#line 1 "Main.cpp"
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <utility>
#include <atcoder/modint>
#line 2 "nachia\\math\\floor-of-kth-root.hpp"

#include <cassert>

namespace nachia{

namespace internal{

// mod 2^64
constexpr unsigned long long PowerOfULongLong(unsigned long long a, unsigned long long i){
    unsigned long long res = 1;
    while(i){ if(i&1){ res *= a; } i /= 2; a *= a; }
    return res;
}

}

unsigned long long FloorOfKthRoot(unsigned long long real, unsigned long long k){
    using u64 = unsigned long long;
    assert(k != 0);
    if(real <= 1) return real;
    if(k >= 64) return 1;
    if(k == 1) return real;
    struct Precalc{
        // a^i <= x
        static constexpr bool lesseq(u64 a, int i, u64 x) {
            if (a == 0) return true;
            for(int j=0; j<i; j++) x /= a;
            return x >= 1;
        }
        unsigned long long BORDER[64];
        constexpr Precalc() : BORDER() {
            for (int idx = 2; idx <= 63; idx++) {
                u64 l = 0, r = 1ull << 33;
                while (l + 1 < r) {
                    u64 m = (l + r) / 2;
                    if (lesseq(m, idx, ~0ull)) l = m;
                    else r = m;
                }
                BORDER[idx] = r;
            }
        };
    };
    constexpr Precalc precalc;
    u64 l = 0, r = precalc.BORDER[k];
    while (l + 1 < r) {
        u64 m = (l + r) / 2;
        if(internal::PowerOfULongLong(m, k) <= real) l = m;
        else r = m;
    }
    return l;
}

unsigned long long CeilOfKthRoot(unsigned long long real, unsigned long long k){
    if(real <= 1) return real;
    if(k >= 64) return 2;
    if(k == 1) return real;
    unsigned long long x = FloorOfKthRoot(real, k);
    if(internal::PowerOfULongLong(x, k) != real) x++;
    return x;
}

} // namespace nachia
#line 8 "Main.cpp"
using namespace std;
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
const i64 INF = 1001001001001001001;

using Modint = atcoder::static_modint<998244353>;


int main(){
    int N; cin >> N;
    vector<i64> X(N), Y(N), T(N);
    rep(i,N) cin >> X[i] >> Y[i] >> T[i];
    vector<i64> Q(N, INF);
    vector<int> vis(N);
    vector<int> bfs = {0};
    auto dist = [&](int a, int b) -> i64 {
        if(T[a] == T[b]) return (X[a]-X[b])*(X[a]-X[b])+(Y[a]-Y[b])*(Y[a]-Y[b]);
        i64 asq = X[a]*X[a]+Y[a]*Y[a];
        i64 bsq = X[b]*X[b]+Y[b]*Y[b];
        return asq + bsq - nachia::FloorOfKthRoot(4 * asq * bsq, 2);
    };
    i64 ans = 0;
    Q[0] = 0;
    rep(i,N){
        int s = bfs[i];
        ans = max(ans, Q[s]);
        vis[s] = 1;
        if(s == N-1) break;
        rep(j,N) if(vis[j] == 0) Q[j] = min(Q[j], dist(i,j));
        int nx = -1;
        rep(j,N) if(vis[j] == 0) if(nx == -1 || Q[nx] > Q[j]) nx = j;
        bfs.push_back(nx);
    }
    cout << ans << endl;
    return 0;
}



struct ios_do_not_sync{
    ios_do_not_sync(){
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
    }
} ios_do_not_sync_instance;