Lasers Everywhere

Vivek likes playing with lasers, but his friend Divyansh says that reading biographies is much more interesting. In order to prove that lasers are fun too, Vivek proposed an interesting task involving them: You are given $N$ points in a plane (numbered $1$ through $N$); for each valid $i$, the $i$-th point is $P_i = (i, A_i)$. There are $N-1$ line segments between them (numbered $1$ through $N-