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