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;

const int Z = 1e9+7;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(NULL);

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

    int pow2[n+1];
    for (int i = 0; i <= n; i++) {
        pow2[i] = i == 0 ? 1 : 2 * pow2[i-1] % Z;
    }

    int ans = 0;
    for (int i = 0; i < n; i++) {
        ans = (ans + (1ll * (n - 1 - i) * pow2[n-2] + pow2[n-1]) % Z * c[i]) % Z;
    }

    ans = 1ll * ans * pow2[n] % Z;

    cout << ans << endl;

    return 0;
}
