"""simple docstring"""
from collections import defaultdict
from math import ceil, sqrt





def    lowerCAmelCase__    (			_UpperCamelCase       :				int = 1_0_0_0_0_0_0 ,			_UpperCamelCase       :				int = 1_0					)					->				int:





						"""simple docstring"""






						snake_case								=			defaultdict(_UpperCamelCase					)

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

												hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

												for hole_width in range(_UpperCamelCase ,			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() = }""")



"""simple docstring"""
import math





def    lowerCAmelCase__    (			_UpperCamelCase       :				int					)					->				bool:





						"""simple docstring"""






						return math.sqrt(_UpperCamelCase					) * math.sqrt(_UpperCamelCase					) == num





def    lowerCAmelCase__    (			_UpperCamelCase       :				int					)					->				bool:





						"""simple docstring"""






						snake_case								=			0
						snake_case								=			n
						while left <= right:
												snake_case								=			(left + right) // 2
												if mid**2 == n:
																		return True
												elif mid**2 > n:
																		snake_case								=			mid - 1
												else:
																		snake_case								=			mid + 1
						return False


if __name__ == "__main__":
					import doctest

					doctest.testmod()


