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>
#define modd 1000000007
using namespace std;
typedef long long int ll;
ll pow2[400001];
int main()
{
    pow2[0]=1;
    for(int i=1;i<=400000;i++)
    {
        pow2[i] = pow2[i-1]*2;
        pow2[i] = pow2[i]%modd;
        //cout<<pow2[i]<<endl;
    }
    ll ans=0;
    ll n;
    cin>>n;
    ll c[n];
    for(int i=0;i<n;i++)
    {
        cin>>c[i];
    }
    sort(c,c+n);
    for(ll i=0;i<n;i++)
    {
        ans = (ans + (n+1-i)*c[i])%modd;
    }
    ans = (ans*pow2[2*(n-1)])%modd;
    cout<<ans<<"\n";
}
