import sys sys.setrecursionlimit(10**6) class UnionFind(): def __init__(self, n): self.n = n self.parents = [-1] * n def find(self, x): if self.parents[x] < 0: return x else: self.parents[x] = self.find(self.parents[x]) return self.parents[x] def union(self, x, y): x = self.find(x) y = self.find(y) if x == y: return if self.parents[x] > self.parents[y]: x, y = y, x self.parents[x] += self.parents[y] self.parents[y] = x def size(self, x): return -self.parents[self.find(x)] def same(self, x, y): return self.find(x) == self.find(y) def members(self, x): root = self.find(x) return [i for i in range(self.n) if self.find(i) == root] def roots(self): return [i for i, x in enumerate(self.parents) if x < 0] def group_count(self): return len(self.roots()) def all_group_members(self): return {r: self.members(r) for r in self.roots()} def __str__(self): return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots()) N=int(input()) P=[list(map(int,input().split())) for _ in range(N)] d=[] for i in range(N): Xi,Yi,Ti=P[i] x=Xi**2+Yi**2 for j in range(i+1,N): Xj,Yj,Tj=P[j] y=Xj**2+Yj**2 if Ti==Tj: d.append(((Xi-Xj)**2+(Yi-Yj)**2,i,j)) else: l,r=-1,2*(x+y) while r-l>1: mid=(l+r)//2 if mid*(mid-2*(x+y))<=4*x*y-x**2-y**2-2*x*y: r=mid else: l=mid d.append((r,i,j)) d.sort() uf=UnionFind(N) for i in range(len(d)): dis,s,t=d[i] uf.union(s,t) if uf.find(0)==uf.find(N-1): print(dis) break