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.
Input
The first line contains a single integer |S| (1≤|S|≤1000) − the number of vertices of tree S.
Next |S|-1 lines contain two integers ui and vi (1≤ui,vi≤|S|) and describe edges of tree S.
The next line contains a single integer |T| (1≤|T|≤12) − the number of vertices of tree T.
Next |T|-1 lines contain two integers xi and yi (1≤xi,yi≤|T|) and describe edges of tree T.
Output
On the first line output a single integer − the answer to the given task modulo 109+7.