Two Groups

This problem has no story, so we at least wish you good luck solving it. Consider a multiset $S$ which contains $A$ copies of the integer $1$, $B$ copies of $2$ and $C$ copies of $3$. For example, if $A = 3$, $B = 3$ and $C = 3$, then $S = \{1, 1, 1, 2, 2, 2, 3, 3, 3\}$. Your goal is to divide the elements of $S$ into two groups (multisets); each element of $S$ must be in exactly one of thes