Numbers \(1,2,\dots,20\) are written on a whiteboard. In one go Louise is allowed to wipe out any two numbers \(a\) and \(b\), and write instead
(a) \(a+b-1\); (b) \(a\times b\).
As you already know, Louise enjoys erasing the numbers, and has fun until only one number is left on the whiteboard. What number is it?