
    i                        S SK r S SKrS SKrS SKJrJr  S SKJrJrJ	r	J
r
JrJrJrJrJr  S SKrS SKJr  S SKJrJr  S SKJrJrJrJrJrJrJrJ r J!r!J"r"J#r#J$r$J%r%J&r'J(r(J)r*  S SK+J,r-  S SK.J/r/  S S	K0J1r1  S S
K2J3r3  S SK4J5r5  S SK6J7r7  S SK8J9r9J:r:J;r;J<r<  S SK=J>r>  S SK?J@r@  S\AS\AS\4S jrB\(       a	  S SKCJDrDJErE  O	\B" SS5      rE\B" SS5      rF\B" SS5      rG\B" SS5      rH/ SQrISrJ\K" S \R                  R                  S5      SS   5       5      S!:  rN\>" S"S#9SS SSSSSSSSS SS$.S%\R                  S&\R                  \A   S-  S'\QS(\QS-  S)\Q\R-  S-  S*\Q\R-  S-  S+\SS-  S,\SS-  S-\SS-  S.\SS-  S/\SS-  S0\7S1\7S-  S\R                  \   4S2 jj5       rT " S3 S4\R                  5      rUSS5 jrV\
" S6S7S89rW\
" S9S:S89rX\SSS;S<.S%\S=\R                  S=   4   S>\Q\R                  \Q   -  \-  \R                  \   -  S?\R                  \   \\A\4   -  S-  S@\R                  \   S-  SA\SSSB4SC jj5       rY\SSS;S<.S%\W\R                  \W   -  S>\Q\R                  \Q   -  \-  \R                  \   -  S?\R                  \   \\A\4   -  S-  S@\R                  \   S-  SA\SSSD4SE jj5       rY\>" S"S#9SSS;S<.S%\W\R                  \W   -  S>\Q\R                  \Q   -  \-  \R                  \   -  S?\R                  \   \\A\4   -  S-  S@\R                  \   S-  SA\SSSD4SF jj5       rY\>" 5       S\R                  \R                     4SG j5       rZSH\;S\;4SI jr[\[S\R                  SJ   4SK j5       r\SL r]\SMSN.SO\ASP\	SQ   S\R                  SR   4SS jj5       r^\SMSN.SO\ASP\	ST   S\R                  SU   4SV jj5       r^\SMSN.SO\ASP\	SW   S\R                  SX   4SY jj5       r^\SMSN.SO\ASP\	SZ   S\R                  S[   4S\ jj5       r^\SMS]S^.SO\ASP\\	S]      S\R                  S_   4S` jj5       r^\[SMS]S^.SO\ASP\	S]   \\	S]      -  S\R                  S_   4Sa jj5       r^\SMSN.SO\ASP\	SQ   S\R                  Sb   4Sc jj5       r_\SMSN.SO\ASP\	ST   S\R                  Sd   4Se jj5       r_\SMSN.SO\ASP\	SW   S\R                  Sf   4Sg jj5       r_\SMSN.SO\ASP\	SZ   S\R                  Sh   4Si jj5       r_\SMS]S^.SO\ASP\\	S]      S\R                  Sj   4Sk jj5       r_\[SMS]S^.SO\ASP\	S]   \\	S]      -  S\R                  Sj   4Sl jj5       r_\SMSN.SO\ASP\	ST   S\R                  Sm   4Sn jj5       r`\SMSN.SO\ASP\	SW   S\R                  So   4Sp jj5       r`\SMSN.SO\ASP\	SZ   S\R                  Sq   4Sr jj5       r`\SMSN.SO\ASP\	Ss   S\R                  St   4Su jj5       r`\SMSvS^.SO\ASP\\	Sw      S\R                  Sx   4Sy jj5       r`\[SMSvS^.SO\ASP\	Sw   \\	Sw      -  S\R                  Sx   4Sz jj5       r`\SMSN.SO\ASP\	SZ   S\R                  S{   4S| jj5       ra\SMSN.SO\ASP\	Ss   S\R                  S}   4S~ jj5       ra\SMSN.SO\ASP\	S   S\R                  S   4S jj5       ra\SMSS^.SO\ASP\\	S      S\R                  S   4S jj5       ra\[SMSS^.SO\ASP\	S   \\	S      -  S\R                  S   4S jj5       ra\/S 5       rb\[SSSMS.S\AS\ASO\AS\R                  S   4S jj5       rc\[SSSMS.S\AS\ASO\AS\R                  S   4S jj5       rd\[SMSSTS.SO\AS\QS\QS\R                  S   4S jj5       re\[SMSSTS.SO\AS\QS\QS\R                  S   4S jj5       rfS rg\[\Z" 5       4SSS;S.S\R                  \R                     S'\QS(\QS\SS\R                  \R                     4
S jjj5       rh\>" 5       \Z" 5       4SSS.S\R                  \R                     S\QS\QS-  S\R                  \R                     4S jjj5       ri\1" \*5      S 5       r)S\*R                   S3\)lj        \1" \'5      S 5       r&S\'R                   S3\&lj        \S SSS.S>\S\QS\QS-  S\	S;   S\	S;   S\R                  \ \K\ S4   -     4S jj5       rk\S SSSS.S>\S\QS\QS-  S\	S;   S\	S"   S\R                  \!\K\!S4   -     4S jj5       rk\S SS.S>\S\QS\QS-  S\	S"   S\	S;   S\R                  \\K\S4   -     4S jj5       rk\S SSS.S>\S\QS\QS-  S\	S"   S\	S"   S\R                  \\K\S4   -     4S jj5       rk\>" 5       S SS;S"S.S>\S\QS\QS-  S\SS\SS\R                  \   4S jj5       rk\
" S\R                  S89rm\\"" 5       S.S>\S\R                  \   SS4S jj5       rn\\"" 5       S.S>\S\R                  \   S%SSS4S jj5       rn\>" 5       \"" 5       \R                  " \Q5      S.S>\S\R                  \   S%SSS4S jj5       rnS roS rpS\q\9   S\R                  \9   S-  4S jrrg)    N)MappingSequence)	TYPE_CHECKINGAnyLiteralTypeVarUnioncastget_args
get_originoverload)
strategies)HypothesisExceptionInvalidArgument)_BIENDIM_MAX
BasicIndexBasicIndexStrategyBroadcastableShapesShape_BIENoEllipsis_BIENoEllipsisNoNewaxis_BIENoNewaxisarray_shapesbroadcastable_shapescheck_argumentcheck_valid_dimsmutually_broadcastable_shapesorder_checkvalid_tuple_axes)utils)check_function)proxies)
check_type)unwrap_strategies)Real)ExMappedStrategyTcheck_strategy)defines_strategy)note_deprecationmod_name	attr_namereturnc                 x    SU;  d   e [         R                  " U 5      n[        X!S 5      $ ! [         a     g f = f)N.)	importlibimport_modulegetattrImportError)r-   r.   mods      U/var/www/html/ai-image-ml/venv/lib/python3.13/site-packages/hypothesis/extra/numpy.py_try_importr8   A   sD    i%%h/st,, s   !, 
99)	DTypeLikeNDArrayznumpy.typingr:   	ArrayLikeznumpy._typing._nested_sequence_NestedSequenceznumpy._typing._array_like_SupportsArray)r   array_dtypesr   arraysbasic_indicesboolean_dtypesr   byte_string_dtypescomplex_number_dtypesdatetime64_dtypesfloating_dtypes
from_dtypeinteger_array_indicesinteger_dtypesr   nested_dtypesscalar_dtypestimedelta64_dtypesunicode_string_dtypesunsigned_integer_dtypesr    )YMDhmsmsusnspsfsasc              #   8   #    U  H  n[        U5      v   M     g 7fN)int.0xs     r7   	<genexpr>r`   n   s     G)FAQ)Fs   r1      )      T)force_reusable_values)alphabetmin_sizemax_size	min_value	max_value	allow_nanallow_infinityallow_subnormalexclude_minexclude_maxmin_magnitudemax_magnitudedtypere   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   c                  ^ ^ [        [        R                  T S5        [        5       R	                  5        VVs0 s H  u  pUS:w  d  M  Uc  M  X_M     snnmT R
                  bV  T R                  bI  T R
                   Vs/ s H  n[        T R                  U   S   40 TD6PM!     nn[        R                  " U6 $ T R                  b  T R                  u  nn[        UUTS9$ U U4S jnT R                  S:X  a  [        R                  " 5       nGO2T R                  S:X  aN  [        R                  " S/S[        [         S	   [#        S
T R$                  -  S5      5      0U" SSSSSSS5      D6nGOT R                  S:X  aL  [        R&                  " S/S[        [         S   [#        S
T R$                  -  S5      5      0U" SSSSS5      D6nGOxT R                  S;   aB  T R$                  =(       d    Sn[        R(                  " S/0 U" SUS9D6R+                  S 5      nGO&T R                  S:X  a2  U" SSS
T R$                  -  -  S-
  S9n[        R,                  " S/0 UD6nGOT R                  S :X  a6  SS
T R$                  -  S-
  -  n[        R,                  " S/0 U" U* US-
  S9D6nGOT R                  S!:X  ax  T R$                  =(       d    SS"-  =(       d    Sn[.        (       a  S#T;  a  [        R0                  " 5       TS#'   [        R2                  " S/0 U" S#SUS9D6R+                  S$ 5      nGOT R                  S%;   a  S&T R4                  ;   a6  [        R6                  " T R4                  R9                  S&5      S'   SS' 5      nO[        R:                  " [<        5      nUS(La/  [        R,                  " S)S*5      [        R6                  " S+5      -  nO[        R,                  " S,S*5      n[        R>                  " T R@                  UU5      nO8T R                  S-:X  a  [        RB                  " [D        5      $ [G        S.T  35      eURI                  T R@                  5      $ s  snnf s  snf )0a  Creates a strategy which can generate any value of the given dtype.

