#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
using namespace std;
using std::cout;
using std::cin;
using std::endl;
using ll=long long;
using ld=long double;
ll ILL=2167167167167167167;
const int INF=2100000000;
const ll mod=998244353;
#define rep(i,a,b) for (ll i=a;i<b;i++)
#define all(p) p.begin(),p.end()
template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;
template<class T> ll LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> ll UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}
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> void So(vector<T> &v) {sort(v.begin(),v.end());}
template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}
void yneos(bool a){if(a) cout<<"Yes\n"; else cout<<"No\n";}
template<class T> void vec_out(vector<T> &p){for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";}
template<class T> T min(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;}
template<class T> T max(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;}
template<class T> T sum(vector<T> &a){assert(!a.empty());T ans=a[0]-a[0];for(auto &x:a) ans+=x;return ans;}



void solve();
// oddloop
int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	
	int t=1;
	//cin>>t;
	rep(i,0,t) solve();
}

void solve(){
	int N;
	cin>>N;
	vector<ll> X(N),Y(N),T(N);
	rep(i,0,N) cin>>X[i]>>Y[i]>>T[i];
	auto h=[&](ll a,ll b)->ll{
		return a*a+b*b;
	};
	auto g=[&](ll a,ll b)->ll{
		if(a<b) swap(a,b);
		ll l=-1,r=a+1;
		while(r-l>1){
			ll med=(l+r)/2;
			if(h(a+b-med,0)<=4*a*b) r=med;
			else l=med;
		}
		//cout<<a<<" "<<b<<" "<<r<<endl;
		return r;
	};
	_pq<pair<ll,int>> pq;
	vector<ll> seen(N,ILL);
	seen[0]=0;
	pq.push({0,0});
	while(!pq.empty()){
		int ind;
		ll dist;
		tie(dist,ind)=pq.top();
		pq.pop();
		if(seen[ind]<dist) continue;
		//cout<<ind<<" "<<dist<<endl;
		rep(i,0,N){
			ll n_cost=dist;
			if(T[ind]==T[i]){
				chmax(n_cost,h(X[i]-X[ind],Y[i]-Y[ind]));
			}else{
				chmax(n_cost,g(h(X[i],Y[i]),h(X[ind],Y[ind])));
			}
			//cout<<ind<<"->"<<i<<" "<<n_cost<<endl;
			if(chmin(seen[i],n_cost)) pq.push({n_cost,i});
		}
	}
	//vec_out(seen);
	cout<<seen[N-1]<<"\n";
}