# Random Permutation

Suppose $\pi$ is a random permutation of $\mathbb{Z}_n$. How would you determine the probability that $\pi(i+1)-\pi(i) \pmod n < n/2$? We know that $\pi(i+1)-\pi(i)$ is maximum at $n-1$ in $\mathbb{Z}_n$.
Perhaps we could use Inclusion-Exclusion? In other words, find the probability that $\pi(i+1)-\pi(i) > n/2$ (i.e. the $i$th and $i+1$-st places differ by more than $n/2$?