Maximize Hamming Distance

You are given $M$ strings, each of length $N$. The $i$-th string is called $S_i$. The strings contain only the characters $0$, $1$, or $?$. You must replace *every* $?$ with either a $0$ or a $1$, hence obtaining $M$ binary strings. If you perform these replacements optimally, find the **maximum** possible sum of Hamming distances between each pair of strings. Formally, your aim is to maxim