Chef and Ants

Chef has been researching ant colonies for many years and finally discovered all their secrets. An ant colony consists of $N$ distinct lines (numbered $1$ through $N$) that pass through a point $\mathsf{O}$, which is the queen's home. For each valid $i$, there are $M_i$ ants on the $i$-th line. For each valid $i$ and $j$, the $j$-th ant on the $i$-th line initially has a non-zero coordinate