#include <bits/stdc++.h>
using namespace std;
#define int long long

#define d double

double leftt = -1000;
double bot = -1000;
double rightt = 1000;
double top = 1000;

int n;
vector<pair<d, d>> pos; // x, y
vector<d> rad;

vector<pair<double, double>> getpoints()
{
  d tot_x = rightt - leftt;
  d tot_y = top - bot;
  return {
    {leftt + tot_x * 3.0 / 8, bot + tot_y * 3.0 / 8}, // BL
    {leftt + tot_x * 5.0 / 8, bot + tot_y * 3.0 / 8}, // BR
    {leftt + tot_x * 3.0 / 8, bot + tot_y * 5.0 / 8}, // TL
    {leftt + tot_x * 5.0 / 8, bot + tot_y * 5.0 / 8}  // TR
  };
}

d getworstdist(d tx, d ty)
{
  d ret = 0;
  for(int i = 0; i < n; i++)
  {
    auto [x, y] = pos[i];
    d r = rad[i];
    d dx = tx - x;
    d dy = ty - y;
    d cur_dist = sqrtl(dx * dx + dy * dy) - r;
    cur_dist = max<d>(cur_dist, 0);
    ret = max<d>(cur_dist, ret);
  }
  return ret;
}

void rec()
{
  d best_d = 40000;
  int best_i = 0;
  auto pts = getpoints();
  for(int i = 0; i < 4; i++)
  {
    auto [x, y] = pts[i];
    d cur_d = getworstdist(x, y);
    if(cur_d < best_d)
    {
      best_d = cur_d;
      best_i = i;
    }
  }
  d d_x = (rightt - leftt) * 3.0 / 4 / 2;
  d d_y = (top - bot) * 3.0 / 4 / 2;
  auto [new_x, new_y] = pts[best_i];
  switch(best_i)
  {
  case 0: // BL
    rightt = new_x + d_x;
    top = new_y + d_y;
    break;
  case 1: // BR
    leftt = new_x - d_x;
    top = new_y + d_y;
    break;
  case 2: // TL
    rightt = new_x + d_x;
    bot = new_y - d_y;
    break;
  case 3: // TR
    leftt = new_x - d_x;
    bot = new_y - d_y;
    break;
  }
}

void solve()
{
  n;
  cin >> n;
  pos = vector<pair<double, double>>(n);
  rad = vector<double>(n);
  for(int i =0 ; i  < n; i++)
    cin >> pos[i].first >> pos[i].second >> rad[i];

  for(int i =0 ; i < 200; i++)
  {
    // d x = (rightt + leftt) / 2;
    // d y = (top + bot) / 2;
    rec();
    // cout << x << ' ' << y << " -> " << getworstdist(x, y) << '\n';
  }
  d x = (rightt + leftt) / 2;
  d y = (top + bot) / 2;
  cout << getworstdist(x, y) << '\n';
}

int32_t main()
{
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(10);
  cin.tie(0);

  solve();

  return 0;
}