6530: ABC186 —— D - Sum of difference
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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 $\displaystyle{\sum_{i=1}^{N-1}\sum_{j=i+1}^{N} |A_i-A_j|}$.
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:
$N\\
A_1\ \ldots\ A_N$
$N\\
A_1\ \ldots\ A_N$
Output
Print the answer.
Constraints
$2≤N≤2×10^5$
$|A_i|\leq 10^8$
$A_i$ is an integer.
$|A_i|\leq 10^8$
$A_i$ 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