
    ЦiO1                       S r SSKJr  SSKJr  SSKJrJrJr  SSK	J
r
  SSKJr  SSKJr  0 SS	 S
4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_S S! S"4/_S#S$ S%4/_S&S' S(4/_S)S* S+4/_S,S- S.4/_S/S0 S14/_S2S3 S(4/_S4S5 S64/_S7S8 S94/_0 S:S; S<4/_S=S> S?4/_S@SA SB4/_SCSD SE4/_SFSG SH4/_SISJ SK4/_SLSM SN4/_SOSP SQ4/_SRSS ST4/_SUSV SW4/_SXSY SZ4/_S[S\ S]4/_S^S_ S^4/_S`Sa S`4/_SbSc Sd4/_SeSf Sd4/_SgSh Si4/_E0 SjSk Sl4/_SmSn So4/_SpSq Sr4/_SsSt So4/_SuSv Sw4/_SxSy Sz4/_S{S| S}4/_S~S S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_E0 SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_E0 SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_SS S4/_E0 SS GS 4/_GSGS GS4/_GSGS GS4/_GSGS GS	4/_GS
GS GS4/_GSGS GS4/_GSGS GS4/_GSGS GS4/_GSGS GS4/_GSGS GS4/_GSGS GS4/_GSGS  GS!4/_GS"GS# GS$4/_GS%GS& GS'4/_GS(GS) GS*4/_GS+GS, GS+4/_GS-GS. GS/4/_EGS0 GS14/GS2 GS34/GS4.Er " GS5 GS6\5      rGS7 rGg8(9  z
Mathematica code printer
    )annotations)Any)BasicExprFloat)default_sort_key)CodePrinter)
precedenceexpc                    gNT xs    Y/var/www/html/ai-image-ml/venv/lib/python3.13/site-packages/sympy/printing/mathematica.py<lambda>r          t    Explogc                    gr   r   r   s    r   r   r      r   r   Logsinc                    gr   r   r   s    r   r   r      r   r   Sincosc                    gr   r   r   s    r   r   r      r   r   Costanc                    gr   r   r   s    r   r   r      r   r   Tancotc                    gr   r   r   s    r   r   r      r   r   Cotsecc                    gr   r   r   s    r   r   r      r   r   Seccscc                    gr   r   r   s    r   r   r      r   r   Cscasinc                    gr   r   r   s    r   r   r          r   ArcSinacosc                    gr   r   r   s    r   r   r      r-   r   ArcCosatanc                    gr   r   r   s    r   r   r      r-   r   ArcTanacotc                    gr   r   r   s    r   r   r      r-   r   ArcCotasecc                    gr   r   r   s    r   r   r      r-   r   ArcSecacscc                    gr   r   r   s    r   r   r      r-   r   ArcCscatan2c                     gr   r   r   s    r   r   r          $r   sinhc                    gr   r   r   s    r   r   r      r-   r   Sinhcoshc                    gr   r   r   s    r   r   r       r-   r   Coshtanhc                    gr   r   r   s    r   r   r   !   r-   r   Tanhcothc                    gr   r   r   s    r   r   r   "   r-   r   Cothsechc                    gr   r   r   s    r   r   r   #   r-   r   Sechcschc                    gr   r   r   s    r   r   r   $   r-   r   Cschasinhc                    gr   r   r   s    r   r   r   %       r   ArcSinhacoshc                    gr   r   r   s    r   r   r   &   rU   r   ArcCoshatanhc                    gr   r   r   s    r   r   r   '   rU   r   ArcTanhacothc                    gr   r   r   s    r   r   r   (   rU   r   ArcCothasechc                    gr   r   r   s    r   r   r   )   rU   r   ArcSechacschc                    gr   r   r   s    r   r   r   *   rU   r   ArcCschsincc                    gr   r   r   s    r   r   r   +   r-   r   Sinc	conjugatec                    gr   r   r   s    r   r   r   ,       Tr   	ConjugateMaxc                     gr   r   r   s    r   r   r   -   r-   r   Minc                     gr   r   r   s    r   r   r   .   r-   r   erfc                    gr   r   r   s    r   r   r   /   r   r   Erferf2c                     gr   r   r   s    r   r   r   0   rU   r   erfcc                    gr   r   r   s    r   r   r   1   r-   r   Erfcerfic                    gr   r   r   s    r   r   r   2   r-   r   Erfierfinvc                    gr   r   r   s    r   r   r   3   r@   r   
InverseErferfcinvc                    gr   r   r   s    r   r   r   4       4r   InverseErfcerf2invc                     gr   r   r   s    r   r   r   5       Dr   expintc                     gr   r   r   s    r   r   r   6   r   r   ExpIntegralEEic                    gr   r   r   s    r   r   r   7       dr   ExpIntegralEifresnelcc                    gr   r   r   s    r   r   r   8   r   r   FresnelCfresnelsc                    gr   r   r   s    r   r   r   9   r   r   FresnelSgammac                    gr   r   r   s    r   r   r   :   rU   r   Gamma
