Let $S$ be the set $1,2,3,\dots ,17$. For $a,b\in S$, define $a\succ b$ to mean that either $0<a-b\le 8$ or $b-a>8$. How many ordered quadruples $(w,x,y,z)$ of elements of $S$ have the property that $w\succ x$, $x\succ y$, $y\succ z$, and $z\succ w$?