Binary Inversion

You are given $N$ binary strings $S_1, S_2, \dots, S_N$, each of length $M$. You want to concatenate **all** the $N$ strings in some order to form a single large string of length $N \cdot M$. Find the minimum possible number of inversions the resulting string can have. A binary string is defined as a string consisting only of '$0$' and '$1$'. An *inversion* in a binary string $S$ is a pair of in