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 (7.3.0) (judge verdict: Time Limit Exceeded)

import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
from itertools import accumulate, permutations, combinations, product, islice
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left
from fractions import gcd
from heapq import heappush, heappop
from functools import reduce, lru_cache
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10**9 + 7

N = INT()
xy = [LIST() for _ in range(N-1)]
tree = [[] for _ in range(N)]
for x, y in xy:
    tree[x-1].append(y-1)
    tree[y-1].append(x-1)

def DFS(i, par, c):  # c:0->white, 1->black
    if par and len(tree[i]) == 1:
        return 1
    if c == 0:
        cnt = 1
        for node in tree[i]:
            if node != par:
                cnt *= (DFS(node, i, 0) + DFS(node, i, 1))
                cnt %= mod
        return cnt
    elif c == 1:
        cnt = 1
        for node in tree[i]:
            if node != par:
                cnt *= DFS(node, i, 0)
                cnt %= mod
        return cnt

ans = DFS(0, None, 0)+DFS(0, None, 1)
print(ans%mod)