Compatible parameters are passed to the inferred strategy function while
inapplicable ones are ignored.
This allows you, for example, to customise the min and max values,
control the length or contents of strings, or exclude non-finite
numbers. This is particularly useful when kwargs are passed through from
:func:`arrays` which allow a variety of numeric dtypes, as it seamlessly
handles the ``width`` or representable bounds for you.
rq   Nr   )elementsc            
        > 1 SkR                  U5      (       d   e[        T5      R                  U5       H  nST< SU STU   < SX   < 3nX   c  M   UR                  S5      (       a  X   TU   :  a  [	        US-  5      eUR                  S5      (       d  Mg  X   TU   :  d  Mt  [	        US	-  5      e   UR                  TR                  5        VVs0 s H  u  pEX@;   d  XA;   d  M  XE_M     snn5        U$ s  snnf )
zDUpdate default args to the strategy with user-supplied keyword args.>   rg   ri   rh   zdtype z
 requires =z
 to be %s min_)zat leastmax_)zat most)
issupersetsetintersection
startswithr   updateitems)argskwkeymsgkvrq   kwargss         r7   	compat_kwfrom_dtype.<locals>.compat_kw   s    5@@DDDDv;++B/C5):cU!F3K?*RWKXCw">>&))bgs.C)#*=>>^^F++&+0E)#*<== 0 			FLLNKNDAai17414NKL	 Ls   C<
,C<
bfwidth       @      r   rh   ri   rj   rk   rl   rm   rn   c)r   r      r   ro   rp   )Sarf   )rg   c                     U SS  S:g  $ )N     r   s    r7   <lambda>from_dtype.<locals>.<lambda>   s    afo    ura   rb   )rh   ri   iU   re   c                     U SS  S:g  $ )Nr    r   r   s    r7   r   r      s    afnr   rR   rO   [r   Fl         l    NaTl OzNo strategy inference for r   )%r$   nprq   localsr}   namesfieldsrF   sttuplessubdtyper?   kindbooleansfloatsr
   r   minitemsizecomplex_numbersbinaryfilterintegersNP_FIXED_UNICODE
characterstextstrjustsplitsampled_fromTIME_RESOLUTIONSbuildstype	from_typeobjectr   map)rq   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   r   r   namesubssubtypeshaper   resultr   overflowreselemsr   s   `                        @r7   rF   rF   q   s   6 rxx(%x~~/R/tq1<dAdad/RF {{5<<#;HMT
5<<-a0;F;Tyy$ ~~!guv66 zzS)+	s	 
wz*CENN0BB,GH
 !
 
s	## 
$c!enn*<c&B
  !	
 
