Problem Statement

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).

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).

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq C_i \leq 10^9$
• All values in input are integers.

Sample Input 1

1
1000000000

Sample Output 1

999999993

There are two pairs (S, T) of different sequences of length 2 consisting of 0 and 1, as follows:

• S = (0), T = (1): by changing S_1 to 1, we can have S = T at the cost of 1000000000, so f(S, T) = 1000000000.
• S = (1), T = (0): by changing S_1 to 0, we can have S = T at the cost of 1000000000, so f(S, T) = 1000000000.

The sum of these is 2000000000, and we should print it modulo (10^9+7), that is, 999999993.

Sample Input 2

2
5 8

Sample Output 2

124

There are 12 pairs (S, T) of different sequences of length 3 consisting of 0 and 1, which include:

• S = (0, 1), T = (1, 0)

In this case, if we first change S_1 to 1 then change S_2 to 0, the total cost is $5 \times 2 + 8 = 18$. We cannot have S = T at a smaller cost, so f(S, T) = 18.

Sample Input 3

5
52 67 72 25 79

Sample Output 3

269312

见题面 Input 部分

见题面 Output 部分