There is an array $a_1,\dotsc,a_n$ whose elements are pairwise distinct. We define a reverse order pair to be an ordered pair $(a_i,a_j)$ such that $i < j$ and $a_i > a_j$. Consider the total number of reverse order pairs $N$.

Assume the array is permuted uniformly and randomly, it is well known that $E[N] = \frac{n(n+1)}{4}$. What is the probability distribution of $N$?