Score: $300$ points

问题陈述

对于正整数 $x$ 和 $y$，定义 $f(x, y)$ 为 $(x + y)$ 除以 $10^8$ 的余数。

给定一个长度为 $N$ 的正整数序列 $A = (A_1, \ldots, A_N)$。找出以下表达式的值：

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

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

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:

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

Constraints

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

Input

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

$N$

$A_1$ $\ldots$ $A_N$

Output

Print the answer.

Sample Input 1

3
3 50000001 50000002

Sample Output 1

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 Input 2

5
1 3 99999999 99999994 1000000

Sample Output 2

303999988