# Rainbow 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 |