE/-f(HLd$ \D$  DL$DD$l$D$`  Ǆ$H     $   :O$H  D$`  D$  l$5' DD$DL$d$ ^ffEҸ3D  fEҸfA(@ fA(fA(fA(DD$ A\Xf(d$DL$|$DT$(|$HLDT$(D$  Ǆ$H     \D$`  $   <N$H  D$`  D$  |$DL$d$5& DD$ xfEҸ   :fEҸ   +5     AVf(1   AUf(ATUSHH   f(*  H$8  Hl$PH)$      HHHM f(* $x  )$P  ff/H$`  H H$0  r{-% f/rqf/   f/   f/T$i  f/\$q  f(d$ X\) t$\) f/}" vKf   ffCH;kH   []A\A]A^@ ffΐL$   H$  LTL$h  $  D$  s  T$f-$ t$d$ f.DD$z  AYT$ u  f\$ f(^\( fYf/t  fD(ɺ    ( fA.AYEtfA.E;  fEfD/+  f/!  fD/  f/  H|$0DD$(t$d$|$d$t$L$0D$8f/|$DD$(   f.     \HLD$  DD$t$d$$  Ǆ$h     $@  J$h  $  D$  d$t$DD$-K#    D$ f(X^f/' mf(\rf/ff(>\f(5f/   f\fI~f     HLD$  $  L$@  Ǆ$h     I$h  $  D$  t@ 1fEuF-t    f.     ff(fD  ff(-F    \fI~ff.     HLD$  $  L$@  Ǆ$h     I$h  $  D$  t/ff.     @ AV1   f(AUfATUSHH   f/H$8  Hl$PD$f(% H   HT$HHm  )$   f(% \$H$`  H( $x  H$0  )$P  Y  a f/K  l$f/  |$f/  f/d$   L$   H$  LG$h  $  D$    l$f\$ f/x  f/$ Ll$0wW  @ HLD$  $  Ǆ$h     aG$h  $  D$  \$(v  D$T$f(Ld$ \$(D$0D$@\D$d$ $@  g
   f@ ffSH#CH   []A\A]A^@ p \# ffYf/wzf(-#     Yl$f.Etf.EuGff/w=f/ w3f/w-f/ w#f(H|$0d$ D$8d$  \D$HLD$  $  Ǆ$h     $@  E$h  $  D$     \$l$Yf(X^f/-" f(^G \fD  ff(fD  ff(sfD  ff([fD  \L$fI~ff.     fHLD$  $  L$@  Ǆ$h     D$h  $  D$  t1fEux    ~    ff.     AV1   f(AUfATUSHH   f/H$8  Hl$PD$f(`! H   HT$HH E )$   f(=! \$H$`  H $x  H$0  )$P  Y   f/K  l$f/w  |$f/w  f/d$ G  L$   H$  L{C$h  $  D$    l$f\$ f/   f/p  Ll$0wW  @ HLD$  $  Ǆ$h     C$h  $  D$  \$(  D$L$f(Ld$ \$(&D$0D$@\D$d$ $@  g
   f@ ffSH#CH   []A\A]A^@ ff(ΐff(뾐ff(뮐\L$fI~D  HLD$  $  L$@  Ǆ$h     A$h  $  D$  t1fBEd  t    'f.     |$Y|$   \$2 ^\-z ffYf/wxf.    W YL$Etf.EuIff/w?f/ w5f/w/f/ w%f(H|$0d$ AD$8d$ D  \D$HLD$  $  Ǆ$h     $@  @$h  $  D$  D$f(X^f/  \(    fD  AV1f(   AUfATUSHH   f/D$ H$X  f( Hl$pH   HT$H H] )$@  f( \$H$P  d$$  )$p     f/  t$f/   f/  f/  L$@  H$  L@?$  $  D$    t$ff/     fD  D$T$f(H|$0L$d$(JD$0D$@\D$ d$($`    HLD$  $  Ǆ$     >$  $  D$  g  f/% ]L$\$f    l$YYV f(f(Y-F Xf.^Ef.E!f/  :  u&^5 f(\f/wf/*  f\D$ $`  	@ ffSH#CH   []A\A]A^@ ff(f     ff(붐\L$ fI~D  HLD$  $  L$`  Ǆ$     !=$  $  D$  t1fJ   E<o    *D  
   ffft \f(H|$Pd$(D$Xd$( AVf(1   AUf(ATUSHH   f(w w H$8  Hl$PH)$      HHH f(M $x  )$P  ff/H$0    5 f/  f/  f/  f/$  f/f(  f/  f/  f/  f( D@ l$X|$\\fA/N  f(T$ XfT d$\\fA/.  L$   H$  L;$h  D$  D$  `  T$ f5 d$|$f.l$D$zfI~p  ff.z  f    fD.ADE   f.     \f(HLD$  d$ T$DL$|$,$D$  Ǆ$h     $@  ):,$$h  D$  D$  |$DL$T$d$ 5 Q  fA(fXf/  f.˺    Et	E  fA(f(H|$0|$(l$ DD$d$T$D$ֵL$0D$8D$T$d$DD$l$ |$(f/\ffEfA(CHDsH   []A\A]A^ÐfEfA(    fEfA(    fEfA(fIn\HL,$D$  |$D$  Ǆ$h     $@  z8,$$h  D$  D$  |$5    f/sf(\|ffEfA(ff(fE   fE   f/   \fI~HLD$  D$  L$@  Ǆ$h     7$h  D$  D$  t1f`   ER5;    @\fI~HLD$  D$  L$@  Ǆ$h     (7$h  D$  D$  tuD  AV1   AUATUSHH   f(= D H$8  Hl$PH)$      HHf(= Ht D$x  )$P  ff/H$0  D  f(8 f/.  f/f(P  f/F  f/T$  f/fD(?  f/5  f/  f/  f(% = l$Xt$\\f/  fA(DL$(XfT d$ \\f/  L$   HD$  L5$h  $  D$  R  fDL$(" d$ t$fD.l$T$zp  ff.z  Xf/fI~B  fff.      f/X  f(fA(f(d$ H|$0fInDL$l$|$!l$HLD$0|$D$  Ǆ$h     $  \$@  {4$h  f$  D$  l$DL$d$ C#  fD  ff(ǉCH;CH   []A\A]A^@ ff(f     ff(f\HLD$  t$l$$  Ǆ$h     $@  3$h  $  D$  l$t$6 M  f/rf(\|D  ff(f\HLD$  t$l$$  Ǆ$h     $@  2$h  $  D$  l$t$    f/sf(\|fff(sf(HLd$\D$  DL$l$$  Ǆ$h     $@  S2$h  f$  D$  l$DL$d$1f   E    f   f   fff.     f/   f(fA(f(d$ H|$0fInDL$t$|$t$HLD$8|$D$  Ǆ$h     $  \$@  ;1$h  f$  D$  t$DL$d$ CfD  f(HLd$\D$  DL$t$$  Ǆ$h     $@  0$h  f$  D$  t$DL$d$USfHHf/T$$v3~G$T$1Y\ӉCHHC    H[ÐfҸD  SHHT$$(GT$\$HC    HC    ^H[ff.     fAV1   f(AUf(ffI~ATUSHH  f( f/ H$   Hl$H   H)$   HH@ f( $8  H$   H )$  H$   R   f/D  f/f  f/`  f(- \$XfT $$\\f/   L$   H$@  L.$(  $@  D$     $$\$f/   f(fIn$$l$׿$$HLl$D$  Ǆ$(     \$@  $   .$(  $$$@  D$  t1fu(E        ffCH+CH  []A\A]A^@ ffΐf(fIn$l$$HLl$D$  Ǆ$(     \$@  $   8-$(  $$@  D$  tf   ?fX    +ff.      AU1f(   ATUSHH  D$H$  f(	 Hl$ H   H$H)$   Hp f(	 H$0  H )$   ff/H$   Hz H$H     l f/   L$ f( f.f(   <$f/=C     l$f/   Xl$ f(fT \\f/k vyff/w_ f۸   @ ff۸CHCH  []A\A]fD   f۸D  f۸f(붐HQ d$L$   H$P  P$f(f(\$d$R\D$\$Ǆ$8     D$  $P  $  HL*$8  $P  D$  d$t1f	EtW    D  0    fD  AW1   f(AVfAUATUSHH  f/H$   Hl$$f(/ H   HHHJ )$   f(* H$   H )$  H$   H H$8  rj f/r`f.  f/  X$% f(fTO \\f// vMff/w# fҺ   ffҺSHCH  []A\A]A^A_f f(\$L$   q \$F fI~f(H fI~H$@  GffInfInT$\$T$Ǆ$(     D$  $@  $   HLp($(  $@  D$  t1f   E    @ fҺf(fD  fҺf(fD  fD(ffD/<  UfD(SHHf/ D% EY-  AY,څ  kf*Dl$ DL$T$4fT$*$f(l$^l$T$Y\\$pl$fDl$ DL$fD(fD%6 f(T$XfD/AXAYvWfA(f(l$(T$DD$DL$$zH$DL$T$l$(f(DD$Dl$ ` l$8Dl$0XL$(T$ DD$\$DL$r3DL$$fA(L\$DL$YA\\$\DD$L$(f(fD(D5C D=R fA(T$ DL$fE(YDl$0l$8fD%  f(AYf/rQtMf*f(X^AXAYA^DYDYAXf(XAYXfA/sD f(f     f(AYf/r]X- f(fE(f(\^f*DYf(XAXAYAYXD^fA/AYXsfA(f(\AXfHHf(f[]           f(X f(f    fD/wf(9     f(fA(AYFfoflfof.     f.     f.     fH~fofoH f(fnfH~H .(fnzwuu.z  f.      .      < 0 L$D$\D$D$(T$D$~D$fD  f    .Et.EuMf.zu/  v%  /wD\$L$~L$T$D$~D${ /((h4@ H,fH*.zuH@H  H   HPcH   xH  fHHHи   !    (YYY\(XHt!((YYYYX\(HH9}f/ (TT/  .Ժ    E   .E   b ^^(If.     @ f.((YYY\X((((Y(YYX\(YYYY\X((( ^YX(^fY\X YY( ^YX(YX\f ^YY(If.     f    f.Et!f.Et ffD  f    f(f.f(EtQf.EtCf/f(f(wU| L$D$\D$D$a~ f(@ ff.R  L  f/ >  %Ƒ f/,  H,fH*f.    H-H   H  HPcH      H= fHHHf(Ǹ   "fD  f(YYY\f(XHt$f(f(YYYYX\f(HH9~ff/~ f(fTfTf/   f.ú    E   f.E   ^^f(f(D  ÿf(f(YYY\Xf(f(f(f(YYYX\f(Yf(YYY\Xf(f(f(f(^YXf^f(Y\XYYf(f(^Yf(YXXf(\^YYff.     @ l$    l$l$(l$8Et+Et/
     f.     ú    Et%Et)  ff.               L$l$    H|$/H|$I  H|$^  HD$HcH=      HT$   HHHT$<ff.     ff.     ff.      HtHH9~   q@f6     &     |$(|$8|$|$K $ |$l$l$|$l$ r0    EtDEt<N)D  fH~D$H D$~D$邸ffH~foH fnf.     fH~D$H D$~D$´ffH~D$H D$~D$ffH~D$H D$~D$BffH~D$H D$~D$¹ffH~D$H D$~D$鲴ffH~D$H D$~D$BffH~D$H D$~D$钴ffH~D$H D$~D$鲰ffH~D$H D$~D$"ffH~D$H D$~D$"ffH~D$H D$~D$邲ffH~D$H D$~D$ffH~D$H D$~D$ffH~D$H D$~D$ffH~D$H D$~D$鲰f鋸ff.     f(f(f(ff.     @ {ff.     ff.     髴ff.     ff.     ˰ff.     ˴ff.     髳ff.     黵ff.     ۭff.     Kff.     黵ff.     ff.     ۬ff.     ff.     鋲ff.     黵ff.     l$l$|$|$髵ff.     黶ff.     ۵ff.     ff.     鋱ff.     髰ff.     [ff.     ;ff.     Kff.     ff.     ff.     Kff.     [ff.     Kff.     ff.     雴   HH                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           invalid input argument _err_test_function _cython_3_2_4 eval_genlaguerre invalid value for n invalid value for p invalid signm or signn failed to allocate memory V invalid condition on `p - 1` needs an argument %.200s() %s takes no keyword arguments takes exactly one argument %.200s() %s (%zd given) takes no arguments Bad call flags for CyFunction <cyfunction %U at %p> __pyx_capi__ __loader__ loader __file__ origin __package__ parent __path__ submodule_search_locations eval_hermitenorm hyperu an integer is required keywords must be strings q xn ompr btdtrik Computational error Unknown error. eval_hermite float division scipy.special._boxcox.boxcox __init__ exactly stdtridf nrdtrisd std nrdtrimn nctdtrinc nctdtridf nbdtrin btdtrin ncfdtrinc ncfdtridfn ncfdtridfd nbdtrik numpy._core._multiarray_umath numpy.core._multiarray_umath _UFUNC_API _UFUNC_API not found _UFUNC_API is NULL pointer numpy.import_ufunc _ARRAY_API _ARRAY_API is NULL pointer numpy.import_array name '%U' is not defined scipy/special/_ufuncs.pyx builtins cython_runtime __builtins__ does not match decompress zlib numpy dtype flatiter broadcast ndarray generic number unsignedinteger complexfloating flexible character variable scipy.special._ufuncs_cxx scipy.special._ellip_harm_2 scipy._cyutility _beta_pdf _beta_ppf _binom_cdf _binom_isf _binom_pmf _binom_ppf _binom_sf _cauchy_isf _cauchy_ppf _cosine_cdf _cosine_invcdf _ellip_harm _factorial _hypergeom_cdf _hypergeom_mean _hypergeom_pmf _hypergeom_sf _hypergeom_skewness _hypergeom_variance _igam_fac _invgauss_isf _invgauss_ppf _kolmogc _kolmogci _kolmogp _lanczos_sum_expg_scaled _landau_cdf _landau_isf _landau_pdf _landau_ppf _landau_sf _lgam1p _nbinom_cdf _nbinom_isf _nbinom_kurtosis_excess _nbinom_mean _nbinom_pmf _nbinom_ppf _nbinom_sf _nbinom_skewness _nbinom_variance _ncf_isf _ncf_kurtosis_excess _ncf_mean _ncf_pdf _ncf_sf _ncf_skewness _ncf_variance _nct_isf _nct_kurtosis_excess _nct_mean _nct_pdf _nct_sf _nct_skewness _nct_variance _ncx2_isf _ncx2_pdf _ncx2_sf _sf_error_test_function Private function; do not use. _skewnorm_cdf _skewnorm_isf _skewnorm_ppf _smirnovc _smirnovci _smirnovp _stirling2_inexact _struve_asymp_large_z _struve_bessel_series _struve_power_series agm betainc betaincc betainccinv betaincinv btdtria btdtrib chdtr chdtrc chdtri chdtriv chndtr chndtridf chndtrinc chndtrix elliprc elliprd elliprf elliprg elliprj erfcinv erfinv eval_chebyc eval_chebys eval_chebyt eval_chebyu eval_gegenbauer eval_jacobi eval_laguerre eval_legendre eval_sh_chebyt eval_sh_chebyu eval_sh_jacobi eval_sh_legendre expn fdtrc gdtr gdtrc gdtria gdtrib gdtrix hyp0f1 inv_boxcox inv_boxcox1p kl_div kolmogi kolmogorov lpmv nbdtr nbdtrc nbdtri ncfdtr ncfdtri nctdtr nctdtrit ndtri ndtri_exp owens_t pdtr pdtrc pdtri pdtrik poch powm1 pseudo_huber rel_entr round shichi sici smirnov smirnovi spence stdtr stdtrit tklmbda wrightomega cannot import name %S init scipy.special._ufuncs __enter__ __exit__ scipy.special._ufuncs.geterr items keys scipy.special._ufuncs.seterr __reduce__ __module__ __dictoffset__ __vectorcalloffset__ __weaklistoffset__ func_doc __doc__ func_name __name__ __qualname__ func_dict __dict__ func_globals __globals__ func_closure __closure__ func_code __code__ func_defaults __defaults__ __kwdefaults__ __annotations__ _is_coroutine CythonUnboundCMethod hyp2f1 psi k1e chyp1f1 hypU itstruve0 it2struve0 itmodstruve0 airye: exp10 k0 k0e k1 kve: spherical_kn sindg cosdg tandg cotdg Computational Error spherical_in spherical_yn digamma hankel2e: hankel1: hankel1e: hankel2: jv: jv(yv): spherical_jn bei ker kei berp beip kerp keip klvna mathieu_a wright_bessel pbwa memory allocation error pro_cv obl_cv mathieu_modcem1 mathieu_modsem1 mathieu_modcem2 mathieu_modsem2 pbdv pbvv pro_ang1 prol_ang1 obl_ang1 pro_ang1_cv obl_ang1_cv pro_rad1 pro_rad1_cv obl_rad1 obl_rad1_cv pro_rad2_cv pro_rad2 obl_rad2 obl_rad2_cv y1 jv y0 zeta kv: erf erfc ellpe ellpk ellik ellpj lambertw Gamma lgam igam lbeta incbet incbi gammaincc gammainc gammaincinv gammainccinv ikv_temme iv(iv_asymptotic) ikv_temme(CF1_ik) ikv_temme(temme_ik_series) ikv_temme(CF2_ik) ikv_asymptotic_uniform Jv yv: yv yv(jv): yve: ive: ive(kv): iv: iv(kv): loggamma jve: jve(yve): struve mathieu_b airy: mathieu_sem mathieu_cem ? scipy.special/%s: (%s) %s scipy.special/%s: %s scipy.special SpecialFunctionWarning SpecialFunctionError floating point overflow floating point underflow floating point invalid value no error singularity too slow convergence loss of precision no result obtained domain error other error memory allocation failed     polynomial defined only for alpha > -1          Shared Cython type %.200s is not a type object  Shared Cython type %.200s has the wrong size, try recompiling   __int__ returned non-int (type %.200s).  The ability to return an instance of a strict subclass of int is deprecated, and may be removed in a future version of Python. __int__ returned non-int (type %.200s)  %.200s does not export expected C %.8s %.200s   C %.8s %.200s.%.200s has wrong signature (expected %.500s, got %.500s)  Interpreter change detected - this module can only be loaded into one interpreter per process.  polynomial only defined for nonnegative n       can't convert negative value to sf_action_t     value too large to convert to sf_action_t       unbound method %.200S() needs an argument       __annotations__ must be set to a dict object    __kwdefaults__ must be set to a dict object     changes to cyfunction.__kwdefaults__ will not currently affect the values used in function calls        __defaults__ must be set to a tuple object      changes to cyfunction.__defaults__ will not currently affect the values used in function calls  __qualname__ must be set to a string object     __name__ must be set to a string object %.200s.%.200s is not a type object      %.200s.%.200s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObject      cannot fit '%.200s' into an index-sized integer Input parameter %s is out of range      Answer appears to be lower than lowest search bound (%g)        Answer appears to be higher than highest search bound (%g)      Two internal parameters that should sum to 1.0 do not.  non-integer arg n is deprecated, removed in SciPy 1.7.x  while calling a Python object  NULL result without error in PyObject_Call      floating point number truncated to an integer   can't convert negative value to sf_error_t      value too large to convert to sf_error_t        scipy.special._boxcox.boxcox1p  scipy.special._hyp0f1._hyp0f1_cmplx     scipy.special._hyp0f1._hyp0f1_real      scipy.special._hyp0f1._hyp0f1_asy       %.200s() takes %.8s %zd positional argument%.1s (%zd given)     scipy/special/_ufuncs_extra_code.pxi    scipy.special._ufuncs.errstate.__init__ _multiarray_umath failed to import      _UFUNC_API is not PyCapsule object      ../../tmp/build-env-vm5wde73/lib/python3.11/site-packages/numpy/__init__.cython-30.pxd  _ARRAY_API is not PyCapsule object      module compiled against ABI version 0x%x but this version of numpy is 0x%x      module was compiled against NumPy C-API version 0x%x (NumPy 1.23) but the running NumPy has C-API version 0x%x. Check the section C-API incompatibility at the Troubleshooting ImportError section at https://numpy.org/devdocs/user/troubleshooting-importerror.html#c-api-incompatibility for indications on how to solve this problem.       FATAL: module compiled as unknown endian        FATAL: module compiled as little endian, but detected different endianness at runtime   '%.200s' object is not subscriptable    scipy/special/_ufuncs_extra_code_common.pxi     Module '_ufuncs' has already been imported. Re-initialisation is not supported. compile time Python version %d.%d of module '%.100s' %s runtime version %d.%d   Failed to import '%.20s.decompress' - cannot initialise module strings. String compression was configured with the C macro 'CYTHON_COMPRESS_STRINGS=%d'.        _beta_pdf(x, a, b)

Probability density function of beta distribution.

Parameters
----------
x : array_like
    Real-valued such that :math:`0 \leq x \leq 1`,
    the upper limit of integration
a, b : array_like
       Positive, real-valued parameters

Returns
-------
scalar or ndarray _beta_ppf(x, a, b)

Percent point function of beta distribution.

Parameters
----------
x : array_like
    Real-valued such that :math:`0 \leq x \leq 1`,
    the upper limit of integration
a, b : array_like
       Positive, real-valued parameters

Returns
-------
scalar or ndarray       _binom_cdf(x, n, p)

Cumulative density function of binomial distribution.

Parameters
----------
x : array_like
    Real-valued
n : array_like
    Positive, integer-valued parameter
p : array_like
    Positive, real-valued parameter

Returns
-------
scalar or ndarray    _binom_isf(x, n, p)

Inverse survival function of binomial distribution.

Parameters
----------
x : array_like
    Real-valued
n : array_like
    Positive, integer-valued parameter
p : array_like
    Positive, real-valued parameter

Returns
-------
scalar or ndarray      _binom_pmf(x, n, p)

Probability mass function of binomial distribution.

Parameters
----------
x : array_like
    Real-valued
n : array_like
    Positive, integer-valued parameter
p : array_like
    Positive, real-valued parameter

Returns
-------
scalar or ndarray      _binom_ppf(x, n, p)

Percent point function of binomial distribution.

Parameters
----------
x : array_like
    Real-valued
n : array_like
    Positive, integer-valued parameter
p : array_like
    Positive, real-valued parameter

Returns
-------
scalar or ndarray _binom_sf(x, n, p)

Survival function of binomial distribution.

Parameters
----------
x : array_like
    Real-valued
n : array_like
    Positive, integer-valued parameter
p : array_like
    Positive, real-valued parameter

Returns
-------
scalar or ndarray       _cauchy_isf(p, loc, scale)

Inverse survival function of the Cauchy distribution.

Parameters
----------
p : array_like
    Probabilities
loc : array_like
    Location parameter of the distribution.
scale : array_like
    Scale parameter of the distribution.

Returns
-------
scalar or ndarray   _cauchy_ppf(p, loc, scale)

Percent point function (i.e. quantile) of the Cauchy distribution.

Parameters
----------
p : array_like
    Probabilities
loc : array_like
    Location parameter of the distribution.
scale : array_like
    Scale parameter of the distribution.

Returns
-------
scalar or ndarray      _cosine_cdf(x)

Cumulative distribution function (CDF) of the cosine distribution::

             {             0,              x < -pi
    cdf(x) = { (pi + x + sin(x))/(2*pi),   -pi <= x <= pi
             {             1,              x > pi

Parameters
----------
x : array_like
    `x` must contain real numbers.

Returns
-------
scalar or ndarray
    The cosine distribution CDF evaluated at `x`.       _cosine_invcdf(p)

Inverse of the cumulative distribution function (CDF) of the cosine
distribution.

The CDF of the cosine distribution is::

    cdf(x) = (pi + x + sin(x))/(2*pi)

This function computes the inverse of cdf(x).

Parameters
----------
p : array_like
    `p` must contain real numbers in the interval ``0 <= p <= 1``.
    `nan` is returned for values of `p` outside the interval [0, 1].

Returns
-------
scalar or ndarray
    The inverse of the cosine distribution CDF evaluated at `p`.   Internal function, use `ellip_harm` instead.    Internal function, do not use.  _hypergeom_cdf(x, r, N, M)

Cumulative density function of hypergeometric distribution.

Parameters
----------
x : array_like
    Real-valued
r, N, M : array_like
    Positive, integer-valued parameter

Returns
-------
scalar or ndarray    _hypergeom_mean(r, N, M)

Mean of hypergeometric distribution.

Parameters
----------
r, N, M : array_like
    Positive, integer-valued parameter

Returns
-------
scalar or ndarray    _hypergeom_pmf(x, r, N, M)

Probability mass function of hypergeometric distribution.

Parameters
----------
x : array_like
    Real-valued
r, N, M : array_like
    Positive, integer-valued parameter

Returns
-------
scalar or ndarray      _hypergeom_sf(x, r, N, M)

Survival function of hypergeometric distribution.

Parameters
----------
x : array_like
    Real-valued
r, N, M : array_like
    Positive, integer-valued parameter

Returns
-------
scalar or ndarray       _hypergeom_skewness(r, N, M)

Skewness of hypergeometric distribution.

Parameters
----------
r, N, M : array_like
    Positive, integer-valued parameter

Returns
-------
scalar or ndarray    _hypergeom_variance(r, N, M)

Mean of hypergeometric distribution.

Parameters
----------
r, N, M : array_like
    Positive, integer-valued parameter

Returns
-------
scalar or ndarray        _invgauss_isf(x, mu, s)

Inverse survival function of inverse gaussian distribution.

Parameters
----------
x : array_like
    Positive real-valued
mu : array_like
    Positive, real-valued parameters
s : array_like
    Positive, real-valued parameters

Returns
-------
scalar or ndarray _invgauss_ppf(x, mu)

Percent point function of inverse gaussian distribution.

Parameters
----------
x : array_like
    Positive real-valued
mu : array_like
    Positive, real-valued parameters

Returns
-------
scalar or ndarray   _landau_cdf(x, loc, scale)

Cumulative distribution function of the Landau distribution.

Parameters
----------
x : array_like
    Real-valued argument
loc : array_like
    Real-valued distribution location
scale : array_like
    Positive, real-valued distribution scale

Returns
-------
scalar or ndarray       _landau_isf(p, loc, scale)

Inverse survival function of the Landau distribution.

Parameters
----------
p : array_like
    Real-valued argument between 0 and 1
loc : array_like
    Real-valued distribution location
scale : array_like
    Positive, real-valued distribution scale

Returns
-------
scalar or ndarray      _landau_pdf(x, loc, scale)

Probability density function of the Landau distribution.

Parameters
----------
x : array_like
    Real-valued argument
loc : array_like
    Real-valued distribution location
scale : array_like
    Positive, real-valued distribution scale

Returns
-------
scalar or ndarray   _landau_ppf(p, loc, scale)

Percent point function of the Landau distribution.

Parameters
----------
p : array_like
    Real-valued argument between 0 and 1
loc : array_like
    Real-valued distribution location
scale : array_like
    Positive, real-valued distribution scale

Returns
-------
scalar or ndarray _landau_sf(x, loc, scale)

Survival function of the Landau distribution.

Parameters
----------
x : array_like
    Real-valued argument
loc : array_like
    Real-valued distribution location
scale : array_like
    Positive, real-valued distribution scale

Returns
-------
scalar or ndarray       _nbinom_cdf(x, r, p)

Cumulative density function of negative binomial distribution.

Parameters
----------
x : array_like
    Real-valued
r : array_like
    Positive, integer-valued parameter
p : array_like
    Positive, real-valued parameter

Returns
-------
scalar or ndarray  _nbinom_isf(x, r, p)

Inverse survival function of negative binomial distribution.

Parameters
----------
x : array_like
    Real-valued
r : array_like
    Positive, integer-valued parameter
p : array_like
    Positive, real-valued parameter

Returns
-------
scalar or ndarray    _nbinom_kurtosis_excess(r, p)

Kurtosis excess of negative binomial distribution.

Parameters
----------
r : array_like
    Positive, integer-valued parameter
p : array_like
    Positive, real-valued parameter

Returns
-------
scalar or ndarray    _nbinom_mean(r, p)

Mean of negative binomial distribution.

Parameters
----------
r : array_like
    Positive, integer-valued parameter
p : array_like
    Positive, real-valued parameter

Returns
-------
scalar or ndarray  _nbinom_pmf(x, r, p)

Probability mass function of negative binomial distribution.

Parameters
----------
x : array_like
    Real-valued
r : array_like
    Positive, integer-valued parameter
p : array_like
    Positive, real-valued parameter

Returns
-------
scalar or ndarray    _nbinom_ppf(x, r, p)

Percent point function of negative binomial distribution.

Parameters
----------
x : array_like
    Real-valued
r : array_like
    Positive, integer-valued parameter
p : array_like
    Positive, real-valued parameter

Returns
-------
scalar or ndarray       _nbinom_sf(x, r, p)

Survival function of negative binomial distribution.

Parameters
----------
x : array_like
    Real-valued
r : array_like
    Positive, integer-valued parameter
p : array_like
    Positive, real-valued parameter

Returns
-------
scalar or ndarray     _nbinom_skewness(r, p)

Skewness of negative binomial distribution.

Parameters
----------
r : array_like
    Positive, integer-valued parameter
p : array_like
    Positive, real-valued parameter

Returns
-------
scalar or ndarray  _nbinom_variance(r, p)

Variance of negative binomial distribution.

Parameters
----------
r : array_like
    Positive, integer-valued parameter
p : array_like
    Positive, real-valued parameter

Returns
-------
scalar or ndarray  _ncf_isf(x, v1, v2, l)

Inverse survival function of noncentral F-distribution.

Parameters
----------
x : array_like
    Positive real-valued
v1, v2, l : array_like
    Positive, real-valued parameters

Returns
-------
scalar or ndarray   _ncf_kurtosis_excess(v1, v2, l)

Kurtosis excess of noncentral F-distribution.

Parameters
----------
v1, v2, l : array_like
    Positive, real-valued parameters

Returns
-------
scalar or ndarray    _ncf_mean(v1, v2, l)

Mean of noncentral F-distribution.

Parameters
----------
v1, v2, l : array_like
    Positive, real-valued parameters

Returns
-------
scalar or ndarray  _ncf_pdf(x, v1, v2, l)

Probability density function of noncentral F-distribution.

Parameters
----------
x : array_like
    Positive real-valued
v1, v2, l : array_like
    Positive, real-valued parameters

Returns
-------
scalar or ndarray        _ncf_sf(x, v1, v2, l)

Survival function of noncentral F-distribution.

Parameters
----------
x : array_like
    Positive real-valued
v1, v2, l : array_like
    Positive, real-valued parameters

Returns
-------
scalar or ndarray    _ncf_skewness(v1, v2, l)

Skewness of noncentral F-distribution.

Parameters
----------
v1, v2, l : array_like
    Positive, real-valued parameters

Returns
-------
scalar or ndarray  _ncf_variance(v1, v2, l)

Variance of noncentral F-distribution.

Parameters
----------
v1, v2, l : array_like
    Positive, real-valued parameters

Returns
-------
scalar or ndarray  _nct_isf(x, v, l)

Inverse survival function of noncentral t-distribution.

Parameters
----------
x : array_like
    Real-valued
v : array_like
    Positive, real-valued parameters
l : array_like
    Real-valued parameters

Returns
-------
scalar or ndarray       _nct_kurtosis_excess(v, l)

Kurtosis excess of noncentral t-distribution.

Parameters
----------
v : array_like
    Positive, real-valued parameters
l : array_like
    Real-valued parameters

Returns
-------
scalar or ndarray       _nct_mean(v, l)

Mean of noncentral t-distribution.

Parameters
----------
v : array_like
    Positive, real-valued parameters
l : array_like
    Real-valued parameters

Returns
-------
scalar or ndarray     _nct_pdf(x, v, l)

Probability density function of noncentral t-distribution.

Parameters
----------
x : array_like
    Real-valued
v : array_like
    Positive, real-valued parameters
l : array_like
    Real-valued parameters

Returns
-------
scalar or ndarray    _nct_sf(x, v, l)

Survival function of noncentral t-distribution.

Parameters
----------
x : array_like
    Real-valued
v : array_like
    Positive, real-valued parameters
l : array_like
    Real-valued parameters

Returns
-------
scalar or ndarray        _nct_skewness(v, l)

Skewness of noncentral t-distribution.

Parameters
----------
v : array_like
    Positive, real-valued parameters
l : array_like
    Real-valued parameters

Returns
-------
scalar or ndarray     _nct_variance(v, l)

Variance of noncentral t-distribution.

Parameters
----------
v : array_like
    Positive, real-valued parameters
l : array_like
    Real-valued parameters

Returns
-------
scalar or ndarray     _ncx2_isf(x, k, l)

Inverse survival function of Non-central chi-squared distribution.

Parameters
----------
x : array_like
    Positive real-valued
k, l : array_like
    Positive, real-valued parameters

Returns
-------
scalar or ndarray _ncx2_pdf(x, k, l)

Probability density function of Non-central chi-squared distribution.

Parameters
----------
x : array_like
    Positive real-valued
k, l : array_like
    Positive, real-valued parameters

Returns
-------
scalar or ndarray      _ncx2_sf(x, k, l)

Survival function of Non-central chi-squared distribution.

Parameters
----------
x : array_like
    Positive real-valued
k, l : array_like
    Positive, real-valued parameters

Returns
-------
scalar or ndarray  _skewnorm_cdf(x, l, sc, sh)

Cumulative density function of skewnorm distribution.

Parameters
----------
x : array_like
    Real-valued
l : array_like
    Real-valued parameters
sc : array_like
    Positive, Real-valued parameters
sh : array_like
    Real-valued parameters

Returns
-------
scalar or ndarray   _skewnorm_isf(x, l, sc, sh)

Inverse survival function of skewnorm distribution.

Parameters
----------
x : array_like
    Real-valued
l : array_like
    Real-valued parameters
sc : array_like
    Positive, Real-valued parameters
sh : array_like
    Real-valued parameters

Returns
-------
scalar or ndarray     _skewnorm_ppf(x, l, sc, sh)

Percent point function of skewnorm distribution.

Parameters
----------
x : array_like
    Real-valued
l : array_like
    Real-valued parameters
sc : array_like
    Positive, Real-valued parameters
sh : array_like
    Real-valued parameters

Returns
-------
scalar or ndarray        _smirnovc(n, d)
 Internal function, do not use. _smirnovp(n, p)
 Internal function, do not use. _struve_asymp_large_z(v, z, is_h)

Internal function for testing `struve` & `modstruve`

Evaluates using asymptotic expansion

Returns
-------
v, err   _struve_bessel_series(v, z, is_h)

Internal function for testing `struve` & `modstruve`

Evaluates using Bessel function series

Returns
-------
v, err _struve_power_series(v, z, is_h)

Internal function for testing `struve` & `modstruve`

Evaluates using power series

Returns
-------
v, err    agm(a, b, out=None)

Compute the arithmetic-geometric mean of `a` and `b`.

Start with a_0 = a and b_0 = b and iteratively compute::

    a_{n+1} = (a_n + b_n)/2
    b_{n+1} = sqrt(a_n*b_n)

a_n and b_n converge to the same limit as n increases; their common
limit is agm(a, b).

Parameters
----------
a, b : array_like
    Real values only. If the values are both negative, the result
    is negative. If one value is negative and the other is positive,
    `nan` is returned.
out : ndarray, optional
    Optional output array for the function values

Returns
-------
scalar or ndarray
    The arithmetic-geometric mean of `a` and `b`.

Examples
--------
>>> import numpy as np
>>> from scipy.special import agm
>>> a, b = 24.0, 6.0
>>> agm(a, b)
13.458171481725614

Compare that result to the iteration:

>>> while a != b:
...     a, b = (a + b)/2, np.sqrt(a*b)
...     print("a = %19.16f  b=%19.16f" % (a, b))
...
a = 15.0000000000000000  b=12.0000000000000000
a = 13.5000000000000000  b=13.4164078649987388
a = 13.4582039324993694  b=13.4581390309909850
a = 13.4581714817451772  b=13.4581714817060547
a = 13.4581714817256159  b=13.4581714817256159

When array-like arguments are given, broadcasting applies:

>>> a = np.array([[1.5], [3], [6]])  # a has shape (3, 1).
>>> b = np.array([6, 12, 24, 48])    # b has shape (4,).
>>> agm(a, b)
array([[  3.36454287,   5.42363427,   9.05798751,  15.53650756],
       [  4.37037309,   6.72908574,  10.84726853,  18.11597502],
       [  6.        ,   8.74074619,  13.45817148,  21.69453707]])      bdtr(k, n, p, out=None)

Binomial distribution cumulative distribution function.

Sum of the terms 0 through `floor(k)` of the Binomial probability density.

.. math::
    \mathrm{bdtr}(k, n, p) =
    \sum_{j=0}^{\lfloor k \rfloor} {{n}\choose{j}} p^j (1-p)^{n-j}

Parameters
----------
k : array_like
    Number of successes (double), rounded down to the nearest integer.
n : array_like
    Number of events (int).
p : array_like
    Probability of success in a single event (float).
out : ndarray, optional
    Optional output array for the function values

Returns
-------
y : scalar or ndarray
    Probability of `floor(k)` or fewer successes in `n` independent events with
    success probabilities of `p`.

Notes
-----
The terms are not summed directly; instead the regularized incomplete beta
function is employed, according to the formula,

.. math::
    \mathrm{bdtr}(k, n, p) =
    I_{1 - p}(n - \lfloor k \rfloor, \lfloor k \rfloor + 1).

Wrapper for the Cephes [1]_ routine `bdtr`.

References
----------
.. [1] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/     bdtrc(k, n, p, out=None)

Binomial distribution survival function.

Sum of the terms `floor(k) + 1` through `n` of the binomial probability
density,

.. math::
    \mathrm{bdtrc}(k, n, p) =
    \sum_{j=\lfloor k \rfloor +1}^n {{n}\choose{j}} p^j (1-p)^{n-j}

Parameters
----------
k : array_like
    Number of successes (double), rounded down to nearest integer.
n : array_like
    Number of events (int)
p : array_like
    Probability of success in a single event.
out : ndarray, optional
    Optional output array for the function values

Returns
-------
y : scalar or ndarray
    Probability of `floor(k) + 1` or more successes in `n` independent
    events with success probabilities of `p`.

See Also
--------
bdtr
betainc

Notes
-----
The terms are not summed directly; instead the regularized incomplete beta
function is employed, according to the formula,

.. math::
    \mathrm{bdtrc}(k, n, p) = I_{p}(\lfloor k \rfloor + 1, n - \lfloor k \rfloor).

Wrapper for the Cephes [1]_ routine `bdtrc`.

References
----------
.. [1] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/   bdtri(k, n, y, out=None)

Inverse function to `bdtr` with respect to `p`.

