Boris Notkin composes melodies. He represents them as a sequence of notes, where each note is encoded as an integer from $0$ to $127$ inclusive. The interval between two notes $a$ and $b$ is equal to $|a - b|$ semitones.

Boris considers a melody perfect if the interval between each two adjacent notes is either $5$ semitones or $7$ semitones.

After composing his latest melodies, he enthusiastically shows you his collection of works. Help Boris Notkin understand whether his melodies are perfect.

Input

The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of melodies.

Each melody is described by two lines.

The first line contains an integer $n$ ($2 \leq n \leq 50$) — the number of notes in the melody.

The second line contains $n$ integers $a_{1}, a_{2}, \dots, a_{n}$ ($0 \leq a_{i} \leq 127$) — the notes of the melody.

Output

For each melody, output "YES", if it is perfect; otherwise, output "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Samples

8
2
114 109
2
17 10
3
76 83 88
8
38 45 38 80 85 92 99 106
5
63 58 65 58 65
8
117 124 48 53 48 43 54 49
5
95 102 107 114 121
10
72 77 82 75 70 75 68 75 68 75

YES
YES
YES
NO
YES
NO
YES
YES