FI-MO 2014 Problem 3

The points $P = (a, b)$ and $Q = (c, d)$ are in the first quadrant of the $xy$ plane, and $a, b, c$ and $d$ are integers satisfying $a < b, a < c, b < d$ and $c < d$ . A route from point $P$ to point $Q$ is a broken line consisting of unit steps in the directions of the positive coordinate axes. An allowed route is a route not touching the line $x = y$ . Tetermine the number of allowed routes.