Finds the event probability `p` such that the sum of the terms 0 through
`k` of the binomial probability density is equal to the given cumulative
probability `y`.

Parameters
----------
k : array_like
    Number of successes (float), rounded down to the nearest integer.
n : array_like
    Number of events (float)
y : array_like
    Cumulative probability (probability of `k` or fewer successes in `n`
    events).
out : ndarray, optional
    Optional output array for the function values

Returns
-------
p : scalar or ndarray
    The event probability such that `bdtr(\lfloor k \rfloor, n, p) = y`.

See Also
--------
bdtr
betaincinv

Notes
-----
The computation is carried out using the inverse beta integral function
and the relation,::

    1 - p = betaincinv(n - k, k + 1, y).

Wrapper for the Cephes [1]_ routine `bdtri`.

References
----------
.. [1] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/      bdtrik(y, n, p, out=None)

Inverse function to `bdtr` with respect to `k`.

Finds the number of successes `k` such that the sum of the terms 0 through
`k` of the Binomial probability density for `n` events with probability
`p` is equal to the given cumulative probability `y`.

Parameters
----------
y : array_like
    Cumulative probability (probability of `k` or fewer successes in `n`
    events).
n : array_like
    Number of events (float).
p : array_like
    Success probability (float).
out : ndarray, optional
    Optional output array for the function values

Returns
-------
k : scalar or ndarray
    The number of successes `k` such that `bdtr(k, n, p) = y`.

See Also
--------
bdtr

Notes
-----
Formula 26.5.24 of [1]_ (or equivalently [2]_) is used to reduce the binomial
distribution to the cumulative incomplete beta distribution.

Computation of `k` involves a search for a value that produces the desired
value of `y`. The search relies on the monotonicity of `y` with `k`.

Wrapper for the CDFLIB [3]_ Fortran routine `cdfbin`.

References
----------
.. [1] Milton Abramowitz and Irene A. Stegun, eds.
       Handbook of Mathematical Functions with Formulas,
       Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [2] NIST Digital Library of Mathematical Functions
       https://dlmf.nist.gov/8.17.5#E5
.. [3] Barry Brown, James Lovato, and Kathy Russell,
       CDFLIB: Library of Fortran Routines for Cumulative Distribution
       Functions, Inverses, and Other Parameters.      bdtrin(k, y, p, out=None)

Inverse function to `bdtr` with respect to `n`.

Finds the number of events `n` such that the sum of the terms 0 through
`k` of the Binomial probability density for events with probability `p` is
equal to the given cumulative probability `y`.

Parameters
----------
k : array_like
    Number of successes (float).
y : array_like
    Cumulative probability (probability of `k` or fewer successes in `n`
    events).
p : array_like
    Success probability (float).
out : ndarray, optional
    Optional output array for the function values

Returns
-------
n : scalar or ndarray
    The number of events `n` such that `bdtr(k, n, p) = y`.

See Also
--------
bdtr

Notes
-----
Formula 26.5.24 of [1]_ (or equivalently [2]_) is used to reduce the binomial
distribution to the cumulative incomplete beta distribution.

Computation of `n` involves a search for a value that produces the desired
value of `y`. The search relies on the monotonicity of `y` with `n`.

Wrapper for the CDFLIB [3]_ Fortran routine `cdfbin`.

References
----------
.. [1] Milton Abramowitz and Irene A. Stegun, eds.
       Handbook of Mathematical Functions with Formulas,
       Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [2] NIST Digital Library of Mathematical Functions
       https://dlmf.nist.gov/8.17.5#E5
.. [3] Barry Brown, James Lovato, and Kathy Russell,
       CDFLIB: Library of Fortran Routines for Cumulative Distribution
       Functions, Inverses, and Other Parameters.     betainc(a, b, x, out=None)

Regularized incomplete beta function.

Computes the regularized incomplete beta function, defined as [1]_:

.. math::

    I_x(a, b) = \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)} \int_0^x
    t^{a-1}(1-t)^{b-1}dt,

for :math:`0 \leq x \leq 1`.

This function is the cumulative distribution function for the beta
distribution; its range is [0, 1].

Parameters
----------
a, b : array_like
       Positive, real-valued parameters
x : array_like
    Real-valued such that :math:`0 \leq x \leq 1`,
    the upper limit of integration
out : ndarray, optional
    Optional output array for the function values

Returns
-------
scalar or ndarray
    Value of the regularized incomplete beta function

See Also
--------
beta : beta function
betaincinv : inverse of the regularized incomplete beta function
betaincc : complement of the regularized incomplete beta function
scipy.stats.beta : beta distribution

Notes
-----
The term *regularized* in the name of this function refers to the
scaling of the function by the gamma function terms shown in the
formula.  When not qualified as *regularized*, the name *incomplete
beta function* often refers to just the integral expression,
without the gamma terms.  One can use the function `beta` from
`scipy.special` to get this "nonregularized" incomplete beta
function by multiplying the result of ``betainc(a, b, x)`` by
``beta(a, b)``.

``betainc(a, b, x)`` is treated as a two parameter family of functions
of a single variable `x`, rather than as a function of three variables.
This impacts only the limiting cases ``a = 0``, ``b = 0``, ``a = inf``,
``b = inf``.

In general

.. math::

    \lim_{(a, b) \rightarrow (a_0, b_0)} \mathrm{betainc}(a, b, x)

is treated as a pointwise limit in ``x``. Thus for example,
``betainc(0, b, 0)`` equals ``0`` for ``b > 0``, although it would be
indeterminate when considering the simultaneous limit ``(a, x) -> (0+, 0+)``.

This function wraps the ``ibeta`` routine from the
Boost Math C++ library [2]_.

References
----------
.. [1] NIST Digital Library of Mathematical Functions
       https://dlmf.nist.gov/8.17
.. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------

Let :math:`B(a, b)` be the `beta` function.

>>> import scipy.special as sc

The coefficient in terms of `gamma` is equal to
:math:`1/B(a, b)`. Also, when :math:`x=1`
the integral is equal to :math:`B(a, b)`.
Therefore, :math:`I_{x=1}(a, b) = 1` for any :math:`a, b`.

>>> sc.betainc(0.2, 3.5, 1.0)
1.0

It satisfies
:math:`I_x(a, b) = x^a F(a, 1-b, a+1, x)/ (aB(a, b))`,
where :math:`F` is the hypergeometric function `hyp2f1`:

>>> a, b, x = 1.4, 3.1, 0.5
>>> x**a * sc.hyp2f1(a, 1 - b, a + 1, x)/(a * sc.beta(a, b))
0.8148904036225295
>>> sc.betainc(a, b, x)
0.8148904036225296

This functions satisfies the relationship
:math:`I_x(a, b) = 1 - I_{1-x}(b, a)`:

>>> sc.betainc(2.2, 3.1, 0.4)
0.49339638807619446
>>> 1 - sc.betainc(3.1, 2.2, 1 - 0.4)
0.49339638807619446      betaincc(a, b, x, out=None)

Complement of the regularized incomplete beta function.

Computes the complement of the regularized incomplete beta function,
defined as [1]_:

.. math::

    \bar{I}_x(a, b) = 1 - I_x(a, b)
                    = 1 - \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)} \int_0^x
                              t^{a-1}(1-t)^{b-1}dt,

for :math:`0 \leq x \leq 1`.

Parameters
----------
a, b : array_like
       Positive, real-valued parameters
x : array_like
    Real-valued such that :math:`0 \leq x \leq 1`,
    the upper limit of integration
out : ndarray, optional
    Optional output array for the function values

Returns
-------
scalar or ndarray
    Value of the regularized incomplete beta function

See Also
--------
betainc : regularized incomplete beta function
betaincinv : inverse of the regularized incomplete beta function
betainccinv :
    inverse of the complement of the regularized incomplete beta function
beta : beta function
scipy.stats.beta : beta distribution

Notes
-----
.. versionadded:: 1.11.0

Like `betainc`, ``betaincc(a, b, x)`` is treated as a two parameter
family of functions of a single variable `x`, rather than as a function of
three variables. See the `betainc` docstring for more info on how this
impacts limiting cases.

This function wraps the ``ibetac`` routine from the
Boost Math C++ library [2]_.

References
----------
.. [1] NIST Digital Library of Mathematical Functions
       https://dlmf.nist.gov/8.17
.. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
>>> from scipy.special import betaincc, betainc

The naive calculation ``1 - betainc(a, b, x)`` loses precision when
the values of ``betainc(a, b, x)`` are close to 1:

>>> 1 - betainc(0.5, 8, [0.9, 0.99, 0.999])
array([2.0574632e-09, 0.0000000e+00, 0.0000000e+00])

By using ``betaincc``, we get the correct values:

>>> betaincc(0.5, 8, [0.9, 0.99, 0.999])
array([2.05746321e-09, 1.97259354e-17, 1.96467954e-25])       betainccinv(a, b, y, out=None)

Inverse of the complemented regularized incomplete beta function.

Computes :math:`x` such that:

.. math::

    y = 1 - I_x(a, b) = 1 - \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}
    \int_0^x t^{a-1}(1-t)^{b-1}dt,

where :math:`I_x` is the normalized incomplete beta function `betainc`
and :math:`\Gamma` is the `gamma` function [1]_.

Parameters
----------
a, b : array_like
    Positive, real-valued parameters
y : array_like
    Real-valued input
out : ndarray, optional
    Optional output array for function values

Returns
-------
scalar or ndarray
    Value of the inverse of the regularized incomplete beta function

See Also
--------
betainc : regularized incomplete beta function
betaincc : complement of the regularized incomplete beta function

Notes
-----
.. versionadded:: 1.11.0

This function wraps the ``ibetac_inv`` routine from the
Boost Math C++ library [2]_.

References
----------
.. [1] NIST Digital Library of Mathematical Functions
       https://dlmf.nist.gov/8.17
.. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
>>> from scipy.special import betainccinv, betaincc

This function is the inverse of `betaincc` for fixed
values of :math:`a` and :math:`b`.

>>> a, b = 1.2, 3.1
>>> y = betaincc(a, b, 0.2)
>>> betainccinv(a, b, y)
0.2

>>> a, b = 7, 2.5
>>> x = betainccinv(a, b, 0.875)
>>> betaincc(a, b, x)
0.875   betaincinv(a, b, y, out=None)

Inverse of the regularized incomplete beta function.

Computes :math:`x` such that:

.. math::

    y = I_x(a, b) = \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}
    \int_0^x t^{a-1}(1-t)^{b-1}dt,

where :math:`I_x` is the normalized incomplete beta function `betainc`
and :math:`\Gamma` is the `gamma` function [1]_.

Parameters
----------
a, b : array_like
    Positive, real-valued parameters
y : array_like
    Real-valued input
out : ndarray, optional
    Optional output array for function values

Returns
-------
scalar or ndarray
    Value of the inverse of the regularized incomplete beta function

See Also
--------
betainc : regularized incomplete beta function
gamma : gamma function

Notes
-----
This function wraps the ``ibeta_inv`` routine from the
Boost Math C++ library [2]_.

References
----------
.. [1] NIST Digital Library of Mathematical Functions
       https://dlmf.nist.gov/8.17
.. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
>>> import scipy.special as sc

This function is the inverse of `betainc` for fixed
values of :math:`a` and :math:`b`.

>>> a, b = 1.2, 3.1
>>> y = sc.betainc(a, b, 0.2)
>>> sc.betaincinv(a, b, y)
0.2
>>>
>>> a, b = 7.5, 0.4
>>> x = sc.betaincinv(a, b, 0.5)
>>> sc.betainc(a, b, x)
0.5    boxcox(x, lmbda, out=None)

Compute the Box-Cox transformation.

The Box-Cox transformation is::

    y = (x**lmbda - 1) / lmbda  if lmbda != 0
        log(x)                  if lmbda == 0

Returns `nan` if ``x < 0``.
Returns `-inf` if ``x == 0`` and ``lmbda < 0``.

Parameters
----------
x : array_like
    Data to be transformed.
lmbda : array_like
    Power parameter of the Box-Cox transform.
out : ndarray, optional
    Optional output array for the function values

Returns
-------
y : scalar or ndarray
    Transformed data.

Notes
-----

.. versionadded:: 0.14.0

Examples
--------
>>> from scipy.special import boxcox
>>> boxcox([1, 4, 10], 2.5)
array([   0.        ,   12.4       ,  126.09110641])
>>> boxcox(2, [0, 1, 2])
array([ 0.69314718,  1.        ,  1.5       ])    boxcox1p(x, lmbda, out=None)

Compute the Box-Cox transformation of 1 + `x`.

The Box-Cox transformation computed by `boxcox1p` is::

    y = ((1+x)**lmbda - 1) / lmbda  if lmbda != 0
        log(1+x)                    if lmbda == 0

Returns `nan` if ``x < -1``.
Returns `-inf` if ``x == -1`` and ``lmbda < 0``.

Parameters
----------
x : array_like
    Data to be transformed.
lmbda : array_like
    Power parameter of the Box-Cox transform.
out : ndarray, optional
    Optional output array for the function values

Returns
-------
y : scalar or ndarray
    Transformed data.

Notes
-----

.. versionadded:: 0.14.0

Examples
--------
>>> from scipy.special import boxcox1p
>>> boxcox1p(1e-4, [0, 0.5, 1])
array([  9.99950003e-05,   9.99975001e-05,   1.00000000e-04])
>>> boxcox1p([0.01, 0.1], 0.25)
array([ 0.00996272,  0.09645476])     btdtria(p, b, x, out=None)

Inverse of `betainc` with respect to `a`.

This is the inverse of the beta cumulative distribution function, `betainc`,
considered as a function of `a`, returning the value of `a` for which
`betainc(a, b, x) = p`, or

.. math::
    p = \int_0^x \frac{\Gamma(a + b)}{\Gamma(a)\Gamma(b)} t^{a-1} (1-t)^{b-1}\,dt

Parameters
----------
p : array_like
    Cumulative probability, in [0, 1].
b : array_like
    Shape parameter (`b` > 0).
x : array_like
    The quantile, in [0, 1].
out : ndarray, optional
    Optional output array for the function values

Returns
-------
a : scalar or ndarray
    The value of the shape parameter `a` such that `betainc(a, b, x) = p`.

See Also
--------
betainc : Regularized incomplete beta function
betaincinv : Inverse of the regularized incomplete beta function
btdtrib : Inverse of the beta cumulative distribution function, with respect to `b`.

Notes
-----
This function wraps the ``ibeta_inva`` routine from the
Boost Math C++ library [1]_.

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
>>> import scipy.special as sc

This function is the inverse of `betainc` for fixed
values of :math:`b` and :math:`x`.

>>> a, b, x = 1.2, 3.1, 0.2
>>> y = sc.betainc(a, b, x)
>>> sc.btdtria(y, b, x)
1.2        btdtria(a, p, x, out=None)

Inverse of `betainc` with respect to `b`.

This is the inverse of the beta cumulative distribution function, `betainc`,
considered as a function of `b`, returning the value of `b` for which
`betainc(a, b, x) = p`, or

.. math::
    p = \int_0^x \frac{\Gamma(a + b)}{\Gamma(a)\Gamma(b)} t^{a-1} (1-t)^{b-1}\,dt

Parameters
----------
a : array_like
    Shape parameter (`a` > 0).
p : array_like
    Cumulative probability, in [0, 1].
x : array_like
    The quantile, in [0, 1].
out : ndarray, optional
    Optional output array for the function values

Returns
-------
b : scalar or ndarray
    The value of the shape parameter `b` such that `betainc(a, b, x) = p`.

See Also
--------
betainc : Regularized incomplete beta function
betaincinv : Inverse of the regularized incomplete beta function with
             respect to `x`.
btdtria : Inverse of the beta cumulative distribution function, with respect to `a`.

Notes
-----
Wrapper for the `ibeta_invb` routine from the Boost Math C++ library [1]_.

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
>>> import scipy.special as sc
>>> a, b, x = 1.2, 3.1, 0.2
>>> y = sc.betainc(a, b, x)

`btdtrib` is the inverse of `betainc` for fixed values of :math:`a` and
:math:`x`:

>>> sc.btdtrib(a, y, x)
3.1    chdtr(v, x, out=None)

Chi square cumulative distribution function.

Returns the area under the left tail (from 0 to `x`) of the Chi
square probability density function with `v` degrees of freedom:

.. math::

    \frac{1}{2^{v/2} \Gamma(v/2)} \int_0^x t^{v/2 - 1} e^{-t/2} dt

Here :math:`\Gamma` is the Gamma function; see `gamma`. This
integral can be expressed in terms of the regularized lower
incomplete gamma function `gammainc` as
``gammainc(v / 2, x / 2)``. [1]_

Parameters
----------
v : array_like
    Degrees of freedom.
x : array_like
    Upper bound of the integral.
out : ndarray, optional
    Optional output array for the function results.

Returns
-------
scalar or ndarray
    Values of the cumulative distribution function.

See Also
--------
chdtrc, chdtri, chdtriv, gammainc

References
----------
.. [1] Chi-Square distribution,
    https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm

Examples
--------
>>> import numpy as np
>>> import scipy.special as sc

It can be expressed in terms of the regularized lower incomplete
gamma function.

>>> v = 1
>>> x = np.arange(4)
>>> sc.chdtr(v, x)
array([0.        , 0.68268949, 0.84270079, 0.91673548])
>>> sc.gammainc(v / 2, x / 2)
array([0.        , 0.68268949, 0.84270079, 0.91673548])  chdtrc(v, x, out=None)

Chi square survival function.

Returns the area under the right hand tail (from `x` to infinity)
of the Chi square probability density function with `v` degrees of
freedom:

.. math::

    \frac{1}{2^{v/2} \Gamma(v/2)} \int_x^\infty t^{v/2 - 1} e^{-t/2} dt

Here :math:`\Gamma` is the Gamma function; see `gamma`. This
integral can be expressed in terms of the regularized upper
incomplete gamma function `gammaincc` as
``gammaincc(v / 2, x / 2)``. [1]_

Parameters
----------
v : array_like
    Degrees of freedom.
x : array_like
    Lower bound of the integral.
out : ndarray, optional
    Optional output array for the function results.

Returns
-------
scalar or ndarray
    Values of the survival function.

See Also
--------
chdtr, chdtri, chdtriv, gammaincc

References
----------
.. [1] Chi-Square distribution,
    https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm

Examples
--------
>>> import numpy as np
>>> import scipy.special as sc

It can be expressed in terms of the regularized upper incomplete
gamma function.

>>> v = 1
>>> x = np.arange(4)
>>> sc.chdtrc(v, x)
array([1.        , 0.31731051, 0.15729921, 0.08326452])
>>> sc.gammaincc(v / 2, x / 2)
array([1.        , 0.31731051, 0.15729921, 0.08326452]) chdtri(v, p, out=None)

Inverse to `chdtrc` with respect to `x`.

Returns `x` such that ``chdtrc(v, x) == p``.

Parameters
----------
v : array_like
    Degrees of freedom.
p : array_like
    Probability.
out : ndarray, optional
    Optional output array for the function results.

Returns
-------
x : scalar or ndarray
    Value so that the probability a Chi square random variable
    with `v` degrees of freedom is greater than `x` equals `p`.

See Also
--------
chdtrc, chdtr, chdtriv

References
----------
.. [1] Chi-Square distribution,
    https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm

Examples
--------
>>> import scipy.special as sc

It inverts `chdtrc`.

>>> v, p = 1, 0.3
>>> sc.chdtrc(v, sc.chdtri(v, p))
0.3
>>> x = 1
>>> sc.chdtri(v, sc.chdtrc(v, x))
1.0  chdtriv(p, x, out=None)

Inverse to `chdtr` with respect to `v`.

Returns `v` such that ``chdtr(v, x) == p``.

Parameters
----------
p : array_like
    Probability that the Chi square random variable is less than
    or equal to `x`.
x : array_like
    Nonnegative input.
out : ndarray, optional
    Optional output array for the function results.

Returns
-------
scalar or ndarray
    Degrees of freedom.

See Also
--------
chdtr, chdtrc, chdtri

Notes
-----
This function wraps routines from the Boost Math C++ library [1]_.

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
.. [2] Chi-Square distribution,
    https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm

Examples
--------
>>> import scipy.special as sc

It inverts `chdtr`.

>>> p, x = 0.5, 1
>>> sc.chdtr(sc.chdtriv(p, x), x)
0.5000000000000003
>>> v = 1
>>> sc.chdtriv(sc.chdtr(v, x), v)
1.0 chndtr(x, df, nc, out=None)

Non-central chi square cumulative distribution function

The cumulative distribution function is given by:

.. math::

    P(\chi^{\prime 2} \vert \nu, \lambda) =\sum_{j=0}^{\infty}
    e^{-\lambda /2}
    \frac{(\lambda /2)^j}{j!} P(\chi^{\prime 2} \vert \nu + 2j),

where :math:`\nu > 0` is the degrees of freedom (``df``) and
:math:`\lambda \geq 0` is the non-centrality parameter (``nc``).

Parameters
----------
x : array_like
    Upper bound of the integral; must satisfy ``x >= 0``
df : array_like
    Degrees of freedom; must satisfy ``df > 0``
nc : array_like
    Non-centrality parameter; must satisfy ``nc >= 0``
out : ndarray, optional
    Optional output array for the function results

Returns
-------
x : scalar or ndarray
    Value of the non-central chi square cumulative distribution function.

See Also
--------
chndtrix: Noncentral Chi Squared distribution quantile
chndtridf: Inverse of `chndtr` with respect to `df`
chndtrinc: Inverse of `chndtr` with respect to `nc`
scipy.stats.ncx2: Non-central chi-squared distribution

Notes
-----
The noncentral chi squared distribution is also available in
`scipy.stats.ncx2`. ``scipy.stats.ncx2.cdf`` is equivalent to `chndtr`.

This function wraps routines from the Boost Math C++ library [1]_.

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
>>> import numpy as np
>>> import scipy.special as sc

Compute the noncentral chi squared distribution CDF at one point.

>>> x = 4.0
>>> df = 1.0
>>> nc = 5.0
>>> sc.chndtr(x, df, nc)
0.40667858759710945

Plot the noncentral chi squared distribution CDF for different parameters.

>>> import matplotlib.pyplot as plt
>>> x = np.linspace(0, 40, 1000)
>>> plt.plot(x, sc.chndtr(x, 1, 5), label=r"$df=1,\ nc=5$")
>>> plt.plot(x, sc.chndtr(x, 5, 10), label=r"$df=5,\ nc=10$")
>>> plt.legend()
>>> plt.show()  chndtridf(x, p, nc, out=None)

Inverse to `chndtr` vs `df`

Calculated using a search to find a value for `df` that produces the
desired value of `p`.

Parameters
----------
x : array_like
    Upper bound of the integral; must satisfy ``x >= 0``
p : array_like
    Probability; must satisfy ``0 <= p < 1``
nc : array_like
    Non-centrality parameter; must satisfy ``nc >= 0``
out : ndarray, optional
    Optional output array for the function results

Returns
-------
df : scalar or ndarray
    Degrees of freedom

See Also
--------
chndtr : Noncentral chi-squared distribution CDF
chndtrix : inverse of `chndtr` with respect to `x`
chndtrinc : inverse of `chndtr` with respect to `nc`
scipy.stats.ncx2 : Non-central chi-squared distribution

Notes
-----
The noncentral chi squared distribution is also available in
`scipy.stats.ncx2`.

This function wraps routines from the Boost Math C++ library [1]_.

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
>>> from scipy.special import chndtridf, chndtr

Compute the noncentral chi squared distribution CDF at one point.

>>> x, df, nc = 3, 5, 10
>>> p = chndtr(x, df, nc)

`chndtridf` is the inverse of `chndtr` with respect to `df`:

>>> chndtridf(x, p, nc)
5.0        chndtrinc(x, df, p, out=None)

Inverse to `chndtr` vs `nc`

Calculated using a search to find a value for `df` that produces the
desired value of `p`.

Parameters
----------
x : array_like
    Upper bound of the integral; must satisfy ``x >= 0``
df : array_like
    Degrees of freedom; must satisfy ``df > 0``
p : array_like
    Probability; must satisfy ``0 <= p < 1``
out : ndarray, optional
    Optional output array for the function results

Returns
-------
nc : scalar or ndarray
    Non-centrality

See Also
--------
chndtr : Noncentral chi-squared distribution CDF
chndtridf : inverse of `chndtr` with respect to `df`
chndtrinc : inverse of `chndtr` with respect to `nc`
scipy.stats.ncx2 : Non-central chi-squared distribution

Notes
-----
The noncentral chi squared distribution is also available in
`scipy.stats.ncx2`.

This function wraps routines from the Boost Math C++ library [1]_.

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
>>> from scipy.special import chndtrinc, chndtr

Compute the noncentral chi squared distribution CDF at one point.

>>> x, df, nc = 3, 5, 10
>>> p = chndtr(x, df, nc)

`chndtrinc` is the inverse of `chndtr` with respect to `nc`:

>>> chndtrinc(x, df, p)
10.0        chndtrix(p, df, nc, out=None)

Inverse to `chndtr` vs `x`

Calculated using a search to find a value for `x` that produces the
desired value of `p`.

Parameters
----------
p : array_like
    Probability; must satisfy ``0 <= p < 1``
df : array_like
    Degrees of freedom; must satisfy ``df > 0``
nc : array_like
    Non-centrality parameter; must satisfy ``nc >= 0``
out : ndarray, optional
    Optional output array for the function results

Returns
-------
x : scalar or ndarray
    Value so that the probability a non-central Chi square random variable
    with `df` degrees of freedom and non-centrality, `nc`, is greater than
    `x` equals `p`.

See Also
--------
chndtr : Noncentral chi-squared distribution CDF
chndtridf : inverse of `chndtr` with respect to `cdf`
chndtrinc : inverse of `chndtr` with respect to `nc`
scipy.stats.ncx2 : Non-central chi-squared distribution

Notes
-----
The noncentral chi squared distribution is also available in
`scipy.stats.ncx2`. ``scipy.stats.ncx2.ppf`` is equivalent to `chndtrix`.

This function wraps routines from the Boost Math C++ library [1]_.

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
>>> from scipy.special import chndtrix, chndtr

Compute the noncentral chi squared distribution CDF at one point.
>>> x, df, nc = 3, 5, 10
>>> p = chndtr(x, df, nc)

`chndtrix` is the inverse of `chndtr` with respect to `x`:

>>> chndtrix(p, df, nc)
3.0   elliprc(x, y, out=None)

Degenerate symmetric elliptic integral.

The function RC is defined as [1]_

.. math::

    R_{\mathrm{C}}(x, y) =
       \frac{1}{2} \int_0^{+\infty} (t + x)^{-1/2} (t + y)^{-1} dt
       = R_{\mathrm{F}}(x, y, y)

Parameters
----------
x, y : array_like
    Real or complex input parameters. `x` can be any number in the
    complex plane cut along the negative real axis. `y` must be non-zero.
out : ndarray, optional
    Optional output array for the function values

Returns
-------
R : scalar or ndarray
    Value of the integral. If `y` is real and negative, the Cauchy
    principal value is returned. If both of `x` and `y` are real, the
    return value is real. Otherwise, the return value is complex.

See Also
--------
elliprf : Completely-symmetric elliptic integral of the first kind.
elliprd : Symmetric elliptic integral of the second kind.
elliprg : Completely-symmetric elliptic integral of the second kind.
elliprj : Symmetric elliptic integral of the third kind.

Notes
-----
RC is a degenerate case of the symmetric integral RF: ``elliprc(x, y) ==
elliprf(x, y, y)``. It is an elementary function rather than an elliptic
integral.

The code implements Carlson's algorithm based on the duplication theorems
and series expansion up to the 7th order. [2]_

.. versionadded:: 1.8.0

References
----------
.. [1] B. C. Carlson, ed., Chapter 19 in "Digital Library of Mathematical
       Functions," NIST, US Dept. of Commerce.
       https://dlmf.nist.gov/19.16.E6
.. [2] B. C. Carlson, "Numerical computation of real or complex elliptic
       integrals," Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.
       https://arxiv.org/abs/math/9409227
       https://doi.org/10.1007/BF02198293

Examples
--------
Basic homogeneity property:

>>> import numpy as np
>>> from scipy.special import elliprc

>>> x = 1.2 + 3.4j
>>> y = 5.
>>> scale = 0.3 + 0.4j
>>> elliprc(scale*x, scale*y)
(0.5484493976710874-0.4169557678995833j)

>>> elliprc(x, y)/np.sqrt(scale)
(0.5484493976710874-0.41695576789958333j)

When the two arguments coincide, the integral is particularly
simple:

>>> x = 1.2 + 3.4j
>>> elliprc(x, x)
(0.4299173120614631-0.3041729818745595j)

>>> 1/np.sqrt(x)
(0.4299173120614631-0.30417298187455954j)

Another simple case: the first argument vanishes:

>>> y = 1.2 + 3.4j
>>> elliprc(0, y)
(0.6753125346116815-0.47779380263880866j)

>>> np.pi/2/np.sqrt(y)
(0.6753125346116815-0.4777938026388088j)

When `x` and `y` are both positive, we can express
:math:`R_C(x,y)` in terms of more elementary functions.  For the
case :math:`0 \le x < y`,

>>> x = 3.2
>>> y = 6.
>>> elliprc(x, y)
0.44942991498453444

>>> np.arctan(np.sqrt((y-x)/x))/np.sqrt(y-x)
0.44942991498453433

And for the case :math:`0 \le y < x`,

>>> x = 6.
>>> y = 3.2
>>> elliprc(x,y)
0.4989837501576147

>>> np.log((np.sqrt(x)+np.sqrt(x-y))/np.sqrt(y))/np.sqrt(x-y)
0.49898375015761476  elliprd(x, y, z, out=None)

Symmetric elliptic integral of the second kind.

The function RD is defined as [1]_

.. math::

    R_{\mathrm{D}}(x, y, z) =
       \frac{3}{2} \int_0^{+\infty} [(t + x) (t + y)]^{-1/2} (t + z)^{-3/2}
       dt

Parameters
----------
x, y, z : array_like
    Real or complex input parameters. `x` or `y` can be any number in the
    complex plane cut along the negative real axis, but at most one of them
    can be zero, while `z` must be non-zero.
out : ndarray, optional
    Optional output array for the function values

Returns
-------
R : scalar or ndarray
    Value of the integral. If all of `x`, `y`, and `z` are real, the
    return value is real. Otherwise, the return value is complex.

See Also
--------
elliprc : Degenerate symmetric elliptic integral.
elliprf : Completely-symmetric elliptic integral of the first kind.
elliprg : Completely-symmetric elliptic integral of the second kind.
elliprj : Symmetric elliptic integral of the third kind.

Notes
-----
RD is a degenerate case of the elliptic integral RJ: ``elliprd(x, y, z) ==
elliprj(x, y, z, z)``.

The code implements Carlson's algorithm based on the duplication theorems
and series expansion up to the 7th order. [2]_

.. versionadded:: 1.8.0

References
----------
.. [1] B. C. Carlson, ed., Chapter 19 in "Digital Library of Mathematical
       Functions," NIST, US Dept. of Commerce.
       https://dlmf.nist.gov/19.16.E5
.. [2] B. C. Carlson, "Numerical computation of real or complex elliptic
       integrals," Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.
       https://arxiv.org/abs/math/9409227
       https://doi.org/10.1007/BF02198293

Examples
--------
Basic homogeneity property:

>>> import numpy as np
>>> from scipy.special import elliprd

>>> x = 1.2 + 3.4j
>>> y = 5.
>>> z = 6.
>>> scale = 0.3 + 0.4j
>>> elliprd(scale*x, scale*y, scale*z)
(-0.03703043835680379-0.24500934665683802j)

>>> elliprd(x, y, z)*np.power(scale, -1.5)
(-0.0370304383568038-0.24500934665683805j)

All three arguments coincide:

>>> x = 1.2 + 3.4j
>>> elliprd(x, x, x)
(-0.03986825876151896-0.14051741840449586j)

>>> np.power(x, -1.5)
(-0.03986825876151894-0.14051741840449583j)

The so-called "second lemniscate constant":

>>> elliprd(0, 2, 1)/3
0.5990701173677961

>>> from scipy.special import gamma
>>> gamma(0.75)**2/np.sqrt(2*np.pi)
0.5990701173677959     elliprf(x, y, z, out=None)

Completely-symmetric elliptic integral of the first kind.

The function RF is defined as [1]_

.. math::

    R_{\mathrm{F}}(x, y, z) =
       \frac{1}{2} \int_0^{+\infty} [(t + x) (t + y) (t + z)]^{-1/2} dt

Parameters
----------
x, y, z : array_like
    Real or complex input parameters. `x`, `y`, or `z` can be any number in
    the complex plane cut along the negative real axis, but at most one of
    them can be zero.
out : ndarray, optional
    Optional output array for the function values

Returns
-------
R : scalar or ndarray
    Value of the integral. If all of `x`, `y`, and `z` are real, the return
    value is real. Otherwise, the return value is complex.

See Also
--------
elliprc : Degenerate symmetric integral.
elliprd : Symmetric elliptic integral of the second kind.
elliprg : Completely-symmetric elliptic integral of the second kind.
elliprj : Symmetric elliptic integral of the third kind.

Notes
-----
The code implements Carlson's algorithm based on the duplication theorems
and series expansion up to the 7th order (cf.:
https://dlmf.nist.gov/19.36.i) and the AGM algorithm for the complete
integral. [2]_

.. versionadded:: 1.8.0

References
----------
.. [1] B. C. Carlson, ed., Chapter 19 in "Digital Library of Mathematical
       Functions," NIST, US Dept. of Commerce.
       https://dlmf.nist.gov/19.16.E1
.. [2] B. C. Carlson, "Numerical computation of real or complex elliptic
       integrals," Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.
       https://arxiv.org/abs/math/9409227
       https://doi.org/10.1007/BF02198293

Examples
--------
Basic homogeneity property:

>>> import numpy as np
>>> from scipy.special import elliprf

>>> x = 1.2 + 3.4j
>>> y = 5.
>>> z = 6.
>>> scale = 0.3 + 0.4j
>>> elliprf(scale*x, scale*y, scale*z)
(0.5328051227278146-0.4008623567957094j)

>>> elliprf(x, y, z)/np.sqrt(scale)
(0.5328051227278147-0.4008623567957095j)

All three arguments coincide:

>>> x = 1.2 + 3.4j
>>> elliprf(x, x, x)
(0.42991731206146316-0.30417298187455954j)

>>> 1/np.sqrt(x)
(0.4299173120614631-0.30417298187455954j)

The so-called "first lemniscate constant":

>>> elliprf(0, 1, 2)
1.3110287771460598

>>> from scipy.special import gamma
>>> gamma(0.25)**2/(4*np.sqrt(2*np.pi))
1.3110287771460598   elliprg(x, y, z, out=None)

Completely-symmetric elliptic integral of the second kind.

The function RG is defined as [1]_

.. math::

    R_{\mathrm{G}}(x, y, z) =
       \frac{1}{4} \int_0^{+\infty} [(t + x) (t + y) (t + z)]^{-1/2}
       \left(\frac{x}{t + x} + \frac{y}{t + y} + \frac{z}{t + z}\right) t
       dt

Parameters
----------
x, y, z : array_like
    Real or complex input parameters. `x`, `y`, or `z` can be any number in
    the complex plane cut along the negative real axis.
out : ndarray, optional
    Optional output array for the function values

Returns
-------
R : scalar or ndarray
    Value of the integral. If all of `x`, `y`, and `z` are real, the return
    value is real. Otherwise, the return value is complex.

See Also
--------
elliprc : Degenerate symmetric integral.
elliprd : Symmetric elliptic integral of the second kind.
elliprf : Completely-symmetric elliptic integral of the first kind.
elliprj : Symmetric elliptic integral of the third kind.

Notes
-----
The implementation uses the relation [1]_

.. math::

    2 R_{\mathrm{G}}(x, y, z) =
       z R_{\mathrm{F}}(x, y, z) -
       \frac{1}{3} (x - z) (y - z) R_{\mathrm{D}}(x, y, z) +
       \sqrt{\frac{x y}{z}}

and the symmetry of `x`, `y`, `z` when at least one non-zero parameter can
be chosen as the pivot. When one of the arguments is close to zero, the AGM
method is applied instead. Other special cases are computed following Ref.
[2]_

.. versionadded:: 1.8.0

References
----------
.. [1] B. C. Carlson, "Numerical computation of real or complex elliptic
       integrals," Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.
       https://arxiv.org/abs/math/9409227
       https://doi.org/10.1007/BF02198293
.. [2] B. C. Carlson, ed., Chapter 19 in "Digital Library of Mathematical
       Functions," NIST, US Dept. of Commerce.
       https://dlmf.nist.gov/19.16.E1
       https://dlmf.nist.gov/19.20.ii

Examples
--------
Basic homogeneity property:

>>> import numpy as np
>>> from scipy.special import elliprg

>>> x = 1.2 + 3.4j
>>> y = 5.
>>> z = 6.
>>> scale = 0.3 + 0.4j
>>> elliprg(scale*x, scale*y, scale*z)
(1.195936862005246+0.8470988320464167j)

>>> elliprg(x, y, z)*np.sqrt(scale)
(1.195936862005246+0.8470988320464165j)

Simplifications:

>>> elliprg(0, y, y)
1.756203682760182

>>> 0.25*np.pi*np.sqrt(y)
1.7562036827601817

>>> elliprg(0, 0, z)
1.224744871391589

>>> 0.5*np.sqrt(z)
1.224744871391589

The surface area of a triaxial ellipsoid with semiaxes ``a``, ``b``, and
``c`` is given by

.. math::

    S = 4 \pi a b c R_{\mathrm{G}}(1 / a^2, 1 / b^2, 1 / c^2).

>>> def ellipsoid_area(a, b, c):
...     r = 4.0 * np.pi * a * b * c
...     return r * elliprg(1.0 / (a * a), 1.0 / (b * b), 1.0 / (c * c))
>>> print(ellipsoid_area(1, 3, 5))
108.62688289491807      elliprj(x, y, z, p, out=None)

Symmetric elliptic integral of the third kind.

The function RJ is defined as [1]_

.. math::

    R_{\mathrm{J}}(x, y, z, p) =
       \frac{3}{2} \int_0^{+\infty} [(t + x) (t + y) (t + z)]^{-1/2}
       (t + p)^{-1} dt

.. warning::
    This function should be considered experimental when the inputs are
    unbalanced.  Check correctness with another independent implementation.

Parameters
----------
x, y, z, p : array_like
    Real or complex input parameters. `x`, `y`, or `z` are numbers in
    the complex plane cut along the negative real axis (subject to further
    constraints, see Notes), and at most one of them can be zero. `p` must
    be non-zero.
out : ndarray, optional
    Optional output array for the function values

Returns
-------
R : scalar or ndarray
    Value of the integral. If all of `x`, `y`, `z`, and `p` are real, the
    return value is real. Otherwise, the return value is complex.

