


class        __SCREAMING_SNAKE_CASE					:






							def __init__(						self  , __lowerCAmelCase  ):
														UpperCamelCase__				     =			set_counts
														UpperCamelCase__				     =			max(lowercase__  )
														UpperCamelCase__				     =			len(lowercase__  )
														UpperCamelCase__				     =			[1] * num_sets
														UpperCamelCase__				     =			list(range(lowercase__  )  )






							def 				_lowerCamelCase		(						self  , __lowerCAmelCase  , __lowerCAmelCase  ):
														UpperCamelCase__				     =			self.get_parent(lowercase__  )
														UpperCamelCase__				     =			self.get_parent(lowercase__  )

														if src_parent == dst_parent:
																					return False

														if self.ranks[dst_parent] >= self.ranks[src_parent]:
																					self.set_counts[dst_parent] += self.set_counts[src_parent]
																					UpperCamelCase__				     =			0
																					UpperCamelCase__				     =			dst_parent
																					if self.ranks[dst_parent] == self.ranks[src_parent]:
																												self.ranks[dst_parent] += 1
																					UpperCamelCase__				     =			self.set_counts[dst_parent]
														else:
																					self.set_counts[src_parent] += self.set_counts[dst_parent]
																					UpperCamelCase__				     =			0
																					UpperCamelCase__				     =			src_parent
																					UpperCamelCase__				     =			self.set_counts[src_parent]

														UpperCamelCase__				     =			max(self.max_set  , lowercase__  )
														return True







							def 				_lowerCamelCase		(						self  , __lowerCAmelCase  ):






														if self.parents[disj_set] == disj_set:
																					return disj_set
														UpperCamelCase__				     =			self.get_parent(self.parents[disj_set]  )
														return self.parents[disj_set]











from math import ceil, sqrt





def     _UpperCamelCase     (a__   :int = 100_0000       ):






							"""simple docstring"""





							UpperCamelCase__				     =			0

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




