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 <stdio.h>
#include <math.h>

int n,x[55],y[55];
double gx,gy;

int main()
{
  scanf ("%d",&n);
  for (int i=0;i<n;i++) scanf ("%d %d",&x[i],&y[i]), gx +=x[i], gy += y[i];
  gx /= n, gy /= n;
  
double ans;
  for (double p=1;p>=1e-8;p*=0.999){
int idx = -1; double dist = -1;
    for (int i=0;i<n;i++){
		double d = hypot(x[i]-gx,y[i]-gy);
      if (dist < d) dist = d, idx = i;
    }
    gx += (x[idx] - gx) * p;
    gy += (y[idx] - gy) * p;
    ans = dist;
  }
  
  printf ("%.12lf\n",ans);
return 0;
}