Ninjaclasher, MCPT's self-proclaimed President, has an obsession with all things perfect. One day, while he was working on a tree problem, he began wondering how many perfect trees existed in the problem. As such, he has hired you to find the number of perfect trees on a given tree.

More specifically, he wants to know the number of non-empty subset of nodes in the tree that form a perfect tree, modulo ~10^9+7~. A subset of nodes is a perfect tree if there is a root of that subset of nodes that satisfies these properties:

1. The subset of nodes forms a connected tree.
2. Every non-leaf node in the tree has the same amount of children ~k~ ~(k \ge 2)~.
3. Every leaf is equidistant to the root node.

Input Specification

The first line will contain the integer ~N~ ~(1 \le N \le 2000)~, the number of nodes in the tree.

The next ~N-1~ lines will each contain two integers, ~u_i~ and ~v_i~ ~(1 \le u_i, v_i \le N)~, indicating that nodes ~u_i~ and ~v_i~ are connected by an edge.

Output Specification

The number of subset of nodes of the tree that form a perfect tree, modulo ~10^9+7~.

Subtasks

Subtask 1 [27%]

~N \le 100~

Subtask 2 [73%]

No additional constraints.

Sample Input for Subtask 1

8
1 2
1 3
1 4
2 5
2 6
4 7
4 8

Sample Output for Subtask 1

21

Explanation for Sample for Subtask 1

The following tree is given:

The following are the ~21~ perfect trees, with the roots in red:

Sample Input for Subtask 2

15
1 2
1 3
1 4
1 5
1 6
2 7
2 8
2 9
2 10
6 11
6 12
6 13
6 14
11 15

Sample Output for Subtask 2

130