#include <bits/stdc++.h>
using namespace std;
#define int long long
int32_t main(){
    int n;
    cin>>n;
    vector<int> x(n),y(n),t(n);
    for(int i=0;i<n;i++)cin>>x[i]>>y[i]>>t[i];
    int high,low;
    high=1e9;low=0;
    while(high-low>1){
        int mid=(high+low)/2;
        queue<int> que;
        que.push(0);
        vector<int> dist(n,1e9);
        dist[0]=0;
        while(!que.empty()){
            int px=que.front();
            que.pop();
            for(int i=0;i<n;i++){
                double d;
                if(t[px]!=t[i]){
                    int a,b;
                    a=x[i ]*x[i ]+y[i ]*y[i ];
                    b=x[px]*x[px]+y[px]*y[px];
                    double hq,lq;
                    hq=1e9;lq=0;
                    while(hq-lq>0.00001){
                        double mq=(hq+lq)/2.0;
                        if(mq*mq>(double)4.0*a*b){
                            hq=mq;
                        }else{
                            lq=mq;
                        }
                    }
                    d=(double)a+b-lq;
                }else{
                    d=(x[i ]-x[px])*(x[i ]-x[px])
                    + (y[i ]-y[px])*(y[i ]-y[px]);
                }
                if(d<=mid
                && dist[i]>dist[px]+1
                ){
                    dist[i]=dist[px]+1;
                    que.push(i);
                }
            }
        }
        if(dist[n-1]==1e9){
            low=mid;
        }else{
            high=mid;
        }
    }
    cout<<high<<endl;
    return 0;
}