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Problem2195--ABC238C - digitnum

_{[Creator : ]}

Time Limit : 1.000 sec Memory Limit : 128 MB

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 is given from Standard Input in the following format:

$N$

Print the answer as an integer.

sample 1:

For a positive integer $x$ between $1$ and $9$ , the positive integers at most $x$ with the same number of digits as $x$ are $1,2,\dots,x$ $1, 2, \dots, x$ .
- 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 $10,11,\dots,x$ $10, 11, \dots, x$ .
- Thus, we have $f (10) = 1, f (11) = 2, . . ., f (16) = 7$ .

The final answer is $73$ .

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