Maximum Diversity

For a given array $B$, we can divide the array into $2$ **non-empty** [subsequences](https://en.wikipedia.org/wiki/Subsequence), such that, each element of the array is present in **exactly** one of the subsequences. Let $X$ and $Y$ denote the [GCD](https://en.wikipedia.org/wiki/Greatest_common_divisor) of all elements of the first and second subsequence respectively. We define the *maximum di