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;

const int N=2e+5+4;
long long int M=1e+9+7;
int n;
long long int c[N];
long long int powe(int i)
{
    if(i==0)
        return 1;
    long long int a=powe(i/2);
    a=(a*a)%M;
    if(i%2==1)
        a=(a*4)%M;
    return a;
}

int main()
{
    long long int ans=0;
    cin>>n;
    for(int i=1;i<=n;i++)
        cin>>c[i];
    sort(c+1,c+n+1,greater<long long int>());
    for(int i=1;i<=n;i++)
    {
        // long long int tans=pow(4,n-i);
        ans=(ans+(i+1)*c[i])%M;
    }
    ans=(ans*powe(n-1))%M;
    cout<<ans;
}