CF1841A.Game with Board

Alice and Bob play a game. They have a blackboard; initially, there are $n$ integers written on it, and each integer is equal to $1$.

Alice and Bob take turns; Alice goes first. On their turn, the player has to choose several (at least two) equal integers on the board, wipe them and write a new integer which is equal to their sum.

For example, if the board currently contains integers ${1, 1, 2, 2, 2, 3}$, then the following moves are possible:

• choose two integers equal to $1$, wipe them and write an integer $2$, then the board becomes ${2, 2, 2, 2, 3}$;
• choose two integers equal to $2$, wipe them and write an integer $4$, then the board becomes ${1, 1, 2, 3, 4}$;
• choose three integers equal to $2$, wipe them and write an integer $6$, then the board becomes ${1, 1, 3, 6}$.

If a player cannot make a move (all integers on the board are different), that player wins the game.

Determine who wins if both players play optimally.

爱丽丝和鲍勃进行一场游戏。他们有一块黑板，初始时黑板上写有 $n$ 个整数，每个整数均为 $1$。

爱丽丝和鲍勃轮流进行操作，爱丽丝先手。在每一轮中，当前玩家必须在黑板上选择若干（至少两个）相等的整数，将它们擦除，并写下一个等于这些整数之和的新整数。

例如，若黑板当前包含整数 ${1, 1, 2, 2, 2, 3}$，则以下操作是可行的：

• 选择两个值为 $1$ 的整数，擦除它们并写入整数 $2$，此时黑板变为 ${2, 2, 2, 2, 3}$；
• 选择两个值为 $2$ 的整数，擦除它们并写入整数 $4$，此时黑板变为 ${1, 1, 2, 3, 4}$；
• 选择三个值为 $2$ 的整数，擦除它们并写入整数 $6$，此时黑板变为 ${1, 1, 3, 6}$。

若某位玩家无法进行操作（即黑板上所有整数互不相同），则该玩家获胜。

假设双方均以最优策略进行游戏，判断谁将获胜。

The first line contains one integer $t$ ($1 \le t \le 99$) — the number of test cases.

Each test case consists of one line containing one integer $n$ ($2 \le n \le 100$) — the number of integers equal to $1$ on the board.

第一行包含一个整数 $t$（$1 \le t \le 99$）—— 测试用例的数量。

每个测试用例由一行组成，该行包含一个整数 $n$（$2 \le n \le 100$）—— 黑板上等于 $1$ 的整数的个数。

For each test case, print Alice if Alice wins when both players play optimally. Otherwise, print Bob.

对于每个测试用例，如果双方都采取最优策略时 Alice 获胜，则输出 Alice；否则输出 Bob。

In the first test case, $n = 3$, so the board initially contains integers ${1, 1, 1}$. We can show that Bob can always win as follows: there are two possible first moves for Alice.

• if Alice chooses two integers equal to $1$, wipes them and writes $2$, the board becomes ${1, 2}$. Bob cannot make a move, so he wins;
• if Alice chooses three integers equal to $1$, wipes them and writes $3$, the board becomes ${3}$. Bob cannot make a move, so he wins.

In the second test case, $n = 6$, so the board initially contains integers ${1, 1, 1, 1, 1, 1}$. Alice can win by, for example, choosing two integers equal to $1$, wiping them and writing $2$ on the first turn. Then the board becomes ${1, 1, 1, 1, 2}$, and there are three possible responses for Bob:

• if Bob chooses four integers equal to $1$, wipes them and writes $4$, the board becomes ${2,4}$. Alice cannot make a move, so she wins;
• if Bob chooses three integers equal to $1$, wipes them and writes $3$, the board becomes ${1,2,3}$. Alice cannot make a move, so she wins;
• if Bob chooses two integers equal to $1$, wipes them and writes $2$, the board becomes ${1, 1, 2, 2}$. Alice can continue by, for example, choosing two integers equal to $2$, wiping them and writing $4$. Then the board becomes ${1,1,4}$. The only possible response for Bob is to choose two integers equal to $1$ and write $2$ instead of them; then the board becomes ${2,4}$, Alice cannot make a move, so she wins.

在第一个测试用例中，$n = 3$，因此初始棋盘上包含整数 ${1, 1, 1}$。我们可以如下说明 Bob 总是获胜：Alice 有两种可能的首次操作。

• 若 Alice 选择两个值为 $1$ 的整数，将其擦除并写入 $2$，则棋盘变为 ${1, 2}$。Bob 无法进行任何操作，因此 Bob 获胜；
• 若 Alice 选择三个值为 $1$ 的整数，将其擦除并写入 $3$，则棋盘变为 ${3}$。Bob 无法进行任何操作，因此 Bob 获胜。

在第二个测试用例中，$n = 6$，因此初始棋盘上包含整数 ${1, 1, 1, 1, 1, 1}$。Alice 可以通过如下方式获胜（例如）：在第一回合选择两个值为 $1$ 的整数，将其擦除并写入 $2$。此时棋盘变为 ${1, 1, 1, 1, 2}$，Bob 有三种可能的回应：

• 若 Bob 选择四个值为 $1$ 的整数，将其擦除并写入 $4$，则棋盘变为 ${2,4}$。Alice 无法进行任何操作，因此 Alice 获胜；
• 若 Bob 选择三个值为 $1$ 的整数，将其擦除并写入 $3$，则棋盘变为 ${1,2,3}$。Alice 无法进行任何操作，因此 Alice 获胜；
• 若 Bob 选择两个值为 $1$ 的整数，将其擦除并写入 $2$，则棋盘变为 ${1, 1, 2, 2}$。接着 Alice 可继续操作（例如）：选择两个值为 $2$ 的整数，将其擦除并写入 $4$，此时棋盘变为 ${1,1,4}$。Bob 唯一可能的操作是选择两个值为 $1$ 的整数，并将其替换为 $2$；此时棋盘变为 ${2,4}$，Alice 无法进行任何操作，因此 Alice 获胜。