There are N trees $($numbered from $0$ to N$1)$ in a forest. The K$-$th tree is located at coordinates $($X$[$K$],$ Y$[$K$]).$

We want to build the widest possible vertical path, such that there is no tree on it$.$ The path must be built somewhere between a leftmost and a rightmost tree, which means that the width of the path cannot be infinite.

What is the width of the widest possible path that can be built?