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;
#define rep(i,x,y) for(int i=x;i<y;i++)
#define range(a) (a).begin(),(a).end()
#define print(A,n) rep(i,0,n){cout<<(i ? " ":"")<<A[i];}cout<<endl;
#define pprint(A,m,n) rep(j,0,m){print(A[j],n);}
const long mod=1e9+7;
const int size=1e5;
const int inf=1e9;
int main(){
	int N;cin>>N;
	long C[N];
	rep(i,0,N) cin>>C[i];
	sort(C,C+N);
	long ans=0;
    long A[N+1],B[N+1]; A[0]=1;B[0]=1;
    rep(i,0,N){
        A[i+1]=(2*A[i])%mod;
        B[i+1]=(A[i]+2*B[i])%mod;
    }
	rep(i,0,N){
		long temp=A[i]*B[N-1-i]%mod;
		(temp*=C[i])%=mod;
		(ans+=temp)%=mod;
	}
    cout<<(ans*A[N])%mod<<endl;
}