VMO 1990 Problem 2

At least $n - 1$ numbers are removed from the set $\{1, 2, \ldots, 2n - 1\}$ according to the following rules: (i) If $a$ is removed, so is $2a$ ; (ii) If $a$ and $b$ are removed, so is $a + b$ . Find the way of removing numbers such that the sum of the remaining numbers is maximum possible.