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<iomanip>
#include<cmath>

int const MAXN = 50;

int x[MAXN], y[MAXN], N;


int main() {
  std::cin >> N;
  double cx = 0.0, cy = 0.0;
  for(int i = 0; i < N; ++i) {
    std::cin >> x[i] >> y[i];
    cx += x[i]; cy += y[i];
  }
  cx /= N; cy /= N;
  double ans2;
  for(double lr=0.1; lr > 1e-9; lr*=0.999) {
    int mI = 0;
    double dx = x[mI] - cx, dy = y[mI] - cy;
    double mD2 = dx*dx + dy*dy;
    for(int i = 1; i < N; ++i) {
      dx = x[i] - cx; dy = y[i] - cy;
      double d2 = dx*dx + dy*dy;
      if(d2 > mD2) { mI = i; mD2 = d2; }
    }
    cx += (x[mI]-cx)*lr;
    cy += (y[mI]-cy)*lr;
    ans2 = mD2;
  }
  std::cout << std::setprecision(10) << std::fixed << std::sqrt(ans2) << std::endl;
  return 0;
}