z	! >>)TFYzHEFMM%
 
s	aA4F.G!.KL"r"	s	U^^+a/0VyH9STUV	s	NN'aA-5
& 8!#F:P9ZhOPWW$
 
z	!%))''%))//#.r23B78C
 //"23CE!KK)4rwwu~EEKKi8E5::uc2	s	||F## :5'BCC::ejj!!{ S
 Us   Q	QQ &Q#c                   B   ^  \ rS rSrU 4S jrS rSS.S jrS rSrU =r	$ )	ArrayStrategy   c                    > [         TU ]  5         [        U5      U l        X@l        [        [        R                  " U5      5      U l        X0l	        Xl
        XPl        UR                  S;  U l        g )N)r   V)super__init__tupler   fillr\   r   prod
array_sizerq   element_strategyuniquer   _check_elements)selfr   r   rq   r   r   	__class__s         r7   r   ArrayStrategy.__init__   sS    5\
	bggen-
 0$zz;r   c                     SU R                   < SU R                   SU R                  < SU R                  < SU R                  < S3$ )NzArrayStrategy(z, shape=z, dtype=z, fill=z	, unique=))r   r   rq   r   r   )r   s    r7   __repr__ArrayStrategy.__repr__   sJ    T225Xdjj\ JZZN'$))iaQ	
r   Fr   c                X    XU'    U R
                  =(       a    XU   :g  =(       a    X:H  nU(       a  U(       a  U R                  OU R                  nU R                  R                  S:X  af   S[        U5      s=:  =(       a-    [        R                  " U R                  5      R                  :  Os  nU(       a  [        S
U SU SX#   < S35      e[        SU< SU< SU R                  < SX#   < S[        X#   5      < S35      eg ! [          a;  n[        SU< S[        US[        U5      5       SUR                  < S35      UeS nAff = f! [         a;  n[        SU< S[        US[        U5      5      < SUR                  < 35      UeS nAff = f! [         a    S	n Nf = f)NzCould not add element=z of rq   z to array of z- - possible mismatch of time units in dtypes?z%Internal error when checking element=r   r   FzGenerated subnormal float z from strategy z resulted in zx, probably as a result of NumPy being built with flush-to-zero compiler options. Consider passing allow_subnormal=False.zGenerated array element z from   cannot be represented as dtype z - instead it becomes z (type zc).  Consider using a more precise strategy, for example passing the `width` argument to `floats()`.)	TypeErrorr   r4   r   rq   r   	Exceptionr   r   r   r   absr   finfotiny)	r   valr   idxr   errelem_changedstrategyis_subnormals	            r7   set_elementArrayStrategy.set_element   s   	3K		//UC#;4FU3:L $(tyyd.C.CHzz#%)#$s3x#K#K"((4::2F2K2K#KL
  )4SE#*M&+ A11  "*3'| D((,

~5K;/fk):(= >!! ) %  	!(t3c34M<<""OQ 		  	 &7wd3c36m<<"$ 		" ! ) $)L)sA   D
 %E -AF 

E6E

E
F6FFF)(F)c                    SU R                   ;   a)  [        R                  " U R                  U R                   S9$ U R                  R                  S;   =(       a    U R                  R
                  S:H  n[        R                  " U R                  U(       a  [        OU R                  S9nU R                  R                  (       a  U R                  (       al  [        R                  " U R                  U R                  U R                  SS9n[        UR                  U5      5       H  u  pVU R!                  XcU5        M     GO[#        [%        U5      5       H.  nU R!                  UR                  U R                  5      X55        M0     GOF[&        R(                  " USU R                  [+        SU R                  -  [-        S[.        R0                  " U R                  5      5      5      S	9n[        R2                  " U R                  S5      n[5        5       n	UR7                  5       (       a  UR9                  SU R                  S
-
  5      nX   (       d  UR;                  5         MO  U R!                  UR                  U R                  5      X55        U R                  (       a-  X5   U	;   a  UR;                  5         M  U	R=                  X5   5        SX'   UR7                  5       (       a  M  UR?                  5       (       a  [        R                  " S
U(       a  [        OU R                  S9n
U R!                  UR                  U R                  5      U
SSS9  U(       a  U
RA                  U R                  5      n
U
S   nU R                  (       a-   [        RB                  " U5      nU(       d  [G        SU< 35      e[        RH                  " X8U
5        U(       a\  URA                  U R                  5      nX:g  nUR?                  5       (       a&  [G        SX>   < SU R                  < SX   < S35      eUnURK                  U R                   5      RM                  5       nURN                  b   eU$ ! [D         a    Sn Nf = f)Nr   )rq   r   )r   r   r   )r   rq   T)rf   rg   r   g?
   )rf   rg   average_sizerb   Fr   z,Cannot fill unique array with non-NaN value zArray elements r   z - instead they become zk.  Use a more precise strategy, e.g. without trailing null bytes, as this will be an error future versions.)(r   r   zerosrq   r   r   r   r   r   is_emptyr   r   listsr   	enumeratedrawr   rangelencumanyr   maxmathsqrtfullry   moredraw_integerrejectaddanyastypeisnanr   r   putmaskreshapecopybase)r   dataunsized_string_dtyper   r   r   r   rs   
needs_fillseenone_element
fill_valueis_nanoutmismatchs                  r7   do_drawArrayStrategy.do_draw4  s{   

?88$**DJJ??
 JJOO.K4::3F3F!3K 	 //3GTZZ
 99 {{))!__!__	 &dii&67DA$$Q2 8 s6{+A$$TYYt/D/D%EvQ , ww !$//)DIIdoo67H $7J5D--//%%a1)<=!}OO%  4+@+@!A6M;;yD( ) HHVY' %
 --// ~~ !hh-A6tzz   499!5{AD Q'"-"4"4TZZ"@K(^
;;'!#*!5 "-J:.Y  