    If `p` is real and negative, while `x`, `y`, and `z` are real,
    non-negative, and at most one of them is zero, the Cauchy principal
    value is returned. [1]_ [2]_

See Also
--------
elliprc : Degenerate symmetric integral.
elliprd : Symmetric elliptic integral of the second kind.
elliprf : Completely-symmetric elliptic integral of the first kind.
elliprg : Completely-symmetric elliptic integral of the second kind.

Notes
-----
The code implements Carlson's algorithm based on the duplication theorems
and series expansion up to the 7th order. [3]_ The algorithm is slightly
different from its earlier incarnation as it appears in [1]_, in that the
call to `elliprc` (or ``atan``/``atanh``, see [4]_) is no longer needed in
the inner loop. Asymptotic approximations are used where arguments differ
widely in the order of magnitude. [5]_

The input values are subject to certain sufficient but not necessary
constraints when input arguments are complex. Notably, ``x``, ``y``, and
``z`` must have non-negative real parts, unless two of them are
non-negative and complex-conjugates to each other while the other is a real
non-negative number. [1]_ If the inputs do not satisfy the sufficient
condition described in Ref. [1]_ they are rejected outright with the output
set to NaN.

In the case where one of ``x``, ``y``, and ``z`` is equal to ``p``, the
function ``elliprd`` should be preferred because of its less restrictive
domain.

.. versionadded:: 1.8.0

References
----------
.. [1] B. C. Carlson, "Numerical computation of real or complex elliptic
       integrals," Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995.
       https://arxiv.org/abs/math/9409227
       https://doi.org/10.1007/BF02198293
.. [2] B. C. Carlson, ed., Chapter 19 in "Digital Library of Mathematical
       Functions," NIST, US Dept. of Commerce.
       https://dlmf.nist.gov/19.20.iii
.. [3] B. C. Carlson, J. FitzSimmons, "Reduction Theorems for Elliptic
       Integrands with the Square Root of Two Quadratic Factors," J.
       Comput. Appl. Math., vol. 118, nos. 1-2, pp. 71-85, 2000.
       https://doi.org/10.1016/S0377-0427(00)00282-X
.. [4] F. Johansson, "Numerical Evaluation of Elliptic Functions, Elliptic
       Integrals and Modular Forms," in J. Blumlein, C. Schneider, P.
       Paule, eds., "Elliptic Integrals, Elliptic Functions and Modular
       Forms in Quantum Field Theory," pp. 269-293, 2019 (Cham,
       Switzerland: Springer Nature Switzerland)
       https://arxiv.org/abs/1806.06725
       https://doi.org/10.1007/978-3-030-04480-0
.. [5] B. C. Carlson, J. L. Gustafson, "Asymptotic Approximations for
       Symmetric Elliptic Integrals," SIAM J. Math. Anls., vol. 25, no. 2,
       pp. 288-303, 1994.
       https://arxiv.org/abs/math/9310223
       https://doi.org/10.1137/S0036141092228477

Examples
--------
Basic homogeneity property:

>>> import numpy as np
>>> from scipy.special import elliprj

>>> x = 1.2 + 3.4j
>>> y = 5.
>>> z = 6.
>>> p = 7.
>>> scale = 0.3 - 0.4j
>>> elliprj(scale*x, scale*y, scale*z, scale*p)
(0.10834905565679157+0.19694950747103812j)

>>> elliprj(x, y, z, p)*np.power(scale, -1.5)
(0.10834905565679556+0.19694950747103854j)

Reduction to simpler elliptic integral:

>>> elliprj(x, y, z, z)
(0.08288462362195129-0.028376809745123258j)

>>> from scipy.special import elliprd
>>> elliprd(x, y, z)
(0.08288462362195136-0.028376809745123296j)

All arguments coincide:

>>> elliprj(x, x, x, x)
(-0.03986825876151896-0.14051741840449586j)

>>> np.power(x, -1.5)
(-0.03986825876151894-0.14051741840449583j)   entr(x, out=None)

Elementwise function for computing entropy.

.. math:: \text{entr}(x) = \begin{cases} - x \log(x) & x > 0  \\ 0 & x = 0
          \\ -\infty & \text{otherwise} \end{cases}

Parameters
----------
x : ndarray
    Input array.
out : ndarray, optional
    Optional output array for the function values

Returns
-------
res : scalar or ndarray
    The value of the elementwise entropy function at the given points `x`.

See Also
--------
kl_div, rel_entr, scipy.stats.entropy

Notes
-----
.. versionadded:: 0.15.0

This function is concave.

The origin of this function is in convex programming; see [1]_.
Given a probability distribution :math:`p_1, \ldots, p_n`,
the definition of entropy in the context of *information theory* is

.. math::

    \sum_{i = 1}^n \mathrm{entr}(p_i).

To compute the latter quantity, use `scipy.stats.entropy`.

References
----------
.. [1] Boyd, Stephen and Lieven Vandenberghe. *Convex optimization*.
       Cambridge University Press, 2004.
       :doi:`https://doi.org/10.1017/CBO9780511804441`   erfcinv(y, out=None)

Inverse of the complementary error function.

Computes the inverse of the complementary error function.

In the complex domain, there is no unique complex number w satisfying
erfc(w)=z. This indicates a true inverse function would be multivalued.
When the domain restricts to the real, 0 < x < 2, there is a unique real
number satisfying erfc(erfcinv(x)) = erfcinv(erfc(x)).

It is related to inverse of the error function by erfcinv(1-x) = erfinv(x)

Parameters
----------
y : ndarray
    Argument at which to evaluate. Domain: [0, 2]
out : ndarray, optional
    Optional output array for the function values

Returns
-------
erfcinv : scalar or ndarray
    The inverse of erfc of y, element-wise

See Also
--------
erf : Error function of a complex argument
erfc : Complementary error function, ``1 - erf(x)``
erfinv : Inverse of the error function

Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy.special import erfcinv

>>> erfcinv(0.5)
0.4769362762044699

>>> y = np.linspace(0.0, 2.0, num=11)
>>> erfcinv(y)
array([        inf,  0.9061938 ,  0.59511608,  0.37080716,  0.17914345,
       -0.        , -0.17914345, -0.37080716, -0.59511608, -0.9061938 ,
              -inf])

Plot the function:

>>> y = np.linspace(0, 2, 200)
>>> fig, ax = plt.subplots()
>>> ax.plot(y, erfcinv(y))
>>> ax.grid(True)
>>> ax.set_xlabel('y')
>>> ax.set_title('erfcinv(y)')
>>> plt.show() erfinv(y, out=None)

Inverse of the error function.

Computes the inverse of the error function.

In the complex domain, there is no unique complex number w satisfying
erf(w)=z. This indicates a true inverse function would be multivalued.
When the domain restricts to the real, -1 < x < 1, there is a unique real
number satisfying erf(erfinv(x)) = x.

Parameters
----------
y : ndarray
    Argument at which to evaluate. Domain: [-1, 1]
out : ndarray, optional
    Optional output array for the function values

Returns
-------
erfinv : scalar or ndarray
    The inverse of erf of y, element-wise

See Also
--------
erf : Error function of a complex argument
erfc : Complementary error function, ``1 - erf(x)``
erfcinv : Inverse of the complementary error function

Notes
-----
This function wraps the ``erf_inv`` routine from the
Boost Math C++ library [1]_.

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy.special import erfinv, erf

>>> erfinv(0.5)
0.4769362762044699

>>> y = np.linspace(-1.0, 1.0, num=9)
>>> x = erfinv(y)
>>> x
array([       -inf, -0.81341985, -0.47693628, -0.22531206,  0.        ,
        0.22531206,  0.47693628,  0.81341985,         inf])

Verify that ``erf(erfinv(y))`` is ``y``.

>>> erf(x)
array([-1.  , -0.75, -0.5 , -0.25,  0.  ,  0.25,  0.5 ,  0.75,  1.  ])

Plot the function:

>>> y = np.linspace(-1, 1, 200)
>>> fig, ax = plt.subplots()
>>> ax.plot(y, erfinv(y))
>>> ax.grid(True)
>>> ax.set_xlabel('y')
>>> ax.set_title('erfinv(y)')
>>> plt.show()    eval_chebyc(n, x, out=None)

Evaluate Chebyshev polynomial of the first kind on [-2, 2] at a
point.

These polynomials are defined as

.. math::

    C_n(x) = 2 T_n(x/2)

where :math:`T_n` is a Chebyshev polynomial of the first kind. See
22.5.11 in [AS]_ (or equivalently [DLMF]_) for details.

Parameters
----------
n : array_like
    Degree of the polynomial. If not an integer, the result is
    determined via the relation to `eval_chebyt`.
x : array_like
    Points at which to evaluate the Chebyshev polynomial
out : ndarray, optional
    Optional output array for the function values

Returns
-------
C : scalar or ndarray
    Values of the Chebyshev polynomial

See Also
--------
roots_chebyc : roots and quadrature weights of Chebyshev
               polynomials of the first kind on [-2, 2]
chebyc : Chebyshev polynomial object
numpy.polynomial.chebyshev.Chebyshev : Chebyshev series
eval_chebyt : evaluate Chebycshev polynomials of the first kind

References
----------
.. [AS] Milton Abramowitz and Irene A. Stegun, eds.
    Handbook of Mathematical Functions with Formulas,
    Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [DLMF] NIST Digital Library of Mathematical Functions,
    https://dlmf.nist.gov/18.1.E3

Examples
--------
>>> import numpy as np
>>> import scipy.special as sc

They are a scaled version of the Chebyshev polynomials of the
first kind.

>>> x = np.linspace(-2, 2, 6)
>>> sc.eval_chebyc(3, x)
array([-2.   ,  1.872,  1.136, -1.136, -1.872,  2.   ])
>>> 2 * sc.eval_chebyt(3, x / 2)
array([-2.   ,  1.872,  1.136, -1.136, -1.872,  2.   ])     eval_chebys(n, x, out=None)

Evaluate Chebyshev polynomial of the second kind on [-2, 2] at a
point.

These polynomials are defined as

.. math::

    S_n(x) = U_n(x/2)

where :math:`U_n` is a Chebyshev polynomial of the second kind.
See 22.5.13 in [AS]_ (or equivalently [DLMF]_) for details.

Parameters
----------
n : array_like
    Degree of the polynomial. If not an integer, the result is
    determined via the relation to `eval_chebyu`.
x : array_like
    Points at which to evaluate the Chebyshev polynomial
out : ndarray, optional
    Optional output array for the function values

Returns
-------
S : scalar or ndarray
    Values of the Chebyshev polynomial

See Also
--------
roots_chebys : roots and quadrature weights of Chebyshev
               polynomials of the second kind on [-2, 2]
chebys : Chebyshev polynomial object
eval_chebyu : evaluate Chebyshev polynomials of the second kind

References
----------
.. [AS] Milton Abramowitz and Irene A. Stegun, eds.
    Handbook of Mathematical Functions with Formulas,
    Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [DLMF] NIST Digital Library of Mathematical Functions,
    https://dlmf.nist.gov/18.1.E3

Examples
--------
>>> import numpy as np
>>> import scipy.special as sc

They are a scaled version of the Chebyshev polynomials of the
second kind.

>>> x = np.linspace(-2, 2, 6)
>>> sc.eval_chebys(3, x)
array([-4.   ,  0.672,  0.736, -0.736, -0.672,  4.   ])
>>> sc.eval_chebyu(3, x / 2)
array([-4.   ,  0.672,  0.736, -0.736, -0.672,  4.   ])       eval_chebyt(n, x, out=None)

Evaluate Chebyshev polynomial of the first kind at a point.

The Chebyshev polynomials of the first kind can be defined via the
Gauss hypergeometric function :math:`{}_2F_1` as

.. math::

    T_n(x) = {}_2F_1(n, -n; 1/2; (1 - x)/2).

When :math:`n` is an integer the result is a polynomial of degree
:math:`n`. See 22.5.47 in [AS]_ (or equivalently [DLMF]_) for details.

Parameters
----------
n : array_like
    Degree of the polynomial. If not an integer, the result is
    determined via the relation to the Gauss hypergeometric
    function.
x : array_like
    Points at which to evaluate the Chebyshev polynomial
out : ndarray, optional
    Optional output array for the function values

Returns
-------
T : scalar or ndarray
    Values of the Chebyshev polynomial

See Also
--------
roots_chebyt : roots and quadrature weights of Chebyshev
               polynomials of the first kind
chebyu : Chebychev polynomial object
eval_chebyu : evaluate Chebyshev polynomials of the second kind
hyp2f1 : Gauss hypergeometric function
numpy.polynomial.chebyshev.Chebyshev : Chebyshev series

Notes
-----
This routine is numerically stable for `x` in ``[-1, 1]`` at least
up to order ``10000``.

References
----------
.. [AS] Milton Abramowitz and Irene A. Stegun, eds.
    Handbook of Mathematical Functions with Formulas,
    Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [DLMF] NIST Digital Library of Mathematical Functions,
    https://dlmf.nist.gov/18.5.E11_2 eval_chebyu(n, x, out=None)

Evaluate Chebyshev polynomial of the second kind at a point.

The Chebyshev polynomials of the second kind can be defined via
the Gauss hypergeometric function :math:`{}_2F_1` as

.. math::

    U_n(x) = (n + 1) {}_2F_1(-n, n + 2; 3/2; (1 - x)/2).

When :math:`n` is an integer the result is a polynomial of degree
:math:`n`. See 22.5.48 in [AS]_ (or equivalently [DLMF]_) for details.

Parameters
----------
n : array_like
    Degree of the polynomial. If not an integer, the result is
    determined via the relation to the Gauss hypergeometric
    function.
x : array_like
    Points at which to evaluate the Chebyshev polynomial
out : ndarray, optional
    Optional output array for the function values

Returns
-------
U : scalar or ndarray
    Values of the Chebyshev polynomial

See Also
--------
roots_chebyu : roots and quadrature weights of Chebyshev
               polynomials of the second kind
chebyu : Chebyshev polynomial object
eval_chebyt : evaluate Chebyshev polynomials of the first kind
hyp2f1 : Gauss hypergeometric function

References
----------
.. [AS] Milton Abramowitz and Irene A. Stegun, eds.
    Handbook of Mathematical Functions with Formulas,
    Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [DLMF] NIST Digital Library of Mathematical Functions,
    https://dlmf.nist.gov/18.5.E11_4  eval_gegenbauer(n, alpha, x, out=None)

Evaluate Gegenbauer polynomial at a point.

The Gegenbauer polynomials can be defined via the Gauss
hypergeometric function :math:`{}_2F_1` as

.. math::

    C_n^{(\alpha)} = \frac{(2\alpha)_n}{\Gamma(n + 1)}
      {}_2F_1(-n, 2\alpha + n; \alpha + 1/2; (1 - z)/2).

When :math:`n` is an integer the result is a polynomial of degree
:math:`n`. See 22.5.46 in [AS]_ (or equivalently [DLMF]_) for details.

Parameters
----------
n : array_like
    Degree of the polynomial. If not an integer, the result is
    determined via the relation to the Gauss hypergeometric
    function.
alpha : array_like
    Parameter
x : array_like
    Points at which to evaluate the Gegenbauer polynomial
out : ndarray, optional
    Optional output array for the function values

Returns
-------
C : scalar or ndarray
    Values of the Gegenbauer polynomial

See Also
--------
roots_gegenbauer : roots and quadrature weights of Gegenbauer
                   polynomials
gegenbauer : Gegenbauer polynomial object
hyp2f1 : Gauss hypergeometric function

References
----------
.. [AS] Milton Abramowitz and Irene A. Stegun, eds.
    Handbook of Mathematical Functions with Formulas,
    Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [DLMF] NIST Digital Library of Mathematical Functions,
    https://dlmf.nist.gov/18.5.E9        eval_genlaguerre(n, alpha, x, out=None)

Evaluate generalized Laguerre polynomial at a point.

The generalized Laguerre polynomials can be defined via the
confluent hypergeometric function :math:`{}_1F_1` as

.. math::

    L_n^{(\alpha)}(x) = \binom{n + \alpha}{n}
      {}_1F_1(-n, \alpha + 1, x).

When :math:`n` is an integer the result is a polynomial of degree
:math:`n`. See 22.5.54 in [AS]_ or [DLMF]_ for details. The Laguerre
polynomials are the special case where :math:`\alpha = 0`.

Parameters
----------
n : array_like
    Degree of the polynomial. If not an integer, the result is
    determined via the relation to the confluent hypergeometric
    function.
alpha : array_like
    Parameter; must have ``alpha > -1``
x : array_like
    Points at which to evaluate the generalized Laguerre
    polynomial
out : ndarray, optional
    Optional output array for the function values

Returns
-------
L : scalar or ndarray
    Values of the generalized Laguerre polynomial

See Also
--------
roots_genlaguerre : roots and quadrature weights of generalized
                    Laguerre polynomials
genlaguerre : generalized Laguerre polynomial object
hyp1f1 : confluent hypergeometric function
eval_laguerre : evaluate Laguerre polynomials

References
----------
.. [AS] Milton Abramowitz and Irene A. Stegun, eds.
    Handbook of Mathematical Functions with Formulas,
    Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [DLMF] NIST Digital Library of Mathematical Functions,
    https://dlmf.nist.gov/18.5.E12      eval_hermite(n, x, out=None)

Evaluate physicist's Hermite polynomial at a point.

Defined by

.. math::

    H_n(x) = (-1)^n e^{x^2} \frac{d^n}{dx^n} e^{-x^2};

:math:`H_n` is a polynomial of degree :math:`n`. See 22.11.7 in
[AS]_ or [DLMF]_ for details.

Parameters
----------
n : array_like
    Degree of the polynomial
x : array_like
    Points at which to evaluate the Hermite polynomial
out : ndarray, optional
    Optional output array for the function values

Returns
-------
H : scalar or ndarray
    Values of the Hermite polynomial

See Also
--------
roots_hermite : roots and quadrature weights of physicist's
                Hermite polynomials
hermite : physicist's Hermite polynomial object
numpy.polynomial.hermite.Hermite : Physicist's Hermite series
eval_hermitenorm : evaluate Probabilist's Hermite polynomials

References
----------
.. [AS] Milton Abramowitz and Irene A. Stegun, eds.
    Handbook of Mathematical Functions with Formulas,
    Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [DLMF] NIST Digital Library of Mathematical Functions,
    https://dlmf.nist.gov/18.5.T1  eval_hermitenorm(n, x, out=None)

Evaluate probabilist's (normalized) Hermite polynomial at a
point.

Defined by

.. math::

    He_n(x) = (-1)^n e^{x^2/2} \frac{d^n}{dx^n} e^{-x^2/2};

:math:`He_n` is a polynomial of degree :math:`n`. See 22.11.8 in
[AS]_ or [DLMF]_ for details.

Parameters
----------
n : array_like
    Degree of the polynomial
x : array_like
    Points at which to evaluate the Hermite polynomial
out : ndarray, optional
    Optional output array for the function values

Returns
-------
He : scalar or ndarray
    Values of the Hermite polynomial

See Also
--------
roots_hermitenorm : roots and quadrature weights of probabilist's
                    Hermite polynomials
hermitenorm : probabilist's Hermite polynomial object
numpy.polynomial.hermite_e.HermiteE : Probabilist's Hermite series
eval_hermite : evaluate physicist's Hermite polynomials

References
----------
.. [AS] Milton Abramowitz and Irene A. Stegun, eds.
    Handbook of Mathematical Functions with Formulas,
    Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [DLMF] NIST Digital Library of Mathematical Functions,
    https://dlmf.nist.gov/18.5.T1 eval_jacobi(n, alpha, beta, x, out=None)

Evaluate Jacobi polynomial at a point.

The Jacobi polynomials can be defined via the Gauss hypergeometric
function :math:`{}_2F_1` as

.. math::

    P_n^{(\alpha, \beta)}(x) = \frac{(\alpha + 1)_n}{\Gamma(n + 1)}
      {}_2F_1(-n, 1 + \alpha + \beta + n; \alpha + 1; (1 - z)/2)

where :math:`(\cdot)_n` is the Pochhammer symbol; see `poch`. When
:math:`n` is an integer the result is a polynomial of degree
:math:`n`. See 22.5.42 in [AS]_ or [DLMF]_ for details.

Parameters
----------
n : array_like
    Degree of the polynomial. If not an integer the result is
    determined via the relation to the Gauss hypergeometric
    function.
alpha : array_like
    Parameter
beta : array_like
    Parameter
x : array_like
    Points at which to evaluate the polynomial
out : ndarray, optional
    Optional output array for the function values

Returns
-------
P : scalar or ndarray
    Values of the Jacobi polynomial

See Also
--------
roots_jacobi : roots and quadrature weights of Jacobi polynomials
jacobi : Jacobi polynomial object
hyp2f1 : Gauss hypergeometric function

References
----------
.. [AS] Milton Abramowitz and Irene A. Stegun, eds.
    Handbook of Mathematical Functions with Formulas,
    Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [DLMF] NIST Digital Library of Mathematical Functions,
    https://dlmf.nist.gov/18.5.E7     eval_laguerre(n, x, out=None)

Evaluate Laguerre polynomial at a point.

The Laguerre polynomials can be defined via the confluent
hypergeometric function :math:`{}_1F_1` as

.. math::

    L_n(x) = {}_1F_1(-n, 1, x).

See 22.5.16 and 22.5.54 in [AS]_ (or equivalently [DLMF1]_ and [DLMF2]_)
for details. When :math:`n` is an integer the result is a polynomial
of degree :math:`n`.

Parameters
----------
n : array_like
    Degree of the polynomial. If not an integer the result is
    determined via the relation to the confluent hypergeometric
    function.
x : array_like
    Points at which to evaluate the Laguerre polynomial
out : ndarray, optional
    Optional output array for the function values

Returns
-------
L : scalar or ndarray
    Values of the Laguerre polynomial

See Also
--------
roots_laguerre : roots and quadrature weights of Laguerre
                 polynomials
laguerre : Laguerre polynomial object
numpy.polynomial.laguerre.Laguerre : Laguerre series
eval_genlaguerre : evaluate generalized Laguerre polynomials

References
----------
.. [AS] Milton Abramowitz and Irene A. Stegun, eds.
    Handbook of Mathematical Functions with Formulas,
    Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [DLMF1] NIST Digital Library of Mathematical Functions,
    https://dlmf.nist.gov/18.1#I1.ix7.p1
.. [DLMF2] NIST Digital Library of Mathematical Functions,
    https://dlmf.nist.gov/18.5.E12  eval_legendre(n, x, out=None)

Evaluate Legendre polynomial at a point.

The Legendre polynomials can be defined via the Gauss
hypergeometric function :math:`{}_2F_1` as

.. math::

    P_n(x) = {}_2F_1(-n, n + 1; 1; (1 - x)/2).

When :math:`n` is an integer the result is a polynomial of degree
:math:`n`. See 22.5.49 in [AS]_ (or equivalently [DLMF]_) for details.

Parameters
----------
n : array_like
    Degree of the polynomial. If not an integer, the result is
    determined via the relation to the Gauss hypergeometric
    function.
x : array_like
    Points at which to evaluate the Legendre polynomial
out : ndarray, optional
    Optional output array for the function values

Returns
-------
P : scalar or ndarray
    Values of the Legendre polynomial

See Also
--------
roots_legendre : roots and quadrature weights of Legendre
                 polynomials
legendre : Legendre polynomial object
hyp2f1 : Gauss hypergeometric function
numpy.polynomial.legendre.Legendre : Legendre series

References
----------
.. [AS] Milton Abramowitz and Irene A. Stegun, eds.
    Handbook of Mathematical Functions with Formulas,
    Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [DLMF] NIST Digital Library of Mathematical Functions,
    https://dlmf.nist.gov/15.9.E7

Examples
--------
>>> import numpy as np
>>> from scipy.special import eval_legendre

Evaluate the zero-order Legendre polynomial at x = 0

>>> eval_legendre(0, 0)
1.0

Evaluate the first-order Legendre polynomial between -1 and 1

>>> X = np.linspace(-1, 1, 5)  # Domain of Legendre polynomials
>>> eval_legendre(1, X)
array([-1. , -0.5,  0. ,  0.5,  1. ])

Evaluate Legendre polynomials of order 0 through 4 at x = 0

>>> N = range(0, 5)
>>> eval_legendre(N, 0)
array([ 1.   ,  0.   , -0.5  ,  0.   ,  0.375])

Plot Legendre polynomials of order 0 through 4

>>> X = np.linspace(-1, 1)

>>> import matplotlib.pyplot as plt
>>> for n in range(0, 5):
...     y = eval_legendre(n, X)
...     plt.plot(X, y, label=r'$P_{}(x)$'.format(n))

>>> plt.title("Legendre Polynomials")
>>> plt.xlabel("x")
>>> plt.ylabel(r'$P_n(x)$')
>>> plt.legend(loc='lower right')
>>> plt.show()       eval_sh_chebyt(n, x, out=None)

Evaluate shifted Chebyshev polynomial of the first kind at a
point.

These polynomials are defined as

.. math::

    T_n^*(x) = T_n(2x - 1)

where :math:`T_n` is a Chebyshev polynomial of the first kind. See
22.5.14 in [AS]_ (or equivalently [DLMF]_) for details.

Parameters
----------
n : array_like
    Degree of the polynomial. If not an integer, the result is
    determined via the relation to `eval_chebyt`.
x : array_like
    Points at which to evaluate the shifted Chebyshev polynomial
out : ndarray, optional
    Optional output array for the function values

Returns
-------
T : scalar or ndarray
    Values of the shifted Chebyshev polynomial

See Also
--------
roots_sh_chebyt : roots and quadrature weights of shifted
                  Chebyshev polynomials of the first kind
sh_chebyt : shifted Chebyshev polynomial object
eval_chebyt : evaluate Chebyshev polynomials of the first kind
numpy.polynomial.chebyshev.Chebyshev : Chebyshev series

References
----------
.. [AS] Milton Abramowitz and Irene A. Stegun, eds.
    Handbook of Mathematical Functions with Formulas,
    Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [DLMF] NIST Digital Library of Mathematical Functions,
    https://dlmf.nist.gov/18.7.E7  eval_sh_chebyu(n, x, out=None)

Evaluate shifted Chebyshev polynomial of the second kind at a
point.

These polynomials are defined as

.. math::

    U_n^*(x) = U_n(2x - 1)

where :math:`U_n` is a Chebyshev polynomial of the first kind. See
22.5.15 in [AS]_ (or equivalently [DLMF]_) for details.

Parameters
----------
n : array_like
    Degree of the polynomial. If not an integer, the result is
    determined via the relation to `eval_chebyu`.
x : array_like
    Points at which to evaluate the shifted Chebyshev polynomial
out : ndarray, optional
    Optional output array for the function values

Returns
-------
U : scalar or ndarray
    Values of the shifted Chebyshev polynomial

See Also
--------
roots_sh_chebyu : roots and quadrature weights of shifted
                  Chebychev polynomials of the second kind
sh_chebyu : shifted Chebyshev polynomial object
eval_chebyu : evaluate Chebyshev polynomials of the second kind

References
----------
.. [AS] Milton Abramowitz and Irene A. Stegun, eds.
    Handbook of Mathematical Functions with Formulas,
    Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [DLMF] NIST Digital Library of Mathematical Functions,
    https://dlmf.nist.gov/18.7.E8       eval_sh_jacobi(n, p, q, x, out=None)

Evaluate shifted Jacobi polynomial at a point.

Defined by

.. math::

    G_n^{(p, q)}(x)
      = \binom{2n + p - 1}{n}^{-1} P_n^{(p - q, q - 1)}(2x - 1),

where :math:`P_n^{(\cdot, \cdot)}` is the n-th Jacobi polynomial.
See 22.5.2 in [AS]_ (or equivalently [DLMF]_)  for details.

Parameters
----------
n : int
    Degree of the polynomial. If not an integer, the result is
    determined via the relation to `binom` and `eval_jacobi`.
p : float
    Parameter
q : float
    Parameter
out : ndarray, optional
    Optional output array for the function values

Returns
-------
G : scalar or ndarray
    Values of the shifted Jacobi polynomial.

See Also
--------
roots_sh_jacobi : roots and quadrature weights of shifted Jacobi
                  polynomials
sh_jacobi : shifted Jacobi polynomial object
eval_jacobi : evaluate Jacobi polynomials

References
----------
.. [AS] Milton Abramowitz and Irene A. Stegun, eds.
    Handbook of Mathematical Functions with Formulas,
    Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [DLMF] NIST Digital Library of Mathematical Functions,
    https://dlmf.nist.gov/18.1.E2    eval_sh_legendre(n, x, out=None)

Evaluate shifted Legendre polynomial at a point.

These polynomials are defined as

.. math::

    P_n^*(x) = P_n(2x - 1)

where :math:`P_n` is a Legendre polynomial. See 2.2.11 in [AS]_
or [DLMF]_ for details.

Parameters
----------
n : array_like
    Degree of the polynomial. If not an integer, the value is
    determined via the relation to `eval_legendre`.
x : array_like
    Points at which to evaluate the shifted Legendre polynomial
out : ndarray, optional
    Optional output array for the function values

Returns
-------
P : scalar or ndarray
    Values of the shifted Legendre polynomial

See Also
--------
roots_sh_legendre : roots and quadrature weights of shifted
                    Legendre polynomials
sh_legendre : shifted Legendre polynomial object
eval_legendre : evaluate Legendre polynomials
numpy.polynomial.legendre.Legendre : Legendre series

References
----------
.. [AS] Milton Abramowitz and Irene A. Stegun, eds.
    Handbook of Mathematical Functions with Formulas,
    Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [DLMF] NIST Digital Library of Mathematical Functions,
    https://dlmf.nist.gov/18.7.E10        expn(n, x, out=None)

Generalized exponential integral En.

For integer :math:`n \geq 0` and real :math:`x \geq 0` the
generalized exponential integral is defined as [DLMF]_

.. math::

    E_n(x) = x^{n - 1} \int_x^\infty \frac{e^{-t}}{t^n} dt.

Parameters
----------
n : array_like
    Non-negative integers
x : array_like
    Real argument
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    Values of the generalized exponential integral

See Also
--------
exp1 : special case of :math:`E_n` for :math:`n = 1`
expi : related to :math:`E_n` when :math:`n = 1`

References
----------
.. [DLMF] Digital Library of Mathematical Functions, 8.19.2
          https://dlmf.nist.gov/8.19#E2

Examples
--------
>>> import numpy as np
>>> import scipy.special as sc

Its domain is nonnegative n and x.

>>> sc.expn(-1, 1.0), sc.expn(1, -1.0)
(nan, nan)

It has a pole at ``x = 0`` for ``n = 1, 2``; for larger ``n`` it
is equal to ``1 / (n - 1)``.

>>> sc.expn([0, 1, 2, 3, 4], 0)
array([       inf,        inf, 1.        , 0.5       , 0.33333333])

For n equal to 0 it reduces to ``exp(-x) / x``.

>>> x = np.array([1, 2, 3, 4])
>>> sc.expn(0, x)
array([0.36787944, 0.06766764, 0.01659569, 0.00457891])
>>> np.exp(-x) / x
array([0.36787944, 0.06766764, 0.01659569, 0.00457891])

For n equal to 1 it reduces to `exp1`.

>>> sc.expn(1, x)
array([0.21938393, 0.04890051, 0.01304838, 0.00377935])
>>> sc.exp1(x)
array([0.21938393, 0.04890051, 0.01304838, 0.00377935]) fdtr(dfn, dfd, x, out=None)

F cumulative distribution function.

Returns the value of the cumulative distribution function of the
F-distribution, also known as Snedecor's F-distribution or the
Fisher-Snedecor distribution.

The F-distribution with parameters :math:`d_n` and :math:`d_d` is the
distribution of the random variable,

.. math::
    X = \frac{U_n/d_n}{U_d/d_d},

where :math:`U_n` and :math:`U_d` are random variables distributed
:math:`\chi^2`, with :math:`d_n` and :math:`d_d` degrees of freedom,
respectively.

Parameters
----------
dfn : array_like
    First parameter (positive float).
dfd : array_like
    Second parameter (positive float).
x : array_like
    Argument (nonnegative float).
out : ndarray, optional
    Optional output array for the function values

Returns
-------
y : scalar or ndarray
    The CDF of the F-distribution with parameters `dfn` and `dfd` at `x`.

See Also
--------
fdtrc : F distribution survival function
fdtri : F distribution inverse cumulative distribution
scipy.stats.f : F distribution

Notes
-----
The regularized incomplete beta function is used, according to the
formula,

.. math::
    F(d_n, d_d; x) = I_{xd_n/(d_d + xd_n)}(d_n/2, d_d/2).

Wrapper for a routine from the Boost Math C++ library [1]_. The
F distribution is also available as `scipy.stats.f`. Calling
`fdtr` directly can improve performance compared to the ``cdf``
method of `scipy.stats.f` (see last example below).

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.


Examples
--------
Calculate the function for ``dfn=1`` and ``dfd=2`` at ``x=1``.

>>> import numpy as np
>>> from scipy.special import fdtr
>>> fdtr(1, 2, 1)
0.5773502691896258

Calculate the function at several points by providing a NumPy array for
`x`.

>>> x = np.array([0.5, 2., 3.])
>>> fdtr(1, 2, x)
array([0.4472136 , 0.70710678, 0.77459667])

Plot the function for several parameter sets.

>>> import matplotlib.pyplot as plt
>>> dfn_parameters = [1, 5, 10, 50]
>>> dfd_parameters = [1, 1, 2, 3]
>>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
>>> parameters_list = list(zip(dfn_parameters, dfd_parameters,
...                            linestyles))
>>> x = np.linspace(0, 30, 1000)
>>> fig, ax = plt.subplots()
>>> for parameter_set in parameters_list:
...     dfn, dfd, style = parameter_set
...     fdtr_vals = fdtr(dfn, dfd, x)
...     ax.plot(x, fdtr_vals, label=rf"$d_n={dfn},\, d_d={dfd}$",
...             ls=style)
>>> ax.legend()
>>> ax.set_xlabel("$x$")
>>> ax.set_title("F distribution cumulative distribution function")
>>> plt.show()

The F distribution is also available as `scipy.stats.f`. Using `fdtr`
directly can be much faster than calling the ``cdf`` method of
`scipy.stats.f`, especially for small arrays or individual values.
To get the same results one must use the following parametrization:
``stats.f(dfn, dfd).cdf(x)=fdtr(dfn, dfd, x)``.

>>> from scipy.stats import f
>>> dfn, dfd = 1, 2
>>> x = 1
>>> fdtr_res = fdtr(dfn, dfd, x)  # this will often be faster than below
>>> f_dist_res = f(dfn, dfd).cdf(x)
>>> fdtr_res == f_dist_res  # test that results are equal
True        fdtrc(dfn, dfd, x, out=None)

F survival function.

Returns the complemented F-distribution function (the integral of the
density from `x` to infinity).

Parameters
----------
dfn : array_like
    First parameter (positive float).
dfd : array_like
    Second parameter (positive float).
x : array_like
    Argument (nonnegative float).
out : ndarray, optional
    Optional output array for the function values

Returns
-------
y : scalar or ndarray
    The complemented F-distribution function with parameters `dfn` and
    `dfd` at `x`.

See Also
--------
fdtr : F distribution cumulative distribution function
fdtri : F distribution inverse cumulative distribution function
scipy.stats.f : F distribution

Notes
-----
The regularized incomplete beta function is used, according to the
formula,

.. math::
    F(d_n, d_d; x) = I_{d_d/(d_d + xd_n)}(d_d/2, d_n/2).

Wrapper for a routine from the Boost Math C++ library [1]_. The
F distribution is also available as `scipy.stats.f`. Calling
`fdtrc` directly can improve performance compared to the ``sf``
method of `scipy.stats.f` (see last example below).

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
Calculate the function for ``dfn=1`` and ``dfd=2`` at ``x=1``.

>>> import numpy as np
>>> from scipy.special import fdtrc
>>> fdtrc(1, 2, 1)
0.42264973081037427

Calculate the function at several points by providing a NumPy array for
`x`.

>>> x = np.array([0.5, 2., 3.])
>>> fdtrc(1, 2, x)
array([0.5527864 , 0.29289322, 0.22540333])

Plot the function for several parameter sets.

>>> import matplotlib.pyplot as plt
>>> dfn_parameters = [1, 5, 10, 50]
>>> dfd_parameters = [1, 1, 2, 3]
>>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
>>> parameters_list = list(zip(dfn_parameters, dfd_parameters,
...                            linestyles))
>>> x = np.linspace(0, 30, 1000)
>>> fig, ax = plt.subplots()
>>> for parameter_set in parameters_list:
...     dfn, dfd, style = parameter_set
...     fdtrc_vals = fdtrc(dfn, dfd, x)
...     ax.plot(x, fdtrc_vals, label=rf"$d_n={dfn},\, d_d={dfd}$",
...             ls=style)
>>> ax.legend()
>>> ax.set_xlabel("$x$")
>>> ax.set_title("F distribution survival function")
>>> plt.show()

The F distribution is also available as `scipy.stats.f`. Using `fdtrc`
directly can be much faster than calling the ``sf`` method of
`scipy.stats.f`, especially for small arrays or individual values.
To get the same results one must use the following parametrization:
``stats.f(dfn, dfd).sf(x)=fdtrc(dfn, dfd, x)``.

>>> from scipy.stats import f
>>> dfn, dfd = 1, 2
>>> x = 1
>>> fdtrc_res = fdtrc(dfn, dfd, x)  # this will often be faster than below
>>> f_dist_res = f(dfn, dfd).sf(x)
>>> f_dist_res == fdtrc_res  # test that results are equal
True        fdtri(dfn, dfd, p, out=None)

The `p`-th quantile of the F-distribution.

This function is the inverse of the F-distribution CDF, `fdtr`, returning
the `x` such that `fdtr(dfn, dfd, x) = p`.

Parameters
----------
dfn : array_like
    First parameter (positive float).
dfd : array_like
    Second parameter (positive float).
p : array_like
    Cumulative probability, in [0, 1].
out : ndarray, optional
    Optional output array for the function values

Returns
-------
x : scalar or ndarray
    The quantile corresponding to `p`.

See Also
--------
fdtr : F distribution cumulative distribution function
fdtrc : F distribution survival function
scipy.stats.f : F distribution

Notes
-----
Wrapper for a routine from the Boost Math C++ library [1]_. The
F distribution is also available as `scipy.stats.f`. Calling
`fdtri` directly can improve performance compared to the ``ppf``
method of `scipy.stats.f` (see last example below).

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
`fdtri` represents the inverse of the F distribution CDF which is
available as `fdtr`. Here, we calculate the CDF for ``df1=1``, ``df2=2``
at ``x=3``. `fdtri` then returns ``3`` given the same values for `df1`,
`df2` and the computed CDF value.

