Brain Game
Medium Accuracy: 7.61% Submissions: 1092 Points: 4

2 players A & B takes turns alternatively and play a game. The game is that they have N numbers on a paper. At any turn a player can replace one of the numbers by any of its factor ( except for 1 & itself ). The player who is unable to make a move looses the game. Find the winner of the game if A starts the game and both play optimally.

Input:
The first line has an integer T denoting the number of test cases.Then T test cases follow. The first line of each test case has an integer N denoting the number of numbers on the paper. The next line consists of N numbers.

Output:
For each test case print in a new line the winner, ie either A or B.

Constraints:
1<=T<=100
1<=N<=1000
1<=Ai<=1000

Example:
Input:

2
3
5 7 3
4
2 4 7 11

Output:
B
A

Explanation:
In the first case, the numbers cannot be replaced by any other number so A can not make a move and B is the winner.
In the second case, player A can replace 4 by 2 and thus the numbers left will be 2 2 7 & 11 and all are irreplacable and thus A is the winner.