410484: GYM104025 J Stones

Aqua and Hiyori love playing games.

There are $$$n$$$ piles of stones, the $$$i$$$-th pile has $$$a_i$$$ stones.

They take turns to make a move. Aqua makes the first move.

In one move, the player must choose a non-empty pile $$$i$$$ and select an integer $$$x$$$ from the chosen set satisfying $$$2\leq 2x\leq a_i+1$$$. Then the player should remove $$$x$$$ stones from the pile $$$i$$$.

The player who can not make a move loses the game.

You want to know whether Aqua will win the game, if both of them play optimally.

The first line contains an integer $$$n\ (1\leq n\leq 10^6)$$$, indicating the number of the piles.

The second line contains $$$n$$$ integers $$$a_1,a_2,...,a_n\ (0\leq a_i\leq 10^9)$$$, indicating the number of stones in each pile.

Print "Alice" (without quotes) if the Aqua will win, otherwise print "Bob" (without quotes).

8
2704 3196 108 820 520 1976 3524 3520

Bob

3
3 5 9

Alice

Make sure to print "Alice" and "Bob" instead of "Aqua" and "Hiyori".