
    \h0                     >   S SK JrJrJr  S SKJrJrJr  S SKJ	r	  S SK
JrJr  S SKJrJr  S SKJr  S SKJrJr  S SKJrJrJr  S S	KJr  S S
KJrJr  S SKJrJ r   S SK!J"r"J#r#  \" S5      u  r$r%r&r'r(\" SSS9u  r)r*r+r,\" S5      r-\" S5      r.\" S5      r/\#S 5       r0S r1g)    )
DerivativeFunctiondiff)IRationalpi)Eq)Symbolsymbols)explog)sqrt)cossin)Eierferfi)Integral)checkodesolchecksysodesol)besseljbessely)raisesslowzC0:5zu,x:zT)realfghc                     [        [        S 5        [        [        S 5        [        [        [        5      R                  [        5      [        [        [        [        5      [        5      5      S[        [        5      R                  [        5      * [        [        [        5      R                  [        5      -   S-
  4:X  d   e[        [        [        5      R                  [        5      [        [        [        5      [        5      5      SLd   e[        [        [        5      R                  [        5      [        [        [        5      [        5      5      S:X  d   e[        [        [        5      S-  S[        [        5      -  -   S	[        [        5      -  -
  [        -   S
5      n [        [        U R                  [        5      U 5      S:X  d   e[        [        U R                  [        5      [        [        [        5      5      -  U 5      S:X  d   e[        [        U R                  [        S	5      U 5      S:X  d   e[        [        U R                  [        S	5      [        [        [        5      5      -  U 5      S:X  d   e[        [        U R                  [        S5      U 5      S:X  d   e[        [        U R                  [        S5      [        [        [        5      5      -  U 5      S:X  d   e[        [        U R                  [        S5      [        [        [        5      [        [        [        5      -  5      5      SS[        S-  -  [        [        5      S-   S	-  [        [        5      -   -  [        [        5      S-   -  [        [        5      S	-  -  S[        S-  -  [        [        5      S-  -  -
  S-
  4:X  d   e[        [        [        [        [        5      5      [        -   [        5      [        -  [        [        [        [        5      5      [        -   S
5      5      S:X  d   e[        [        [        [        [        5      5      [        -   [        5      [        -  [        [        [        [        5      5      [        -   S
5      SS9S:X  d   e[        [        [        5      R                  [        S	5      [        [        [        5      [        [        [        -  -   5      [        [        [        5      [        [        [        -  -   5      [        [        [        5      [        [        -  [        [        S	-  -  -   5      /5      SSS[        4/:X  d   e[        [        [        5      R                  [        S	5      [        [        [        5      [        [        [        -  -   5      [        [        [        5      [        [        [        -  -   5      [        [        [        5      [        [        -  [        [        S	-  -  -   5      15      SSS[        41:X  d   e[        [        [        5      R                  [        5      S[        [        5      -  S	-  -
  [        [        [        5      S	-  [        5      5      SS/:X  d   e[        [        [        5      R                  [        5      [        [        5      -
  [        [        [        [        5      -  [        [        5      5      5      S:X  d   e[        [        [        [        5      [        -  5      -  [        [        5      -   [        [        [        5      R                  [        5      -  -
