We call a permutation p₀, p₁, ... , p_n-1 of integers 0, 1, ... , n-1 anti-arithmetic, when there are no three-term arithmetic series in this permutation, i.e. there are no such three indices i < j < k, that integers p_i, p_j, p_k make an arithmetic series. For example, the series of integers 3, 1, 0, 4, 2 is an anti-arithmetic permutation of integers 0, 1, 2, 3, 4. The series 0, 5, 4, 3, 1, 2 is not an antiarithmetic permutation, because its first, fifth and sixth term: 0, 1, 2 form an arithmetic series (as well as its second, fourth and fifth term: 5, 3, 1 and second third and fourth term: 5, 4, 3 form arithmetic series). Given a permutation of length n determine whether the given permutation is anti-arithmetic or not.

입력 형식

Input starts with an integer T, the number of test cases.</p>

Each test case consists of two lines. First line contains an integer n. Next line contains n integers separated by a single space. These n integers denotes a permutation of 0, 1, .., n-1. n is between 3 and 50 inclusive.

출력 형식

For each test case, the output contains a 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 or “NO” otherwise. Quotes are for clarity only. 

예제 입력

12
4
3 1 0 2
9
0 8 4 6 2 3 7 5 1
7
1 5 3 2 6 4 0
6
3 2 5 1 4 0
10
0 8 4 2 6 9 1 5 3 7
6
3 1 5 2 4 0
3
1 0 2
3
2 0 1
5
0 4 2 1 3
7
1 5 3 0 4 2 6
6
2 0 4 5 1 3
10
4 3 1 6 9 2 5 8 0 7

예제 출력

Case #1: YES
Case #2: YES
Case #3: YES
Case #4: NO
Case #5: YES
Case #6: YES
Case #7: YES
Case #8: YES
Case #9: YES
Case #10: YES
Case #11: YES
Case #12: NO