For a string $S$ consisting of digits from `1` through `9`, let $f(S)$ be the string $T$ obtained by the following procedure. ($S_i$ denotes the $i$-th character of $S$.)

-   Let $T$ be an initially empty string.
-   For $i=1, 2, \dots, |S| - 1$, perform the following operation:
    -   Append $n$ copies of $S_i$ to the tail of $T$, where $n$ is the value when $S_{i+1}$ is interpreted as an integer.

For example, $S =$ `313` yields $f(S) =$ `3111` by the following steps.

-   $T$ is initially empty.
-   For $i=1$, we have $n = 1$. Append one copy of `3` to $T$, which becomes `3`.
-   For $i=2$, we have $n = 3$. Append three copies of `1` to $T$, which becomes `3111`.
-   Terminate the procedure. We obtain $T =$ `3111`.

You are given a length-$N$ string $S$ consisting of digits from `1` through `9`.  
You repeat the following operation until the length of $S$ becomes $1$: replace $S$ with $f(S)$.  
Find how many times, modulo $998244353$, you perform the operation until you complete it. If you will repeat the operation indefinitely, print `-1` instead.

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

```
$N$
$S$
```

Print the number of times, modulo $998244353$, that you perform the operation until you complete it. If you will repeat the operation indefinitely, print `-1` instead.

-   $2 \leq N \leq 10^6$
-   $S$ is a length-$N$ string consisting of `1`, `2`, `3`, `4`, `5`, `6`, `7`, `8`, and `9`.

4

If S= 313, the length of S be comes 1 after four operations.

• We have f(S)= 3111. Replace S with 3111.
• We have f(S)= 311. Replace S with 311.
• We have f(S)= 31. Replace S with 31.
• We have f(S)= 3. Replace S with 3.
• Now that the length of S is 1, terminate the repetition.

-1

If S= 123456789, you indefinitely repeat the operation. In this case, -1 should be printed.