


"""simple docstring"""


from __future__ import annotations

from typing import Any






def    a__       ( *__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    a__       ( __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    a__       ( __lowercase   ,	__lowercase      )		->		list[list[float]]:
				return [[x * n for x in row] for row in matrix]






def    a__       ( __lowercase   ,	__lowercase      )		->		list[list[int]]:
				if _check_not_integer(__lowercase      ) and _check_not_integer(__lowercase      ):
								_A     ,						_A         =	_verify_matrix_sizes(__lowercase   ,	__lowercase      )

				if cols[0] != rows[1]:
								_A         =	(
								    "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    a__       ( __lowercase      )		->		list[list[int]]:
				_A         =	int(__lowercase      )
				return [[int(row == column      ) for column in range(__lowercase      )] for row in range(__lowercase      )]






def    a__       ( __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    a__       ( __lowercase   ,	__lowercase   ,	__lowercase      )		->		list[list[int]]:
				_A         =	matrix[:row] + matrix[row + 1 :]
				return [row[:column] + row[column + 1 :] for row in minor]






def    a__       ( __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    a__       ( __lowercase      )		->		list[list[float]] | None:
				_A         =	determinant(__lowercase      )
				if det == 0:
								return None

				_A         =	[
				    [determinant(minor(__lowercase   ,	__lowercase   ,	__lowercase      )      ) for j in range(len(__lowercase      )      )]
				    for i in range(len(__lowercase      )      )
				]

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






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






def    a__       ( __lowercase      )		->		tuple[int, int]:
				return len(__lowercase      ), len(matrix[0]      )






def    a__       ( __lowercase   ,	__lowercase      )		->		tuple[tuple[int, int], tuple[int, int]]:
				_A         =	_shape(__lowercase      ) + _shape(__lowercase      )
				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(__lowercase      )
				return (shape[0], shape[2]), (shape[1], shape[3])






def    a__       ( )		->		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(__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"""


def    a__       ( __lowercase = 20      )		->		int:

				try:
								_A         =	int(__lowercase      )
				except (TypeError, ValueError):
								raise TypeError("Parameter n must be int or castable to int."      )
				if n <= 0:
								raise ValueError("Parameter n must be greater than or equal to one."      )
				_A         =	0
				while 1:
								i += n * (n - 1)
								_A         =	0
								for j in range(2   ,	__lowercase      ):
												if i % j != 0:
																_A         =	1
																break
								if nfound == 0:
												if i == 0:
																_A         =	1
												return i
				return None


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