>>> import numpy as np
>>> from scipy.special import fdtri, fdtr
>>> df1, df2 = 1, 2
>>> x = 3
>>> cdf_value =  fdtr(df1, df2, x)
>>> fdtri(df1, df2, cdf_value)
3.000000000000006

Calculate the function at several points by providing a NumPy array for
`x`.

>>> x = np.array([0.1, 0.4, 0.7])
>>> fdtri(1, 2, x)
array([0.02020202, 0.38095238, 1.92156863])

Plot the function for several parameter sets.

>>> import matplotlib.pyplot as plt
>>> dfn_parameters = [50, 10, 1, 50]
>>> dfd_parameters = [0.5, 1, 1, 5]
>>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
>>> parameters_list = list(zip(dfn_parameters, dfd_parameters,
...                            linestyles))
>>> x = np.linspace(0, 1, 1000)
>>> fig, ax = plt.subplots()
>>> for parameter_set in parameters_list:
...     dfn, dfd, style = parameter_set
...     fdtri_vals = fdtri(dfn, dfd, x)
...     ax.plot(x, fdtri_vals, label=rf"$d_n={dfn},\, d_d={dfd}$",
...             ls=style)
>>> ax.legend()
>>> ax.set_xlabel("$x$")
>>> title = "F distribution inverse cumulative distribution function"
>>> ax.set_title(title)
>>> ax.set_ylim(0, 30)
>>> plt.show()

The F distribution is also available as `scipy.stats.f`. Using `fdtri`
directly can be much faster than calling the ``ppf`` method of
`scipy.stats.f`, especially for small arrays or individual values.
To get the same results one must use the following parametrization:
``stats.f(dfn, dfd).ppf(x)=fdtri(dfn, dfd, x)``.

>>> from scipy.stats import f
>>> dfn, dfd = 1, 2
>>> x = 0.7
>>> fdtri_res = fdtri(dfn, dfd, x)  # this will often be faster than below
>>> f_dist_res = f(dfn, dfd).ppf(x)
>>> f_dist_res == fdtri_res  # test that results are equal
True      fdtridfd(dfn, p, x, out=None)

Inverse to `fdtr` vs dfd

Finds the F density argument dfd such that ``fdtr(dfn, dfd, x) == p``.

Parameters
----------
dfn : array_like
    First parameter (positive float).
p : array_like
    Cumulative probability, in [0, 1].
x : array_like
    Argument (nonnegative float).
out : ndarray, optional
    Optional output array for the function values

Returns
-------
dfd : scalar or ndarray
    `dfd` such that ``fdtr(dfn, dfd, x) == p``.

See Also
--------
fdtr : F distribution cumulative distribution function
fdtrc : F distribution survival function
fdtri : F distribution quantile function
scipy.stats.f : F distribution

Examples
--------
Compute the F distribution cumulative distribution function for one
parameter set.

>>> from scipy.special import fdtridfd, fdtr
>>> dfn, dfd, x = 10, 5, 2
>>> cdf_value = fdtr(dfn, dfd, x)
>>> cdf_value
0.7700248806501017

Verify that `fdtridfd` recovers the original value for `dfd`:

>>> fdtridfd(dfn, cdf_value, x)
5.0        gdtr(a, b, x, out=None)

Gamma distribution cumulative distribution function.

Returns the integral from zero to `x` of the gamma probability density
function,

.. math::

    F = \int_0^x \frac{a^b}{\Gamma(b)} t^{b-1} e^{-at}\,dt,

where :math:`\Gamma` is the gamma function.

Parameters
----------
a : array_like
    The rate parameter of the gamma distribution, sometimes denoted
    :math:`\beta` (float).  It is also the reciprocal of the scale
    parameter :math:`\theta`.
b : array_like
    The shape parameter of the gamma distribution, sometimes denoted
    :math:`\alpha` (float).
x : array_like
    The quantile (upper limit of integration; float).
out : ndarray, optional
    Optional output array for the function values

Returns
-------
F : scalar or ndarray
    The CDF of the gamma distribution with parameters `a` and `b`
    evaluated at `x`.

See Also
--------
gdtrc : 1 - CDF of the gamma distribution.
scipy.stats.gamma: Gamma distribution

Notes
-----
The evaluation is carried out using the relation to the incomplete gamma
integral (regularized gamma function).

Wrapper for the Cephes [1]_ routine `gdtr`. Calling `gdtr` directly can
improve performance compared to the ``cdf`` method of `scipy.stats.gamma`
(see last example below).

References
----------
.. [1] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/

Examples
--------
Compute the function for ``a=1``, ``b=2`` at ``x=5``.

>>> import numpy as np
>>> from scipy.special import gdtr
>>> import matplotlib.pyplot as plt
>>> gdtr(1., 2., 5.)
0.9595723180054873

Compute the function for ``a=1`` and ``b=2`` at several points by
providing a NumPy array for `x`.

>>> xvalues = np.array([1., 2., 3., 4])
>>> gdtr(1., 1., xvalues)
array([0.63212056, 0.86466472, 0.95021293, 0.98168436])

`gdtr` can evaluate different parameter sets by providing arrays with
broadcasting compatible shapes for `a`, `b` and `x`. Here we compute the
function for three different `a` at four positions `x` and ``b=3``,
resulting in a 3x4 array.

>>> a = np.array([[0.5], [1.5], [2.5]])
>>> x = np.array([1., 2., 3., 4])
>>> a.shape, x.shape
((3, 1), (4,))

>>> gdtr(a, 3., x)
array([[0.01438768, 0.0803014 , 0.19115317, 0.32332358],
       [0.19115317, 0.57680992, 0.82642193, 0.9380312 ],
       [0.45618688, 0.87534798, 0.97974328, 0.9972306 ]])

Plot the function for four different parameter sets.

>>> a_parameters = [0.3, 1, 2, 6]
>>> b_parameters = [2, 10, 15, 20]
>>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
>>> parameters_list = list(zip(a_parameters, b_parameters, linestyles))
>>> x = np.linspace(0, 30, 1000)
>>> fig, ax = plt.subplots()
>>> for parameter_set in parameters_list:
...     a, b, style = parameter_set
...     gdtr_vals = gdtr(a, b, x)
...     ax.plot(x, gdtr_vals, label=fr"$a= {a},\, b={b}$", ls=style)
>>> ax.legend()
>>> ax.set_xlabel("$x$")
>>> ax.set_title("Gamma distribution cumulative distribution function")
>>> plt.show()

The gamma distribution is also available as `scipy.stats.gamma`. Using
`gdtr` directly can be much faster than calling the ``cdf`` method of
`scipy.stats.gamma`, especially for small arrays or individual values.
To get the same results one must use the following parametrization:
``stats.gamma(b, scale=1/a).cdf(x)=gdtr(a, b, x)``.

>>> from scipy.stats import gamma
>>> a = 2.
>>> b = 3
>>> x = 1.
>>> gdtr_result = gdtr(a, b, x)  # this will often be faster than below
>>> gamma_dist_result = gamma(b, scale=1/a).cdf(x)
>>> gdtr_result == gamma_dist_result  # test that results are equal
True  gdtrc(a, b, x, out=None)

Gamma distribution survival function.

Integral from `x` to infinity of the gamma probability density function,

.. math::

    F = \int_x^\infty \frac{a^b}{\Gamma(b)} t^{b-1} e^{-at}\,dt,

where :math:`\Gamma` is the gamma function.

Parameters
----------
a : array_like
    The rate parameter of the gamma distribution, sometimes denoted
    :math:`\beta` (float). It is also the reciprocal of the scale
    parameter :math:`\theta`.
b : array_like
    The shape parameter of the gamma distribution, sometimes denoted
    :math:`\alpha` (float).
x : array_like
    The quantile (lower limit of integration; float).
out : ndarray, optional
    Optional output array for the function values

Returns
-------
F : scalar or ndarray
    The survival function of the gamma distribution with parameters `a`
    and `b` evaluated at `x`.

See Also
--------
gdtr: Gamma distribution cumulative distribution function
scipy.stats.gamma: Gamma distribution
gdtrix

Notes
-----
The evaluation is carried out using the relation to the incomplete gamma
integral (regularized gamma function).

Wrapper for the Cephes [1]_ routine `gdtrc`. Calling `gdtrc` directly can
improve performance compared to the ``sf`` method of `scipy.stats.gamma`
(see last example below).

References
----------
.. [1] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/

Examples
--------
Compute the function for ``a=1`` and ``b=2`` at ``x=5``.

>>> import numpy as np
>>> from scipy.special import gdtrc
>>> import matplotlib.pyplot as plt
>>> gdtrc(1., 2., 5.)
0.04042768199451279

Compute the function for ``a=1``, ``b=2`` at several points by providing
a NumPy array for `x`.

>>> xvalues = np.array([1., 2., 3., 4])
>>> gdtrc(1., 1., xvalues)
array([0.36787944, 0.13533528, 0.04978707, 0.01831564])

`gdtrc` can evaluate different parameter sets by providing arrays with
broadcasting compatible shapes for `a`, `b` and `x`. Here we compute the
function for three different `a` at four positions `x` and ``b=3``,
resulting in a 3x4 array.

>>> a = np.array([[0.5], [1.5], [2.5]])
>>> x = np.array([1., 2., 3., 4])
>>> a.shape, x.shape
((3, 1), (4,))

>>> gdtrc(a, 3., x)
array([[0.98561232, 0.9196986 , 0.80884683, 0.67667642],
       [0.80884683, 0.42319008, 0.17357807, 0.0619688 ],
       [0.54381312, 0.12465202, 0.02025672, 0.0027694 ]])

Plot the function for four different parameter sets.

>>> a_parameters = [0.3, 1, 2, 6]
>>> b_parameters = [2, 10, 15, 20]
>>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
>>> parameters_list = list(zip(a_parameters, b_parameters, linestyles))
>>> x = np.linspace(0, 30, 1000)
>>> fig, ax = plt.subplots()
>>> for parameter_set in parameters_list:
...     a, b, style = parameter_set
...     gdtrc_vals = gdtrc(a, b, x)
...     ax.plot(x, gdtrc_vals, label=fr"$a= {a},\, b={b}$", ls=style)
>>> ax.legend()
>>> ax.set_xlabel("$x$")
>>> ax.set_title("Gamma distribution survival function")
>>> plt.show()

The gamma distribution is also available as `scipy.stats.gamma`.
Using `gdtrc` directly can be much faster than calling the ``sf`` method
of `scipy.stats.gamma`, especially for small arrays or individual
values. To get the same results one must use the following parametrization:
``stats.gamma(b, scale=1/a).sf(x)=gdtrc(a, b, x)``.

>>> from scipy.stats import gamma
>>> a = 2
>>> b = 3
>>> x = 1.
>>> gdtrc_result = gdtrc(a, b, x)  # this will often be faster than below
>>> gamma_dist_result = gamma(b, scale=1/a).sf(x)
>>> gdtrc_result == gamma_dist_result  # test that results are equal
True    gdtria(p, b, x, out=None)

Inverse of `gdtr` vs a.

Returns the inverse with respect to the parameter `a` of ``p =
gdtr(a, b, x)``, the cumulative distribution function of the gamma
distribution.

Parameters
----------
p : array_like
    Probability values.
b : array_like
    `b` parameter values of `gdtr(a, b, x)`. `b` is the "shape" parameter
    of the gamma distribution.
x : array_like
    Nonnegative real values, from the domain of the gamma distribution.
out : ndarray, optional
    If a fourth argument is given, it must be a numpy.ndarray whose size
    matches the broadcast result of `a`, `b` and `x`.  `out` is then the
    array returned by the function.

Returns
-------
a : scalar or ndarray
    Values of the `a` parameter such that ``p = gdtr(a, b, x)`.  ``1/a``
    is the "scale" parameter of the gamma distribution.

See Also
--------
gdtr : CDF of the gamma distribution.
gdtrib : Inverse with respect to `b` of `gdtr(a, b, x)`.
gdtrix : Inverse with respect to `x` of `gdtr(a, b, x)`.

Notes
-----
Wrapper for the CDFLIB [1]_ Fortran routine `cdfgam`.

The cumulative distribution function `p` is computed using a routine by
DiDinato and Morris [2]_. Computation of `a` involves a search for a value
that produces the desired value of `p`. The search relies on the
monotonicity of `p` with `a`.

References
----------
.. [1] Barry Brown, James Lovato, and Kathy Russell,
       CDFLIB: Library of Fortran Routines for Cumulative Distribution
       Functions, Inverses, and Other Parameters.
.. [2] DiDinato, A. R. and Morris, A. H.,
       Computation of the incomplete gamma function ratios and their
       inverse.  ACM Trans. Math. Softw. 12 (1986), 377-393.

Examples
--------
First evaluate `gdtr`.

>>> from scipy.special import gdtr, gdtria
>>> p = gdtr(1.2, 3.4, 5.6)
>>> print(p)
0.94378087442

Verify the inverse.

>>> gdtria(p, 3.4, 5.6)
1.2 gdtrib(a, p, x, out=None)

Inverse of `gdtr` vs b.

Returns the inverse with respect to the parameter `b` of ``p =
gdtr(a, b, x)``, the cumulative distribution function of the gamma
distribution.

Parameters
----------
a : array_like
    `a` parameter values of ``gdtr(a, b, x)`. ``1/a`` is the "scale"
    parameter of the gamma distribution.
p : array_like
    Probability values.
x : array_like
    Nonnegative real values, from the domain of the gamma distribution.
out : ndarray, optional
    If a fourth argument is given, it must be a numpy.ndarray whose size
    matches the broadcast result of `a`, `b` and `x`.  `out` is then the
    array returned by the function.

Returns
-------
b : scalar or ndarray
    Values of the `b` parameter such that `p = gdtr(a, b, x)`.  `b` is
    the "shape" parameter of the gamma distribution.

See Also
--------
gdtr : CDF of the gamma distribution.
gdtria : Inverse with respect to `a` of `gdtr(a, b, x)`.
gdtrix : Inverse with respect to `x` of `gdtr(a, b, x)`.

Notes
-----

The cumulative distribution function `p` is computed using the Cephes [1]_
routines `igam` and `igamc`. Computation of `b` involves a search for a value
that produces the desired value of `p` using Chandrupatla's bracketing
root finding algorithm [2]_.

Note that there are some edge cases where `gdtrib` is extended by taking
limits where they are uniquely defined. In particular
``x == 0`` with ``p > 0`` and ``p == 0`` with ``x > 0``.
For these edge cases, a numerical result will be returned for
``gdtrib(a, p, x)`` even though ``gdtr(a, gdtrib(a, p, x), x)`` is
undefined.

References
----------
.. [1] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/
.. [2] Chandrupatla, Tirupathi R.
       "A new hybrid quadratic/bisection algorithm for finding the zero of a
       nonlinear function without using derivatives".
       Advances in Engineering Software, 28(3), 145-149.
       https://doi.org/10.1016/s0965-9978(96)00051-8

Examples
--------
First evaluate `gdtr`.

>>> from scipy.special import gdtr, gdtrib
>>> p = gdtr(1.2, 3.4, 5.6)
>>> print(p)
0.94378087442

Verify the inverse.

>>> gdtrib(1.2, p, 5.6)
3.3999999999999995    gdtrix(a, b, p, out=None)

Inverse of `gdtr` vs x.

Returns the inverse with respect to the parameter `x` of ``p =
gdtr(a, b, x)``, the cumulative distribution function of the gamma
distribution. This is also known as the pth quantile of the
distribution.

Parameters
----------
a : array_like
    `a` parameter values of ``gdtr(a, b, x)``. ``1/a`` is the "scale"
    parameter of the gamma distribution.
b : array_like
    `b` parameter values of ``gdtr(a, b, x)``. `b` is the "shape" parameter
    of the gamma distribution.
p : array_like
    Probability values.
out : ndarray, optional
    If a fourth argument is given, it must be a numpy.ndarray whose size
    matches the broadcast result of `a`, `b` and `x`. `out` is then the
    array returned by the function.

Returns
-------
x : scalar or ndarray
    Values of the `x` parameter such that `p = gdtr(a, b, x)`.

See Also
--------
gdtr : CDF of the gamma distribution.
gdtria : Inverse with respect to `a` of ``gdtr(a, b, x)``.
gdtrib : Inverse with respect to `b` of ``gdtr(a, b, x)``.

Notes
-----
Wrapper for the CDFLIB [1]_ Fortran routine `cdfgam`.

The cumulative distribution function `p` is computed using a routine by
DiDinato and Morris [2]_. Computation of `x` involves a search for a value
that produces the desired value of `p`. The search relies on the
monotonicity of `p` with `x`.

References
----------
.. [1] Barry Brown, James Lovato, and Kathy Russell,
       CDFLIB: Library of Fortran Routines for Cumulative Distribution
       Functions, Inverses, and Other Parameters.
.. [2] DiDinato, A. R. and Morris, A. H.,
       Computation of the incomplete gamma function ratios and their
       inverse.  ACM Trans. Math. Softw. 12 (1986), 377-393.

Examples
--------
First evaluate `gdtr`.

>>> from scipy.special import gdtr, gdtrix
>>> p = gdtr(1.2, 3.4, 5.6)
>>> print(p)
0.94378087442

Verify the inverse.

>>> gdtrix(1.2, 3.4, p)
5.5999999999999996    huber(delta, r, out=None)

Huber loss function.

.. math:: \text{huber}(\delta, r) = \begin{cases} \infty & \delta < 0  \\
          \frac{1}{2}r^2 & 0 \le \delta, | r | \le \delta \\
          \delta ( |r| - \frac{1}{2}\delta ) & \text{otherwise} \end{cases}

Parameters
----------
delta : ndarray
    Input array, indicating the quadratic vs. linear loss changepoint.
r : ndarray
    Input array, possibly representing residuals.
out : ndarray, optional
    Optional output array for the function values

Returns
-------
scalar or ndarray
    The computed Huber loss function values.

See Also
--------
pseudo_huber : smooth approximation of this function

Notes
-----
`huber` is useful as a loss function in robust statistics or machine
learning to reduce the influence of outliers as compared to the common
squared error loss, residuals with a magnitude higher than `delta` are
not squared [1]_.

Typically, `r` represents residuals, the difference
between a model prediction and data. Then, for :math:`|r|\leq\delta`,
`huber` resembles the squared error and for :math:`|r|>\delta` the
absolute error. This way, the Huber loss often achieves
a fast convergence in model fitting for small residuals like the squared
error loss function and still reduces the influence of outliers
(:math:`|r|>\delta`) like the absolute error loss. As :math:`\delta` is
the cutoff between squared and absolute error regimes, it has
to be tuned carefully for each problem. `huber` is also
convex, making it suitable for gradient based optimization.

.. versionadded:: 0.15.0

References
----------
.. [1] Peter Huber. "Robust Estimation of a Location Parameter",
       1964. Annals of Statistics. 53 (1): 73 - 101.

Examples
--------
Import all necessary modules.

>>> import numpy as np
>>> from scipy.special import huber
>>> import matplotlib.pyplot as plt

Compute the function for ``delta=1`` at ``r=2``

>>> huber(1., 2.)
1.5

Compute the function for different `delta` by providing a NumPy array or
list for `delta`.

>>> huber([1., 3., 5.], 4.)
array([3.5, 7.5, 8. ])

Compute the function at different points by providing a NumPy array or
list for `r`.

>>> huber(2., np.array([1., 1.5, 3.]))
array([0.5  , 1.125, 4.   ])

The function can be calculated for different `delta` and `r` by
providing arrays for both with compatible shapes for broadcasting.

>>> r = np.array([1., 2.5, 8., 10.])
>>> deltas = np.array([[1.], [5.], [9.]])
>>> print(r.shape, deltas.shape)
(4,) (3, 1)

>>> huber(deltas, r)
array([[ 0.5  ,  2.   ,  7.5  ,  9.5  ],
       [ 0.5  ,  3.125, 27.5  , 37.5  ],
       [ 0.5  ,  3.125, 32.   , 49.5  ]])

Plot the function for different `delta`.

>>> x = np.linspace(-4, 4, 500)
>>> deltas = [1, 2, 3]
>>> linestyles = ["dashed", "dotted", "dashdot"]
>>> fig, ax = plt.subplots()
>>> combined_plot_parameters = list(zip(deltas, linestyles))
>>> for delta, style in combined_plot_parameters:
...     ax.plot(x, huber(delta, x), label=fr"$\delta={delta}$", ls=style)
>>> ax.legend(loc="upper center")
>>> ax.set_xlabel("$x$")
>>> ax.set_title(r"Huber loss function $h_{\delta}(x)$")
>>> ax.set_xlim(-4, 4)
>>> ax.set_ylim(0, 8)
>>> plt.show()     hyp0f1(v, z, out=None)

Confluent hypergeometric limit function 0F1.

Parameters
----------
v : array_like
    Real-valued parameter
z : array_like
    Real- or complex-valued argument
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    The confluent hypergeometric limit function

Notes
-----
This function is defined as:

.. math:: _0F_1(v, z) = \sum_{k=0}^{\infty}\frac{z^k}{(v)_k k!}.

It's also the limit as :math:`q \to \infty` of :math:`_1F_1(q; v; z/q)`,
and satisfies the differential equation :math:`f''(z) + vf'(z) =
f(z)`. See [1]_ for more information.

References
----------
.. [1] Wolfram MathWorld, "Confluent Hypergeometric Limit Function",
       http://mathworld.wolfram.com/ConfluentHypergeometricLimitFunction.html

Examples
--------
>>> import numpy as np
>>> import scipy.special as sc

It is one when `z` is zero.

>>> sc.hyp0f1(1, 0)
1.0

It is the limit of the confluent hypergeometric function as `q`
goes to infinity.

>>> q = np.array([1, 10, 100, 1000])
>>> v = 1
>>> z = 1
>>> sc.hyp1f1(q, v, z / q)
array([2.71828183, 2.31481985, 2.28303778, 2.27992985])
>>> sc.hyp0f1(v, z)
2.2795853023360673

It is related to Bessel functions.

>>> n = 1
>>> x = np.linspace(0, 1, 5)
>>> sc.jv(n, x)
array([0.        , 0.12402598, 0.24226846, 0.3492436 , 0.44005059])
>>> (0.5 * x)**n / sc.factorial(n) * sc.hyp0f1(n + 1, -0.25 * x**2)
array([0.        , 0.12402598, 0.24226846, 0.3492436 , 0.44005059])     hyp1f1(a, b, x, out=None)

Confluent hypergeometric function 1F1.

The confluent hypergeometric function is defined by the series

.. math::

   {}_1F_1(a; b; x) = \sum_{k = 0}^\infty \frac{(a)_k}{(b)_k k!} x^k.

See [DLMF]_ for more details. Here :math:`(\cdot)_k` is the
Pochhammer symbol; see `poch`.

Parameters
----------
a, b : array_like
    Real parameters
x : array_like
    Real or complex argument
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    Values of the confluent hypergeometric function

See Also
--------
hyperu : another confluent hypergeometric function
hyp0f1 : confluent hypergeometric limit function
hyp2f1 : Gaussian hypergeometric function

Notes
-----
For real values, this function uses the ``hyp1f1`` routine from the C++ Boost
library [2]_, for complex values a C translation of the specfun
Fortran library [3]_.

References
----------
.. [DLMF] NIST Digital Library of Mathematical Functions
          https://dlmf.nist.gov/13.2#E2
.. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
.. [3] Zhang, Jin, "Computation of Special Functions", John Wiley
       and Sons, Inc, 1996.

Examples
--------
>>> import numpy as np
>>> import scipy.special as sc

It is one when `x` is zero:

>>> sc.hyp1f1(0.5, 0.5, 0)
1.0

It is singular when `b` is a nonpositive integer.

>>> sc.hyp1f1(0.5, -1, 0)
inf

It is a polynomial when `a` is a nonpositive integer.

>>> a, b, x = -1, 0.5, np.array([1.0, 2.0, 3.0, 4.0])
>>> sc.hyp1f1(a, b, x)
array([-1., -3., -5., -7.])
>>> 1 + (a / b) * x
array([-1., -3., -5., -7.])

It reduces to the exponential function when ``a = b``.

>>> sc.hyp1f1(2, 2, [1, 2, 3, 4])
array([ 2.71828183,  7.3890561 , 20.08553692, 54.59815003])
>>> np.exp([1, 2, 3, 4])
array([ 2.71828183,  7.3890561 , 20.08553692, 54.59815003])     hyperu(a, b, x, out=None)

Confluent hypergeometric function U

It is defined as the solution to the equation

.. math::

   x \frac{d^2w}{dx^2} + (b - x) \frac{dw}{dx} - aw = 0

which satisfies the property

.. math::

   U(a, b, x) \sim x^{-a}

as :math:`x \to \infty`. See [DLMF]_ for more details.

Parameters
----------
a, b : array_like
    Real-valued parameters
x : array_like
    Real-valued argument
out : ndarray, optional
    Optional output array for the function values

Returns
-------
scalar or ndarray
    Values of `U`

References
----------
.. [DLMF] NIST Digital Library of Mathematics Functions
          https://dlmf.nist.gov/13.2#E6

Examples
--------
>>> import numpy as np
>>> import scipy.special as sc

It has a branch cut along the negative `x` axis.

>>> x = np.linspace(-0.1, -10, 5)
>>> sc.hyperu(1, 1, x)
array([nan, nan, nan, nan, nan])

It approaches zero as `x` goes to infinity.

>>> x = np.array([1, 10, 100])
>>> sc.hyperu(1, 1, x)
array([0.59634736, 0.09156333, 0.00990194])

It satisfies Kummer's transformation.

>>> a, b, x = 2, 1, 1
>>> sc.hyperu(a, b, x)
0.1926947246463881
>>> x**(1 - b) * sc.hyperu(a - b + 1, 2 - b, x)
0.1926947246463881        inv_boxcox(y, lmbda, out=None)

Compute the inverse of the Box-Cox transformation.

Find ``x`` such that::

    y = (x**lmbda - 1) / lmbda  if lmbda != 0
        log(x)                  if lmbda == 0

Parameters
----------
y : array_like
    Data to be transformed.
lmbda : array_like
    Power parameter of the Box-Cox transform.
out : ndarray, optional
    Optional output array for the function values

Returns
-------
x : scalar or ndarray
    Transformed data.

Notes
-----

.. versionadded:: 0.16.0

Examples
--------
>>> from scipy.special import boxcox, inv_boxcox
>>> y = boxcox([1, 4, 10], 2.5)
>>> inv_boxcox(y, 2.5)
array([1., 4., 10.])        inv_boxcox1p(y, lmbda, out=None)

Compute the inverse of the Box-Cox transformation.

Find ``x`` such that::

    y = ((1+x)**lmbda - 1) / lmbda  if lmbda != 0
        log(1+x)                    if lmbda == 0

Parameters
----------
y : array_like
    Data to be transformed.
lmbda : array_like
    Power parameter of the Box-Cox transform.
out : ndarray, optional
    Optional output array for the function values

Returns
-------
x : scalar or ndarray
    Transformed data.

Notes
-----

.. versionadded:: 0.16.0

Examples
--------
>>> from scipy.special import boxcox1p, inv_boxcox1p
>>> y = boxcox1p([1, 4, 10], 2.5)
>>> inv_boxcox1p(y, 2.5)
array([1., 4., 10.])      kl_div(x, y, out=None)

Elementwise function for computing Kullback-Leibler divergence.

.. math::

    \mathrm{kl\_div}(x, y) =
      \begin{cases}
        x \log(x / y) - x + y & x > 0, y > 0 \\
        y & x = 0, y \ge 0 \\
        \infty & \text{otherwise}
      \end{cases}

Parameters
----------
x, y : array_like
    Real arguments
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    Values of the Kullback-Liebler divergence.

See Also
--------
entr, rel_entr, scipy.stats.entropy

Notes
-----
.. versionadded:: 0.15.0

This function is non-negative and is jointly convex in `x` and `y`.

The origin of this function is in convex programming; see [1]_ for
details. This is why the function contains the extra :math:`-x
+ y` terms over what might be expected from the Kullback-Leibler
divergence. For a version of the function without the extra terms,
see `rel_entr`.

References
----------
.. [1] Boyd, Stephen and Lieven Vandenberghe. *Convex optimization*.
       Cambridge University Press, 2004.
       :doi:`https://doi.org/10.1017/CBO9780511804441`    kn(n, x, out=None)

Modified Bessel function of the second kind of integer order `n`

Returns the modified Bessel function of the second kind for integer order
`n` at real `z`.

These are also sometimes called functions of the third kind, Basset
functions, or Macdonald functions.

Parameters
----------
n : array_like of int
    Order of Bessel functions (floats will truncate with a warning)
x : array_like of float
    Argument at which to evaluate the Bessel functions
out : ndarray, optional
    Optional output array for the function results.

Returns
-------
scalar or ndarray
    Value of the Modified Bessel function of the second kind,
    :math:`K_n(x)`.

See Also
--------
kv : Same function, but accepts real order and complex argument
kvp : Derivative of this function

Notes
-----
Wrapper for AMOS [1]_ routine `zbesk`.  For a discussion of the
algorithm used, see [2]_ and the references therein.

References
----------
.. [1] Donald E. Amos, "AMOS, A Portable Package for Bessel Functions
       of a Complex Argument and Nonnegative Order",
       http://netlib.org/amos/
.. [2] Donald E. Amos, "Algorithm 644: A portable package for Bessel
       functions of a complex argument and nonnegative order", ACM
       TOMS Vol. 12 Issue 3, Sept. 1986, p. 265

Examples
--------
Plot the function of several orders for real input:

>>> import numpy as np
>>> from scipy.special import kn
>>> import matplotlib.pyplot as plt
>>> x = np.linspace(0, 5, 1000)
>>> for N in range(6):
...     plt.plot(x, kn(N, x), label='$K_{}(x)$'.format(N))
>>> plt.ylim(0, 10)
>>> plt.legend()
>>> plt.title(r'Modified Bessel function of the second kind $K_n(x)$')
>>> plt.show()

Calculate for a single value at multiple orders:

>>> kn([4, 5, 6], 1)
array([   44.23241585,   360.9605896 ,  3653.83831186])      kolmogi(p, out=None)

Inverse Survival Function of Kolmogorov distribution

It is the inverse function to `kolmogorov`.
Returns y such that ``kolmogorov(y) == p``.

Parameters
----------
p : float array_like
    Probability
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    The value(s) of kolmogi(p)

See Also
--------
kolmogorov : The Survival Function for the distribution
scipy.stats.kstwobign : Provides the functionality as a continuous distribution
smirnov, smirnovi : Functions for the one-sided distribution

Notes
-----
`kolmogorov` is used by `stats.kstest` in the application of the
Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this
function is exposed in `scpy.special`, but the recommended way to achieve
the most accurate CDF/SF/PDF/PPF/ISF computations is to use the
`stats.kstwobign` distribution.

Examples
--------
>>> from scipy.special import kolmogi
>>> kolmogi([0, 0.1, 0.25, 0.5, 0.75, 0.9, 1.0])
array([        inf,  1.22384787,  1.01918472,  0.82757356,  0.67644769,
        0.57117327,  0.        ])   kolmogorov(y, out=None)

Complementary cumulative distribution (Survival Function) function of
Kolmogorov distribution.

Returns the complementary cumulative distribution function of
Kolmogorov's limiting distribution (``D_n*\sqrt(n)`` as n goes to infinity)
of a two-sided test for equality between an empirical and a theoretical
distribution. It is equal to the (limit as n->infinity of the)
probability that ``sqrt(n) * max absolute deviation > y``.

Parameters
----------
y : float array_like
  Absolute deviation between the Empirical CDF (ECDF) and the target CDF,
  multiplied by sqrt(n).
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    The value(s) of kolmogorov(y)

See Also
--------
kolmogi : The Inverse Survival Function for the distribution
scipy.stats.kstwobign : Provides the functionality as a continuous distribution
smirnov, smirnovi : Functions for the one-sided distribution

Notes
-----
`kolmogorov` is used by `stats.kstest` in the application of the
Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this
function is exposed in `scpy.special`, but the recommended way to achieve
the most accurate CDF/SF/PDF/PPF/ISF computations is to use the
`stats.kstwobign` distribution.

Examples
--------
Show the probability of a gap at least as big as 0, 0.5 and 1.0.

>>> import numpy as np
>>> from scipy.special import kolmogorov
>>> from scipy.stats import kstwobign
>>> kolmogorov([0, 0.5, 1.0])
array([ 1.        ,  0.96394524,  0.26999967])

Compare a sample of size 1000 drawn from a Laplace(0, 1) distribution against
the target distribution, a Normal(0, 1) distribution.

>>> from scipy.stats import norm, laplace
>>> rng = np.random.default_rng()
>>> n = 1000
>>> lap01 = laplace(0, 1)
>>> x = np.sort(lap01.rvs(n, random_state=rng))
>>> np.mean(x), np.std(x)
(-0.05841730131499543, 1.3968109101997568)

Construct the Empirical CDF and the K-S statistic Dn.

>>> target = norm(0,1)  # Normal mean 0, stddev 1
>>> cdfs = target.cdf(x)
>>> ecdfs = np.arange(n+1, dtype=float)/n
>>> gaps = np.column_stack([cdfs - ecdfs[:n], ecdfs[1:] - cdfs])
>>> Dn = np.max(gaps)
>>> Kn = np.sqrt(n) * Dn
>>> print('Dn=%f, sqrt(n)*Dn=%f' % (Dn, Kn))
Dn=0.043363, sqrt(n)*Dn=1.371265
>>> print(chr(10).join(['For a sample of size n drawn from a N(0, 1) distribution:',
...   ' the approximate Kolmogorov probability that sqrt(n)*Dn>=%f is %f' %
...    (Kn, kolmogorov(Kn)),
...   ' the approximate Kolmogorov probability that sqrt(n)*Dn<=%f is %f' %
...    (Kn, kstwobign.cdf(Kn))]))
For a sample of size n drawn from a N(0, 1) distribution:
 the approximate Kolmogorov probability that sqrt(n)*Dn>=1.371265 is 0.046533
 the approximate Kolmogorov probability that sqrt(n)*Dn<=1.371265 is 0.953467

Plot the Empirical CDF against the target N(0, 1) CDF.

>>> import matplotlib.pyplot as plt
>>> plt.step(np.concatenate([[-3], x]), ecdfs, where='post', label='Empirical CDF')
>>> x3 = np.linspace(-3, 3, 100)
>>> plt.plot(x3, target.cdf(x3), label='CDF for N(0, 1)')
>>> plt.ylim([0, 1]); plt.grid(True); plt.legend();
>>> # Add vertical lines marking Dn+ and Dn-
>>> iminus, iplus = np.argmax(gaps, axis=0)
>>> plt.vlines([x[iminus]], ecdfs[iminus], cdfs[iminus],
...            color='r', linestyle='dashed', lw=4)
>>> plt.vlines([x[iplus]], cdfs[iplus], ecdfs[iplus+1],
...            color='r', linestyle='dashed', lw=4)
>>> plt.show()       lpmv(m, v, x, out=None)

Associated Legendre function of integer order and real degree.

Defined as

.. math::

    P_v^m = (-1)^m (1 - x^2)^{m/2} \frac{d^m}{dx^m} P_v(x)

where

.. math::

    P_v = \sum_{k = 0}^\infty \frac{(-v)_k (v + 1)_k}{(k!)^2}
            \left(\frac{1 - x}{2}\right)^k

is the Legendre function of the first kind. Here :math:`(\cdot)_k`
is the Pochhammer symbol; see `poch`.

Parameters
----------
m : array_like
    Order (int or float). If passed a float not equal to an
    integer the function returns NaN.
v : array_like
    Degree (float).
x : array_like
    Argument (float). Must have ``|x| <= 1``.
out : ndarray, optional
    Optional output array for the function results

Returns
-------
pmv : scalar or ndarray
    Value of the associated Legendre function.

Notes
-----
Note that this implementation includes the Condon-Shortley phase.

References
----------
.. [1] Zhang, Jin, "Computation of Special Functions", John Wiley
       and Sons, Inc, 1996. nbdtr(k, n, p, out=None)

Negative binomial cumulative distribution function.

Returns the sum of the terms 0 through `k` of the negative binomial
distribution probability mass function,

.. math::

    F = \sum_{j=0}^k {{n + j - 1}\choose{j}} p^n (1 - p)^j.

In a sequence of Bernoulli trials with individual success probabilities
`p`, this is the probability that `k` or fewer failures precede the nth
success.

Parameters
----------
k : array_like
    The maximum number of allowed failures (nonnegative int).
n : array_like
    The target number of successes (positive int).
p : array_like
    Probability of success in a single event (float).
out : ndarray, optional
    Optional output array for the function results

Returns
-------
F : scalar or ndarray
    The probability of `k` or fewer failures before `n` successes in a
    sequence of events with individual success probability `p`.

See Also
--------
nbdtrc : Negative binomial survival function
nbdtrik : Negative binomial quantile function
scipy.stats.nbinom : Negative binomial distribution

Notes
-----
If floating point values are passed for `k` or `n`, they will be truncated
to integers.

The terms are not summed directly; instead the regularized incomplete beta
function is employed, according to the formula,

.. math::
    \mathrm{nbdtr}(k, n, p) = I_{p}(n, k + 1).

Wrapper for the Cephes [1]_ routine `nbdtr`.

The negative binomial distribution is also available as
`scipy.stats.nbinom`. Using `nbdtr` directly can improve performance
compared to the ``cdf`` method of `scipy.stats.nbinom` (see last example).

References
----------
.. [1] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/

Examples
--------
Compute the function for ``k=10`` and ``n=5`` at ``p=0.5``.

>>> import numpy as np
>>> from scipy.special import nbdtr
>>> nbdtr(10, 5, 0.5)
0.940765380859375

Compute the function for ``n=10`` and ``p=0.5`` at several points by
providing a NumPy array or list for `k`.

>>> nbdtr([5, 10, 15], 10, 0.5)
array([0.15087891, 0.58809853, 0.88523853])

Plot the function for four different parameter sets.

>>> import matplotlib.pyplot as plt
>>> k = np.arange(130)
>>> n_parameters = [20, 20, 20, 80]
>>> p_parameters = [0.2, 0.5, 0.8, 0.5]
>>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
>>> parameters_list = list(zip(p_parameters, n_parameters,
...                            linestyles))
>>> fig, ax = plt.subplots(figsize=(8, 8))
>>> for parameter_set in parameters_list:
...     p, n, style = parameter_set
...     nbdtr_vals = nbdtr(k, n, p)
...     ax.plot(k, nbdtr_vals, label=rf"$n={n},\, p={p}$",
...             ls=style)
>>> ax.legend()
>>> ax.set_xlabel("$k$")
>>> ax.set_title("Negative binomial cumulative distribution function")
>>> plt.show()

The negative binomial distribution is also available as
`scipy.stats.nbinom`. Using `nbdtr` directly can be much faster than
calling the ``cdf`` method of `scipy.stats.nbinom`, especially for small
arrays or individual values. To get the same results one must use the
following parametrization: ``nbinom(n, p).cdf(k)=nbdtr(k, n, p)``.