uppergammac                     gr   r   r   s    r   r   r   ;       tr   	polygammac                     gr   r   r   s    r   r   r   <       dr   	PolyGammaloggammac                    gr   r   r   s    r   r   r   =   r   r   LogGammabetac                     gr   r   r   s    r   r   r   >   rU   r   BetaCic                    gr   r   r   s    r   r   r   ?   r   r   CosIntegralSic                    gr   r   r   s    r   r   r   @   r   r   SinIntegralChic                    gr   r   r   s    r   r   r   A   r   r   CoshIntegralShic                    gr   r   r   s    r   r   r   B   r   r   SinhIntegrallic                    gr   r   r   s    r   r   r   C   r   r   LogIntegral	factorialc                    gr   r   r   s    r   r   r   D   rk   r   	Factorial
factorial2c                    gr   r   r   s    r   r   r   E   r   r   
Factorial2subfactorialc                    gr   r   r   s    r   r   r   F       r   Subfactorialcatalanc                    gr   r   r   s    r   r   r   G   r   r   CatalanNumberharmonicc                     gr   r   r   s    r   r   r   H   rk   r   HarmonicNumberlucasc                    gr   r   r   s    r   r   r   I   rU   r   LucasLRisingFactorialc                     gr   r   r   s    r   r   r   J   s    Dr   
PochhammerFallingFactorialc                     gr   r   r   s    r   r   r   K   s    Tr   FactorialPowerlaguerrec                     gr   r   r   s    r   r   r   L   rk   r   	LaguerreLassoc_laguerrec                     gr   r   r   s    r   r   r   M       4r   hermitec                     gr   r   r   s    r   r   r   N   r   r   HermiteHjacobic                     gr   r   r   s    r   r   r   O   r   r   JacobiP
gegenbauerc                     gr   r   r   s    r   r   r   P   r   r   GegenbauerC
chebyshevtc                     gr   r   r   s    r   r   r   Q   r   r   
ChebyshevT
chebyshevuc                     gr   r   r   s    r   r   r   R   r   r   
ChebyshevUlegendrec                     gr   r   r   s    r   r   r   S   rk   r   	LegendrePassoc_legendrec                     gr   r   r   s    r   r   r   T   r   r   mathieucc                     gr   r   r   s    r   r   r   U   rk   r   MathieuCmathieusc                     gr   r   r   s    r   r   r   V   rk   r   MathieuSmathieucprimec                     gr   r   r   s    r   r   r   W       $r   MathieuCPrimemathieusprimec                     gr   r   r   s    r   r   r   X   r   r   MathieuSPrime	stieltjesc                    gr   r   r   s    r   r   r   Y   rk   r   StieltjesGamma
elliptic_ec                     gr   r   r   s    r   r   r   Z   r   r   	EllipticE
elliptic_fc                     gr   r   r   s    r   r   r   [   r   r   
elliptic_kc                    gr   r   r   s    r   r   r   \   r   r   	EllipticKelliptic_pic                     gr   r   r   s    r   r   r   ]   r   r   
EllipticPizetac                     gr   r   r   s    r   r   r   ^   rU   r   Zetadirichlet_etac                    gr   r   r   s    r   r   r   _   s    r   DirichletEta
riemann_xic                    gr   r   r   s    r   r   r   `   r   r   	RiemannXibesselic                     gr   r   r   s    r   r   r   a   r   r   BesselIbesseljc                     gr   r   r   s    r   r   r   b   r   r   BesselJbesselkc                     gr   r   r   s    r   r   r   c   r   r   BesselKbesselyc                     gr   r   r   s    r   r   r   d   r   r   BesselYhankel1c                     gr   r   r   s    r   r   r   e   r   r   HankelH1hankel2c                     gr   r   r   s    r   r   r   f   r   r   HankelH2airyaic                    gr   r   r   s    r   r   r   g   r@   r   AiryAiairybic                    