#line 1 "A.cpp"
#include<bits/stdc++.h>
using namespace std;

using ll = long long;
using ull = unsigned long long;
template <class T>
using pq = priority_queue<T>;
template <class T>
using qp = priority_queue<T, vector<T>, greater<T>>;
#define vec(T, A, ...) vector<T> A(__VA_ARGS__);
#define vvec(T, A, h, ...) vector<vector<T>> A(h, vector<T>(__VA_ARGS__));
#define vvvec(T, A, h1, h2, ...) vector<vector<vector<T>>> A(h1, vector<vector<T>>(h2, vector<T>(__VA_ARGS__)));

#define endl "\n"
#define spa ' '
#define len(A) A.size()
#define all(A) begin(A), end(A)

#define fori1(a) for(ll _ = 0; _ < (a); _++)
#define fori2(i, a) for(ll i = 0; i < (a); i++)
#define fori3(i, a, b) for(ll i = (a); i < (b); i++)
#define fori4(i, a, b, c) for(ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c))
#define overload4(a, b, c, d, e, ...) e
#define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__)

#define INT(...) int __VA_ARGS__; inp(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__);
#define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__);
#define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__);
#define VEC(T, A, n) vector<T> A(n); inp(A);
#define VVEC(T, A, n, m) vector<vector<T>> A(n, vector<T>(m)); inp(A);

const ll MOD1 = 1000000007;
const ll MOD9 = 998244353;

template<class T> auto min(const T& a){
    return *min_element(all(a));
}
template<class T> auto max(const T& a){
    return *max_element(all(a));
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

void print(){cout << endl;}
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
    cout << head;
    if (sizeof...(Tail)) cout << spa;
    print(forward<Tail>(tail)...);
}
template<typename T>
void print(vector<T> &A){
    int n = A.size();
    for(int i = 0; i < n; i++){
        cout << A[i];
        if(i == n - 1) cout << endl;
        else cout << spa;
    }
}
template<typename T>
void print(vector<vector<T>> &A){
    for(auto &row: A) print(row);
}
template<typename T, typename S>
void print(pair<T, S> &A){
    cout << A.first << spa << A.second << endl;
}
template<typename T, typename S>
void prisep(vector<T> &A, S sep){
    int n = A.size();
    for(int i = 0; i < n; i++){
        cout << A[i];
        if(i == n - 1) cout << endl;
        else cout << sep;
    }
}
template<typename T, typename S>
void priend(T A, S end){
    cout << A << end;
}
template<typename T>
void priend(T A){
    priend(A, spa);
}
template<class... T>
void inp(T&... a){
    (cin >> ... >> a);
}
template<typename T>
void inp(vector<T> &A){
    for(auto &a:A) cin >> a;
}
template<typename T>
void inp(vector<vector<T>> &A){
    for(auto &row:A) inp(row);
}
template<typename T, typename S>
void inp(pair<T, S> &A){
    inp(A.first, A.second);
}

template<typename T>
T sum(vector<T> &A){
    T tot = 0;
    for(auto a:A) tot += a;
    return tot;
}

#line 2 "Library/C++/data_structure/UnionFind.hpp"

struct UnionFind{
    int n;
    vector<int> par;
    int group;

    UnionFind(int n) : n(n){
        par.assign(n, -1);
        group = n;
    }

    int find(int x){
        if(par[x] < 0) return x;
        par[x] = find(par[x]);
        return par[x];
    }

    bool unite(int x, int y){
        x = find(x);
        y = find(y);
        if(x == y) return false;
        if(par[x] > par[y]) swap(x, y);
        group--;
        par[x] += par[y];
        par[y] = x;
        return true;
    }

    bool same(int x, int y){
        return find(x) == find(y);
    }

    int size(int x){
        return -par[find(x)];
    }

    vector<int> roots(){
        vector<int> ret;
        for(int i = 0; i < n; i++){
            if(i == find(i)) ret.push_back(i);
        }
        return ret;
    }

};
#line 117 "A.cpp"

void solve(){
    INT(n);
    vec(ll, X, n);
    vec(ll, Y, n);
    vec(ll, T, n);
    fori(i, n) inp(X[i], Y[i], T[i]);
    
    vector<pair<ll, pair<int, int>>> edges;
    fori(i, n) fori(j, i + 1, n){
        if(T[i] != T[j]){
            ll d1 = X[i] * X[i] + Y[i] * Y[i];
            ll d2 = X[j] * X[j] + Y[j] * Y[j];
            if(d2 > d1) swap(d1, d2);
            if(d1 == d2){
                edges.push_back({0, {i, j}});
                continue;
            }
            ll a = d1, b = d2;
            ll l = -1;
            ll r = a + b;

            auto ok=[&](ll c){
                return 4 * a * b >= (c - a - b) * (c - a - b);
            };


            while(r - l > 1){
                ll c = (l + r) / 2;
                if(ok(c)){
                    r = c;
                }
                else l = c;
            }
            edges.push_back({r, {i, j}});
        }
        else{
            ll dx = X[j] - X[i];
            ll dy = Y[j] - Y[i];
            ll d = dx * dx + dy * dy;
            edges.push_back({d, {i, j}});

        }
    }
    UnionFind UF(n);
    sort(all(edges));
    for(auto tmp:edges){
        UF.unite(tmp.second.first, tmp.second.second);
        if(UF.same(0, n - 1)){
            print(tmp.first);
            break;
        }
    }
}

int main(){
    cin.tie(0)->sync_with_stdio(0);
    int t;
    t = 1;
    // cin >> t;
    while(t--) solve();
    return 0;
}