Consider the set $A = \{1, 2, 3, ..., 2n - 1\}$, where $n \ge 2$ is a positive integer. We remove from the set $A$ at least $n - 1$ elements such that: • if $a \in A$ has been removed, and $2a \in A$, then $2a$ has also been removed, • if $a, b \in A (a \ne b)$ have been removed and $a + b \in A$, then $a + b$ has also been removed. Which numbers have to be removed such that the sum of the remaining numbers is maximum?