Problem:
Score : 600 points

Problem Statement

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}.

Sample Input 1

2
0 0
1 0

Sample Output 1

0.500000000000000000

Both points are contained in the circle centered at (0.5,0) with a radius of 0.5.

Sample Input 2

3
0 0
0 1
1 0

Sample Output 2

0.707106781186497524

Sample Input 3

10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9

Sample Output 3

6.726812023536805158

If the absolute or relative error from our answer is at most 10^{-6}, the output will be considered correct.

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

// F.

#include <iostream>
#include <sstream>
#include <algorithm>
#include <vector>
#include <numeric>
#include <cmath>

using namespace std;

int main(int argc, char* argv[]) {
	cout.precision(20);
#ifdef _MSC_VER
	while (true)
#endif
	{
		int n = -1;
		cin >> n;
		if (n <= 0) return 0;
		vector<double> x(n), y(n);
		for (int i = 0; i < n; ++i) {
			cin >> x[i] >> y[i];
		}
		double r = 0;
		for (int i = 0; i < n; ++i) {
			for (int j = 0; j < n; ++j) {
				double dx = x[i] - x[j], dy = y[i] - y[j];
				r = max(r, sqrt(dx * dx + dy * dy));
			}
		}
		cout << (r / 2) << endl;
	}
	return 0;
}