  n[        [        [        5      [        [        [        [        -  5      [        * -  5      5      n[        X5      S   R                  [        [        5      5      (       a   e[        [        [        [        [        [        5      [        5      -  [        5      [        -  [        [        5      5      n[        [        [        5      [        [        [        [        5      -  -   [        [        5      -   [        [        5      -
  5      n[        X4S	SS9S
   (       d   e[        S	-  [        [        5      R                  [        S	5      -  [        [        [        5      R                  [        5      -  -   S	[        S	-  -  S-   [        [        5      -  -   n[        [        [        5      [        [!        S["        -  [%        S	5      [        -  5      -  [        ['        S["        -  [%        S	5      [        -  5      -  -   5      n[        XT5      S:X  d   e[        [        [        5      R                  [        5      [        [        5      [)        [        5      -   5      [        [)        [        5      R                  [        5      [        [        5      [)        [        5      -   5      /n[        [        [        5      [        * [        [        S	[        -  5      -  -   5      [        [)        [        5      [        [        [        S	[        -  5      -  -   5      /n[        Xd5      SS
S
/4:X  d   eg )Nc            	          [        [        [        [        5      R	                  [        5      [        [        [        [        5      [        5      5      $ N)r   r   xyr   r	        ^/var/www/auris/envauris/lib/python3.13/site-packages/sympy/solvers/ode/tests/test_subscheck.py<lambda>"test_checkodesol.<locals>.<lambda>   s%    {1Q7<<?BqAwNKr%   c            	          [        [        [        5      R                  [        5      [	        [        [        [
        5      [        5      [        [        [
        5      5      $ r!   )r   r   r"   r   r	   r#   r$   r%   r&   r'   r(      s2    {1Q499Q<AaG:Aw r%   F   T)Fr*            r   )Tr      <      	   )solve_for_func)orderr2      )r   
ValueErrorr   r   r"   r   r	   r#   lhsr   r   C1C2hasr   r   r   r   r   r   r   )sol1eq3sol3eqnsoleqeqss          r&   test_checkodesolrA      s    :KL
:  qtyy|R!Q^4	11!QQ/!345 5 5qtyy|R!a[1===qtyy|R!a[1Z???adAg1Q4!AaD&(1,a0DtDHHa($/9<<<tDHHa(QqT2D9YFFFtDHHa+T2i???tDHHa+C!I5t<	IIItDHHa+T2i???tDHHa+C!I5t<	IIItDHHa+R!aAh-?@	1a4#a&1*q3q612A
FAI !!Q$s1vqy 01345 	66 6 6 tC!IM1-a/C!IM11EF  tC!IM1-a/C!IM11E!*+ + +qtyyAAaD"r!t))<
1Q4bdR!bdR1Wn5)7 8	Ir{+, , , qtyyAAaD"r!t))<
1Q4bdR!bdR1Wn5)7 8	Ir{+, , , qtyy|a!fQh.1Q47A?	I  qtyy|ad*Br#a&y!A$,?@IMMM C!QK-!A$
1Q499Q<
/CadCBqD	QB()D3%a(,,QqT2222
Z*QqT1--q1!3SV
<C
QqT23q6	>CF*RU2
3Csq?BBB	
AqtyyA	!QqTYYq\"2	2a1fbj!A$5F	FB
QqT2gac4719--71Q3Q	3J0JJ
KCr9,,,adiilAaD1Q4K("QqTYYq\1Q4!A$;*G
HCadRC"S1X+%&1Q4bQqSk1A(B
CCs TAq6N222r%   c                  lH   [        S[        S9u  pn[        S5      n[        [	        U " U5      U5      SU" U5      -  5      [        [	        U" U5      U5      SU " U5      -  5      4n[        U " U5      S[
        -  [        S[        S5      -  U-  5      -  S[        -  [        S[        S5      -  U-  5      -  -   5      [        U" U5      S[        S5      -  [
        -  [        S[        S5      -  U-  5      -  S[        S5      -  [        -  [        S[        S5      -  U-  5      -  -   5      /n[        XE5      S	S
S
/4:X  d   e[        [	        U " U5      U5      SU " U5      -  SU" U5      -  -   5      [        [	        U" U5      U5      SU " U5      -  SU" U5      -  -   5      4n[        U " U5      S[
