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 PyPy3 (2.4.0) (judge verdict: Runtime Error)

#!/usr/bin/env python3
import sys
from collections import defaultdict
from collections import deque
INF = float("inf")

MOD = 1000000007  # type: int


class Graph(object):
    def __init__(self, N):
        self.N = N
        self.E = defaultdict(list)

    def add_edge(self, f, t, w=1):
        self.E[f].append((t, w))
        self.E[t].append((f, w))


def solve(N: int, x: "List[int]", y: "List[int]"):

    g = Graph(N)
    for xx, yy in zip(x, y):
        g.add_edge(xx-1, yy-1)

    white = [-1]*N
    black = [-1]*N

    def rec(node, pre):
        if white[node] > 0:
            return white[node], black[node]

        # nodeを黒と塗る場合
        bbb = 1
        www = 1
        for t, _ in g.E[node]:
            if t != pre:
                w, b = rec(t, node)
                bbb *= w
                www *= (w+b)
        black[node] = bbb % MOD
        white[node] = www % MOD
        return white[node], black[node]

    w, b = rec(0, -1)
    print((w+b) % MOD)
    return


def main():

    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    x = [int()] * (N - 1)  # type: "List[int]"
    y = [int()] * (N - 1)  # type: "List[int]"
    for i in range(N - 1):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    solve(N, x, y)


if __name__ == '__main__':
    main()