All of these business ideas are too serious! Like the clown you are, you decide to open up a circus to entertain the people of Adelaide.

For your first act, you are expected to balance ~n~ plates at once. Each plate has a weight ~w_i~, and the "instability" of your act is defined as the sum of the absolute differences between the weights of all pairs of plates.

For example, if you had 4 plates weighing 5, 2, 3 and 5 units respectively, your instability would be:

~I = |5-2| + |5-3| + |5-5| + |2-3| + |2-5| + |3-5| = 3 + 2 + 0 + 1 + 3 + 2 = 11~

Input

The first line contains a single integer ~n~ ~(1 \leq n \leq 10^5)~, the number of plates you are expected to balance.

The next line contains the weights of each of the plates, integers ~w_1, \dots, w_n~ ~(1 \leq w_i \leq 100)~.

Output

For each test case, output the instability of your balancing act.

Example

Input 1

4
10 9 8 7

Output 1

10

The instability is equal to ~|10-9| + |10-8| + |10-7| + |9-8| + |9-7| + |8-7| = 1 + 2 + 3 + 1 + 2 + 1 = 10~

Input 2

2
1 2

Output 2

1

The instability is equal to ~|1-2| = 1~.

Input 3

1
100

Output 3

0

There is no instability, as there are no pairs of plates.