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 int long long
using namespace std;
const int mod=1e9+7;

int n,res=0;
int a[200005];

int quick_power(int a,int b)
{
	if (b==0)  return 1;
	
	int res=1;
	for (;b;b=b>>1,a=(a*a)%mod)
	{
		if (b&1)  res=(res*a)%mod;
	}
	return res;
}

bool cmp(int a,int b)
{
	return a>b;
}

signed main()
{
    cin>>n;
    for (int i=1;i<=n;i++)  cin>>a[i];
 	
 	sort(a+1,a+n+1,cmp);
 
    int tmp3=quick_power(2,n*2-2);
    int tmp2=(tmp3*2)%mod;
    int res=0;
 
    for (int i=1;i<=n;i++)
    {
        int tmp=(tmp2*a[i])%mod;
        res=(res+tmp)%mod;
        tmp2=(tmp2+tmp3)%mod;
    }
    cout<<res<<endl;
    
    return 0;
}