Changing Numbers

You are given two arrays $A$ = $A_1, A_2, \ldots, A_N$ and $B$ = $B_1, B_2, \ldots, B_N$. We want to make these two arrays identical. That is, for each $1 \leq i \leq N$, we want to make $A_i$ = $B_i$. To do this, we are allowed to make many operations of the following type: In a single operation, we choose two integers $x$ and $y$, and replace all the occurrences of $x$ in both the arrays with $