Contest Duration: ~ (local time) (100 minutes) Back to Home
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Time Limit: 2 sec / Memory Limit: 1024 MB

制約

• 2 \leq N \leq 10^5
• 1 \leq A_i \leq 10^9
• 入力はすべて整数である

入力

N
A_1
:
A_N


入力例 1

5
6
8
1
2
3


出力例 1

21


3,8,1,6,2 の順に並べたとき、隣り合う要素の差の合計は 21 になり、 これが達成できる最大の値です。

入力例 2

6
3
1
4
1
5
9


出力例 2

25


入力例 3

3
5
5
1


出力例 3

8


Score : 400 points

Problem Statement

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.

Sample Input 1

5
6
8
1
2
3


Sample Output 1

21


When the integers are arranged as 3,8,1,6,2, the sum of the absolute differences between the adjacent elements is |3 - 8| + |8 - 1| + |1 - 6| + |6 - 2| = 21. This is the maximum possible sum.

Sample Input 2

6
3
1
4
1
5
9


Sample Output 2

25


Sample Input 3

3
5
5
1


Sample Output 3

8