Problem A
Permuted Arithmetic Sequence

An arithmetic sequence is a list of values where the difference between consecutive values is always the same. For example, $3,7,11,15$ qualifies and so does $25,15,5,-5,-15$. However $2,4,7$ and $3,6,9,6$ are not arithmetic sequences.

Input

Input begins with an integer, $1\le n\le 100$, on a line by itself. Following this are $n$ lines, each describing a sequence. Each line begins with an integer, $3\le m\le 100$, giving the length of the sequence. This is followed by the $m$ integer values that actually make up the sequence. Each of the sequence integers is in the range $[-{10}^6,{10}^6]$.

Output

For each sequence, output a line that says “arithmetic” if the sequence is an arithmetic sequence. Output “permuted arithmetic” if the sequence can be reordered to make an arithmetic sequence. Otherwise, output “non-arithmetic”.

3
5 1 2 3 4 5
3 20 6 13
4 5 9 15 19

arithmetic
permuted arithmetic
non-arithmetic