10594: ABC357 —— D - 88888888
[Creator : ]
Description
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 $998244353$.
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 $998244353$.
Input
The input is given from Standard Input in the following format:
```
$N$
```
```
$N$
```
Output
Print the remainder when $V_N$ is divided by $998244353$.
Constraints
- $1 \leq N \leq 10^{18}$
- $N$ is an integer.
- $N$ is an integer.
Sample 1 Input
5
Sample 1 Output
55555
The remainder when $V_5=55555$ is divided by $998244353$ is $55555$.
Sample 2 Input
9
Sample 2 Output
1755646
The remainder when $V_9=999999999$ is divided by $998244353$ is $1755646$.
Sample 3 Input
10000000000
Sample 3 Output
468086693