6{;--

+C}H||~~%%f&6%9 :  $

~-D}' (UU  F

+002{{"""5 % '!&'s   Q, ,Q;:Q;)r   r   rq   r   r   r   r   )
__name__
__module____qualname____firstlineno__r   r   r   r  __static_attributes____classcell__)r   s   @r7   r   r      s$    <
 5: 4lx xr   r   c                     Uc4  U(       d  U R                   (       d  [        R                  " 5       nU$ U n U$ [        X#(       a  U S3OS5        U$ )Nz.fillr   )has_reusable_valuesr   nothingr*   )rs   r   r   r   s       r7   fill_forr    sM    |55::<D
 K D K 	ttvU^@Kr   rP   r9   )boundGz
np.genericFrs   r   r   znp.dtype[G]r   rs   r   r   zst.SearchStrategy[NDArray[G]]c                    g r[   r   rq   r   rs   r   r   s        r7   r?   r?     s     '*r   zst.SearchStrategy[NDArray[Any]]c                    g r[   r   r#  s        r7   r?   r?     s     ),r   c                  ^ ^^^^ [        T 5      [        [        S[        5       5      [        4;   a$  [
        R                  " S T R                   5       6 m [        T [
        R                  5      (       a  T R                  UUUU4S j5      $ [        T[
        R                  5      (       a  TR                  U UUU4S j5      $ [        R                  " T 5      m [        T [        R                  5      (       d   eTb  [        T[        5      (       a  T R                  S;   ae  ST R                  ;  aU  [
        R                   " ["        5      R%                  T R                  S-   R&                  5      R                  UUU4S j5      $ [)        T 40 T=(       d    0 D6m[+        TS	5        [-        T5      n[        U[.        5      (       a?  UR0                  T R                   :X  a%  UR2                  m[        US
S5      (       a  STl        [        T[6        5      (       a  T4m[9        T5      m[;        [=        S T 5       5      ST5        [?        TTTS9m[A        TTT TT5      $ )a  Returns a strategy for generating :class:`numpy:numpy.ndarray`\ s.

* ``dtype`` may be any valid input to :class:`~numpy:numpy.dtype`
  (this includes :class:`~numpy:numpy.dtype` objects), or a strategy that
  generates such values.
* ``shape`` may be an integer >= 0, a tuple of such integers, or a
  strategy that generates such values.
* ``elements`` is a strategy for generating values to put in the array.
  If it is None a suitable value will be inferred based on the dtype,
  which may give any legal value (including eg NaN for floats).
  If a mapping, it will be passed as ``**kwargs`` to ``from_dtype()``
* ``fill`` is a strategy that may be used to generate a single background
  value for the array. If None, a suitable default will be inferred
  based on the other arguments. If set to
  :func:`~hypothesis.strategies.nothing` then filling
  behaviour will be disabled entirely and every element will be generated
  independently.
* ``unique`` specifies if the elements of the array should all be
  distinct from one another. Note that in this case multiple NaN values
  may still be allowed. If fill is also set, the only valid values for
  it to return are NaN values (anything for which :obj:`numpy:numpy.isnan`
  returns True. So e.g. for complex numbers ``nan+1j`` is also a valid fill).
  Note that if ``unique`` is set to ``True`` the generated values must be
  hashable.

Arrays of specified ``dtype`` and ``shape`` are generated for example
like this:

.. code-block:: pycon

  >>> import numpy as np
  >>> arrays(np.int8, (2, 3)).example()
  array([[-8,  6,  3],
         [-6,  4,  6]], dtype=int8)
  >>> arrays(np.float, 3, elements=st.floats(0, 1)).example()
  array([ 0.88974794,  0.77387938,  0.1977879 ])

Array values are generated in two parts:

1. Some subset of the coordinates of the array are populated with a value
   drawn from the elements strategy (or its inferred form).
2. If any coordinates were not assigned in the previous step, a single
   value is drawn from the ``fill`` strategy and is assigned to all remaining
   places.

You can set :func:`fill=nothing() <hypothesis.strategies.nothing>` to
disable this behaviour and draw a value for every element.

If ``fill=None``, then it will attempt to infer the correct behaviour
automatically. If ``unique`` is ``True``, no filling will occur by default.
Otherwise, if it looks safe to reuse the values of elements across
multiple coordinates (this will be the case for any inferred strategy, and
for most of the builtins, but is not the case for mutable values or
strategies built with flatmap, map, composite, etc) then it will use the
elements strategy as the fill, else it will default to having no fill.

Having a fill helps Hypothesis craft high quality examples, but its
main importance is when the array generated is large: Hypothesis is
primarily designed around testing small examples. If you have arrays with
hundreds or more elements, having a fill value is essential if you want
your tests to run in reasonable time.
	UnionTypec              3   `   #    U  H$  n[        [        R                  " U5      5      v   M&     g 7fr[   )rF   r   rq   )r^   ds     r7   r`   arrays.<locals>.<genexpr>  s      L^Jrxx{33^s   ,.c                    > [        U TTTTS9$ Nr!  r?   )r(  rs   r   r   r   s    r7   r   arrays.<locals>.<lambda>'  s    fQtFSr   c                    > [        TU TTTS9$ r+  r,  )rS   rq   rs   r   r   s    r7   r   r-  +  s    fUAtFSr   r   r   z[{}]c                    > [        U TTTS9$ )N)r   r   r   r,  )r(  r   r   r   s    r7   r   r-  9  s    6!5tF#Sr   rs   force_has_reusable_valuesFTc              3   B   #    U  H  n[        U[        5      v   M     g 7fr[   
isinstancer\   r^   rS   s     r7   r`   r)  H  s     .1Jq#   zDArray shape must be integer in each dimension, provided shape was {})rs   r   r   )!r   r4   typesr   r	   r   one_of__args__r3  SearchStrategyflatmapr   rq   r   r   r   r   r   r   formatrF   r*   r%   r(   packmapped_strategyr0  r\   r   r   allr  r   )rq   r   rs   r   r   	unwrappeds   ````` r7   r?   r?     s   R E{wuk68<eDD		LU^^LM %**++}}S
 	
