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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main {

    static long mod = (long) (1e9 + 7);

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        int n = in.nextInt();
        Vertex[] vs = new Vertex[n + 1];
        for (int i = 1; i <= n; i++) {
            vs[i] = new Vertex(i);
        }
        for (int i = 0; i < n - 1; i++) {
            int x = in.nextInt();
            int y = in.nextInt();
            vs[x].adj.add(vs[y]);
            vs[y].adj.add(vs[x]);
        }
        Set<Vertex> visited = new HashSet<>();
        dfs(vs[1], visited);
        out.println((vs[1].black + vs[1].white) % mod);
        out.close();
    }

    private static void dfs(Vertex v, Set<Vertex> visited) {
        visited.add(v);
        for (Vertex n : v.adj) {
            if (!visited.contains(n)) {
                dfs(n, visited);
                v.black = (v.black * n.white) % mod;
                v.white = (v.white * (n.white + n.black) % mod) % mod;
            }
        }
    }

    static class Vertex {
        int i;
        long black = 1;
        long white = 1;

        public Vertex(int i) {
            this.i = i;
        }

        List<Vertex> adj = new ArrayList<>();

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Vertex vertex = (Vertex) o;
            return i == vertex.i;
        }

        @Override
        public int hashCode() {
            return Objects.hash(i);
        }
    }


    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

    }
}