In a certain circle, the chord of a $$d$$-degree arc is 22 centimeters long, and the chord of a $$2d$$-degree arc is 20 centimeters longer than the chord of a $$3d$$-degree arc, where $$d < 120.$$ The length of the chord of a $$3d$$-degree arc is $$- m + \sqrt {n}$$ centimeters, where $$m$$ and $$n$$ are positive integers. Find $$m + n.$$

(第十九届AIME1 2001 第13题)