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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
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.
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.
For each test case output whether the permutation is ambiguous or not.
Adhere to the format shown in the sample output.
4 1 4 3 2 5 2 3 4 5 1 1 1 0
ambiguous not ambiguous ambiguous
|Time Limit:||10 sec|
|Source Limit:||50000 Bytes|
|Languages:||ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.3.2, CPP 4.9.2, CPP14, CS2, D, ERL, FORT, FS, GO, HASK, ICK, ICON, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, NODEJS, PAS fpc, PAS gpc, PERL, PHP, PIKE, PRLG, PYPY, PYTH, PYTH 3.4, RUBY, SCALA, SCM chicken, SCM guile, SCM qobi, ST, TEXT, WSPC|
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If you are still having problems, see a sample solution here.