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.

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.

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.

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

见题面 Input 部分

见题面 Output 部分