#include <bits/stdc++.h>
#include <atcoder/all>
typedef long long int ll;
using namespace std;
typedef pair<ll, ll> P;
using namespace atcoder;
template<typename T> using min_priority_queue = priority_queue<T, vector<T>, greater<T>>;
#define USE998244353
#ifdef USE998244353
const ll MOD = 998244353;
using mint = modint998244353;
#else
const ll MOD = 1000000007;
using mint = modint1000000007;
#endif
const int MAX = 2000005;
long long fac[MAX], finv[MAX], inv[MAX];
void COMinit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i < MAX; i++){
        fac[i] = fac[i - 1] * i % MOD;
        inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
        finv[i] = finv[i - 1] * inv[i] % MOD;
    }
}
long long COM(int n, int k){
    if (n < k) return 0;
    if (n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}
ll gcd(ll x, ll y) {
   if (y == 0) return x;
   else if (y > x) {
       return gcd (y, x); 
   }
   else return gcd(x % y, y);
}
ll lcm(ll x, ll y) {
   return x / gcd(x, y) * y;
}
ll my_sqrt(ll x) {
    // 
    ll m = 0;
    ll M = 3000000001;
    while (M - m > 1) {
        ll now = (M + m) / 2;
        if (now * now <= x) {
            m = now;
        }
        else {
            M = now;
        }
    }
    return m;
}
ll keta(ll num, ll arity) {
    ll ret = 0;
    while (num) {
        num /= arity;
        ret++;
    }
    return ret;
}
ll ceil(ll n, ll m) {
    // n > 0, m > 0
    ll ret = n / m;
    if (n % m) ret++;
    return ret;
}
ll pow_ll(ll x, ll n) {
    if (n == 0) return 1;
    if (n % 2) {
        return pow_ll(x, n - 1) * x;
    }
    else {
        ll tmp = pow_ll(x, n / 2);
        return tmp * tmp;
    }
}
vector<ll> compress(vector<ll>& v) {
    // [3 5 5 6 1 1 10 1] -> [1 2 2 3 0 0 4 0] 
    vector<ll> u = v;
    sort(u.begin(), u.end());
    u.erase(unique(u.begin(),u.end()),u.end());
    map<ll, ll> mp;
    for (int i = 0; i < u.size(); i++) {
        mp[u[i]] = i;
    }
    for (int i = 0; i < v.size(); i++) {
        v[i] = mp[v[i]];
    }
    return v;
}

ll dis(ll x1, ll y1) {
    return x1 * x1 + y1 * y1;
}
bool canGo(ll x1, ll y1, ll x2, ll y2, ll s) {
    ll r1 = dis(x1, y1);
    ll r2 = dis(x2, y2);
    ll left = r1 + r2 - s; 
    if (left < 0) return true;
    return left * left <= 4 * r1 * r2;
} 
int main() {
    int n;
    cin >> n;
    ll x[n];
    ll y[n];
    ll t[n];
    for (int i = 0; i < n; i++) cin >> x[i] >> y[i] >> t[i];
    ll M = (ll)1e10;
    ll m = -1;
    while (M - m > 1) {
        ll mid = (M + m) / 2;
        // check if we can go to n-th planet in level of mid
        dsu d(n);
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                if (t[i] == t[j]) {
                    if (dis(x[i] - x[j], y[i] - y[j]) <= mid) {
                        d.merge(i, j);
                    }
                }
                else {
                    if (canGo(x[i], y[i], x[j], y[j], mid)) {
                        d.merge(i, j);
                    }
                }
            }
        }
        if (d.same(0, n - 1)) {
            // can go with level mid
            M = mid;
        }
        else {
            m = mid;
        }
    }
    cout << M << endl;
    return 0;
}