Modular Minimization

You are given an array $A$ of length $N$. Each element of $A$ is $0, 1, $ or $2$. You can perform the following operation as many times as you like: - Choose an index $i$ ($1 \leq i < |A|$), delete $A_i$ and $A_{i+1}$ from the array, and insert $(A_i + A_{i+1}) \bmod 3$ in their place. Note that this operation reduces the length of $A$ by $1$. Define $f(A)$ to be the lexicographically minimu