Triplet Maximization

Chef has an array $A$ of length $(X+Y)$. The first $X$ elements of this array are all equal to $1$, and the remaining $Y$ elements are equal to $2$. That is, the array satisfies $A_1 = A_2 = \ldots = A_X = 1$ and $A_{X+1} = \ldots = A_{X+Y} = 2$. Further, it is guaranteed that $(X+Y)$ is a multiple of $3$. Chef will then perform the following process: - Let $S$ be a set of integers. Initiall