Problem9727--ABC194 —— C - Squared Error

9727: ABC194 —— C - Squared Error

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Time Limit : 1.000 sec  Memory Limit : 512 MiB

Description

Given is a number sequence $A$ of length $N$.  
Find the sum of squared differences of every pair of elements: $\displaystyle \sum_{i = 2}^{N} \sum_{j = 1}^{i - 1} (A_i - A_j)^2$.

Input

Input is given from Standard Input in the following format:

```
$N$
$A_1$ $A_2$ $A_3$ $\cdots$ $A_N$
```

Output

Print the answer.

Constraints

-   $2 \le N \le 3 \times 10^5$
-   $|A_i| \le 200$
-   All values in input are integers.

Sample 1 Input

3
2 8 4

Sample 1 Output

56
We have $\sum_{i=2}^{N} {\sum_{j=1}^{i−1}{(A_i−A_j)^2}}=(8−2)^2+(4−2)^2+(4−8)^2=56$.

Sample 2 Input

5
-5 8 9 -4 -3

Sample 2 Output

950

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