Harold, Tanya, and Ulysses paint a very long picket fence. Harold starts with the first picket and paints every $$h$$th picket; Tanya starts with the second picket and paints every $$t$$th picket; and Ulysses starts with the third picket and paints every $$u$$th picket. Call the positive integer $$100h+10t+u$$ $$\textit{paintable}$$ when the triple $$(h,t,u)$$ of positive integers results in every picket being painted exactly once. Find the sum of all the paintable integers.

(第二十届AIME1 2002 第9题)