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;
typedef long long ll;
#define rep(i,n) for(int i=0;i<n;i++)
ll mod=1e9+7;

ll power(ll x,ll n){
    if(n==0) return 1;
    ll res=power(x*x%mod,n/2);
    if(n&1) res=res*x%mod;
    return res;
}

int main(){
  int n;
  cin>>n;
  ll a[n];
  rep(i,n) cin>>a[i];
  sort(a,a+n);
  ll ans=0;
  rep(i,n){
    ans=(ans+(n+1-i)*a[i]%mod)%mod;
  }
  cout<<ans*power(4,n-1)%mod<<endl;
}

