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 rep(i,n) for(int i = 0; i < (int)(n); i++)
#define all(vec) vec.begin(), vec.end()
#define END return 0
typedef int64_t ll;
const int mod7 = 1e9 + 7;
const int mod9 = 1e9 + 9;
const int inf = 1 << 30;
const ll INF = 1LL << 60;
template<typename T> T gcd(T a, T b) {return b ? gcd(b, a % b) : abs(a);}
template<typename T> T lcm(T a, T b) {return a / gcd(a, b) * b;}
template<typename T> bool chmax(T &a, T b) {if (a < b) {a = b; return true;} return false;}
template<typename T> bool chmin(T &a, T b) {if (a > b) {a = b; return true;} return false;}
template<typename A, size_t N, typename T> void Fill(A (&array)[N], const T &val) {fill((T*)array, (T*)(array+N), val);}

int xx[50], yy[50];

void twotype() {
    printf("%.10lf\n",hypot(xx[0]-xx[1],yy[0]-yy[1]) / 2);
}

int main() {
    int n;
    cin >> n;
    double ans = 1e9;
    rep(i, n) cin >> xx[i] >> yy[i];
    if(n == 2) {twotype(); END;}
    rep(i1, 50)
        rep(i2, 50)
            rep(i3,50)
    {
        double x1,y1,x2,y2,x3,y3;
        x1 = xx[i1], y1 = yy[i1],
        x2 = xx[i2], y2 = yy[i2],
        x3 = xx[i3], y3 = yy[i3];
		double a1=2*(x2-x1);
		double b1=2*(y2-y1);
		double c1=x1*x1-x2*x2+y1*y1-y2*y2;
		double a2=2*(x3-x1);
		double b2=2*(y3-y1);
		double c2=x1*x1-x3*x3+y1*y1-y3*y3;
		double x=(b1*c2-b2*c1)/(a1*b2-a2*b1);
		double y=(c1*a2-c2*a1)/(a1*b2-a2*b1);
		double r=hypot(x-x1,y-y1);
        bool alok = true;
        printf("%.5lf %.5lf %.5lf\n",x,y,r);
        rep(i, 50) {
            double X = xx[i], Y = yy[i];
            if(hypot(x - X, y - Y) > r) alok = false;
        }
		if(alok) chmin(ans, r);
    }
    printf("%.10lf\n",ans);
}