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;

long long n, m = 0;
long long c[200000], y[200001];
const long long M = 1000000007;

int main()
{
    cin >> n;

    y[0] = 1;
    y[1] = 2;
    for (int i = 1; i < n; i++)
        y[i + 1] = y[i] * 2 % M;

    for (int i = 0; i < n; i++)
        cin >> c[i];

    sort(c, c + n);

    if (n > 1) {
        for (int i = 0; i < n; i++)
            m = (m + (((n - i + 1) * y[n - 2] % M) * y[n] % M) * c[i]) % M;
    }
    else
        m = 2 * c[0] % M;
 
    cout << m << endl;

    return 0;
}
