


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




class      lowerCamelCase_  :






      def __init__(   self							:       int		,		_A							:       list[list[int]]					):


          '''simple docstring'''


          UpperCAmelCase__     :						Tuple						=							TypeError(
              '''Matrices must be formed from a list of zero or more lists containing at '''
              '''least one and the same number of values, each of which must be of type '''
              '''int or float.'''					)
          if len(_A					) != 0:
              UpperCAmelCase__     :						Any						=							len(rows[0]					)
              if cols == 0:
                  raise error
              for row in rows:
                  if len(_A					) != cols:
                      raise error
                  for value in row:
                      if not isinstance(_A		,		(int, float)					):
                          raise error
              UpperCAmelCase__     :						Union[str, Any]						=							rows
          else:
              UpperCAmelCase__     :						str						=							[]






      def lowercase_				(   self							:       Optional[Any]					):


          '''simple docstring'''


          return [[row[i] for row in self.rows] for i in range(len(self.rows[0]					)					)]






      @property
      def lowercase_				(   self							:       Optional[int]					):


          '''simple docstring'''


          return len(self.rows					)






      @property
      def lowercase_				(   self							:       int					):


          '''simple docstring'''


          return len(self.rows[0]					)






      @property
      def lowercase_				(   self							:       List[Any]					):


          '''simple docstring'''


          return (self.num_rows, self.num_columns)






      @property
      def lowercase_				(   self							:       List[Any]					):


          '''simple docstring'''


          return self.order[0] == self.order[1]






      def lowercase_				(   self							:       Optional[Any]					):


          '''simple docstring'''


          UpperCAmelCase__     :						str						=							[
              [0 if column_num != row_num else 1 for column_num in range(self.num_rows					)]
              for row_num in range(self.num_rows					)
          ]
          return Matrix(_A					)






      def lowercase_				(   self							:       Any					):


          '''simple docstring'''


          if not self.is_square:
              return 0
          if self.order == (0, 0):
              return 1
          if self.order == (1, 1):
              return int(self.rows[0][0]					)
          if self.order == (2, 2):
              return int(
                  (self.rows[0][0] * self.rows[1][1])
                  - (self.rows[0][1] * self.rows[1][0])					)
          else:
              return sum(
                  self.rows[0][column] * self.cofactors().rows[0][column]
                  for column in range(self.num_columns					)					)






      def lowercase_				(   self							:       Dict					):


          '''simple docstring'''


          return bool(self.determinant()					)






      def lowercase_				(   self							:       int		,		_A							:       int		,		_A							:       int					):


          '''simple docstring'''


          UpperCAmelCase__     :						Union[str, Any]						=							[
              [
                  self.rows[other_row][other_column]
                  for other_column in range(self.num_columns					)
                  if other_column != column
              ]
              for other_row in range(self.num_rows					)
              if other_row != row
          ]
          return Matrix(_A					).determinant()






      def lowercase_				(   self							:       Union[str, Any]		,		_A							:       int		,		_A							:       int					):


          '''simple docstring'''


          if (row + column) % 2 == 0:
              return self.get_minor(_A		,		_A					)
          return -1 * self.get_minor(_A		,		_A					)






      def lowercase_				(   self							:       int					):


          '''simple docstring'''


          return Matrix(
              [
                  [self.get_minor(_A		,		_A					) for column in range(self.num_columns					)]
                  for row in range(self.num_rows					)
              ]					)






      def lowercase_				(   self							:       Optional[Any]					):


          '''simple docstring'''


          return Matrix(
              [
                  [
                      self.minors().rows[row][column]
                      if (row + column) % 2 == 0
                      else self.minors().rows[row][column] * -1
                      for column in range(self.minors().num_columns					)
                  ]
                  for row in range(self.minors().num_rows					)
              ]					)






      def lowercase_				(   self							:       Optional[Any]					):


          '''simple docstring'''


          UpperCAmelCase__     :						Tuple						=							[
              [self.cofactors().rows[column][row] for column in range(self.num_columns					)]
              for row in range(self.num_rows					)
          ]
          return Matrix(_A					)






      def lowercase_				(   self							:       List[Any]					):


          '''simple docstring'''


          UpperCAmelCase__     :						Union[str, Any]						=							self.determinant()
          if not determinant:
              raise TypeError('''Only matrices with a non-zero determinant have an inverse'''					)
          return self.adjugate() * (1 / determinant)






      def __repr__(   self							:       int					):


          '''simple docstring'''


          return str(self.rows					)






      def __str__(   self							:       Any					):


          '''simple docstring'''


          if self.num_rows == 0:
              return "[]"
          if self.num_rows == 1:
              return "[[" + ". ".join(str(self.rows[0]					)					) + "]]"
          return (
              "["
              + "\n ".join(
                  [
                      '''[''' + '''. '''.join([str(_A					) for value in row]					) + '''.]'''
                      for row in self.rows
                  ]					)
              + "]"
          )






      def lowercase_				(   self							:       Tuple		,		_A							:       list[int]		,		_A							:       int | None = None					):


          '''simple docstring'''


