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)

#ifndef __INTMOD_H__0001__
#define __INTMOD_H__0001__

#include <vector>
#include <iostream>
#include <cassert>
#include <iostream>

/* Modulus must be less than 0x80000000, and must not be 0. */
template <uint32_t Modulus>
class IntMod {
	typedef int Int;
	typedef unsigned int UInt;
	typedef long long Long;
	typedef unsigned long long ULong;

public:
	template <uint32_t Modulus_>
	friend bool operator==(const IntMod<Modulus_>& left, const IntMod<Modulus_>& right);
	template <uint32_t Modulus_>
	friend bool operator!=(const IntMod<Modulus_>& left, const IntMod<Modulus_>& right);
	template <uint32_t Modulus_>
	friend bool operator<(const IntMod<Modulus_>& left, const IntMod<Modulus_>& right);
	template <uint32_t Modulus_>
	friend bool operator<=(const IntMod<Modulus_>& left, const IntMod<Modulus_>& right);
	template <uint32_t Modulus_>
	friend bool operator>(const IntMod<Modulus_>& left, const IntMod<Modulus_>& right);
	template <uint32_t Modulus_>
	friend bool operator>=(const IntMod<Modulus_>& left, const IntMod<Modulus_>& right);

private:
	UInt value_m;

public:
	IntMod() { value_m = 0; }
	IntMod(UInt value) { value_m = value % Modulus; }
	IntMod(ULong value) { value_m = value % Modulus; }
	IntMod(Int value) {
		Int tmp = value % (Int)Modulus;
		value_m = tmp >= 0 ? tmp : Modulus - (unsigned int)(-tmp);
	}
	IntMod(Long value) {
		Int tmp = value % (Long)Modulus;
		value_m = tmp >= 0 ? tmp : Modulus - (unsigned int)(-tmp);
	}
	IntMod(const IntMod& other) : value_m(other.value_m) {}
	IntMod& operator=(const IntMod& other) { value_m = other.value_m; return *this; }
	
	const IntMod& operator+() const { return *this; }
	IntMod operator-() const { return IntMod(Modulus - value_m); }
	IntMod& operator++() {
		++value_m;
		if (value_m == Modulus) value_m = 0;
		return *this;
	}
	IntMod& operator--() {
		if (value_m == 0) value_m = Modulus;
		--value_m;
		return *this;
	}
	IntMod operator++(int dummy) {
		IntMod tmp(*this);
		++(*this);
		return tmp;
	}
	IntMod operator--(int dummy) {
		IntMod tmp(*this);
		--(*this);
		return tmp;
	}
	IntMod& operator+=(const IntMod& right) {
		value_m += right.value_m;		// value_m < 0x80000000
		if (value_m >= Modulus) value_m -= Modulus;
		return *this;
	}
	IntMod& operator-=(const IntMod& right) {
		if (value_m < right.value_m) value_m += Modulus;
		value_m -= right.value_m;
		return *this;
	}
	IntMod& operator*=(const IntMod& right) {
		value_m = ((ULong)value_m * right.value_m) % Modulus;
		return *this;
	}	
	IntMod& operator/=(const IntMod& right) {
		(*this) *= (right.Inverse());
		return *this;
	}
	// for power
	IntMod operator[](ULong exp) const {
		return Pow(exp);
	}

	/* Modulus must be a prime. */
	IntMod Inverse() const { return (*this).Pow(Modulus - 2); }
	IntMod Pow(ULong exp) const {
		IntMod product = 1;
		IntMod factor(*this);
		while (exp > 0) {
			if (exp & 1) product *= factor;
			factor *= factor;
			exp >>= 1;
		}
		return product;
	}
	UInt Get_value() const {
		return value_m;
	}

	static IntMod Fact(UInt num) {
		static std::vector<IntMod> table(1, 1);
		if (table.size() > num) return table[num];

		int old_size = table.size();
		table.resize(num + 1);
		for (int i = old_size; i <= num; i++) {
			table[i] = table[i - 1] * i;
		}
		return table[num];
	}

