Submit | All submissions | Best solutions | Back to list |

## 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.

### Sample Input

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 |