 %**++}}S
 	
 HHUOEeRXX&&&&:h88::#599(<  01eii&(001ST
 e8B88Z( "(+I)^,,5::1M,,995AA15H.%%LE...N
 Xf4@D5%v>>r   c            
          [         R                  " [        5       [        5       [	        5       [        5       [        5       [        5       [        5       5      $ )z@Return a strategy that can return any non-flexible scalar dtype.)	r   r7  rA   rH   rM   rE   rC   rD   rK   r   r   r7   rJ   rJ   P  s?     99! r   stratc                 J   ^  [        5       [        T 5      U 4S j5       5       nU$ )Nc                  N   > T" U 0 UD6R                  [        R                  5      $ r[   )r   r   rq   )r~   r   rA  s     r7   inner%defines_dtype_strategy.<locals>.inner_  s$     d%f%))"((33r   )r+   r#   )rA  rD  s   ` r7   defines_dtype_strategyrF  ^  s+    U^4  4 Lr   znp.dtype[np.bool_]c                  .    [         R                  " S5      $ )z%Return a strategy for boolean dtypes.?)r   r   r   r   r7   rA   rA   g  s     773<r   c                 .  ^ Sn[        X4;   SUU5        Tbz  [        U[        5      (       a  U4n[        US5        [        [        U4S jU 5       5      SUT5        [        S U 5       5      (       a  [	        U Vs1 s H  oUS-  iM	     sn5      n[
        R                  " U5      nSU ;  a  U S-  n US	:X  a=  UR                  S
U -   R                  5      UR                  SU -   R                  5      -  $ UR                  X0-   R                  5      $ s  snf )N)rH  <ru   >z)Unknown endianness: was {}, must be in {}z+Dtype must have at least one possible size.c              3   ,   >#    U  H	  oT;   v   M     g 7fr[   r   )r^   rS   valid_sizess     r7   r`    dtype_factory.<locals>.<genexpr>{  s     0%Q[ %s   z7Invalid sizes: was {} must be an item or sequence in {}c              3   B   #    U  H  n[        U[        5      v   M     g 7fr[   r2  r4  s     r7   r`   rN    s     15az!S!!5r5  r   z{}rH  rJ  rK  )	r   r3  r\   r>  sortedr   r   r   r;  )r   sizesrM  
endiannessvalid_endianrS   rA  s     `    r7   dtype_factoryrT  m  s   'L"3	 eS!!HEuKL0%00E		
 15111E2EqFE23EOOE"E4Syy#*,,-		3::M:M0NNN99j'//00 3s   <DrH  )rR  rR  rQ  r   znp.dtype[np.uint8]c                     g r[   r   rR  rQ  s     r7   rM   rM         
 /2r   r   znp.dtype[np.uint16]c                     g r[   r   rV  s     r7   rM   rM         
 03r   r   znp.dtype[np.uint32]c                     g r[   r   rV  s     r7   rM   rM     rY  r   r   znp.dtype[np.uint64]c                     g r[   r   rV  s     r7   rM   rM     rY  r   r   r   r   r   rV  z!np.dtype[np.unsignedinteger[Any]]c                     g r[   r   rV  s     r7   rM   rM     s    
 >Ar   c                     [        SUSU 5      $ )ab  Return a strategy for unsigned integer dtypes.

endianness may be ``<`` for little-endian, ``>`` for big-endian,
``=`` for native byte order, or ``?`` to allow either byte order.
This argument only applies to dtypes of more than one byte.

sizes must be a collection of integer sizes in bits.  The default
(8, 16, 32, 64) covers the full range of sizes.
r   r\  rT  rV  s     r7   rM   rM     s    ( e_jAAr   znp.dtype[np.int8]c                     g r[   r   rV  s     r7   rH   rH     s    
 .1r   znp.dtype[np.int16]c                     g r[   r   rV  s     r7   rH   rH     rW  r   znp.dtype[np.int32]c                     g r[   r   rV  s     r7   rH   rH     rW  r   znp.dtype[np.int64]c                     g r[   r   rV  s     r7   rH   rH     rW  r   znp.dtype[np.signedinteger[Any]]c                     g r[   r   rV  s     r7   rH   rH     s    
 <?r   c                     [        SUSU 5      $ )zwReturn a strategy for signed integer dtypes.

endianness and sizes are treated as for
:func:`unsigned_integer_dtypes`.
r   r\  r_  rV  s     r7   rH   rH     s      e_jAAr   znp.dtype[np.float16]c                     g r[   r   rV  s     r7   rE   rE         
 14r   znp.dtype[np.float32]c                     g r[   r   rV  s     r7   rE   rE     rg  r   znp.dtype[np.float64]c                     g r[   r   rV  s     r7   rE   rE     rg  r   r   znp.dtype[np.float128]c                     g r[   r   rV  s     r7   rE   rE     s    
 25r   r   r   r   r   `   r   znp.dtype[np.floating[Any]]c                     g r[   r   rV  s     r7   rE   rE   $  s    
 7:r   c                     [        SUSU 5      $ )ap  Return a strategy for floating-point dtypes.

sizes is the size in bits of floating-point number.  Some machines support
96- or 128-bit floats, but these are not generated by default.

Larger floats (96 and 128 bit real parts) are not supported on all
platforms and therefore disabled by default.  To generate these dtypes,
include these values in the sizes argument.
r   rk  r_  rV  s     r7   rE   rE   ,  s    & e%:JGGr   znp.dtype[np.complex64]c                     g r[   r   rV  s     r7   rC   rC   B  s    
 36r   znp.dtype[np.complex128]c                     g r[   r   rV  s     r7   rC   rC   J      
 47r      znp.dtype[np.complex256]c                     g r[   r   rV  s     r7   rC   rC   R  rq  r   )r   r   r   r      rr  z&np.dtype[np.complexfloating[Any, Any]]c                     g r[   r   rV  s     r7   rC   rC   Z  s	    
 CFr   c                     [        SUSU 5      $ )zReturn a strategy for complex-number dtypes.

sizes is the total size in bits of a complex number, which consists
of two floats.  Complex halves (a 16-bit real part) are not supported
by numpy and will not be generated by this strategy.
r   rt  r_  rV  s     r7   rC   rC   b  s     e%8*EEr   c                     [        U [        ;   SU [        5        [        U[        ;   SU[        5        [        R                  U 5      n[        R                  U5      S-   n[        X#:  SU [        U5        [        X# $ )Nz.max_period {} must be a valid resolution in {}z.min_period {} must be a valid resolution in {}rb   z?max_period {} must be earlier in sequence {} than min_period {})r   r   index)
max_period
min_periodstartends       r7   validate_time_slicer~  t  s    &&8	 &&8	 "":.E

 
 
,q
0CI E&&r   rN   rV   rz  r{  rR  rz  r{  znp.dtype[np.datetime64]c                 8    [        S[        X5      [        U5      $ )zYReturn a strategy for datetime64 dtypes, with various precisions from
year to attosecond.zdatetime64[{}]rT  r~  r   r  s      r7   rD   rD     s"     J3	 r   znp.dtype[np.timedelta64]c                 8    [        S[        X5      [        U5      $ )zZReturn a strategy for timedelta64 dtypes, with various precisions from
year to attosecond.ztimedelta64[{}]r  r  s      r7   rK   rK     s"     J3	 r   rb   rR  min_lenmax_lenr  r  znp.dtype[np.bytes_]c           
      b    [        SSX5        [        S[        [        XS-   5      5      SU 5      $ )a  Return a strategy for generating bytestring dtypes, of various lengths
and byteorder.

