D - Sum of difference

Score : $400$ points

Problem Statement

Given are $N$ integers $A_1,\ldots,A_N$.

Find the sum of $|A_i-A_j|$ over all pairs $i,j$ such that $1\leq i < j \leq N$.

In other words, find $\displaystyle{\sum_{i=1}^{N-1}\sum_{j=i+1}^{N} |A_i-A_j|}$.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $|A_i|\leq 10^8$
• $A_i$ is an integer.

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $\ldots$ $A_N$

Output

Print the answer.

3
5 1 2

8

We have $|5-1|+|5-2|+|1-2|=8$.

5
31 41 59 26 53

176