





"""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()







"""simple docstring"""


from collections import defaultdict
from math import ceil, sqrt




def 					lowercase__    (					lowercase_ = 1_000_000		,lowercase_ = 10			)					->		int:




      """simple docstring"""

      _UpperCamelCase      :	defaultdict						=       defaultdict(lowercase_			)

      for outer_width in range(3		,(t_limit // 4) + 2			):
            if outer_width * outer_width > t_limit:
                  _UpperCamelCase      :	Any						=       max(
                      ceil(sqrt(outer_width * outer_width - t_limit			)			)		,1			)
            else:
                  _UpperCamelCase      :	str						=       1

            hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

            for hole_width in range(lowercase_		,outer_width - 1		,2			):
                  count[outer_width * outer_width - hole_width * hole_width] += 1

      return sum(1 for n in count.values() if 1 <= n <= 10			)


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