For two sequences S and T of length N consisting of 0 and 1, let us define f(S, T) as follows:

* Consider repeating the following operation on S so that S will be equal to T. f(S, T) is the minimum possible total cost of those operations.

* Change S_i (from 0 to 1 or vice versa). The cost of this operation is D \times C_i, where D is the number of integers j such that S_j \neq T_j (1 \leq j \leq N) just before this change.



There are 2^N \times (2^N - 1) pairs (S, T) of different sequences of length N consisting of 0 and 1. Compute the sum of f(S, T) over all of those pairs, modulo (10^9+7).

Constraints

* 1 \leq N \leq 2 \times 10^5
* 1 \leq C_i \leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
C_1 C_2 \cdots C_N


Output

Print the sum of f(S, T), modulo (10^9+7).

Examples

Input

1
1000000000


Output

999999993


Input

2
5 8


Output

124


Input

5
52 67 72 25 79


Output

269312
#include<bits/stdc++.h>
using namespace std;

typedef long long ll;
const int MAX=210000;
const int MOD=1e9+7;

ll mod_pow(ll x, ll n){ //べき乗
    ll ans=1;
    while(n!=0){
        if(n&1) ans=ans*x%MOD;
        x=x*x%MOD;
        n=n>>1;
    }
    return ans;
}

int main(){
    int N; cin >> N;
    ll c[N];
    for(int i=0;i<N;i++) cin >> c[i];
    sort(c,c+N,greater<ll>());
    if(N==1){
        cout << c[0]*2%MOD << endl;
        return 0;
    }
    ll ans=0;
    ll tmp;
    for(int i=0;i<N;i++){
        tmp=mod_pow(2,N+MOD-1)+i*mod_pow(2,N+MOD-2);
        tmp%=MOD;
        //cout << tmp << endl;
        ans+=tmp*c[i];
        ans%=MOD;
    }
    ans*=mod_pow(2,N-1);
    ans%=MOD;
    cout << ans << endl;
}