Add with Mod

For a given pair of arrays $A$ and $B$, both of size $N$, we define: - $f(A, B)$ is defined as the minimum cost of a sequence of operations that transforms the array $A$ into the array $B$ using the following operations: - Rearrange the array $A$ arbitrarily for $0$ cost. - Choose some index $i$ ($1 \le i \le N$), modify $A_i$ to $(A_i + 1) \bmod N$ for a cost of $1$. For example, for $N