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)