from collections import * from itertools import * from functools import * from heapq import * import math,sys input = sys.stdin.readline N = int(input()) dist = [[0]*N for _ in range(N)] XYT = [tuple(map(int,input().split())) for _ in range(N)] for i in range(N-1): xi,yi,ti = XYT[i] for j in range(i+1,N): xj,yj,tj = XYT[j] if ti==tj: td = (xi-xj)**2 + (yi-yj)**2 else: td = (math.sqrt(xi**2+yi**2)-math.sqrt(xj**2+yj**2))**2 dist[i][j]=td dist[j][i]=td class DSU: def __init__(self, n): self._n = n self.parent_or_size = [-1] * n def merge(self, a, b): assert 0 <= a < self._n assert 0 <= b < self._n x, y = self.leader(a), self.leader(b) if x == y: return x if -self.parent_or_size[x] < -self.parent_or_size[y]: x, y = y, x self.parent_or_size[x] += self.parent_or_size[y] self.parent_or_size[y] = x return x def same(self, a, b): assert 0 <= a < self._n assert 0 <= b < self._n return self.leader(a) == self.leader(b) def leader(self, a): assert 0 <= a < self._n if self.parent_or_size[a] < 0: return a self.parent_or_size[a] = self.leader(self.parent_or_size[a]) return self.parent_or_size[a] def size(self, a): assert 0 <= a < self._n return -self.parent_or_size[self.leader(a)] def groups(self): leader_buf = [self.leader(i) for i in range(self._n)] result = [[] for _ in range(self._n)] for i in range(self._n): result[leader_buf[i]].append(i) return [r for r in result if r != []] def is_ok(s): D = DSU(N) for i in range(N-1): for j in range(i+1,N): if dist[i][j]<=s: D.merge(i,j) return D.same(0,N-1) x = -1 y = 10**18 while y-x>1: mid = (y+x)//2 if is_ok(mid): y = mid else: x = mid print(y)