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)