Sliders by the Box

A food truck sells sliders only in boxes of 4 4 and boxes of 5 5 . Call an order size "fillable" if it can be hit exactly using any combination of those boxes (for example 9=4+5 9 = 4 + 5 and 40=5⋅8 40 = 5 \cdot 8 are fillable). How many of the order sizes 1,2,…,1000 1, 2, \ldots, 1000 are fillable?

Answer

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