#include <bits/stdc++.h>
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define codefor int test;cin>>test;while(test--)
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define vector2d(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define vector3d(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))
using namespace std;
using ll = long long;
template<class T> using rpriority_queue = priority_queue<T, vector<T>, greater<T>>;
template<class T> istream& operator>>(istream& is, vector<T>& vec) {for(T& x : vec)is >> x;return is;}
template<class T> ostream& operator<<(ostream& os, const vector<T>& vec) {if(vec.empty())return os;os << vec[0];for(auto it = vec.begin(); ++it!= vec.end();)os << ' ' << *it;return os;}
void in(){}
template <class Head, class... Tail> void in(Head& head, Tail&... tail){cin >> head;in(tail...);}
void out(){cout << '\n';}
template<class T>void out(const T& a){cout << a << '\n';}
template <class Head, class... Tail> void out(const Head& head,const Tail&... tail){cout << head << ' ';out(tail...);}
const int INF = 1 << 30;
const long long INF2 = 1ll << 60;
template<class T> void chmax(T &a,const T b){if(b>a)a=b;}
template<class T> void chmin(T &a,const T b){if(b<a)a=b;}

struct dsu {
    public:
    int csz;
    dsu() : _n(0) {}
    dsu(int n) : _n(n), csz(n), parent_or_size(n, -1) {}

    int merge(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        int x = leader(a), y = leader(b);
        if (x == y) return x;
        if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
        csz--;
        parent_or_size[x] += parent_or_size[y];
        parent_or_size[y] = x;
        return x;
    }

    bool same(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        return leader(a) == leader(b);
    }

    int leader(int a) {
        assert(0 <= a && a < _n);
        if (parent_or_size[a] < 0) return a;
        return parent_or_size[a] = leader(parent_or_size[a]);
    }

    int size(int a) {
        assert(0 <= a && a < _n);
        return -parent_or_size[leader(a)];
    }

    std::vector<std::vector<int>> groups() {
        std::vector<int> leader_buf(_n), group_size(_n);
        for (int i = 0; i < _n; i++) {
            leader_buf[i] = leader(i);
            group_size[leader_buf[i]]++;
        }
        std::vector<std::vector<int>> result(_n);
        for (int i = 0; i < _n; i++) {
            result[i].reserve(group_size[i]);
        }
        for (int i = 0; i < _n; i++) {
            result[leader_buf[i]].push_back(i);
        }
        result.erase(
            std::remove_if(result.begin(), result.end(),
                           [&](const std::vector<int>& v) { return v.empty(); }),
            result.end());
        return result;
    }

    private:
    int _n;
    // root node: -1 * component size
    // otherwise: parent
    std::vector<int> parent_or_size;
};

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    INT(n);
    vector<tuple<ll,ll,ll>> a(n);
    ll x, y, t, x1, y1, t1;
    for(int i = 0; i < n; i++){
        cin >> x >> y >> t;
        a[i] = make_tuple(x, y, t);
    }
    auto g = [&](ll s, ll x, ll y, ll x1, ll y1){
        ll c1 = x * x + y * y, c2 = x1 * x1 + y1 * y1;
        ll c = c1 + c2 - s;
        if(c1 == c2) return true;
        if(c1 < c2)swap(c1, c2);
        ll ok = 0, ng = 1ll << 30, mid;
        while(ok + 1 < ng){
            mid = (ok + ng) / 2;
            if(mid * mid <= c1 * c2)ok = mid;
            else ng = mid;
        }
        return (c1 + c2 - 2 * ok <= s);
    };
    auto f = [&](ll s){
        dsu uf(n);
        for(int i = 0; i < n; i++){
            tie(x, y, t) = a[i];
            for(int j = i + 1; j < n; j++){
                tie(x1, y1, t1) = a[j];
                if(t != t1){
                    if(g(s, x, y, x1, y1))uf.merge(i, j);
                }else{
                    ll dx = x - x1, dy = y - y1;
                    if(dx * dx + dy * dy <= s)uf.merge(i, j);
                }
            }
        }
        return uf.same(0, n - 1);
    };
    ll ng = -1, ok = 1ll << 60, mid;
    while(ng + 1 < ok){
        mid = (ng + ok) / 2;
        if(f(mid))ok = mid;
        else ng = mid;
    }
    out(ok);
}