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 <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <ctime>
#include <algorithm>
#include <iostream>
#include <vector>
using namespace std;
#define REP(i, n) for(int i = 0; i < (int)(n); ++i)

typedef long long ll;
typedef complex<double> P;
P ps[55];

int main(void) {
  int n;
  scanf("%d", &n);
  REP(i, n) {
    double x, y;
    scanf("%lf%lf", &x, &y);
    ps[i] = P(x, y);
  }
  P o(0, 0);
  double ans = 1e9;
  REP(t, 1000000) {
    // cerr << o.real() << " " << o.imag() << endl;
    double r = 0;
    int idx = -1;
    REP(i, n) {
      double d = abs(ps[i] - o);
      if(d > r) {
        r = d;
        idx = i;
      }
    }
    ans = min(ans, r);
    o += (ps[idx] - o) / double(1+t);
  }
  printf("%.10f\n", ans);
  
  return 0;
}