



'''simple docstring'''







from __future__ import annotations

from typing import Any







def  SCREAMING_SNAKE_CASE__ (				*SCREAMING_SNAKE_CASE     ):
		if all(_check_not_integer(SCREAMING_SNAKE_CASE     ) for m in matrix_s     ):
				for i in matrix_s[1:]:
						_verify_matrix_sizes(matrix_s[0] ,		SCREAMING_SNAKE_CASE     )
				return [[sum(SCREAMING_SNAKE_CASE     ) for t in zip(*SCREAMING_SNAKE_CASE     )] for m in zip(*SCREAMING_SNAKE_CASE     )]
		raise TypeError('Expected a matrix, got int/list instead'     )







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







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		return [[x * n for x in row] for row in matrix]







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		if _check_not_integer(SCREAMING_SNAKE_CASE     ) and _check_not_integer(SCREAMING_SNAKE_CASE     ):
				SCREAMING_SNAKE_CASE_						,		SCREAMING_SNAKE_CASE_						:Dict										=      _verify_matrix_sizes(SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     )

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







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE     ):
		SCREAMING_SNAKE_CASE_						:Dict										=      int(SCREAMING_SNAKE_CASE     )
		return [[int(row == column     ) for column in range(SCREAMING_SNAKE_CASE     )] for row in range(SCREAMING_SNAKE_CASE     )]







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE = True     ):
		if _check_not_integer(SCREAMING_SNAKE_CASE     ):
				if return_map:
						return map(SCREAMING_SNAKE_CASE ,		zip(*SCREAMING_SNAKE_CASE     )     )
				else:
						return list(map(SCREAMING_SNAKE_CASE ,		zip(*SCREAMING_SNAKE_CASE     )     )     )
		raise TypeError('Expected a matrix, got int/list instead'     )







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		SCREAMING_SNAKE_CASE_						:Any										=      matrix[:row] + matrix[row + 1 :]
		return [row[:column] + row[column + 1 :] for row in minor]







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE     ):
		if len(SCREAMING_SNAKE_CASE     ) == 1:
				return matrix[0][0]

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







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE     ):
		SCREAMING_SNAKE_CASE_						:int										=      determinant(SCREAMING_SNAKE_CASE     )
		if det == 0:
				return None

		SCREAMING_SNAKE_CASE_						:int										=      [
		    [determinant(minor(SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     )     ) for j in range(len(SCREAMING_SNAKE_CASE     )     )]
		    for i in range(len(SCREAMING_SNAKE_CASE     )     )
		]

		SCREAMING_SNAKE_CASE_						:Optional[Any]										=      [
		    [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]     )]
		    for row in range(len(SCREAMING_SNAKE_CASE     )     )
		]
		SCREAMING_SNAKE_CASE_						:int										=      list(transpose(SCREAMING_SNAKE_CASE     )     )
		return scalar_multiply(SCREAMING_SNAKE_CASE ,		1 / det     )







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE     ):
		return not isinstance(SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ) and not isinstance(matrix[0] ,		SCREAMING_SNAKE_CASE     )







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE     ):
		return len(SCREAMING_SNAKE_CASE     ), len(matrix[0]     )







def  SCREAMING_SNAKE_CASE__ (				SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ):
		SCREAMING_SNAKE_CASE_						:Tuple										=      _shape(SCREAMING_SNAKE_CASE     ) + _shape(SCREAMING_SNAKE_CASE     )
		if shape[0] != shape[3] or shape[1] != shape[2]:
				SCREAMING_SNAKE_CASE_						:Union[str, Any]										=      (
				    'operands could not be broadcast together with shape '
				    F'({shape[0], shape[1]}), ({shape[2], shape[3]})'
				)
				raise ValueError(SCREAMING_SNAKE_CASE     )
		return (shape[0], shape[2]), (shape[1], shape[3])







def  SCREAMING_SNAKE_CASE__ (				):
		SCREAMING_SNAKE_CASE_						:Union[str, Any]										=      [[12, 10], [3, 9]]
		SCREAMING_SNAKE_CASE_						:Dict										=      [[3, 4], [7, 4]]
		SCREAMING_SNAKE_CASE_						:str										=      [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
		SCREAMING_SNAKE_CASE_						:Any										=      [[3, 0, 2], [2, 0, -2], [0, 1, 1]]
		print(F'Add Operation, {add(SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ) = } \n'     )
		print(
		    F'Multiply Operation, {multiply(SCREAMING_SNAKE_CASE ,		SCREAMING_SNAKE_CASE     ) = } \n' ,		)
		print(F'Identity: {identity(5     )}\n'     )
		print(F'Minor of {matrix_c} = {minor(SCREAMING_SNAKE_CASE ,		1 ,		2     )} \n'     )
		print(F'Determinant of {matrix_b} = {determinant(SCREAMING_SNAKE_CASE     )} \n'     )
		print(F'Inverse of {matrix_d} = {inverse(SCREAMING_SNAKE_CASE     )}\n'     )


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							main()








def       _a   (							lowerCamelCase__				)  ->      list[int]:
 if len(lowerCamelCase__				) > 1:
  lowerCamelCase_							:    Optional[Any]							=     len(lowerCamelCase__				) // 2  # Finds the middle of the array
  lowerCamelCase_							:    int							=     arr[
      :middle_length
  ]  # Creates an array of the elements in the first half.
  lowerCamelCase_							:    List[Any]							=     arr[
      middle_length:
  ]  # Creates an array of the elements in the second half.
  lowerCamelCase_							:    Optional[Any]							=     len(lowerCamelCase__				)
  lowerCamelCase_							:    Optional[Any]							=     len(lowerCamelCase__				)
  merge(lowerCamelCase__				)  # Starts sorting the left.
  merge(lowerCamelCase__				)  # Starts sorting the right
  lowerCamelCase_							:    Dict							=     0  # Left Counter
  lowerCamelCase_							:    str							=     0  # Right Counter
  lowerCamelCase_							:    Tuple							=     0  # Position Counter
  while (
      left_index < left_size and right_index < right_size
  ):  # Runs until the lowers size of the left and right are sorted.
   if left_array[left_index] < right_array[right_index]:
    lowerCamelCase_							:    Optional[int]							=     left_array[left_index]
    left_index += 1
   else:
    lowerCamelCase_							:    Union[str, Any]							=     right_array[right_index]
    right_index += 1
   index += 1
  while (
      left_index < left_size
  ):  # Adds the left over elements in the left half of the array
   lowerCamelCase_							:    Tuple							=     left_array[left_index]
   left_index += 1
   index += 1
  while (
      right_index < right_size
  ):  # Adds the left over elements in the right half of the array
   lowerCamelCase_							:    Optional[int]							=     right_array[right_index]
   right_index += 1
   index += 1
 return arr


if __name__ == "__main__":
       import doctest

       doctest.testmod()