>>> from scipy.stats import nbinom
>>> k, n, p = 5, 3, 0.5
>>> nbdtr_res = nbdtr(k, n, p)  # this will often be faster than below
>>> stats_res = nbinom(n, p).cdf(k)
>>> stats_res, nbdtr_res  # test that results are equal
(0.85546875, 0.85546875)

`nbdtr` can evaluate different parameter sets by providing arrays with
shapes compatible for broadcasting for `k`, `n` and `p`. Here we compute
the function for three different `k` at four locations `p`, resulting in
a 3x4 array.

>>> k = np.array([[5], [10], [15]])
>>> p = np.array([0.3, 0.5, 0.7, 0.9])
>>> k.shape, p.shape
((3, 1), (4,))

>>> nbdtr(k, 5, p)
array([[0.15026833, 0.62304687, 0.95265101, 0.9998531 ],
       [0.48450894, 0.94076538, 0.99932777, 0.99999999],
       [0.76249222, 0.99409103, 0.99999445, 1.        ]])    nbdtrc(k, n, p, out=None)

Negative binomial survival function.

Returns the sum of the terms `k + 1` to infinity of the negative binomial
distribution probability mass function,

.. math::

    F = \sum_{j=k + 1}^\infty {{n + j - 1}\choose{j}} p^n (1 - p)^j.

In a sequence of Bernoulli trials with individual success probabilities
`p`, this is the probability that more than `k` failures precede the nth
success.

Parameters
----------
k : array_like
    The maximum number of allowed failures (nonnegative int).
n : array_like
    The target number of successes (positive int).
p : array_like
    Probability of success in a single event (float).
out : ndarray, optional
    Optional output array for the function results

Returns
-------
F : scalar or ndarray
    The probability of `k + 1` or more failures before `n` successes in a
    sequence of events with individual success probability `p`.

See Also
--------
nbdtr : Negative binomial cumulative distribution function
nbdtrik : Negative binomial percentile function
scipy.stats.nbinom : Negative binomial distribution

Notes
-----
If floating point values are passed for `k` or `n`, they will be truncated
to integers.

The terms are not summed directly; instead the regularized incomplete beta
function is employed, according to the formula,

.. math::
    \mathrm{nbdtrc}(k, n, p) = I_{1 - p}(k + 1, n).

Wrapper for the Cephes [1]_ routine `nbdtrc`.

The negative binomial distribution is also available as
`scipy.stats.nbinom`. Using `nbdtrc` directly can improve performance
compared to the ``sf`` method of `scipy.stats.nbinom` (see last example).

References
----------
.. [1] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/

Examples
--------
Compute the function for ``k=10`` and ``n=5`` at ``p=0.5``.

>>> import numpy as np
>>> from scipy.special import nbdtrc
>>> nbdtrc(10, 5, 0.5)
0.059234619140624986

Compute the function for ``n=10`` and ``p=0.5`` at several points by
providing a NumPy array or list for `k`.

>>> nbdtrc([5, 10, 15], 10, 0.5)
array([0.84912109, 0.41190147, 0.11476147])

Plot the function for four different parameter sets.

>>> import matplotlib.pyplot as plt
>>> k = np.arange(130)
>>> n_parameters = [20, 20, 20, 80]
>>> p_parameters = [0.2, 0.5, 0.8, 0.5]
>>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
>>> parameters_list = list(zip(p_parameters, n_parameters,
...                            linestyles))
>>> fig, ax = plt.subplots(figsize=(8, 8))
>>> for parameter_set in parameters_list:
...     p, n, style = parameter_set
...     nbdtrc_vals = nbdtrc(k, n, p)
...     ax.plot(k, nbdtrc_vals, label=rf"$n={n},\, p={p}$",
...             ls=style)
>>> ax.legend()
>>> ax.set_xlabel("$k$")
>>> ax.set_title("Negative binomial distribution survival function")
>>> plt.show()

The negative binomial distribution is also available as
`scipy.stats.nbinom`. Using `nbdtrc` directly can be much faster than
calling the ``sf`` method of `scipy.stats.nbinom`, especially for small
arrays or individual values. To get the same results one must use the
following parametrization: ``nbinom(n, p).sf(k)=nbdtrc(k, n, p)``.

>>> from scipy.stats import nbinom
>>> k, n, p = 3, 5, 0.5
>>> nbdtr_res = nbdtrc(k, n, p)  # this will often be faster than below
>>> stats_res = nbinom(n, p).sf(k)
>>> stats_res, nbdtr_res  # test that results are equal
(0.6367187499999999, 0.6367187499999999)

`nbdtrc` can evaluate different parameter sets by providing arrays with
shapes compatible for broadcasting for `k`, `n` and `p`. Here we compute
the function for three different `k` at four locations `p`, resulting in
a 3x4 array.

>>> k = np.array([[5], [10], [15]])
>>> p = np.array([0.3, 0.5, 0.7, 0.9])
>>> k.shape, p.shape
((3, 1), (4,))

>>> nbdtrc(k, 5, p)
array([[8.49731667e-01, 3.76953125e-01, 4.73489874e-02, 1.46902600e-04],
       [5.15491059e-01, 5.92346191e-02, 6.72234070e-04, 9.29610100e-09],
       [2.37507779e-01, 5.90896606e-03, 5.55025308e-06, 3.26346760e-13]])        nbdtri(k, n, y, out=None)

Returns the inverse with respect to the parameter `p` of
``y = nbdtr(k, n, p)``, the negative binomial cumulative distribution
function.

Parameters
----------
k : array_like
    The maximum number of allowed failures (nonnegative int).
n : array_like
    The target number of successes (positive int).
y : array_like
    The probability of `k` or fewer failures before `n` successes (float).
out : ndarray, optional
    Optional output array for the function results

Returns
-------
p : scalar or ndarray
    Probability of success in a single event (float) such that
    `nbdtr(k, n, p) = y`.

See Also
--------
nbdtr : Cumulative distribution function of the negative binomial.
nbdtrc : Negative binomial survival function.
scipy.stats.nbinom : negative binomial distribution.
nbdtrik : Inverse with respect to `k` of `nbdtr(k, n, p)`.
nbdtrin : Inverse with respect to `n` of `nbdtr(k, n, p)`.
scipy.stats.nbinom : Negative binomial distribution

Notes
-----
Wrapper for the Cephes [1]_ routine `nbdtri`.

The negative binomial distribution is also available as
`scipy.stats.nbinom`. Using `nbdtri` directly can improve performance
compared to the ``ppf`` method of `scipy.stats.nbinom`.

References
----------
.. [1] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/

Examples
--------
`nbdtri` is the inverse of `nbdtr` with respect to `p`.
Up to floating point errors the following holds:
``nbdtri(k, n, nbdtr(k, n, p))=p``.

>>> import numpy as np
>>> from scipy.special import nbdtri, nbdtr
>>> k, n, y = 5, 10, 0.2
>>> cdf_val = nbdtr(k, n, y)
>>> nbdtri(k, n, cdf_val)
0.20000000000000004

Compute the function for ``k=10`` and ``n=5`` at several points by
providing a NumPy array or list for `y`.

>>> y = np.array([0.1, 0.4, 0.8])
>>> nbdtri(3, 5, y)
array([0.34462319, 0.51653095, 0.69677416])

Plot the function for three different parameter sets.

>>> import matplotlib.pyplot as plt
>>> n_parameters = [5, 20, 30, 30]
>>> k_parameters = [20, 20, 60, 80]
>>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
>>> parameters_list = list(zip(n_parameters, k_parameters, linestyles))
>>> cdf_vals = np.linspace(0, 1, 1000)
>>> fig, ax = plt.subplots(figsize=(8, 8))
>>> for parameter_set in parameters_list:
...     n, k, style = parameter_set
...     nbdtri_vals = nbdtri(k, n, cdf_vals)
...     ax.plot(cdf_vals, nbdtri_vals, label=rf"$k={k},\ n={n}$",
...             ls=style)
>>> ax.legend()
>>> ax.set_ylabel("$p$")
>>> ax.set_xlabel("$CDF$")
>>> title = "nbdtri: inverse of negative binomial CDF with respect to $p$"
>>> ax.set_title(title)
>>> plt.show()

`nbdtri` can evaluate different parameter sets by providing arrays with
shapes compatible for broadcasting for `k`, `n` and `p`. Here we compute
the function for three different `k` at four locations `p`, resulting in
a 3x4 array.

>>> k = np.array([[5], [10], [15]])
>>> y = np.array([0.3, 0.5, 0.7, 0.9])
>>> k.shape, y.shape
((3, 1), (4,))

>>> nbdtri(k, 5, y)
array([[0.37258157, 0.45169416, 0.53249956, 0.64578407],
       [0.24588501, 0.30451981, 0.36778453, 0.46397088],
       [0.18362101, 0.22966758, 0.28054743, 0.36066188]])      nbdtrik(y, n, p, out=None)

Negative binomial percentile function.

Returns the inverse with respect to the parameter `k` of
``y = nbdtr(k, n, p)``, the negative binomial cumulative distribution
function.

Parameters
----------
y : array_like
    The probability of `k` or fewer failures before `n` successes (float).
n : array_like
    The target number of successes (positive int).
p : array_like
    Probability of success in a single event (float).
out : ndarray, optional
    Optional output array for the function results

Returns
-------
k : scalar or ndarray
    The maximum number of allowed failures such that `nbdtr(k, n, p) = y`.

See Also
--------
nbdtr : Cumulative distribution function of the negative binomial.
nbdtrc : Survival function of the negative binomial.
nbdtri : Inverse with respect to `p` of `nbdtr(k, n, p)`.
nbdtrin : Inverse with respect to `n` of `nbdtr(k, n, p)`.
scipy.stats.nbinom : Negative binomial distribution

Notes
-----
Wrapper for the CDFLIB [1]_ Fortran routine `cdfnbn`.

Formula 26.5.26 of [2]_ or [3]_,

.. math::
    \sum_{j=k + 1}^\infty {{n + j - 1}
    \choose{j}} p^n (1 - p)^j = I_{1 - p}(k + 1, n),

is used to reduce calculation of the cumulative distribution function to
that of a regularized incomplete beta :math:`I`.

Computation of `k` involves a search for a value that produces the desired
value of `y`.  The search relies on the monotonicity of `y` with `k`.

References
----------
.. [1] Barry Brown, James Lovato, and Kathy Russell,
       CDFLIB: Library of Fortran Routines for Cumulative Distribution
       Functions, Inverses, and Other Parameters.
.. [2] Milton Abramowitz and Irene A. Stegun, eds.
       Handbook of Mathematical Functions with Formulas,
       Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [3] NIST Digital Library of Mathematical Functions
       https://dlmf.nist.gov/8.17.E24

Examples
--------
Compute the negative binomial cumulative distribution function for an
exemplary parameter set.

>>> import numpy as np
>>> from scipy.special import nbdtr, nbdtrik
>>> k, n, p = 5, 2, 0.5
>>> cdf_value = nbdtr(k, n, p)
>>> cdf_value
0.9375

Verify that `nbdtrik` recovers the original value for `k`.

>>> nbdtrik(cdf_value, n, p)
5.0

Plot the function for different parameter sets.

>>> import matplotlib.pyplot as plt
>>> p_parameters = [0.2, 0.5, 0.7, 0.5]
>>> n_parameters = [30, 30, 30, 80]
>>> linestyles = ['solid', 'dashed', 'dotted', 'dashdot']
>>> parameters_list = list(zip(p_parameters, n_parameters, linestyles))
>>> cdf_vals = np.linspace(0, 1, 1000)
>>> fig, ax = plt.subplots(figsize=(8, 8))
>>> for parameter_set in parameters_list:
...     p, n, style = parameter_set
...     nbdtrik_vals = nbdtrik(cdf_vals, n, p)
...     ax.plot(cdf_vals, nbdtrik_vals, label=rf"$n={n},\ p={p}$",
...             ls=style)
>>> ax.legend()
>>> ax.set_ylabel("$k$")
>>> ax.set_xlabel("$CDF$")
>>> ax.set_title("Negative binomial percentile function")
>>> plt.show()

The negative binomial distribution is also available as
`scipy.stats.nbinom`. The percentile function  method ``ppf``
returns the result of `nbdtrik` rounded up to integers:

>>> from scipy.stats import nbinom
>>> q, n, p = 0.6, 5, 0.5
>>> nbinom.ppf(q, n, p), nbdtrik(q, n, p)
(5.0, 4.800428460273882)        nbdtrin(k, y, p, out=None)

Inverse of `nbdtr` vs `n`.

Returns the inverse with respect to the parameter `n` of
``y = nbdtr(k, n, p)``, the negative binomial cumulative distribution
function.

Parameters
----------
k : array_like
    The maximum number of allowed failures (nonnegative int).
y : array_like
    The probability of `k` or fewer failures before `n` successes (float).
p : array_like
    Probability of success in a single event (float).
out : ndarray, optional
    Optional output array for the function results

Returns
-------
n : scalar or ndarray
    The number of successes `n` such that `nbdtr(k, n, p) = y`.

See Also
--------
nbdtr : Cumulative distribution function of the negative binomial.
nbdtri : Inverse with respect to `p` of `nbdtr(k, n, p)`.
nbdtrik : Inverse with respect to `k` of `nbdtr(k, n, p)`.

Notes
-----
Wrapper for the CDFLIB [1]_ Fortran routine `cdfnbn`.

Formula 26.5.26 of [2]_ or [3]_,

.. math::
    \sum_{j=k + 1}^\infty {{n + j - 1}
    \choose{j}} p^n (1 - p)^j = I_{1 - p}(k + 1, n),

is used to reduce calculation of the cumulative distribution function to
that of a regularized incomplete beta :math:`I`.

Computation of `n` involves a search for a value that produces the desired
value of `y`.  The search relies on the monotonicity of `y` with `n`.

References
----------
.. [1] Barry Brown, James Lovato, and Kathy Russell,
       CDFLIB: Library of Fortran Routines for Cumulative Distribution
       Functions, Inverses, and Other Parameters.
.. [2] Milton Abramowitz and Irene A. Stegun, eds.
       Handbook of Mathematical Functions with Formulas,
       Graphs, and Mathematical Tables. New York: Dover, 1972.
.. [3] NIST Digital Library of Mathematical Functions
       https://dlmf.nist.gov/8.17.E24

Examples
--------
Compute the negative binomial cumulative distribution function for an
exemplary parameter set.

>>> from scipy.special import nbdtr, nbdtrin
>>> k, n, p = 5, 2, 0.5
>>> cdf_value = nbdtr(k, n, p)
>>> cdf_value
0.9375

Verify that `nbdtrin` recovers the original value for `n` up to floating
point accuracy.

>>> nbdtrin(k, cdf_value, p)
1.999999999998137     ncfdtr(dfn, dfd, nc, f, out=None)

Cumulative distribution function of the non-central F distribution.

The non-central F describes the distribution of,

.. math::
    Z = \frac{X/d_n}{Y/d_d}

where :math:`X` and :math:`Y` are independently distributed, with
:math:`X` distributed non-central :math:`\chi^2` with noncentrality
parameter `nc` and :math:`d_n` degrees of freedom, and :math:`Y`
distributed :math:`\chi^2` with :math:`d_d` degrees of freedom.

Parameters
----------
dfn : array_like
    Degrees of freedom of the numerator sum of squares.  Range (0, inf).
dfd : array_like
    Degrees of freedom of the denominator sum of squares.  Range (0, inf).
nc : array_like
    Noncentrality parameter.  Range [0, inf).
f : array_like
    Quantiles, i.e. the upper limit of integration.
out : ndarray, optional
    Optional output array for the function results

Returns
-------
cdf : scalar or ndarray
    The calculated CDF.  If all inputs are scalar, the return will be a
    float.  Otherwise it will be an array.

See Also
--------
ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.
ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.
ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.
ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.
scipy.stats.ncf : Non-central F distribution.

Notes
-----
This function calculates the CDF of the non-central f distribution using
the Boost Math C++ library [1]_.

The cumulative distribution function is computed using Formula 26.6.20 of
[2]_:

.. math::
    F(d_n, d_d, n_c, f) = \sum_{j=0}^\infty e^{-n_c/2}
    \frac{(n_c/2)^j}{j!} I_{x}(\frac{d_n}{2} + j, \frac{d_d}{2}),

where :math:`I` is the regularized incomplete beta function, and
:math:`x = f d_n/(f d_n + d_d)`.

Note that argument order of `ncfdtr` is different from that of the
similar ``cdf`` method of `scipy.stats.ncf`: `f` is the last
parameter of `ncfdtr` but the first parameter of ``scipy.stats.ncf.cdf``.

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
.. [2] Milton Abramowitz and Irene A. Stegun, eds.
       Handbook of Mathematical Functions with Formulas,
       Graphs, and Mathematical Tables. New York: Dover, 1972.

Examples
--------
>>> import numpy as np
>>> from scipy import special
>>> from scipy import stats
>>> import matplotlib.pyplot as plt

Plot the CDF of the non-central F distribution, for nc=0.  Compare with the
F-distribution from scipy.stats:

>>> x = np.linspace(-1, 8, num=500)
>>> dfn = 3
>>> dfd = 2
>>> ncf_stats = stats.f.cdf(x, dfn, dfd)
>>> ncf_special = special.ncfdtr(dfn, dfd, 0, x)

>>> fig = plt.figure()
>>> ax = fig.add_subplot(111)
>>> ax.plot(x, ncf_stats, 'b-', lw=3)
>>> ax.plot(x, ncf_special, 'r-')
>>> plt.show()     ncfdtri(dfn, dfd, nc, p, out=None)

Inverse with respect to `f` of the CDF of the non-central F distribution.

See `ncfdtr` for more details.

Parameters
----------
dfn : array_like
    Degrees of freedom of the numerator sum of squares.  Range (0, inf).
dfd : array_like
    Degrees of freedom of the denominator sum of squares.  Range (0, inf).
nc : array_like
    Noncentrality parameter.  Range [0, inf).
p : array_like
    Value of the cumulative distribution function.  Must be in the
    range [0, 1].
out : ndarray, optional
    Optional output array for the function results

Returns
-------
f : scalar or ndarray
    Quantiles, i.e., the upper limit of integration.

See Also
--------
ncfdtr : CDF of the non-central F distribution.
ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.
ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.
ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.
scipy.stats.ncf : Non-central F distribution.

Notes
-----
This function calculates the Quantile of the non-central f distribution
using the Boost Math C++ library [1]_.

Note that argument order of `ncfdtri` is different from that of the
similar ``ppf`` method of `scipy.stats.ncf`. `p` is the last parameter
of `ncfdtri` but the first parameter of ``scipy.stats.ncf.ppf``.

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
>>> from scipy.special import ncfdtr, ncfdtri

Compute the CDF for several values of `f`:

>>> f = [0.5, 1, 1.5]
>>> p = ncfdtr(2, 3, 1.5, f)
>>> p
array([ 0.20782291,  0.36107392,  0.47345752])

Compute the inverse.  We recover the values of `f`, as expected:

>>> ncfdtri(2, 3, 1.5, p)
array([ 0.5,  1. ,  1.5])     ncfdtridfd(dfn, p, nc, f, out=None)

Calculate degrees of freedom (denominator) for the noncentral F-distribution.

This is the inverse with respect to `dfd` of `ncfdtr`.
See `ncfdtr` for more details.

Parameters
----------
dfn : array_like
    Degrees of freedom of the numerator sum of squares.  Range (0, inf).
p : array_like
    Value of the cumulative distribution function.  Must be in the
    range [0, 1].
nc : array_like
    Noncentrality parameter.  Should be in range (0, 1e4).
f : array_like
    Quantiles, i.e., the upper limit of integration.
out : ndarray, optional
    Optional output array for the function results

Returns
-------
dfd : scalar or ndarray
    Degrees of freedom of the denominator sum of squares.

See Also
--------
ncfdtr : CDF of the non-central F distribution.
ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.
ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.
ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.

Notes
-----
The value of the cumulative noncentral F distribution is not necessarily
monotone in either degrees of freedom. There thus may be two values that
provide a given CDF value. This routine assumes monotonicity and will
find an arbitrary one of the two values.

Examples
--------
>>> from scipy.special import ncfdtr, ncfdtridfd

Compute the CDF for several values of `dfd`:

>>> dfd = [1, 2, 3]
>>> p = ncfdtr(2, dfd, 0.25, 15)
>>> p
array([ 0.8097138 ,  0.93020416,  0.96787852])

Compute the inverse.  We recover the values of `dfd`, as expected:

>>> ncfdtridfd(2, p, 0.25, 15)
array([ 1.,  2.,  3.])        ncfdtridfn(p, dfd, nc, f, out=None)

Calculate degrees of freedom (numerator) for the noncentral F-distribution.

This is the inverse with respect to `dfn` of `ncfdtr`.
See `ncfdtr` for more details.

Parameters
----------
p : array_like
    Value of the cumulative distribution function. Must be in the
    range [0, 1].
dfd : array_like
    Degrees of freedom of the denominator sum of squares. Range (0, inf).
nc : array_like
    Noncentrality parameter.  Should be in range (0, 1e4).
f : float
    Quantiles, i.e., the upper limit of integration.
out : ndarray, optional
    Optional output array for the function results

Returns
-------
dfn : scalar or ndarray
    Degrees of freedom of the numerator sum of squares.

See Also
--------
ncfdtr : CDF of the non-central F distribution.
ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.
ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.
ncfdtrinc : Inverse of `ncfdtr` with respect to `nc`.

Notes
-----
The value of the cumulative noncentral F distribution is not necessarily
monotone in either degrees of freedom. There thus may be two values that
provide a given CDF value. This routine assumes monotonicity and will
find an arbitrary one of the two values.

Examples
--------
>>> from scipy.special import ncfdtr, ncfdtridfn

Compute the CDF for several values of `dfn`:

>>> dfn = [1, 2, 3]
>>> p = ncfdtr(dfn, 2, 0.25, 15)
>>> p
array([ 0.92562363,  0.93020416,  0.93188394])

Compute the inverse. We recover the values of `dfn`, as expected:

>>> ncfdtridfn(p, 2, 0.25, 15)
array([ 1.,  2.,  3.])  ncfdtrinc(dfn, dfd, p, f, out=None)

Calculate non-centrality parameter for non-central F distribution.

This is the inverse with respect to `nc` of `ncfdtr`.
See `ncfdtr` for more details.

Parameters
----------
dfn : array_like
    Degrees of freedom of the numerator sum of squares. Range (0, inf).
dfd : array_like
    Degrees of freedom of the denominator sum of squares. Range (0, inf).
p : array_like
    Value of the cumulative distribution function. Must be in the
    range [0, 1].
f : array_like
    Quantiles, i.e., the upper limit of integration.
out : ndarray, optional
    Optional output array for the function results

Returns
-------
nc : scalar or ndarray
    Noncentrality parameter.

See Also
--------
ncfdtr : CDF of the non-central F distribution.
ncfdtri : Quantile function; inverse of `ncfdtr` with respect to `f`.
ncfdtridfd : Inverse of `ncfdtr` with respect to `dfd`.
ncfdtridfn : Inverse of `ncfdtr` with respect to `dfn`.

Examples
--------
>>> from scipy.special import ncfdtr, ncfdtrinc

Compute the CDF for several values of `nc`:

>>> nc = [0.5, 1.5, 2.0]
>>> p = ncfdtr(2, 3, nc, 15)
>>> p
array([ 0.96309246,  0.94327955,  0.93304098])

Compute the inverse. We recover the values of `nc`, as expected:

>>> ncfdtrinc(2, 3, p, 15)
array([ 0.5,  1.5,  2. ])    nctdtr(df, nc, t, out=None)

Cumulative distribution function of the non-central `t` distribution.

Parameters
----------
df : array_like
    Degrees of freedom of the distribution. Should be in range (0, inf).
nc : array_like
    Noncentrality parameter.
t : array_like
    Quantiles, i.e., the upper limit of integration.
out : ndarray, optional
    Optional output array for the function results

Returns
-------
cdf : scalar or ndarray
    The calculated CDF. If all inputs are scalar, the return will be a
    float. Otherwise, it will be an array.

See Also
--------
nctdtrit : Inverse CDF (iCDF) of the non-central t distribution.
nctdtridf : Calculate degrees of freedom, given CDF and iCDF values.
nctdtrinc : Calculate non-centrality parameter, given CDF iCDF values.

Notes
-----
This function calculates the CDF of the non-central t distribution using
the Boost Math C++ library [1]_.

Note that the argument order of `nctdtr` is different from that of the
similar ``cdf`` method of `scipy.stats.nct`: `t` is the last
parameter of `nctdtr` but the first parameter of ``scipy.stats.nct.cdf``.

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
>>> import numpy as np
>>> from scipy import special
>>> from scipy import stats
>>> import matplotlib.pyplot as plt

Plot the CDF of the non-central t distribution, for nc=0. Compare with the
t-distribution from scipy.stats:

>>> x = np.linspace(-5, 5, num=500)
>>> df = 3
>>> nct_stats = stats.t.cdf(x, df)
>>> nct_special = special.nctdtr(df, 0, x)

>>> fig = plt.figure()
>>> ax = fig.add_subplot(111)
>>> ax.plot(x, nct_stats, 'b-', lw=3)
>>> ax.plot(x, nct_special, 'r-')
>>> plt.show()      nctdtridf(p, nc, t, out=None)

Calculate degrees of freedom for non-central t distribution.

See `nctdtr` for more details.

Parameters
----------
p : array_like
    CDF values, in range (0, 1].
nc : array_like
    Noncentrality parameter. Should be in range (-1e6, 1e6).
t : array_like
    Quantiles, i.e., the upper limit of integration.
out : ndarray, optional
    Optional output array for the function results

Returns
-------
df : scalar or ndarray
    The degrees of freedom. If all inputs are scalar, the return will be a
    float. Otherwise, it will be an array.

See Also
--------
nctdtr :  CDF of the non-central `t` distribution.
nctdtrit : Inverse CDF (iCDF) of the non-central t distribution.
nctdtrinc : Calculate non-centrality parameter, given CDF iCDF values.

Examples
--------
>>> from scipy.special import nctdtr, nctdtridf

Compute the CDF for several values of `df`:

>>> df = [1, 2, 3]
>>> p = nctdtr(df, 0.25, 1)
>>> p
array([0.67491974, 0.716464  , 0.73349456])

Compute the inverse. We recover the values of `df`, as expected:

>>> nctdtridf(p, 0.25, 1)
array([1., 2., 3.])   nctdtrinc(df, p, t, out=None)

Calculate non-centrality parameter for non-central t distribution.

See `nctdtr` for more details.

Parameters
----------
df : array_like
    Degrees of freedom of the distribution. Should be in range (0, inf).
p : array_like
    CDF values, in range (0, 1].
t : array_like
    Quantiles, i.e., the upper limit of integration.
out : ndarray, optional
    Optional output array for the function results

Returns
-------
nc : scalar or ndarray
    Noncentrality parameter

See Also
--------
nctdtr :  CDF of the non-central `t` distribution.
nctdtrit : Inverse CDF (iCDF) of the non-central t distribution.
nctdtridf : Calculate degrees of freedom, given CDF and iCDF values.

Examples
--------
>>> from scipy.special import nctdtr, nctdtrinc

Compute the CDF for several values of `nc`:

>>> nc = [0.5, 1.5, 2.5]
>>> p = nctdtr(3, nc, 1.5)
>>> p
array([0.77569497, 0.45524533, 0.1668691 ])

Compute the inverse. We recover the values of `nc`, as expected:

>>> nctdtrinc(3, p, 1.5)
array([0.5, 1.5, 2.5])      nctdtrit(df, nc, p, out=None)

Inverse cumulative distribution function of the non-central t distribution.

See `nctdtr` for more details.

Parameters
----------
df : array_like
    Degrees of freedom of the distribution. Should be in range (0, inf).
nc : array_like
    Noncentrality parameter.
p : array_like
    CDF values, in range (0, 1].
out : ndarray, optional
    Optional output array for the function results

Returns
-------
t : scalar or ndarray
    Quantiles

See Also
--------
nctdtr :  CDF of the non-central `t` distribution.
nctdtridf : Calculate degrees of freedom, given CDF and iCDF values.
nctdtrinc : Calculate non-centrality parameter, given CDF iCDF values.

Notes
-----
This function calculates the quantile of the non-central t distribution using
the Boost Math C++ library [1]_.

Note that the argument order of `nctdtrit` is different from that of the
similar ``ppf`` method of `scipy.stats.nct`: `t` is the last
parameter of `nctdtrit` but the first parameter of ``scipy.stats.nct.ppf``.

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
>>> from scipy.special import nctdtr, nctdtrit

Compute the CDF for several values of `t`:

>>> t = [0.5, 1, 1.5]
>>> p = nctdtr(3, 1, t)
>>> p
array([0.29811049, 0.46922687, 0.6257559 ])

Compute the inverse. We recover the values of `t`, as expected:

>>> nctdtrit(3, 1, p)
array([0.5, 1. , 1.5])       ndtri(y, out=None)

Inverse of `ndtr` vs x

Returns the argument x for which the area under the standard normal
probability density function (integrated from minus infinity to `x`)
is equal to y.

Parameters
----------
p : array_like
    Probability
out : ndarray, optional
    Optional output array for the function results

Returns
-------
x : scalar or ndarray
    Value of x such that ``ndtr(x) == p``.

See Also
--------
ndtr : Standard normal cumulative probability distribution
ndtri_exp : Inverse of log_ndtr

Examples
--------
`ndtri` is the percentile function of the standard normal distribution.
This means it returns the inverse of the cumulative density `ndtr`. First,
let us compute a cumulative density value.

>>> import numpy as np
>>> from scipy.special import ndtri, ndtr
>>> cdf_val = ndtr(2)
>>> cdf_val
0.9772498680518208

Verify that `ndtri` yields the original value for `x` up to floating point
errors.

>>> ndtri(cdf_val)
2.0000000000000004

Plot the function. For that purpose, we provide a NumPy array as argument.

>>> import matplotlib.pyplot as plt
>>> x = np.linspace(0.01, 1, 200)
>>> fig, ax = plt.subplots()
>>> ax.plot(x, ndtri(x))
>>> ax.set_title("Standard normal percentile function")
>>> plt.show() ndtri_exp(y, out=None)

Inverse of `log_ndtr` vs x. Allows for greater precision than
`ndtri` composed with `numpy.exp` for very small values of y and for
y close to 0.

Parameters
----------
y : array_like of float
    Function argument
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    Inverse of the log CDF of the standard normal distribution, evaluated
    at y.

See Also
--------
log_ndtr : log of the standard normal cumulative distribution function
ndtr : standard normal cumulative distribution function
ndtri : standard normal percentile function

Examples
--------
>>> import numpy as np
>>> import scipy.special as sc

`ndtri_exp` agrees with the naive implementation when the latter does
not suffer from underflow.

>>> sc.ndtri_exp(-1)
-0.33747496376420244
>>> sc.ndtri(np.exp(-1))
-0.33747496376420244

For extreme values of y, the naive approach fails

>>> sc.ndtri(np.exp(-800))
-inf
>>> sc.ndtri(np.exp(-1e-20))
inf

whereas `ndtri_exp` is still able to compute the result to high precision.

>>> sc.ndtri_exp(-800)
-39.88469483825668
>>> sc.ndtri_exp(-1e-20)
9.262340089798409        nrdtrimn(p, std, x, out=None)

Calculate mean of normal distribution given other params.

Parameters
----------
p : array_like
    CDF values, in range (0, 1].
std : array_like
    Standard deviation.
x : array_like
    Quantiles, i.e. the upper limit of integration.
out : ndarray, optional
    Optional output array for the function results

Returns
-------
mn : scalar or ndarray
    The mean of the normal distribution.

See Also
--------
scipy.stats.norm : Normal distribution
ndtr : Standard normal cumulative probability distribution
ndtri : Inverse of standard normal CDF with respect to quantile
nrdtrisd : Inverse of normal distribution CDF with respect to
           standard deviation

Examples
--------
`nrdtrimn` can be used to recover the mean of a normal distribution
if we know the CDF value `p` for a given quantile `x` and the
standard deviation `std`. First, we calculate
the normal distribution CDF for an exemplary parameter set.

>>> from scipy.stats import norm
>>> mean = 3.
>>> std = 2.
>>> x = 6.
>>> p = norm.cdf(x, loc=mean, scale=std)
>>> p
0.9331927987311419

Verify that `nrdtrimn` returns the original value for `mean`.

>>> from scipy.special import nrdtrimn
>>> nrdtrimn(p, std, x)
3.0000000000000004     nrdtrisd(mn, p, x, out=None)

Calculate standard deviation of normal distribution given other params.

Parameters
----------
mn : scalar or ndarray
    The mean of the normal distribution.
p : array_like
    CDF values, in range (0, 1].
x : array_like
    Quantiles, i.e. the upper limit of integration.

out : ndarray, optional
    Optional output array for the function results

Returns
-------
std : scalar or ndarray
    Standard deviation.

See Also
--------
scipy.stats.norm : Normal distribution
ndtr : Standard normal cumulative probability distribution
ndtri : Inverse of standard normal CDF with respect to quantile
nrdtrimn : Inverse of normal distribution CDF with respect to
           mean

Examples
--------
`nrdtrisd` can be used to recover the standard deviation of a normal
distribution if we know the CDF value `p` for a given quantile `x` and
the mean `mn`. First, we calculate the normal distribution CDF for an
exemplary parameter set.

>>> from scipy.stats import norm
>>> mean = 3.
>>> std = 2.
>>> x = 6.
>>> p = norm.cdf(x, loc=mean, scale=std)
>>> p
0.9331927987311419

Verify that `nrdtrisd` returns the original value for `std`.

>>> from scipy.special import nrdtrisd
>>> nrdtrisd(mean, p, x)
2.0000000000000004       owens_t(h, a, out=None)

Owen's T Function.

The function T(h, a) gives the probability of the event
(X > h and 0 < Y < a * X) where X and Y are independent
standard normal random variables.

Parameters
----------
h: array_like
    Input value.
a: array_like
    Input value.
out : ndarray, optional
    Optional output array for the function results

Returns
-------
t: scalar or ndarray
    Probability of the event (X > h and 0 < Y < a * X),
    where X and Y are independent standard normal random variables.

References
----------
.. [1] M. Patefield and D. Tandy, "Fast and accurate calculation of
       Owen's T Function", Statistical Software vol. 5, pp. 1-25, 2000.

Examples
--------
>>> from scipy import special
>>> a = 3.5
>>> h = 0.78
>>> special.owens_t(h, a)
0.10877216734852274     pdtr(k, m, out=None)

Poisson cumulative distribution function.

Defined as the probability that a Poisson-distributed random
variable with event rate :math:`m` is less than or equal to
:math:`k`. More concretely, this works out to be [1]_

.. math::

   \exp(-m) \sum_{j = 0}^{\lfloor{k}\rfloor} \frac{m^j}{j!}.

Parameters
----------
k : array_like
    Number of occurrences (nonnegative, real)
m : array_like
    Shape parameter (nonnegative, real)
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    Values of the Poisson cumulative distribution function

See Also
--------
pdtrc : Poisson survival function
pdtrik : inverse of `pdtr` with respect to `k`
pdtri : inverse of `pdtr` with respect to `m`

References
----------
.. [1] https://en.wikipedia.org/wiki/Poisson_distribution

Examples
--------
>>> import numpy as np
>>> import scipy.special as sc

It is a cumulative distribution function, so it converges to 1
monotonically as `k` goes to infinity.

>>> sc.pdtr([1, 10, 100, np.inf], 1)
array([0.73575888, 0.99999999, 1.        , 1.        ])

It is discontinuous at integers and constant between integers.

>>> sc.pdtr([1, 1.5, 1.9, 2], 1)
array([0.73575888, 0.73575888, 0.73575888, 0.9196986 ]) pdtrc(k, m, out=None)

Poisson survival function

Returns the sum of the terms from k+1 to infinity of the Poisson
distribution: sum(exp(-m) * m**j / j!, j=k+1..inf) = gammainc(
k+1, m). Arguments must both be non-negative doubles.

Parameters
----------
k : array_like
    Number of occurrences (nonnegative, real)
m : array_like
    Shape parameter (nonnegative, real)
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    Values of the Poisson survival function

See Also
--------
pdtr : Poisson cumulative distribution function
pdtrik : inverse of `pdtr` with respect to `k`
pdtri : inverse of `pdtr` with respect to `m`

Examples
--------
>>> import numpy as np
>>> import scipy.special as sc

It is a survival function, so it decreases to 0
monotonically as `k` goes to infinity.

>>> k = np.array([1, 10, 100, np.inf])
>>> sc.pdtrc(k, 1)
array([2.64241118e-001, 1.00477664e-008, 3.94147589e-161, 0.00000000e+000])

It can be expressed in terms of the lower incomplete gamma
function `gammainc`.

>>> sc.gammainc(k + 1, 1)
array([2.64241118e-001, 1.00477664e-008, 3.94147589e-161, 0.00000000e+000])    pdtri(k, y, out=None)

Inverse to `pdtr` vs m

Returns the Poisson variable `m` such that the sum from 0 to `k` of
the Poisson density is equal to the given probability `y`:
calculated by ``gammaincinv(k + 1, y)``. `k` must be a nonnegative
integer and `y` between 0 and 1.

Parameters
----------
k : array_like
    Number of occurrences (nonnegative, real)
y : array_like
    Probability
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    Values of the shape parameter `m` such that ``pdtr(k, m) = p``

See Also
--------
pdtr : Poisson cumulative distribution function
pdtrc : Poisson survival function
pdtrik : inverse of `pdtr` with respect to `k`

Examples
--------
>>> import scipy.special as sc

Compute the CDF for several values of `m`:

>>> m = [0.5, 1, 1.5]
>>> p = sc.pdtr(1, m)
>>> p
array([0.90979599, 0.73575888, 0.5578254 ])

Compute the inverse. We recover the values of `m`, as expected:

>>> sc.pdtri(1, p)
array([0.5, 1. , 1.5])      pdtrik(p, m, out=None)

Inverse to `pdtr` vs `k`.

Parameters
----------
p : array_like
    Probability
m : array_like
    Shape parameter (nonnegative, real)
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    The number of occurrences `k` such that ``pdtr(k, m) = p``

Notes
-----
This function relies on the ``gamma_q_inva`` function from the Boost
Math C++ library [1]_.

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

See Also
--------
pdtr : Poisson cumulative distribution function
pdtrc : Poisson survival function
pdtri : inverse of `pdtr` with respect to `m`

Examples
--------
>>> import scipy.special as sc

Compute the CDF for several values of `k`:

>>> k = [1, 2, 3]
>>> p = sc.pdtr(k, 2)
>>> p
array([0.40600585, 0.67667642, 0.85712346])

Compute the inverse. We recover the values of `k`, as expected:

>>> sc.pdtrik(p, 2)
array([1., 2., 3.])   poch(z, m, out=None)

Pochhammer symbol.

