Problem:
Score : 100 points

Problem Statement

There is a tree with N vertices, numbered 1, 2, \ldots, N.
For each i (1 \leq i \leq N - 1), the i-th edge connects Vertex x_i and y_i.

Taro has decided to paint each vertex in white or black.
Here, it is not allowed to paint two adjacent vertices both in black.

Find the number of ways in which the vertices can be painted, modulo 10^9 + 7.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq x_i, y_i \leq N

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_{N - 1} y_{N - 1}

Output

Print the number of ways in which the vertices can be painted, modulo 10^9 + 7.

Sample Input 1

3
1 2
2 3

Sample Output 1

5

There are five ways to paint the vertices, as follows:

Sample Input 2

4
1 2
1 3
1 4

Sample Output 2

9

There are nine ways to paint the vertices, as follows:

Sample Input 3

1

Sample Output 3

2

Sample Input 4

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

Sample Output 4

157

Solution in Python (3.4.3) (judge verdict: Runtime Error)

n = int(input())
graph = [[] for _ in range(n)]

for _ in range(n-1):
    x, y = map(int, input().split())
    x -= 1
    y -= 1
    graph[x].append(y)
    graph[y].append(x)

mod = 10**9 + 7

memo = [0] * n
# dp[v][0]:= 頂点vを白に塗ったときの、vを親とする部分木の塗り方の総数
# dp[v][1]:= 頂点vを黒に塗ったときの、vを親とする部分木の塗り方の総数
dp = [[0, 0] for _ in range(n+1)]


def dfs(v):
    if memo[v] != 0:
        return
    memo[v] = 1
    dp[v][0] = 1
    dp[v][1] = 1
    for nv in graph[v]:
        if memo[nv] != 0:
            continue
        dfs(nv)
        dp[v][0] *= (dp[nv][0] + dp[nv][1])
        dp[v][0] %= mod

        dp[v][1] *= dp[nv][0]
        dp[v][1] %= mod

dfs(0)
print((dp[0][0] + dp[0][1]) % mod)