Problem Description

Given an undirected tree, find the number of distinct independent sets.

Input Format

The first line contains an integer \( n \), the number of nodes in the tree (\( n \leq 5 \times 10^5 \)).

The next \( n-1 \) lines each contain two integers \( u \) and \( v \), indicating an edge between nodes \( u \) and \( v \).

Output Format

Output a single integer, the number of distinct independent sets modulo \( 10^9 + 7 \).

Sample Input and Output

Sample Input #1

1

Sample Output #1

2

Sample Input #2

5
1 2
1 3
1 4
1 5

Sample Output #2

6

Sample Input #3

6
1 2
1 3
1 4
4 5
4 6

Sample Output #3

9

见题面 Input 部分

见题面 Output 部分