Every positive integer is marked with a number from the set $\{0,1,2\}$, according to the following rule:  
if a positive integer $k$ is marked with $j$, then the integer $k+j$ is marked with 0.  
Let $S$ denote the sum of marks of the first 2019 positive integers. Determine the maximum possible value of $S$.

Let's think step by step and output the final answer within \boxed{}.
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