	static IntMod Combi(UInt n, UInt r) {
		if (n < r) throw "okashii";
		return IntMod::Fact(n) / (IntMod::Fact(n - r) * IntMod::Fact(r));
	}

	static std::vector<IntMod> Inverse_list(int size) {
		assert(size < Modulus);
		std::vector<IntMod> ret_arr(size + 1);
		ret_arr[1] = 1;
		for (int i = 2; i <= size; ++i) {
			ret_arr[i] = ((ULong)(Modulus - Modulus / i) * ret_arr[Modulus % i].Get_value()) % Modulus;
		}
		return ret_arr;
	}
};

template <uint32_t Modulus>
IntMod<Modulus> operator+(const IntMod<Modulus>& left, const IntMod<Modulus>& right) {
	IntMod<Modulus> ret(left);
	ret += right;
	return ret;
}

template <uint32_t Modulus>
IntMod<Modulus> operator-(const IntMod<Modulus>& left, const IntMod<Modulus>& right) {
	IntMod<Modulus> ret(left);
	ret -= right;
	return ret;
}

template <uint32_t Modulus>
IntMod<Modulus> operator*(const IntMod<Modulus>& left, const IntMod<Modulus>& right) {
	IntMod<Modulus> ret(left);
	ret *= right;
	return ret;
}

template <uint32_t Modulus>
IntMod<Modulus> operator/(const IntMod<Modulus>& left, const IntMod<Modulus>& right) {
	IntMod<Modulus> ret(left);
	ret /= right;
	return ret;
}


template <uint32_t Modulus>
bool operator==(const IntMod<Modulus>& left, const IntMod<Modulus>& right) { return left.value_m == right.value_m; }
template <uint32_t Modulus>
bool operator!=(const IntMod<Modulus>& left, const IntMod<Modulus>& right) { return left.value_m != right.value_m; }
/* for set/map */
template <uint32_t Modulus>
bool operator<(const IntMod<Modulus>& left, const IntMod<Modulus>& right) { return left.value_m < right.value_m; }
template <uint32_t Modulus>
bool operator<=(const IntMod<Modulus>& left, const IntMod<Modulus>& right) { return left.value_m <= right.value_m; }
template <uint32_t Modulus>
bool operator>(const IntMod<Modulus>& left, const IntMod<Modulus>& right) { return left.value_m > right.value_m; }
template <uint32_t Modulus>
bool operator>=(const IntMod<Modulus>& left, const IntMod<Modulus>& right) { return left.value_m >= right.value_m; }

template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator+(const IntMod<Modulus>& left, Integer right) { return left + IntMod<Modulus>(right); }
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator+(Integer left, const IntMod<Modulus>& right) { return IntMod<Modulus>(left) + right; }
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator-(const IntMod<Modulus>& left, Integer right) { return left - IntMod<Modulus>(right); }
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator-(Integer left, const IntMod<Modulus>& right) { return IntMod<Modulus>(left) - right; }
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator*(const IntMod<Modulus>& left, Integer right) { return left * IntMod<Modulus>(right); }
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator*(Integer left, const IntMod<Modulus>& right) { return IntMod<Modulus>(left) * right; }
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator/(const IntMod<Modulus>& left, Integer right) { return left / IntMod<Modulus>(right); }
template <uint32_t Modulus, class Integer>
IntMod<Modulus> operator/(Integer left, const IntMod<Modulus>& right) { return IntMod<Modulus>(left) / right; }

template <uint32_t Modulus>
std::istream& operator<<(std::istream& ist, const IntMod<Modulus>& val) {
	uint64_t tmp;
	ist >> tmp;
	val = tmp;
	return ist;
}

template <uint32_t Modulus>
std::ostream& operator<<(std::ostream& ost, const IntMod<Modulus>& val) {
	ost << val.Get_value();
	return ost;
}

typedef IntMod<1000000007> MInt;

