A permutation of the integers 1 to $$n$$ is obtained by placing these numbers in a certain order. A logical way to represent permutations is thus lists. For $$n = 5$$ a permutation can, for example, be represented in the following way:

2, 3, 4, 5, 1

However, there is another way to represent permutations: as a list of integeres, where the $$i$$-th number indicates the position of the number $$i$$ in the permutation. This second representation is called an inverse permutation. The inverse permutation of the above example is thus:

5, 1, 2, 3, 4

because number 1 is at position 5 in the permutation, number 2 is at position 1 in the permutation, …

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.

Assignment

Write a function inversePermutationto which a list of integers must be passed as argument. This list must represent a permutation of the numbers 1 to $$n$$, where $$n$$ is equal to the length of the list. The function must return a new list as a result, which represents the inverse permutation.
Use the inversePermutation function to write a function ambiguousPermutation.To this function, a list of integers must be passed as an argument, which is a permutation of the numbers 1 to $$n$$ (with $$n$$ equalling the length of the list). The function must return a Boolean value as a result, which indicates whether the given list is ambiguous or not.

Example

>>> inversePermutation([1, 4, 3, 2])
[1, 4, 3, 2]
>>> inversePermutation([2, 3, 4, 5, 1])
[5, 1, 2, 3, 4]
>>> inversePermutation([1]) 
[1]

>>> ambiguousPermutation([1, 4, 3, 2])
True
>>> ambiguousPermutation([2, 3, 4, 5, 1])
False
>>> ambiguousPermutation([1]) 
True