Binary Grid Forces

You are given a list $L$ consisting of $N$ **binary** strings, each of length $M$. You can do the following operation any (possibly zero) number of times: - Swap $2$ positions in $L_i$ if the same $2$ positions are both $1$ currently in $L_{i + 1}$. More formally, in one operation, you can: - Pick $3$ integers $i, j, k$ such that: - $1 \le i \lt N$; - $1 \le j \lt k \le M$; - $L_{(i + 1,