E. Not a Nim Problemtime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputTwo 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.InputThe 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 $$$3 \cdot 10^5$$$.OutputFor each test case, output Alice if Alice wins, or Bob if Bob wins.ExampleInput333 2 943 3 6 151 2 3 4 5OutputBob Alice Bob