        -  [        U[        S5      * S-  [        SS5      -   -  5      -  S[        -  [        U[        S5      S-  [        SS5      -   -  5      -  -   5      [        U" U5      [
        [        S5      * S-  [        SS5      -   -  [        U[        S5      * S-  [        SS5      -   -  5      -  [        [        SS5      [        S5      S-  -   -  [        U[        S5      S-  [        SS5      -   -  5      -  -   5      /n[        XE5      S	S
S
/4:X  d   e[        [	        U " U5      U5      U " U5      U" U5      -   5      [        [	        U" U5      U5      SU " U5      -  SU" U5      -  -   5      4n[        U " U5      [
        [        [        S5      U-  S-  5      -  [        [        [        S5      U-  S-  5      -  -   [        U[        SS5      -  5      -  5      [        U" U5      [
        S-  [        S5      [        -  S-  -
  [        [        S5      U-  S-  5      -  [        S5      [
        -  S-  [        S-  -   [        [        S5      U-  S-  5      -  -   [        U[        SS5      -  5      -  5      /n[        XE5      S	S
S
/4:X  d   e[        [	        U " U5      U5      U " U5      U" U5      -   S-   5      [        [	        U" U5      U5      SU " U5      -  SU" U5      -  -   S-   5      4n[        U " U5      [
        [        U[        S5      * S-   -  5      -  [        [        U[        S5      S-   -  5      -  -   [        SS5      -
  5      [        U" U5      [
        [        S5      * S-   -  [        U[        S5      * S-   -  5      -  [        S[        S5      -   -  [        U[        S5      S-   -  5      -  -   [        SS5      -
  5      /n[        XE5      S	S
S
/4:X  d   e[        [	        U " U5      U5      U " U5      U" U5      -   S-   5      [        [	        U" U5      U5      SU " U5      -  U" U5      -   S-   5      4n[        U " U5      [
        [        [        S5      U-  5      -  [        [        [        S5      U-  5      -  -   [        U5      -  [        SS5      -
  5      [        U" U5      [        S5      [
        -  [        [        S5      U-  5      -  [        S5      [        -  [        [        S5      U-  5      -  -
  [        U5      -  [        SS5      -
  5      /n[        XE5      S	S
S
/4:X  d   e[        [	        U " U5      U5      SU-  U " U5      -  SU" U5      -  -   5      [        [	        U" U5      U5      SU " U5      -  SU-  U" U5      -  -   5      4n[        U " U5      [
        [        [        SU5      R                  5       5      -  [        [        [        SU5      R                  5       * 5      -  -   [        [        SU-  U5      R                  5       5      -  5      [        U" U5      [
        [        [        SU5      R                  5       5      -  [        [        [        SU5      R                  5       * 5      -  -
  [        [        SU-  U5      R                  5       5      -  5      /n[        XE5      S	S
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/4:X  d   e[        [	        U " U5      U5      SU-  U " U5      -  US-  U" U5      -  -   5      [        [	        U" U5      U5      US-  * U " U5      -  SU-  U" U5      -  -   5      4n[        U " U5      [
        [        [        US-  U5      R                  5       5      -  [        [        [        US-  U5      R                  5       5      -  -   [        [        SU-  U5      R                  5       5      -  5      [        U" U5      [
        * [        [        US-  U5      R                  5       5      -  [        [        [        US-  U5      R                  5       5      -  -   [        [        SU-  U5      R                  5       5      -  5      /n[        XE5      S	S
