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).

-----Sample Input-----
1
1000000000

-----Sample Output-----
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.

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