Please reason step by step, and put your final answer within \boxed{}.
Several numbers are written on the board. It is allowed to erase any two numbers \( a \) and \( b \), and then write the number \( \frac{a+b}{4} \) in place of one of them. What is the smallest number that can remain on the board after 2018 such operations, if initially, there are 2019 units written on it?
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