Change a Little Bit

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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N C_1 C_2 \cdots C_N

outputFormat

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

样例

2
5 8

124