

"""simple docstring"""

from __future__ import annotations

from typing import Any



def 			SCREAMING_SNAKE_CASE       (   *lowercase__      ) ->	list[list[int]]:
 if all(_check_not_integer(lowercase__      ) for m in matrix_s      ):
  for i in matrix_s[1:]:
   _verify_matrix_sizes(matrix_s[0]				,				lowercase__      )
  return [[sum(lowercase__      ) for t in zip(*lowercase__      )] for m in zip(*lowercase__      )]
 raise TypeError("Expected a matrix, got int/list instead"      )



def 			SCREAMING_SNAKE_CASE       (   lowercase__				,				lowercase__      ) ->	list[list[int]]:
 if (
     _check_not_integer(lowercase__      )
     and _check_not_integer(lowercase__      )
     and _verify_matrix_sizes(lowercase__				,				lowercase__      )
 ):
  return [[i - j for i, j in zip(*lowercase__      )] for m in zip(lowercase__				,				lowercase__      )]
 raise TypeError("Expected a matrix, got int/list instead"      )



def 			SCREAMING_SNAKE_CASE       (   lowercase__				,				lowercase__      ) ->	list[list[float]]:
 return [[x * n for x in row] for row in matrix]



def 			SCREAMING_SNAKE_CASE       (   lowercase__				,				lowercase__      ) ->	list[list[int]]:
 if _check_not_integer(lowercase__      ) and _check_not_integer(lowercase__      ):
  lowerCAmelCase__ ,	lowerCAmelCase__      :							Union[str, Any]    =							_verify_matrix_sizes(lowercase__				,				lowercase__      )

 if cols[0] != rows[1]:
  lowerCAmelCase__      :							str    =							(
      "Cannot multiply matrix of dimensions "
      F"""({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})"""
  )
  raise ValueError(lowercase__      )
 return [
     [sum(m * n for m, n in zip(lowercase__				,				lowercase__      )      ) for j in zip(*lowercase__      )] for i in matrix_a
 ]



def 			SCREAMING_SNAKE_CASE       (   lowercase__      ) ->	list[list[int]]:
 lowerCAmelCase__      :							List[str]    =							int(lowercase__      )
 return [[int(row == column      ) for column in range(lowercase__      )] for row in range(lowercase__      )]



def 			SCREAMING_SNAKE_CASE       (   lowercase__				,				lowercase__ = True      ) ->	list[list[int]] | map[list[int]]:
 if _check_not_integer(lowercase__      ):
  if return_map:
   return map(lowercase__				,				zip(*lowercase__      )      )
  else:
   return list(map(lowercase__				,				zip(*lowercase__      )      )      )
 raise TypeError("Expected a matrix, got int/list instead"      )



def 			SCREAMING_SNAKE_CASE       (   lowercase__				,				lowercase__				,				lowercase__      ) ->	list[list[int]]:
 lowerCAmelCase__      :							Optional[Any]    =							matrix[:row] + matrix[row + 1 :]
 return [row[:column] + row[column + 1 :] for row in minor]



def 			SCREAMING_SNAKE_CASE       (   lowercase__      ) ->	Any:
 if len(lowercase__      ) == 1:
  return matrix[0][0]

 return sum(
     x * determinant(minor(lowercase__				,				0				,				lowercase__      )      ) * (-1) ** i
     for i, x in enumerate(matrix[0]      )      )



def 			SCREAMING_SNAKE_CASE       (   lowercase__      ) ->	list[list[float]] | None:
 lowerCAmelCase__      :							Union[str, Any]    =							determinant(lowercase__      )
 if det == 0:
  return None

 lowerCAmelCase__      :							Dict    =							[
     [determinant(minor(lowercase__				,				lowercase__				,				lowercase__      )      ) for j in range(len(lowercase__      )      )]
     for i in range(len(lowercase__      )      )
 ]

 lowerCAmelCase__      :							str    =							[
     [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]      )]
     for row in range(len(lowercase__      )      )
 ]
 lowerCAmelCase__      :							Tuple    =							list(transpose(lowercase__      )      )
 return scalar_multiply(lowercase__				,				1 / det      )



def 			SCREAMING_SNAKE_CASE       (   lowercase__      ) ->	bool:
 return not isinstance(lowercase__				,				lowercase__      ) and not isinstance(matrix[0]				,				lowercase__      )



def 			SCREAMING_SNAKE_CASE       (   lowercase__      ) ->	tuple[int, int]:
 return len(lowercase__      ), len(matrix[0]      )



def 			SCREAMING_SNAKE_CASE       (   lowercase__				,				lowercase__      ) ->	tuple[tuple[int, int], tuple[int, int]]:
 lowerCAmelCase__      :							int    =							_shape(lowercase__      ) + _shape(lowercase__      )
 if shape[0] != shape[3] or shape[1] != shape[2]:
  lowerCAmelCase__      :							Tuple    =							(
      "operands could not be broadcast together with shape "
      F"""({shape[0], shape[1]}), ({shape[2], shape[3]})"""
  )
  raise ValueError(lowercase__      )
 return (shape[0], shape[2]), (shape[1], shape[3])



def 			SCREAMING_SNAKE_CASE       (   ) ->	None:
 lowerCAmelCase__      :							int    =							[[1_2, 1_0], [3, 9]]
 lowerCAmelCase__      :							Any    =							[[3, 4], [7, 4]]
 lowerCAmelCase__      :							Optional[int]    =							[[1_1, 1_2, 1_3, 1_4], [2_1, 2_2, 2_3, 2_4], [3_1, 3_2, 3_3, 3_4], [4_1, 4_2, 4_3, 4_4]]
 lowerCAmelCase__      :							List[str]    =							[[3, 0, 2], [2, 0, -2], [0, 1, 1]]
 print(F"""Add Operation, {add(lowercase__				,				lowercase__      ) = } \n"""      )
 print(
     F"""Multiply Operation, {multiply(lowercase__				,				lowercase__      ) = } \n"""				,				)
 print(F"""Identity: {identity(5      )}\n"""      )
 print(F"""Minor of {matrix_c} = {minor(lowercase__				,				1				,				2      )} \n"""      )
 print(F"""Determinant of {matrix_b} = {determinant(lowercase__      )} \n"""      )
 print(F"""Inverse of {matrix_d} = {inverse(lowercase__      )}\n"""      )


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    main()









"""simple docstring"""

from itertools import product



def 			SCREAMING_SNAKE_CASE       (   lowercase__ = 1_5      ) ->	int:
 lowerCAmelCase__      :							float    =							0.0
 lowerCAmelCase__      :							float
 lowerCAmelCase__      :							int
 lowerCAmelCase__      :							int
 lowerCAmelCase__      :							int
 lowerCAmelCase__      :							int
 lowerCAmelCase__      :							tuple[int, ...]

 for series in product(range(2      )				,				repeat=lowercase__      ):
  lowerCAmelCase__      :							Optional[int]    =							series.count(1      )
  lowerCAmelCase__      :							Dict    =							num_turns - num_blue
  if num_red >= num_blue:
   continue
  lowerCAmelCase__      :							Dict    =							1.0
  for ind, col in enumerate(lowercase__				,				2      ):
   if col == 0:
    prob *= (ind - 1) / ind
   else:
    prob *= 1 / ind

  total_prob += prob

 return int(1 / total_prob      )


if __name__ == "__main__":
    print(f"{solution() = }")






