Problem: Given are N points (x_i, y_i) in a two-dimensional plane.

Find the minimum radius of a circle such that all the points are inside or on it.

Constraints

* 2 \leq N \leq 50
* 0 \leq x_i \leq 1000
* 0 \leq y_i \leq 1000
* The given N points are all different.
* The values in input are all integers.

Input

Input is given from Standard Input in the following format:


N
x_1 y_1
:
x_N y_N


Output

Print the minimum radius of a circle such that all the N points are inside or on it.

Your output will be considered correct if the absolute or relative error from our answer is at most 10^{-6}.

Examples

Input

2
0 0
1 0


Output

0.500000000000000000


Input

3
0 0
0 1
1 0


Output

0.707106781186497524


Input

10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9


Output

6.726812023536805158

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> P;
#define DUMP(x) cout << #x << " = " << (x) << endl;
#define FOR(i, m, n) for (ll i = m; i < n; i++)
#define IFOR(i, m, n) for (ll i = n - 1; i >= m; i--)
#define REP(i, n) FOR(i, 0, n)
#define IREP(i, n) IFOR(i, 0, n)
#define FOREACH(x, a) for (auto&(x) : (a))
#define ALL(v) (v).begin(), (v).end()
#define SZ(x) ll(x.size())

double dist(double a, double b) { return a * a + b * b; }

int main() {
  ll n;
  cin >> n;
  vector<ll> x(n), y(n);
  double X = 0, Y = 0;
  REP(i, n) {
    cin >> x[i] >> y[i];
    X += x[i];
    Y += y[i];
  }
  X /= n, Y /= n;
  double P = 0.1;
  double d, e;
  for (int i = 0; i < 30000; i++) {
    int f = 0;
    d = dist(X - x[0], Y - y[0]);
    for (int j = 1; j < n; j++) {
      e = dist(X - x[j], Y - y[j]);
      if (d < e) {
        d = e;
        f = j;
      }
    }
    X += (x[f] - X) * P;
    Y += (y[f] - Y) * P;
    P *= 0.999;
  }
  cout << fixed << setprecision(10) << sqrt(d) << endl;
}