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 ll MOD = 1e9 + 7;

int main() {
    int N;
    cin >> N;
    vector<double> x(N), y(N);
    rep(i, N) cin >> x[i] >> y[i];
    double lx = 0, hx = 1000, ans = 2e6;
    rep(i, 500) {
        double mx[2] = {(lx * 2 + hx) / 3, (lx + hx * 2) / 3}, dx[2] = {2e6, 2e6};
        rep(j, 2) {
            double ly = 0, hy = 1000;
            rep(k, 500) {
                double my[2] = {(ly * 2 + hy) / 3, (ly + hy * 2) / 3}, dy[2] = {0, 0};
                rep(l, 2) {
                    rep(m, N) {
                        dy[l] = max(dy[l], (mx[j] - x[m]) * (mx[j] - x[m]) + (my[l] - y[m]) * (my[l] - y[m]));
                    }
                    dx[j] = min(dx[j], dy[l]);
                }
                if (dy[0] < dy[1]) hy = my[1];
                else ly = my[0];
            }
            ans = min(ans, dx[j]);
        }
        if (dx[0] < dx[1]) hx = mx[1];
        else lx = mx[0];
    }
    cout << setprecision(20) << sqrt(ans) << endl;
}