Problem Statement

You are given an ordered tree with N vertices rooted at vertex 1.
When performing a DFS on this ordered tree from the root, there are two kinds of moves: "descending from a parent to a child" and "returning from a child to its parent". We call them move A and move B, respectively.
Also, let M be the number of times the move "changes from move A to move B, or from move B to move A" during the DFS of this ordered tree.
Find the number, modulo MOD $10^9 + 7$, of ordered trees with N vertices for which the number of times the move "changes from move A to move B, or from move B to move A" during the DFS is equal to M.

Input

$N$
$a_1\ b_1$
$a_i\ b_i$
$a_{N - 1}\ b_{N - 1}$

The first line gives the number of vertices $N (1 \le N \le 10^5)$.
The following N - 1 lines give the edges; each edge connects vertex $a_i$ and vertex $b_i$ with each other.
$1 \le a_i, b_i \le N$

Output

Output the number of ordered trees modulo MOD $10^9 + 7$.

Sample

5
1 2 
2 3
2 4
3 5

6

10
1 2
1 3
3 4
3 5
4 6
2 7
5 8
4 9
7 10

1176

30
1 2
2 3
2 4
4 5
3 6
1 7
3 8
3 9
3 10
10 11
8 12
8 13
10 14
10 15
12 16
3 17
5 18
1 19
16 20
13 21
21 22
7 23
7 24
17 25
25 26
21 27
14 28
18 29
23 30

493001124