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 int long long
const int MOD = (int)1e9 + 7;

signed main() {
  int N;
  cin >> N;
  vector<int> C(N);
  for(int i=0; i<N; i++) cin >> C[i];
  sort(C.begin(),C.end());


  vector<int> b(N+1);
  b[0] = 1;
  for(int i=1; i<=N; i++) b[i] = (b[i-1]*2) % MOD;

  int ans = 0;
  for(int i=0; i<N; i++) ans = (ans + (C[N-1-i] * (i+2))) % MOD;
  ans = (ans * ((b[N-1] * b[N-1]) % MOD)) % MOD;
  cout << ans << endl;
}