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)

#include <bits/stdc++.h>
using namespace std;
#define debug(x) cout << #x " = " << (x) << '\n';
#define P(x) cout << #x << '\n';    
#define int long long
typedef pair<int, int> pii;
const int mod = 1000000007;
using ld = long double;
const int maxn = 100;
ld x[maxn], y[maxn];
ld dist(ld x1, ld y1, ld x2, ld y2)
{
	return abs(x1 - x2) * abs(x1 - x2) + abs(y1 - y2) * abs(y1 - y2);
}

int32_t main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cout << fixed << setprecision(15);
	#ifdef LOCAL_DEFINE
		freopen("in.txt", "rt", stdin);
	#endif
	
	
	int n;
	cin >> n;
	for(int i = 0; i < n; ++ i)
		cin >> x[i] >> y[i];
	ld ans = 1e18;
	for(int i = 0; i < n; ++ i)
	{
		for(int j = 0; j < n; ++ j)
		{
			if(j == i) continue;
			ld midx = (x[i] + x[j]) / 2.0;
			ld midy = (y[i] + y[j]) / 2.0;
			ld rad = dist(x[i], y[i], x[j], y[j]) / 4.0;
			// debug(rad);
			// debug(midx);
			// debug(midy);
			bool ok = true;
			for(int p = 0; p < n; ++ p)
			{
				ld cur = dist(midx, midy, x[p], y[p]);
				// debug(x[p]);
				// debug(y[p]);
				// debug(cur);
				ok &= (cur <= rad);
			}
			if(ok)
				ans = min(ans, rad);
		}
	}
	cout << sqrtl(ans) << '\n';
	
	return 0;
}