



'''simple docstring'''



from math import ceil, sqrt



def   _A       (   _lowerCAmelCase = 1_000_000					):



							"""simple docstring"""



							__lowercase       	=0

							for outer_width in range(3  ,   (limit // 4) + 2					):
														if outer_width**2 > limit:
																					__lowercase       	=max(ceil(sqrt(outer_width**2 - limit					)					)  ,   1					)
														else:
																					__lowercase       	=1
														if (outer_width - hole_width_lower_bound) % 2:
																					hole_width_lower_bound += 1

														answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

							return answer


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








'''simple docstring'''



from functools import lru_cache



def   _A       (   _lowerCAmelCase					):



							"""simple docstring"""



							__lowercase       	=2
							__lowercase       	=set()
							while i * i <= n:
														if n % i:
																					i += 1
														else:
																					n //= i
																					factors.add(_lowerCAmelCase					)
							if n > 1:
														factors.add(_lowerCAmelCase					)
							return factors



@lru_cache
def   _A       (   _lowerCAmelCase					):



							"""simple docstring"""



							return len(unique_prime_factors(_lowerCAmelCase					)					)



def   _A       (   _lowerCAmelCase					):



							"""simple docstring"""



							return len(set(_lowerCAmelCase					)					) in (0, 1)



def   _A       (   _lowerCAmelCase					):



							"""simple docstring"""



							__lowercase       	=2

							while True:
														# Increment each value of a generated range
														__lowercase       	=[base + i for i in range(_lowerCAmelCase					)]

														# Run elements through out unique_prime_factors function
														# Append our target number to the end.
														__lowercase       	=[upf_len(_lowerCAmelCase					) for x in group]
														checker.append(_lowerCAmelCase					)

														# If all numbers in the list are equal, return the group variable.
														if equality(_lowerCAmelCase					):
																					return group

														# Increment our base variable by 1
														base += 1



def   _A       (   _lowerCAmelCase = 4					):



							"""simple docstring"""



							__lowercase       	=run(_lowerCAmelCase					)
							return results[0] if len(_lowerCAmelCase					) else None


if __name__ == "__main__":
		print(solution())



