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 <algorithm>
using namespace std;
int c[200005];
const int mod=1e9+7;
int fast_pow(int a,int n)
{
    int res=1;
    int temp=a;
    while(n)
    {
        if(n&1)
        {
            res=(1ll*res*temp)%mod;
        }
        temp=(1ll*temp*temp)%mod;
        n>>=1;
    }
    return res%mod;
}
bool cmp(int aa,int bb)
{
    return aa>bb;
}
int main()
{
    int n;
    cin>>n;
    int res=fast_pow(4,n-1);
    for(int i=0;i<n;i++)
    {
        cin>>c[i];
    }
    sort(c,c+n,cmp);
    int ans=0;
    for(int i=1;i<=n;i++)
    {
        ans=(ans+1ll*(i+1)*c[i-1])%mod;
    }
    res=(1ll*res*ans)%mod;
    cout<<res;
    return 0;
}