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 <cmath>
#include <random>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
int main() {
	int N;
	cin >> N;
	vector<int> X(N), Y(N);
	for (int i = 0; i < N; ++i) {
		cin >> X[i] >> Y[i];
	}
	double xa = 0.0, ya = 0.0, cur = 0.0, delta = 1.0;
	for (int i = 0; i < N; ++i) {
		cur = max(cur, (X[i] - xa) * (X[i] - xa) + (Y[i] - ya) * (Y[i] - ya));
	}
	mt19937 mt(2002042358);
	uniform_real_distribution<double> p(-1.0, 1.0);
	for (int i = 0; i < 5000000; ++i) {
		double nxa = xa + delta * p(mt);
		double nya = ya + delta * p(mt);
		double ncur = 0.0;
		for (int j = 0; j < N; ++j) {
			ncur = max(ncur, (X[j] - nxa) * (X[j] - nxa) + (Y[j] - nya) * (Y[j] - nya));
		}
		if (cur > ncur) {
			cur = ncur;
			xa = nxa;
			ya = nya;
		}
		delta *= 0.99999;
	}
	cout.precision(15);
	cout << sqrt(cur) << endl;
	return 0;
}