#if 1
MInt operator"" _m(unsigned long long num) { return MInt(num); }
#endif

#endif

#define _CRT_SECURE_NO_WARNINGS
#define _SCL_SECURE_NO_WARNINGS
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cassert>
#include <iostream>
#include <string>
#include <vector>
#include <list>
#include <utility>
#include <algorithm>
#include <functional>
#include <cmath>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <iomanip>
#include <sstream>
#include <bitset>
#include <limits>
#include <numeric>
#include <valarray>
#include <fstream>

using namespace std;
typedef unsigned int uint;
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<LL, LL> PP;
#define REP(i, a, n) for(LL i = (a), i##_max = (n); i < i##_max; ++i)
#define REM(i, a, n) for(LL i = (LL)(n) - 1, i##min = (a); i >= i##min; --i)
#define ALL(arr) (arr).begin(), (arr).end()
#define FLOAT fixed << setprecision(16)
#define SPEEDUP {cin.tie(NULL); ios::sync_with_stdio(false);}
const int INF = 0x3FFFFFFF;
const LL INFLL = 0x3FFFFFFF3FFFFFFF;
const double INFD = 1.0e+308;
const string INFSTR = "\x7f";
const double EPS = 1.0e-9;

void YesNo(bool b) { cout << (b ? "Yes" : "No") << endl; }
void YESNO(bool b) { cout << (b ? "YES" : "NO") << endl; }
template <class T, class U>
istream& operator>>(istream& ist, pair<T, U>& right) { return ist >> right.first >> right.second; }
template <class T, class U>
ostream& operator<<(ostream& ost, const pair<T, U>& right) { return ost << right.first << ' ' << right.second; }
template <class T, class TCompatible, size_t N>
void Fill(T(&dest)[N], const TCompatible& val) { fill(dest, dest + N, val); }
template <class T, class TCompatible, size_t M, size_t N>
void Fill(T(&dest)[M][N], const TCompatible& val) { for (int i = 0; i < M; ++i) Fill(dest[i], val); }
template<class T>
T Compare(T left, T right) { return left > right ? 1 : (left < right ? -1 : 0); }
istream& Ignore(istream& ist) { string s; ist >> s; return ist; }
bool Inside(int i, int j, int h, int w) { return i >= 0 && i < h && j >= 0 && j < w; }
template <class T>
T Next() { T buf; cin >> buf; return buf; }

#ifdef ONLY_MY_ENVIR
#include "IntMod.h"
#include "UnionFind.h"
#include "Graph.h"
#include "Range.h"
#include "Global.h"
#include "FlowSolver.h"
#include "Tree.h"
#include "SuffixArray.h"
#include "Geometry.h"
#include "Matrix.h"
#include "SegmentTree.h"
#include "SegmentTree2D.h"
#include "BIT.h"
#include "Rational.h"
#include "Position.h"
#include "Factorization.h"
#include "Math.h"
#endif

#ifdef __GNUC__
typedef __int128 LLL;
istream& operator>> (istream& ist, __int128& val) { LL tmp;  ist >> tmp; val = tmp; return ist; }
ostream& operator<< (ostream& ost, __int128 val) { LL tmp = val; ost << tmp; return ost; }
#endif

#if 1234567891
#include <array>
#include <random>
#include <unordered_set>
#include <unordered_map>
template<typename T>
using PriorityQ = priority_queue<T, vector<T>, greater<T> >;
// template <class T>
// auto Is(const T& value) { return [value](const auto& comparand) -> bool { return comparand == value; }; }
#endif

int N;
vector<int> G[100000];

bool used[100000];
pair<MInt, MInt> DP(int from, int prev) {
	if (used[from]) return make_pair(1, 0);
	used[from] = true;

	pair<MInt, MInt> ret(1, 1);
	for (int to : G[from]) {
		if (to == prev) continue;

		auto p = DP(to, from);
		ret.first *= p.first + p.second;
		ret.second *= p.first;
	}
	return ret;
}

int main() {
	cin >> N;
	REP(i, 1, N) {
		int a, b;
		cin >> a >> b;
		--a; --b;
		G[a].push_back(b);
		G[b].push_back(a);
	}

	MInt prod = 1;
	REP(i, 0, N) {
		auto a = DP(i, -1);
		prod *= a.first + a.second;
	}
	cout << prod << endl;
	return 0;
}