from heapq import heappop,heappush
def isqrt(n):
    rn = int(n**0.5)
    l = max(0, rn - 1)
    r = int(rn + 2)
    while r > l+1:
        m = (r+l)//2
        if m*m <= n:
            l = m
        else:
            r = m
    return l

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

inf = 10**20

dist = [[0]*n for i in range(n)]
for i in range(n):
    for j in range(i):
        x,y,t = XYT[i]
        nx,ny,nt = XYT[j]
        if t == nt:
            d = (x-nx)**2+(y-ny)**2
            
        else:
            r1 = (x**2+y**2)
            r2 = (nx**2+ny**2)

            d = r1+r2 - isqrt(4*r1*r2)
        dist[i][j] = dist[j][i] = d

dis = [inf]*n

dis[0] = 0
h = [[0,0]]

while h:
    d,now = heappop(h)
    if dis[now] != d:
        continue
    for j in range(n):
        if now == j:
            continue
        dnex = max(d,dist[now][j])
        if dis[j] > dnex:
            dis[j] = dnex
            heappush(h,[dnex,j])
print(dis[-1])