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/4:X  d   e[        [	        U " U5      U5      SU-  U " U5      -  US-  U" U5      -  -   5      [        [	        U" U5      U5      US-  * U " U5      -  SU-  SUS-  -  -   U" U5      -  -   5      4n[        U " U5      [
        [        [        S5      * S-  [        SS5      -   [        US-  U5      R                  5       -  5      -  [        [        [        S5      S-  [        SS5      -   [        US-  U5      R                  5       -  5      -  -   [        [        SU-  U5      R                  5       5      -  5      [        U" U5      [
        [        S5      * S-  [        SS5      -   -  [        [        S5      * S-  [        SS5      -   [        US-  U5      R                  5       -  5      -  [        [        S5      S-  [        SS5      -   -  [        [        S5      S-  [        SS5      -   [        US-  U5      R                  5       -  5      -  -   [        [        SU-  U5      R                  5       5      -  5      /n[        XE5      S	S
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/4:X  d   e[        [	        U " U5      X35      SU " U5      -  SU" U5      -  -   5      [        [	        U" U5      X35      U " U5      SU" U5      -  -   5      4n[        [        S5      * S-   5      * n[        [        S5      * S-   5      n[        [        S5      S-   5      * n[        [        S5      S-   5      n	[        U " U5      S[
        -  [        X6-  5      -  S[        -  [        X7-  5      -  -   S[        -  [        X8-  5      -  -   S[         -  [        X9-  5      -  -   5      [        U" U5      [
        US-  S-
  -  [        X6-  5      -  [        US-  S-
  -  [        X7-  5      -  -   [        US-  S-
  -  [        X8-  5      -  -   [         U	S-  S-
  -  [        X9-  5      -  -   5      /n[        XE5      S	S
S
/4:X  d   e[        [	        U " U5      X35      SU " U5      -  SU" U5      -  -   S-   5      [        [	        U" U5      X35      SU " U5      -  SU" U5      -  -   S-   5      4n[        [        S5      * S-  [        SS5      -   5      * n[        [        S5      * S-  [        SS5      -   5      n[        [        S5      S-  [        SS5      -   5      * n[        [        S5      S-  [        SS5      -   5      n	[        U " U5      S[
        -  [        X6-  5      -  S[        -  [        X7-  5      -  -   S[        -  [        X8-  5      -  -   S[         -  [        X9-  5      -  -   [        SS 5      -
  5      [        U" U5      [
        US-  S-
  -  [        X6-  5      -  [        US-  S-
  -  [        X7-  5      -  -   [        US-  S-
  -  [        X8-  5      -  -   [         U	S-  S-
  -  [        X9-  5      -  -   [        S!S 5      -   5      /n[        XE5      S	S
S
/4:X  d   e[        [	        U " U5      X35      S[	        U" U5      U5      -  -
  SU " U5      -  -   S
5      [        [	        U" U5      X35      S[	        U " U5      U5      -  -   SU" U5      -  -   S
5      4n[        U " U5      [
        [        U[        SS5      [        S5      S-  -   -  5      -  [        [        U[        SS5      [        S5      S-  -   -  5      -  -   [        [        U[        S5      * S-  [        SS5      -   -  5      -  -   [         [        U[        S5      * S-  [        SS5      -   -  5      -  -   5      [        U" U5      [
        * [        U[        SS5      [        S5      S-  -   -  5      -  [        [        U[        SS5      [        S5      S-  -   -  5      -  -   [        [        U[        S5      * S-  [        SS5      -   -  5      -  -
  [         [        U[        S5      * S-  [        SS5      -   -  5      -  -   5      /n[        XE5      S	S
