Minimize the Bits

You are given a **binary** string $A$ of length $N$. The [decimal representation](https://en.wikipedia.org/wiki/Binary_number#Binary_counting) of this string could be huge. Your task is to find out two binary strings $B$ and $C$, each of length $N$, such that: - $(A)_{10} = (B)_{10} - (C)_{10}$; - The total count of $1$s in $B$ and $C$ is **minimum**. If multiple such strings $B$ and $C$ e