Shayan is playing a game by himself. He picks **relatively prime** integers $a$ and $b$ such that $1 < a < b < 2020$. He wins if every integer $m \geq \frac{ab}{2}$ can be expressed in the form $ax + by$ for nonnegative integers $x$ and $y$. He hasn't been winning often, so he decides to write down all winning pairs $(a, b)$, from $(a_1, b_1)$ to $(a_n, b_n)$. What is $b_1 + b_2 + \ldots + b_n$?

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