A sequence of $n > 0$ integers is called a jolly jumper if the absolute values of the difference between successive elements take on all the values $1$ through $n-1$. For instance,
1 4 2 3
is a jolly jumper, because the absolutes differences are $3$, $2$, and $1$ respectively. The definition implies that any sequence of a single integer is a jolly jumper. You are to write a program to determine whether or not each of a number of sequences is a jolly jumper.
Each line of input contains an integer $n \le 3000$ followed by $n$ integers representing the sequence. The values in the sequence are at most $300\, 000$ in absolute value. Input contains at most $10$ lines.
For each line of input, generate a line of output saying “Jolly” or “Not jolly”.
|Sample Input 1||Sample Output 1|
4 1 4 2 3 5 1 4 2 -1 6
Jolly Not jolly