// clang-format off #ifdef _LOCAL #include #else #include #define cerr if (false) cerr #define debug_bar #define debug(...) #define debug2(vv) #define debug3(vvv) #endif using namespace std; using ll = long long; using ld = long double; using str = string; #define FOR(i,l,r) for (ll i = (l); i < (r); ++i) #define RFOR(i,l,r) for (ll i = (r)-1; (l) <= i; --i) #define REP(i,n) FOR(i,0,n) #define RREP(i,n) RFOR(i,0,n) #define ALL(c) (c).begin(), (c).end() #define SORT(c) sort(ALL(c)) #define RSORT(c) sort((c).rbegin(), (c).rend()) #define MIN(c) *min_element(ALL(c)) #define MAX(c) *max_element(ALL(c)) #define COUNT(c,v) count(ALL(c),(v)) #define SZ(c) ((ll)(c).size()) #define BIT(b,i) (((b)>>(i)) & 1) #define PCNT(b) ((ll)__builtin_popcountll(b)) #define LB(c,v) distance((c).begin(), lower_bound(ALL(c), (v))) #define UB(c,v) distance((c).begin(), upper_bound(ALL(c), (v))) #define UQ(c) do { SORT(c); (c).erase(unique(ALL(c)), (c).end()); (c).shrink_to_fit(); } while (0) #define END(...) do { print(__VA_ARGS__); exit(0); } while (0) template void input(T&... a) { (cin >> ... >> a); } void print() { cout << '\n'; } template void print(const T& a) { cout << a << '\n'; } template void print(const pair& a) { cout << a.first << " " << a.second << '\n'; } template void print(const T& a, const Ts&... b) { cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; } template void cout_line(const vector& ans, int l, int r) { for (int i = l; i < r; i++) { if (i != l) { cout << ' '; } cout << ans[i]; } cout << '\n'; } template void print(const vector& a) { cout_line(a, 0, a.size()); } template bool chmin(T& a, const T b) { if (b < a) { a = b; return 1; } return 0; } template bool chmax(T& a, const T b) { if (a < b) { a = b; return 1; } return 0; } template T SUM(const vector& A) { return accumulate(ALL(A), T(0)); } template vector cumsum(const vector& A, bool offset = false) { int N = A.size(); vector S(N+1, 0); for (int i = 0; i < N; i++) { S[i+1] = S[i] + A[i]; } if (not offset) { S.erase(S.begin()); } return S; } template string to_binary(T x, int B = 0) { string s; while (x) { s += ('0' + (x & 1)); x >>= 1; } while ((int)s.size() < B) { s += '0'; } reverse(s.begin(), s.end()); return s; } template ll binary_search(const F& is_ok, ll ok, ll ng) { while (abs(ok - ng) > 1) { ll m = (ok + ng) / 2; (is_ok(m) ? ok : ng) = m; } return ok; } template double binary_search_real(const F& is_ok, double ok, double ng, int iter = 90) { for (int i = 0; i < iter; i++) { double m = (ok + ng) / 2; (is_ok(m) ? ok : ng) = m; } return ok; } template ll len(const vector& a) { return (ll)a.size(); } ll min(int a, ll b) { return min((ll)a, b); } ll min(ll a, int b) { return min(a, (ll)b); } ll max(int a, ll b) { return max((ll)a, b); } ll max(ll a, int b) { return max(a, (ll)b); } ll mod(ll x, ll m) { assert(m > 0); return (x % m + m) % m; } ll ceil(ll a, ll b) { if (b < 0) { return ceil(-a, -b); } assert(b > 0); return (a < 0 ? a / b : (a + b - 1) / b); } ll floor(ll a, ll b) { if (b < 0) { return floor(-a, -b); } assert(b > 0); return (a > 0 ? a / b : (a - b + 1) / b); } ll powint(ll x, ll n) { assert(n >= 0); if (n == 0) { return 1; }; ll res = powint(x, n>>1); res *= res; if (n & 1) { res *= x; } return res; } pair divmod(ll a, ll b) { assert(b != 0); ll q = floor(a, b); return make_pair(q, a - q * b); } ll bitlen(ll b) { if (b <= 0) { return 0; } return (64LL - __builtin_clzll(b)); } ll digitlen(ll n) { assert(n >= 0); if (n == 0) { return 1; } ll sum = 0; while (n > 0) { sum++; n /= 10; } return sum; } ll msb(ll b) { return (b <= 0 ? -1 : (63 - __builtin_clzll(b))); } ll lsb(ll b) { return (b <= 0 ? -1 : __builtin_ctzll(b)); } int a2i(const char& c) { assert(islower(c)); return (c - 'a'); } int A2i(const char& c) { assert(isupper(c)); return (c - 'A'); } int d2i(const char& d) { assert(isdigit(d)); return (d - '0'); } char i2a(const int& i) { assert(0 <= i && i < 26); return ('a' + i); } char i2A(const int& i) { assert(0 <= i && i < 26); return ('A' + i); } char i2d(const int& i) { assert(0 <= i && i <= 9); return ('0' + i); } template using PQ_max = priority_queue; template using PQ_min = priority_queue, greater>; using P = pair; using VP = vector

; using VVP = vector; using VC = vector; using VS = vector; using VVS = vector; using VI = vector; using VVI = vector; using VVVI = vector; using VLL = vector; using VVLL = vector; using VVVLL = vector; using VB = vector; using VVB = vector; using VVVB = vector; using VD = vector; using VVD = vector; using VVVD = vector; using VLD = vector; using VVLD = vector; using VVVLD = vector; const ld EPS = 1e-10; const ld PI = acosl(-1.0); constexpr int inf = (1 << 30) - 1; // 1073741824 - 1 constexpr ll INF = (1LL << 62) - 1; // 4611686018427387904 - 1 // -------------------------------------------------------- #include using namespace atcoder; uint64_t kth_root_integer(uint64_t a, uint64_t k) { if (a == 0 || a == 1 || k == 1) { return a; } if (64 <= k) { return 1; } auto kth_power_integer = [](uint64_t x, uint64_t k) -> __uint128_t { __uint128_t b = 1, m = x; while (k) { if (k & 1) { b *= m; } m *= m; k >>= 1; } return b; }; uint64_t x = pow(a, nextafter(1.0 / k, 0)); while (kth_power_integer(x + 1, k) <= a) { x++; } return x; } // clang-format on int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); ll N; input(N); VLL X(N), Y(N), T(N); REP (i, N) { input(X[i], Y[i], T[i]); } auto is_ok = [&](ll s) -> bool { dsu uf(N); REP (i, N) { FOR (j, i + 1, N) { if (T[i] == T[j]) { ll dx = X[i] - X[j]; ll dy = Y[i] - Y[j]; if (dx * dx + dy * dy <= s) { uf.merge(i, j); } } else { ll z1 = X[i] * X[i] + Y[i] * Y[i]; ll z2 = X[j] * X[j] + Y[j] * Y[j]; ll sq = kth_root_integer(4 * z1 * z2, 2); if (z1 + z2 - s <= sq) { uf.merge(i, j); } } } } return uf.same(0, N - 1); }; ll ok = 4e9; ll ng = -1; ll res = binary_search(is_ok, ok, ng); print(res); return 0; }