2020 South Central USA Regional Contest

#### Start

2021-03-06 10:00 AKST

## 2020 South Central USA Regional Contest

#### End

2021-03-06 15:00 AKST
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# Problem LRainbow Numbers

Define a rainbow number as an integer that, when represented in base $10$ with no leading zeros, has no two adjacent digits the same.

Given lower and upper bounds, count the number of rainbow numbers between them (inclusive).

## Input

The first line of input contains a single integer $L$ ($1 \le L < 10^{10^5}$), which is the lower bound.

The second line of input contains a single integer $U$ ($1 \le U < 10^{10^5}$), which is the upper bound.

It is guaranteed that $L \le U$. Note that the limits are not a misprint; $L$ and $U$ can be up to $10^5$ digits long.

## Output

Output a single integer, which is the number of rainbow numbers between $L$ and $U$ (inclusive). Because this number may be very large, output it modulo $998\, 244\, 353$.

Sample Input 1 Sample Output 1
1
10

10

Sample Input 2 Sample Output 2
12345
65432

35882