Anti-Arithmetic Permutation

A permutation $p_0, p_1, \dots, p_{n-1}$ of the integers $0, 1, \dots, n-1$ is anti-arithmetic when no three of its terms form an arithmetic series. That is, there are no three indices $i < j < k$ for which $p_i, p_j, p_k$ is an arithmetic series, which happens exactly when $p_j - p_i = p_k - p_j$, or equivalently $p_i + p_k = 2 p_j$.

For example, 3, 1, 0, 4, 2 is an anti-arithmetic permutation of $0, 1, 2, 3, 4$. The sequence 0, 5, 4, 3, 1, 2 is not anti-arithmetic. Its first, fifth and sixth terms 0, 1, 2 form an arithmetic series, and so do its second, fourth and fifth terms 5, 3, 1 and its second, third and fourth terms 5, 4, 3.

Given a permutation of length $n$, decide whether it is anti-arithmetic.

The first line contains an integer $T$, the number of test cases.

Each test case consists of two lines. The first line contains an integer $n$. The next line contains $n$ integers separated by a single space, a permutation of $0, 1, \dots, n-1$. $n$ is between 3 and 50 inclusive.

For each test case, print one line in the format Case #x: M, where $x$ is the case number starting from 1 and $M$ is YES when the given permutation is anti-arithmetic and NO otherwise.