Digit Counting

Problem Description

Given an integer $n$, solve the following problem:

Let $f(x) =$ the number of positive integers that do not exceed $x$ and have the same number of digits as $x$.

Compute $f(1) + f(2) + \dots + f(n)$, modulo $998244353$.

Input Format

One integer $N$.

Output Format

One integer — the answer to the problem above, modulo $998244353$.

Sample Input 1

16

Sample Output 1

73

Sample Explanation

For each $x$ from $1$ to $9$, the positive integers not exceeding $x$ with the same number of digits as $x$ are $1, 2, \dots, x$; hence $f(1) = 1, f(2) = 2, \dots, f(9) = 9$. For each $x$ from $10$ to $16$, they are $10, 11, \dots, x$; hence $f(10) = 1, f(11) = 2, \dots, f(16) = 7$. The answer is therefore $73$.

Sample Input 2

238

Sample Output 2

13870

Sample Input 3

999999999999999999

Sample Output 3

762062362

Constraints

For all data, $1 \leq N < 10^{18}$, and $N$ is an integer.