Chef and Dice

Chef has $N$ [6-sided standard dice](https://en.wikipedia.org/wiki/Dice). Each die has dimensions $1 \times 1 \times 1$. Since Chef is bored during the quarantine, he decides to stack dice for fun. First, Chef forms four vertical stacks of dice (not necessarily with the same height; empty stacks are allowed) on his table, which together make up a pile of dice with base area up to $2 \times 2$.