

"""simple docstring"""





from __future__ import annotations




class 					_lowerCAmelCase  :







 """simple docstring"""







 def __init__(			self							:			Optional[Any],					UpperCAmelCase__							:			list[list[int]]	):
    __lowercase								=						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(UpperCAmelCase__	) != 0:
       __lowercase								=						len(rows[0]	)
       if cols == 0:
          raise error
       for row in rows:
          if len(UpperCAmelCase__	) != cols:
             raise error
          for value in row:
             if not isinstance(UpperCAmelCase__,					(int, float)	):
                raise error
       __lowercase								=						rows
    else:
       __lowercase								=						[]


 def 					_lowercase (			self							:			int	):
    return [[row[i] for row in self.rows] for i in range(len(self.rows[0]	)	)]


 @property
 def 					_lowercase (			self							:			str	):
    return len(self.rows	)


 @property
 def 					_lowercase (			self							:			str	):
    return len(self.rows[0]	)


 @property
 def 					_lowercase (			self							:			List[str]	):
    return (self.num_rows, self.num_columns)


 @property
 def 					_lowercase (			self							:			int	):
    return self.order[0] == self.order[1]


 def 					_lowercase (			self							:			Union[str, Any]	):
    __lowercase								=						[
        [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(UpperCAmelCase__	)


 def 					_lowercase (			self							:			List[Any]	):
    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	):
    return bool(self.determinant()	)


 def 					_lowercase (			self							:			Tuple,					UpperCAmelCase__							:			int,					UpperCAmelCase__							:			int	):
    __lowercase								=						[
        [
            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(UpperCAmelCase__	).determinant()


 def 					_lowercase (			self							:			Optional[Any],					UpperCAmelCase__							:			int,					UpperCAmelCase__							:			int	):
    if (row + column) % 2 == 0:
       return self.get_minor(UpperCAmelCase__,					UpperCAmelCase__	)
    return -1 * self.get_minor(UpperCAmelCase__,					UpperCAmelCase__	)


 def 					_lowercase (			self							:			Optional[int]	):
    return Matrix(
        [
            [self.get_minor(UpperCAmelCase__,					UpperCAmelCase__	) for column in range(self.num_columns	)]
            for row in range(self.num_rows	)
        ]	)


 def 					_lowercase (			self							:			Tuple	):
    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							:			List[str]	):
    __lowercase								=						[
        [self.cofactors().rows[column][row] for column in range(self.num_columns	)]
        for row in range(self.num_rows	)
    ]
    return Matrix(UpperCAmelCase__	)


 def 					_lowercase (			self							:			str	):
    __lowercase								=						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]	):
    return str(self.rows	)


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


 def 					_lowercase (			self							:			List[Any],					UpperCAmelCase__							:			list[int],					UpperCAmelCase__							:			int | None = None	):
    __lowercase								=						TypeError("Row must be a list containing all ints and/or floats"	)
    if not isinstance(UpperCAmelCase__,					UpperCAmelCase__	):
       raise type_error
    for value in row:
       if not isinstance(UpperCAmelCase__,					(int, float)	):
          raise type_error
    if len(UpperCAmelCase__	) != 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(UpperCAmelCase__	)
    else:
       __lowercase								=						self.rows[0:position] + [row] + self.rows[position:]


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


 def __eq__(			self							:			List[Any],					UpperCAmelCase__							:			object	):
    if not isinstance(UpperCAmelCase__,					UpperCAmelCase__	):
       return NotImplemented
    return self.rows == other.rows


 def __ne__(			self							:			Any,					UpperCAmelCase__							:			object	):
    return not self == other


 def __neg__(			self							:			Tuple	):
    return self * -1


 def __add__(			self							:			List[Any],					UpperCAmelCase__							:			Matrix	):
    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,					UpperCAmelCase__							:			Matrix	):
    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,					UpperCAmelCase__							:			Matrix | int | float	):
    if isinstance(UpperCAmelCase__,					(int, float)	):
       return Matrix(
           [[int(element * other	) for element in row] for row in self.rows]	)
    elif isinstance(UpperCAmelCase__,					UpperCAmelCase__	):
       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(UpperCAmelCase__,					UpperCAmelCase__	) 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,					UpperCAmelCase__							:			int	):
    if not isinstance(UpperCAmelCase__,					UpperCAmelCase__	):
       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"	)
    __lowercase								=						self
    for _ in range(other - 1	):
       result *= self
    return result



 @classmethod
 def 					_lowercase (			cls							:			str,					UpperCAmelCase__							:			list[int],					UpperCAmelCase__							:			list[int]	):
    return sum(row[i] * column[i] for i in range(len(UpperCAmelCase__	)	)	)


if __name__ == "__main__":
   import doctest

   doctest.testmod()










"""simple docstring"""


from __future__ import annotations


def 					UpperCAmelCase__       (snake_case__							:					list[int]		,   snake_case__							:					int    ):
  """simple docstring"""

  if len(snake_case__    ) < k or k < 0:
    raise ValueError("""Invalid Input"""    )
  _snake_case							:		Optional[int]								=  sum(array[:k]    )
  for i in range(len(snake_case__    ) - k    ):
    _snake_case							:		Optional[Any]								=  current_sum - array[i] + array[i + k]
    _snake_case							:		List[str]								=  max(snake_case__		,   snake_case__    )
  return max_sum


if __name__ == "__main__":
     from doctest import testmod
     from random import randint

     testmod()
     A_						=				[randint(-10_00, 10_00) for i in range(1_00)]
     A_						=				randint(0, 1_10)
     print(F'''The maximum sum of {k} consecutive elements is {max_sum_in_array(array,k)}''')


