Align

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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 : A_N

outputFormat

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

样例

3
5
5
1

8