S
/4:X  d   e[        [	        U " U5      X35      SU-  [	        U" U5      U5      -  SU" U5      -  -
  5      [        [	        U" U5      X35      SU-  [	        U " U5      U5      -  SU " U5      -  -
  5      4n[        S5      S[        S"S5      -  -  [        ["        5      -  [%        [        S5      S[        S"S5      -  -  U-  S-  5      -  S-  [        S[        S5      -  US-  -  S-  5      U-  -
  n
[        S5      * S[        S"S5      -  -  [        ["        5      -  ['        [        S5      S[        S"S5      -  -  U-  S-  5      -  S-  [        S#[        S5      -  US-  -  S-  5      U-  -
  n[        U " U5      [        U-  US[
        -  U
-  S[        -  U-  -   -  -   5      [        U" U5      [         U-  US[        S5      -  [
        -  U
-  S[        S5      -  [        -  U-  -
  -  -   5      /n[        XE5      S	S
S
/4:X  d   e[        [	        U " U5      U5      S$U " U5      -  5      [        [	        U" U5      U5      S%U " U5      -  SU" U5      -  -   5      [        [	        U" U5      U5      SU " U5      -  SU" U5      -  -   SU" U5      -  -   5      4n[        U " U5      [
        [        S$U-  5      -  5      [        U" U5      S%[
        -  [        S$U-  5      -  S&-  [        [        SU-  5      -  -   5      [        U" U5      S'[
        -  [        S$U-  5      -  S(-  S[        -  [        SU-  5      -  S-  -
  [        [        SU-  5      -  -   5      /n[        XE5      S	/ S)Q4:X  d   e[        [	        U " U5      U5      SU" U5      -  S*U" U5      -  -
  5      [        [	        U" U5      U5      SU" U5      -  SU " U5      -  -
  5      [        [	        U" U5      U5      S*U " U5      -  SU" U5      -  -
  5      4n[        U " U5      S[(        -  [        S+5      [
        -  [        [        S+5      U-  5      -  -   S[
        -  S-  S,[        -  S-  -   [        [        S+5      U-  5      -  -   5      [        U" U5      S*[(        -  [        S+5      [        -  [        [        S+5      U-  5      -  -   S-[
        -  S-  S[        -  S-  -
  [        [        S+5      U-  5      -  -   5      [        U" U5      S[(        -  [        S+5      S.[
        -  S-  S*[        -  S-  -
  -  [        [        S+5      U-  5      -  -   S*[
        -  S[        -  -
  [        [        S+5      U-  5      -  -   5      /n[        XE5      S	/ S)Q4:X  d   e[        S[	        U " U5      U5      -  S/U" U5      U" U5      -
  -  5      [        S[	        U" U5      U5      -  SU" U5      U " U5      -
  -  5      [        S[	        U" U5      U5      -  SU " U5      U" U5      -
  -  5      4n[        U " U5      [(        S[        S5      -  [
        -  [        S[        S5      -  U-  5      -  -   S[
        -  S-  S0[        -  S-  -   [        S[        S5      -  U-  5      -  -   5      [        U" U5      [(        S[        S5      -  [        -  [        S[        S5      -  U-  5      -  -   S1[
        -  S2-  S[        -  S-  -
  [        S[        S5      -  U-  5      -  -   5      [        U" U5      [(        S[        S5      -  S3[
        -  S4-  S5[        -  S4-  -
  -  [        S[        S5      -  U-  5      -  -   S[
        -  S-  S[        -  S-  -
  [        S[        S5      -  U-  5      -  -   5      /n[        XE5      S	/ S)Q4:X  d   e[        [	        U " U5      U5      SU " U5      -  U" U5      -
  5      [        [	        U" U5      U5      SU " U5      -  SU" U5      -  -   U" U5      -
  5      [        [	        U" U5      U5      SU " U5      -  U" U5      -   5      4n[        U " U5      [
