





from __future__ import annotations







class 				__lowerCAmelCase       :







      def __init__(    self		,      lowerCAmelCase__							)   ->						int:



        '''simple docstring'''




        a__	:					Optional[Any]										=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(lowerCAmelCase__							) != 0:
          a__	:					str										=len(rows[0]							)
          if cols == 0:
            raise error
          for row in rows:
            if len(lowerCAmelCase__							) != cols:
              raise error
            for value in row:
              if not isinstance(lowerCAmelCase__		,      (int, float)							):
                raise error
          a__	:					Union[str, Any]										=rows
        else:
          a__	:					List[Any]										=[]







      def    _lowercase  (    self							)   ->						list[list[int]]:



        '''simple docstring'''




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







      @property
      def    _lowercase  (    self							)   ->						int:



        '''simple docstring'''




        return len(self.rows							)







      @property
      def    _lowercase  (    self							)   ->						int:



        '''simple docstring'''




        return len(self.rows[0]							)







      @property
      def    _lowercase  (    self							)   ->						tuple[int, int]:



        '''simple docstring'''




        return (self.num_rows, self.num_columns)







      @property
      def    _lowercase  (    self							)   ->						bool:



        '''simple docstring'''




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







      def    _lowercase  (    self							)   ->						Matrix:



        '''simple docstring'''




        a__	:					Any										=[
            [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(lowerCAmelCase__							)







      def    _lowercase  (    self							)   ->						int:



        '''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							)   ->						bool:



        '''simple docstring'''




        return bool(self.determinant()							)







      def    _lowercase  (    self		,      lowerCAmelCase__		,      lowerCAmelCase__							)   ->						int:



        '''simple docstring'''




        a__	:					int										=[
            [
                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(lowerCAmelCase__							).determinant()







      def    _lowercase  (    self		,      lowerCAmelCase__		,      lowerCAmelCase__							)   ->						int:



        '''simple docstring'''




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







      def    _lowercase  (    self							)   ->						Matrix:



        '''simple docstring'''




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







      def    _lowercase  (    self							)   ->						Matrix:



        '''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							)   ->						Matrix:



        '''simple docstring'''




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







      def    _lowercase  (    self							)   ->						Matrix:



        '''simple docstring'''




        a__	:					List[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							)   ->						str:



        '''simple docstring'''




        return str(self.rows							)







      def __str__(    self							)   ->						str:



        '''simple docstring'''




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







      def    _lowercase  (    self		,      lowerCAmelCase__		,      lowerCAmelCase__ = None							)   ->						None:



        '''simple docstring'''




        a__	:					Union[str, Any]										=TypeError("Row must be a list containing all ints and/or floats"							)
        if not isinstance(lowerCAmelCase__		,      lowerCAmelCase__							):
          raise type_error
        for value in row:
          if not isinstance(lowerCAmelCase__		,      (int, float)							):
            raise type_error
        if len(lowerCAmelCase__							) != 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(lowerCAmelCase__							)
        else:
          a__	:					Optional[int]										=self.rows[0:position] + [row] + self.rows[position:]







      def    _lowercase  (    self		,      lowerCAmelCase__		,      lowerCAmelCase__ = None							)   ->						None:



        '''simple docstring'''




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







      def __eq__(    self		,      lowerCAmelCase__							)   ->						bool:



        '''simple docstring'''




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







      def __ne__(    self		,      lowerCAmelCase__							)   ->						bool:



        '''simple docstring'''




        return not self == other







      def __neg__(    self							)   ->						Matrix:



        '''simple docstring'''




        return self * -1







      def __add__(    self		,      lowerCAmelCase__							)   ->						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		,      lowerCAmelCase__							)   ->						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		,      lowerCAmelCase__							)   ->						Matrix:



        '''simple docstring'''




        if isinstance(lowerCAmelCase__		,      (int, float)							):
          return Matrix(
              [[int(element * other							) for element in row] for row in self.rows]							)
        elif isinstance(lowerCAmelCase__		,      lowerCAmelCase__							):
          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(lowerCAmelCase__		,      lowerCAmelCase__							) 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		,      lowerCAmelCase__							)   ->						Matrix:



        '''simple docstring'''




        if not isinstance(lowerCAmelCase__		,      lowerCAmelCase__							):
          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"							)
        a__	:					List[str]										=self
        for _ in range(other - 1							):
          result *= self
        return result







      @classmethod
      def    _lowercase  (    cls		,      lowerCAmelCase__		,      lowerCAmelCase__							)   ->						int:



        '''simple docstring'''




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


if __name__ == "__main__":
     import doctest

     doctest.testmod()













def      _A       (		SCREAMING_SNAKE_CASE     :   int = 50						):





  """simple docstring"""



  a__	:					Any										=[1] * (length + 1)

  for row_length in range(3       ,       length + 1						):
    for block_length in range(3       ,       row_length + 1						):
      for block_start in range(row_length - block_length						):
        ways_number[row_length] += ways_number[
            row_length - block_start - block_length - 1
        ]

      ways_number[row_length] += 1

  return ways_number[length]


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






