Score : $350$ points

问题陈述

对于一个正整数 $N$，让 $V_N$ 是通过将 $N$ 连接 $N$ 次形成的整数。 更精确地说，将 $N$ 视为一个字符串，连接 $N$ 个副本，并将结果视为一个整数以得到 $V_N$。 例如，$V_3=333$ 且 $V_{10}=10101010101010101010$。

找出 $V_N$ 除以 $998244353$ 时的余数。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

For a positive integer $N$, let $V_N$ be the integer formed by concatenating $N$ exactly $N$ times.
More precisely, consider $N$ as a string, concatenate $N$ copies of it, and treat the result as an integer to get $V_N$.
For example, $V_3=333$ and $V_{10}=10101010101010101010$.

Find the remainder when $V_N$ is divided by $998244353$.

Constraints

• $1 \leq N \leq 10^{18}$
• $N$ is an integer.

Input

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

$N$

Output

Print the remainder when $V_N$ is divided by $998244353$.

Sample Input 1

5

Sample Output 1

55555

The remainder when $V_5=55555$ is divided by $998244353$ is $55555$.

Sample Input 2

9

Sample Output 2

1755646

The remainder when $V_9=999999999$ is divided by $998244353$ is $1755646$.

Sample Input 3

10000000000

Sample Output 3

468086693

Note that the input may not fit into a $32$-bit integer type.