





from typing import List

import numpy as np

def    __snake_case  (    _lowerCAmelCase       :       dict		)       ->  List[Any]:
   A_    : str								=	{key: len(_lowerCamelCase		) for key, value in gen_kwargs.items() if isinstance(_lowerCamelCase , _lowerCamelCase		)}
   if len(set(lists_lengths.values()		)		) > 1:
      raise RuntimeError(
          (
              "Sharding is ambiguous for this dataset: "
              + "we found several data sources lists of different lengths, and we don't know over which list we should parallelize:\n"
              + "\n".join(f"\t- key {key} has length {length}" for key, length in lists_lengths.items()		)
              + "\nTo fix this, check the 'gen_kwargs' and make sure to use lists only for data sources, "
              + "and use tuples otherwise. In the end there should only be one single list, or several lists with the same length."
          )		)
   A_    : Optional[int]								=	max(lists_lengths.values() , default=0		)
   return max(1 , _lowerCamelCase		)

def    __snake_case  (    _lowerCAmelCase       :       int , _lowerCAmelCase       :       int		)       ->  Union[str, Any]:
   A_    : int								=	[]
   for group_idx in range(_lowerCamelCase		):
      A_    : Tuple								=	num_shards // max_num_jobs + (group_idx < (num_shards % max_num_jobs))
      if num_shards_to_add == 0:
         break
      A_    : Optional[Any]								=	shards_indices_per_group[-1].stop if shards_indices_per_group else 0
      A_    : List[str]								=	range(_lowerCamelCase , start + num_shards_to_add		)
      shards_indices_per_group.append(_lowerCamelCase		)
   return shards_indices_per_group

def    __snake_case  (    _lowerCAmelCase       :       dict , _lowerCAmelCase       :       int		)       ->  str:
   A_    : Dict								=	_number_of_shards_in_gen_kwargs(_lowerCamelCase		)
   if num_shards == 1:
      return [dict(_lowerCamelCase		)]
   else:
      A_    : List[Any]								=	_distribute_shards(num_shards=_lowerCamelCase , max_num_jobs=_lowerCamelCase		)
      return [
          {
              key: [value[shard_idx] for shard_idx in shard_indices_per_group[group_idx]]
              if isinstance(_lowerCamelCase , _lowerCamelCase		)
              else value
              for key, value in gen_kwargs.items()
          }
          for group_idx in range(len(_lowerCamelCase		)		)
      ]

def    __snake_case  (    _lowerCAmelCase       :       List[dict]		)       ->  str:
   return {
       key: [value for gen_kwargs in gen_kwargs_list for value in gen_kwargs[key]]
       if isinstance(gen_kwargs_list[0][key] , _lowerCamelCase		)
       else gen_kwargs_list[0][key]
       for key in gen_kwargs_list[0]
   }





def    __snake_case  (    _lowerCAmelCase       :       np.random.Generator , _lowerCAmelCase       :       dict		)       ->  Dict:
   A_    : int								=	{len(_lowerCamelCase		) for value in gen_kwargs.values() if isinstance(_lowerCamelCase , _lowerCamelCase		)}
   A_    : Any								=	{}
   for size in list_sizes:
      A_    : int								=	list(range(_lowerCamelCase		)		)
      rng.shuffle(indices_per_size[size]		)
   # Now let's copy the gen_kwargs and shuffle the lists based on their sizes
   A_    : Tuple								=	dict(_lowerCamelCase		)
   for key, value in shuffled_kwargs.items():
      if isinstance(_lowerCamelCase , _lowerCamelCase		):
         A_    : Union[str, Any]								=	[value[i] for i in indices_per_size[len(_lowerCamelCase		)]]
   return shuffled_kwargs







'''simple docstring'''

from __future__ import annotations

from decimal import Decimal

from numpy import array





def 						UpperCamelCase				(							_lowerCamelCase					:					list[list[float]]       ):
    A__				=			Decimal

    # Check if the provided matrix has 2 rows and 2 columns
    # since this implementation only works for 2x2 matrices
    if len(_lowerCamelCase       ) == 2 and len(matrix[0]       ) == 2 and len(matrix[1]       ) == 2:
        # Calculate the determinant of the matrix
        A__				=			float(
            d(matrix[0][0]       ) * d(matrix[1][1]       ) - d(matrix[1][0]       ) * d(matrix[0][1]       )       )
        if determinant == 0:
            raise ValueError("This matrix has no inverse."       )

