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 (auto i = (decltype(n))0; i < (n); ++i)
using namespace std;
typedef long long ll;

const double PHI = (1 + sqrt(5)) / 2;

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

template <class F>
double f(double a, double b, F f) {
  for (auto e = (PHI - 2) * (a - b), c = a + e, d = b - e; c < d; e *= PHI - 1) {
    if (f(c) < f(d)) {
      b = d;
      d = c;
      c = b - e;
    } else {
      a = c;
      c = d;
      d = a + e;
    }
  }
  return f((a + b) / 2);
}

int main() {
  cin >> N;
  rep(i, N) cin >> X[i] >> Y[i];
  printf("%.13f\n", sqrt(f(0, 1000, [](double x) {
           return f(0, 1000, [=](double y) {
             double r = 0;
             rep(i, N) {
               auto dx = X[i] - x, dy = Y[i] - y;
               r = max(r, dx * dx + dy * dy);
             }
             return r;
           });
         })));
  return 0;
}