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<iostream>
#include<vector>
#include<algorithm>
#include<string>
//#include <bits/stdc++.h> 

using namespace std;
//ABC150E
int main(){
    int N;
    cin>>N;
    long int C[N];
    for (int i=0;i<N;i++) cin>>C[i];
    sort(C,C+N,greater<long int>());
    long int n=1,INF=1000000007;
    if (N==1){
        cout<<(2*C[0])%INF<<endl;
        return 0;
    }
    for (int i=0;i<N-2;i++){
        n=2*n;
        n=n%INF;
    }
    long long x=1,ans=0;
    for (int i=0;i<N;i++){
        x=(i+2)*n;
        x=x%INF;
        x=x*C[i];
        x=x%INF;
        ans+=x;
        ans=ans%INF;
    }
    ans=ans*n*4;
    ans=ans%INF;
    cout<<ans<<endl;
  
    return 0;
}