Score: $400$ points

问题陈述

对于正整数 $x$ 和 $y$，定义 $f(x, y)$ 如下：

• 将 $x$ 和 $y$ 的十进制表示视为字符串，并将它们按此顺序连接起来，得到一个字符串 $z$。$f(x, y)$ 的值是将 $z$ 解释为十进制整数时的值。

例如，$f(3, 14) = 314$ 且 $f(100, 1) = 1001$。

给定一个长度为 $N$ 的正整数序列 $A = (A_1, \ldots, A_N)$。求以下表达式的值对 $998244353$ 取模：

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

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 follows:

• Interpret the decimal representations of $x$ and $y$ as strings and concatenate them in this order to obtain a string $z$. The value of $f(x, y)$ is the value of $z$ when interpreted as a decimal integer.

For example, $f(3, 14) = 314$ and $f(100, 1) = 1001$.

You are given a sequence of positive integers $A = (A_1, \ldots, A_N)$ of length $N$. Find the value of the following expression modulo $998244353$:

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

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq A_i \leq 10^9$
• 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 14 15

Sample Output 1

2044

• $f(A_1, A_2) = 314$
• $f(A_1, A_3) = 315$
• $f(A_2, A_3) = 1415$

Thus, the answer is $f(A_1, A_2) + f(A_1, A_3) + f(A_2, A_3) = 2044$.

Sample Input 2

5
1001 5 1000000 1000000000 100000

Sample Output 2

625549048

Be sure to calculate the value modulo $998244353$.