Problem Statement

Takahashi has decided to put a web counter on his webpage.
The accesses to his webpage are described as follows:

• For $i=0,1,2,\\ldots,23$, there is a possible access at $i$ o'clock every day:
  • If $c_i=$T, Takahashi accesses the webpage with a probability of $X$ percent.
  • If $c_i=$A, Aoki accesses the webpage with a probability of $Y$ percent.
  • Whether or not Takahashi or Aoki accesses the webpage is determined independently every time.
• There is no other access.

Also, Takahashi believes it is preferable that the $N$-th access since the counter is put is not made by Takahashi himself.

If Takahashi puts the counter right before $0$ o'clock of one day, find the probability, modulo $998244353$, that the $N$-th access is made by Aoki.

Notes

We can prove that the sought probability is always a finite rational number. Moreover, under the constraints of this problem, when the value is represented as $\\frac{P}{Q}$ with two coprime integers $P$ and $Q$, we can prove that 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

• $1 \\leq N \\leq 10^{18}$
• $1 \\leq X,Y \\leq 99$
• $c_i$ is T or A.
• $N$, $X$, and $Y$ are integers.

Input

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

$N$ $X$ $Y$ $c_0 c_1 \\ldots c_{23}$

Output

Print the answer.

Sample Input 1

1 50 50
ATATATATATATATATATATATAT

Sample Output 1

665496236

The $1$-st access since Takahashi puts the web counter is made by Aoki with a probability of $\\frac{2}{3}$.

Sample Input 2

271 95 1
TTTTTTTTTTTTTTTTTTTTTTTT

Sample Output 2

0

There is no access by Aoki.

Sample Input 3

10000000000000000 62 20
ATAATTATATTTAAAATATTATAT

Sample Output 3

744124544