Score : $300$ points

Problem Statement

You are given $N$-digit positive integers $A$ and $B$ whose topmost digits are not $0$.

You can repeat the following operation any number of times (possibly zero).

• Choose an integer $i$ such that $1 \le i \le N$ and swap the $i$-th lowest digits of $A$ and $B$.

Find the smallest possible value of $A \times B$ after your operations, modulo $998244353$.

Note that you are not asked to minimize the remainder when $A \times B$ is divided by $998244353$.

Constraints

• $1 \le N \le 200000$
• $A$ and $B$ are $N$-digit positive integers whose topmost digits are not $0$.

Input

The input is given from Standard Input in the following format:

$N$

$A$

$B$

Output

Print a single line containing the answer.

2
13
22

276

You can make $A \times B = 276$ by performing the operation once, as follows.

• Choose $i=1$ to swap the bottommost digits of $A$ and $B$, making $A=12, B=23$.

You cannot make $A \times B = 275$ or less, so the answer is $276$.

8
20220122
21002300

54558365

Find the value modulo $998244353$.