$N$ people numbered $1$ to $N$ are standing in a circle, in the clockwise order of Person $1$, Person $2$, $\cdots$, Person $N$. The direction each person faces is given by a string $S$ of length $N$. For each $i$ $(1 \leq i \leq N)$, Person $i$ is facing in the counter-clockwise direction if $S_i = $ `L`, and clockwise direction if $S_i = $ `R`.

The following operation will be repeated $N-1$ times.

-   Choose one of the remaining people with equal probability, and remove from the circle the nearest person seen from the chosen person. This incurs a cost equal to the distance from the chosen person to the removed person.

Here, the distance from Person $i$ to Person $j$ $(i \neq j)$ is defined as follows.

1.  When Person $i$ is facing in the clockwise direction:
    -   $j-i$ if $i \lt j$;
    -   $j-i+N$ if $i \gt j$.
2.  When Person $i$ is facing in the counter-clockwise direction:
    -   $i-j+N$ if $i \lt j$;
    -   $i-j$ if $i \gt j$.

Find the expected value of the total cost incurred, modulo $998244353$ (see Notes).

Notes

It can be proved that the sought expected value is always a rational number. Additionally, under the Constraints of this problem, when that value is expressed as $\frac{P}{Q}$ using two coprime integers $P$ and $Q$, there is a unique integer $R$ such that $R \times Q \equiv P\pmod{998244353}$ and $0 \leq R \lt 998244353$. Find this $R$.

Input is given from Standard Input in the following format:

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

Print the answer.

-   $2 \leq N \leq 300$
-   $N$ is an integer.
-   $S$ is a string of length $N$ consisting of `L` and `R`.

831870297

The sought expected value is $\frac{17}{6}$. We have 831870297×6≡17 (mod 998244353), so 831870297 should be printed.

For your reference, here is one possible scenario.

1. Person 2 is chosen. The nearest person seen from Person 2 remaining in the circle is Person 1, who gets removed from the circle.
2. Person 2 is chosen again. The nearest person seen from Person 2 remaining in the circle is Person 3, who gets removed from the circle.

In this case, the total cost incurred is 3(=1+2).