from math import sqrt
from collections import deque

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

G=[[0 for _ in range(n)] for _ in range(n)]
dist=[0]
dist_set=set([0])

def max_sqrt(a):
    l=1
    r=int(sqrt(a)+1)
    while(r-l>1):
        mid=(r+l)//2
        if(mid**2<=a):
            l=mid
        else:
            r=mid
    return l




for i in range(n-1):
    for j in range(i+1,n):
        if i==j:
            continue
        if Z[i][2]==Z[j][2]:
            d=(Z[i][0]-Z[j][0])**2+(Z[i][1]-Z[j][1])**2
        else:
            d1=Z[i][0]**2+Z[i][1]**2
            d2=Z[j][0]**2+Z[j][1]**2
            d=d1+d2-max_sqrt(4*d1*d2)

        G[i][j]=d
        G[j][i]=d
        if d not in dist_set:
            dist.append(d)
            dist_set.add(d)

def dfs(G,d):
    not_visit=set([i for i in range(1,n)])
    Q=deque()
    Q.append(0)
    while(Q):
        v=Q.pop()
        visit=set()
        for i in not_visit:
            if G[v][i]<=d:
                visit.add(i)
                Q.append(i)
                if i==n-1:
                    return True
        not_visit-=visit
    return False

dist.sort()
l=-1
r=len(dist)-1
while(r-l>1):
    mid=(r+l)//2
    if(dfs(G,dist[mid])):
        r=mid
    else:
        l=mid


print(dist[r])