Description

Original problem from: HDU 1536

Two players are playing a game with the following rules: There are $n$ piles of stones, with $a_1, a_2, \cdots, a_n$ stones respectively. In each turn, a player must take some stones from one pile, but the number of stones taken must be one of the predefined values in the set $\{s_1, s_2, \cdots, s_k\}$. The player who cannot make a move loses.

Input Format

Multiple test cases.

For each test case, the first line contains an integer $k$, followed by $k$ integers representing $s_1, s_2, \cdots, s_k$;
The second line contains an integer $m$, indicating that $m$ game states will be provided;
The next $m$ lines each start with an integer $n$, followed by $n$ integers representing $a_1, a_2, \cdots, a_n$.

If $k=0$, it signifies the end of input.

Output Format

For each test case, output a string of $m$ characters, where each character indicates whether the corresponding game state is a winning position (W) or a losing position (L).

Sample 1

2 2 5
3
2 5 12
3 2 4 7
4 2 3 7 12
5 1 2 3 4 5
3
2 5 12
3 2 4 7
4 2 3 7 12
0

LWW
WWL

Data Range and Hint

For all data, $0 < n, m, k \le 100$, and $0 < s_i, a_i \le 10^4$.