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 <vector>
#include <complex>
#include <cmath>
#include <iomanip>

using Comp = std::complex<double>;

int main() {
	int n;
	std::cin >> n;
	
	std::vector<Comp> ps(n);
	for (auto&& p : ps) {
		int x, y;
		std::cin >> x >> y;

		p = Comp(x, y);
	}

	auto contains = [&](const Comp& c, double r, int a) {
		return std::abs(ps[a] - c) <= r;
	};

	auto check = [&](double r) -> bool{
		for (int a = 0; a < n; ++a) {
			for (int b = 0; b < n; ++b) {
				if (a == b)
					continue;

				const Comp v = ps[a] - ps[b];
				const Comp w(v.imag(), -v.real());
				const double l = std::abs(v);
				
				if (r/l < 0.5)
					continue;

				const double k = std::sqrt(r/l*r/l - 0.25);

				const Comp center = ps[b] + 0.5 * v + k * w;
				
				bool isOK = true;
				for (int i = 0; i < n; ++i) {
					if (i == a || i == b)
						continue;

					if (!contains(center, r, i)) {
						isOK = false;
						break;
					}
				}

				if (isOK)
					return true;
			}
		}

		return false;
	};

	double l = 0, r = 1000;
	for (int i = 0; i < 35; ++i) {
		double mid = (l + r) / 2;
		if (check(mid))
			r = mid;
		else
			l = mid;
	}

	std::cout << std::fixed << std::setprecision(7) << l << std::endl;
}