#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
//using mint = modint1000000007;
//const int mod = 1000000007;
//using mint = modint998244353;
//const int mod = 998244353;
const int INF = 1e9;
const long long LINF = 1e18;
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep2(i,l,r)for(int i=(l);i<(r);++i)
#define rrep(i, n) for (int i = (n-1); i >= 0; --i)
#define rrep2(i,l,r)for(int i=(r-1);i>=(l);--i)
#define all(x) (x).begin(),(x).end()
#define allR(x) (x).rbegin(),(x).rend()
#define endl "\n"
#define P pair<int,int>
template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }
long long sqrt(long long n) {
	long long ok = 0;
	long long ng = 2 * INF + 10;
	while (1 < abs(ok - ng)) {
		long long c = (ng + ok) / 2;
		if ((c * c) <= n) ok = c;
		else ng = c;
	}
	//cout << n << " " << ok << endl;
	return ok;
}
int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int n; cin >> n;
	vector<long long>x(n), y(n), t(n);
	rep(i, n) cin >> x[i] >> y[i] >> t[i];
	vector<pair<long long, P>>v;
	rep(i, n)rep2(j, i + 1, n) {
		if (t[i] == t[j]) {
			long long d2 = 0;
			d2 += (x[i] - x[j]) *  (x[i] - x[j]);
			d2 += (y[i] - y[j]) *  (y[i] - y[j]);
			v.push_back({ d2, {i,j} });
			//cout << i << j << "_" << d2 << endl;
		}
		else {
			long long d1, d0;
			d0 = x[i] * x[i] + y[i] * y[i];
			d1 = x[j] * x[j] + y[j] * y[j];
			if (d0 > d1)swap(d0, d1);
			long long ng = -1;
			long long ok = LINF + 1;
			long long sq = sqrt(4 * d0 * d1);
			while (1 < abs(ok - ng)) {
				long long mid = (ng + ok) / 2;
				auto check = [&]() {
					// (sqrt(d2)-sqrt(d1))^2<=mid
					// d1 + d2 - 2 * sqrt(d1*d2) <= mid * mid
					// d1 + d2 + mid * mid <= sqrt(4 * d1 * d2);
					return (d0 + d1 - mid <= sq);
				};
				if (check()) ok = mid;
				else ng = mid;
			}
			//cout << i << j << " " << ok << endl;
			v.push_back({ ok, {i,j} });
		}
	}
	sort(all(v));
	dsu uf(n);
	rep(i, v.size()) {
		uf.merge(v[i].second.first, v[i].second.second);
		if (uf.same(0, n - 1)) {
			cout << v[i].first << endl;
			break;
		}
	}
	return 0;
}