'''simple docstring'''

from __future__ import annotations

from typing import Any


def __a			(						*__lowerCamelCase      :    list[list[int]]					)						->				list[list[int]]:
      '''simple docstring'''


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


def __a			(						__lowerCamelCase      :    list[list[int]]			,		__lowerCamelCase      :    list[list[int]]					)						->				list[list[int]]:
      '''simple docstring'''


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


def __a			(						__lowerCamelCase      :    list[list[int]]			,		__lowerCamelCase      :    int | float					)						->				list[list[float]]:
      '''simple docstring'''


      return [[x * n for x in row] for row in matrix]


def __a			(						__lowerCamelCase      :    list[list[int]]			,		__lowerCamelCase      :    list[list[int]]					)						->				list[list[int]]:
      '''simple docstring'''


      if _check_not_integer(__lowerCamelCase					) and _check_not_integer(__lowerCamelCase					):
            lowercase_			,				lowercase_     			=   _verify_matrix_sizes(__lowerCamelCase			,		__lowerCamelCase					)

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


def __a			(						__lowerCamelCase      :    int					)						->				list[list[int]]:
      '''simple docstring'''


      lowercase_     			=   int(__lowerCamelCase					)
      return [[int(row == column					) for column in range(__lowerCamelCase					)] for row in range(__lowerCamelCase					)]


def __a			(						__lowerCamelCase      :    list[list[int]]			,		__lowerCamelCase      :    bool = True					)						->				list[list[int]] | map[list[int]]:
      '''simple docstring'''


      if _check_not_integer(__lowerCamelCase					):
            if return_map:
                  return map(__lowerCamelCase			,		zip(*__lowerCamelCase					)					)
            else:
                  return list(map(__lowerCamelCase			,		zip(*__lowerCamelCase					)					)					)
      raise TypeError("Expected a matrix, got int/list instead"					)


def __a			(						__lowerCamelCase      :    list[list[int]]			,		__lowerCamelCase      :    int			,		__lowerCamelCase      :    int					)						->				list[list[int]]:
      '''simple docstring'''


      lowercase_     			=   matrix[:row] + matrix[row + 1 :]
      return [row[:column] + row[column + 1 :] for row in minor]


def __a			(						__lowerCamelCase      :    list[list[int]]					)						->				Any:
      '''simple docstring'''


      if len(__lowerCamelCase					) == 1:
            return matrix[0][0]

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


def __a			(						__lowerCamelCase      :    list[list[int]]					)						->				list[list[float]] | None:
      '''simple docstring'''


      lowercase_     			=   determinant(__lowerCamelCase					)
      if det == 0:
            return None

      lowercase_     			=   [
          [determinant(minor(__lowerCamelCase			,		__lowerCamelCase			,		__lowerCamelCase					)					) for j in range(len(__lowerCamelCase					)					)]
          for i in range(len(__lowerCamelCase					)					)
      ]

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


def __a			(						__lowerCamelCase      :    list[list[int]]					)						->				bool:
      '''simple docstring'''


      return not isinstance(__lowerCamelCase			,		__lowerCamelCase					) and not isinstance(matrix[0]			,		__lowerCamelCase					)


def __a			(						__lowerCamelCase      :    list[list[int]]					)						->				tuple[int, int]:
      '''simple docstring'''


      return len(__lowerCamelCase					), len(matrix[0]					)


def __a			(						__lowerCamelCase      :    list[list[int]]			,		__lowerCamelCase      :    list[list[int]]					)						->				tuple[tuple[int, int], tuple[int, int]]:
      '''simple docstring'''


      lowercase_     			=   _shape(__lowerCamelCase					) + _shape(__lowerCamelCase					)
      if shape[0] != shape[3] or shape[1] != shape[2]:
            lowercase_     			=   (
                "operands could not be broadcast together with shape "
                f'({shape[0], shape[1]}), ({shape[2], shape[3]})'
            )
            raise ValueError(__lowerCamelCase					)
      return (shape[0], shape[2]), (shape[1], shape[3])


def __a			(						)						->				None:
      '''simple docstring'''


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


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       main()







'''simple docstring'''

import timeit





class 				lowercase    :


   def __init__( self					:						Dict ,		__lowerCAmelCase					:						Any)   ->       Optional[int]:
         if isinstance(__lowerCAmelCase ,		__lowerCAmelCase):  # Initializes a matrix identical to the one provided.
               lowercase_     			=   arg
               lowercase_     			=   len(__lowerCAmelCase)
         else:  # Initializes a square matrix of the given size and set values to zero.
               lowercase_     			=   arg
               lowercase_     			=   [[0 for _ in range(self.n)] for _ in range(self.n)]


   def __mul__( self					:						int ,		__lowerCAmelCase					:						List[str])   ->       Union[str, Any]:
         lowercase_     			=   Matrix(self.n)
         for i in range(self.n):
               for j in range(self.n):
                     for k in range(self.n):
                           matrix.t[i][j] += self.t[i][k] * b.t[k][j]
         return matrix




def __a			(						__lowerCamelCase      :    List[str]			,		__lowerCamelCase      :    Dict					)						->				Optional[Any]:
      '''simple docstring'''


      lowercase_     			=   Matrix([[1, 0], [0, 1]]					)
      while b > 0:
            if b & 1:
                  matrix *= a
            a *= a
            b >>= 1
      return matrix


def __a			(						__lowerCamelCase      :    Tuple			,		__lowerCamelCase      :    Tuple			,		__lowerCamelCase      :    List[Any]					)						->				Dict:
      '''simple docstring'''


      if n == 1:
            return fa
      elif n == 2:
            return fa
      lowercase_     			=   Matrix([[1, 1], [1, 0]]					)
      lowercase_     			=   modular_exponentiation(__lowerCamelCase			,		n - 2					)
      return fa * matrix.t[0][0] + fa * matrix.t[0][1]


def __a			(						__lowerCamelCase      :    List[Any]			,		__lowerCamelCase      :    Union[str, Any]			,		__lowerCamelCase      :    List[str]					)						->				Optional[Any]:
      '''simple docstring'''


      if n == 1:
            return fa
      elif n == 2:
            return fa

      lowercase_     			=   fa
      lowercase_     			=   fa
      n -= 2

      while n > 0:
            lowercase_			,				lowercase_     			=   fn_a + fn_a, fn_a
            n -= 1

      return fn_a


def __a			(						)						->				str:
      '''simple docstring'''


      lowercase_     			=   "\nfrom random import randint\nfrom __main__ import fibonacci_with_matrix_exponentiation\n"
      lowercase_     			=   "fibonacci_with_matrix_exponentiation(randint(1,70000), 1, 1)"
      lowercase_     			=   timeit.timeit(setup=__lowerCamelCase			,		stmt=__lowerCamelCase			,		number=100					)
      print("With matrix exponentiation the average execution time is "			,		exec_time / 100					)
      return exec_time


def __a			(						)						->				Optional[Any]:
      '''simple docstring'''


      lowercase_     			=   "\nfrom random import randint\nfrom __main__ import simple_fibonacci\n"
      lowercase_     			=   "simple_fibonacci(randint(1,70000), 1, 1)"
      lowercase_     			=   timeit.timeit(setup=__lowerCamelCase			,		stmt=__lowerCamelCase			,		number=100					)
      print(
          "Without matrix exponentiation the average execution time is "			,		exec_time / 100					)
      return exec_time


def __a			(						)						->				Tuple:
      '''simple docstring'''


      matrix_exponentiation_time()
      simple_fibonacci_time()


if __name__ == "__main__":
       main()