        [        SU-  5      -  [        U-  [        SU-  5      -  -   [        [        SU-  5      -  -   [        US-  -  [        SU-  5      -  S-  -   [        U-  [        SU-  5      -  -   [        [        SU-  5      -  -   5      [        U" U5      [
        [        SU-  5      -  [        U-  [        SU-  5      -  -   [        [        SU-  5      -  -   [        US-  -  [        SU-  5      -  S-  -   [        U-  [        SU-  5      -  -   5      [        U" U5      S[
        -  [        SU-  5      -  S[        -  U-  [        SU-  5      -  -   [        [        SU-  5      -  -   [        US-  -  [        SU-  5      -  -   [        U-  [        SU-  5      -  -   [        [        SU-  5      -  -   5      /n[        XE5      S	/ S)Q4:X  d   e[        [	        U " U5      U5      SU " U5      -  U" U5      -
  SU" U5      -  -
  5      [        [	        U" U5      U5      SU " U5      -  U" U5      -   SU" U5      -  -
  5      [        [	        U" U5      U5      SU " U5      -  SU" U5      -  -
  5      4n[        U " U5      [
        [        SU-  5      -  [        [        U5      * S[        U5      -  -   -  -   [        S[        U5      -  [        U5      -   -  -   5      [        U" U5      [        [        U5      * S[        U5      -  -   -  [        S[        U5      -  [        U5      -   -  -   5      [        U" U5      [
        [        SU-  5      -  S[        -  [        U5      -  -   S[        -  [        U5      -  -   5      /n[        XE5      S	/ S)Q4:X  d   e[        [	        U " U5      U5      U " U5      U" U5      S-  -  5      [        [	        U" U5      U5      U" U5      S-  5      4n[        U " U5      [
        [        S6S[        -  SU-  -   -  [        S6S5      -  5      -  5      [        U" U5      S6S[        -  SU-  -   -  [        S"S5      -  * 5      [        U " U5      [
        [        S6S6S[        -  SU-  -   -  [        S"S5      -  -  5      -  5      [        U" U5      S6S[        -  SU-  -   -  [        S"S5      -  5      [        U " U5      [
        [        [*        * S6S[        -  SU-  -   -  [        S"S5      -  -  5      -  5      [        U" U5      [*        * S6S[        -  SU-  -   -  [        S"S5      -  -  5      [        U " U5      [
        [        [*        S6S[        -  SU-  -   -  [        S"S5      -  -  5      -  5      [        U" U5      [*        S6S[        -  SU-  -   -  [        S"S5      -  -  5      /n[        XE5      S	S
S
/4:X  d   e[        [	        U " U5      U5      [        SU " U5      -  5      U" U5      S-  -  5      [        [	        U" U5      U5      U" U5      S-  5      4n[        U " U5      [-        [
        SS6S[        -  SU-  -   -  [        S"S5      -  -  -
  5      * S-  5      [        U" U5      S6S[        -  SU-  -   -  [        S"S5      -  * 5      [        U " U5      [-        [
        SS6S[        -  SU-  -   -  [        S"S5      -  -  -   5      * S-  5      [        U" U5      S6S[        -  SU-  -   -  [        S"S5      -  5      [        U " U5      [-        [
        S[*        -  S6S[        -  SU-  -   -  [        S"S5      -  -  -   5      * S-  5      [        U" U5      [*        * S6S[        -  SU-  -   -  [        S"S5      -  -  5      [        U " U5      [-        [
        S[*        -  S6S[        -  SU-  -   -  [        S"S5      -  -  -
  5      * S-  5      [        U" U5      [*        S6S[        -  SU-  -   -  [        S"S5      -  -  5      /n[        XE5      S	S
S
/4:X  d   e[        U " U5      U[	        U " U5      U5      -  [	        U " U5      U5      [	        U" U5      U5      -  -   5      [        U" U5      U[	        U" U5      U5      -  [	        U" U5      U5      S-  -   5      4n[        U " U5      [
        [        -  [
