Score : $400$ points

Problem Statement

For a string $T=T_1T_2\dots T_n$ of length $n\ (2\leq n)$ consisting of A and B, we define a string $f(T)$ of length $n-1$ as follows.

• Let $a_1 < a_2 < \dots < a_{m}$ be the indices $i\ (1\leq i \leq n-1)$ such that $T_i={}$A, and $b_1 < b_2 < \dots < b_k$ be the indices $i\ (1\leq i \leq n-1)$ such that $T_i={}$B. Then, let $f(T)=T_{a_1+1}T_{a_2+1}\dots T_{a_m+1}T_{b_1+1}T_{b_2+1}\dots T_{b_k+1}$.

For example, for the string $T={}$ABBABA, the indices $i\ (1\leq i \leq 5)$ with $T_i={}$A are $i=1,4$, and the indices $i\ (1\leq i \leq 5)$ with $T_i={}$B are $i=2,3,5$, so $f(T)$ is $T_{1+1}T_{4+1}T_{2+1}T_{3+1}T_{5+1}={}$BBBAA.

You are given a string $S$ of length $N$ consisting of A and B.

Find $S$ after replacing $S$ with $f(S)$ $(N-1)$ times.

You have $T$ test cases to solve.

Constraints

• $1 \leq T \leq 10^5$
• $2 \leq N \leq 3 \times 10^5$
• $S$ is a string of length $N$ consisting of A and B.
• All numbers in the input are integers.
• The sum of $N$ over the test cases in a single input file is at most $3 \times 10^5$.

Input

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

$T$

$\mathrm{case}_1$

$\vdots$

$\mathrm{case}_T$

Each case is given in the following format:

$N$

$S$

Output

Print $T$ lines. The $i$-th line should contain the answer to the $i$-th test case.

3
2
AB
3
AAA
4
ABAB

B
A
A

In the first test case, $S$ changes as AB${}\rightarrow {}$B.

In the second test case, $S$ changes as AAA${} \rightarrow {}$AA${} \rightarrow {}$A.

In the third test case, $S$ changes as ABAB${}\rightarrow {}$BBA${} \rightarrow {}$BA${} \rightarrow {}$A.