from collections import deque
import math

INF = 4 * 10 ** 9

n = int(input())
points = [list(map(int, input().split())) for _ in range(n)]

dist = [[0 for _ in range(n)] for _ in range(n)]
for u in range(n - 1):
  xu, yu, tu = points[u]
  for v in range(u + 1, n):
    xv, yv, tv = points[v]
    if tu == tv:
      d = (xv - xu) ** 2 + (yv - yu) ** 2
    else:
      ok = 0
      ng = INF
      target = 4 * (xu ** 2 + yu ** 2) * (xv ** 2 + yv ** 2)
      while abs(ok - ng) > 1:
        mid = (ok + ng) // 2
        if mid * mid <= target:
          ok = mid
        else:
          ng = mid

      d = (xu ** 2 + yu ** 2) + (xv ** 2 + yv ** 2) - ok
    
    dist[u][v] = d
    dist[v][u] = d

src = 0
dst = n - 1

ng = -1
ok = INF
while abs(ok - ng) > 1:
  mid = (ok + ng) // 2
  d = [INF for _ in range(n)]
  d[src] = 0
  dq = deque([src])
  while len(dq) > 0:
    cur = dq.popleft()
    for nxt in range(n):
      if d[nxt] < INF or dist[cur][nxt] > mid:
        continue

      d[nxt] = d[cur] + 1
      dq.append(nxt)

  if d[dst] < INF:
    ok = mid
  else:
    ng = mid

print(ok)