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 <algorithm>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <queue>
#include <utility>
#include <vector>
using namespace std;

int n;
double x[50], y[50];
double dis(double x1, double y1, double x2, double y2) {
  return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
}

double calc(double xx, double yy) {
  double res = 0.0;
  for (int i = 0; i < n; i++) {
    res = max(res, dis(xx, yy, x[i], y[i]));
  }
  return res;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%lf%lf", &x[i], &y[i]);
    x[i] += 2.0;
  }
  double cx = 2.5, cy = 0.5, r, left = 0.0, right, alpha = 1e2;
  for (int i = 0; i < 5000000; i++) {
    double dx = (sqrt(calc(cx + 1e-7, cy)) - sqrt(calc(cx-1e-7, cy))) / 2e-7;
    double dy = (sqrt(calc(cx, cy + 1e-7)) - sqrt(calc(cx, cy-1e-7))) / 2e-7;
    cx -= alpha * dx;
    cy -= alpha * dy;
    alpha *= 0.9999;
  }
  printf("%.10f\n", sqrt(calc(cx, cy)));
}