#include <algorithm>
#include <atcoder/all>
#include <bitset>
#include <cassert>
#include <cmath>
#include <ctime>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using namespace atcoder;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repr(i, n) for (int i = (int)(n) - 1; i >= 0; i--)
#define repk(i, k, n) for (int i = k; i < (int)(n); i++)
#define all(v) v.begin(), v.end()
#define mod1 1000000007
#define mod2 998244353
#define mod3 100000007
#define vi vector<int>
#define vs vector<string>
#define vc vector<char>
#define vl vector<ll>
#define vb vector<bool>
#define vvi vector<vector<int>>
#define vvc vector<vector<char>>
#define vvl vector<vector<ll>>
#define vvb vector<vector<bool>>
#define vvvi vector<vector<vector<int>>>
#define vvvl vector<vector<vector<ll>>>
#define pii pair<int, int>
#define pil pair<int, ll>
#define pli pair<ll, int>
#define pll pair<ll, ll>
#define vpii vector<pair<int, int>>
#define vpll vector<pair<ll, ll>>
#define vvpii vector<vector<pair<int, int>>>
#define vvpll vector<vector<pair<ll, ll>>>

template <typename T>
void debug(T e) {
    cerr << e << endl;
}

template <typename T>
void debug(vector<T> &v) {
    rep(i, v.size()) { cerr << v[i] << " "; }
    cerr << endl;
}

template <typename T>
void debug(vector<vector<T>> &v) {
    rep(i, v.size()) {
        rep(j, v[i].size()) { cerr << v[i][j] << " "; }
        cerr << endl;
    }
}

template <typename T>
void debug(vector<pair<T, T>> &v) {
    rep(i, v.size()) { cerr << v[i].first << " " << v[i].second << endl; }
}

template <typename T>
void debug(set<T> &st) {
    for (auto itr = st.begin(); itr != st.end(); itr++) {
        cerr << *itr << " ";
    }
    cerr << endl;
}

template <typename T>
void debug(multiset<T> &ms) {
    for (auto itr = ms.begin(); itr != ms.end(); itr++) {
        cerr << *itr << " ";
    }
    cerr << endl;
}

template <typename T>
void debug(map<T, T> &mp) {
    for (auto itr = mp.begin(); itr != mp.end(); itr++) {
        cerr << itr->first << " " << itr->second << endl;
    }
}

void debug_out() { cerr << endl; }

template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << H << " ";
    debug_out(T...);
}

using mint = modint998244353;

bool s1(ll x1, ll y1, ll x2, ll y2, ll s) {
    return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2) <= s;
}

bool s2(ll x1, ll y1, ll x2, ll y2, ll s) {
    ll left = x1 * x1 + y1 * y1 + x2 * x2 + y2 * y2 - s;
    if (x1 * x1 + y1 * y1 + x2 * x2 + y2 * y2 - s < 0) {
        return true;
    }
    return left * left <= 4 * (x1 * x1 + y1 * y1) * (x2 * x2 + y2 * y2);
}

int main() {
    ll N;
    cin >> N;
    vector<ll> X(N);
    vector<ll> Y(N);
    vector<ll> T(N);
    for (ll i = 0; i < N; i++) {
        cin >> X[i] >> Y[i] >> T[i];
    }
    ll ng = -1;
    ll ok = 4000000000;
    while (ok - ng > 1) {
        ll s = (ok + ng) / 2;
        queue<ll> que;
        que.push(0);
        vector<bool> visited(N, false);
        visited[0] = true;
        while (que.size()) {
            ll p = que.front();
            que.pop();
            for (ll i = 0; i < N; i++) {
                if (visited[i]) {
                    continue;
                }
                if (T[i] == T[p]) {
                    if (s1(X[i], Y[i], X[p], Y[p], s)) {
                        visited[i] = true;
                        que.push(i);
                    }
                } else {
                    if (s2(X[i], Y[i], X[p], Y[p], s)) {
                        visited[i] = true;
                        que.push(i);
                    }
                }
            }
        }
        if (visited[N - 1]) {
            ok = s;
        } else {
            ng = s;
        }
    }
    cout << ok << endl;
}