We say that an array $$$a$$$ of size $$$n$$$ is bad if and only if there exists $$$1 \leq i \leq n - 4$$$ such that one of the following conditions holds:

$$$a_i \lt a_{i+1} \lt a_{i+2} \lt a_{i+3} \lt a_{i+4}$$$
$$$a_i \gt a_{i+1} \gt a_{i+2} \gt a_{i+3} \gt a_{i+4}$$$

An array is good if and only if it's not bad. For example:

$$$a = [3, \color{red}{1, 2, 4, 5, 6}]$$$ is bad because $$$a_2 \lt a_3 \lt a_4 \lt a_5 \lt a_6$$$.
$$$a = [\color{red}{7, 6, 5, 4, 1}, 2, 3]$$$ is bad because $$$a_1 \gt a_2 \gt a_3 \gt a_4 \gt a_5$$$.
$$$a = [7, 6, 5, 1, 2, 3, 4]$$$ is good.

You're given a permutation$$$^{\text{∗}}$$$ $$$p_1, p_2, \ldots, p_n$$$.

You must perform $$$n$$$ turns. At each turn, you must remove either the leftmost or the rightmost remaining element in $$$p$$$. Let $$$q_i$$$ be the element removed at the $$$i$$$-th turn.

Choose which element to remove at each turn so that the resulting array $$$q$$$ is good. We can show that under the given constraints, it's always possible.

$$$^{\text{∗}}$$$A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array), and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10\,000$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$5 \leq n \leq 100\,000$$$) — the length of the array.

The second line of each test case contains $$$n$$$ integers $$$p_1, p_2, \ldots, p_n$$$ ($$$1 \leq p_i \leq n$$$, $$$p_i$$$ are pairwise distinct) — elements of the permutation.

It is guaranteed that the sum of $$$n$$$ over all test cases doesn't exceed $$$200\,000$$$.

Output

For each test case, you must output a string $$$s$$$ of length $$$n$$$. For every $$$1 \leq i \leq n$$$, at the $$$i$$$-th turn:

$$$s_i = \texttt{L}$$$ means that you removed the leftmost element of $$$p$$$
$$$s_i = \texttt{R}$$$ means that you removed the rightmost element of $$$p$$$

We can show that an answer always exists. If there are multiple solutions, print any of them.

Note

In the first test case, the sequence $$$\color{blue}{\texttt{RRR}}\color{red}{\texttt{LLLL}}$$$ results in $$$q = [\color{blue}{7}, \color{blue}{6}, \color{blue}{5}, \color{red}{1}, \color{red}{2}, \color{red}{3}, \color{red}{4}]$$$.

In the second test case, the sequence $$$\color{red}{\texttt{LL}}\color{blue}{\texttt{RR}}\color{red}{\texttt{LL}}\color{blue}{\texttt{RR}}\color{red}{\texttt{L}}$$$ results in $$$q = [\color{red}{1}, \color{red}{3}, \color{blue}{2}, \color{blue}{4}, \color{red}{6}, \color{red}{8}, \color{blue}{5}, \color{blue}{7}, \color{red}{9}]$$$.

Deque Process

Examples