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

1 4 3 2
2 3 4 5 1

Sample Output

not ambiguous

hide comments
gautam: 2016-04-03 12:36:27

easy one....;-)

utkarsh538: 2016-03-31 07:09:42

easy question :)

chalarangelo: 2016-03-15 20:09:11

I have submitted multiple solutions in Python 3.4 and all give wrong answer, although I checked with a whole lot of input and the output is corret. Is there some formatting trick I need to know like end of lines etc.?

neil145912: 2016-03-14 21:34:46

WA for "ambigous" instead of "ambiguous" :(

dokz: 2016-01-05 11:29:28

Spent so much time getting the WA. The problem was in word spelling: it is "ambiguous", not "ambigious". Oh, English...

tarunver123: 2015-12-13 08:10:58

AC in 2nd go ...did a silly mistake..:)

raghav12345: 2015-11-14 08:28:58

easy one....

Divyansh Khanna: 2015-10-29 18:19:27

AC in the 1st go!! 6 lines of code!

abhisheshfreak: 2015-10-21 19:58:29

read it carefully...... Piece of cake ;-)

vishals: 2015-10-18 14:46:50

ac in one go... just read Ambiguous Permutation :)
happy coding !!!

Added by:Adrian Kuegel
Time limit:10s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL 6
Resource:own problem, used in University of Ulm Local Contest 2005