


from __future__ import annotations

from collections.abc import Iterator







class 	snake_case_       :
					def __init__(				self       :str      ,__snake_case       :str				) ->   List[Any]:
												a__					=					value
												a__					=					None
												a__					=					None







class 	snake_case_       :
					def __init__(				self       :Dict      ,__snake_case       :List[str]				) ->   List[Any]:
												a__					=					tree
					def 			lowerCamelCase__(				self       :Optional[Any]      ,__snake_case       :Dict				) ->   Optional[Any]:

												if node is None:
																			return 0
												return node.value + (
												    self.depth_first_search(node.left				) + self.depth_first_search(node.right				)
												)



					def __iter__(				self       :Optional[Any]				) ->   str:
												yield self.depth_first_search(self.tree				)


if __name__ == "__main__":
						import doctest

						doctest.testmod()





from collections import defaultdict
from math import ceil, sqrt






def 							__lowercase       (			__lowerCAmelCase							:    int = 1_0_0_0_0_0_0 ,   __lowerCAmelCase							:    int = 1_0       ):
							a__					=					defaultdict(__lowerCAmelCase       )

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

														hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

														for hole_width in range(__lowerCAmelCase ,   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 <= 1_0       )


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