While Hypothesis' string strategies can generate empty strings, string
dtypes with length 0 indicate that size is still to be determined, so
the minimum length for string dtypes is 1.
r   rb   r   Nr   rT  listr   r  s      r7   rB   rB     /     q'+d5A+#>?zRRr   znp.dtype[np.str_]c           
      b    [        SSX5        [        S[        [        XS-   5      5      SU 5      $ )a  Return a strategy for generating unicode string dtypes, of various
lengths and byteorder.

While Hypothesis' string strategies can generate empty strings, string
dtypes with length 0 indicate that size is still to be determined, so
the minimum length for string dtypes is 1.
r   rb   r   Nr  r  s      r7   rL   rL     r  r   c                     [        5       nU  HD  tp#[        U[        5      (       d  M  UR                  U5      (       a    gUR	                  U5        MF     g)NFT)ry   r3  r   rz   r|   )lsr  title_and_name_s       r7   #_no_title_is_name_of_a_titled_fieldr    sJ    5D ne,,  00 KK' ! r      )rf   rg   allow_subarrayssubtype_strategyr  c          
         [        SSX5        [        R                  " SS5      R                  SR                  5      [        R
                  " SS9-  n[        R                  " U[        R                  " XD5      R                  S 5      5      n[        R                  " XP5      nU(       a"  U[        R                  " XP[        SSS	95      -  n[        R                  " UUUS
 S 4S9R                  [        5      $ )zmReturn a strategy for generating array (compound) dtypes, with members
drawn from the given subtype strategy.sizer      zf{}rb   )rf   c                     U S   U S   :g  $ Nr   rb   r   )rV   s    r7   r   array_dtypes.<locals>.<lambda>  s    ber!unr   ra   )max_dimsmax_sidec                 L    [        U S   [        5      (       a  U S   $ U S   S   $ )Nr   r3  r   r(  s    r7   r   r    (    j1s33ad@1a@r   c                 L    [        U S   [        5      (       a  U S   $ U S   S   $ r  r  r  s    r7   r   r    r  r   )rs   rf   rg   	unique_by)r   r   r   r   r;  r   r7  r   r   r   r   r  )r  rf   rg   r  field_namesname_titlesrs   s          r7   r>   r>     s     8. ++a%))%,,7"''1:MMK))
		++223LMK *,;)QHBII<Q+O
 	
 88 A@	
	
 f01
2r   r   )
max_leavesmax_itemsizer  r  c                X   ^ [         R                  " U S US9R                  U4S j5      $ )a(  Return the most-general dtype strategy.

Elements drawn from this strategy may be simple (from the
subtype_strategy), or several such values drawn from
:func:`array_dtypes` with ``allow_subarrays=True``. Subdtypes in an
array dtype may be nested to any depth, subject to the max_leaves
argument.
c                     [        U SS9$ )NT)r  )r>   )r_   s    r7   r   nested_dtypes.<locals>.<lambda>	  s    ,q$7r   )r  c                 8   > TS L =(       d    U R                   T:*  $ r[   )r   )r(  r  s    r7   r   r    s    |t+Iqzz\/IIr   )r   	recursiver   )r  r  r  s     `r7   rI   rI     s-     <<7 fIJ	Kr   c                      [        U 0 UD6$ r[   )_valid_tuple_axesr~   r   s     r7   r    r      s    d-f--r   z
    Return a strategy for generating permissible tuple-values for the
    ``axis`` argument for a numpy sequential function (e.g.
    :func:`numpy:numpy.sum`), given an array of the specified
    dimensionality.

    z
    c                      [        U 0 UD6$ r[   )_mutually_broadcastable_shapesr  s     r7   r   r     s    )4:6::r   a  

    **Use with Generalised Universal Function signatures**

    A :doc:`universal function <numpy:reference/ufuncs>` (or ufunc for short) is a function
    that operates on ndarrays in an element-by-element fashion, supporting array
    broadcasting, type casting, and several other standard features.
    A :doc:`generalised ufunc <numpy:reference/c-api/generalized-ufuncs>` operates on
    sub-arrays rather than elements, based on the "signature" of the function.
    Compare e.g. :obj:`numpy.add() <numpy:numpy.add>` (ufunc) to
    :obj:`numpy.matmul() <numpy:numpy.matmul>` (gufunc).

    To generate shapes for a gufunc, you can pass the ``signature`` argument instead of
    ``num_shapes``.  This must be a gufunc signature string; which you can write by
    hand or access as e.g. ``np.matmul.signature`` on generalised ufuncs.

    In this case, the ``side`` arguments are applied to the 'core dimensions' as well,
    ignoring any frozen dimensions.  ``base_shape``  and the ``dims`` arguments are
    applied to the 'loop dimensions', and if necessary, the dimensionality of each
    shape is silently capped to respect the 32-dimension limit.

    The generated ``result_shape`` is the real result shape of applying the gufunc
    to arrays of the generated ``input_shapes``, even where this is different to
    broadcasting the loop dimensions.

    gufunc-compatible shapes shrink their loop dimensions as above, towards omitting
    optional core dimensions, and smaller-size core dimensions.

    .. code-block:: pycon

        >>> # np.matmul.signature == "(m?,n),(n,p?)->(m?,p?)"
        >>> for _ in range(3):
        ...     mutually_broadcastable_shapes(signature=np.matmul.signature).example()
        BroadcastableShapes(input_shapes=((2,), (2,)), result_shape=())
        BroadcastableShapes(input_shapes=((3, 4, 2), (1, 2)), result_shape=(3, 4))
        BroadcastableShapes(input_shapes=((4, 2), (1, 2, 3)), result_shape=(4, 3))

    .)min_dimsr  allow_newaxisr  r  r  allow_ellipsisc                    g r[   r   r   r  r  r  r  s        r7   r@   r@   K  s     r   )r  r  r  r  c                    g r[   r   r  s        r7   r@   r@   X  s	     DGr   )r  r  c                    g r[   r   r  s        r7   r@   r@   c  s	     FIr   )r  r  r  c                    g r[   r   r  s        r7   r@   r@   n  s     25r   c          	         [        [        U S5        [        [        S U  5       5      SU < S35        [        [        US5        [        [        US5        [        [
        US5        U[        U 5      :  a"  U(       d  [        SU S	[        U 5       S
3SSS9  [        US5        UcH  U(       a'  [        [        [        U 5      U5      S-   [        5      nO\[        [        U 5      [        5      nOB[        [
        US5        U[        U 5      :  a"  U(       d  [        SU S	[        U 5       S
3SSS9  [        US5        [        SSX5        [        U UUUUSS9$ )a  Return a strategy for :doc:`basic indexes <numpy:reference/routines.indexing>` of
arrays with the specified shape, which may include dimensions of size zero.

