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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
using Pair = System.Tuple<int, int>;
using Edge = System.Tuple<int, int, long>;
//using Debug;
//using static System.Globalization.CultureInfo;

class Program
{
    private static long[,] memo;
    static bool[] th;
    static void Main(string[] args)
    {
        var num = Input.num;
        var adj = Enumerable.Repeat(0, num).Select(v => new List<int>()).ToArray();
        for(var i=0; i < num - 1; i++)
        {
            var inp = Input.ar;
            adj[inp[0] - 1].Add(inp[1] - 1);
            adj[inp[1] - 1].Add(inp[0] - 1);
        }
        memo = new long[num, 2];
        th = new bool[num];
        dp(adj, 0);
        WriteLine((memo[0, 0] + memo[0, 1]) % Input.MOD);
    }
    private static void dp(List<int>[] adj,int index)
    {
        memo[index, 0] = 1;
        memo[index, 1] = 1;
        th[index] = true;
        foreach (var ad in adj[index])
            if (!th[ad])
            {
                dp(adj, ad);
                memo[index, 0] = (memo[ad, 0] + memo[ad, 1]) % Input.MOD * memo[index, 0] % Input.MOD;
                memo[index, 1] = memo[ad, 0] * memo[index, 1] % Input.MOD;
            }
    }
}

public class Input
{
    public static string read => ReadLine();
    public  static int[] ar => Array.ConvertAll(read.Split(' '), int.Parse);
    public  static int num => ToInt32(read);
    public static long[] arL => Array.ConvertAll(read.Split(' '), long.Parse);
    public  static long numL => ToInt64(read);
    public static char[][] gred(int h) 
        => Enumerable.Repeat(0, h).Select(v => read.ToCharArray()).ToArray();
    public static int[][] twodim(int num)
        => Enumerable.Repeat(0, num).Select(v => ar).ToArray();
    public static long[][] twodimL(int num)
        => Enumerable.Repeat(0, num).Select(v => arL).ToArray();
    public const long Inf = (long)1e18;
    public const double eps = 1e-6;
    public  const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}