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;
//test
int main(void){
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    long long n,sum=0;
    cin>>n;
    
    vector<long long> costs(n);
    for(int i=0;i<n;i++){
        cin>>costs[i];
    }
    
    sort(costs.begin(),costs.end(),greater<int>());
    
    long long cal=1,ft=1,tol=1;
    for(int i=0;i<n;i++){
        cal=(cal*2)%1000000007;
        if(i<n-1) ft=cal;
        if(i<n-2) tol=cal;
    }
    
    for(int i=0;i<n;i++){
        sum=(sum+ft*costs[i])%1000000007;
        ft=(ft+tol)%1000000007;
    }
    
    cout<<(sum*cal)%1000000007<<endl;
}