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;
long long a[200005],mod=1e9+7;
long long qpow(long long a,long long b){
    long long res=1;
    while(b){
        if(b&1) res=res*a%mod;
        a=a*a%mod;
        b/=2;
    }
    return res%mod;
}
int main(){
    long long n;
    cin>>n;
    for(long long i=1;i<=n;i++){
        cin>>a[i];
    }
    sort(a+1,a+1+n);
    long long num=qpow(4,n-1),sum=0;
    for(long long i=1;i<=n;i++){
        sum+=num%mod*(n-i+2)%mod*a[i]%mod;
        sum%=mod;
    }
    cout<<sum%mod<<endl;
}