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
//
// Created by munaiyi on 2020/3/21.
//
#include <bits/stdc++.h>

using namespace std;

const int maxn = 2e5 + 5;
const int mod = 1e9 + 7;

int c[maxn];

int main() {
    int n;
    scanf("%d", &n);
    for (int i = 0; i < n; i++) {
        scanf("%d", c + i);
    }
    sort(c, c + n, [](int x, int y) -> bool { return x > y; });
    long long ans = c[0];
    long long two = 1;
    for (int i = 1; i < n; i++) {
        ans = ans * 2;
        ans = (ans + (two * i % mod + two * 2) * c[i]) % mod;
        two = two * 2 % mod;
    }
    ans = ans * two * 2 % mod;
    printf("%lld\n", ans);
    return 0;
}
