If \(\{a_1,a_2,a_3,\ldots,a_n\}\) is a set of real numbers, indexed so that \(a_1 < a_2 < a_3 < \cdots < a_n,\) its complex power sum is defined to be \(a_1i + a_2i^2+ a_3i^3 + \cdots + a_ni^n,\) where \(i^2 = - 1.\) Let \(S_n\) be the sum of the complex power sums of all nonempty subsets of \(\{1,2,\ldots,n\}.\) Given that \(S_8 = - 176 - 64i\) and \(S_9 = p + qi,\) where \(p\) and \(q\) are integers, find \(|p| + |q|.\)
(第十六届AIME1998 第13题)