## PERMUT2 - Ambiguous Permutations

Some programming contest problems are really tricky: not only do they require a different output format from what you might have expected, but also the sample output does not show the difference. For an example, let us look at permutations.
A permutation of the integers 1 to n is an ordering of these integers. So the natural way to represent a permutation is to list the integers in this order. With n = 5, a permutation might look like 2, 3, 4, 5, 1.
However, there is another possibility of representing a permutation: You create a list of numbers where the i-th number is the position of the integer i in the permutation. Let us call this second possibility an inverse permutation. The inverse permutation for the sequence above is 5, 1, 2, 3, 4.
An ambiguous permutation is a permutation which cannot be distinguished from its inverse permutation. The permutation 1, 4, 3, 2 for example is ambiguous, because its inverse permutation is the same. To get rid of such annoying sample test cases, you have to write a program which detects if a given permutation is ambiguous or not.

### Input Specification

The input contains several test cases.
The first line of each test case contains an integer n (1 ≤ n ≤ 100000). Then a permutation of the integers 1 to n follows in the next line. There is exactly one space character between consecutive integers. You can assume that every integer between 1 and n appears exactly once in the permutation.
The last test case is followed by a zero.

### Output Specification

For each test case output whether the permutation is ambiguous or not. Adhere to the format shown in the sample output.

```4
1 4 3 2
5
2 3 4 5 1
1
1
0
```

### Sample Output

```ambiguous
not ambiguous
ambiguous
```

 Added by: Adrian Kuegel Date: 2005-06-24 Time limit: 10s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: C C++ 4.3.2 CPP CPP14 JAVA JS-RHINO JS-MONKEY PYTHON PYTHON3 Resource: own problem, used in University of Ulm Local Contest 2005