Let $n$ be a positive integer. Each point $(x,y)$ in the plane, where $x$ and $y$ are non-negative integers with $x+y < n$, is colored red or blue, subject to the following condition:if a point $(x,y)$ is red, then so are all the points $(x',y')$ with $x'\le x$ and $y'\le y$ Let $A$ be the number of ways choose $n$ blue points with distinct $x$-coordinates. and let B be the number of ways to choose $n$ blue points with distinct $y$-coordinates. Prove that $A=B$