You are given N integers; the i-th of them is A_i. Find the maximum possible sum of the absolute differences between the adjacent elements after arranging these integers in a row in any order you like.

Constraints

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

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the maximum possible sum of the absolute differences between the adjacent elements after arranging the given integers in a row in any order you like.

Examples

Input

5
6
8
1
2
3

Output

21

Input

6
3
1
4
1
5
9

Output

25

Input

3
5
5
1

Output

8

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