P17443 Vanishing Inversions / Vanishing Inversions

Alice and Bob play a game on a permutation, with Alice moving first. A sequence of length $n$ is called a **permutation** if and only if every integer in $1,2,\dots,n$ appears in the sequence exactly once. Initially, a permutation $a_1,a_2,\ldots,a_n$ of length $n$ is given. At any moment during the game, the current sequence is always a permutation of length $m$. The two players take turns, and on each turn they must choose one of the following operations: - Choose an index $i$ $(1\le ia_{i+1}$, and swap $a_i$ and $a_{i+1}$. - Choose an index $i$ $(1\le i

**This problem has multiple test cases.** The first line contains an integer $T$ $(1\le T\le 5000)$, the number of test cases. For each test case: - The first line contains an integer $n$ $(1\le n\le 5000)$. - The second line contains $n$ integers $a_1,a_2,\ldots,a_n$, and it is guaranteed that $a$ is a permutation of length $n$. It is guaranteed that the sum of $n$ over all test cases does not exceed $5000$.

For each test case, if Alice wins, output `Alice`; otherwise output `Bob`.

Translated by ChatGPT 5