Problem Statement

$N$ 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 $R$.

Constraints

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

Input

Input is given from Standard Input in the following format:

$N$ $S$

Output

Print the answer.

Sample Input 1

3
LLR

Sample Output 1

831870297

The sought expected value is $\\frac{17}{6}$. We have $831870297 \\times 6 \\equiv 17\\pmod{998244353}$, 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 $3(=1+2)$.

Sample Input 2

10
RRRRRRLLRR

Sample Output 2

460301586