Deleting Divisors

题意翻译

Alice 和 Bob 正在玩游戏，他们都**绝顶聪明**。 开始时有一个整数 $n$，二者轮流行动，每次行动可以在当前的 $n$ 上减去其一个非 $1$ 非 $n$ 的因子。 若 Alice 先手，某一方无法进行操作则判输，谁会赢呢？

题目描述

Alice and Bob are playing a game. They start with a positive integer $ n $ and take alternating turns doing operations on it. Each turn a player can subtract from $ n $ one of its divisors that isn't $ 1 $ or $ n $ . The player who cannot make a move on his/her turn loses. Alice always moves first. Note that they subtract a divisor of the current number in each turn. You are asked to find out who will win the game if both players play optimally.

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \leq t \leq 10^4 $ ) — the number of test cases. Then $ t $ test cases follow. Each test case contains a single integer $ n $ ( $ 1 \leq n \leq 10^9 $ ) — the initial number.

输出格式

For each test case output "Alice" if Alice will win the game or "Bob" if Bob will win, if both players play optimally.

输入输出样例

输入样例 #1

4
1
4
12
69

输出样例 #1

Bob
Alice
Alice
Bob

说明

In the first test case, the game ends immediately because Alice cannot make a move. In the second test case, Alice can subtract $ 2 $ making $ n = 2 $ , then Bob cannot make a move so Alice wins. In the third test case, Alice can subtract $ 3 $ so that $ n = 9 $ . Bob's only move is to subtract $ 3 $ and make $ n = 6 $ . Now, Alice can subtract $ 3 $ again and $ n = 3 $ . Then Bob cannot make a move, so Alice wins.