Or Sum

Let's define $Score$ of an array $B$ of length $M$ as $\sum_{i=1}^{M} \sum_{j=i}^{M} f(i,j)$, where $f(i,j) = B_i$ $|$ $B_{i+1}$ $|$ $\dots$ $|$ $B_j$ (Here $|$ denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#OR)) You are given an array $A$, consisting of $N$ **distinct** elements. Find the sum of $Score$ over all $N!$ possible permutations of $A$. Since the a