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)

// Template
#include <bits/stdc++.h>
#define rep_override(x, y, z, name, ...) name
#define rep2(i, n) for (int i = 0; i < (int)(n); ++i)
#define rep3(i, l, r) for (int i = (int)(l); i < (int)(r); ++i)
#define rep(...) rep_override(__VA_ARGS__, rep3, rep2)(__VA_ARGS__)
#define per(i, n) for (int i = (int)(n) - 1; i >= 0; --i)
#define all(x) (x).begin(), (x).end()
using namespace std;
using ll = long long;
constexpr int inf = 1001001001;
constexpr ll INF = 3003003003003003003;
template <typename T> inline bool chmin(T& x, const T& y) {if (x > y) {x = y; return 1;} return 0;}
template <typename T> inline bool chmax(T& x, const T& y) {if (x < y) {x = y; return 1;} return 0;}
struct IOSET {IOSET() {cin.tie(0); ios::sync_with_stdio(0); cout << fixed << setprecision(10);}} ioset;

// Mod-Int
constexpr int MOD = 1000000007;
struct ModInt {
    ll val;
    ModInt() = default;
    ModInt(ll x) : val(x % MOD + (x < 0 ? MOD : 0)) {}
    ModInt &operator+= (const ModInt &x) {if ((val += x.val) >= MOD) val -= MOD; return *this;}
    ModInt &operator-= (const ModInt &x) {if ((val -= x.val) < 0) val += MOD; return *this;}
    ModInt &operator*= (const ModInt &x) {(val *= x.val) %= MOD; return *this;}
    ModInt operator+ (const ModInt &x) const {return ModInt(*this) += x;}
    ModInt operator- (const ModInt &x) const {return ModInt(*this) -= x;}
    ModInt operator* (const ModInt &x) const {return ModInt(*this) *= x;}
    ModInt pow(ll t) const {
        if (!t) return ModInt(1);
        ModInt m = pow(t / 2);
        m *= m;
        if (t & 1) m *= *this;
        return m;
    }
    ModInt inv() const {return pow(MOD - 2);}
    ModInt &operator/= (const ModInt &x) {return *this *= x.inv();}
    ModInt operator/ (const ModInt &x) const {return ModInt(*this) /= x;}
    friend istream &operator>> (istream &is, ModInt &x) {is >> x.val; return is;}
    friend ostream &operator<< (ostream &os, const ModInt &x) {os << x.val; return os;}
};

// Main
int main() {
    int n;
    cin >> n;
    vector<vector<int>> g(n);
    rep(i, n - 1) {
        int x, y;
        cin >> x >> y;
        --x; --y;
        g[x].push_back(y); g[y].push_back(x);
    }
    
    auto dfs = [&](auto f, int v, int p) -> pair<ModInt, ModInt> {
        pair<ModInt, ModInt> res(ModInt(1), ModInt(1));
        for (int u: g[v]) {
            if (u == p) continue;
            pair<ModInt, ModInt> x = f(f, u, v);
            res.first *= (x.first + x.second);
            res.second *= x.first;
        }
        return res;
    };
    pair<ModInt, ModInt> ans = dfs(dfs, 0, -1);
    cout << ans.first + ans.second << "\n";
}