






from __future__ import annotations

from typing import Any




def   lowercase__   (  *__snake_case					:							list[list[int]]						):


     '''simple docstring'''


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




def   lowercase__   (  __snake_case					:							list[list[int]]  , __snake_case					:							list[list[int]]						):


     '''simple docstring'''


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




def   lowercase__   (  __snake_case					:							list[list[int]]  , __snake_case					:							int | float						):


     '''simple docstring'''


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




def   lowercase__   (  __snake_case					:							list[list[int]]  , __snake_case					:							list[list[int]]						):


     '''simple docstring'''


     if _check_not_integer(__snake_case						) and _check_not_integer(__snake_case						):
          UpperCAmelCase_					:   str   =		_verify_matrix_sizes(__snake_case  , __snake_case						)

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




def   lowercase__   (  __snake_case					:							int						):


     '''simple docstring'''


     UpperCAmelCase_					:   Optional[Any]   =		int(__snake_case						)
     return [[int(row == column						) for column in range(__snake_case						)] for row in range(__snake_case						)]




def   lowercase__   (  __snake_case					:							list[list[int]]  , __snake_case					:							bool = True						):


     '''simple docstring'''


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




def   lowercase__   (  __snake_case					:							list[list[int]]  , __snake_case					:							int  , __snake_case					:							int						):


     '''simple docstring'''


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




def   lowercase__   (  __snake_case					:							list[list[int]]						):


     '''simple docstring'''


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

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




def   lowercase__   (  __snake_case					:							list[list[int]]						):


     '''simple docstring'''


     UpperCAmelCase_					:   Optional[int]   =		determinant(__snake_case						)
     if det == 0:
          return None

     UpperCAmelCase_					:   List[str]   =		[
         [determinant(minor(__snake_case  , __snake_case  , __snake_case						)						) for j in range(len(__snake_case						)						)]
         for i in range(len(__snake_case						)						)
     ]

     UpperCAmelCase_					:   List[str]   =		[
         [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]						)]
         for row in range(len(__snake_case						)						)
     ]
     UpperCAmelCase_					:   Tuple   =		list(transpose(__snake_case						)						)
     return scalar_multiply(__snake_case  , 1 / det						)




def   lowercase__   (  __snake_case					:							list[list[int]]						):


     '''simple docstring'''


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




def   lowercase__   (  __snake_case					:							list[list[int]]						):


     '''simple docstring'''


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




def   lowercase__   (  __snake_case					:							list[list[int]]  , __snake_case					:							list[list[int]]						):


     '''simple docstring'''


     UpperCAmelCase_					:   Optional[Any]   =		_shape(__snake_case						) + _shape(__snake_case						)
     if shape[0] != shape[3] or shape[1] != shape[2]:
          UpperCAmelCase_					:   Optional[int]   =		(
              'operands could not be broadcast together with shape '
              F"({shape[0], shape[1]}), ({shape[2], shape[3]})"
          )
          raise ValueError(__snake_case						)
     return (shape[0], shape[2]), (shape[1], shape[3])




def   lowercase__   (  ):


     '''simple docstring'''


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


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()














def   lowercase__   (  __snake_case					:							int  , __snake_case					:							int  , __snake_case					:							int  , __snake_case					:							int						):


					'''simple docstring'''


					return len_board * len_board_column * row + column




def   lowercase__   (  __snake_case					:							list[list[str]]  , __snake_case					:							str  , __snake_case					:							int  , __snake_case					:							int  , __snake_case					:							int  , __snake_case					:							set[int]  , ):


					'''simple docstring'''


					if board[row][column] != word[word_index]:
										return False

					if word_index == len(__snake_case						) - 1:
										return True

					UpperCAmelCase_					:   Dict   =		[(0, 1), (0, -1), (-1, 0), (1, 0)]
					UpperCAmelCase_					:   Union[str, Any]   =		len(__snake_case						)
					UpperCAmelCase_					:   List[Any]   =		len(board[0]						)
					for direction in traverts_directions:
										UpperCAmelCase_					:   Optional[int]   =		row + direction[0]
										UpperCAmelCase_					:   Optional[int]   =		column + direction[1]
										if not (0 <= next_i < len_board and 0 <= next_j < len_board_column):
															continue

										UpperCAmelCase_					:   Tuple   =		get_point_key(__snake_case  , __snake_case  , __snake_case  , __snake_case						)
										if key in visited_points_set:
															continue

										visited_points_set.add(__snake_case						)
										if exits_word(__snake_case  , __snake_case  , __snake_case  , __snake_case  , word_index + 1  , __snake_case						):
															return True

										visited_points_set.remove(__snake_case						)

					return False




def   lowercase__   (  __snake_case					:							list[list[str]]  , __snake_case					:							str						):


					'''simple docstring'''


					UpperCAmelCase_					:   Any   =		(
					    'The board should be a non empty matrix of single chars strings.'
					)

					UpperCAmelCase_					:   Optional[Any]   =		len(__snake_case						)
					if not isinstance(__snake_case  , __snake_case						) or len(__snake_case						) == 0:
										raise ValueError(__snake_case						)

					for row in board:
										if not isinstance(__snake_case  , __snake_case						) or len(__snake_case						) == 0:
															raise ValueError(__snake_case						)

										for item in row:
															if not isinstance(__snake_case  , __snake_case						) or len(__snake_case						) != 1:
																				raise ValueError(__snake_case						)

    # Validate word
					if not isinstance(__snake_case  , __snake_case						) or len(__snake_case						) == 0:
										raise ValueError(
										    'The word parameter should be a string of length greater than 0.'						)

					UpperCAmelCase_					:   Any   =		len(board[0]						)
					for i in range(__snake_case						):
										for j in range(__snake_case						):
															if exits_word(
															    __snake_case  , __snake_case  , __snake_case  , __snake_case  , 0  , {get_point_key(__snake_case  , __snake_case  , __snake_case  , __snake_case						)}						):
																				return True

					return False


if __name__ == "__main__":
		import doctest

		doctest.testmod()






