





"""simple docstring"""


def 					lowercase__    (					lowercase_		,lowercase_		,lowercase_			)					->		Tuple:




      """simple docstring"""

      def update_area_of_max_square(lowercase_		,lowercase_			) -> int:
            # BASE CASE
            if row >= rows or col >= cols:
                  return 0

            _UpperCamelCase      :	int						=       update_area_of_max_square(_lowerCamelCase		,col + 1			)
            _UpperCamelCase      :	List[str]						=       update_area_of_max_square(row + 1		,col + 1			)
            _UpperCamelCase      :	List[Any]						=       update_area_of_max_square(row + 1		,_lowerCamelCase			)

            if mat[row][col]:
                  _UpperCamelCase      :	Any						=       1 + min([right, diagonal, down]			)
                  _UpperCamelCase      :	List[Any]						=       max(largest_square_area[0]		,_lowerCamelCase			)
                  return sub_problem_sol
            else:
                  return 0

      _UpperCamelCase      :	Union[str, Any]						=       [0]
      update_area_of_max_square(0		,0			)
      return largest_square_area[0]




def 					lowercase__    (					lowercase_		,lowercase_		,lowercase_			)					->		int:




      """simple docstring"""

      def update_area_of_max_square_using_dp_array(
          lowercase_		,lowercase_		,lowercase_			) -> int:
            if row >= rows or col >= cols:
                  return 0
            if dp_array[row][col] != -1:
                  return dp_array[row][col]

            _UpperCamelCase      :	List[str]						=       update_area_of_max_square_using_dp_array(_lowerCamelCase		,col + 1		,_lowerCamelCase			)
            _UpperCamelCase      :	List[str]						=       update_area_of_max_square_using_dp_array(row + 1		,col + 1		,_lowerCamelCase			)
            _UpperCamelCase      :	Union[str, Any]						=       update_area_of_max_square_using_dp_array(row + 1		,_lowerCamelCase		,_lowerCamelCase			)

            if mat[row][col]:
                  _UpperCamelCase      :	int						=       1 + min([right, diagonal, down]			)
                  _UpperCamelCase      :	Any						=       max(largest_square_area[0]		,_lowerCamelCase			)
                  _UpperCamelCase      :	Union[str, Any]						=       sub_problem_sol
                  return sub_problem_sol
            else:
                  return 0

      _UpperCamelCase      :	int						=       [0]
      _UpperCamelCase      :	Tuple						=       [[-1] * cols for _ in range(_lowerCamelCase			)]
      update_area_of_max_square_using_dp_array(0		,0		,_lowerCamelCase			)

      return largest_square_area[0]




def 					lowercase__    (					lowercase_		,lowercase_		,lowercase_			)					->		List[str]:




      """simple docstring"""

      _UpperCamelCase      :	Optional[int]						=       [[0] * (cols + 1) for _ in range(rows + 1			)]
      _UpperCamelCase      :	Any						=       0
      for row in range(rows - 1		,-1		,-1			):
            for col in range(cols - 1		,-1		,-1			):
                  _UpperCamelCase      :	str						=       dp_array[row][col + 1]
                  _UpperCamelCase      :	int						=       dp_array[row + 1][col + 1]
                  _UpperCamelCase      :	Dict						=       dp_array[row + 1][col]

                  if mat[row][col] == 1:
                        _UpperCamelCase      :	Tuple						=       1 + min(_lowerCamelCase		,_lowerCamelCase		,_lowerCamelCase			)
                        _UpperCamelCase      :	Optional[Any]						=       max(dp_array[row][col]		,_lowerCamelCase			)
                  else:
                        _UpperCamelCase      :	List[str]						=       0

      return largest_square_area




def 					lowercase__    (					lowercase_		,lowercase_		,lowercase_			)					->		int:




      """simple docstring"""

      _UpperCamelCase      :	Optional[int]						=       [0] * (cols + 1)
      _UpperCamelCase      :	List[Any]						=       [0] * (cols + 1)
      _UpperCamelCase      :	str						=       0
      for row in range(rows - 1		,-1		,-1			):
            for col in range(cols - 1		,-1		,-1			):
                  _UpperCamelCase      :	Optional[Any]						=       current_row[col + 1]
                  _UpperCamelCase      :	int						=       next_row[col + 1]
                  _UpperCamelCase      :	Union[str, Any]						=       next_row[col]

                  if mat[row][col] == 1:
                        _UpperCamelCase      :	Optional[int]						=       1 + min(_lowerCamelCase		,_lowerCamelCase		,_lowerCamelCase			)
                        _UpperCamelCase      :	Union[str, Any]						=       max(current_row[col]		,_lowerCamelCase			)
                  else:
                        _UpperCamelCase      :	str						=       0
            _UpperCamelCase      :	Tuple						=       current_row

      return largest_square_area


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  print(largest_square_area_in_matrix_bottom_up(2, 2, [[1, 1], [1, 1]]))







"""simple docstring"""


class      __SCREAMING_SNAKE_CASE    :







  '''simple docstring'''


  def __init__(		self   :       Optional[Any]					,   __a   :       list[int]	)		->				None:
        _UpperCamelCase      :	Tuple						=       len(__a	)
        _UpperCamelCase      :	Dict						=       [0] * len_array

        if len_array > 0:
              _UpperCamelCase      :	Optional[Any]						=       array[0]

        for i in range(1					,   __a	):
              _UpperCamelCase      :	Tuple						=       self.prefix_sum[i - 1] + array[i]

  def    __SCREAMING_SNAKE_CASE				(		self   :       Dict					,   __a   :       int					,   __a   :       int	)		->				int:
        if start == 0:
              return self.prefix_sum[end]

        return self.prefix_sum[end] - self.prefix_sum[start - 1]


  def    __SCREAMING_SNAKE_CASE				(		self   :       Optional[Any]					,   __a   :       int	)		->				bool:
        _UpperCamelCase      :	int						=       {0}
        for sum_item in self.prefix_sum:
              if sum_item - target_sum in sums:
                    return True

              sums.add(__a	)

        return False


if __name__ == "__main__":
  import doctest

  doctest.testmod()
