



"""simple docstring"""






from __future__ import annotations

from typing import Any


def 							A__ (     *UpperCamelCase__    ):


  '''simple docstring'''


  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__ (     UpperCamelCase__       ,							UpperCamelCase__    ):


  '''simple docstring'''


  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__ (     UpperCamelCase__       ,							UpperCamelCase__    ):


  '''simple docstring'''


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


def 							A__ (     UpperCamelCase__       ,							UpperCamelCase__    ):


  '''simple docstring'''


  if _check_not_integer(lowercase__    ) and _check_not_integer(lowercase__    ):
    _SCREAMING_SNAKE_CASE        =			_verify_matrix_sizes(lowercase__       ,							lowercase__    )

  if cols[0] != rows[1]:
    _SCREAMING_SNAKE_CASE        =			(
        '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__ (     UpperCamelCase__    ):


  '''simple docstring'''


  _SCREAMING_SNAKE_CASE        =			int(lowercase__    )
  return [[int(row == column    ) for column in range(lowercase__    )] for row in range(lowercase__    )]


def 							A__ (     UpperCamelCase__       ,							UpperCamelCase__ = True    ):


  '''simple docstring'''


  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__ (     UpperCamelCase__       ,							UpperCamelCase__       ,							UpperCamelCase__    ):


  '''simple docstring'''


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


def 							A__ (     UpperCamelCase__    ):


  '''simple docstring'''


  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__ (     UpperCamelCase__    ):


  '''simple docstring'''


  _SCREAMING_SNAKE_CASE        =			determinant(lowercase__    )
  if det == 0:
    return None

  _SCREAMING_SNAKE_CASE        =			[
      [determinant(minor(lowercase__       ,							lowercase__       ,							lowercase__    )    ) for j in range(len(lowercase__    )    )]
      for i in range(len(lowercase__    )    )
  ]

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


def 							A__ (     UpperCamelCase__    ):


  '''simple docstring'''


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


def 							A__ (     UpperCamelCase__    ):


  '''simple docstring'''


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


def 							A__ (     UpperCamelCase__       ,							UpperCamelCase__    ):


  '''simple docstring'''


  _SCREAMING_SNAKE_CASE        =			_shape(lowercase__    ) + _shape(lowercase__    )
  if shape[0] != shape[3] or shape[1] != shape[2]:
    _SCREAMING_SNAKE_CASE        =			(
        '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__ (     ):


  '''simple docstring'''


  _SCREAMING_SNAKE_CASE        =			[[12, 10], [3, 9]]
  _SCREAMING_SNAKE_CASE        =			[[3, 4], [7, 4]]
  _SCREAMING_SNAKE_CASE        =			[[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
  _SCREAMING_SNAKE_CASE        =			[[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()




from __future__ import annotations

import random
import string



class      snake_case__	:
				def __init__(	self  ,   _UpperCAmelCase = None   ):




										"""simple docstring"""




										__magic_name__					:				Union[str, Any]				=   passcode or self.__passcode_creator()
										__magic_name__					:				Any				=   self.__make_key_list()
										__magic_name__					:				Tuple				=   self.__make_shift_key()
				def __str__(	self   ):




										"""simple docstring"""




										return "".join(self.__passcode   )
				def 			UpperCamelCase_    (	self  ,   _UpperCAmelCase   ):




										"""simple docstring"""




										for i in range(1  ,   len(_UpperCAmelCase   )  ,   2   ):
																iterlist[i] *= -1
										return iterlist
				def 			UpperCamelCase_    (	self   ):




										"""simple docstring"""




										__magic_name__					:				Any				=   string.ascii_letters + string.digits
										__magic_name__					:				Optional[Any]				=   [random.choice(_UpperCAmelCase   ) for _ in range(random.randint(10  ,   20   )   )]
										return password
				def 			UpperCamelCase_    (	self   ):




										"""simple docstring"""




										__magic_name__					:				Any				=   (
										    string.ascii_letters + string.digits + string.punctuation + ' \t\n'
										)

										__magic_name__					:				List[str]				=   []

										# creates points known as breakpoints to break the key_list_options at those
										# points and pivot each substring
										__magic_name__					:				List[Any]				=   sorted(set(self.__passcode   )   )
										__magic_name__					:				list[str]				=   []

										# algorithm for creating a new shuffled list, keys_l, out of key_list_options
										for i in key_list_options:
																temp_list.extend(_UpperCAmelCase   )

																# checking breakpoints at which to pivot temporary sublist and add it into
																# keys_l
																if i in breakpoints or i == key_list_options[-1]:
																						keys_l.extend(temp_list[::-1]   )
																						temp_list.clear()

        # returning a shuffled keys_l to prevent brute force guessing of shift key
										return keys_l
				def 			UpperCamelCase_    (	self   ):




										"""simple docstring"""




										__magic_name__					:				Dict				=   sum(self.__neg_pos([ord(_UpperCAmelCase   ) for x in self.__passcode]   )   )
										return num if num > 0 else len(self.__passcode   )
				def 			UpperCamelCase_    (	self  ,   _UpperCAmelCase   ):




										"""simple docstring"""




										__magic_name__					:				List[Any]				=   ''

										# decoding shift like Caesar cipher algorithm implementing negative shift or
										# reverse shift or left shift
										for i in encoded_message:
																__magic_name__					:				int				=   self.__key_list.index(_UpperCAmelCase   )
																decoded_message += self.__key_list[
																    (position - self.__shift_key) % -len(self.__key_list   )
																]

										return decoded_message





				def 			UpperCamelCase_    (	self  ,   _UpperCAmelCase   ):




										"""simple docstring"""




										__magic_name__					:				List[Any]				=   ''

										# encoding shift like Caesar cipher algorithm implementing positive shift or
										# forward shift or right shift
										for i in plaintext:
																__magic_name__					:				Dict				=   self.__key_list.index(_UpperCAmelCase   )
																encoded_message += self.__key_list[
																    (position + self.__shift_key) % len(self.__key_list   )
																]

										return encoded_message






def 			__SCREAMING_SNAKE_CASE							(					lowercase__	:str = "Hello, this is a modified Caesar cipher"					)							->	str:
						__magic_name__					:				List[str]				=   ShuffledShiftCipher()
						return cipa.decrypt(cipa.encrypt(lowercase__					)					)


if __name__ == "__main__":
			import doctest

			doctest.testmod()