        # Creates a copy of the matrix with swapped positions of the elements
        A__				=			[[0.0, 0.0], [0.0, 0.0]]
        A__,	A__				=			matrix[1][1], matrix[0][0]
        A__,	A__				=			-matrix[1][0], -matrix[0][1]

        # Calculate the inverse of the matrix
        return [
            [(float(d(_lowerCamelCase       )       ) / determinant) or 0.0 for n in row] for row in swapped_matrix
        ]
    elif (
        len(_lowerCamelCase       ) == 3
        and len(matrix[0]       ) == 3
        and len(matrix[1]       ) == 3
        and len(matrix[2]       ) == 3
    ):
        # Calculate the determinant of the matrix using Sarrus rule
        A__				=			float(
            (
                (d(matrix[0][0]       ) * d(matrix[1][1]       ) * d(matrix[2][2]       ))
                + (d(matrix[0][1]       ) * d(matrix[1][2]       ) * d(matrix[2][0]       ))
                + (d(matrix[0][2]       ) * d(matrix[1][0]       ) * d(matrix[2][1]       ))
            )
            - (
                (d(matrix[0][2]       ) * d(matrix[1][1]       ) * d(matrix[2][0]       ))
                + (d(matrix[0][1]       ) * d(matrix[1][0]       ) * d(matrix[2][2]       ))
                + (d(matrix[0][0]       ) * d(matrix[1][2]       ) * d(matrix[2][1]       ))
            )       )
        if determinant == 0:
            raise ValueError("This matrix has no inverse."       )

        # Creating cofactor matrix
        A__				=			[
            [d(0.0       ), d(0.0       ), d(0.0       )],
            [d(0.0       ), d(0.0       ), d(0.0       )],
            [d(0.0       ), d(0.0       ), d(0.0       )],
        ]
        A__				=			(d(matrix[1][1]       ) * d(matrix[2][2]       )) - (
            d(matrix[1][2]       ) * d(matrix[2][1]       )
        )
        A__				=			-(
            (d(matrix[1][0]       ) * d(matrix[2][2]       )) - (d(matrix[1][2]       ) * d(matrix[2][0]       ))
        )
        A__				=			(d(matrix[1][0]       ) * d(matrix[2][1]       )) - (
            d(matrix[1][1]       ) * d(matrix[2][0]       )
        )
        A__				=			-(
            (d(matrix[0][1]       ) * d(matrix[2][2]       )) - (d(matrix[0][2]       ) * d(matrix[2][1]       ))
        )
        A__				=			(d(matrix[0][0]       ) * d(matrix[2][2]       )) - (
            d(matrix[0][2]       ) * d(matrix[2][0]       )
        )
        A__				=			-(
            (d(matrix[0][0]       ) * d(matrix[2][1]       )) - (d(matrix[0][1]       ) * d(matrix[2][0]       ))
        )
        A__				=			(d(matrix[0][1]       ) * d(matrix[1][2]       )) - (
            d(matrix[0][2]       ) * d(matrix[1][1]       )
        )
        A__				=			-(
            (d(matrix[0][0]       ) * d(matrix[1][2]       )) - (d(matrix[0][2]       ) * d(matrix[1][0]       ))
        )
        A__				=			(d(matrix[0][0]       ) * d(matrix[1][1]       )) - (
            d(matrix[0][1]       ) * d(matrix[1][0]       )
        )

        # Transpose the cofactor matrix (Adjoint matrix)
        A__				=			array(_lowerCamelCase       )
        for i in range(3       ):
            for j in range(3       ):
                A__				=			cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
        A__				=			array(_lowerCamelCase       )
        for i in range(3       ):
            for j in range(3       ):
                inverse_matrix[i][j] /= d(_lowerCamelCase       )

        # Calculate the inverse of the matrix
        return [[float(d(_lowerCamelCase       )       ) or 0.0 for n in row] for row in inverse_matrix]
    raise ValueError("Please provide a matrix of size 2x2 or 3x3."       )