It generates tuples containing some mix of integers, :obj:`python:slice`
objects, ``...`` (an ``Ellipsis``), and ``None``. When a length-one tuple
would be generated, this strategy may instead return the element which will
index the first axis, e.g. ``5`` instead of ``(5,)``.

* ``shape`` is the shape of the array that will be indexed, as a tuple of
  positive integers. This must be at least two-dimensional for a tuple to be
  a valid index; for one-dimensional arrays use
  :func:`~hypothesis.strategies.slices` instead.
* ``min_dims`` is the minimum dimensionality of the resulting array from use
  of the generated index. When ``min_dims == 0``, scalars and zero-dimensional
  arrays are both allowed.
* ``max_dims`` is the maximum dimensionality of the resulting array,
  defaulting to ``len(shape) if not allow_newaxis else
  max(len(shape), min_dims) + 2``.
* ``allow_newaxis`` specifies whether ``None`` is allowed in the index.
* ``allow_ellipsis`` specifies whether ``...`` is allowed in the index.
r   c              3   Z   #    U  H!  n[        U[        5      =(       a    US :  v   M#     g7fr   Nr2  r]   s     r7   r`    basic_indices.<locals>.<genexpr>  s#     95aJq#)16)5   )+shape=z3, but all dimensions must be non-negative integers.r  r  r  z	min_dims=z is larger than len(shape)=zZ, but allow_newaxis=False makes it impossible for an indexing operation to add dimensions.z
2021-09-15F)sincehas_codemodra   r  z	max_dims=dimsr   T)r  r  r  r  allow_fewer_indices_than_dims)r$   r   r   r>  boolr\   r   r,   r   r   r   r   r   r   r  s        r7   r@   r@   y  sU   D ueW%95995(EF t^%56t]O4sHj)#e*]z!<SZL I+ + 	
 Xz*3s5z84q8(CH3u:x0H3*-c%j H:%@U M/ / #! Xz*8.%#&* r   I)result_shaper  z=st.SearchStrategy[tuple[NDArray[np.signedinteger[Any]], ...]]c                    g r[   r   )r   r  s     r7   rG   rG     s	    
 GJr   znp.dtype[I]z)st.SearchStrategy[tuple[NDArray[I], ...]]c                    g r[   r   )r   r  rq   s      r7   rG   rG     s     36r   )r  rq   z=np.dtype[I] | np.dtype[np.signedinteger[Any] | np.bool[bool]]c                  ^ ^^^ [        [        T S5        [        T =(       a    [        S T  5       5      ST < S35        [	        US5        [        [
        R                  " T[
        R                  5      ST< S35        [
        R                  " T[
        R                  5      mUU4S jmUR                  UU 4S	 j5      $ )
a  Return a search strategy for tuples of integer-arrays that, when used
to index into an array of shape ``shape``, given an array whose shape
was drawn from ``result_shape``.

Examples from this strategy shrink towards the tuple of index-arrays::

    len(shape) * (np.zeros(drawn_result_shape, dtype), )

* ``shape`` a tuple of integers that indicates the shape of the array,
  whose indices are being generated.
* ``result_shape`` a strategy for generating tuples of integers, which
  describe the shape of the resulting index arrays. The default is
  :func:`~hypothesis.extra.numpy.array_shapes`.  The shape drawn from
  this strategy determines the shape of the array that will be produced
  when the corresponding example from ``integer_array_indices`` is used
  as an index.
* ``dtype`` the integer data type of the generated index-arrays. Negative
  integer indices can be generated if a signed integer type is specified.

Recall that an array can be indexed using a tuple of integer-arrays to
access its members in an arbitrary order, producing an array with an
arbitrary shape. For example:

.. code-block:: pycon

    >>> from numpy import array
    >>> x = array([-0, -1, -2, -3, -4])
    >>> ind = (array([[4, 0], [0, 1]]),)  # a tuple containing a 2D integer-array
    >>> x[ind]  # the resulting array is commensurate with the indexing array(s)
    array([[-4,  0],
           [0, -1]])

Note that this strategy does not accommodate all variations of so-called
'advanced indexing', as prescribed by NumPy's nomenclature.  Combinations
of basic and advanced indexes are too complex to usefully define in a
standard strategy; we leave application-specific strategies to the user.
Advanced-boolean indexing can be defined as ``arrays(shape=..., dtype=bool)``,
and is similarly left to the user.
r   c              3   Z   #    U  H!  n[        U[        5      =(       a    US :  v   M#     g7fr  r2  r]   s     r7   r`   (integer_array_indices.<locals>.<genexpr>  s#     BEqjC(2QU2Er  r  z* must be a non-empty tuple of integers > 0r  zdtype=z must be an integer dtypec           	      ^   > [        TU [        R                  " T(       a  U* OSUS-
  5      S9$ )Nr   rb   )rq   r   rs   )r?   r   r   )index_shaper  rq   signeds     r7   	array_for(integer_array_indices.<locals>.array_for  s.    [[&$aB
 	
