HMMT November 2018 U15

On a computer screen is the single character a. The computer has two keys: c (copy) and p (paste), which may be pressed in any sequence. Pressing $p$ increases the number of a's on screen by the number that were there the last time $c$ was pressed. c doesn't change the number of a's on screen. Determine the fewest number of keystrokes required to attain at least 2018 a's on screen. (Note: pressing p before the first press of c does nothing).