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;
int main(){
  long long N,c,q=0,z=1e9+7;
  cin >>N;
  vector<int> C(N,0);
  for(int i=0; i<N; i++){
    cin >>c;
    C[i]=c;
  }
  if(N==1){
    q=C[0]*2%z;
  }
  else{
    sort(C.begin(), C.end());
    for(int i=0; i<N; i++){
      q+=(N+1-i)*C[i];
      q%=z;
    }
    for(int i=0; i<2*N-2; i++){
      q*=2;
      q%=z;
    }
  }
  cout <<q <<endl;
}