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>
#define rep(i, n) for (int i = 0; i < (n); ++i)
using namespace std;
typedef long long ll;

const int E = 100;

int N;
int X[50], Y[50];

double f(double x, double y) {
  double ret = 0;
  rep(i, N) {
    auto dx = X[i] - x, dy = Y[i] - y;
    ret = max(ret, dx * dx + dy * dy);
  }
  return ret;
}

double fx(double x) {
  double y1 = 0, y2 = 1000;
  rep(_, E) {
    auto y3 = (y1 + y1 + y2) / 3, y4 = (y1 + y2 + y2) / 3;
    if (f(x, y3) < f(x, y4))
      y2 = y4;
    else
      y1 = y3;
  }
  return f(x, (y1 + y2) / 2);
}

int main() {
  cin >> N;
  rep(i, N) cin >> X[i] >> Y[i];
  double x1 = 0, x2 = 1000;
  rep(_, E) {
    auto x3 = (x1 + x1 + x2) / 3, x4 = (x1 + x2 + x2) / 3;
    if (fx(x3) < fx(x4))
      x2 = x4;
    else
      x1 = x3;
  }
  printf("%.15f\n", sqrt(fx((x1 + x2) / 2)));
  return 0;
}