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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
// Macros for easier access
#define ll long long
#define endl '\n'
#define F first
#define S second
#define umap unordered_map
#define uset unordered_set
#define test ll cases; cin>>cases; for(ll testCase = 1; testCase <= cases; testCase++)
#define fill(name, val) memset(name, val, sizeof(name));
#define mop(a, op, b)    (a%mod op b%mod)%mod
#define precise fixed<<setprecision(50)
#define vll vector<ll>
#define vvll vector<vll>
#define pll pair<ll, ll>
#define get(a, n)    for(ll it = 0; it < n; it++)    cin>>a[it];
#define boost ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#define debug(x) cerr << #x << " : " << (x) << endl
// Constants
#define MX 100001
#define mod 1000000007LL
#define inf 1000000000000000000LL
void init(){
	boost;
	#ifndef ONLINE_JUDGE
		freopen("input.txt", "r", stdin);
		freopen("output.txt", "w", stdout);
	#endif
}

/*	Author: 🆉🅴🅽🅾🅻🆄🆂	*/

ll n, dp[MX][2];	vvll g;
ll calc(ll i, ll pi, bool allowed){
	if(dp[i][allowed] != -1)	return dp[i][allowed];
	ll w = 1, b = allowed;
	for(auto x : g[i]){
		if(x == pi)	continue;
		w = mop(w, *, calc(x, i, 1));
		if(allowed)	b = mop(b, *, calc(x, i, 0));
	}
	return dp[i][allowed] = mop(w, +, b);
}
int main(){
	init();	fill(dp, -1);
	cin>>n;	g.resize(n+1);
	ll x, y;
	for(ll i = 1; i < n; i++){
		cin>>x>>y;
		g[x].push_back(y);
		g[y].push_back(x);
	}
	cout<<calc(1, 0, 1);
}