Define a domino to be an ordered pair of distinct positive integers. A proper sequence of dominos is a list of distinct dominos in which the first coordinate of each pair after the first equals the second coordinate of the immediately preceding pair, and in which $$(i,j)$$ and $$(j,i)$$ do not both appear for any $$i$$ and $$j$$. Let $$D_{40}$$ be the set of all dominos whose coordinates are no larger than 40. Find the length of the longest proper sequence of dominos that can be formed using the dominos of $$D_{40}.$$

(第十六届AIME1998 第15题)