#D12228. Tree nesting
Tree nesting
Tree nesting
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.
Examples
Input
5 1 2 2 3 3 4 4 5 3 1 2 2 3
Output
3
Input
3 2 3 3 1 3 1 2 1 3
Output
1
Input
7 1 2 1 3 1 4 1 5 1 6 1 7 4 4 1 4 2 4 3
Output
20
Input
5 1 2 2 3 3 4 4 5 4 4 1 4 2 4 3
Output
0
inputFormat
outputFormat
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.
Examples
Input
5 1 2 2 3 3 4 4 5 3 1 2 2 3
Output
3
Input
3 2 3 3 1 3 1 2 1 3
Output
1
Input
7 1 2 1 3 1 4 1 5 1 6 1 7 4 4 1 4 2 4 3
Output
20
Input
5 1 2 2 3 3 4 4 5 4 4 1 4 2 4 3
Output
0
样例
3
2 3
3 1
3
1 2
1 3
1