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 $2\ \mathbf{xor}\ 4\ \mathbf{xor}\ 7 = 1$).
 - 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 player’s 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.

Understandably it is no fun to play a game when both players know how to play perfectly (ignorance is bliss). Fortunately, 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 $k$ ($1 \le k \le 100$) describing the size of $S$, followed by $k$ numbers $s_ i$ ($1 \le s_ i \le 10000$) describing $S$. The second line contains a number $m$ ($1 \le m \le 100$) describing the number of positions to evaluate. The next $m$ lines each contain a number $l$ ($1 \le l \le 100$) describing the number of heaps and $l$ numbers $h_ i$ ($0 \le h_ i \le 10000$) describing the number of beads in the heaps.

-----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’.

-----Examples-----
Sample Input:
2 2 5
3
2 5 12
3 2 4 7
4 2 3 7 12
Sample Output:
LWW

Source: kattis | Difficulty: MEDIUM


Solutions: