Let $S$ be the set $1,2,3,\dots ,13$. For $a,b\in S$, define $a\succ b$ to mean that either $0<a-b\le 6$ or $b-a>6$. How many ordered triples $(x,y,z)$ of elements of $S$ have the property that $x\succ y$, $y\succ z$, and $z\succ x$?