gr   r   r   s    r   r   r   h   r@   r   AiryBiairyaiprimec                    gr   r   r   s    r   r   r   i   r   r   AiryAiPrimeairybiprimec                    gr   r   r   s    r   r   r   j   r   r   AiryBiPrimepolylogc                     gr   r   r   s    r   r   r   k   r   r   PolyLoglerchphic                     gr   r   r   s    r   r   r   l   rk   r   LerchPhigcdc                     gr   r   r   s    r   r   r   m   r-   r   GCDlcmc                     gr   r   r   s    r   r   r   n   r-   r   LCMjnc                     gr   r   r   s    r   r   r   o   r   r   SphericalBesselJync                     gr   r   r   s    r   r   r   p   r   r   SphericalBesselYhyperc                     gr   r   r   s    r   r   r   q   r@   r   HypergeometricPFQmeijergc                     gr   r   r   s    r   r   r   r   r   r   MeijerGappellf1c                     gr   r   r   s    r   r   r   s   rk   r   AppellF1
DiracDeltac                    gr   r   r   s    r   r   r   t   r   r   	Heavisidec                    gr   r   r   s    r   r   r   u   rk   r   HeavisideThetac                     gr   r   r   s    r   r   r   v   r   r   KroneckerDeltac                    gr   r   r   s    r   r   r   w   r-   r   Sqrt)rH  sqrtc                  b  ^  \ rS rSr% SrSrSr\" \R                  40 S0 S.D6r	S\
S'   \" 5       rS	\
S
'   \" 5       rS\
S'   0 4S jrS rS rU 4S jrS rS rS rS rS rS rS rS rS rS rS rS rS rS rS r S  r!S! r"\"r#\"r$S" r%S# r&S$ r'S% r(S& r)\)r*S' r+S( r,S) r-S* r.S+ r/S,r0U =r1$ )-MCodePrinter{   zUA printer to convert Python expressions to
strings of the Wolfram's Mathematica code
_mcodezWolfram Language   )	precisionuser_functionszdict[str, Any]_default_settingszset[tuple[Expr, Float]]_number_symbolsz
set[Basic]_not_supportedc                >   [         R                  " X5        [        [        5      U l        UR	                  S0 5      R                  5       nUR                  5        H$  u  p4[        U[        5      (       a  M  S U4/X#'   M&     U R                  R                  U5        g)z+Register function mappings supplied by userrR  c                     gr   r   r   s    r   r   'MCodePrinter.__init__.<locals>.<lambda>   s    Dr   N)
r	   __init__dictknown_functionsgetcopyitems
isinstancelistupdate)selfsettings	userfuncskvs        r   rY  MCodePrinter.__init__   s|    T,#O4LL!126;;=	OO%DAa&&!0! 45	 & 	##I.r   c                    U$ Nr   )rb  liness     r   _format_codeMCodePrinter._format_code   s    r   c                    [        U5      nU R                  UR                  U5      < SU R                  UR                  U5      < 3$ )N^)r
   parenthesizebaser   )rb  exprPRECs      r   
_print_PowMCodePrinter._print_Pow   s>    $++DIIt<++DHHd;= 	=r   c                   >^ ^ [        U5      mUR                  5       u  p#[        TT ]  UR                  " U6 5      nU(       a$  US-  nUSR                  UU 4S jU 5       5      -  nU$ )N*z**c              3  H   >#    U  H  nTR                  UT5      v   M     g 7fri  )ro  ).0arr  rb  s     r   	<genexpr>*MCodePrinter._print_Mul.<locals>.<genexpr>   s!     DAT..q$77s   ")r
   args_cncsuper
_print_Mulfuncjoin)rb  rq  cncresrr  	__class__s   `    @r   r~  MCodePrinter._print_Mul   s[    $g A/3JC499DDDDC
r   c                    U R                  UR                  5      nU R                  UR                  5      nUR                  nSR	                  X$U5      $ )Nz{} {} {})_printlhsrhsrel_opformat)rb  rq  lhs_coderhs_codeops        r   _print_RelationalMCodePrinter._print_Relational   sB    ;;txx(;;txx([[  x88r   c                    g)N0r   rb  rq  s     r   _print_ZeroMCodePrinter._print_Zero       r   c                    g)N1r   r  s     r   
