Clamp Paths on Tree

You are given a tree with $N$ vertices (numbered $1$ through $N$). A simple path between two different vertices $a$ and $b$ ($a \lt b$) is called a *clamp path* if it does not contain any vertices with numbers smaller then $a$ or greater than $b$. Calculate the number of clamp paths in the given tree. ### Input - The first line of the input contains a single integer $N$. - The second line conta