"""simple docstring"""


from graphs.minimum_spanning_tree_kruskal import kruskal




def 					lowercase__    (					)					->		List[Any]:




      """simple docstring"""

      _UpperCamelCase      :	Tuple						=       9
      _UpperCamelCase      :	List[str]						=       [
          [0, 1, 4],
          [0, 7, 8],
          [1, 2, 8],
          [7, 8, 7],
          [7, 6, 1],
          [2, 8, 2],
          [8, 6, 6],
          [2, 3, 7],
          [2, 5, 4],
          [6, 5, 2],
          [3, 5, 14],
          [3, 4, 9],
          [5, 4, 10],
          [1, 7, 11],
      ]

      _UpperCamelCase      :	List[str]						=       kruskal(lowerCAmelCase__		,lowerCAmelCase__			)

      _UpperCamelCase      :	List[Any]						=       [
          [7, 6, 1],
          [2, 8, 2],
          [6, 5, 2],
          [0, 1, 4],
          [2, 5, 4],
          [2, 3, 7],
          [0, 7, 8],
          [3, 4, 9],
      ]

      assert sorted(lowerCAmelCase__			) == sorted(lowerCAmelCase__			)







"""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() = }""")
