Make same

You are given three binary strings$^\dagger$ $S_{1}, S_{2}, S_{3}$ each of length $N$. Your goal is to make each string contain identical characters (all $0's$ or all $1's$). To achieve this, you can perform the following operation: - Choose $x, y$ from $\{1, 2, 3\}$. - Choose index $i, j$ such that $0 \leq i, j \lt N$. - Swap $S_{xi}$ and $S_{yj}$ (character at $i^{th}$ index in $S_{x}$ and cha