#line 1 "test.cpp"
//#pragma GCC target("avx2")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include <debug.hpp>
#define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...) (static_cast<void>(0))
#endif
using ll = long long;
using ld = long double;
using pll = pair<ll,ll>;
using pii = pair<int,int>;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vpii = vector<pii>;
using vpll = vector<pll>;
using vs = vector<string>;
template<class T> using pq = priority_queue<T,vector<T>,greater<T>>;
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload3(a,b,c,name,...) name
#define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER)
#define rep2(i, n) for (ll i = 0; i < (n); ++i)
#define rep3(i, a, b) for (ll i = (a); i < (b); ++i)
#define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(n) for(ll i = (n) - 1;i >= 0;i--)
#define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--)
#define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--)
#define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define all1(i) begin(i),end(i)
#define all2(i,a) begin(i),begin(i)+a
#define all3(i,a,b) begin(i)+a,begin(i)+b
#define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__)
#define sum(...) accumulate(all(__VA_ARGS__),0LL)
template<class T> bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; }
template<class T> bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; }
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... Ts> void in(Ts&... t);
#define INT(...) int __VA_ARGS__; in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__; in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__; in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__; in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__; in(__VA_ARGS__)
#define VEC(type, name, size) vector<type> name(size); in(name)
#define VV(type, name, h, w) vector<vector<type>> name(h, vector<type>(w)); in(name)
ll intpow(ll a, ll b){ ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;}
ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
ll GCD(ll a,ll b) { if(a == 0 || b == 0) return a + b; if(a % b == 0) return b; else return GCD(b,a%b);}
ll LCM(ll a,ll b) { if(a == 0) return b; if(b == 0) return a;return a / GCD(a,b) * b;}
namespace IO{
#define VOID(a) decltype(void(a))
struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(12);}} setting;
template<int I> struct P : P<I-1>{};
template<> struct P<0>{};
template<class T> void i(T& t){ i(t, P<3>{}); }
void i(vector<bool>::reference t, P<3>){ int a; i(a); t = a; }
template<class T> auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; }
template<class T> auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); }
template<class T, size_t... idx> void ituple(T& t, index_sequence<idx...>){
    in(get<idx>(t)...);}
template<class T> auto i(T& t, P<0>) -> VOID(tuple_size<T>{}){
    ituple(t, make_index_sequence<tuple_size<T>::value>{});}
#undef VOID
}
#define unpack(a) (void)initializer_list<int>{(a, 0)...}
template<class... Ts> void in(Ts&... t){ unpack(IO :: i(t)); }
#undef unpack
constexpr int mod = 1000000007;
//constexpr int mod = 998244353;
static const double PI = 3.1415926535897932;
template <class F> struct REC {
    F f;
    REC(F &&f_) : f(forward<F>(f_)) {}
    template <class... Args> auto operator()(Args &&...args) const { return f(*this, forward<Args>(args)...); }};

#line 2 "library/graph/graph-template.hpp"
template <typename T> 
struct Edge {
	int from, to;
	T cost;
	Edge() = default;
	Edge(int _to, T _cost) : from(-1), to(_to), cost(_cost) {}
	Edge(int _from, int _to, T _cost) : from(_from), to(_to), cost(_cost) {}
	bool operator < (const Edge &a) const { return cost < a.cost; }
	bool operator > (const Edge &a) const { return cost > a.cost; }
    Edge &operator = (const int &x) {
        to = x;
        return *this;
    }
    operator int() const { return to; }
    friend ostream operator<<(ostream &os, Edge &edge) { return os << edge.to; }
};
 
template <typename T>
using Edges = vector<Edge<T>>;
template <typename T>
using Wgraph = vector<Edges<T>>;
using Ugraph = vector<vector<int>>;
Ugraph uinput(int N, int M = -1, bool is_directed = false, int origin = 1) {
    Ugraph g(N);
    if (M == -1) M = N - 1;
    while(M--) {
        int a,b;
        cin >> a >> b;
        a -= origin, b -= origin;
        g[a].push_back(b);
        if(!is_directed) g[b].push_back(a);
    }
    return g;
}
template <typename T>
Wgraph<T> winput(int N, int M = -1, bool is_directed = false,int origin = 1) {
    Wgraph<T> g(N);
    if (M == -1) M = N - 1;
    while(M--) {
        int a,b;
        T c;
        cin >> a >> b >> c;
        a -= origin, b -= origin;
        g[a].emplace_back(b,c);
        if(!is_directed) g[b].emplace_back(a,c);
    }
    return g;
}
#line 87 "test.cpp"

int main() {
    INT(n);
    vi x(n),y(n),t(n);
    rep(i,n) cin >> x[i] >> y[i] >> t[i];
    Wgraph<ll> g(n);
    auto calc_dist = [](const int &x1,const int &y1,const int &x2,const int &y2) -> ll {
        ll dist = 1LL * (x1 - x2) * (x1 - x2) + 1LL * (y1 - y2) * (y1 - y2);
        return dist;
    };
    rep(i,n) {
        rep(j,i+1,n) {
            if(t[i] != t[j]) {
                ll A = calc_dist(0,0,x[i],y[i]);
                ll B = calc_dist(0,0,x[j],y[j]);
                if(A < B) swap(A,B);
                ll hi = 2e9;
                ll lo = -1;
                ld C = 2 * sqrtl(A * B) + (ld)1e-11;
                while(hi - lo > 1) {
                    ll mid = (hi + lo) / 2;
                    if(mid > C) hi = mid;
                    else lo = mid;
                }
                ll cost = A - lo + B;
                g[i].emplace_back(j,cost);
                g[j].emplace_back(i,cost);
            }
            else {
                ll cost = calc_dist(x[i],y[i],x[j],y[j]);
                g[i].emplace_back(j,cost);
                g[j].emplace_back(i,cost);
            }
        }
    }
    vl dist(n,1e18);
    dist[0] = 0;
    pq<pair<ll,int>> q;
    q.emplace(0,0);
    while(!q.empty()) {
        auto [dis,id] = q.top();
        q.pop();
        if(dist[id] != dis) continue;
        for(auto &nex:g[id]) {
            if(chmin(dist[nex],max(dis,nex.cost))) q.emplace(dist[nex],nex);
        }
    }
    cout << dist[n-1] << '\n';
}