A15001. I love AAAB

Let's call a string good if its length is at least $2$ and all of its characters are $\texttt{A}$ except for the last character which is $\texttt{B}$ . The good strings are $\texttt{AB},\texttt{AAB},\texttt{AAAB},\ldots$ . Note that $\texttt{B}$ is not a good string.

You are given an initially empty string $s_1$ .

You can perform the following operation any number of times:

- Choose any position of $s_1$ and insert some good string in that position.

Given a string $s_2$ , can we turn $s_1$ into $s_2$ after some number of operations?

Each test contains multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 10^4$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single string $s_2$ ( $1 \leq |s_2| \leq 2 \cdot 10^5$ ).

It is guaranteed that $s_2$ consists of only the characters $\texttt{A}$ and $\texttt{B}$ .

It is guaranteed that the sum of $|s_2|$ over all test cases does not exceed $2 \cdot 10^5$ .

For each test case, print "YES" (without quotes) if we can turn $s_1$ into $s_2$ after some number of operations, and "NO" (without quotes) otherwise.

You can output "YES" and "NO" in any case (for example, strings "yEs", "yes" and "Yes" will be recognized as a positive response).

In the first test case, we transform $s_1$ as such: $\varnothing \to \color{red}{\texttt{AAB}} \to \texttt{A}\color{red}{\texttt{AB}}\texttt{AB}$ .

In the third test case, we transform $s_1$ as such: $\varnothing \to \color{red}{\texttt{AAAAAAAAB}}$ .

In the second and fourth test case, it can be shown that it is impossible to turn $s_1$ into $s_2$ .