Editorial

If the number of zeros in the string is equal to the number of ones, the answer is «Yes». One of the possible ways is to color all the ones in red. We will get all zeros in the first string and all ones in the second.

Can there be other cases where the answer is «Yes»? No, because in other cases, there will either be too many zeros, which will lead to having $0$ in the same position in both strings, or too many ones.