PERMUT2 - Ambiguous Permutations

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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 Pentium G860 3GHz)
Languages:All except: NODEJS PERL 6 SCM chicken VB.net
Resource:own problem, used in University of Ulm Local Contest 2005

hide comments
ritu: 2015-06-24 01:15:37

AC in frst :D

jitendra: 2015-06-21 20:18:34

AC in first go... feeling awesome

cassiano: 2015-06-19 03:15:37

The answer is given on the question statement... =P

Ankush : 2015-06-08 09:04:35

Don't use Python. it caused me 2 TLEs in such an easy question :(

sunil gowda: 2015-05-28 21:48:50

good question

pk: 2015-05-20 09:18:50

AC in one go... my 30th problem... :)

Arpan Mukherjee: 2015-05-18 19:59:52

For those who're having problem for the language. Check this-http://discuss.codechef.com/questions/15383/ambiguous-permutations-explain-the-statement

AC in 1 go ^_^

Subhashis Bhowmik: 2015-05-07 10:51:58

Getting a WA, even though the given test case works :(

arjun: 2015-03-27 19:05:44

Thanks @Adrian Kuegel.
Ac on 1st go. Done in O(n);
read the comment of Adrian Kuegel, The Main Logic is given there.

Parikshith Rai: 2015-03-07 10:01:02

@gulbarga master check whether ur writing ambiguous and not ambiguous properly....cost me 1 wa. :)