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<iostream>
#include<algorithm>
using namespace std;

int main() {
  int DIV = 1e+9 + 7;
  int N; cin >> N;
  int C[N];
  for (int i = 0; i < N; i++) cin >> C[i];
  sort(C, C + N);
  long res = 0;
  for (int i = 0; i < N; i++) {
    res += (long) (N + 1 - i) * (long) C[i];
    res %= DIV;
  }
  for (int i = 0; i < 2 * (N - 1); i++) {
    res *= 2;
    res %= DIV;
  }
  cout << res << endl;
}
