#include <math.h>
#include <bits/stdc++.h>
#include <atcoder/all>
#pragma warning(disable: 4996)
using namespace std;
using namespace atcoder;
#define print(n) cout << (n) << endl
#define fprint(n) cout << setprecision(16) << (n) << endl
#define ceil_div(a, b) (((a) - 1) / (b) + 1)
#define rep(i, l, n) for (int i = (l); i < (n); i++)
#define itrep(itr, st) for (auto itr = st.begin(); itr != st.end(); itr++)
#define ite(i, a) for (auto& i : a)
#define last(v) v[v.size() - 1]
#define all(x) x.begin(), x.end()
#define lb(A, x) (lower_bound(all(A), x) - A.begin())
#define ub(A, x) (upper_bound(all(A), x) - A.begin())
#define INF 4611686018427387903ll
#define inf 2147483647
#define mod 1000000007ll
#define MOD 998244353ll
using str = string;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using Pair = pair<int, int>;
using mint = modint1000000007;
using Mint = modint998244353;
template <class T>	using V = vector<T>;
template <class T>	using VV = V<V<T> >;
template <class T>	using PQ = priority_queue<T, V<T>, greater<T> >;
template <class T>	using PQR = priority_queue<T>;
template <class T>	using BIT = fenwick_tree<T>;
template <class T>  inline V<T> getList(int n) { V<T> res(n); rep(i, 0, n) { cin >> res[i]; }return res; }
template <class T>  inline VV<T> getGrid(int m, int n) { VV<T> res(m, V<T>(n)); rep(i, 0, m) { res[i] = getList<T>(n); }return res; }
template <class T> inline void prints(V<T>& vec) { if (vec.size() == 0)return; cout << vec[0];	rep(i, 1, vec.size()) { cout << ' ' << vec[i]; } cout << '\n'; }
template<class T> inline vector<tuple<size_t, T> > enumerate(const vector<T>& values) { auto length = values.size(); auto values_with_indices = vector<tuple<size_t, T>>(length); for (size_t i = 0; i < length; ++i) { values_with_indices[i] = make_tuple(i, values[i]); } return values_with_indices; }
inline V<int> dtois(string& s) { V<int> vec = {}; ite(e, s) { vec.push_back(e - '0'); } return vec; }
inline V<int> atois(string& s) { V<int> vec = {}; ite(e, s) { vec.push_back(e - 'a'); } return vec; }
inline V<int> Atois(string& s) { V<int> vec = {}; ite(e, s) { vec.push_back(e - 'A'); } return vec; }

#define squ(x) ((x) * (x))

ll isqrt(ll x) {
	ll ok = 0;
	ll ng = inf;
	while (ng - ok > 1) {
		ll mid = (ok + ng) >> 1;
		if (squ(mid) <= x) {
			ok = mid;
		}
		else {
			ng = mid;
		}
	}
	return ok;
}


int main(void) {
	int n;	cin >> n;
	V<V<ll> > p = getGrid<ll>(n, 3);

	V<V<ll> > dist(n, V<ll>(n, INF));
	rep(i, 0, n - 1) {
		rep(j, i + 1, n) {
			if (p[i][2] == p[j][2]) {
				dist[i][j] = dist[j][i] = squ(p[i][0] - p[j][0]) + squ(p[i][1] - p[j][1]);
			}
			else {
				ll r1 = squ(p[i][0]) + squ(p[i][1]);
				ll r2 = squ(p[j][0]) + squ(p[j][1]);
				dist[i][j] = dist[j][i] = r1 + r2 - isqrt(4 * r1 * r2);
				// cout << i << ' ' << j << ' ' << dist[i][j] << endl;
			}
		}
	}

	V<ll> visited(n, INF);	visited[0] = 0;
	PQ<pair<ll, int> > que = {};
	que.push({ 0,0 });
	while (que.empty() == false) {
		pair<ll, int> pa = que.top();	que.pop();
		ll c_now = pa.first, v_now = pa.second;
		if (v_now == n - 1) {
			break;
		}
		if (c_now > visited[v_now]) {
			continue;
		}
		rep(v_next, 0, n) {
			ll c_next = max(c_now, dist[v_now][v_next]);
			// cout << v_now << ' ' << v_next << ' ' << dist[v_now][v_next] << endl;
			if (c_next >= visited[v_next]) {
				continue;
			}
			visited[v_next] = c_next;
			que.push({ c_next,v_next });
		}
	}
	print(visited[n - 1]);

	return 0;
}