GAIC Math 2024 Problem 123

Let $A$ and $B$ be two subsets of the set $\{1,2, \ldots, 20\}$, where $A \cap B = \varnothing$, and if $n \in A$, then $2n + 2 \in B$. Let $M(A)$ denote the sum of the elements of $A$. The maximum value of $M(A)$ is: