Suppose that $$|x_i| < 1$$ for $$i = 1, 2, \dots, n$$. Suppose further that $$|x_1| + |x_2| + \dots + |x_n| = 19 + |x_1 + x_2 + \dots + x_n|$$. What is the smallest possible value of $$n$$?

(第六届AIME1988 第4题)