Problem Statement

Given an integer N, solve the following problem.
Let f(x)= (The number of positive integers at most x with the same number of digits as x).
Find $f(1)+f(2)+\dots+f(N) modulo 998244353$.

Input

Input is given from Standard Input in the following format:
N

Output

Print the answer as an integer.

Constraints

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

Sample Input 1

16

Sample Output 1

73

• For a positive integer x between 1 and 9, the positive integers at most x with the same number of digits as x are $1,2,\dots,x$.

• Thus, we have f(1)=1,f(2)=2,...,f(9)=9.

• For a positive integer x between 10 and 16, the positive integers at most x with the same number of digits as x are $10,11,\dots,x$.

• Thus, we have f(10)=1,f(11)=2,...,f(16)=7.

The final answer is 73.

Sample Input 2

238

Sample Output 2

13870

Sample Input 3

999999999999999999

Sample Output 3

762062362

Be sure to find the sum modulo 998244353.

见题面 Input 部分

见题面 Output 部分