[Python] S-Nim

Arthur and his sister Carol have been playing a game called Nim for some time now. Nim is played as follows:

- The starting position has a number of heaps, all containing some, not necessarily equal, number of beads.

- The players take turns chosing a heap and removing a positive number of beads from it.

- The first player not able to make a move, loses.

Arthur and Carol really enjoyed playing this simple game until they recently learned an easy way to always be able to find the best move:

- Xor the number of beads in the heaps in the current position (i.e., if we have 2, 4 and 7 the xor-sum will be 1 since 2 xor 4 xor 7 = 1).

- If the xor-sum is 0, too bad, you will lose.

- Otherwise, move such that the xor-sum becomes 0. This is always possible.

It is quite easy to convince oneself that this works. Consider these facts:

- The player that takes the last bead wins.

- After the winning players last move the xor-sum will be 0.

- The xor-sum will change after every move.

Which means that if you make sure that the xor-sum always is 0 when you have made your move, your opponent will never be able to win, and, thus, you will win.

Understandibly it is no fun to play a game when both players know how to play perfectly (ignorance is bliss). Fourtunately, Arthur and Carol soon came up with a similar game, S-Nim, that seemed to solve this problem. Each player is now only allowed to remove a number of beads in some predefined set S, e.g. if we have S = {2,5} each player is only allowed to remove 2 or 5 beads. Now it is not always possible to make the xor-sum 0 and, thus, the strategy above is useless. Or is it?

Your job is to write a program that determines if a position of S-Nim is a losing or a winning position. A position is a winning position if there is at least one move to a losing position. A position is a losing position if there are no moves to a losing position. This means, as expected, that a position with no legal moves is a losing position.

Input

The first line of input contains a number describing the size of S, followed by k numbers describing S. The second line contains a number describing the number of positions to evaluate. The next m lines each contain a number describing the number of heaps and l numbers describing the number of beads in the heap

Output

For each position:

- If the described position is a winning position print a W.

- If the described position is a losing position print an L.

Print a newline after each test case.

k (1 k 100)