_print_OneMCodePrinter._print_One   r  r   c                    g)Nz-1r   r  s     r   _print_NegativeOneMCodePrinter._print_NegativeOne       r   c                    g)Nz1/2r   r  s     r   _print_HalfMCodePrinter._print_Half   s    r   c                    g)NIr   r  s     r   _print_ImaginaryUnit!MCodePrinter._print_ImaginaryUnit   r  r   c                    g)NInfinityr   r  s     r   _print_InfinityMCodePrinter._print_Infinity   s    r   c                    g)Nz	-Infinityr   r  s     r   _print_NegativeInfinity$MCodePrinter._print_NegativeInfinity   s    r   c                    g)NComplexInfinityr   r  s     r   _print_ComplexInfinity#MCodePrinter._print_ComplexInfinity   s     r   c                    g)NIndeterminater   r  s     r   
_print_NaNMCodePrinter._print_NaN   s    r   c                    g)NEr   r  s     r   _print_Exp1MCodePrinter._print_Exp1   r  r   c                    g)NPir   r  s     r   	_print_PiMCodePrinter._print_Pi   r  r   c                    g)NGoldenRatior   r  s     r   _print_GoldenRatioMCodePrinter._print_GoldenRatio   s    r   c                X    UR                  SS9n[        U5      nU R                  X#5      $ )NT)r  )expandr
   ro  )rb  rq  expandedrr  s       r   _print_TribonacciConstant&MCodePrinter._print_TribonacciConstant   s-    ;;D;)$  00r   c                    g)N
EulerGammar   r  s     r   _print_EulerGammaMCodePrinter._print_EulerGamma   s    r   c                    g)NCatalanr   r  s     r   _print_CatalanMCodePrinter._print_Catalan   s    r   c                F   ^  SSR                  U 4S jU 5       5      -   S-   $ )N{, c              3  F   >#    U  H  nTR                  U5      v   M     g 7fri  doprintrx  ry  rb  s     r   rz  +MCodePrinter._print_list.<locals>.<genexpr>   s     =1t||A   !}r  r  s   ` r   _print_listMCodePrinter._print_list   s"    TYY====CCr   c                @    U R                  UR                  5       5      $ ri  r  tolistr  s     r   _print_ImmutableDenseMatrix(MCodePrinter._print_ImmutableDenseMatrix       ||DKKM**r   c                h   ^ ^^ U 4S jmUU4S jnUU 4S jnSR                  U" 5       U" 5       5      $ )Nc                   > SR                  TR                  U S   S-   U S   S-   45      TR                  U5      5      $ )N{} -> {}r      r  r  posvalrb  s     r   
print_rule=MCodePrinter._print_ImmutableSparseMatrix.<locals>.print_rule   sD    $$LL#a&(CF1H-.S0AC Cr   c                    > [        TR                  5       R                  5       [        S9n SSR	                  U4S jU  5       5      -   S-   $ )N)keyr  r  c              3  8   >#    U  H  u  pT" X5      v   M     g 7fri  r   )rx  re  rf  r  s      r   rz  PMCodePrinter._print_ImmutableSparseMatrix.<locals>.print_data.<locals>.<genexpr>   s     =utq*Q**us   r  )sortedtodokr^  r   r  )r^  rq  r  s    r   
print_data=MCodePrinter._print_ImmutableSparseMatrix.<locals>.print_data   sF    4::<--/5EFE		=u==> r   c                 :   > TR                  T R                  5      $ ri  r  shaperq  rb  s   r   
print_dims=MCodePrinter._print_ImmutableSparseMatrix.<locals>.print_dims   s    <<

++r   SparseArray[{}, {}]r  )rb  rq  r  r  r  s   ``  @r   _print_ImmutableSparseMatrix)MCodePrinter._print_ImmutableSparseMatrix   s,    	C		, %++JL*,GGr   c                @    U R                  UR                  5       5      $ ri  r  r  s     r   _print_ImmutableDenseNDimArray+MCodePrinter._print_ImmutableDenseNDimArray   r  r   c                |   ^ ^^^^ S mS mU 4S jmUUUU4S jnUU 4S jnSR                  U" 5       U" 5       5      $ )Nc                >    SSR                  S U  5       5      -   S-   $ )Nr  r  c              3  $   #    U  H  ov   M     g 7fri  r   )rx  ry  s     r   rz  ZMCodePrinter._print_ImmutableSparseNDimArray.<locals>.print_string_list.<locals>.<genexpr>   s     ":k1ks   r  r  )string_lists    r   print_string_listGMCodePrinter._print_ImmutableSparseNDimArray.<locals>.print_string_list   s!    ":k":::S@@r   c                 &    [        S U  5       5      $ )zHelper function to change Python style indexing to
Pathematica indexing.

