Blackboard Game
Blackboard Game
Initially, the integers from $0$ to $n-1$ are written on a blackboard.
In one round,
- Alice chooses an integer $a$ on the blackboard and erases it;
- Then Bob chooses an integer $b$ on the blackboard such that $a+b \equiv 3 \pmod 4$ and erases it.
Rounds take place in succession until a player is unable to make a move $-$ the first player who is unable to make a move loses. Determine who wins with optimal play.
The first line contains an integer $t$ ($1 \leq t \leq 100$) $-$ the number of test cases.
The only line of each test case contains an integer $n$ ($1\leq n \leq 100$) $-$ the number of integers written on the blackboard.
For each test case, output on a single line $Alice$ if Alice wins with optimal play, and $Bob$ if Bob wins with optimal play.
You can output the answer in any case (upper or lower). For example, the strings $aLiCe$, $alice$, $ALICE$, and $alICE$ will be recognized as $Alice$.
| # | Input.txt | Output.txt |
|---|---|---|
| 1 |
2 3 |
5 |
| 2 |
-2 7 |
5 |
In the first sample, suppose Alice chooses $0$, then Bob cannot choose any number so Alice wins immediately.
In the second sample, suppose Alice chooses $0$, then Bob can choose $3$. Then suppose Alice chooses $2$, then Bob can choose $1$. Then Alice has no numbers remaining, so Bob wins.
Yechimini yuborish
Masalani yechish uchun tizimga kiring yoki ro'yxatdan o'ting.