Problem: We have 2N pots. The market price of the i-th pot (1 ≤ i ≤ 2N) is p_i yen (the currency of Japan).

Now, you and Lunlun the dachshund will alternately take one pot. You will go first, and we will continue until all the pots are taken by you or Lunlun. Since Lunlun does not know the market prices of the pots, she will always choose a pot randomly from the remaining pots with equal probability. You know this behavior of Lunlun, and the market prices of the pots.

Let the sum of the market prices of the pots you take be S yen. Your objective is to maximize the expected value of S. Find the expected value of S when the optimal strategy is adopted.

Constraints

* 1 ≤ N ≤ 10^5
* 1 ≤ p_i ≤ 2 × 10^5
* All input values are integers.

Input

Input is given from Standard Input in the following format:


N
p_1
:
p_{2N}


Output

Print the expected value of S when the strategy to maximize the expected value of S is adopted. The output is considered correct if its absolute or relative error from the judge's output is at most 10^{-9}.

Examples

Input

1
150000
108


Output

150000.0


Input

2
50000
50000
100000
100000


Output

183333.3333333333

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i,n) for(int i=0;i<(int)(n);++i)
#define rrep(i,n) for(int i=(int)(n)-1;i>=0;--i)
#define srep(i,s,t) for(int i=(int)(s);i<(int)(t);++i)
#define each(a,b) for(auto (a): (b))
#define all(v) (v).begin(),(v).end()
#define len(v) (int)(v).size()
#define zip(v) sort(all(v)),v.erase(unique(all(v)),v.end())
#define cmx(x,y) x=max(x,y)
#define cmn(x,y) x=min(x,y)
#define fi first
#define se second
#define pb push_back
#define show(x) cout<<#x<<" = "<<(x)<<endl
#define spair(p) cout<<#p<<": "<<p.fi<<" "<<p.se<<endl
#define svec(v) cout<<#v<<":";rep(kbrni,v.size())cout<<" "<<v[kbrni];cout<<endl
#define sset(s) cout<<#s<<":";each(kbrni,s)cout<<" "<<kbrni;cout<<endl
#define smap(m) cout<<#m<<":";each(kbrni,m)cout<<" {"<<kbrni.first<<":"<<kbrni.second<<"}";cout<<endl

using namespace std;

typedef pair<int,int> P;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<P> vp;
typedef vector<string> vs;

const int MAX_N = 100005;

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n;
    cin >> n;
    vd p(2*n);
    rep(i,2*n){
        cin >> p[i];
    }
    sort(all(p),greater<ll>());
    double ans = 0;
    srep(i,1,2*n+1){
        ans += p[i-1]*(2*n-i)/(2*n-1);
    }
    printf("%.10f\n",ans);
    return 0;
}