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)