#include <stdio.h>

int main () {
  int n = 0;
  long long x[800] = {};
  long long y[800] = {};
  int t[800] = {};
  
  int res = 0;
  
  long long e[800][800] = {};
  long long d[800] = {};
  
  int v = 0;
  int used[800] = {};
  
  res = scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    res = scanf("%lld", x+i);
    res = scanf("%lld", y+i);
    res = scanf("%d", t+i);
  }
  
  for (int i = 1; i < n; i++) {
    for (int j = 0; j < i; j++) {
      if (t[i] == t[j]) {
        long long diff_x = x[i]-x[j];
        long long diff_y = y[i]-y[j];
        long long dist = diff_x*diff_x+diff_y*diff_y;
        e[j][i] = dist;
        e[i][j] = dist;
      } else {
        long long a = x[i]*x[i]+y[i]*y[i];
        long long b = x[j]*x[j]+y[j]*y[j];
        long long s[2] = { -1LL, a+b };
        while (s[1]-s[0] > 1LL) {
          long long nxt = (s[0]+s[1])/2LL;
          long long tmp = a+b-nxt;
          if (tmp*tmp > 4LL*a*b) {
            s[0] = nxt;
          } else {
            s[1] = nxt;
          }
        }
        e[j][i] = s[1];
        e[i][j] = s[1];
      }
    }
  }
  
  for (int i = 0; i < n; i++) {
    d[i] = 1000000000000000000LL;
  }
  
  d[0] = 0LL;
  v = 0;
  while (v >= 0) {
    long long min = 1000000000000000000LL;
    used[v] = 1;
    for (int i = 0; i < n; i++) {
      long long max = d[v];
      if (max < e[v][i]) {
        max = e[v][i];
      }
      if (d[i] > max) {
        d[i] = max;
      }
    }
    v = -1;
    for (int i = 0; i < n; i++) {
      if (used[i] <= 0 && d[i] < min) {
        v = i;
        min = d[i];
      }
    }
  }
  
  printf("%lld\n", d[n-1]);
  return 0;
}