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;
int64_t mod=1000000007;
int64_t pw(int64_t x,int64_t y){
  int64_t z;
  if (y==0) return 1;
  else{
    z=pw(x,y/2)*pw(x,y/2)%mod;
    if(y%2==1) z=z*x%mod;
    return z;
  }
}
int main(){
  int64_t n,i,ans=0;
  cin>>n;
  vector<int64_t> c(n);
  for(i=0;i<n;i++) cin>>c.at(i);
  sort(c.begin(),c.end());
  for(i=0;i<n;i++) ans=(ans+(n+1-i)*c.at(i)%mod)%mod;
  ans=ans*pw(4,n-1)%mod;
  cout<<ans<<endl;
}