Python indexing (0, 1 ... n-1)
-> Mathematica indexing (1, 2 ... n)
c              3  *   #    U  H	  oS -   v   M     g7f)r  Nr   )rx  is     r   rz  ]MCodePrinter._print_ImmutableSparseNDimArray.<locals>.to_mathematica_index.<locals>.<genexpr>  s     -1Qs   )tuple)argss    r   to_mathematica_indexJMCodePrinter._print_ImmutableSparseNDimArray.<locals>.to_mathematica_index   s     ----r   c                d   > SR                  TR                  U 5      TR                  U5      5      $ )z.Helper function to print a rule of Mathematicar  r  r  s     r   r  @MCodePrinter._print_ImmutableSparseNDimArray.<locals>.print_rule	  s(    $$T\\#%6S8IJJr   c                    > T" [        TR                  R                  5       5       V Vs/ s H   u  pT" T" TR                  U 5      6 U5      PM"     snn 5      $ s  snn f )zHelper function to print data part of Mathematica
sparse array.

It uses the fourth notation ``SparseArray[data,{d1,d2,...}]``
from
https://reference.wolfram.com/language/ref/SparseArray.html

``data`` must be formatted with rule.
)r  _sparse_arrayr^  _get_tuple_index)r  valuerq  r  r  r  s     r   r  @MCodePrinter._print_ImmutableSparseNDimArray.<locals>.print_data  sn     % #)););)A)A)C"DF #EJC (4+@+@+EG #EF Fs   'A
c                 :   > TR                  T R                  5      $ )zHelper function to print dimensions part of Mathematica
sparse array.

It uses the fourth notation ``SparseArray[data,{d1,d2,...}]``
from
https://reference.wolfram.com/language/ref/SparseArray.html
r  r  s   r   r  @MCodePrinter._print_ImmutableSparseNDimArray.<locals>.print_dims  s     <<

++r   r  r  )rb  rq  r  r  r  r  r  s   ``  @@@r   _print_ImmutableSparseNDimArray,MCodePrinter._print_ImmutableSparseNDimArray   s<    	A	.	K	 	"	, %++JL*,GGr   c                  ^  UR                   R                  T R                  ;   ai  T R                  UR                   R                     nU H?  u  p4U" UR                  6 (       d  M  U< ST R	                  UR                  S5      < S3s  $    OUR                   R                  T R
                  ;   au  T R
                  UR                   R                     u  pVT R                  U5      (       a:  [        U 4S jU 5       5      (       a   T R                  UR                  U5      5      $ UR                   R                  ST R	                  UR                  S5      -  -   $ )N[r  ]c              3  F   >#    U  H  nTR                  U5      v   M     g 7fri  )
_can_print)rx  frb  s     r   rz  /MCodePrinter._print_Function.<locals>.<genexpr>3  s     0Y[1C1C[r  z[%s])
r  __name__r[  r  	stringify_rewriteable_functionsr  allr  rewrite)rb  rq  
cond_mfunccondmfunctarget_frequired_fss   `      r   _print_FunctionMCodePrinter._print_Function*  s   99!5!55--dii.@.@AJ)##',dnnTYY.MNN  * YY4#>#>>$($?$?		@R@R$S!Hx((S0Y[0Y-Y-Y{{4<<#9::yy!!FT^^DIIt-L$LLLr   c                "   [        UR                  5      S:X  a-  SR                  U R                  UR                  S   5      5      $ SR                  U R                  UR                  S   5      U R                  UR                  S   5      5      $ )Nr  zProductLog[{}]r   zProductLog[{}, {}])lenr  r  r  r  s     r   _print_LambertWMCodePrinter._print_LambertW9  sp    tyy>Q#**4;;tyy|+DEE#**KK		!