Problem Statement

capra is very indecisive and cannot decide anything.
Even when he attends a meeting, he never makes it clear whether it is YES or NO, and only talks about things that are beside the point.
Trying to take advantage of him, autumn gave capra a string $S$ of length $N$ and instructed him to act according to it.

This string $S$ consists only of the 7 kinds of strings ["YES", "NO", "and", "or", "random", "(", ")"],
and capra evaluates the string $S$ in the following way and says the final result.

Below, $x$ and $y$ denote expressions that evaluate to YES or NO.

1. The expression `$x\ or\ y$` is $\mathrm{YES}$ if at least one of them is $\mathrm{YES}$, and $\mathrm{NO}$ otherwise.
2. The expression `$x\ and\ y$` is $\mathrm{YES}$ if both of them are $\mathrm{YES}$, and $\mathrm{NO}$ otherwise.
3. The expression `$random(x\ y)$` becomes $\mathrm{YES}$ with probability $P$ if both of them are $\mathrm{YES}$, and becomes $\mathrm{YES}$ with probability $Q$ otherwise.
If it does not become $\mathrm{YES}$, it becomes $\mathrm{NO}$.
4. The contents of parentheses are computed first.
5. $\mathrm{and}$ takes precedence over $\mathrm{or}$.
6. Operations of the same precedence are performed from the left.
7. Since following instructions exactly would be boring, each time capra evaluates an $\mathrm{or}$ or an $\mathrm{and}$, with probability $R$ he changes its result, turning $\mathrm{YES}$ into $\mathrm{NO}$ and $\mathrm{NO}$ into $\mathrm{YES}$.
8. All probabilities are independent and uniform.

Thistle, who has secretly obtained the instructions, wants to know how likely it is that capra says YES.
For Thistle's sake, please write a program that returns the probability as a percentage.

It has been confirmed that this problem can be solved with plenty of margin in PyPy3.
A case is considered correct if the difference between the answer (the true value) and the submitted value is at most 1. (Added 08/22 19:31)

Input

$N$
$P$ $Q$ $R$
$S$

$N$ is an integer satisfying $2\leq N\leq 10^6$.

$P,Q,R$ are real numbers satisfying $0\leq P,Q,R\leq 1$.
They are given with at most 3 digits after the decimal point.

$S$ is a string of length $N$. It consists only of ["YES", "NO", "and", "or", "random", "(", ")"], and it is guaranteed to be grammatically correct.

Output

Compute the probability as a percentage, truncate the digits after the decimal point, and output it on one line.
Print a newline at the end of the line.

Sample

3
0.8 0.2 0.5
YES

100

15
0.8 0.2 0.5
YESand(YESorNO)

50

13
1.0 0.8 0.4
random(YESNO)

80