### Ambiguous permutations

Time Limit: 1000 ms
Memory Limit: 65536 KiB

#### Problem Description

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

However, there is another possibility of representing a permutation: You create a list of numbers where the

An

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

The input contains several test cases.

The first line of each test case contains an integer

The last test case is followed by a zero.

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

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

#### Sample Input

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

#### Sample Output

ambiguous not ambiguous ambiguous

#### Hint

#### Source

2005~2006 University of Ulm Local Contest