%t{{499Q<'@B 	Br   c                   ^  [        UR                  5      S:X  a6  UR                  S   SS  (       d  UR                  S   UR                  S   /nOUR                  nSSR	                  U 4S jU 5       5      -   S-   $ )Nr  r   zHold[Integrate[r  c              3  F   >#    U  H  nTR                  U5      v   M     g 7fri  r  r  s     r   rz  /MCodePrinter._print_Integral.<locals>.<genexpr>D  s     ,KdT\\!__dr  ]])r.  	variableslimitsr  r  )rb  rq  r  s   `  r   _print_IntegralMCodePrinter._print_Integral?  sh    t~~!#DKKN12,>IIaL$.."34D99D 499,Kd,K#KKdRRr   c                Z   ^  SSR                  U 4S jUR                   5       5      -   S-   $ )Nz	Hold[Sum[r  c              3  F   >#    U  H  nTR                  U5      v   M     g 7fri  r  r  s     r   rz  *MCodePrinter._print_Sum.<locals>.<genexpr>G  s     &J	1t||A	r  r4  )r  r  r  s   ` r   
_print_SumMCodePrinter._print_SumF  s&    TYY&J		&JJJTQQr   c                   ^  UR                   nUR                   Vs/ s H  o3S   S:X  a  US   OUPM     nnSSR                  U 4S jU/U-    5       5      -   S-   $ s  snf )Nr  r   zHold[D[r  c              3  F   >#    U  H  nTR                  U5      v   M     g 7fri  r  r  s     r   rz  1MCodePrinter._print_Derivative.<locals>.<genexpr>L  s     $NoT\\!__or  r4  )rq  variable_countr  )rb  rq  dexprr	  dvarss   `    r   _print_DerivativeMCodePrinter._print_DerivativeI  se    		373F3FG3Fa11)3FG499$Nugo$NNNQUUU Hs   Ac                $    SR                  U5      $ )Nz(* {} *)r  )rb  texts     r   _get_commentMCodePrinter._get_commentO  s      &&r   )r[  )2r!  
__module____qualname____firstlineno____doc__printmethodlanguagerZ  r	   rS  __annotations__setrT  rU  rY  rk  rs  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  _print_tuple_print_Tupler  r  r  r  r+  _print_MinMaxBaser/  r7  r<  rD  rH  __static_attributes____classcell__)r  s   @r   rM  rM  {   s    K!H(,[-J-J )O )~ 
 03uO,4!$NJ& " /=
9
!
1
DLL+H"+,H\M (BSRV' 'r   rM  c                6    [        U5      R                  U 5      $ )zConverts an expr to a string of the Wolfram Mathematica code

Examples
========

>>> from sympy import mathematica_code as mcode, symbols, sin
>>> x = symbols('x')
>>> mcode(sin(x).series(x).removeO())
'(1/120)*x^5 - 1/6*x^3 + x'
)rM  r  )rq  rc  s     r   mathematica_coderX  S  s     !))$//r   N)rM  
__future__r   typingr   
sympy.corer   r   r   sympy.core.sortingr   sympy.printing.codeprinterr	   sympy.printing.precedencer
   r[  rM  rX  r   r   r   <module>r_     sN	   #  ) ) / 2 0i	^U#$i	^U#$i 
^U#$i 
^U#$	i
 
^U#$i 
^U#$i 
^U#$i 
^U#$i nh'(i nh'(i nh'(i nh'(i nh'(i nh'(i )*i  nf%&!i" nf%&#i$ nf%&%i& nf%&'i( nf%&)i* nf%&+i, ~y)*-i. ~y)*/i0 ~y)*1i2 ~y)*3i4 ~y)*5i6 ~y)*7i8 nf%&9i: >;/0;i< 
_e$%=i> 
_e$%?i@ 
^U#$AiB ou%&CiD nf%&EiF nf%&GiH -.IiJ /0KiL ,/0MiN 01OiP 	NO,
-QiR .*-.SiT .*-.UiV ~w'(WiX OW-.YiZ ?K01[i\ .*-.]i^ ov&'_i` 	NM*
+aib 	NM*
+cid 
^^,-eif 
^^,-gih 	NM*
+iij >;/0kil NL12min nn56oip 12qir /#345sit ~x()uiv ,78wix /+;<=yiz /;/0{i| 56}i~ *-.i@ +,AiB O]34CiD O\23EiF O\23GiH /;/0IiJ 56KiL /:./MiN /:./OiP 89QiR 89SiT >#345UiV O[12WiX O[12YiZ NK01[i\ _l34]i^ ov&'_i` ~~67aib NK01cid ),-eif ),-gih ),-iij ),-kil *-.min *-.oip )*qir )*sit ^]34uiv ^]34wix ),-yiz /:./{i| 
_e$%}i~ 
_e$%i@ 	O/0
1AiB 	O/0
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