The most important observation is that there exists a solution in which at most two cyclic swaps are needed. We can divide the solution into a few separate cases:

1. Starting array is sorted – in this case, there is no need for any swap.
2. One swap is enough – If there is number ~a~ at the position ~P~ in starting array and in position ~a~ there is number ~b~, at position ~b~ number ~c~, …, at position ~z~ there is number ~P~, then this configuration is called interesting. For example, starting array ~[5, 4, 1, 3, 2]~ is one big interesting configuration. In this case, only one swap is necessary.
3. Two swaps are enough – it is easy to show that starting array can be partitioned into a finite number of interesting configurations (or subsets). If we make a cyclic swap with one number from every interesting subset, they all will combine into one big interesting configuration for which is then only one swap needed.