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 mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define pb push_back
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define rep(i, k, n) for (int i = (int)(k); i < (int)(n); ++i)
#define rrep(i, k, n) for (int i = (int)(n) - 1; i >= (int)(k); --i)

typedef pair<int, int> ii;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<vi> vvi;
typedef vector<vii> vv_ii;
typedef pair<int,ii> i_ii;
typedef vector<i_ii> vi_ii;
typedef long long ll;
typedef unsigned long long ull;
typedef double db;

template <class T>
inline ostream& operator<<(ostream & o, vector<T> const& v) {
    for (int i = 0; i < (int)(v.size()) - 1; ++i)
        o << v[i] << ' ';
    if (!v.empty())
        o << v.back();
    return o;
}

template <class T, class Q>
inline ostream& operator<<(ostream & o, pair<T,Q> const& p) {
    o << "(" << p.fi << "," << p.se << ")";
    return o;
}

#define EPS 1e16
using T = db;
struct pt {
    T x, y;
    pt operator+(pt p) const { return { x + p.x, y + p.y }; }
    pt operator-(pt p) const { return { x - p.x, y - p.y }; }
    pt operator*(T d) const { return { x*d, y*d }; }
    pt operator/(T d) const { return { x / d, y / d }; } // only for floating-point

    bool operator==(pt o) const { return x == o.x && y == o.y; }
    bool operator!=(pt o) const { return !(*this == o); }

    bool operator<(pt o) const {
        if (fabs(x - o.x) < EPS)
            return y < o.y;
        return x < o.x;
    }
};

double dist(pt a, pt b) {
    return hypot(a.x - b.x, a.y - b.y);
}

int main(){

    ios::sync_with_stdio(false);
    cin.tie(nullptr); cout.tie(nullptr);

    int n;
    cin >> n;

    vector<pt> v(n);
    rep(i, 0, n) {
        cin >> v[i].x >> v[i].y;
    }
    
    
    db ans;
    if (n == 1)
        ans = 0.0;
    else {
      // WA
        ans = dist(v[0], v[1]);
        rep(i, 0, n) {
            rep(j, 0, n) {
                if (i != j) {
                    ans = max(ans, dist(v[i], v[j]));
                }
            }
        }
        ans /= 2.0;
    }
    cout << fixed << setprecision(18) << ans << '\n';
    
    return 0;
}