Let \(u\) and \(v\) be integers satisfying \(0 < v < u\). Let \(A = (u,v)\), let \(B\) be the reflection of \(A\) across the line \(y = x\), let \(C\) be the reflection of \(B\) across the y-axis, let \(D\) be the reflection of \(C\) across the x-axis, and let \(E\) be the reflection of \(D\) across the y-axis. The area of pentagon \(ABCDE\) is \(451\). Find \(u + v\).
(第十八届AIME1 2000 第2题)