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 ith 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:  20050624 
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
pk:
20150520 09:18:50
AC in one go... my 30th problem... :) 

Arpan Mukherjee:
20150518 19:59:52
For those who're having problem for the language. Check thishttp://discuss.codechef.com/questions/15383/ambiguouspermutationsexplainthestatement


Subhashis Bhowmik:
20150507 10:51:58
Getting a WA, even though the given test case works :( 

arjun:
20150327 19:05:44
Thanks @Adrian Kuegel.


Parikshith Rai:
20150307 10:01:02
@gulbarga master check whether ur writing ambiguous and not ambiguous properly....cost me 1 wa. :)


gulbarga master:
20150220 06:59:41
can i pls have some additional test cases for this ? The ones given, work for me and yet i get a WA. 

thelazycoder:
20150217 21:56:56
good question :D


Adrian Kuegel:
20120920 12:35:58
"You create a list of numbers where the ith number is the position of the integer i in the permutation."


Abhimanyu:
20120917 15:07:37
can anybody please help me understand how 51234 is the inverse permutation of 23451 ??? 