Number of connected components P81115

You are given a tree, that is, an undirected, connected graph with no cycles. Can you count how many (non-empty) connected subgraphs it contains?

Input

Input consists of several trees, each one with the number of vertices $n$, followed by its $n - 1$ edges. You can assume $1 \le n \le 10^5$, that vertices are numbered between 0 and $n - 1$, and that the given edges indeed form a tree.

Output

For every given tree, print its number of connected subgraphs. As this number may be large, make the computations modulo $10^8 + 7$.