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 <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <cmath>
#include <iomanip>


#define REP(i, n) for (ll i = 0; i < n; i++)
using ll = long long;
using ld = long double;

using namespace std;

#define K 1000


ll N;
ld x[50];
ld y[50];

inline ld dist(ld ax, ld ay, ld bx, ld by) {
  return (ax - bx) * (ax - bx) + (ay - by) * (ay - by);
}

int main() {
  cin >> N;

  for (int i = 0; i < N; i++) {
    cin >> x[i] >> y[i];
  }

  ld delta = 1.0;
  ld diff = 0;

  ld rx, ry;
  rx = ry = 500;

  while (delta > 1e-8) {
    for (ll t = 0; t < K; t++) {
      diff = 0;
      ll k = 0;

      REP(i, N) {
        ld d = hypot(rx - x[i], ry - y[i]);
        if (d > diff) {
          diff = d;
          k = i;
        }
      }

      rx += (x[k] - rx) * delta;
      ry += (y[k] - ry) * delta;
    }

    delta /= 2.0;
  }

  cout << setprecision(15) << diff << endl;

  return 0;
}