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 <vector>
#include <algorithm>

#define int long long int

using namespace std;

signed main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie( 0);

    const int mod = 1E9 + 7;
    int n, res = 0;
    cin >> n;
    vector<int> c(n);
    for (int i = 0; i < n; i++)
        cin >> c[i];
    sort(c.rbegin(), c.rend());

    int pow_4 = 1;
    for (int i = 0; i < n - 1; i++)
    {
        pow_4 *= 4;
        pow_4 %= mod;
    }

    for (int i = 0; i < n; i++)
    {
        long long add = (c[i] * (i + 2)) % mod;
        add = (add * pow_4) % mod;
        res = (res + add) % mod;
    }

    cout << res << "\n";

    return 0;
}
