Chef and Elephant Tree

Let's define an *elephant tree* with size $N$ as a rooted tree with $N$ vertices (numbered $1$ through $N$) such that: - vertex $1$ is the root - for any three vertices $u$, $v$ and $w$ such that $u \lt v \lt w$, if $w$ is a (direct or indirect) descendant of $u$, then $v$ is also a descendant of $u$ Little Chef has an elephant tree with size $N$. Today, he wants to use the leaves of this tre