Chefina and Sums

You are given a sequence A1,A2,…,AN. For each k (1≤k≤N), let's define a function f(k) in the following way: 1. Consider a sequence B1,B2,…,BN, which is created by setting Ak=0. Formally, Bk=0 and Bi=Ai for each valid i≠k. 2. f(k) is the number of ways to split the sequence B into two non-empty contiguous subsequences with equal sums. Find the sum S=f(1)+f(2)+…+f(N). Input: 1. The fi