Problem: 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}.

Examples

Input

2
0 0
1 0


Output

0.500000000000000000


Input

3
0 0
0 1
1 0


Output

0.707106781186497524


Input

10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9


Output

6.726812023536805158

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

#define rep(i,n) for(ll i=0;i<n;i++)
#define REP(i,a,n) for(ll i=a;i<n;i++)

typedef long long ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef tuple<int,int,int> tiii;
typedef pair<ll, ll> pll;

const int INF = 100000000;
const ll LINF = 1e18+5;

ll N;

ll X[50];
ll Y[50];

ld distance(ld x1, ld y1, ld x2, ld y2){
    return sqrt((x1-x2)*(x1-x2) + (y1-y2)*(y1-y2));
}

ld f(ld x, ld y) {
    ld maxn = -1.0;
    rep(i,N) {
        maxn = max(maxn, distance(x, y, X[i], Y[i]));
    }
    return maxn;
}

// xはfix
ld g(ld x) {
    ld lhs = 0.0;
    ld rhs = 2000.0;
    rep(i,300) {
        ld y1 = (lhs * 2 + rhs) / 3.0;
        ld y2 = (lhs + rhs * 2) / 3.0;
        if(f(x,y1)>f(x,y2)) lhs = y1;
        else rhs = y2;
    }
    return f(x, (lhs+rhs)/2.0);
}

ld h() {
    ld lhs = 0.0;
    ld rhs = 2000.0;
    rep(i,300) {
        ld x1 = (lhs * 2 + rhs) / 3.0;
        ld x2 = (lhs + rhs * 2) / 3.0;
        if(g(x1) > g(x2)) lhs = x1;
        else rhs = x2;
    }
    return g((lhs+rhs)/2.0);
}

int main() {
    cin >> N;
    rep(i,N) {
        cin >> X[i] >> Y[i];
    }
    cout << fixed;
    cout << setprecision(8) << h() << endl;
    return 0;
}