


from __future__ import annotations


class      __lowerCAmelCase  :






  """simple docstring"""





  def __init__(  self							:							Optional[Any]     ,					_lowerCAmelCase							:							list[list[int]]	) ->			Optional[Any]:




     """simple docstring"""
     snake_case_            =       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:
        snake_case_            =       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
        snake_case_            =       rows
     else:
        snake_case_            =       []



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




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



  @property
  def        lowerCAmelCase__	(  self							:							Any	) ->			int:




     """simple docstring"""
     return len(self.rows	)



  @property
  def        lowerCAmelCase__	(  self							:							Dict	) ->			int:




     """simple docstring"""
     return len(self.rows[0]	)



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




     """simple docstring"""
     return (self.num_rows, self.num_columns)



  @property
  def        lowerCAmelCase__	(  self							:							str	) ->			bool:




     """simple docstring"""
     return self.order[0] == self.order[1]



  def        lowerCAmelCase__	(  self							:							Dict	) ->			Matrix:




     """simple docstring"""
     snake_case_            =       [
         [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        lowerCAmelCase__	(  self							:							int	) ->			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        lowerCAmelCase__	(  self							:							Union[str, Any]	) ->			bool:




     """simple docstring"""
     return bool(self.determinant()	)



  def        lowerCAmelCase__	(  self							:							Union[str, Any]     ,					_lowerCAmelCase							:							int     ,					_lowerCAmelCase							:							int	) ->			int:




     """simple docstring"""
     snake_case_            =       [
         [
             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        lowerCAmelCase__	(  self							:							int     ,					_lowerCAmelCase							:							int     ,					_lowerCAmelCase							:							int	) ->			int:




     """simple docstring"""
     if (row + column) % 2 == 0:
        return self.get_minor(_lowerCAmelCase     ,					_lowerCAmelCase	)
     return -1 * self.get_minor(_lowerCAmelCase     ,					_lowerCAmelCase	)



  def        lowerCAmelCase__	(  self							:							Optional[int]	) ->			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        lowerCAmelCase__	(  self							:							Union[str, Any]	) ->			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        lowerCAmelCase__	(  self							:							List[Any]	) ->			Matrix:




     """simple docstring"""
     snake_case_            =       [
         [self.cofactors().rows[column][row] for column in range(self.num_columns	)]
         for row in range(self.num_rows	)
     ]
     return Matrix(_lowerCAmelCase	)



  def        lowerCAmelCase__	(  self							:							List[Any]	) ->			Matrix:




     """simple docstring"""
     snake_case_            =       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							:							Optional[int]	) ->			str:




     """simple docstring"""
     return str(self.rows	)



  def __str__(  self							:							Union[str, Any]	) ->			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        lowerCAmelCase__	(  self							:							Union[str, Any]     ,					_lowerCAmelCase							:							list[int]     ,					_lowerCAmelCase							:							int | None = None	) ->			None:




     """simple docstring"""
     snake_case_            =       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:
        snake_case_            =       self.rows[0:position] + [row] + self.rows[position:]



  def        lowerCAmelCase__	(  self							:							str     ,					_lowerCAmelCase							:							list[int]     ,					_lowerCAmelCase							:							int | None = None	) ->			None:




     """simple docstring"""
     snake_case_            =       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:
        snake_case_            =       [self.rows[i] + [column[i]] for i in range(self.num_rows	)]
     else:
        snake_case_            =       [
            self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
            for i in range(self.num_rows	)
        ]



  def __eq__(  self							:							Union[str, Any]     ,					_lowerCAmelCase							:							object	) ->			bool:




     """simple docstring"""
     if not isinstance(_lowerCAmelCase     ,					_lowerCAmelCase	):
        return NotImplemented
     return self.rows == other.rows



  def __ne__(  self							:							List[str]     ,					_lowerCAmelCase							:							object	) ->			bool:




     """simple docstring"""
     return not self == other



  def __neg__(  self							:							Union[str, Any]	) ->			Matrix:




     """simple docstring"""
     return self * -1



  def __add__(  self							:							Tuple     ,					_lowerCAmelCase							:							Matrix	) ->			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							:							Any     ,					_lowerCAmelCase							:							Matrix	) ->			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							:							str     ,					_lowerCAmelCase							:							Matrix | int | float	) ->			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							:							Optional[int]     ,					_lowerCAmelCase							:							int	) ->			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"	)
     snake_case_            =       self
     for _ in range(other - 1	):
        result *= self
     return result



  @classmethod
  def        lowerCAmelCase__	(  cls							:							List[Any]     ,					_lowerCAmelCase							:							list[int]     ,					_lowerCAmelCase							:							list[int]	) ->			int:




     """simple docstring"""
     return sum(row[i] * column[i] for i in range(len(_lowerCAmelCase	)	)	)


if __name__ == "__main__":
   import doctest

   doctest.testmod()








def       _lowerCAmelCase    (				lowerCAmelCase_				:int		,    lowerCAmelCase_				:int				)->str:
   '''simple docstring'''






   if not isinstance(lowerCAmelCase_		,    lowerCAmelCase_				):
      raise ValueError("iterations must be defined as integers"				)
   if not isinstance(lowerCAmelCase_		,    lowerCAmelCase_				) or not number >= 1:
      raise ValueError(
          "starting number must be\n                         and integer and be more than 0"				)
   if not iterations >= 1:
      raise ValueError("Iterations must be done more than 0 times to play FizzBuzz"				)

   snake_case_            =       ""
   while number <= iterations:
      if number % 3 == 0:
         out += "Fizz"
      if number % 5 == 0:
         out += "Buzz"
      if 0 not in (number % 3, number % 5):
         out += str(lowerCAmelCase_				)

      # print(out)
      number += 1
      out += " "
   return out


if __name__ == "__main__":
   import doctest

   doctest.testmod()




