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

hide comments
theabd123: 2018-05-29 11:10:24

AC in one go...Everyone have right to celebrate

m_sundriyal: 2018-03-27 10:24:14

For those who are having a hard time to understand the problem.
Example: 1 4 3 2
1 is at the 1st position so, 1XXX
2 is at the 4th position so, 14XX
3 is at the 3rd position so, 143X
4 is at the 2nd position so, 1432
Now the newly created number(inverse) is same as the previous one, so it's "ambiguous"

yaswanth desu: 2018-03-25 13:22:23

Take care of the sentence, "where the i-th number is the position of the integer i in the permutation" . Read it by considering the above examples mentioned in the question.

venuraja1432: 2018-03-25 11:23:43

is 1,2,3,4 is ambigous or not?

vkash: 2018-03-11 12:32:44

AC after 4 hours:Happy Ending::

pksri1996: 2018-02-12 10:29:19

Can i get the corner cases for this.

shashankpathak: 2018-02-03 17:59:01

Ac in one go!

bradyawn: 2018-01-23 22:18:48

always see people bragging about ac in one go but that just means they don't solve hard enough problems

maansari525: 2018-01-20 19:13:59

AC in one go!

sayasaiteja: 2017-12-13 18:42:04

ac in one go!!!


Added by:Adrian Kuegel
Date:2005-06-24
Time limit:10s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL6 VB.NET
Resource:own problem, used in University of Ulm Local Contest 2005