Problem Description

Given an unrooted tree, find the number of essentially different independent sets in it.

Input Format

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

Lines $2$ to $n$ each contain two integers $u$ and $v$, indicating that there is an edge connecting $u$ and $v$.

Output Format

Output a single integer: the number of valid ways modulo $10^9+7$.

1

2

5
1 2
1 3
1 4
1 5

6

6
1 2
1 3
1 4
4 5
4 6

9

Hint

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