## DOM - Domino's effect

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Original problem statement (in Polish) can be found here.

Dominik "Domino" Domański is a scientist. He's conducting research on quantum physics. Lately, he started taking a closer look at certain very interesting effect, which can be observed when some quantum objects interact.

In his next experiment, he placed n infinitely thin lines on the table, perpendicularly to the surface, in a row. Lines have different heights, distances between the lines can also differ. (Dominik calls these lines "domino tiles"). Looking from the front, they look like n segments, standing vertically on the X axis of the Cartesian coordinate system.

Domino tiles can be toppled. If a tile has a height of h, it will topple other tiles at most h units away. More precisely, if tile is placed at the position x, and is knocked over to the right, it will topple the tiles placed at positions x+1, x+2, ..., x+h. If this tile is knocked over to the left, it will topple the tiles at positions x-1, x-2, ..., x-h.

Dominik observed a very interesting phenomenon, which he called "Domino's effect" - toppling one domino tile can cause other tiles to topple, which can in turn topple other tiles. He started to wonder how to take advantage of this effect in a best possible way. What is the minimum number of tiles that need to be toppled, in order for all the dominoes to fall?

### Input

The first line contains a single integer t, denoting the number of testcases. Then, testcases follow.

The description of a single testcase begins with a single integer n (1 <= n <= 1000) - the number of domino tiles in an arrangement.

It is followed by n integers hi - heights of subsequent tiles.

It ends with n-1 integers di - distances between neighboring tiles.

(1 <= hi, di <= 106).

### Output

For every testcase you should find a sequence of domino tiles, that will knock down the whole arrangement. It should begin with an integer k (1 <= k <= n), denoting the number of tiles to be pushed. Then, descriptions of moves should follow. One move is described by one integer xi (1 <= xi <= n) and one letter (either L or P). It means that during the i-th move, we topple a tile number xi (counting from 1, according to original arrangement). L means that we knock it over to the left, P means knocking over to the right.

The sequence should knock over all the tiles, while using as few moves as possible.

Input:

```1
6
1 5 1 1 1 1
2 1 2 1 1```

Output:

```2
2 P
1 L```

### Explanation

First we topple the domino tile number 2 (of length 5) to the right, which knocks over everything to the right of that tile. Then, we topple tile number 1 - the only one that remains.