Need to explain what is Ambiguous Permutations and why the solution works . c++

Please, explain what is Ambiguous Permutations.  why does the solution works ?  I mean I know how operator ^ works, I just do not understand how mathematically define ambiguous/ non ambiguous permutation.

May there is some youtube video.

//// Ambiguous Permutations
//
//All submissions for this problem are available.
//
//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

#include <iostream>
using namespace std; 
int main()
{
	int n, i, j, k;
	long long int s;

	cin >> n;
	while (n)
	{
		s = 0;
		for (j = 1;j <= n;j++)
		{
			cin >> k;
			if (k != j)
			{
				s ^= (k*j);
			}
		}
		(s == 0) ? printf("ambiguous\n") : printf("not ambiguous\n");

		cin >> n;
	}
	return 0;
}

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