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;

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

long long A[200005], two[400005];

int main()
{
    ios::sync_with_stdio(0);
    cin.tie(NULL), cout.tie(NULL);

    int N;
    cin >> N;

    two[0] = 1;

    for(int i=1; i<=N; i++)
        cin >> A[i];
    for(int i=1; i<=2*N; i++)
        two[i] = two[i-1] * 2 % MOD;

    sort(A+1, A+1+N);
    long long ans = 0;

    for(int i=1; i<=N; i++)
        ans += two[2*N-2] * (N - i + 2) % MOD * A[i] % MOD;

    cout << ans % MOD << "\n";
    return 0;
}
