AB or C

You are given $3$ arrays of positive integers $A$, $B$ and $C$, all of length $N$. Now, you need to construct another array $D$ of length $N$ such that $D_i$ is either $A_i$, $B_i$ or $C_i$ for each $1 \le i \le N$. You can independently choose which value to take for each index. Find the minimum possible value of $\max(D) - \min(D)$ when we optimally choose the array $D$. Here, $\max(D)$ repr