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 <map>
#include <queue>
#include <cmath>
#include <vector>
#include <string>
#include <algorithm>
#include <functional>
using namespace std;

int N;
double X[10009], Y[10009];

double getscore(double px, double py) {
	double maxn = 0;
	for (int i = 1; i <= N; i++) {
		double dst = sqrt((px - X[i]) * (px - X[i]) + (py - Y[i]) * (py - Y[i]));
		maxn = max(maxn, dst);
	}
	return maxn;
}

double getscore_Y(double px) {
	double L = -1e9, R = 1e9, c1, c2, ans = 1e9;
	for (int i = 0; i < 100; i++) {
		c1 = (L + L + R) / 3.0;
		c2 = (L + R + R) / 3.0;
		double a1 = getscore(px, c1);
		double a2 = getscore(px, c2);
		ans = min(ans, min(a1, a2));
		if (a1 > a2) L = c1;
		else R = c2;
	}
	return ans;
}

int main() {
	cin >> N;
	for (int i = 1; i <= N; i++) cin >> X[i] >> Y[i];

	double L = -1e9, R = 1e9, c1, c2, ans = 1e9;
	for (int i = 0; i < 100; i++) {
		c1 = (L + L + R) / 3.0;
		c2 = (L + R + R) / 3.0;
		double a1 = getscore_Y(c1);
		double a2 = getscore_Y(c2);
		ans = min(ans, min(a1, a2));
		if (a1 > a2) L = c1;
		else R = c2;
	}

	printf("%.12lf\n", ans);
	return 0;
}