          UpperCAmelCase__     :						Optional[Any]						=							TypeError('''Row must be a list containing all ints and/or floats'''					)
          if not isinstance(_A		,		_A					):
              raise type_error
          for value in row:
              if not isinstance(_A		,		(int, float)					):
                  raise type_error
          if len(_A					) != self.num_columns:
              raise ValueError(
                  '''Row must be equal in length to the other rows in the matrix'''					)
          if position is None:
              self.rows.append(_A					)
          else:
              UpperCAmelCase__     :						List[Any]						=							self.rows[0:position] + [row] + self.rows[position:]






      def lowercase_				(   self							:       Any		,		_A							:       list[int]		,		_A							:       int | None = None					):


          '''simple docstring'''


          UpperCAmelCase__     :						List[str]						=							TypeError(
              '''Column must be a list containing all ints and/or floats'''					)
          if not isinstance(_A		,		_A					):
              raise type_error
          for value in column:
              if not isinstance(_A		,		(int, float)					):
                  raise type_error
          if len(_A					) != self.num_rows:
              raise ValueError(
                  '''Column must be equal in length to the other columns in the matrix'''					)
          if position is None:
              UpperCAmelCase__     :						Dict						=							[self.rows[i] + [column[i]] for i in range(self.num_rows					)]
          else:
              UpperCAmelCase__     :						Union[str, Any]						=							[
                  self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
                  for i in range(self.num_rows					)
              ]






      def __eq__(   self							:       Optional[int]		,		_A							:       object					):


          '''simple docstring'''


          if not isinstance(_A		,		_A					):
              return NotImplemented
          return self.rows == other.rows






      def __ne__(   self							:       Optional[int]		,		_A							:       object					):


          '''simple docstring'''


          return not self == other






      def __neg__(   self							:       str					):


          '''simple docstring'''


          return self * -1






      def __add__(   self							:       Dict		,		_A							:       Matrix					):


          '''simple docstring'''


          if self.order != other.order:
              raise ValueError('''Addition requires matrices of the same order'''					)
          return Matrix(
              [
                  [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns					)]
                  for i in range(self.num_rows					)
              ]					)






      def __sub__(   self							:       int		,		_A							:       Matrix					):


          '''simple docstring'''


          if self.order != other.order:
              raise ValueError('''Subtraction requires matrices of the same order'''					)
          return Matrix(
              [
                  [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns					)]
                  for i in range(self.num_rows					)
              ]					)






      def __mul__(   self							:       Tuple		,		_A							:       Matrix | int | float					):


          '''simple docstring'''


          if isinstance(_A		,		(int, float)					):
              return Matrix(
                  [[int(element * other					) for element in row] for row in self.rows]					)
          elif isinstance(_A		,		_A					):
              if self.num_columns != other.num_rows:
                  raise ValueError(
                      '''The number of columns in the first matrix must '''
                      '''be equal to the number of rows in the second'''					)
              return Matrix(
                  [
                      [Matrix.dot_product(_A		,		_A					) for column in other.columns()]
                      for row in self.rows
                  ]					)
          else:
              raise TypeError(
                  '''A Matrix can only be multiplied by an int, float, or another matrix'''					)






      def __pow__(   self							:       Tuple		,		_A							:       int					):


          '''simple docstring'''


          if not isinstance(_A		,		_A					):
              raise TypeError('''A Matrix can only be raised to the power of an int'''					)
          if not self.is_square:
              raise ValueError('''Only square matrices can be raised to a power'''					)
          if other == 0:
              return self.identity()
          if other < 0:
              if self.is_invertable():
                  return self.inverse() ** (-other)
              raise ValueError(
                  '''Only invertable matrices can be raised to a negative power'''					)
          UpperCAmelCase__     :						List[str]						=							self
          for _ in range(other - 1					):
              result *= self
          return result






      @classmethod
      def lowercase_				(   cls							:       str		,		_A							:       list[int]		,		_A							:       list[int]					):


          '''simple docstring'''


          return sum(row[i] * column[i] for i in range(len(_A					)					)					)


if __name__ == "__main__":
  import doctest

  doctest.testmod()








UpperCAmelCase__      			=						'''Input must be a string of 8 numbers plus letter'''
UpperCAmelCase__      			=						'''TRWAGMYFPDXBNJZSQVHLCKE'''







def     a_   (__A      )				->						bool:



					"""simple docstring"""

					if not isinstance(__A				,       __A      ):
										__a					:						Any      =					f'Expected string as input, found {type(__A      ).__name__}'
										raise TypeError(__A      )

					__a					:						int      =					spanish_id.replace("-"				,       ""      ).upper()
					if len(__A      ) != 9:
										raise ValueError(__A      )

					try:
										__a					:						Tuple      =					int(spanish_id_clean[0:8]      )
										__a					:						Optional[int]      =					spanish_id_clean[8]
					except ValueError as ex:
										raise ValueError(__A      ) from ex

					if letter.isdigit():
										raise ValueError(__A      )

					return letter == LOOKUP_LETTERS[number % 23]


if __name__ == "__main__":
			import doctest

			doctest.testmod()





