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++14 (GCC 5.4.1) (judge verdict: Accepted)

//{{{
#include <bits/stdc++.h>
using namespace std;

#define putchar(x) cout << (x)
#define repeat(x) int _ = 0; _ < (x); ++_

template<typename T> constexpr auto range(T start, T stop, T step) {
    struct iterator {
        T i, step;
        bool operator!=(const iterator& other) const { return i != other.i; }
        auto& operator++() { i += step; return *this; }
        auto& operator*() { return i; }
    };
    struct iterable_wrapper {
        T start, stop, step;
        auto begin() const { return iterator{ start, step }; }
        auto end() const { return iterator{ stop, step }; }
        size_t size() const { return (stop - start) / step; }

        iterable_wrapper(T start_, T stop_, T step_): start(start_), stop(stop_), step(step_) {
            stop = step > 0 ? max(start, stop) : min(start, stop);
            stop += (step - (stop - start) % step) % step;
        }
    };
    return iterable_wrapper(start, stop, step);
};
template<typename T> constexpr auto range(T start, T stop) { return range(start, stop, T(1)); }
template<typename T> constexpr auto range(T stop) { return range(T(0), stop, T(1)); }

template<typename T, typename Iter = decltype(begin(declval<T>()))>
constexpr auto printer(T&& iterable) {
    struct iterator {
        Iter iter, ed;
        auto operator!=(const iterator& other) const {
            auto ret = (iter != other.iter);
            if(not ret) cout << '\n';
            return ret;
        }
        auto& operator++() { ++iter; if(iter != ed) cout << ' '; return *this; }
        auto& operator*() { return *iter; }
    };
    struct iterable_wrapper {
        T iterable;
        auto begin() const { return iterator{ std::begin(iterable), std::end(iterable) }; }
        auto end() const { return iterator{ std::end(iterable), std::end(iterable) }; }
    };
    return iterable_wrapper{ forward<T>(iterable) };
};

template<size_t ...Is, typename T> auto getis(const T& t) { return tie(get<Is>(t)...); }
template<class T> void setmax(T& a, const T& b) { a = max(a, b); }
template<class T> void setmin(T& a, const T& b) { a = min(a, b); }

template<typename T> struct is_const_char_arr_ref : false_type {};
template<size_t N> struct is_const_char_arr_ref<char const (&)[N]> : true_type {};
template<typename T, typename = void> struct is_container : false_type {};
template<typename T>
struct is_container<T, conditional_t<false, decltype(begin(declval<T>())), void>> : true_type {};
template<class T> using IsC = typename enable_if<is_container<T>::value and
    not is_same<T, string>::value>::type;
template<class T> using NotC = typename enable_if<not is_container<T>::value or
    is_same<T, string>::value>::type;
template<class T> inline IsC<T> print_1(const T& v);
template<class T> inline NotC<T> print_1(const T& x) { cout << x; }
template<size_t N> void print_1(const array<char, N>& x) { cout << &x[0]; };
inline void print_1(const tuple<>&) { cout << "()"; };
template<size_t L, size_t I, class T> void print_tuple(const T& t) {
    if(I != 0) cout << ", "; print_1(get<I>(t));
    if(I + 1 < L) print_tuple<L, (I + 1) % L>(t);
}
template<class ...T> inline void print_1(const tuple<T...>& x) {
    cout << "("; print_tuple<sizeof...(T), 0, tuple<T...>>(x); cout << ")";
}
inline void print_n() {}
template<class T, class ...U> inline void print_n(const T& head, const U&... tail);
template<class T, class U> inline void print_1(const pair<T, U>& p) {
    cout << "("; print_1(p.first); cout << ", "; print_1(p.second); cout << ")";
}
template<class T, class ...U> inline void print_n(const T& head, const U&... tail) {
    print_1(head); if(sizeof...(tail)) cout << " "; print_n(tail...);
}
template<class T> inline IsC<T> print_1(const T& v) {
    cout << "[";
    for(auto it = v.begin(); it != v.end(); ++it) { if(it != v.begin()) cout << ", "; print_1(*it); }
    cout << "]";
}
template<class ...T> inline void print(const T& ...args) { print_n(args...); putchar('\n'); }
inline void read() {}
template<class T, class ...U> inline void read(T& head, U&... tail) { cin >> head; read(tail...); }

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
static int fastio = [](){ ios_base::sync_with_stdio(false); cin.tie(0); cout.precision(17); return 0; }();

template<class T> void print_dbg(const string& s, T&& x) {
    if(is_const_char_arr_ref<T>::value) { print_n(x); } else { print_n(s, "=", x); }
}
#define SELECT(_1, _2, _3, _4, _5, _6, _7, _8, NAME,...) NAME
#define dbg1(a) print_dbg(#a, a); cout << endl;
#define dbg2(a, b) print_dbg(#a, a); cout << ", "; dbg1(b);
#define dbg3(a, b, c) print_dbg(#a, a); cout << ", "; dbg2(b, c);
#define dbg4(a, b, c, d) print_dbg(#a, a); cout << ", "; dbg3(b, c, d);
#define dbg5(a, b, c, d, e) print_dbg(#a, a); cout << ", "; dbg4(b, c, d, e);
#define dbg6(a, b, c, d, e, f) print_dbg(#a, a); cout << ", "; dbg5(b, c, d, e, f);
#define dbg7(a, b, c, d, e, f, g) print_dbg(#a, a); cout << ", "; dbg6(b, c, d, e, f, g);
#define dbg8(a, b, c, d, e, f, g, h) print_dbg(#a, a); cout << ", "; dbg7(b, c, d, e, f, g, h);
#define debug(...) SELECT(__VA_ARGS__, dbg8, dbg7, dbg6, dbg5, dbg4, dbg3, dbg2, dbg1)(__VA_ARGS__)
//}}}
using PII = pair<int, int>;
using LL = long long;

const int MOD = 1e9 + 7;
const int INF = 0x3f3f3f3f;
const LL LLINF = 0x3f3f3f3f3f3f3f3f;
const int MAX_N = 25;

struct Solution {
    vector<vector<int>> G;
    pair<LL, LL> dfs(int v, int p) {
        LL b = 1, w = 1, bu, wu;
        for(int u : G[v]) {
            if(u == p) continue;
            tie(bu, wu) = dfs(u, v);
            b = b * wu % MOD;
            w = w * (wu + bu) % MOD;
        }
        //debug(v, b, w);
        return {b, w};
    }

    Solution(int) {
        int N;
        read(N);
        G.resize(N + 1);
        for(repeat(N - 1)) {
            int u, v;
            read(u, v);
            G[u].push_back(v);
            G[v].push_back(u);
        }
        auto res = dfs(1, 0);
        print((res.first + res.second) % MOD);
    }
};

int main() {
    int T = 1;
    //cin >> T;
    for(int i = 1; i <= T; ++i) {
        ignore = Solution(i);
    }
    return 0;
}