The Pochhammer symbol (rising factorial) is defined as

.. math::

    (z)_m = \frac{\Gamma(z + m)}{\Gamma(z)}

For positive integer `m` it reads

.. math::

    (z)_m = z (z + 1) ... (z + m - 1)

See [DLMF]_ for more details.

Parameters
----------
z, m : array_like
    Real-valued arguments.
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    The value of the function.

References
----------
.. [DLMF] Nist, Digital Library of Mathematical Functions
    https://dlmf.nist.gov/5.2#iii

Examples
--------
>>> import scipy.special as sc

It is 1 when m is 0.

>>> sc.poch([1, 2, 3, 4], 0)
array([1., 1., 1., 1.])

For z equal to 1 it reduces to the factorial function.

>>> sc.poch(1, 5)
120.0
>>> 1 * 2 * 3 * 4 * 5
120

It can be expressed in terms of the gamma function.

>>> z, m = 3.7, 2.1
>>> sc.poch(z, m)
20.529581933776953
>>> sc.gamma(z + m) / sc.gamma(z)
20.52958193377696    powm1(x, y, out=None)

Computes ``x**y - 1``.

This function is useful when `y` is near 0, or when `x` is near 1.

The function is implemented for real types only (unlike ``numpy.power``,
which accepts complex inputs).

Parameters
----------
x : array_like
    The base. Must be a real type (i.e. integer or float, not complex).
y : array_like
    The exponent. Must be a real type (i.e. integer or float, not complex).

Returns
-------
array_like
    Result of the calculation

Notes
-----
.. versionadded:: 1.10.0

The underlying code is implemented for single precision and double
precision floats only.  Unlike `numpy.power`, integer inputs to
`powm1` are converted to floating point, and complex inputs are
not accepted.

Note the following edge cases:

* ``powm1(x, 0)`` returns 0 for any ``x``, including 0, ``inf``
  and ``nan``.
* ``powm1(1, y)`` returns 0 for any ``y``, including ``nan``
  and ``inf``.

This function wraps the ``powm1`` routine from the
Boost Math C++ library [1]_.

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
>>> import numpy as np
>>> from scipy.special import powm1

>>> x = np.array([1.2, 10.0, 0.9999999975])
>>> y = np.array([1e-9, 1e-11, 0.1875])
>>> powm1(x, y)
array([ 1.82321557e-10,  2.30258509e-11, -4.68749998e-10])

It can be verified that the relative errors in those results
are less than 2.5e-16.

Compare that to the result of ``x**y - 1``, where the
relative errors are all larger than 8e-8:

>>> x**y - 1
array([ 1.82321491e-10,  2.30258035e-11, -4.68750039e-10])      pseudo_huber(delta, r, out=None)

Pseudo-Huber loss function.

.. math:: \mathrm{pseudo\_huber}(\delta, r) =
          \delta^2 \left( \sqrt{ 1 + \left( \frac{r}{\delta} \right)^2 } - 1 \right)

Parameters
----------
delta : array_like
    Input array, indicating the soft quadratic vs. linear loss changepoint.
r : array_like
    Input array, possibly representing residuals.
out : ndarray, optional
    Optional output array for the function results

Returns
-------
res : scalar or ndarray
    The computed Pseudo-Huber loss function values.

See Also
--------
huber: Similar function which this function approximates

Notes
-----
Like `huber`, `pseudo_huber` often serves as a robust loss function
in statistics or machine learning to reduce the influence of outliers.
Unlike `huber`, `pseudo_huber` is smooth.

Typically, `r` represents residuals, the difference
between a model prediction and data. Then, for :math:`|r|\leq\delta`,
`pseudo_huber` resembles the squared error and for :math:`|r|>\delta` the
absolute error. This way, the Pseudo-Huber loss often achieves
a fast convergence in model fitting for small residuals like the squared
error loss function and still reduces the influence of outliers
(:math:`|r|>\delta`) like the absolute error loss. As :math:`\delta` is
the cutoff between squared and absolute error regimes, it has
to be tuned carefully for each problem. `pseudo_huber` is also
convex, making it suitable for gradient based optimization. [1]_ [2]_

.. versionadded:: 0.15.0

References
----------
.. [1] Hartley, Zisserman, "Multiple View Geometry in Computer Vision".
       2003. Cambridge University Press. p. 619
.. [2] Charbonnier et al. "Deterministic edge-preserving regularization
       in computed imaging". 1997. IEEE Trans. Image Processing.
       6 (2): 298 - 311.

Examples
--------
Import all necessary modules.

>>> import numpy as np
>>> from scipy.special import pseudo_huber, huber
>>> import matplotlib.pyplot as plt

Calculate the function for ``delta=1`` at ``r=2``.

>>> pseudo_huber(1., 2.)
1.2360679774997898

Calculate the function at ``r=2`` for different `delta` by providing
a list or NumPy array for `delta`.

>>> pseudo_huber([1., 2., 4.], 3.)
array([2.16227766, 3.21110255, 4.        ])

Calculate the function for ``delta=1`` at several points by providing
a list or NumPy array for `r`.

>>> pseudo_huber(2., np.array([1., 1.5, 3., 4.]))
array([0.47213595, 1.        , 3.21110255, 4.94427191])

The function can be calculated for different `delta` and `r` by
providing arrays for both with compatible shapes for broadcasting.

>>> r = np.array([1., 2.5, 8., 10.])
>>> deltas = np.array([[1.], [5.], [9.]])
>>> print(r.shape, deltas.shape)
(4,) (3, 1)

>>> pseudo_huber(deltas, r)
array([[ 0.41421356,  1.6925824 ,  7.06225775,  9.04987562],
       [ 0.49509757,  2.95084972, 22.16990566, 30.90169944],
       [ 0.49846624,  3.06693762, 27.37435121, 40.08261642]])

Plot the function for different `delta`.

>>> x = np.linspace(-4, 4, 500)
>>> deltas = [1, 2, 3]
>>> linestyles = ["dashed", "dotted", "dashdot"]
>>> fig, ax = plt.subplots()
>>> combined_plot_parameters = list(zip(deltas, linestyles))
>>> for delta, style in combined_plot_parameters:
...     ax.plot(x, pseudo_huber(delta, x), label=rf"$\delta={delta}$",
...             ls=style)
>>> ax.legend(loc="upper center")
>>> ax.set_xlabel("$x$")
>>> ax.set_title(r"Pseudo-Huber loss function $h_{\delta}(x)$")
>>> ax.set_xlim(-4, 4)
>>> ax.set_ylim(0, 8)
>>> plt.show()

Finally, illustrate the difference between `huber` and `pseudo_huber` by
plotting them and their gradients with respect to `r`. The plot shows
that `pseudo_huber` is continuously differentiable while `huber` is not
at the points :math:`\pm\delta`.

>>> def huber_grad(delta, x):
...     grad = np.copy(x)
...     linear_area = np.argwhere(np.abs(x) > delta)
...     grad[linear_area]=delta*np.sign(x[linear_area])
...     return grad
>>> def pseudo_huber_grad(delta, x):
...     return x* (1+(x/delta)**2)**(-0.5)
>>> x=np.linspace(-3, 3, 500)
>>> delta = 1.
>>> fig, ax = plt.subplots(figsize=(7, 7))
>>> ax.plot(x, huber(delta, x), label="Huber", ls="dashed")
>>> ax.plot(x, huber_grad(delta, x), label="Huber Gradient", ls="dashdot")
>>> ax.plot(x, pseudo_huber(delta, x), label="Pseudo-Huber", ls="dotted")
>>> ax.plot(x, pseudo_huber_grad(delta, x), label="Pseudo-Huber Gradient",
...         ls="solid")
>>> ax.legend(loc="upper center")
>>> plt.show()        rel_entr(x, y, out=None)

Elementwise function for computing relative entropy.

.. math::

    \mathrm{rel\_entr}(x, y) =
        \begin{cases}
            x \log(x / y) & x > 0, y > 0 \\
            0 & x = 0, y \ge 0 \\
            \infty & \text{otherwise}
        \end{cases}

Parameters
----------
x, y : array_like
    Input arrays
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    Relative entropy of the inputs

See Also
--------
entr, kl_div, scipy.stats.entropy

Notes
-----
.. versionadded:: 0.15.0

This function is jointly convex in x and y.

The origin of this function is in convex programming; see
[1]_. Given two discrete probability distributions :math:`p_1,
\ldots, p_n` and :math:`q_1, \ldots, q_n`, the definition of relative
entropy in the context of *information theory* is

.. math::

    \sum_{i = 1}^n \mathrm{rel\_entr}(p_i, q_i).

To compute the latter quantity, use `scipy.stats.entropy`.

See [2]_ for details.

References
----------
.. [1] Boyd, Stephen and Lieven Vandenberghe. *Convex optimization*.
       Cambridge University Press, 2004.
       :doi:`https://doi.org/10.1017/CBO9780511804441`
.. [2] Kullback-Leibler divergence,
       https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence   round(x, out=None)

Round to the nearest integer.

Returns the nearest integer to `x`.  If `x` ends in 0.5 exactly,
the nearest even integer is chosen.

Parameters
----------
x : array_like
    Real valued input.
out : ndarray, optional
    Optional output array for the function results.

Returns
-------
scalar or ndarray
    The nearest integers to the elements of `x`. The result is of
    floating type, not integer type.

Examples
--------
>>> import scipy.special as sc

It rounds to even.

>>> sc.round([0.5, 1.5])
array([0., 2.])      shichi(x, out=None)

Hyperbolic sine and cosine integrals.

The hyperbolic sine integral is

.. math::

  \int_0^x \frac{\sinh{t}}{t}dt

and the hyperbolic cosine integral is

.. math::

  \gamma + \log(x) + \int_0^x \frac{\cosh{t} - 1}{t} dt

where :math:`\gamma` is Euler's constant and :math:`\log` is the
principal branch of the logarithm [1]_ (see also [2]_).

Parameters
----------
x : array_like
    Real or complex points at which to compute the hyperbolic sine
    and cosine integrals.
out : tuple of ndarray, optional
    Optional output arrays for the function results

Returns
-------
si : scalar or ndarray
    Hyperbolic sine integral at ``x``
ci : scalar or ndarray
    Hyperbolic cosine integral at ``x``

See Also
--------
sici : Sine and cosine integrals.
exp1 : Exponential integral E1.
expi : Exponential integral Ei.

Notes
-----
For real arguments with ``x < 0``, ``chi`` is the real part of the
hyperbolic cosine integral. For such points ``chi(x)`` and ``chi(x
+ 0j)`` differ by a factor of ``1j*pi``.

For real arguments the function is computed by calling Cephes'
[3]_ *shichi* routine. For complex arguments the algorithm is based
on Mpmath's [4]_ *shi* and *chi* routines.

References
----------
.. [1] Milton Abramowitz and Irene A. Stegun, eds.
       Handbook of Mathematical Functions with Formulas,
       Graphs, and Mathematical Tables. New York: Dover, 1972.
       (See Section 5.2.)
.. [2] NIST Digital Library of Mathematical Functions
       https://dlmf.nist.gov/6.2.E15 and https://dlmf.nist.gov/6.2.E16
.. [3] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/
.. [4] Fredrik Johansson and others.
       "mpmath: a Python library for arbitrary-precision floating-point
       arithmetic" (Version 0.19) http://mpmath.org/

Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy.special import shichi, sici

`shichi` accepts real or complex input:

>>> shichi(0.5)
(0.5069967498196671, -0.05277684495649357)
>>> shichi(0.5 + 2.5j)
((0.11772029666668238+1.831091777729851j),
 (0.29912435887648825+1.7395351121166562j))

The hyperbolic sine and cosine integrals Shi(z) and Chi(z) are
related to the sine and cosine integrals Si(z) and Ci(z) by

* Shi(z) = -i*Si(i*z)
* Chi(z) = Ci(-i*z) + i*pi/2

>>> z = 0.25 + 5j
>>> shi, chi = shichi(z)
>>> shi, -1j*sici(1j*z)[0]            # Should be the same.
((-0.04834719325101729+1.5469354086921228j),
 (-0.04834719325101729+1.5469354086921228j))
>>> chi, sici(-1j*z)[1] + 1j*np.pi/2  # Should be the same.
((-0.19568708973868087+1.556276312103824j),
 (-0.19568708973868087+1.556276312103824j))

Plot the functions evaluated on the real axis:

>>> xp = np.geomspace(1e-8, 4.0, 250)
>>> x = np.concatenate((-xp[::-1], xp))
>>> shi, chi = shichi(x)

>>> fig, ax = plt.subplots()
>>> ax.plot(x, shi, label='Shi(x)')
>>> ax.plot(x, chi, '--', label='Chi(x)')
>>> ax.set_xlabel('x')
>>> ax.set_title('Hyperbolic Sine and Cosine Integrals')
>>> ax.legend(shadow=True, framealpha=1, loc='lower right')
>>> ax.grid(True)
>>> plt.show()      sici(x, out=None)

Sine and cosine integrals.

The sine integral is

.. math::

  \int_0^x \frac{\sin{t}}{t}dt

and the cosine integral is

.. math::

  \gamma + \log(x) + \int_0^x \frac{\cos{t} - 1}{t}dt

where :math:`\gamma` is Euler's constant and :math:`\log` is the
principal branch of the logarithm [1]_ (see also [2]_).

Parameters
----------
x : array_like
    Real or complex points at which to compute the sine and cosine
    integrals.
out : tuple of ndarray, optional
    Optional output arrays for the function results

Returns
-------
si : scalar or ndarray
    Sine integral at ``x``
ci : scalar or ndarray
    Cosine integral at ``x``

See Also
--------
shichi : Hyperbolic sine and cosine integrals.
exp1 : Exponential integral E1.
expi : Exponential integral Ei.

Notes
-----
For real arguments with ``x < 0``, ``ci`` is the real part of the
cosine integral. For such points ``ci(x)`` and ``ci(x + 0j)``
differ by a factor of ``1j*pi``.

For real arguments the function is computed by calling Cephes'
[3]_ *sici* routine. For complex arguments the algorithm is based
on Mpmath's [4]_ *si* and *ci* routines.

References
----------
.. [1] Milton Abramowitz and Irene A. Stegun, eds.
       Handbook of Mathematical Functions with Formulas,
       Graphs, and Mathematical Tables. New York: Dover, 1972.
       (See Section 5.2.)
.. [2] NIST Digital Library of Mathematical Functions
       https://dlmf.nist.gov/6.2.E9, https://dlmf.nist.gov/6.2.E12,
       and https://dlmf.nist.gov/6.2.E13
.. [3] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/
.. [4] Fredrik Johansson and others.
       "mpmath: a Python library for arbitrary-precision floating-point
       arithmetic" (Version 0.19) http://mpmath.org/

Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy.special import sici, exp1

`sici` accepts real or complex input:

>>> sici(2.5)
(1.7785201734438267, 0.2858711963653835)
>>> sici(2.5 + 3j)
((4.505735874563953+0.06863305018999577j),
(0.0793644206906966-2.935510262937543j))

For z in the right half plane, the sine and cosine integrals are
related to the exponential integral E1 (implemented in SciPy as
`scipy.special.exp1`) by

* Si(z) = (E1(i*z) - E1(-i*z))/2i + pi/2
* Ci(z) = -(E1(i*z) + E1(-i*z))/2

See [1]_ (equations 5.2.21 and 5.2.23).

We can verify these relations:

>>> z = 2 - 3j
>>> sici(z)
((4.54751388956229-1.3991965806460565j),
(1.408292501520851+2.9836177420296055j))

>>> (exp1(1j*z) - exp1(-1j*z))/2j + np.pi/2  # Same as sine integral
(4.54751388956229-1.3991965806460565j)

>>> -(exp1(1j*z) + exp1(-1j*z))/2            # Same as cosine integral
(1.408292501520851+2.9836177420296055j)

Plot the functions evaluated on the real axis; the dotted horizontal
lines are at pi/2 and -pi/2:

>>> x = np.linspace(-16, 16, 150)
>>> si, ci = sici(x)

>>> fig, ax = plt.subplots()
>>> ax.plot(x, si, label='Si(x)')
>>> ax.plot(x, ci, '--', label='Ci(x)')
>>> ax.legend(shadow=True, framealpha=1, loc='upper left')
>>> ax.set_xlabel('x')
>>> ax.set_title('Sine and Cosine Integrals')
>>> ax.axhline(np.pi/2, linestyle=':', alpha=0.5, color='k')
>>> ax.axhline(-np.pi/2, linestyle=':', alpha=0.5, color='k')
>>> ax.grid(True)
>>> plt.show()        smirnov(n, d, out=None)

Kolmogorov-Smirnov complementary cumulative distribution function

Returns the exact Kolmogorov-Smirnov complementary cumulative
distribution function,(aka the Survival Function) of Dn+ (or Dn-)
for a one-sided test of equality between an empirical and a
theoretical distribution. It is equal to the probability that the
maximum difference between a theoretical distribution and an empirical
one based on `n` samples is greater than d.

Parameters
----------
n : int
  Number of samples
d : float array_like
  Deviation between the Empirical CDF (ECDF) and the target CDF.
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    The value(s) of smirnov(n, d), Prob(Dn+ >= d) (Also Prob(Dn- >= d))

See Also
--------
smirnovi : The Inverse Survival Function for the distribution
scipy.stats.ksone : Provides the functionality as a continuous distribution
kolmogorov, kolmogi : Functions for the two-sided distribution

Notes
-----
`smirnov` is used by `stats.kstest` in the application of the
Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this
function is exposed in `scpy.special`, but the recommended way to achieve
the most accurate CDF/SF/PDF/PPF/ISF computations is to use the
`stats.ksone` distribution.

Examples
--------
>>> import numpy as np
>>> from scipy.special import smirnov
>>> from scipy.stats import norm

Show the probability of a gap at least as big as 0, 0.5 and 1.0 for a
sample of size 5.

>>> smirnov(5, [0, 0.5, 1.0])
array([ 1.   ,  0.056,  0.   ])

Compare a sample of size 5 against N(0, 1), the standard normal
distribution with mean 0 and standard deviation 1.

`x` is the sample.

>>> x = np.array([-1.392, -0.135, 0.114, 0.190, 1.82])

>>> target = norm(0, 1)
>>> cdfs = target.cdf(x)
>>> cdfs
array([0.0819612 , 0.44630594, 0.5453811 , 0.57534543, 0.9656205 ])

Construct the empirical CDF and the K-S statistics (Dn+, Dn-, Dn).

>>> n = len(x)
>>> ecdfs = np.arange(n+1, dtype=float)/n
>>> cols = np.column_stack([x, ecdfs[1:], cdfs, cdfs - ecdfs[:n],
...                        ecdfs[1:] - cdfs])
>>> with np.printoptions(precision=3):
...    print(cols)
[[-1.392  0.2    0.082  0.082  0.118]
 [-0.135  0.4    0.446  0.246 -0.046]
 [ 0.114  0.6    0.545  0.145  0.055]
 [ 0.19   0.8    0.575 -0.025  0.225]
 [ 1.82   1.     0.966  0.166  0.034]]
>>> gaps = cols[:, -2:]
>>> Dnpm = np.max(gaps, axis=0)
>>> print(f'Dn-={Dnpm[0]:f}, Dn+={Dnpm[1]:f}')
Dn-=0.246306, Dn+=0.224655
>>> probs = smirnov(n, Dnpm)
>>> print(f'For a sample of size {n} drawn from N(0, 1):',
...       f' Smirnov n={n}: Prob(Dn- >= {Dnpm[0]:f}) = {probs[0]:.4f}',
...       f' Smirnov n={n}: Prob(Dn+ >= {Dnpm[1]:f}) = {probs[1]:.4f}',
...       sep='\n')
For a sample of size 5 drawn from N(0, 1):
 Smirnov n=5: Prob(Dn- >= 0.246306) = 0.4711
 Smirnov n=5: Prob(Dn+ >= 0.224655) = 0.5245

Plot the empirical CDF and the standard normal CDF.

>>> import matplotlib.pyplot as plt
>>> plt.step(np.concatenate(([-2.5], x, [2.5])),
...          np.concatenate((ecdfs, [1])),
...          where='post', label='Empirical CDF')
>>> xx = np.linspace(-2.5, 2.5, 100)
>>> plt.plot(xx, target.cdf(xx), '--', label='CDF for N(0, 1)')

Add vertical lines marking Dn+ and Dn-.

>>> iminus, iplus = np.argmax(gaps, axis=0)
>>> plt.vlines([x[iminus]], ecdfs[iminus], cdfs[iminus], color='r',
...            alpha=0.5, lw=4)
>>> plt.vlines([x[iplus]], cdfs[iplus], ecdfs[iplus+1], color='m',
...            alpha=0.5, lw=4)

>>> plt.grid(True)
>>> plt.legend(framealpha=1, shadow=True)
>>> plt.show()  smirnovi(n, p, out=None)

Inverse to `smirnov`

Returns `d` such that ``smirnov(n, d) == p``, the critical value
corresponding to `p`.

Parameters
----------
n : int
  Number of samples
p : float array_like
    Probability
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    The value(s) of smirnovi(n, p), the critical values.

See Also
--------
smirnov : The Survival Function (SF) for the distribution
scipy.stats.ksone : Provides the functionality as a continuous distribution
kolmogorov, kolmogi : Functions for the two-sided distribution
scipy.stats.kstwobign : Two-sided Kolmogorov-Smirnov distribution, large n

Notes
-----
`smirnov` is used by `stats.kstest` in the application of the
Kolmogorov-Smirnov Goodness of Fit test. For historical reasons this
function is exposed in `scpy.special`, but the recommended way to achieve
the most accurate CDF/SF/PDF/PPF/ISF computations is to use the
`stats.ksone` distribution.

Examples
--------
>>> from scipy.special import smirnovi, smirnov

>>> n = 24
>>> deviations = [0.1, 0.2, 0.3]

Use `smirnov` to compute the complementary CDF of the Smirnov
distribution for the given number of samples and deviations.

>>> p = smirnov(n, deviations)
>>> p
array([0.58105083, 0.12826832, 0.01032231])

The inverse function ``smirnovi(n, p)`` returns ``deviations``.

>>> smirnovi(n, p)
array([0.1, 0.2, 0.3])        spence(z, out=None)

Spence's function, also known as the dilogarithm.

It is defined to be

.. math::
  \int_1^z \frac{\log(t)}{1 - t}dt

for complex :math:`z`, where the contour of integration is taken
to avoid the branch cut of the logarithm. Spence's function is
analytic everywhere except the negative real axis where it has a
branch cut.

Parameters
----------
z : array_like
    Points at which to evaluate Spence's function
out : ndarray, optional
    Optional output array for the function results

Returns
-------
s : scalar or ndarray
    Computed values of Spence's function

Notes
-----
There is a different convention which defines Spence's function by
the integral

.. math::
  -\int_0^z \frac{\log(1 - t)}{t}dt;

this is our ``spence(1 - z)``.

Examples
--------
>>> import numpy as np
>>> from scipy.special import spence
>>> import matplotlib.pyplot as plt

The function is defined for complex inputs:

>>> spence([1-1j, 1.5+2j, 3j, -10-5j])
array([-0.20561676+0.91596559j, -0.86766909-1.39560134j,
       -0.59422064-2.49129918j, -1.14044398+6.80075924j])

For complex inputs on the branch cut, which is the negative real axis,
the function returns the limit for ``z`` with positive imaginary part.
For example, in the following, note the sign change of the imaginary
part of the output for ``z = -2`` and ``z = -2 - 1e-8j``:

>>> spence([-2 + 1e-8j, -2, -2 - 1e-8j])
array([2.32018041-3.45139229j, 2.32018042-3.4513923j ,
       2.32018041+3.45139229j])

The function returns ``nan`` for real inputs on the branch cut:

>>> spence(-1.5)
nan

Verify some particular values: ``spence(0) = pi**2/6``,
``spence(1) = 0`` and ``spence(2) = -pi**2/12``.

>>> spence([0, 1, 2])
array([ 1.64493407,  0.        , -0.82246703])
>>> np.pi**2/6, -np.pi**2/12
(1.6449340668482264, -0.8224670334241132)

Verify the identity::

    spence(z) + spence(1 - z) = pi**2/6 - log(z)*log(1 - z)

>>> z = 3 + 4j
>>> spence(z) + spence(1 - z)
(-2.6523186143876067+1.8853470951513935j)
>>> np.pi**2/6 - np.log(z)*np.log(1 - z)
(-2.652318614387606+1.885347095151394j)

Plot the function for positive real input.

>>> fig, ax = plt.subplots()
>>> x = np.linspace(0, 6, 400)
>>> ax.plot(x, spence(x))
>>> ax.grid()
>>> ax.set_xlabel('x')
>>> ax.set_title('spence(x)')
>>> plt.show()       stdtr(df, t, out=None)

Student t distribution cumulative distribution function

Returns the integral:

.. math::
    \frac{\Gamma((df+1)/2)}{\sqrt{\pi df} \Gamma(df/2)}
    \int_{-\infty}^t (1+x^2/df)^{-(df+1)/2}\, dx

Parameters
----------
df : array_like
    Degrees of freedom
t : array_like
    Upper bound of the integral
out : ndarray, optional
    Optional output array for the function results

Returns
-------
scalar or ndarray
    Value of the Student t CDF at t

See Also
--------
stdtridf : inverse of stdtr with respect to `df`
stdtrit : inverse of stdtr with respect to `t`
scipy.stats.t : student t distribution

Notes
-----
The student t distribution is also available as `scipy.stats.t`.
Calling `stdtr` directly can improve performance compared to the
``cdf`` method of `scipy.stats.t` (see last example below).

The function is computed using the Boost Math library [1]_, which
relies on the incomplete beta function.

References
----------
.. [1] Boost C++ Libraries, http://www.boost.org/

Examples
--------
Calculate the function for ``df=3`` at ``t=1``.

>>> import numpy as np
>>> from scipy.special import stdtr
>>> import matplotlib.pyplot as plt
>>> stdtr(3, 1)
0.8044988905221148

Plot the function for three different degrees of freedom.

>>> x = np.linspace(-10, 10, 1000)
>>> fig, ax = plt.subplots()
>>> parameters = [(1, "solid"), (3, "dashed"), (10, "dotted")]
>>> for (df, linestyle) in parameters:
...     ax.plot(x, stdtr(df, x), ls=linestyle, label=f"$df={df}$")
>>> ax.legend()
>>> ax.set_title("Student t distribution cumulative distribution function")
>>> plt.show()

The function can be computed for several degrees of freedom at the same
time by providing a NumPy array or list for `df`:

>>> stdtr([1, 2, 3], 1)
array([0.75      , 0.78867513, 0.80449889])

It is possible to calculate the function at several points for several
different degrees of freedom simultaneously by providing arrays for `df`
and `t` with shapes compatible for broadcasting. Compute `stdtr` at
4 points for 3 degrees of freedom resulting in an array of shape 3x4.

>>> dfs = np.array([[1], [2], [3]])
>>> t = np.array([2, 4, 6, 8])
>>> dfs.shape, t.shape
((3, 1), (4,))

>>> stdtr(dfs, t)
array([[0.85241638, 0.92202087, 0.94743154, 0.96041658],
       [0.90824829, 0.97140452, 0.98666426, 0.99236596],
       [0.93033702, 0.98599577, 0.99536364, 0.99796171]])

The t distribution is also available as `scipy.stats.t`. Calling `stdtr`
directly can be much faster than calling the ``cdf`` method of
`scipy.stats.t`. To get the same results, one must use the following
parametrization: ``scipy.stats.t(df).cdf(x) = stdtr(df, x)``.

>>> from scipy.stats import t
>>> df, x = 3, 1
>>> stdtr_result = stdtr(df, x)  # this can be faster than below
>>> stats_result = t(df).cdf(x)
>>> stats_result == stdtr_result  # test that results are equal
True  stdtridf(p, t, out=None)

Inverse of `stdtr` vs df

Returns the argument df such that stdtr(df, t) is equal to `p`.

Parameters
----------
p : array_like
    Probability
t : array_like
    Upper bound of the integral
out : ndarray, optional
    Optional output array for the function results

Returns
-------
df : scalar or ndarray
    Value of `df` such that ``stdtr(df, t) == p``

See Also
--------
stdtr : Student t CDF
stdtrit : inverse of stdtr with respect to `t`
scipy.stats.t : Student t distribution

Examples
--------
Compute the student t cumulative distribution function for one
parameter set.

>>> from scipy.special import stdtr, stdtridf
>>> df, x = 5, 2
>>> cdf_value = stdtr(df, x)
>>> cdf_value
0.9490302605850709

Verify that `stdtridf` recovers the original value for `df` given
the CDF value and `x`.

>>> stdtridf(cdf_value, x)
5.0   stdtrit(df, p, out=None)

The `p`-th quantile of the student t distribution.

This function is the inverse of the student t distribution cumulative
distribution function (CDF), returning `t` such that `stdtr(df, t) = p`.

Returns the argument `t` such that stdtr(df, t) is equal to `p`.

Parameters
----------
df : array_like
    Degrees of freedom
p : array_like
    Probability
out : ndarray, optional
    Optional output array for the function results

Returns
-------
t : scalar or ndarray
    Value of `t` such that ``stdtr(df, t) == p``

See Also
--------
stdtr : Student t CDF
stdtridf : inverse of stdtr with respect to `df`
scipy.stats.t : Student t distribution

Notes
-----
The student t distribution is also available as `scipy.stats.t`. Calling
`stdtrit` directly can improve performance compared to the ``ppf``
method of `scipy.stats.t` (see last example below).

The function is computed using the Boost Math library [1]_, which
relies on the incomplete beta function.

References
----------
.. [1] Boost C++ Libraries, http://www.boost.org/

Examples
--------
`stdtrit` represents the inverse of the student t distribution CDF which
is available as `stdtr`. Here, we calculate the CDF for ``df`` at
``x=1``. `stdtrit` then returns ``1`` up to floating point errors
given the same value for `df` and the computed CDF value.

>>> import numpy as np
>>> from scipy.special import stdtr, stdtrit
>>> import matplotlib.pyplot as plt
>>> df = 3
>>> x = 1
>>> cdf_value = stdtr(df, x)
>>> stdtrit(df, cdf_value)
0.9999999994418539

Plot the function for three different degrees of freedom.

>>> x = np.linspace(0, 1, 1000)
>>> parameters = [(1, "solid"), (2, "dashed"), (5, "dotted")]
>>> fig, ax = plt.subplots()
>>> for (df, linestyle) in parameters:
...     ax.plot(x, stdtrit(df, x), ls=linestyle, label=f"$df={df}$")
>>> ax.legend()
>>> ax.set_ylim(-10, 10)
>>> ax.set_title("Student t distribution quantile function")
>>> plt.show()

The function can be computed for several degrees of freedom at the same
time by providing a NumPy array or list for `df`:

>>> stdtrit([1, 2, 3], 0.7)
array([0.72654253, 0.6172134 , 0.58438973])

It is possible to calculate the function at several points for several
different degrees of freedom simultaneously by providing arrays for `df`
and `p` with shapes compatible for broadcasting. Compute `stdtrit` at
4 points for 3 degrees of freedom resulting in an array of shape 3x4.

>>> dfs = np.array([[1], [2], [3]])
>>> p = np.array([0.2, 0.4, 0.7, 0.8])
>>> dfs.shape, p.shape
((3, 1), (4,))

>>> stdtrit(dfs, p)
array([[-1.37638192, -0.3249197 ,  0.72654253,  1.37638192],
       [-1.06066017, -0.28867513,  0.6172134 ,  1.06066017],
       [-0.97847231, -0.27667066,  0.58438973,  0.97847231]])

The t distribution is also available as `scipy.stats.t`. Calling `stdtrit`
directly can be much faster than calling the ``ppf`` method of
`scipy.stats.t`. To get the same results, one must use the following
parametrization: ``scipy.stats.t(df).ppf(x) = stdtrit(df, x)``.

>>> from scipy.stats import t
>>> df, x = 3, 0.5
>>> stdtrit_result = stdtrit(df, x)  # this can be faster than below
>>> stats_result = t(df).ppf(x)
>>> stats_result == stdtrit_result  # test that results are equal
True       tklmbda(x, lmbda, out=None)

Cumulative distribution function of the Tukey lambda distribution.

Parameters
----------
x, lmbda : array_like
    Parameters
out : ndarray, optional
    Optional output array for the function results

Returns
-------
cdf : scalar or ndarray
    Value of the Tukey lambda CDF

See Also
--------
scipy.stats.tukeylambda : Tukey lambda distribution

Examples
--------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy.special import tklmbda, expit

Compute the cumulative distribution function (CDF) of the Tukey lambda
distribution at several ``x`` values for `lmbda` = -1.5.

>>> x = np.linspace(-2, 2, 9)
>>> x
array([-2. , -1.5, -1. , -0.5,  0. ,  0.5,  1. ,  1.5,  2. ])
>>> tklmbda(x, -1.5)
array([0.34688734, 0.3786554 , 0.41528805, 0.45629737, 0.5       ,
       0.54370263, 0.58471195, 0.6213446 , 0.65311266])

When `lmbda` is 0, the function is the logistic sigmoid function,
which is implemented in `scipy.special` as `expit`.

>>> tklmbda(x, 0)
array([0.11920292, 0.18242552, 0.26894142, 0.37754067, 0.5       ,
       0.62245933, 0.73105858, 0.81757448, 0.88079708])
>>> expit(x)
array([0.11920292, 0.18242552, 0.26894142, 0.37754067, 0.5       ,
       0.62245933, 0.73105858, 0.81757448, 0.88079708])

When `lmbda` is 1, the Tukey lambda distribution is uniform on the
interval [-1, 1], so the CDF increases linearly.

>>> t = np.linspace(-1, 1, 9)
>>> tklmbda(t, 1)
array([0.   , 0.125, 0.25 , 0.375, 0.5  , 0.625, 0.75 , 0.875, 1.   ])

In the following, we generate plots for several values of `lmbda`.

The first figure shows graphs for `lmbda` <= 0.

>>> styles = ['-', '-.', '--', ':']
>>> fig, ax = plt.subplots()
>>> x = np.linspace(-12, 12, 500)
>>> for k, lmbda in enumerate([-1.0, -0.5, 0.0]):
...     y = tklmbda(x, lmbda)
...     ax.plot(x, y, styles[k], label=rf'$\lambda$ = {lmbda:-4.1f}')

>>> ax.set_title(r'tklmbda(x, $\lambda$)')
>>> ax.set_label('x')
>>> ax.legend(framealpha=1, shadow=True)
>>> ax.grid(True)

The second figure shows graphs for `lmbda` > 0.  The dots in the
graphs show the bounds of the support of the distribution.

>>> fig, ax = plt.subplots()
>>> x = np.linspace(-4.2, 4.2, 500)
>>> lmbdas = [0.25, 0.5, 1.0, 1.5]
>>> for k, lmbda in enumerate(lmbdas):
...     y = tklmbda(x, lmbda)
...     ax.plot(x, y, styles[k], label=fr'$\lambda$ = {lmbda}')

>>> ax.set_prop_cycle(None)
>>> for lmbda in lmbdas:
...     ax.plot([-1/lmbda, 1/lmbda], [0, 1], '.', ms=8)

>>> ax.set_title(r'tklmbda(x, $\lambda$)')
>>> ax.set_xlabel('x')
>>> ax.legend(framealpha=1, shadow=True)
>>> ax.grid(True)

>>> plt.tight_layout()
>>> plt.show()

The CDF of the Tukey lambda distribution is also implemented as the
``cdf`` method of `scipy.stats.tukeylambda`.  In the following,
``tukeylambda.cdf(x, -0.5)`` and ``tklmbda(x, -0.5)`` compute the
same values:

>>> from scipy.stats import tukeylambda
>>> x = np.linspace(-2, 2, 9)

>>> tukeylambda.cdf(x, -0.5)
array([0.21995157, 0.27093858, 0.33541677, 0.41328161, 0.5       ,
       0.58671839, 0.66458323, 0.72906142, 0.78004843])

>>> tklmbda(x, -0.5)
array([0.21995157, 0.27093858, 0.33541677, 0.41328161, 0.5       ,
       0.58671839, 0.66458323, 0.72906142, 0.78004843])

The implementation in ``tukeylambda`` also provides location and scale
parameters, and other methods such as ``pdf()`` (the probability
density function) and ``ppf()`` (the inverse of the CDF), so for
working with the Tukey lambda distribution, ``tukeylambda`` is more
generally useful.  The primary advantage of ``tklmbda`` is that it is
significantly faster than ``tukeylambda.cdf``. wrightomega(z, out=None)

Wright Omega function.

Defined as the solution to

.. math::

    \omega + \log(\omega) = z

where :math:`\log` is the principal branch of the complex logarithm.

Parameters
----------
z : array_like
    Points at which to evaluate the Wright Omega function
out : ndarray, optional
    Optional output array for the function values

Returns
-------
omega : scalar or ndarray
    Values of the Wright Omega function

See Also
--------
lambertw : The Lambert W function

Notes
-----
.. versionadded:: 0.19.0

The function can also be defined as

.. math::

    \omega(z) = W_{K(z)}(e^z)

where :math:`K(z) = \lceil (\Im(z) - \pi)/(2\pi) \rceil` is the
unwinding number and :math:`W` is the Lambert W function.

The implementation here is taken from [1]_.

References
----------
.. [1] Lawrence, Corless, and Jeffrey, "Algorithm 917: Complex
       Double-Precision Evaluation of the Wright :math:`\omega`
       Function." ACM Transactions on Mathematical Software,
       2012. :doi:`10.1145/2168773.2168779`.

Examples
--------
>>> import numpy as np
>>> from scipy.special import wrightomega, lambertw

>>> wrightomega([-2, -1, 0, 1, 2])
array([0.12002824, 0.27846454, 0.56714329, 1.        , 1.5571456 ])

Complex input:

>>> wrightomega(3 + 5j)
(1.5804428632097158+3.8213626783287937j)

Verify that ``wrightomega(z)`` satisfies ``w + log(w) = z``:

>>> w = -5 + 4j
>>> wrightomega(w + np.log(w))
(-5+4j)

Verify the connection to ``lambertw``:

>>> z = 0.5 + 3j
>>> wrightomega(z)
(0.0966015889280649+1.4937828458191993j)
>>> lambertw(np.exp(z))
(0.09660158892806493+1.4937828458191993j)

>>> z = 0.5 + 4j
>>> wrightomega(z)
(-0.3362123489037213+2.282986001579032j)
>>> lambertw(np.exp(z), k=1)
(-0.33621234890372115+2.282986001579032j)  yn(n, x, out=None)

Bessel function of the second kind of integer order and real argument.

