### Problem Statement

You are given a positive integer $X$ with $N$ digits in decimal representation. None of the digits of $X$ is $0$.  
For a subset $S$ of $\lbrace 1,2, \ldots, N-1 \rbrace $, let $f(S)$ be defined as follows.

> See the decimal representation of $X$ as a string of length $N$, and decompose it into $|S| + 1$ strings by splitting it between the $i$-th and $(i + 1)$-th characters if and only if $i \in S$.  
> Then, see these $|S| + 1$ strings as integers in decimal representation, and let $f(S)$ be the product of these $|S| + 1$ integers.

There are $2^{N-1}$ subsets of $\lbrace 1,2, \ldots, N-1 \rbrace $, including the empty set, which can be $S$. Find the sum of $f(S)$ over all these $S$, modulo $998244353$.

### Input

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

```
$N$
$X$
```

### Output

Print the answer.

### Constraints

-   $2 \leq N \leq 2 \times 10^5$
-   $X$ has $N$ digits in decimal representation, none of which is $0$.
-   All values in the input are integers.

418

For S=∅, we have f(S)=234.
For S={1}, we have f(S)=2×34=68.
For S={2}, we have f(S)=23×4=92.
For S={1,2}, we have f(S)=2×3×4=24.
Thus, you should print 234+68+92+24=418.