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
puneethnaik: 2015-07-24 06:03:23

nice question!!

Vivek: 2015-07-22 19:58:11

Easy.AC in 1st go.
Read this statement multiple time " You create a list of numbers where the i-th number is the position of the integer i in the permutation" . the " i'th number" represents the number at i'th position in the give permutation.

Akshay Aradhya: 2015-07-16 18:48:50

Little Confusing but Easy :P And LOL 10 second Time limit hahahah

poojan : 2015-07-11 14:27:24

ac in 1 go too easy

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... :)