Problem6530--ABC186 —— D - Sum of difference

6530: ABC186 —— D - Sum of difference

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Time Limit : 1.000 sec  Memory Limit : 256 MiB

Description

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 $\displaystyle{\sum_{i=1}^{N-1}\sum_{j=i+1}^{N} |A_i-A_j|}$.

Input

Input is given from Standard Input in the following format:
$N\\
A_1\ \ldots\ A_N$

Output

Print the answer.

Constraints

$2≤N≤2×10^5$
$|A_i|\leq 10^8$
$A_i$ is an integer.

Sample 1 Input

3
5 1 2

Sample 1 Output

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

Sample 2 Input

5
31 41 59 26 53

Sample 2 Output

176

Source/Category

 AtCoder_ABC 100.186.ABC186