Jolly Jumpers

Interview

Time limit1sMemory limit128 MB

Summary

For each sequence, check whether the absolute differences of adjacent elements are exactly the set 1 to n-1.

Level: Easy3 of 10
Topics: Array, Hash map, Implementation, Math
Solved: No attempts yet

Problem

Determine whether an integer sequence is a Jolly jumper.

A sequence of length $1$ is always a Jolly jumper.
A sequence of length $n \ge 2$ is a Jolly jumper if the absolute values of the differences between adjacent numbers include every integer from $1$ to $n-1$ exactly once. (There are exactly $n-1$ adjacent pairs.)

For example, the sequence 1 4 2 3 is a Jolly jumper because the absolute differences of its adjacent numbers are $3, 2, 1$ , which cover all of $1$ through $3$ .

Given several sequences, decide for each one whether it is a Jolly jumper.

Input

The input consists of several lines. Each line starts with the length $n$ ( $1 \le n < 3000$ ) of a sequence, followed by $n$ integers separated by spaces. Lines are given until the end of input.

Output

For each sequence, print Jolly if it is a Jolly jumper and Not jolly otherwise, one result per line.

Examples3

Example 1
Input
```
4 1 4 2 3
5 1 4 2 -1 6
```
Expected output
```
Jolly
Not jolly
```
Example 2
Input
```
1 5
```
Expected output
```
Jolly
```
Example 3
Input
```
2 3 3
```
Expected output
```
Not jolly
```