Assuming $a\ne 1$, $b\ne 2$, $c\ne 3$, and $d\ne 4$, what is the value in simplest form of the following expression:
$\frac{a-1}{2-b}\cdot \frac{b-2}{1-a}\cdot \frac{c-3}{4-d}\cdot \frac{d-4}{3-c}$?