On the number of zero-sum subsequences

For a sequence S of elements from an additive abelian group G  , let f(S)f(S) denote the number of subsequences of S the sum of whose terms is zero. In this paper we characterize all sequences S in G   with f(S)>2|S|-2f(S)>2|S|-2, where |S||S| denotes the number of terms of S.