#include #include typedef long long int ll; using namespace std; typedef pair P; using namespace atcoder; template using min_priority_queue = priority_queue, greater>; #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 compress(vector& v) { // [3 5 5 6 1 1 10 1] -> [1 2 2 3 0 0 4 0] vector u = v; sort(u.begin(), u.end()); u.erase(unique(u.begin(),u.end()),u.end()); map 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; }