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 <cstdio>
#include <cmath>
#include <iostream>
#include <iomanip>
#define ld long double
#define MAX_REPS 40000
using namespace std;

int n, wh;
ld x[1005], y[1005];
ld v1, v2;
ld d, e;
ld p = 0.1;

ld d2(ld a, ld b) {
	return a*a + b*b;
}

int main() {
	cin>>n;
	for (int i = 1; i <= n; i++){
		cin>>x[i]>>y[i];
		v1 += x[i];
        v2 += y[i];
	}
	v1 /= n;
	v2 /= n;
	for (int i = 1; i <= MAX_REPS; i++) {
		wh = 1;
		d = d2(v1 - x[wh], v2 - y[wh]);
		for (int j = 2; j <= n; j++) {
			e = d2(v1 - x[j], v2 - y[j]);
			if (d < e)
				d = e, wh = j;
		}
		v1 += (x[wh] - v1)*p;
		v2 += (y[wh] - v2)*p;
		p *= 0.999;
	}
	cout<<setprecision(15)<<fixed<<sqrt(d)<<'\n';
	return 0;
}