from __future__ import annotations
class     a_			:






 '''simple docstring'''






 def __init__(      self :  List[str]      ,   lowercase__ :  list[list[int]]):







        '''simple docstring'''



        lowerCAmelCase__					     = 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:
               lowerCAmelCase__					     = 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
               lowerCAmelCase__					     = rows
        else:
               lowerCAmelCase__					     = []




 def 		__snake_case						(      self :  Union[str, Any]):







        '''simple docstring'''



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




 @property
 def 		__snake_case						(      self :  Optional[Any]):







        '''simple docstring'''



        return len(self.rows)




 @property
 def 		__snake_case						(      self :  Tuple):







        '''simple docstring'''



        return len(self.rows[0])




 @property
 def 		__snake_case						(      self :  Tuple):







        '''simple docstring'''



        return (self.num_rows, self.num_columns)




 @property
 def 		__snake_case						(      self :  Tuple):







        '''simple docstring'''



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




 def 		__snake_case						(      self :  Tuple):







        '''simple docstring'''



        lowerCAmelCase__					     = [
            [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 		__snake_case						(      self :  Optional[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 		__snake_case						(      self :  Dict):







        '''simple docstring'''



        return bool(self.determinant())




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







        '''simple docstring'''



        lowerCAmelCase__					     = [
            [
                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 		__snake_case						(      self :  str      ,   lowercase__ :  int      ,   lowercase__ :  int):







        '''simple docstring'''



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




 def 		__snake_case						(      self :  Union[str, Any]):







        '''simple docstring'''



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




 def 		__snake_case						(      self :  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 		__snake_case						(      self :  int):







        '''simple docstring'''



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




 def 		__snake_case						(      self :  Union[str, Any]):







        '''simple docstring'''



        lowerCAmelCase__					     = 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 :  List[str]):







        '''simple docstring'''



        return str(self.rows)




 def __str__(      self :  Optional[int]):







        '''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 		__snake_case						(      self :  Optional[Any]      ,   lowercase__ :  list[int]      ,   lowercase__ :  int | None = None):







        '''simple docstring'''



        lowerCAmelCase__					     = 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:
               lowerCAmelCase__					     = self.rows[0:position] + [row] + self.rows[position:]




 def 		__snake_case						(      self :  List[str]      ,   lowercase__ :  list[int]      ,   lowercase__ :  int | None = None):







        '''simple docstring'''



        lowerCAmelCase__					     = 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:
               lowerCAmelCase__					     = [self.rows[i] + [column[i]] for i in range(self.num_rows)]
        else:
               lowerCAmelCase__					     = [
                   self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
                   for i in range(self.num_rows)
               ]




 def __eq__(      self :  Union[str, Any]      ,   lowercase__ :  object):







        '''simple docstring'''



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




 def __ne__(      self :  Optional[Any]      ,   lowercase__ :  object):







        '''simple docstring'''



        return not self == other




 def __neg__(      self :  List[Any]):







        '''simple docstring'''



        return self * -1




 def __add__(      self :  List[str]      ,   lowercase__ :  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 :  Tuple      ,   lowercase__ :  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 :  Union[str, Any]      ,   lowercase__ :  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 :  Any      ,   lowercase__ :  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')
        lowerCAmelCase__					     = self
        for _ in range(other - 1):
               result *= self
        return result




 @classmethod
 def 		__snake_case						(      cls :  List[str]      ,   lowercase__ :  list[int]      ,   lowercase__ :  list[int]):







        '''simple docstring'''



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


if __name__ == "__main__":
    import doctest

    doctest.testmod()
lowerCAmelCase__     						=			'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/'






def 				__lowerCamelCase		(						lowerCAmelCase__     ):
       # Make sure the supplied data is a bytes-like object
       if not isinstance(lowerCAmelCase__     ,  lowerCAmelCase__     ):
              lowerCAmelCase__					     = F"""a bytes-like object is required, not '{data.__class__.__name__}'"""
              raise TypeError(lowerCAmelCase__     )

       lowerCAmelCase__					     = ''.join(bin(lowerCAmelCase__     )[2:].zfill(8     ) for byte in data     )

       lowerCAmelCase__					     = len(lowerCAmelCase__     ) % 6 != 0

       if padding_needed:
              # The padding that will be added later
              lowerCAmelCase__					     = b'=' * ((6 - len(lowerCAmelCase__     ) % 6) // 2)

              # Append binary_stream with arbitrary binary digits (0's by default) to make its
              # length a multiple of 6.
              binary_stream += "0" * (6 - len(lowerCAmelCase__     ) % 6)
       else:
              lowerCAmelCase__					     = b''

       # Encode every 6 binary digits to their corresponding Base64 character
       return (
           "".join(
               B64_CHARSET[int(binary_stream[index : index + 6]     ,  2     )]
               for index in range(0     ,  len(lowerCAmelCase__     )     ,  6     )     ).encode()
           + padding
       )






def 				__lowerCamelCase		(						lowerCAmelCase__     ):
       # Make sure encoded_data is either a string or a bytes-like object
       if not isinstance(lowerCAmelCase__     ,  lowerCAmelCase__     ) and not isinstance(lowerCAmelCase__     ,  lowerCAmelCase__     ):
              lowerCAmelCase__					     = (
                  'argument should be a bytes-like object or ASCII string, '
                  F"""not '{encoded_data.__class__.__name__}'"""
              )
              raise TypeError(lowerCAmelCase__     )

       # In case encoded_data is a bytes-like object, make sure it contains only
       # ASCII characters so we convert it to a string object
       if isinstance(lowerCAmelCase__     ,  lowerCAmelCase__     ):
              try:
                     lowerCAmelCase__					     = encoded_data.decode('utf-8'     )
              except UnicodeDecodeError:
                     raise ValueError('base64 encoded data should only contain ASCII characters'     )

       lowerCAmelCase__					     = encoded_data.count('='     )

       # Check if the encoded string contains non base64 characters
       if padding:
              assert all(
                  char in B64_CHARSET for char in encoded_data[:-padding]     ), "Invalid base64 character(s) found."
       else:
              assert all(
                  char in B64_CHARSET for char in encoded_data     ), "Invalid base64 character(s) found."

       # Check the padding
       assert len(lowerCAmelCase__     ) % 4 == 0 and padding < 3, "Incorrect padding"

       if padding:
              # Remove padding if there is one
              lowerCAmelCase__					     = encoded_data[:-padding]

              lowerCAmelCase__					     = ''.join(
                  bin(B64_CHARSET.index(lowerCAmelCase__     )     )[2:].zfill(6     ) for char in encoded_data     )[: -padding * 2]
       else:
              lowerCAmelCase__					     = ''.join(
                  bin(B64_CHARSET.index(lowerCAmelCase__     )     )[2:].zfill(6     ) for char in encoded_data     )

       lowerCAmelCase__					     = [
           int(binary_stream[index : index + 8]     ,  2     )
           for index in range(0     ,  len(lowerCAmelCase__     )     ,  8     )
       ]

       return bytes(lowerCAmelCase__     )


if __name__ == "__main__":
    import doctest

    doctest.testmod()
