import sys
import math
import heapq as hq
input = sys.stdin.readline
INF = 4611686018427387903
    
def isqrt(n):
    rn = math.sqrt(n)
    ok = max(0, int(rn - 2))
    ng = int(rn + 2)
    while(abs(ok - ng) > 1):
        mid = (ok + ng) // 2
        if(mid ** 2 <= n):
            ok = mid
        else:
            ng = mid
    return ok

'''
Main Code
'''

n = int(input())
planets = [list(map(int, input().split())) for _ in [0] * n]

graph = [[] for _ in [0] * n]
for i in range(n - 1):
    for j in range(i + 1, n):
        x1, y1, t1 = planets[i]
        x2, y2, t2 = planets[j]
        d = (x1 - x2) ** 2 + (y1 - y2) ** 2
        if(t1 != t2):
            r1 = x1 ** 2 + y1 ** 2
            r2 = x2 ** 2 + y2 ** 2
            d = r1 + r2 - isqrt(4 * r1 * r2)
        graph[i].append((j, d))
        graph[j].append((i, d))

dp = [INF] * n
que = [(0, 0)]
while(que):
    c, v = hq.heappop(que)
    if(dp[v] <= c):
        continue
    dp[v] = c
    if(v == n - 1):
        break
    for nv, nd in graph[v]:
        hq.heappush(que, (max(c, nd), nv))
ans = dp[n - 1]
print(ans)