#include <bits/stdc++.h>

#include <atcoder/dsu>
using namespace std;
using namespace atcoder;
void fast_io() {
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
}
long long sq_floor(long long x) {
    long long lo = 0, hi = 9e9;
    while (lo + 1 < hi) {
        long long mid = (lo + hi) / 2;
        if (mid * mid <= x) {
            lo = mid;
        } else {
            hi = mid;
        }
    }
    return lo;
}

int main() {
    fast_io();
    int n;
    cin >> n;
    vector<long long> x(n), y(n), t(n);
    for (int i = 0; i < n; i++) {
        cin >> x[i] >> y[i] >> t[i];
    }
    vector<long long> r(n);
    for (int i = 0; i < n; i++) {
        r[i] = x[i] * x[i] + y[i] * y[i];
    }
    vector<tuple<long long, int, int>> edges;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            if (t[i] == t[j]) {
                edges.push_back({(x[i] - x[j]) * (x[i] - x[j]) +
                                     (y[i] - y[j]) * (y[i] - y[j]),
                                 i, j});
            } else {
                edges.push_back(
                    {r[i] + r[j] - 2 * sq_floor((long long)r[i] * r[j]), i, j});
            }
        }
    }
    sort(edges.begin(), edges.end());
    dsu uf(n);
    for (auto [w, u, v] : edges) {
        uf.merge(u, v);
        if (uf.same(0, n - 1)) {
            cout << w << endl;
            return 0;
        }
    }
}