#include<bits/stdc++.h>
namespace {
#pragma GCC diagnostic ignored "-Wunused-function"
#include<atcoder/all>
#pragma GCC diagnostic warning "-Wunused-function"
using namespace std;
using namespace atcoder;
#define rep(i,n) for(int i = 0; i < (int)(n); i++)
#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--)
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
template<class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; }
template<class T> bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; }
using ll = long long;
using P = pair<int,int>;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;

} int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  struct S {
    ll x, y, t;
  };
  vector<S> a(n);
  for(auto& [x, y, t]: a) cin >> x >> y >> t;
  ll l = -1, r = 1LL << 40;
  auto f2 = [](ll x, ll y) { return x * x + y * y; };
  while(r - l > 1) {
    ll c = (l + r) / 2;
    dsu d(n);
    rep(i, n) rep(j, i) {
      if (a[i].t == a[j].t) {
        if (f2(a[i].x - a[j].x, a[i].y - a[j].y) <= c) {
          d.merge(i, j);
        }
      } else {
        ll x2 = f2(a[i].x, a[i].y);
        ll y2 = f2(a[j].x, a[j].y);
        ll z = max(0LL, x2 + y2 - c);
        if (__int128(z) * z <= __int128(4) * x2 * y2) {
          d.merge(i, j);
        }
      }
    }
    if (d.same(0, n - 1)) {
      r = c;
    } else {
      l = c;
    }
  }
  cout << r << '\n';
}