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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Collections;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Random;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main {
	static long mod;
	
	
	
	public static void main(String[] args) throws IOException {
		
		Reader.init(System.in);
		PrintWriter out=new PrintWriter(System.out);
		StringBuffer output=new StringBuffer("");
		int n=Reader.nextInt();
		ArrayList<Integer>[] revgph=new ArrayList[n+1];
		for(int i=1;i<=n;i++) revgph[i]=new ArrayList<Integer>();
		int[] deg=new int[n+1];
		long[][] dp=new long[n+1][2];
		int[] visited=new int[n+1];
		mod=(long)1e9+7;
		for(int i=1;i<n;i++) {
			int a=Reader.nextInt();int b=Reader.nextInt();
			revgph[a].add(b);revgph[b].add(a);deg[a]++;deg[b]++;
		}
		Queue<Integer> q=new LinkedList<Integer>();
		int last=0;
		for(int i=1;i<=n;i++) {
			if(deg[i]==1) {q.add(i);deg[i]--;}
			visited[i]=1;
		}
	while(q.size()!=0) {
			int a=q.poll();
			dp[a][0]=1;
			dp[a][1]=1;
			deg[a]--;
			last=a;
			for(int i:revgph[a]) {
				if(deg[i]>=1) {
					deg[i]--;
					if(deg[i]==1) {q.add(i);}
				}
				else {
					dp[a][0]*=(dp[i][0]+dp[i][1])%mod;;
					dp[a][1]*=dp[i][0];
					dp[a][0]%=mod;
					dp[a][1]%=mod;
				}
			}
		}
		long ans=dp[last][0]+dp[last][1];
		ans%=mod;
		if(n==1) ans=2;
		if(n==2) ans=3;
		out.println(ans);
		out.flush();
	}
}



class NoD{
	int a,b;
	String s;
	double c,d;
	NoD(int aa,int bb){
		a=aa;b=bb;
		s=a+" "+b;
		
	}
	NoD(double cc, double dd){
		c=cc;d=dd;
	}
//	NoD(int aa,int bb,int cc){
//		a=aa;b=bb;c=cc;
//	}
//	NoD(long m,long l,long r,long t){
//		ms=m;ls=l;rs=r;ts=t;
//	}
	@Override
	public boolean equals(Object o) {
		if(o!=null && o.getClass()==getClass()) {
			NoD c= (NoD) o;
			return c.a==a && c.b==b;
		}
		return false;
	}
	@Override
	public int hashCode() {
		return s.hashCode();
	}
}
class DisJoint {
	int[] arr;
	int[] parent;
	int[] rank;
	DisJoint(int n){
		arr=new int[n+1];
		parent=new int[n+1];
		rank=new int[n+1];
		for(int i=1;i<=n;i++) {
			arr[i]=i;
			parent[i]=i;
			rank[i]=0;
		}
	}

	int find(int value) {
		int par=parent[value];
		if(par==value)
			return par;
		parent[value]=find(par);
		return parent[value];
	}
	
	void union(int data1,int data2) {
		int parent1=find(data1);
		int parent2=find(data2);
		if(parent1!=parent2) {
			if(rank[parent1]>=rank[parent2]) {
				parent[parent2]=parent1;
				if(rank[parent1]==rank[parent2])
					rank[parent1]++;
			}
			else {
				parent[parent1]=parent2;
			}
		}
		
	}
	

}

class Seg{
	long[] st;
	long[] arr;
	long[] lazy;
	Seg(int n){
		st=new long[4*n];
		//lazy=new long[4*n];
		
	}
	void build(int index,int low,int high) {
		if(low==high) {
			st[index]=arr[low];
		}
		else {
			int middle=(low+high)/2;
			build(2*index+1,low,middle);
			build(2*index+2,middle+1,high);
			st[index]=Math.min(st[2*index+1], st[2*index+2]);
		}
	}
	
	long query(int index,int low,int high, int ql,int qh) {
//		if(lazy[index]!=0) {
//			st[index]+=lazy[index];
//			if(low<high) {
//				lazy[2*index+1]+=lazy[index];
//				lazy[2*index+2]+=lazy[index];
//				
//			}
//			lazy[index]=0;
//		}
		
		if(ql<=low && high<=qh) {
			return st[index];
		}
		else if(!(ql>high || qh<low)) {
			int middle=(low+high)/2;
			long left=query(2*index+1,low,middle,ql,qh);
			long right=query(2*index+2,middle+1,high,ql,qh);
			//st[index]=st[2*index+1]+ st[2*index+2];
			return left+right;
			
		}
		return 0;
	}
	
	
	void u1(int index, int low,int high, int pos) {
//		if(lazy[index]!=0) {
//			st[index]+=lazy[index];
//			if(low<high) {
//				lazy[2*index+1]+=lazy[index];
//				lazy[2*index+2]+=lazy[index];
//				
//			}
//			lazy[index]=0;
//		}
		if(low==high) {
			st[index]++;
		}
		else {
			int middle=(low+high)/2;
			if(pos<=middle) u1(2*index+1,low,middle,pos);
			else u1(2*index+2,middle+1,high,pos);
			st[index]=st[2*index+1]+ st[2*index+2];
		}
	}
	
	
}
class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;
    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }
    /** get next word */
    static String nextLine() throws IOException{
    	return reader.readLine();
    }
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }
    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}