Consider you have a permutation of $ 1$ to $ n$ in an array $ s$ . Now select three distinct indices $ a$ ,$ b$ ,$ c$ ,need not to be sorted. Let $ s_a$ , $ s_b$ and $ s_c$ be the values at those indices and now you make a right shift to it ,that is $ new$ $ s_a$ = $ old$ $ s_b$ and $ new$ $ s_b$ = $ old$ $ s_c$ and $ new$ $ s_c$ =$ old$ $ s_a$ . Find the minimum number of operations required to sort the array or if is impossible how to determine it.

Example : Consider $ s= [2, 1, 3]$ ; consider indices $ (1,3,2)$ in the given order after applying one opeartion it is $ s =[1,2,3]$ .

I am thinking of applying a graph approach and solve it using graph traversal, am I right? Or you could explain your apporach.