Chomp#6392

Chomp

1 second

64 megabytes

Hard

Chomp is a two-player strategy game played on a rectangular chocolate bar made up of smaller square blocks (cells). The players take turns choosing one block and "eating" it (removing it from the board), together with all blocks that are above it and to its right. The bottom left block is poisoned, and the player who is forced to eat it loses. The following diagram shows a game beginning with a 3-by-3 board. The X indicates the poisoned cell.

A position in the game is a winning position if there is a move that results in a losing position for the opponent. A position in the game is a losing position if every move from that position either eats the poisoned square (losing the game) or results in a winning position for the opponent.

In the example above, the 1×1 and equal-armed L-shaped positions are losing positions (since the opponent can mirror the current player's moves).

The 3×3, unequal-armed L and 1×n positions are winning positions.

The aim of this problem is to "solve" 3-by-100 Chomp. That is, for each possible position, determine whether it is a winning or losing position, and if it is a winning position, give the next move.

A position in 3-by-100 Chomp is determined by the number $p$ of squares in the bottom row, the number $q$ of squares in the middle row, and the number $r$ of squares in the top row, with

100 \geq p \geq q \geq r \geq 0

100 \geq p \geq q \geq r \geq 0

Write a program which, for each possible position in the 3-by-100 game of Chomp, determines whether it is a winning or losing position, and if it is a winning position, gives the next move (the square to eat next).

Input

The first line contains a single integer $P$ ( $1 \leq P \leq 1000$ 1 \leq P \leq 1000), the number of data sets that follow. Each data set should be processed independently.

Each data set consists of a single line. It contains the data set number $K$ , followed by the counts $p$ , $q$ , $r$ ( $100 \geq p \geq q \geq r \geq 0$ 100 \geq p \geq q \geq r \geq 0) of squares in the bottom row ( $p$ ), middle row ( $q$ ), and top row ( $r$ ), respectively, separated by single spaces.

Output

For each data set, output a single line. If the input position is a losing position, the output line consists of the data set number $K$ , followed by a single space, followed by the capital letter L. Otherwise (the input position is a winning position), output the data set number $K$ , the capital letter W, and the column number and row number of a block to eat which results in a losing position for the next player.

Examples

Example 1