




'''simple docstring'''
from __future__ import annotations

from typing import Any





def  lowerCamelCase(       *SCREAMING_SNAKE_CASE_    )		->		list[list[int]]:
			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  lowerCamelCase(       SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_    )		->		list[list[int]]:
			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  lowerCamelCase(       SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_    )		->		list[list[float]]:
			return [[x * n for x in row] for row in matrix]





def  lowerCamelCase(       SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_    )		->		list[list[int]]:
			if _check_not_integer(SCREAMING_SNAKE_CASE_    ) and _check_not_integer(SCREAMING_SNAKE_CASE_    ):
						A_		,   A_       		=   _verify_matrix_sizes(SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_    )

			if cols[0] != rows[1]:
						A_       		=   (
						    '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  lowerCamelCase(       SCREAMING_SNAKE_CASE_    )		->		list[list[int]]:
			A_       		=   int(SCREAMING_SNAKE_CASE_    )
			return [[int(row == column    ) for column in range(SCREAMING_SNAKE_CASE_    )] for row in range(SCREAMING_SNAKE_CASE_    )]





def  lowerCamelCase(       SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_ = True    )		->		list[list[int]] | map[list[int]]:
			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  lowerCamelCase(       SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_    )		->		list[list[int]]:
			A_       		=   matrix[:row] + matrix[row + 1 :]
			return [row[:column] + row[column + 1 :] for row in minor]





def  lowerCamelCase(       SCREAMING_SNAKE_CASE_    )		->		Any:
			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  lowerCamelCase(       SCREAMING_SNAKE_CASE_    )		->		list[list[float]] | None:
			A_       		=   determinant(SCREAMING_SNAKE_CASE_    )
			if det == 0:
						return None

			A_       		=   [
			    [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_    )    )
			]

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





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





def  lowerCamelCase(       SCREAMING_SNAKE_CASE_    )		->		tuple[int, int]:
			return len(SCREAMING_SNAKE_CASE_    ), len(matrix[0]    )





def  lowerCamelCase(       SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_    )		->		tuple[tuple[int, int], tuple[int, int]]:
			A_       		=   _shape(SCREAMING_SNAKE_CASE_    ) + _shape(SCREAMING_SNAKE_CASE_    )
			if shape[0] != shape[3] or shape[1] != shape[2]:
						A_       		=   (
						    '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  lowerCamelCase(       )		->		None:
			A_       		=   [[12, 10], [3, 9]]
			A_       		=   [[3, 4], [7, 4]]
			A_       		=   [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
			A_       		=   [[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()










'''simple docstring'''
def  lowerCamelCase(       SCREAMING_SNAKE_CASE_    )		->		int:

			if not isinstance(SCREAMING_SNAKE_CASE_					,SCREAMING_SNAKE_CASE_    ) or number < 0:
						raise ValueError('Input must be a non-negative integer'    )

			A_       		=   number & ~(number - 1)
			A_       		=   0
			while intermediate:
						intermediate >>= 1
						index += 1
			return index - 1


if __name__ == "__main__":
							import doctest

							doctest.testmod(verbose=True)




