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)

#pragma GCC optimize ("O3")
#pragma GCC target ("avx")
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for(int i = 0; i < (n); i++)
#define rep1(i, n) for(int i = 1; i <= (n); i++)
#define co(x) cout << (x) << "\n"
#define cosp(x) cout << (x) << " "
#define ce(x) cerr << (x) << "\n"
#define cesp(x) cerr << (x) << " "
#define pb push_back
#define mp make_pair
#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)
#define Would
#define you
#define please

struct P { double x, y; };
double dist(P A, P B) {
	return sqrt((A.x - B.x) * (A.x - B.x) + (A.y - B.y) * (A.y - B.y));
}

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);


	int N;
	cin >> N;

	P XY[50];
	rep(i, N) cin >> XY[i].x >> XY[i].y;
	P O = { 0,0 };

	double kotae = 1e18;

	rep(i, N) rep(j, i) {
		P pi = XY[i];
		P pj = XY[j];

		if (pi.y != pj.y) {

			double L = 0;
			double R = 1000;
			rep(p, 100) {
				double x = L + (R - L) / 3;
				double tmp = dist(O, pi) - dist(O, pj) + 2 * x * (pj.x - pi.x);
				double y = tmp / (pi.y - pj.y) / 2;
				P p1 = { x,y };
				double d1 = 0;
				rep(k, N) chmax(d1, dist(p1, XY[k]));

				x = L + (R - L) * 2 / 3;
				tmp = dist(O, pi) - dist(O, pj) + 2 * x * (pj.x - pi.x);
				y = tmp / (pi.y - pj.y) / 2;
				P p2 = { x,y };
				double d2 = 0;
				rep(k, N) chmax(d2, dist(p2, XY[k]));

				chmin(kotae, min(d1, d2));

				if (d1 < d2) R = p2.x;
				else L = p1.x;
			}

		}
		else {
			double L = 0;
			double R = 1000;
			rep(p, 100) {
				double x = (pi.x + pj.x) / 2;
				double y = L + (R - L) / 3;
				P p1 = { x,y };
				double d1 = 0;
				rep(k, N) chmax(d1, dist(p1, XY[k]));

				y = L + (R - L) * 2 / 3;
				P p2 = { x,y };
				double d2 = 0;
				rep(k, N) chmax(d2, dist(p2, XY[k]));

				chmin(kotae, min(d1, d2));

				if (d1 < d2) R = p2.y;
				else L = p1.y;
			}
		}
	}

	cout << setprecision(12) << kotae << endl;

	Would you please return 0;
}