Parameters
----------
n : array_like
    Order (integer).
x : array_like
    Argument (float).
out : ndarray, optional
    Optional output array for the function results

Returns
-------
Y : scalar or ndarray
    Value of the Bessel function, :math:`Y_n(x)`.

See Also
--------
yv : For real order and real or complex argument.
y0: faster implementation of this function for order 0
y1: faster implementation of this function for order 1

Notes
-----
Wrapper for the Cephes [1]_ routine `yn`.

The function is evaluated by forward recurrence on `n`, starting with
values computed by the Cephes routines `y0` and `y1`. If ``n = 0`` or 1,
the routine for `y0` or `y1` is called directly.

References
----------
.. [1] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/

Examples
--------
Evaluate the function of order 0 at one point.

>>> from scipy.special import yn
>>> yn(0, 1.)
0.08825696421567697

Evaluate the function at one point for different orders.

>>> yn(0, 1.), yn(1, 1.), yn(2, 1.)
(0.08825696421567697, -0.7812128213002888, -1.6506826068162546)

The evaluation for different orders can be carried out in one call by
providing a list or NumPy array as argument for the `v` parameter:

>>> yn([0, 1, 2], 1.)
array([ 0.08825696, -0.78121282, -1.65068261])

Evaluate the function at several points for order 0 by providing an
array for `z`.

>>> import numpy as np
>>> points = np.array([0.5, 3., 8.])
>>> yn(0, points)
array([-0.44451873,  0.37685001,  0.22352149])

If `z` is an array, the order parameter `v` must be broadcastable to
the correct shape if different orders shall be computed in one call.
To calculate the orders 0 and 1 for a 1D array:

>>> orders = np.array([[0], [1]])
>>> orders.shape
(2, 1)

>>> yn(orders, points)
array([[-0.44451873,  0.37685001,  0.22352149],
       [-1.47147239,  0.32467442, -0.15806046]])

Plot the functions of order 0 to 3 from 0 to 10.

>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots()
>>> x = np.linspace(0., 10., 1000)
>>> for i in range(4):
...     ax.plot(x, yn(i, x), label=f'$Y_{i!r}$')
>>> ax.set_ylim(-3, 1)
>>> ax.legend()
>>> plt.show()  too many values to unpack (expected %zd)        need more than %zd value%.1s to unpack  argument after ** must be a mapping, not NoneType       scipy.special._ufuncs.errstate.__enter__        scipy.special._ufuncs.errstate.__exit__ 'NoneType' object has no attribute '%.30s'      dictionary changed size during iteration        'NoneType' object is not iterable       _cython_3_2_4.cython_function_or_method _cython_3_2_4._common_types_metatype    iteration failed to converge: %g + %gj  Input parameter p is out of range       Input parameter a is out of range       Input parameter x is out of range       Indeterminate result for (x, p) == (0, 0).      Computational Error, (%.17g, %.17g, %.17g)      floating point division by zero                 `p0JJJtJtJDJDJDJDJDJJ(L8LKKKKKKKKHLMM\M<M<MMMMMMMN ONNNpNpNpNpNpNOTPdP$PPPOOOOOtPQQQhQhQ8Q8Q8Q8Q8QQ<SLSSRRRRRRR\STTTpTpT@T@T@T@T@TTDVTVVUUUUUUUdVWWWxWxWHWHWHWHWHWWLY\YYXXXXXXXlYZ [ZZZpZpZpZpZpZ[    xZ͏$u_,ˎEdF.3mMO X@
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                                             	   
      	                                                                     	   	                                                   H  	            4     *   fffee        Set how special-function errors are handled.

    Parameters
    ----------
    all : {'ignore', 'warn' 'raise'}, optional
        Set treatment for all type of special-function errors at
        once. The options are:

        - 'ignore' Take no action when the error occurs
        - 'warn' Print a `SpecialFunctionWarning` when the error
          occurs (via the Python `warnings` module)
        - 'raise' Raise a `SpecialFunctionError` when the error
          occurs.

        The default is to not change the current behavior. If
        behaviors for additional categories of special-function errors
        are specified, then ``all`` is applied first, followed by the
        additional categories.
    singular : {'ignore', 'warn', 'raise'}, optional
        Treatment for singularities.
    underflow : {'ignore', 'warn', 'raise'}, optional
        Treatment for underflow.
    overflow : {'ignore', 'warn', 'raise'}, optional
        Treatment for overflow.
    slow : {'ignore', 'warn', 'raise'}, optional
        Treatment for slow convergence.
    loss : {'ignore', 'warn', 'raise'}, optional
        Treatment for loss of accuracy.
    no_result : {'ignore', 'warn', 'raise'}, optional
        Treatment for failing to find a result.
    domain : {'ignore', 'warn', 'raise'}, optional
        Treatment for an invalid argument to a function.
    arg : {'ignore', 'warn', 'raise'}, optional
        Treatment for an invalid parameter to a function.
    other : {'ignore', 'warn', 'raise'}, optional
        Treatment for an unknown error.

    Returns
    -------
    olderr : dict
        Dictionary containing the old settings.

    See Also
    --------
    geterr : get the current way of handling special-function errors
    errstate : context manager for special-function error handling
    numpy.seterr : similar numpy function for floating-point errors

    Examples
    --------
    >>> import scipy.special as sc
    >>> from pytest import raises
    >>> sc.gammaln(0)
    inf
    >>> olderr = sc.seterr(singular='raise')
    >>> with raises(sc.SpecialFunctionError):
    ...     sc.gammaln(0)
    ...
    >>> _ = sc.seterr(**olderr)

    We can also raise for every category except one.

    >>> olderr = sc.seterr(all='raise', singular='ignore')
    >>> sc.gammaln(0)
    inf
    >>> with raises(sc.SpecialFunctionError):
    ...     sc.spence(-1)
    ...
    >>> _ = sc.seterr(**olderr)

              Get the current way of handling special-function errors.

    Returns
    -------
    err : dict
        A dictionary with keys "singular", "underflow", "overflow",
        "slow", "loss", "no_result", "domain", "arg", and "other",
        whose values are from the strings "ignore", "warn", and
        "raise". The keys represent possible special-function errors,
        and the values define how these errors are handled.

    See Also
    --------
    seterr : set how special-function errors are handled
    errstate : context manager for special-function error handling
    numpy.geterr : similar numpy function for floating-point errors

    Notes
    -----
    For complete documentation of the types of special-function errors
    and treatment options, see `seterr`.

    Examples
    --------
    By default all errors are ignored.

    >>> import scipy.special as sc
    >>> for key, value in sorted(sc.geterr().items()):
    ...     print(f'{key}: {value}')
    ...
    arg: ignore
    domain: ignore
    loss: ignore
    memory: raise
    no_result: ignore
    other: ignore
    overflow: ignore
    singular: ignore
    slow: ignore
    underflow: ignore

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W=avOF={Skj/V='eNs*$O!>៤7Faďf|n>ƥRR/>qMX)?fFig#?,@                        ឌϥqX<&rͨA.	<Avt/[xk<6쐦༘}J<o^ϔN6=p!wT%/t=CQ ?ړǼ_Gh=5ҕսl=+)B?iB>TTioY>Tpt?A>B BY?O-iN@                              ?¿rqGk~XX¿@9SsMԿ:(,a(5F[t/!T	 ~z7o              ??98c?Hxi?d?_cJ6?Z>
@Hn-@*S@Ҁ9}@v1@        RmUa<P[T<w"SΊ 3wlXY<Ѣ_ַ<*ċ-1-vv=(&<(="m.HUsE\jSiC={E<e=exX=LPܴ#T4(5՚y0FSA\CT.ېsIHоJLS[?                        @<*I<vWxc<s~Ӽ)=;b,UyGxV=f_sT1Ω=Qҽl?4=g(6 P9%D>ø$>gGD>*cyůN>ϻ޸B	?3%}ƶ]@?<bXISq?jyI#Q?|S<6F?.iєƿJrc*?                        T`0fFV!<A`<ҫ`8箸}<攐*<be~2hϙ]'E_V=sk[=&GCi=fC{~5%t9QO $=uo >["d,->mրVX>na>+A>Rx?I墌k?	b?                        4!\T}b3<r넱^<"P
'&&KF5=bLa$ӛ/=jz<t̾=V4T&>0K5dMv;p>"c쑾$>'doҾY(X?>ZY&+|t(?RBuZ?I ^qa?!N-Ί>?-4pKw?Wӿ*5N?                UUUUUU?llfJ?88C#+K?}<ٰj_AAz?SˆB8?:gG,2D*@%%cN4"@Jᦉ %AWBm3dҶAoFE%@y7TBz{uoBSŮR                                9B.? *?,|l	@yD<d&@:'Q@0-!@5%@!)@Mu5.@t:?1@C3@2;Z6@B*09@F?6;@>@:5/?@@R2B@96SC@wz*E@r4dF@OO<H@EjI@NrdK@e"v M@g|qN@O~#P@@3P@1rSsQ@Y R@@ZS@ cT@J:c|CU@HG,%V@XW@XgyW@=$(X@WRY@nZ@+p\[@0\@>fq]@Ob^@+NT_@ݭC#`@~{`@kbba@YSȐa@nb@1Ib@5cac@c@ͦ3
d@\>d@nz
e@s9Je@FGGʪf@yyuf@ĲC g@Y&g@oFh@·h@aQL i@ai@	F~x*j@&Pj@7k@!+k@VFl@ l@tVm@pZNm@k9ihn@HQOUn@a,~|o@b4nŉp@+e	Ip@cp@)Vp@*q@6Gaq@q@>m#FJq@FK.5r@b)C|r@Wrr@V]
s@rRs@GIqs@>6qs@jB*t@A=rt@fIw|t@d'-u@X+{
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?ZH?zv`?Ŕ(ƅ>ޓ\>O>/!&>7>@>I]>.>^p>2I!H?[oL?=<fD?!@2?#>G(c53'6'(7W/)_ 6=HG3b_z1M-.9о(=R$wN9 )q>i_;\I^=}讶X?⾨GR>o8>QN'kh>nu>!r>PUe>Ҧ>j ~ ?2c]\cAmM^7H-V/?IvO?B?V?7RX?-eW?WU?V;%A{R??YcM?\%F?9L??/}	Q4?ͤTM%?H?Ki7z+^!G(!ۃ.'.61@6=|253}%~3eLho3+3 ꡗ2t1[p'1|j(z?Μ? 4?I3g?%d(.0a*}wvywn=wЀ/@^lc|z
]qtfPl.m`MH*t2?,6"+R?nT\?t˻a?	-d?yzge?2Ze?(e?~[IPe?p.d?lb?Ka?Vz?`?R]?\U)Z?"9HW?                ߼xV4r%B6Nfj2eH%?F7`*0?_l[n1?|ˮ(1?w
M0?3Ҁ.?,嵙[,?VO*?j(?R޾&?L7W%?H{b#?_?ڃj"?B!?DD5 ?eVӃ?Qgp?	o4?MJ?>Zo?<u7?%?F.? ?LF7?6d?Y<?)yF?5fp.?S|y|_- #;DW0U$5>#@l!Ƈcgb˔g`b"bpX4Ip2_dbv
ӌ~.J	!RC / p{QdJ	U3_es`an_u{2"~nqkm쾬_W*,a|
49Pհ67$w$U>}!?De%?ϻO&?Q$?@!?\W?Nu?Hv
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^t_?ߵ3*7V?5rԅGϺ;n$elZdll'NgQg^x%M'w",E>qG?$T?#pZ?S>^?5ښc_?(9_? %]?:d[?>iY?	V?bh"S?JP?Ւ&L?lvG?ZgB?'Q	<?FG5?¿#s,?e ?(_E	?      ?ʿ      ?98c?ٿ      ?Hxirq?̄     ?d@x5?i&    !@ffff     ?_cJ6<cVʷ(U@r^VlzDE@;:y    ?Z>j@BM  09@؂܅Fk@۶mc}:   Q?Hn}@_fFX@cq=HÒ@m;[   Ť?*@I3AkASp@\USŻ@$~  K@Ҁ9Z4AF#LA =wEgEZ3A˟=~X@#v4 dja8@v1IA11<r)KA"2AL>IESSXiA#e@E"RiA} [@P-X/gA=kbx&Az'E40E~AchFxBVwjA7Ww)\AA~	VtWN:@$XHA^@u.UgBKQv  	I8#B3'V=B	>sE8>.<Apaժ58ږpA $rW.@W$u:B:WygB%'.Zo:,\WmBWb£lPBIu4WrlBT)%7pA)8,MٰYp@                              ?¿rqGk~XX¿@9SsMԿ:(,a(5F[t/!T	 ~z7o`&>WFҲtrl<                      ??98c?Hxi?d?_cJ6?Z>
@Hn-@*S@Ҁ9}@v1@P-@$XHAW;A30``p                          ?ox?-jCp^? #Q?@񚥿1>H(?`R}?I,SNO6,ڌ ?G<_P>lmf~D:>F{5>KLKv=EϠ=r}:BnHa=>017QxD\8<ؗҜ<                fY?ӸS?\?gH>%?;ܩ?.vF?\v?SQO?h_	?A]"j?"?(?\y-?
C2Q?K/n+f?[m?saNh?Z y_W?Low?(s)?C?ș?Kݗ"V?AӔ?Rf B?=LH?!?[LГ?D~?'ΧMs?c`?                .2?x P?>ʑ?|"?,?a8??lq1?#L?+sV?ZU?N?)a?>?R0?VΓW?/x?i??x.?F5r<?æ9?Q?9$?
o4??6jHq?-o?PF?˳?Vd?W?W?#?                UUUUUU?llfJ?88C$+K?<ٰj_AAz?SˆB8?5gG;D  '  p[`  h(  h*  rj|*  k*  3l+  md.  n.  Lo.  -p/  xq/  q/  Ss,0  sD<  Du<  x<  a{=  {>  yR  y|d  &ye  /y  ?y  Oy  _yx  oy`  y  yȸ  zȺ  P|  |  P}  }  @~  P~  `~   p~  ~(  ~@  P      0h      0@      p   `    p   8        X    p  00   Ѝx   p    !  P!  p!  !  ,"  t"  "  P#   L#   #   #  ,$   t$  $   %  L%  0%  `%  p%  %  P&  @$&  px&  &  &  &  `&  &   &  @'  ('  0@'  @X'   p'  p'  @(  (  (   (  )  ,)  H)  0\)  )  0)  )  )   <+  P+  +  +  +  P+   ,  4,  H,   l,  ,  ,  ,  p-  `-  -  -  0.  $.  D.  @/  d/  `0  @0  `0  p0  0  (1  @1  T1  @h1  1   1  1  1   1  2  @ 2  82  T2  l2  P2  2  2  2  `	2  P
3  @ 3  PL3  03  (4  X4  4  @4  4  p$5   `5  5    6  !D6  "p6  `(6  /6  p06   17  187   2h7  27   37  37   4(8  4X8   58  58  79  @9D9  =9   @0:  Fl:  0H:  I:  PK:  L:  pN:   P;  Q0;  `SL;  Uh;  V;  pX;  @Z;  d;  g=  Pj`=  l=  mP   rP  xdQ  R  `R  pR  R  S  @S  hS   S  pS  T  $T  PT  @dT  pxT  T   T   V  W  @[  ]  P `a  ta  a  a  ,b  @b  `	\b  	hd  ,d  -d  .d  /d  [e  \0e  ]De  P^\e  we  xe  {e  @f  8f  Јg  0g  dg  g  g  g   @h   i    j  k  l  $l  pl   l  l  @l   0m  \m  m  `m   m  n  <n  @`n  n  pn  o  Po  Po  o  o  o  @o  p  Lp  dp  0|p  p  p  p  p  p  Pq  p
q  `@r  r  !r  !r  0"s   $(s   (\s  )s  *s  ,s   5s  08t   :8t  P:Pt   >|t  0>t  p?t  ?t  @t   At  pAu  A(u  A@u   C`u  Gu  Pu  ^Xv  bv  cv  `fv  @gv  iw  j4w  lTw  mhw  Prw  rw  sw  tw  z<x  |\x  P}px  x  x  x  x   y   Py  @|y  Гy  `y   z  <z  Ppz  z  Ьz  ${  0x{  з{  0{  @|  d|  |  |  }  0}   T}  `l}  }  }  }  }   ~  P(~  <~  P~  Ph~  ~  ~   ~  0~  `    ,  `D  h  `  @      P<  h          0H  @  P    ,  p  0Ԃ  /,  /4   0H  00  @0  05  @5(  p6  6  07  P:   =  =$  =<  P>T  >l  ?  B  E؇   J  R  @S؈  S  PT  bp  0d  f  i  k  p$  qD  pq\  qt  0r  r  sċ  00    0Ќ  p  ,  \     ܎  p        А  P  h        `  <      P  %  0*  `/   5,  @:X  D  M  PV`  X   r  0z(   |D    ܙ  L  Жd  ̛    p(  0X      P    @  `̝    h  `X  p        Цğ  ؟  4   `  0ܠ  (     0  <  p  0  pt  У      `P  ܦ  p\  ܧ  D  pܨ  <  ĩ    `  p  8  L       0  0p  `       p0  t       0(  0    @    0<    pS  S  <T  U  \U  U  MU  P^ V  slV  {LW  W  07W  X  (Y  xY  Y  05@Z  9Z  @WZ  `m [  up[  P|[  \  4\  ЅP\   x\  \  \  В]  ]  0^  X^  ^  ^   ^  p^  _  P,_  P|_  P_  `  P``  `   "`   #a  )a   +a  /b  6pb   9b  0<b  p> c  @KTc   Uc  bd  iPf  qf   f  h   h  (i  0Li   pi  pi  Lj  @|j  j  0k  Phk  k  k  p  Ȁ   
\  \   @      0'   7`  <  pK  Rp  PXȅ  0Z  Pa@  s\  Px  zL    P`  `ԍ  б4  `    0  X       (  |   t  PT  P  0
  D  @     @"P  <  F8  Ix  K  `m|  P}   @     0     x  <  Ц    l  0Ԣ  `0  p  P  л8    `  `L  	  Х  B   P  X  ]  @f  Plx  r  vt  0,  0Ȫ  P0    @  p`      P  0    @  0	ܯ   ,  0$  )̱  5  P?l  K  c  qT    Ћ  ЎT     ط  Х      $  p    @  Щ  $  8  0L  d  0  P        @  T  Pp     Ļ  p  $  P8   h  `     Լ  @  \  P    P&  `/P  2  >  C  X  Y0  ZH  e  0nĿ  s  yD  `~      d  @  Ж  0  8  `    P  H  `\  Pp              @  `    $  8  L   `   t  @  `        Ю        (   <  0P  @d  Px  `  p            Я  ,  @  T   h  0|  @  P  `  p          0  аD  X  l             zR x  $      B    FJw ?;*3$"       D   bQ          X   c          l   cn             cz             `d	             \d	             Xd             Td             `d@    \ c D      ds    BBB E(A0A8FPQ8A0A(B BBBD   D  dx    BBB E(D0A8DPU8A0A(B BBBH     d    BEE B(A0A8D8A0A(B BBB   H     \e    BEE B(A0A8D8A0A(B BBB   D   $  e    BEB B(A0A8Gp8A0A(B BBBD   l  (f    BEB B(A0A8Gp8A0A(B BBBD     f    BBB B(A0C8G`i8A0A(B BBBD     f    BBE B(A0A8G`8A0A(B BBBD   D  `g    BBE B(A0A8G`8A0A(B BBBD     g    BBB B(A0C8G`8A0A(B BBBD     Ph    BBE B(A0A8G`8A0A(B BBBD     h    BBE E(A0A8D`8A0A(B BBBD   d  0i    BBB B(A0C8G`k8A0A(B BBBD     xi    BBE B(A0A8GPj8A0A(B BBBD     i    BBE E(A0A8DPr8A0A(B BBBD   <  jf    BEB B(A0A8FPD8A0A(B BBBD     @j    BEB B(A0A8G`8A0A(B BBBD     j    BEB B(A0A8G`8A0A(B BBBD     k    BBE B(A0A8G`8A0A(B BBBD   \  l    BBE E(A0A8D`8A0A(B BBBD     l    BBE E(A0A8D`8A0A(B BBBD     l    BBE E(A0A8DPo8A0A(B BBBD   4  Pm    BBE E(A0A8DPu8A0A(B BBBD   |  m    BBB B(A0C8G`k8A0A(B BBBD     m    BBE B(A0A8G`8A0A(B BBBH     Xn    BBB B(A0C8G8A0A(B BBB   D   X  n    BBB B(A0C8GP]8A0A(B BBBD     o    BBB B(A0C8GP_8A0A(B BBBD     Lo    BBB B(A0C8GP_8A0A(B BBBD   0	  o    BBE B(A0A8GPi8A0A(B BBBD   x	  o    BBB B(A0C8G`8A0A(B BBBD   	  Dp    BBB B(A0C8G`8A0A(B BBBH   
  p    BEB B(A0C8G8A0A(B BBB   H   T
  `q   BEE B(A0A8G8A0A(B BBB   D   
  4rf    BEB B(A0A8FPD8A0A(B BBBD   
  \rn    BBB E(A0A8FPL8A0A(B BBBD   0  r    BBB B(A0C8G`m8A0A(B BBBD   x  r    BBB B(A0C8G`m8A0A(B BBBD     s    BEB E(A0A8DPx8D0A(B BBBH     lsh   BBB B(A0A8GH8A0A(B BBB     T  t(    Dc    l  t            tE    Qc
DL      t   G
E        Dw    D@
cf  P     x-   BAD H0
 EABF
 EABDL
 AAFD    4  y5          H  z=          \  Hz    H@   t  z    H@     {Z    D U     {1            {9            (|B    Dy      `|    Dp     |   HP     }    D    ,  ~b    D]   D  ~,   BBB B(A0A8GIPIDIDDABDIIIAI`@
8D0A(B BBBG d        BBE B(A0C8DQ
8A0A(B BBBBz
8A0A(B BBBD      @  @X    AV    X  <    Dt
HH
H      |          @     $   AGG0g
GAJd
DAGZ
CAJ                   /    Q]                     ̯|    Ay
Fg
I  (   <  (y    AAD T
DAA     h  |A    dN       j   A
CH
H      )    Ac   t     >   BEE I(K0J8D`hIpJxOEDAADAABL`m8D0A(B BBBT   8  ?H   BEB E(K0D8DPXI`PXAPo8A0A(B BBB   8     @y    BEE G(A0[(C BBB  (     AR   BAD GAB      ܱ       4     x    BDD 
GBGAAB     D  0    f   \  i    | a $   t  P9   j0CC0P
Hh       h    `l
LI   0     ص   `@E
K
HT
TH
Hh        t             I   D 
H~
JL   (      D0r
Jf  4   H  <   aD0
AFPh0Xe0,     ^   AD K
AGO
AH   x        BBB B(D0D8Gc
8G0A(B BBBFK
8D0A(B BBBHQ
8F0A(B BBBH   ,  h}    DE
G (   H      ADD O
AAF (   t  P    ADD O
AAF      h    Do
Eo        $h    Do
Eo        t    ~ hJ W        4    X i
OZ  H      ?@   BEE E(D0D8A@8D0A(B BBB      l  @    D`D     |@    BHE D(D08I@T8A0W(A BBB  P     (   BAD G0
 DABJY
 AABC[
 AABA          d   vpPpf
J   8   D  @K   BHF D(GP)(A ABB        A@    A~   H     A   BBB E(D0A8DPy8D0A(B BBB   0     CN    AGE s
DAEAAA 0     8    BFD0g
ABJHFB   P     LP   h  	       0   |      BFD0g
ABJHFB0         BFD0g
ABJHFB     [    L0N                 D          $  b    D ]   <  (b    P Q   T            h  \    AY0`E         o       
   D 
Of
J        }    Th     }    Th        DP        t    P   (            <      Pu   T  @    Py    l      Dr
JH
H           L`        h    P      @    P (        D@3
IL
DQ
Gp        BKF A(G0E
(I DBBG
(D ABBCQ
(I DBBN|(I ABB  d   |  hN   BBB B(A0A8D
8A0A(B BBBHT
8A0A(B BBBB  ,     P^   AD K
AGO
AH   <        pAD@AADX@H`@    T     AiP
AO(   x  |y    AAD T
DAA  8         HEE L0` KAB\0 8     D    HEE L0` KAB\0 8         HEE L0` KAB\0 l   X  ,*   BBB A(D0D@
0A(A BBBJD
0D(A BBBIX
0A(A BBBH   4        AL0
AJx
AGD
EG   (      DL   AD 
AGg
AH4   ,  hr   A\PN
ID|
AK
EE,   d  s   ALD
EJ
AY           @ c     x    w j ,         KAL0PHAW0,     @    KAL0PHAW0,   $      KAL0PHAW0,   T      KAL0PHAW0,     0    KAL0PHAW0,         KAL0PHAW0,         KAL0PHAW0,          KAL0PHAW0,   D  p    KAL0PHAW0L   t  E   REE J0
 EABF EABEP0  8     f   BBA A(D0T
(D ABBI  d       ;   BBB B(D0D8GP
8A0A(B BBBA
8A0A(B BBBL      h   {   BED D(DPcXE`jXAP{
(C DBBDs
(D ABBDgXO`FhDpOPm
XE`OL
(D ABBK8         oEIX
KBK   (!  Lh   T`
J    D!     d`
J    `!     \`
J    |!     d`
J    !     \`
J    !  p   d`
J    !     dp
J    !  x   dp
J    "     tp
B    $"     tp
J    @"  4   tp
J     \"     vpPpf
J   ,   "  t	   AAD[
KAC   L   "  (   BBA D(D@
(D ABBK
(G ABBD  P    #  U7   KBA A(E0p
(G ABBEA(A ABBA8   T#  8   BDA A(Dp(A ABB   8   #  /;V   BDA A(DpC(A ABB   L   #  *   BBA A(D@
(A ABBGD
(D ABBK   L   $  ,   BBA A(D@A
(D ABBD
(D ABBJ     l$  8/    As
De
C  4   $  =Q    BGD t
ABEDAB   p  $  =_   BBB B(A0A8GbHHK!KFFFFFFFFFFFFFFFFFFFFFFFFFFFFAFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFAHFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF F F F F F F F F F F F F F F F F!F!F!F!F!F!F!F!F!F!F!F!F!F!F!F!F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F"F#F#F#oORTQORTQORTQORTQORTQORTQORTQORTQORTQEFP[fMig[RFbQvcM[[ORTQORTQORTQORTQORTQORTQFHI\ORTQORTQTJMV\fMig\fMig\fMig\ORTQORTQORTQORTQORTQcMig\ORTQORTQORT\ORTQORTQORTQORTQORTQORTQORTQORTQORTQORTQORTQORTQORTQORTQORTQORTQORTQORTQORTQORTQORTQORTQORTQOLFPSORTQORTQORTQHFWcP}F^cP}F^cORTQOchW\RbbP\KSFPXy]R[cAF^fF^_F^_LFW\y]R[\ORTQORTQORTQORTQwcR[ey]R[eORTQORTQjGSJcfMigcmGogcORTQORTQORTQORTQORTQXOjQXOjQXOX`XOX`XOjQvcR[[fMig[ORTQ'HFFQuFTQuFTQuFTQ8HzIJjFpmKFTP]RwMP]DH~IJuFTQuFTQuFTQnF[QnFOQgFI`PF^\ORTQORTQORTQv]R[\fMig\fMig\fMig\fMig\fMig\zkR[dQFiXnF[QwcR[\y]R[dy]R[dy]R[dPF^\mGog\fMig\fMig\vF^iPoF^iPoF^izcR[\y]R[\ORTQORTQy]R[d|]R[d|]R[dORTQv]R[\y]R[\ORTQiGog[y]R[[zcR[\y]R[\mGSJcfMigcfMigcPoT^jORTQcMigcORTQv]R[cy]R[cfMig_\J@Q_Mq`oPoF^jPoF^jPFesORTUy]R[cORTQcMigcXJkUMF^\o&8A0A(B BBB  `   <7     BBB E(D0D8DP
8A0A(B BBBGn
8A0A(B BBBH |   7  4!u   BIB B(A0A8G`NhDpjhA`
8D0A(B BBBHfhPpCxBO`m
hEpL8hEpNhA`    8  4'   BIB A(A0_
0D(A BBBDPLCBOffHAa
0D(A BBBG1
0D(A BBBD$ENA  L   8  h.:   BBB B(A0A8DU
8D0A(B BBBH   \   9  XD,   BBB B(A0A8Gy
8D0A(B BBBI\OA    |9  p          9  5&          9  p,   dpy[p  8   9  q   KAIEAIp       $   9  t8    AHF fAA 4   $:  t   BDA G
 AABG      \:  Ț    AS0|E   |:  8xp         :  y    D@z
BQ     :      HP   :  y    DP   :  z    PP   :            ;  H{           ;  {#      L   4;  |y
   BED D(Gp
(A ABBF
(A ABBA    ;      h@
NZ
F    ;      V w
Ch L   ;  l   BGE E(G0D8G
8A0A(B BBBA       <  ,   V@^
TT@ L   <<  WK   BBE E(A0C8G	
8D0A(B BBBG   L   <  F   BBB E(A0A8J

8A0A(B BBBH   H   <  (   BFB B(A0D8I
8D0A(B BBBIL   (=  d   BBE G(D0C8I
8D0A(B BBBH   H   x=  <   BEB B(A0D8G`
8I0A(B BBBG @   =  x   BEB D(A0G`
0I(A BBBK L   >  <$=   BLI E(A0I8J#
8A0A(B BBBC   L   X>  a}   BKB B(A0A8G#
8A0A(B BBBA      >  <|d   BII B(A0A8GvFnB
8A0A(B BBBA0aKA A1A     \?  C,   BJB E(D0D8I
8D0A(B BBBAvBaKAKAL   ?  [&   BDB B(A0A8J
8A0A(B BBBD   t   4@   f,   BKB E(A0D8Gf^AA

8A0A(B BBBK   L   @  -   BBE E(A0A8I
8D0A(B BBBD   D   @     BBE A(A0D
0D(A BBBF   H   DA  PY   BBB E(D0F8L
8A0A(B BBBFH   A  d   BDB B(A0D8Gl
8J0A(B BBBK L   A  8   BLB B(I0C8Gj
8A0A(B BBBG   H   ,B  x^   BFJ B(A0A8G
8D0A(B BBBK8   xB      BKA I(Gp
(A ABBD    B  @       $   B  $   _H0#EAH0   B  d&)   lP  $   C  x)&   LP!
K
Ta  (   4C  ,   DP6
F
Ga
G  @   `C  /   BKI A(C0GP
0A(A BBBA(   C  3   BMD@
ABAp   C  55   BFB A(A0GX
0A(A BBBE
0A(A BBBC
0E(A BBBA (   DD  0   L`
Na
Ga
GZP   pD  TE   AEF`
AAAz
AAL
AAK
EAJ L   D   M   BFE B(A0A8G
8A0A(F FFBK   L   E  `R   BPB B(A0A8U
8A0A(B BFBA      dE  Z         xE  ^~   Gp
`    E  @bE   CQ@A      E  lc         E  xp   a w   L   E  r   BOB B(A0A8G!
8E0A(B BBBA   L   8F  ̄
   KGO G(F0I8J
8E0A(B BBBE   H   F  |n   BPB B(A0E8IB
8A0A(B BBBGD   F  J   LEO M(I0H8
0E(B BBBA  d   G     BMF B(D0A8GU
8A0A(B BBBA
8D0A(B BBBE  (   G   J   AH@
ASa
EJ   G  $    LQP   G     [OJ JpPp^
 AABF
 AABK   H           0H  t         DH  @9         XH  l      $   lH  (?   D
JY
Ga
O (   H  @   D X
Dg
I`
H $   H  u   Ag<
AE      H  |          H  H    D 
K    I  !       4   ,I     BEA GQ
 AABA   $   dI  p   D0O
Ee
Sq ,   I  X6   H U
Ca
GH
H+
MP   I  h   KFG
JBF
ABE}
ABX
ABDH   J  	   nJA A(D (E ABBHht   \J  X   jFA A(DC(A ABBAxHM
(A ABBE  L   J  /   BJB E(D0A8J

