You are given two trees (connected undirected acyclic graphs) S and T.

Count the number of subtrees (connected subgraphs) of S that are isomorphic to tree T. Since this number can get quite large, output it modulo 109+7.

Two subtrees of tree S are considered different, if there exists a vertex in S that belongs to exactly one of them.

Tree G is called isomorphic to tree H if there exists a bijection f from the set of vertices of G to the set of vertices of H that has the following property: if there is an edge between vertices A and B in tree G, then there must be an edge between vertices f(A) and f(B) in tree H. And vice versa- if there is an edge between vertices A and B in tree H, there must be an edge between f-1(A) and f-1(B) in tree G.

The first line contains a single integer |S| (1 \le |S| \le 1000) - the number of vertices of tree S.

Next |S|-1 lines contain two integers ui and vi (1 \le ui,vi \le |S|) and describe edges of tree S.

The next line contains a single integer |T| (1 \le |T| \le 12) - the number of vertices of tree T.

Next |T|-1 lines contain two integers xi and yi (1 \le xi,yi \le |T|) and describe edges of tree T.

On the first line output a single integer - the answer to the given task modulo 109+7.