You are given a tree consisting of $n$ nodes.

You can select any number of nodes from the tree that you want to save. The remaining nodes will be destroyed but the saved nodes again form a tree.

Find the total number of such ways to form the tree.

Note: You may not select any node or you may save all nodes.

Input format

• The first line contains a single integer $N$ ( 2 ≤ $N$ ≤ $10^5$) denoting the number of nodes in the tree.
• Next $N-1$ lines contain two integers, $u$ and $v$, denoting an edge from node $u$ to node $v$ ($0 \le u,v < N$).

Output format

Print the required number of ways modulo $10^9 + 7$.