Counting paths

Niuniu is interested in counting paths. He has a tree with n vertices initially painted white. For a vertex set S, Niuniu wants to calculate f(S). f(S) is calculated as below. First the vertices in set S are painted black. If there is any white vertex which lies on the path between any two black vertices, f(S)=0. Otherwise, he will choose some set of paths. (a path from x to y is same as y to x, a path from x to x is allowed). The paths in the set cannot contain any black vertices. Next he will paint the vertices in the paths of the set red. f(S) is the number of different path set which makes all adjacent vertices of black vertices black or red. You need to calculate the sum of f(S) for every possible vertex set S. Of course S should contain at least one element. The answer may be large, you only need to calculate it modulo 998244353.