r   c                 B   >^  [         R                  " UU 4S jT 5       6 $ )Nc              3   6   >#    U  H  nT" TU5      v   M     g 7fr[   r   )r^   r  r  r  s     r7   r`   :integer_array_indices.<locals>.<lambda>.<locals>.<genexpr>!  s     'WQV	+t(D(DQVs   )r   r   )r  r  r   s   `r7   r   'integer_array_indices.<locals>.<lambda>!  s    BII'WQV'WXr   )
r$   r   r   r>  r*   r   
issubdtypeintegersignedintegerr:  )r   r  rq   r  r  s   ` `@@r7   rG   rG     s    ` ueW%B#BEBB5(<= <0
eRZZ(VUH4M*N ]]5""2"23F
 X r   c                 8   [        U SS5      nU(       a  [        U 5      [        [        S[        5       5      [        4;  aY  [        U5      S:X  d   e[        US   [        5      (       a+  US   R                  [        R                  :X  d   e[        n U $ US   n U $ )Nr8  r   r&  rb   r   )r4   r   r6  r   r	   r   r3  r   	__bound__r   genericr   )rq   
dtype_argss     r7   _unpack_dtyper  %  s    
B/Jd5k'%fh*OQV)WW:!###jmW--a=**bjj888E L qMELr   c                 D   [        U 5      S::  a  U (       a  [        U S   5      O[        nO[        U 5      S:X  d   e[        U S   5      nU[        L a
  [        5       $ [	        U5      [        [        S[        5       5      [        4;   a  U$ [        R                  " U5      $ )Nrb   r   ra   r&  )r   r  r   rJ   r   r4   r6  r   r	   r   rq   )r~   rq   s     r7   _dtype_from_argsr  3  s    
4yA~ +/d1g&C 4yA~~d1g&|	eVX>F	F88E?r   thingc                    [         R                  " [         R                  " 5       [         R                  " 5       [         R                  " 5       [         R
                  " 5       [         R                  " 5       [         R                  " 5       /5      n[         R                  " [         R                  " 5       [         R                  " 5       [         R                  " 5       [         R
                  " 5       [         R                  " 5       [         R                  " 5       R                  [        R                  5      /5      nU [        R                  :X  aB  [         R                  " [        5       [        5       [        5       [!        5       [#        5       5      $ U [$        :X  a  [         R                  " U[         R&                  " [         R(                  " U5      [         R*                  S9[         R&                  " [         R,                  " [        R.                  5      [         R*                  S95      $ [1        U [2        5      (       aR  [5        U [        R6                  5      (       a3  [        R                  " U 5      nUR8                  S;  a  [;        U5      $ S$ [=        U 5      nUc  U n[?        U 5      nU[@        :X  Ga  [C        U5      S::  d   eU(       a  [         R,                  " US   5      OUn[         R                  " [         R(                  " U5      [         R&                  " [         R*                  " 5       [         R*                  5      [         R&                  " [         R*                  " U5      [         R*                  5      [         R&                  " [         R*                  " Xf5      [         R*                  5      5      $ U[        RD                  RF                  [        R.                  [H        4;   a  [K        U5      n[M        U[O        SS95      $ g)zCalled by st.from_type to try to infer a strategy for thing using numpy.

If we can infer a numpy-specific strategy for thing, we return that; otherwise,
we return None.
)extendOVNrb   r   ra   )r  )(r   r7  r   r   r   r   r   r   r   bytesisasciir   rq   rJ   rB   rL   r>   rI   r;   r  r   r   r   ndarrayr3  r   
issubclassr  r   rF   r   r   r<   r   typingr:   r=   r  r?   r   )r  base_stratsbase_strats_asciirq   originr~   
base_strats          r7   
_from_typer  D  s    ))KKMKKMIIK GGIIIK	
	K 		KKMKKMIIK GGIIIKu}}-	
	 yyO !#NO
 	
 	 yy LL"34RYYGLLbjj1"))D

 
	
 %:eRZZ#@#@$)JJd$:z% DDF~E?D 
 4yA~~.2R\\$q'*
yyHHZ LLbii0LL:.		:LL::BIIF	
 	
 "))##RZZ@@ &e\1566 r   ) )sr2   r   r6  collections.abcr   r   r  r   r   r   r   r	   r
   r   r   r   numpyr   
hypothesisr   r   hypothesis.errorsr   r   hypothesis.extra._array_helpersr   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r   r    r  hypothesis.internal.conjecturer!   r   hypothesis.internal.coverager"   hypothesis.internal.reflectionr#   hypothesis.internal.validationr$   $hypothesis.strategies._internal.lazyr%   'hypothesis.strategies._internal.numbersr&   *hypothesis.strategies._internal.strategiesr'   r(   r)   r*   %hypothesis.strategies._internal.utilsr+   hypothesis.utils.deprecationr,   r   r8   numpy.typingr9   r:   r;   r<   r=   __all__r   r   __version__r   r   rq   r9  r\   floatr  rF   r   r  rP   r   r?   rJ   rF  rA   rT  rM   rH   rE   rC   r~  rD   rK   rB   rL   r  r>   rI   __doc__r@   r  r  rG   r  r  r   r  r   r   r7   <module>r     sV      -
 
 
  ' B    $ 7 7 2 5 B 8  C 9# # #  //.)4G4	>@QR8:JK0 V  G)=)=c)B2A)FGG7R  - /3$($(!"&#'##!%x"88x" $t+x" 	x"
 Djx" U{T!x" U{T!x" d{x" 4Kx" D[x" x" x" x" $;x" sx" .x"vB%% D C{#C|$ 

 CG*.* 1 1- @@A*""3''%/"2C2CE2JJ* $wsCx'884?	*
 

C
 4
'* * %* 
* 

 CG*.,r  ##,""3''%/"2C2CE2JJ, $wsCx'884?	,
 

C
 4
', , ', 
, -
 CG*.x?r  ##x?""3''%/"2C2CE2JJx? $wsCx'884?	x?
 

C
 4
'x? x? 'x? .x?v 
r((2 
 
!   ))*>?  
1: 
 22 1:2 +,	2 
2 
 33 2;3 ,-	3 
3 
 33 2;3 ,-	3 
3 
 33 2;3 ,-	3 
3 
 .=AA GM*+A :;	A 
A  HBB =!HW]-C$DDB :;B B, 
 11 1:1 *+	1 
1 
 22 2;2 +,	2 
2 
 22 2;2 +,	2 
2 
 22 2;2 +,	2 
2 
 .=?? GM*+? 89	? 
?  HBB =!HW]-C$DDB 89B B$ 
 44 2;4 -.	4 
4 
 44 2;4 -.	4 
4 
 44 2;4 -.	4 
4 
 55 3<5 ./	5 
5 
 4@:: G/01: 34	: 
:  THH &'(7;N3O*PPH 34H H* 
 66 2;6 /0	6 
6 
 77 3<7 01	7 
7 
 77 3<7 01	7 
7 
 2;FF G-./F ?@	F 
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 
 QrSS'*S9<S,-S S QrSS'*S9<S*+S S	 4AO 2 ! 2''1 2  2 	 2
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I 
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