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,n) for(int i=0;i<n;i++)
typedef long long ll;
typedef pair<int,int> P;
typedef vector<int> vec;
typedef vector<vec> mat;
int main(){
    ll n,C[200001],mod=1e9+7;
    cin>>n;
    rep(i,n) cin>>C[i];
    ll A[200011];
    A[0]=1;
    rep(i,n+1) A[i+1]=2*A[i]%mod;
    sort(C,C+n,greater<ll>());
    ll ans=0,k=A[n-1],l;
    if(n==1) l=0;
    else l=A[n-2];
    rep(i,n) ans=(ans+k*C[i])%mod,k=(k+l)%mod;
    cout<<A[n]*ans%mod;
}