Stepan's Task

While sorting through his childhood toys, Stepan discovered a collection of $N$ unique rectangles and recalled a problem his old math teacher once posed to him. We define a rectangle as small if there exists another rectangle in the set that can completely cover it. The rectangles can be rotated, but their sides must remain parallel.

For instance, a rectangle with sides $1$ and $10$ can be fully covered by a rectangle with sides $10$ and $3$, but not by a rectangle with sides $9$ and $9$. Rectangles with sides $10$ and $3$, as well as those with sides $9$ and $9$, cannot be covered, so in this set of three rectangles, only one is considered small. Write a program to solve the problem Stepan remembered: determine the number of small rectangles in the given set.