Problem10138--ABC353 —— C - Sigma Problem

10138: ABC353 —— C - Sigma Problem

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Time Limit : 1.000 sec  Memory Limit : 512 MiB

Description

For positive integers $x$ and $y$, define $f(x, y)$ as the remainder of $(x + y)$ divided by $10^8$.

You are given a sequence of positive integers $A = (A_1, \ldots, A_N)$ of length $N$. Find the value of the following expression:

$\displaystyle \sum_{i=1}^{N-1}\sum_{j=i+1}^N f(A_i,A_j)$.

Input

The input is given from Standard Input in the following format:

```
$N$ 
$A_1$ $\ldots$ $A_N$
```

Output

Print the answer.

Constraints

-   $2 \leq N \leq 3\times 10^5$
-   $1 \leq A_i < 10^8$
-   All input values are integers.

Sample 1 Input

3
3 50000001 50000002

Sample 1 Output

100000012
  • $f(A_1,A_2)=50000004$
  • $f(A_1,A_3)=50000005$
  • $f(A_2,A_3)=3$
Thus, the answer is $f(A_1,A_2)+f(A_1,A_3)+f(A_2,A_3)=100000012$.
Note that you are not asked to compute the remainder of the sum divided by $10^8$.

Sample 2 Input

5
1 3 99999999 99999994 1000000

Sample 2 Output

303999988

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