8A0A(B BBBJ      $K   "         8K  	          LK  6   r Tb I    lK  !   r |
J~b x    K      ^ z
Hz      K  ,         K  	          K           K             L  c    | b L   L     AOs
ADZ
AM
IJP
E[
AK    hL  <           |L  Hh   PPx
Hf
J   ,   L     DP]
Gz
F
Sh
H     L  $B   Dpb
JD
D     L  P">    Di @   M  x   BBA Dl
 ABBF
 EBJE4   PM  k   BAD J
 AABF   D   M  L   BBB A(D0J
0A(A BBBD      M  !   D 
V 0   M  "   BJA Dp
 ABBI(    N  %   AID`
AAMD   LN  ';   BFB A(A0G
0I(A BBBA       N   )*   AD@
EI@   N  *   AIGpA
EAHI
EAAoEA <   N  -   AO@
ADQ
AN
IEsE   h   <O  h+   	FF A(Dh
(A ABBE
(A ABBB   8   O  ;
   BAGP
ABC@
ABM       O  E>   AJ-A      P  K   uH q
EE      ,P  OL   AG@K
AD 0   PP  R~   HED GpI
 AABK4   P  P/   AFp
AAT
JB
AB H   P  2   BBB B(A0D8Ie
8F0A(B BBBF ,   Q  SD   AI[
FEm
AJ  L   8Q  W2   RKF B(D0A8G
8F0A(B BBBC   H   Q  b   BEB B(A0A8Gl
8A0A(B BBBFL   Q  w   BBA A(DW
(E ABBEZAIA  L   $R     BJA A(Dp
(E ABBEj
(A ABBE    tR          R  Ԓ   0      R  5w   H0P
A]    R  x6       H   R  T7   BOK D(D0A8G}
8J0A(B BBBD     ,S  O    D D
H\
D   D   PS  Om
   BOJ A(A0G
0E(A BBBE      S  Y   d 
T 0   S  <[   BBA Dl
 IBBF (   S  b   L0
D
C
D   0   T  e   BBA D
 JGBA   LT  Xna    t Y <   dT  n   BOE A(D
(I ABBG       T  v    Pz
Fa
Ga ,   T  v   AIDa
AAG       T  \z    Pz
Fa
Ga $   U  zG    AEG@wAA D   DU   {   zAE DP
 EABE
 AAFG   H   U  ~v   BFE E(A0D8Gp
8A0A(B BBBC 0   U  ́   L0
GH
H)
OA
O   @   V  f   BAA DP|
 AABEI
 FABA      PV  (    DX    hV  ̇*    DY    V      D R    V  e    K i
L]      V  <g    L l
H^   ,   V  _    DP L0LF
FD L0PD    W      | C    W  4    t D    8W  s    D0j
JJ@TPZ    \W      D I    tW       LQ   W  Ȋ          W         T   W  W   BED G@e
 CABC~
 AABFq
 AABC   P   X  [   BID G`
 AABDU
 CABE
 AABF     `X  Ę   BBB A(D0G~
0C(A BBBFI
0A(A BBBG
0A(A BBBJ
0A(A BBBHl
0A(A BBBDd   X     BJD Gj
 CABI
 AABH
 AABGM
 AABG   8   dY  Ц   AJP
AK
AN
AG      Y  C          Y  3          Y     0  0   Y     D0
GH
H)
WE
K   $   Z     _H0#EAH0   @Z  D
         TZ  @      8   hZ  ̸   jEDp
ABJ`Hp   $   Z  0   D0O
Ee
Sq $   Z     D
JY
G
F   Z  (    D c (   [     D T
Hg
I\
D    8[  |(    D c    P[  6   r Tb I   p[  <    D w    [           [  (    D c    [   c    | b    [  XB    Dm    [  (    D c    [  -   \ A
SI0   \     L0
GH
H)
OA
O   H   P\  t	   nJA A(D (E ABBHht   \     jFA A(DC(A ABBAxHM
(A ABBE  4   ]   H   BED0h
EBF{
ABJ     L]  8       4   `]     AL0f
EHa
AN|
AK     ]  |    LQ    ]  D|   D0I
C
N    ]  0   n j     ]     \ n U    ^  $       8   $^     BJE A(DPA
(E ABBG    `^  J    l Y    x^      L@
E    ^  -   H UH   ^     BNJ J(F0A8N
8I0E(B BBBB   ^  <   P 
J    _  ;         ,_     D0
W   H_  |         \_  )   lP  $   x_  
&   LP!
K
Ta  (   _     L0
Ia
G
Na<   _     AL0
APa
AF
EIaA   (   `  ?   L@
Na
Ga
G(   8`     L`
Na
Ga
GZ(   d`      DP.
F
Ia
G  (   `     DP6
F
Ga
G  8   `      AJP
AK
AN
AG   0   `  (<   `NN@dEAJP@ 0   ,a  ),   YNN@hAAAP@ P   `a  *J   [PJ G(DX^
(E IBBH   (   a  1   {NN@
AAH P   a  2J   [PJ G(DX^
(E IBBH   T   4b  9   OADP]
AAEv
AAHa
AAE_AAGAP  (   b  ;Y   AID`M
IAK @   b  ,?G   BEA DPY
 AABGH
 AABT     b  8D   v0P0
d       c  F   r0P0
f  <   Dc  G4	   LIA Dp EABGPp  @   c  P$	   LEA DpG
 EABKPp    c  Y   z@X@
I      c  X\b   D g
E
N     d  ]Z    D M$   (d  ]]   D W
Ej
N      Pd  $_   HP
F    ld  (a   uH q
EE      d  d   N@L
V0P@    d  g)    J0S    d  h)    J0T    d   h)          d  <h)          e  Xh    U0\    $e  hF   ADP
EG    He  kb   D g
E
N      le  Xl   uH q
EE     e  $p)    J0S    e  <p)    J0T    e  Tp)          e  pp)          e  p    W0Z     f  q   H0
EP
I  @   $f  r   ALP:
AP
ID
AYp
AI  $   hf  u    P v
Ja
GH
A    f  dv    Q(   f  v   AQ0
ADE     f  `y   P0
G
C (   f  |   H 
AM
K
E   $   $g  }   H 
Nh
H
O   Lg  8!           `g  Ă   H0
EP
I  $   g  e   qD0*
AH      g     Q   8   g  R   KD0r
AF$
EGtEX0   h         @   h     BIE A(D0HP
0E(A BBBG    \h         8   ph  R   KD0r
AF$
EGtGV08   h  R   KD0r
AF$
EGtEX0,   h  ܍`   yH`v
AHXH`  4   i  ,   iG0
ADH0E  <   Pi  ԏ   BBA A(Jy
(A ABBA   T   i  T   BAA G
 AAFJo
 EABI
 AABJ    i         D   i  ،:	   AIDpl
EAH
AAI
AAE 0   Dj      DP
OA
G
H
C   4   xj  x   BMJ D 
 JAFE   <   j  4   BDA D(I
(E ABBE      j            k  +    \ N @   k  	   ALP
AC
AK
AC)
AV    `k         4   tk  P`   AL`
EG
ALY
AF$   k  x1   A^
AG   T   k      BEA Ds
 FABH
 AALAY
 FABA   @   ,l  8q   ALPI
AIl
AC
AE
AF   pl  t       $   l     D0l
HH
PH  4   l  8   AHph
AFL
EGR
AM    l  %   fa D   l     BEA G
 EABE^
 AAFB     Dm  `    `a    \m  (`    `a (   tm  p   V0q
I
II0   $   m  d   V u
EHP P
H   m  `    `a    m  Th    `a    m  `    `a    n  h    `a    (n  L%   fa $   @n  d   V u
EHP P
H(   hn     V0q
I
II0   (   n   :   PSyP3EP@  T   n     BAA D
 AABW
 AAFI
 AAFA   4   o     V0K
GHP0~
J
E  (   Po     R O
GHP :
E     |o  (F    da    o  `F    da    o      Tad   o  @   XNB B(A0A8Dz
8A0A(B BBBDP   (   ,p     R O
GHP :
E      Xp  Y   L @
D
E     |p  u   H D
D
E ,   p  $   H x
Ha
Gl
D
E 4   p     V0K
GHP0^
J
E  h   q  <   LIA D
 EABF
 AAFCx
 EABP P  h   tq     LOA Di
 EABG
 AAFDy
 KABI P     q  V    Hq
GQ       r  X    `a    r  X    `a    0r  TV    Hq
GQ      Pr      | ]   hr  ,    z Yh   r     LOA Di
 EABG
 AAFDy
 KABI P  h   r     LIA D
 EABF
 AAFCx
 EABP P  0   Xs  l   DP
OA
G
H
C   D   s  X:	   AIDpl
EAH
AAI
AAE D   s  P:	   AIDpl
EAH
AAI
AAE p   t     BBB D(D0Ij
0J(H BBBG
0A(A BBBB
0A(A BBBE  T   t  f	   KMDZ
AAH
EAH
AAEI  ,   t  |,   R0b
Dn
Ja
GhI0   $   u  |   D@
E
HT   @u  "f	   KMDZ
AAH
EAH
AAEI  T   u  +f	   KMDZ
AAH
EAH
AAEI  (   u  "   DP
Dg
Q
T@   v  *	   AH`
AF
AE
AF
AF     `v  3       $   tv  3u   qD0*
AH   L   v  3   BHB E(A0A8J 
8A0A(B BBBI   $   v  A   ADO
AS   L   w  @F   BFB B(A0A8D\
8J0A(B BBBG   $   dw  P8   L@w
Es
EH
H,   w  (:   D0
E`
Pe
KL
T   L   w  L]
   BFB B(A0A8G
8J0A(B BBBA      x  X;&    \I L   $x  p;	   BFB B(A0A8GK
8I0A(B BBBF   L   tx   E   BFB B(A0A8De
8I0A(B BBBG      x  U   G`
a   P   x  Z   [KF A(L
(I ABBHX   4   8y  ,cg	   BAA D
 IABD   4   py  $K   AD0N
ADi
EJL
EG    y  L    sM4   y  TMm	   BAA G
 IEBE   4   y  V   BFA G
 IEBE   0   0z  k&   BJF D` FAB   L   dz   ^   BGG B(A0A8G
8A0A(B BFFC   X   z  w   BPP F(A0GN
0A(A FBBN	
0E(A BBBV,   {  m   AEI
AAA   8   @{  q   ALPJ
ED
EH
Aa   @   |{  hu   ALP:
AP
ID
AYp
AI  <   {  D   BBA F(R
(I IBBI   D    |  x&   KPp\
IH
IJeAJPp
IE,   H|  |   KP`i
AKP`       x|  l+   AP`
II     |  x   APp
II $   |  4}    P v
Ja
GH
A (   |  ̞:   ALGPE
AAEd   }  g
   ZOB B(A0A8IXZ
8I0A(B BBBD L   |}     BBB B(A0A8D
8I0A(B BBBF   L   }  h   BBB B(A0A8D
8I0A(B BBBF   L   ~  b   BAA D`
 FABGd
 KABF# cABL   l~  h|   BBB B(A0A8G
8I0A(B BBBK   L   ~  !   BKE E(A0A8G
8F0A(B BBBC   L     1   BKE E(A0A8G
8F0A(B BBBC   <   \  H1   BGA A(Ga
(I EBBK   D     
   BBB A(A0D
0I(A BBBH            H0X
P D         EA I
 EABGXP  L   H  ,	   BBB B(A0A8G
8I0E(B BBBG   X     
   OBG A(E0D
0E(A BBBHd
0K(A BBBJ  <     `l   BBD A(D
(I ABBC   D   4     BEB A(A0Df
0I(E BBBG      |  (c!   zBB B(A0A8I
8A0A(B BBBD
8K0J(B BBBE
8F0J(G BBBE     l    D I       d    D I L   8     BJE B(D0A8G;
8A0A(B BBBD   ,         PP]XZ`VXIPT
Fa
Ga (         P`ghRpdhA`X
Je   ,     @    \PXXF`VXIPT
Ca
Ga (         \`ZhFpdhA`T
Ke   ,   @  T    AJPkXF`VXIP`
AD  ,   p      AJ`mhFpdhA``
AD  ,     d    \PXXF`VXIPT
Ca
Ga (   Ѓ      \`ZhFpdhA`T
Ke   L     x   BIE D(D0GplxFxIp
0A(A BBBG8   L     OG0{
AFa
AFAGH0  4        AH0
EYc
ADL
AK  8        OG0{
AFa
AFAGH0  $        L@w
Es
EH
H8   $  P   BFD D(DpW
(A ABBG X   `  T&
   OBG A(E0D
0E(A BBBKd
0K(A BBBJ  T     (	   BIA I
 AABHb
 AABB
 AABE             DV    ,  
          @      DS    X            l  
                   @      	   OG@O
AJa
AF
AFDEGH@    ؆     a(     (   Hq
Ga
GU
Ia      	   a`   4  p   BJB B(D0D8Gp/
8A0A(B BBBH_8A0A(B BBB H     L
    BED D(Gp
(A ABBFD(A ABB       
       L     |   BBB E(D0D8J
8A0A(B BBBG      H  
       @   \  (   OG@O
AJa
AF
AFDEGH@4     D
   AH@j
ADd
ACM
AB     ؈     J0}
IeS0,        AL@	
IAl
AI   ,   (  <w   N0
E`
He
CLT0   4   X     EPPC
AO
IIp
AO  ,     T	,   R0b
Dn
Ja
GhI0   (     $9   AH0j
ADd
AC@     (
   KG0E
AHq
EJLEGH0L
EG    0  l   AL@
IM4   T     KAGPD
AAGHP(     @   AD@q
AI
AI8     LY	   AIG
AAY
AAV D        BFE A(A0D
0A(A BBBG   ,   <  X"x-   NNd},
ABA   L   l  O   BBB B(A0A8G>	
8A0A(B BBBI   H     4   `0X
Ha
GL\0b
EJ
E
Ew
E
E8     ]'   AIG
AAL#
EAO D   D   d
   BFE A(A0D
0A(A BBBE   ,     nE.   NN_F-
ABI   L     ؜   BBB B(A0A8G:	
8A0A(B BBBA   D        d@T
Ha
G_@
E9
E 
E
E  @   T  0   BJE D(D0G^
0A(A BBBJ 8     z    BOI D(D0P(A BBB  @   ԍ  g   ALGPT
AAF
AADDAA 0     _    AHG J
AALtAA H   L  x'	   BJB B(A0D8J_
8A0A(B BBBH      1    EJ
IX D     <   ALG2
AAH
AADP
AAF 0      _    AHG J
AALtAA `   4     BJA D(G
(A ABBD
(A ABBBT
(A ABBF      1    EJ
IX <        BNG D(J
(A ABBA   4     l   ADG@d
AANE
AAIL   0  4{   BFE B(A0A8Gn
8D0A(B BBBA   0        BEA D@a
 AABG  0        BEA D@a
 AABG  p        BJB D(D0Gp
0A(A BBBB
0A(A BBBD@
0A(A BBBH     \             p          d     `   BMD B(H0E8Sp
8A0A(B BBBAX
8A0A(B BBBA   d        BIE E(A0C8D`
8C0A(B BBBAs
8A0A(B BBBA   L   T  PP   BJA D(G@
(J ABBES
(A ABBG L     P
#   BJD A(G@
(A ABBG]
(J ABBL        @            <       L     3!   BBB E(A0A8G
8D0A(B BBBA   <   l  '   AMJ0g
JAF|8^@K8A0nAA<     '   AHG0s
JAJt8^@K8A0nAA<      '   AMJ0g
JAF8I@X8A0sAA<   ,  !'   AHG0s
JAJw8I@X8A0sAAD   l  +   AEDp
EAA_
AAI$
AAP  T     1^   BFA Dr
 AABAw
 AABA
 AAFA   ,     7   AHPT
EF
AT     <  ;   D@>
F
[ L   `  dD
   BNB E(D0D8G
8A0A(B BBBD   H     d!    BED A(D@[
(D ABBEr(A ABB  L     N   BNB E(D0D8G
8A0A(B BBBC   H   L  !    BED A(D@[
(D ABBEr(A ABB  L     LY   BIB B(A0A8G
8C0A(B BBBG   H     pY   BLK H(E0E8J`
8A0A(B BBBK       zPLR x}=    P   $   sE    BBJ E(D0A8D
8D0A(B BBBA   @         BBB A(A0GP
0A(A BBBK@     8#o   BBB A(A0GP
0A(A BBBC(   0  d%   ADG 
AAD (   \  &   ADG 
AAD L     w~   BBE B(D0D8N

8C0A(B BBBA   L   ؘ  %
   BFE E(D0A8GD
8A0A(B BBBD   L   (  ܌   BBB E(A0A8N
8C0A(B BBBA   D   H  \'    BBB A(A0G`6
0A(A BBBC      #     `   \      *  r  BBB A(D0GP
0A(A BBBF
0A(A BBBE            !  P   D   8  |+    BFB A(A0G`*
0A(A BBBK      S     `   \     -.    BFB A(D0GP
0A(A BBBF
0A(A BBBE            e  P   L   X  lg   BJE B(A0A8G
8D0A(B BBBA   d     
   BFF E(D0C8Gp4
8A0A(B BBBA
8A0A(B BBBI  d     t7   BJB E(D0D8G
8A0A(B BBBD
8A0A(B BBBA 4   H  L  )  ACBEM.	
J h     D.     BBB A(D0G`
0A(A BBBFhWp]hA`e
0A(A BBBM              `   \     40c    BBB B(A0A8GpxW\xApY
8A0A(B BBBI      p     >  p H   ĝ     BEE E(A0H8G`
8A0A(B BBBEH     t   BHL E(D0D8Dp
8C0A(B BBBA4   ,  	    ACPf
F1.   `   d  @  a  BBE E(D0H8D
8D0A(B BBBGTVZA   P     1   BFB A(A0G`|hHpmhA`@
0A(A BBBC   4   L  (4   AHG0
AADG8I@_8A0                $     '    ACG YAA    ğ      AY   H        BGB E(D0D8J
8A0A(B BBBE   ,      G   0   H      ADD ^
AAGUMF   |  x    G       ,     {   @EG
KAF     ̠                          9               DP      tJ   G>     <      D T    T     Gz
O    p  $                            
      \     DV   ADG@
AAE
AAGU
AAA
AAEK
AAC     D   D0   $   ,  s   WD0
AA(   T  0E   b0B0
X   $     TI   @
T`@   4     |"Q   BEHP
FBWz
FBY     $q      ,     &   D 
E
ML
Tl
L     $  'Q   l i(   <  (    L R
JU
CB
FH  $   h  L)   D 
F
I[ 4     ,H   AVR
AFl
IKB
IE L   ȣ  ,KF   BMF B(A0F8GR
8A0A(B BBBA   ,     ,S   AR0
AIA
AF  (   H  Uw
   AKQ
SAIL   t  `{   AD@
AGD
ACi
AN
ALc
AL   D   Ĥ  @h	   BAF`'
ABEg
ABFU
LBM,     qs   AIP
EIX
ES   8   <  Xt   BOD
ABIN
EBK      x     L@
GH
H  0        BJE G
 AABA   Х      P@
P          u0]4     `
   BMA G
 AABG   @   <     BAG
KBG\
ABIMAB <     d   BMA A(J
(A ABBE   <     Գ   BMF A(J
(A ABBE   D      4   BMF A(A0J
0A(A BBBE   D   H  ̽T   BMF A(A0J
0A(A BBBE   D     J   BMF A(A0J
0A(A BBBE   D   ا     BMF A(A0Jz
0A(A BBBE   D      T{   BMF A(A0JU
0A(A BBBB   D   h     BIB A(A0J
0A(A BBBE         [    AK A
AB    Ԩ  C    AG yA D     @   BMO A(A0J
0A(A BBBE   <   <     BMA A(J`
(A ABBG   L   |  (Z   BMF B(A0A8J 
8A0A(B BBBC   4   ̩  8   UFD`
IAHXX`     F                    ,  K         @            T             h  ,          |  8            D            P            \          ̪  h            t                                              0            D            X            l                                                            Ы                                                             4            H            \            p                                                            Ԭ                                                $            8            L            `            t                                                ĭ            ح                                                 (  |           
 
                                         
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r     (r     r     r      r     r     q     q     q     q     o     o     Xo     `o     Ho     Po     8o     @o     xo     o     ho     po     q     q     q     q     q     q     q     q     q     q     q     q     pq     xq     `q     hq     Pq     Xq     @q     Hq     0q     8q      q     (q     q     q      q     q     p     p     p     p     @n     Hn     p     p     p     p     p     p     p     p     0n     8n     p     p     p     p     pp     xp      n     (n     `p     hp     Pp     Xp     @p     Hp     0p     8p     n     n      p     (p     p     p      p     p     o      o     o     o     n      o     o     o     o     o     n     n     o     o      n     n     m     m     o     o     o     o     o     o     m     m     m     m     m     m                           M          4            B            2            G            3       0     @       `     H            I            6       p                                                                                                                              @                                  0                                  (                                                                                      (                         I                                                                                                                                                                                      k                                                                                                    b                                      }     P                    s     Ж                         0b                         p            9          0            @C                                     !                                )                               3                               <          p                     I                                     S                                     \                                   i                                   u                                                                                                                                               `                               `                               @                               @                               \                                                                                           ?      ?        [     d     4          p                                            GCC: (GNU) 14.2.1 20250110 (Red Hat 14.2.1-7)            GA$3a1 @     @              GA$3a1                       GA$3a1                    GA$3a1 @                   GA$3a1                    GA$3a1                    GA$3a1                      GA$3a1                                                                  Q       <     `            t           n            p     z                 	                 	       "                ?                 Y    @     @       z         s                 x                           0            H                }                    P                                             X    p                                 Ъ                            2                 f                    P     f                                       <                t    `                                                             H                 ~                    `                                              T    0                                P                             ,                j                   к     f           @     n       	                B	    @            x	    м            	    p     h      	         (       "
                H
          E       a
    p           
                 
         -                5       ^    `     =                           @            -         Z       o    p     1                9                B       8    @            |                                         b       B          ,      z                   @      X                                                           p            &         /       @                V         |       y    `     y                A           0     j               )                                           "      H      &    j      y       @          R      S                i    r            q                                    p                P     i       1         9      e                                    `                     I      2    	            y    
               `     ^                              }                                       4    p     h       R         h       l    P                0                5      @          P+            
    &     }       ?    p&     }       m    u                                                                ݔ      K          (      @       @    h            e          N           P                                    	                        ;                i    `      [                            P!                !     b       _    `"     b           "                #                `$            I    `%     
          p'               (                @)            5     *            z    *                P,               .            C     /                /                2               5     N          09     ^      :    :           v    0>               @     y           pA                  B            /    B            ]    C     *          D               @F     L          G     r           M     s      .    T            `     U                U                0V                V            $    0W            R    W            }    0X                X                0Y                Y            >    0Z     E      {    \     f          ]     ;          0b     {          r                 r            (     d           Y     pk     h           l                pn                 p           *!    q           _!     s           !    t           !    `v           !    x           -"    y           c"    p{           "     }           "    ~     	      "               #                  5#    Q            `#                |#     s            #    r            #          V      #    s            #    `           #                $                $          Q       6$    o            x$    r            $    r            $    r            4%    r            r%    r            %    r            %    r            1&    r            p&    r            &    r            &    pr            /'    xr            n'    `r            '    hr            '    Pr            ,(    Xr            l(    @r            (    Hr            (    n            ')    n            a)    n            )    n            )    n            *    (o            M*    0o            *    n            *    n            +    xn            ?+    n            z+    Xn            +    `n            +    hn            ,,    pn            f,    n            ,    n            ,    n            -    n            N-    n            -    Pn            -    0r            	.    8r            L.     r            .    (r            .    r            /    r            \/     r            /    r            /    q            *0    q            r0    q            0    q            1    o            ?1    o            z1    Xo            1    `o            1    Ho            :2    Po            z2    8o            2    @o            2    xo            83    o            t3    ho            3    po            3    q            84    q            z4    q            4    q            4    q            @5    q            5    q            5    q            6    q            B6    q            6    q            6    q            7    pq            C7    xq            7    `q            7    hq            8    Pq            D8    Xq            8    @q            8    Hq            9    0q            _9    8q            9     q            9    (q            !:    q            b:    q            :     q            :    q            !;    p            g;    p            ;    p            ;    p            7<    @n            u<    Hn            <    p            <    p            -=    p            w=    p            =    p            =    p            =>    p            {>    p            >    0n            >    8n            3?    p            p?    p            ?    p            ?    p            1@    pp            t@    xp            @     n            @    (n            1A    `p            oA    hp            A    Pp            A    Xp            ?B    @p            ~B    Hp            B    0p            B    8p            7C    n            uC    n            C     p            C    (p            +D    p            nD    p            D     p            D    p            5E    o            tE     o            E    o            F    o            WF    n            F     o            F    o            1G    o            oG    o            G    o            G    n            +H    n            iH    o            H    o            H     n            !I    n            ]I    m            I    m            I    o            J    o            YJ    o            J    o            J    o            !K    o            cK    m            K    m            K    m            L    m            QL    m            L    m            L    b      _      L                 M                 M    m            QM    m            M    r            M    r            M                 M    `             N    @             :N                  sN                  N    `m            N    Pm            O    m            OO    m             O    l            O    @m            O     m            (P     m             ]P    l            P    l            P    l            Q    l             :Q    0l            rQ    l            Q    @l            Q    `l             R    k            OR     l            R    k            R     l             R    pk            ,S    k            dS    k            S    k             S    k            T    `k            ?T     k            uT    @k             T    j            T     k            U    j            TU    j             U    Pj            U    j            U    `j            5V    j             lV     j             V     j            V    @j            W    i            MW    i            W    i            W    i             W    i            :X    `i     0       qX    i            X    0i            X    i            Y    h             QY    h            Y     i            Y    h            Y    `h            3Z    Ph     
       oZ    h            Z    h             Z     h            ![    g            ^[    @h            [     h             [    g     
       \    g            N\    g            \    g             \    0g     
       \    g            9]    @g            s]    `g             ]    f            ]     g            .^    f            n^     g             ^    pf            ^    f            /_    f            o_    f             _    f            _    @f             `     f            P`    `f            `    e            `    e            `     f            7a    e             pa    Pe            a    e            a    `e             b    e             Yb     e            b     e             b    @e            b    d            .c    d            dc    d            c    d             c    d            d    @d            <d    d            rd    `d             d    0d            d    c            !e     d            ge     d             e    c            e    pc            *f    c            cf    c            f    c             f    c            g    `c            Dg     c            |g    @c             g    b            g     c            %h    b            ]h    b             h    Pb            h    b            i    `b            >i    b             ui    a            i    @b            i     b            j     b             Rj    a            j    a            j    a             j    a            #k    @a            [k    0a            k    a            k    `a             l    `            =l     a            vl    `            l     a             l    `            )m    `            nm    `             m    p`            m    `            0n    ``            jn     `            n    @`             n    _            o     `            Mo    _            o    _             o    P_            o    _            .p    `_            fp    _             p    ^            p    @_            q     _            Dq     _             zq    ^            q    ^            q    ^            3r    ^             or    0^            r    ^            r    @^            (s    `^             ds    ]     
       s    ]            s     ^            t     ^             9t    p]            {t    ]            t    ]            t    ]             >u     ]            tu    ]            u    `]            u    @]             v    \     
       Mv     ]            v    \            v    \             v    P\     
       !w    `\            Uw    \            w    \             w     \            w    [            2x    @\            mx     \             x    [            x    [            y    [            Vy    [             y    0[            y    [            y    @[            0z    `[             dz    Z            z     [            z    Z            ){     [             i{    pZ            {    Z            {    Z            |    Z             B|    Z            x|    `Z            |     Z            |    @Z             }    Y            L}     Z            }    Y            }    Y             }    PY            #~    Y            ^~    `Y            ~    Y             ~    X                @Y            G     Y                 Y                 X                X            (    X            ^    X                 0X            ʀ    X                @X            7    `X             l    W                W            ׁ     X                 X             A    W                W            ɂ    W                W            R    `W                PW     
       ǃ    W                W             ;    V     
       v    @W                 W                 W             $    V     
       _    V                V            ԅ    V                 @V     0       B    V     	       y     V                pV                U     0           U     	       T    U                U            Ç    @U     0           U     	       /     U            e    pU                T            ܈     U                T            [    T                 T            ډ    T                T            _    T                pT                `T            %    XT            h    T                @T                PT            -    0T            o    8T                 T             ߌ    S                 T            @    S            q    S     0           S            ҍ    S                hS            6    PS            i     S     0            S            ̎    R                R            2    R     0       c    R                pR            ȏ    @R                  R            -    R            a    `R                Q             ǐ    Q                 R            .    Q            b    PQ                Q            ̑    `Q                 Q             3    P            i    @Q                 Q            Ԓ     Q                 P            A    P            z    P                P                 0P            !    P            Y    @P                `P             Ɣ     P                 O            +     P            _    O                O             Ǖ    O                O            2    pO            h    O                `O            Җ     O                @O             9    N            n     O                N            ח    N             
    `N            <    N            o    N                 PN            Ә     N                @N            :     N             l    M                M            ә    M                 M            9    M            m    0M                M            ך    @M                `M             >    L            q    L                 M            ٛ     M                 pL            B    L            y    L                L                 L                `L            R     L                @L                 K                 L            )    K            ^    K                  K            Ǟ    K                 @K             0    `K     @       c    J                J             ̟     K                 J     @       4     J             h    `J                 I            Ҡ     J     @           `I             9    I             n    @I                I     @       ֡    H                 I             @    H             t    H     @           `H             ע    @H                H            :    0H            l    G                 H            գ     H                 G            =    G            q    G                G            ؤ    G             
     G     P       A    `G     (       z    F     (           F                 F     P       "    E     (       Z    F     (           E            ̦    @E     P            E     (       ;    E     (       t    D                `D     P            D     (           D     (       U    D                C     P       ɨ    C     (           @C     (       B    C                B     P           @B     (           B     (       6    B            t    A                A                A                 B            Y    A                A            ӫ    A                A            N     A     P           A     (           @     (           @            /     @     P       h    ?     (           @     (       ݭ    ?                @?     P       Q     ?     (           ?     (       Ʈ    >                `>     P       ;     >     (       v    >     (           >                =     P       (    @=     (       c    =     (           (=            ۰    <     P           `<     (       P    0<                 =     (       ȱ    ;     P           `;     (       A     <     (           H;                0;                 ;     0           :            P    :     	           :                p:                :                :             G    :            z    `:                 :            ߴ    @:                 9            C     :            v    9                9             ٵ    9                 `9            B    9            x    P9                 9            ߶    @9                 9             A    8            s    8                8            ط    8             	    8            <    @8            o    8                `8             ո    08            	    7            <     8            p     8                 7            ֹ    7            	    7            =    7             o    p7                @7             Ժ    07                `7            9     7            l    6     @            7             һ    6                 6            9     6             l    `6                 5            Լ     6     @           5             8    5            k    5                5            ӽ    `5             	    @5            @    5            x    05                 5                 4            !     5            [    4                4             ǿ    4                4            .    4            b    p4                @4     0            4                4     	           3            S    3                  4                3                `3            '    3            _    3                 P3                3                @3            0     3             `    3                2     0           2                2            (    2            [    @2     0            2                p2                2            (    1     0       Z    1                1                1                `1             (    @1            \    1                01                 1                 0            -     1            b    0                0                p0     
           0            2    0             d    0     
           `0                 0                @0             5    /             k    /                 0                /     
           /             H    `/                /                P/     
            /             $     /            Z    @/                .     
           .                .            0    .            c    .                 `.                 @.                 .            7    0.            n     .                 -                 .                -            G    p-            }    -                -                -                  -            N    @-                 `-                -                ,                 ,            P     -                ,                ,                 `,            '    ,            ]    P,                 ,                  ,                @,            2    +            h    +                +                +                 +            9    @+            j    +                `+                 0+                *            0     +            c     +                 *                *     0           *            *    p*     	       ]    *                *                `*                 *            +    @*             ]    )                 *                )                 )            "    P)            U    )                `)                )                  )             #     )            \    @)                (                (                 (            9    (            o    (                P(                (            
    `(             ;    @(            n    '     @           '                  (                 '            ;     '             l    @'     @           '                 '                 &     0       3    &            g    &                &     	           @&     0           &            :    p&            p     &     	           %     @           %                 %             ?    p%            s     %                `%                %                @%             <    $             p    $                 %                $                P$            F    $            {    `$                $                 $                @$            K     $             ~     $                h#                #             $    #             ]    #     @           P#                 #     0           "            !    "     	       Q                g                    0               Ж     u                                          P           H                ^                y    0     :          `                X                P                H                p     ,      +                A                \                r                                                                                                    x                 p            6    h            Q    @     h       a                |    `     @                                                                P       
                           0       .   	 9     w	      Y   	 @C                                       8                      Q                          p                                                       F                                    P                     #      &          y
      N                j                   	                 	                                p     x      0   	            K   	             f   	 `              	       H         	 `      p          	       p          	                	       X          	      X          	             <   	 @            Y   	      `       x   	      h          	       h          	      h          	       h       0   	             \    ͝     	       |    ֝     	          	                0s                 s                @s            
   	            9   	              ^   	      H          	       h          	      h          	                	       4                 h       6   	             B   	             d   	 @               	                 	                	                 	                 	 @            #   	 `            @   	             ]    n           |   	       
         	                	 `              	                	            ,    ߝ            K                e                                                    /                @               	                	             5   	              U   	             u   	                 	      (          	 @     0          	       8          	      @          	 `     H       5   	       P       V   	      X       w   	 @     `                              @t                `t                Pt                @                                   @                 p                                                                %                 1                 P                   Z                   f            0       |    0t                                   @                    V          P                     s               E               I                Q               q                               Q          
                
           )         H      <    ,     F      N    @5           U     8     w
         B     {      g     K     	      n    T     s      ~    W               `c               Ph               p}                p~                `     
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      E               h    P	     )      |    `                
     L          P!                                    V           .               ^     g
                     *    `            6                Z    @     =          b     `            	
     
          0                     T                         F                                     F                     1    
     D      T               g     c     h       r    Y            {    0     H                         @               @N     ~                                          `!     W               f      )    Pk     l          +                                                #     &          G
                    ;               z       .    @$           C     [     `       V    @           g                r    
 $                 (     9          `     `                                                                   5    `            B    0a     
      g         Z       q                   P                d               `
     k               	                G       -    `            <    p           L                   P                0               N
     ?          b     6                               J                                                       N     
      	    @                            "    0           -    [     |d      X    @)     e      o    P     ;          0     )           @                                                                                   [       
    [     	      "    @[
           Z    p	           w    `,                `                                                 	                ,     R          g                              F     3       -    PF     C       @    S
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              `     ,         	     E      	   -           :        
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                         @	              ,	     -         pg               '               f     B       $                -    2
           F                 R   P            `   
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                   s                                                      @     -                     6        P      V        F      `   '     R      w   K              
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     J      M   P            Y              `        Y      i   @-               `     &          [              p                                           `w     q         `     ^              e       "              `         :	      l   н              @     
                       `     {         H     E      7  	 `#            X    	                             	                                                           
     )          \                                 x-         	           *        <      C        .      W   p     {      e               q   `0     R      }                        o         4     `         p     c         `	              `
     6         `     ,         T     +       ,   `T     ,      F   p           Z   0     J      p   ^	     Y                        T               @     }         Y     %         
                          4         ]      A   `     g	      f   @     >          P	                   '	                         0Q                                                         S            -               9              G              S   2     &      r   @                             !                   	         `d                    3!         0                           &   pf     (       0   0           <   [     `       G              ]   $     !       h                 T                +                              	                         1         c       E                Y         w                            }               p     c!                               (       !              !               %!         Y	      L!   `            W!        |      b!   4     :	      y!               !   '     '      !        *      !   ]
           "               "   	     5      2"   @     b      ;"              a"              "              "   0           "        `       "   @.     "      "              #               #   "           ##              Q#   @.     
      x#        d      #   @           #              #   0Q     6      #              #              $   @9     E.      >$        '      H$               S$   @     	      $    7           $   N     +      $   p           $         l      $               $   0           %   &           .%   P}     g      Q%               [%   pc     %      d%        h      %              %                %         1       %   `           %   p     $	      %              %               &   T            $&              P&              &    (           &   p           &               &   0
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       '   P	     ~      4'                ?'   0     ,      J'        '      T'   Ч
           |'        f	      '   0           '   7            '         )       '               '   P     b      '        Y       (   	     &      (   p            )(   m           (   @           (   C           (   0            (   H           (   u           )        )       )   o
     	      1)                    ?)                    P)                    d)                    p)                    )                    )                    )                    )                    )                    )                    )                    *                    *                    &*                    7*                    L*                    _*                    7                    m*                    *                    5                    *                    *                    *                    *                    *                    1                    *                    *                    +                    +                    2+                    >+                    U+                    d+                    y-                    w+                    +                    +                    +                    +                    +                    +               +                    	,                    ,                    ,,                    ;, "                   V,                    i,                    v,                    ,                    ,                    ,                    ,                    ,                    6                    ,                    ,                    -                    -                    )-                    ;-                    J-                    _-                    x-                    -                    -                    -                    -                    -                    *                    -                    -                    .                    *.                    :.                    M.                    d.                    w.                    .                    .                    .                    .                    .                    .                    .                    /                    ,/                    A/                    M/                    3                    ^/                    x/                    /                    /                    /                    /                    /                    /                    /                    *                    0                    0                    /0                    D0                    9                    *                    W0                    j0                    *-                    x0                    0                    0                    0                    0                    0                    0                    0                    1                    1                    '1                    <1                    P1                    ^1                    i1                    }1                    1                    1                    1                    1                    1                    1                    1                    2                    !2                    22                    J2                    ^2                    w2                    2                    2                    2                    2                    2                    2                    3                    3                    +3                    1                    >3                    Q3                    b3                    z3                    3                    3                    3                    *                    3                    3                    3                    3                    4                     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2.2.5 _ITM_deregisterTMCloneTable PyIter_Next _Unwind_Resume@GCC_3.0 casinl@GLIBC_2.2.5 modf@GLIBC_2.2.5 PyExc_SystemError PyExc_ImportError ccosf@GLIBC_2.2.5 _PyDict_NewPresized frexp@GLIBC_2.2.5 cabs@GLIBC_2.2.5 logf@GLIBC_2.27 PyGILState_Ensure PyCMethod_New PyObject_GC_Track __gmon_start__ PyCapsule_GetName PyOS_vsnprintf PyType_FromModuleAndSpec PyTuple_GetItem PyUnicode_Concat _ITM_registerTMCloneTable PyMemoryView_FromMemory PyModuleDef_Init PyErr_GivenExceptionMatches cpow@GLIBC_2.2.5 log1p@GLIBC_2.2.5 PyUnicode_FromStringAndSize expm1@GLIBC_2.2.5  .symtab .strtab .shstrtab .note.gnu.build-id .gnu.hash .dynsym .dynstr .gnu.version .gnu.version_r .rela.dyn .rela.plt .init .text .fini .rodata .eh_frame_hdr .eh_frame .gcc_except_table .tdata .init_array .fini_array .data.rel.ro .dynamic .got .got.plt .data .bss .comment .gnu.build.attributes                                                                    H   o       '      '                                 U   o       )      )                                  d             `*      `*      2                           n      B       0]      0]      h                          x                                                         s              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     0                     .                                          P     P                                                         p                               	                           9                                                       )                                                       $                              .   o       (     (      $                             8             P     P                                                    P     0                           @             0     0R                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   GNU feZ/h%qӜ7E                             5                                                 '                                          	                     Q                     <
                                                                                                                                                   !                     l
                                          %                                                               U                     2                     |                     (                                                               ,                     9                                           B                                          
                     D                     }
                     8                                          R                     `                     
                                                               *	                     	                     
                                          !                                                                                    F   "                                                                                  u                                          
                                                               [                                          
                                          s                                           U                                                                
                                          
                     %                     &                                          .                                                                                    	                     
                                          q
                                                                                                         
                     U	                     h	                                                                h                     d                                          
                     8                     c                                                                                                                                                   "                     -                     m                                          o                                                                ;                                                               !                                                                                    3                                          y                                          g                                          :                                                               	                     d                                                                                                           @                     
                                                                t                                          	                     }                                           :                                          
                     
                                                               
                                          k                                          a                     
                                                                T
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                     ]                     
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                                              h                           0]             `*             2      	              o    )      o           o    '      o                                                                                                           __gmon_start__ _ITM_deregisterTMCloneTable _ITM_registerTMCloneTable __cxa_finalize _Py_NoneStruct PyDict_New PyUnicode_FromString malloc scipy_dstevr_ free PyExc_TypeError PyErr_Format PyObject_Vectorcall PyExc_SystemError PyErr_SetString PyDict_Size PyMethod_New PyUnicode_InternFromString PyUnicode_FromFormat PyExc_DeprecationWarning PyErr_WarnFormat _Py_Dealloc PyObject_GC_UnTrack PyObject_ClearWeakRefs PyObject_GC_Del PyTuple_New PyDict_SetDefault PyBytes_FromStringAndSize PyBytes_AsString PyCode_NewWithPosOnlyArgs PyObject_GetAttrString PyDict_GetItemString PyModule_GetName PyExc_ImportError PyCapsule_IsValid PyCapsule_GetName PyCapsule_GetPointer PyDict_SetItemString PyExc_AttributeError PyErr_ExceptionMatches PyErr_Clear PyThreadState_Get PyInterpreterState_GetID PyModule_NewObject PyModule_GetDict log1p expm1 PyLong_AsUnsignedLong PyErr_Occurred PyExc_OverflowError PyLong_Type PyTuple_GetSlice PyTuple_GetItem PyMem_Malloc PyDict_Next PyMem_Free PyErr_NoMemory PyExc_RuntimeWarning PyErr_WarnEx _PyObject_GC_New PyObject_GC_Track PyList_New PyExc_ValueError PyList_Type PyTuple_Type PyLong_FromSsize_t PyObject_GetItem PyNumber_Index PyLong_AsSsize_t PyErr_GivenExceptionMatches PyExc_IndexError PyErr_NormalizeException PyException_SetTraceback PyException_GetTraceback strrchr PyImport_AddModule PyDict_GetItemWithError PyType_FromModuleAndSpec PyGILState_Ensure PyGILState_Release PyBaseObject_Type PyCFunction_Type Py_EnterRecursiveCall Py_LeaveRecursiveCall PyObject_VectorcallDict PyObject_Call _PyThreadState_UncheckedGet PyErr_PrintEx PyErr_WriteUnraisable PyExc_ZeroDivisionError _Py_FalseStruct PyImport_ImportModuleLevelObject _Py_TrueStruct PyObject_GetAttr PyFrame_New PyTraceBack_Here PyCode_NewEmpty memmove PyMem_Realloc PyObject_SetAttr PyMethodDescr_Type PyType_IsSubtype PyCMethod_New PyImport_ImportModule PyExc_ModuleNotFoundError PyCapsule_Type PyExc_RuntimeError PyExc_Exception PyObject_GenericGetAttr _PyObject_GenericGetAttrWithDict PyExc_NameError _PyDict_GetItem_KnownHash PyObject_SetAttrString Py_Version PyOS_snprintf PyUnicode_FromStringAndSize PyMemoryView_FromMemory PyObject_CallFunctionObjArgs PyUnicode_DecodeUTF8 PyUnicode_InternInPlace PyObject_Hash PyLong_FromLong PyType_Type PyTuple_Pack PyImport_GetModuleDict PyDict_Type strlen PyDict_SetItem _PyDict_NewPresized PyObject_SetItem _PyDict_SetItem_KnownHash PyUnicode_Concat PyImport_GetModule PyObject_GetIter PyExc_StopIteration PyDict_Copy PyObject_VectorcallMethod PyIter_Next _PyStack_AsDict PyMethod_Type PySequence_Contains _PyDict_Pop PyArg_ValidateKeywordArguments PyInit__ufuncs PyModuleDef_Init PyObject_GenericGetDict PyObject_GenericSetDict cbrt sincos cabs __muldc3 fma clog modf __divdc3 csqrt cexp ccosh csinh fmax fmin csin _ZSt7nothrow _ZnamRKSt9nothrow_t _ZdaPv frexp ldexp log10 fmod ccos round atan2 log1pf log1pl ceil memset __cxa_throw_bad_array_new_length _Unwind_Resume __gxx_personality_v0 __tls_get_addr PyOS_vsnprintf cpowf cpow cpowl cabsf atan2f cexpf clogf csqrtf ccosf csinf ctanf ccoshf csinhf ctanhf cacosf casinf catanf cacoshf casinhf catanhf ctan ctanh cacos casin catan cacosh casinh catanh cabsl atan2l cexpl clogl csqrtl ccosl csinl ctanl ccoshl csinhl ctanhl cacosl casinl catanl cacoshl casinhl catanhl libscipy_openblas.so libstdc++.so.6 libm.so.6 libgcc_s.so.1 libc.so.6 ld-linux-x86-64.so.2 GLIBC_2.3 GLIBC_2.2.5 GCC_3.0 GCC_4.0.0 CXXABI_1.3 CXXABI_1.3.8 GLIBCXX_3.4 GLIBC_2.27 /opt/_internal/cpython-3.11.13/lib/python3.11/site-packages/scipy_openblas32/lib libscipy_openblas-6cdc3b4a.so $ORIGIN/../../scipy.libs     