        U-  -   5      [        U" U5      [        S-  [        U-  -   5      1n[        XE5      S	S
S
/4:X  d   eg )7Nzx, y, z)clstr1      ir.      Tr   r-   r0   )   i  +   '      r+         Q   :      M   /         m               r*                  )r   r   r   r,         ii      i
   ir4      )r   r   r
   r	   r   r7   r   r   r8   r   r   r   r   r   doitC3C4r   r   r   C0r   r   )r"   r#   zrD   r?   r>   root0root1root2root3I1I2s               r&   test_checksysodesolrr   M   s!"   iX.GA!sA
T!A$q\1QqT6
"BtAaD|R!W$=	>BadAbDRQZ\**QrT#aQik2B-BBCqtRQZ]3r$q'z!|,,qay|C$q'	!<L/LLMOC""taVn444
T!A$q\1QqT6AadF?
+RQqT!b1g1Q4>O-P	QBadAbDQdAQ ?@AAAbDQPTUYPZ[\P\ROQ N J E  1Q4d4j[]Xb!_%D!Ec!dSWj[YZ]RON K G "HROd4jl:;C4:a<RZ[]_`RaCa@b<cc"d efC ""taVn444
T!A$q\1Q4!A$;
'D1aL"QqT'AadF:J)K	LBadRDGAIaK((2c$q'!)A+.>+>>AhqRSnDT@UUVqtr!td1gbjl"CQ	!$44Q
1qD9	
d1gaik
8 (1a. 012 34C ""taVn444
T!A$q\1Q4!A$;?
+RQqT!a!fq1voPR>R-S	TBadBs1tAwhl+,,r#aa1o2F/FFRO 1rDG8a<0Qa15E1FFQGN JDGaK!J"  "$,QN 3 45C ""taVn444
T!A$q\1Q4!A$;+
,bad1r!A$w1~PR?R.S	TBadRDGAI&CQ	N)::CFBXbRS_TUqtd1gbjT!WQY'$q'"*Sa^*CCSVKhWZ\]N^^_aC""taVn444
T!A$q\1Q3qt8a!f,
-r$qtA,!A$1QqT@Q/R	SBadRHQN//122Rhq!n=R=R=T<T8U5UU!A#q	!"# $%'!r#x1~6K6K6M2N/NsXa^!!##$$0%&)8AaC+;*A*A*C&D/E &FGC ""taVn444
T!A$q\1Q3qt8ad1Q4i/
0"T!A$q\AqD51:PQRSPSTUVWTXPXCX2Y	ZBadRXadA.44677"S(1a4QRBSAYAYA[=\:\\!A#q	!"# $%'!s3Aq8I7O7O7Q3R/RsHQT1##%&&0'(+Xac1-=,C,C,E(F/G &HIC ""taVn444
T!A$q\1Q3qt8ad1Q4i/
0"T!A$q\AqD51:QRSTQTUVWXZ[W[U[Q[]^_`]aPaCa2b	cBadRd2hYq[8Aq>9HQT1<M;S;S;UUVVsDHQJ!Q'(1a4*;)A)A)CCDDEFI8TUVWTWYZK[JaJaJcFde fqtb48)A+A./d2hYq[8Aq>5QT\]^`a]acdTeSkSkSm4m0nnR
Xa^#$S$r(1*x1~*EQRTUQUWXHYG_G_Ga)a%bbcdgiqrsturuwxiyhh  iB  eCC DEC ""taVn444
T!A$q^QqtVb1g-
.4!Q>1Q4!AaD&=0Q	RB48)a-  E$r(QE$r(Q,EbAEadBrE#ag,&Bs17|);;beCL>PPSUVXSXY\]^]dYeSeefqtRAs17|+b%(Q,.?AG.LLq1c!'l"#%'A%6s17|%CD EFC ""taVn444
T!A$q^QqtVAadF]2-
.4!Q>1QqT6!AaD&=QSCS0T	UB49*Q,"a011E$s)AQ/0E$s)A+Q/00Ec1xA./EadAbDQW%"S\(99AbDQW<MMPQRTPTUXYZY`UaPaadlmprtduuvqtRAs17|+b%(Q,.?AG.LLq1c!'l"#%'A%6s17|%CDFNsTVFWX YZC ""taVn444
T!A$q^aQqT!n,q1v5a
8"T!A$q^aPTUVWXUYZ[P\n=\_`abcdae_e=efg:h	iBadBs1hq!ntCy{:;<<r#aRSUVZ^_bZcdeZeIeFfBg?ggs1tCyjlXa^+,--.023q49*Q,RSUV:W7X3Y0YZ [\^_`ab_cfhehilmnpxyz|}p~  BF  GJ  BK  LM  BM  qM  nN  jO  fOQAc1,-	..f/13CDI:a<(STVW.;X8Y4Z1Zf[]_`cdehlmphqgqrsgsv~  @A  CD  wE  hE  eF  aG  ^GfG ]HIC ""taVn444
T!A$q^QqSad1-a!f4
5r$qtA.1TRSTURVWX\IYZ[\]^_\`Z`I`7a	bB	aHQN"	"48	+DaHQN9J1J11LQ1N,O	OPQ	QTWXYZ^_`ZaXabcefbfXfghXhTijkTk	kB
q'!Xa^#	#DH	,SaHQN9J1J11LQ1N-O	OPQ	QTWXZ[_`a[bXbcdfgcgXghiXiTjklTl	lBadBqD1ad2g"R/0012adBqD1aQiPRlSUoXYZ^_`ZaXabdXdegXgFgCh<h3i
jC""taVn444
T!A$q\2ad7
#RQqT!b1ga!fn%Er$qQRtTU,XYZ[\]Z^X^_`abcdae_eXefghijkhlflXlGm	nBadBs2a4yL!2adBrE#bd)OB,>C!H,L#MqtSVC1Ic!AbDQqSM!O3bQqSkABDC""tY&7777
T!A$q\!AaD&AaD.
)"T!A$q\!AaD&1Q4-*HDQRSTQUVWLY[\]^_\`Y`abcdefcgagYgIh	iBadAbD49R<DIaK(888BrE!Gc"fQh<NPSTXY\T]^_T_P`;``aqtRUT#Yr\#d3ik"222c"fQhBq6H#dSViXYkJZ5ZZ[qtQrTDIr"uQwBq01#d3ik2BBBbeaPRdlTWX\]`XabcXcTdEddegC ""tY&7777
QtAaD|^C1adO
,R$qtA,sAaD1I-OPRSTUYZ[\]Z^_`UaSabeghijgklmnolpgpbqPr	sBadB472c!DG)A+&666"R%'CF2I:MsSTUYZ[U\S\]^S^O_9__`qtR!DG)B,s1T!W9Q;///3r6"9r"uQw3FAdSTgIVWKHX2XXYqtR!DG)RU2X2b01#aQik2BBBbeAgPRSUPUVWPWFWY\]^_cde_f]fgh]hYiEiijlC ""tY&7777
T!A$q\!AaD&1Q4-
(D1aL1Q4!A$qt9K)LRPTUVWXUYZ[P\]^_`ab_c]cdefgdh]hMi	jBadBs1Q3xK"Q$s1Q3x-/"S1X+=1a4AaC@PQR@RRUWXYUYZ]^_`a^aZbUbbeghklmnolohpeppqqtRAaC[2a4AaC=(2c!A#h;6AqDQqS9I!9KKbQRdSVWXYZWZS[m[\qtQrT#ac(]QrT!VC!H_,r#ac({:R1WS1X=MMPRSTPTUXYZ[\Y\U]P]]`bcfghijgjck`kklnC ""tY&7777
T!A$q\!AaD&1Q4-!AaD&0
1"T!A$q\!AaD&1Q4-QRSTUVSWQWBW2XY[\`abcdaefg\hijklmnkoiopqrsturvpvivYw	xBadBs1Q3xK"s1vg#a&&8"99B#a&3q6@Q<RRSqtR#a&1SV8#$r1SV8c!f+<'==>1Q4CPQRSPSHWXY[W[\_`a\bWbIbefgieijmnojpepIp@qsC""tY&7777
T!A$q\!A$qtQw,
'D1aL1q)A	BBadBsB"qs
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