E. Not a Nim Problem
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Two players, Alice and Bob, are playing a game. They have $$$n$$$ piles of stones, with the $$$i$$$-th pile initially containing $$$a_i$$$ stones.

On their turn, a player can choose any pile of stones and take any positive number of stones from it, with one condition:

  • let the current number of stones in the pile be $$$x$$$. It is not allowed to take from the pile a number of stones $$$y$$$ such that the greatest common divisor of $$$x$$$ and $$$y$$$ is not equal to $$$1$$$.

The player who cannot make a move loses. Both players play optimally (that is, if a player has a strategy that allows them to win, no matter how the opponent responds, they will win). Alice goes first.

Determine who will win.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

Each test case consists of two lines:

  • the first line contains a single integer $$$n$$$ ($$$1 \le n \le 3 \cdot 10^5$$$);
  • the second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^7$$$).

Additional constraint on the input: the sum of $$$n$$$ across all test cases does not exceed $$$3 \cdot 10^5$$$.

Output

For each test case, output Alice if Alice wins, or Bob if Bob wins.

Example
Input
3
3
3 2 9
4
3 3 6 1
5
1 2 3 4 5
Output
Bob
Alice
Bob