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: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i,n) for(int i = 0; i < (int)(n); i++)
#define all(c) begin(c), end(c)
#define dump(x) cerr << __LINE__ << ":\t" #x " = " << x << endl

using ld = long long;
using P = complex<ld>;
using G = vector<P>;
const ld pi = acos(-1);
const ld eps = 1e-10;
const ld inf = 1e12;

ld cross(const P& a, const P& b) { return a.real()*b.imag() - a.imag()*b.real(); }
ld dot(const P& a, const P& b) { return a.real()*b.real() + a.imag()*b.imag(); }

using C = pair<ld, P>;
#define rad first
#define pnt second

C smallest_enclosing_disc(vector<P> ps){
    auto c3 = [](const P &a, const P &b, const P &c){
        ld A = norm(b - c);
        ld B = norm(c - a);
        ld C = norm(a - b);
        ld S = abs(cross(b - a, c - a));
        P p = (A*(B+C-A)*a + B*(C+A-B)*b + C*(A+B-C)*c) / (4*S*S);
        ld r = abs(p - a);
        return make_pair(r, p);
    };

    auto c2 = [](const P &a, const P &b){
        P c = (a + b) / (ld)2;
        ld r = abs(a - c);
        return make_pair(r, c);
    };

    auto in_circle = [](const P &a, const C &c){
        return norm(a - c.pnt) <= c.rad*c.rad + eps;
    };

    int n = ps.size();
    random_shuffle(ps.begin(), ps.end());
    C c = c2(ps[0], ps[1]);
    for(int i = 2; i < n; ++i){
        if(!in_circle(ps[i], c)){
            c = c2(ps[0], ps[i]);
            for(int j = 1; j < i; ++j){
                if(!in_circle(ps[j], c)){
                    c = c2(ps[j], ps[i]);
                    for(int k = 0; k < j; ++k){
                        if(!in_circle(ps[k], c)){
                            c = c3(ps[i], ps[j], ps[k]);
                        }
                    }
                }
            }
        }
    }
    return c;
}




int n,m;
ld  mb;
 
int main(){
    vector<int> ans;
    int k; cin >> k;
    G g(k);
    rep(j,k){
        ld x,y;
        cin >> x >> y;
        g[j] = P(x,y);
    }
    mb = smallest_enclosing_disc(g).rad;
    cout << mb << "\n";
}