Problem:
Score : 1400 points

Problem Statement

There is a tree with N vertices numbered 1 through N.
The i-th of the N-1 edges connects vertices a_i and b_i.

Initially, each edge is painted blue.
Takahashi will convert this blue tree into a red tree, by performing the following operation N-1 times:

Select a simple path that consists of only blue edges, and remove one of those edges.

Then, span a new red edge between the two endpoints of the selected path.

His objective is to obtain a tree that has a red edge connecting vertices c_i and d_i, for each i.

Determine whether this is achievable.

Constraints

2 ≤ N ≤ 10^5

1 ≤ a_i,b_i,c_i,d_i ≤ N

a_i ≠ b_i

c_i ≠ d_i

Both input graphs are trees.

Input

Input is given from Standard Input in the following format:

N
a_1 b_1
:
a_{N-1} b_{N-1}
c_1 d_1
:
c_{N-1} d_{N-1}

Output

Print YES if the objective is achievable; print NO otherwise.

Sample Input 1

3
1 2
2 3
1 3
3 2

Sample Output 1

YES

The objective is achievable, as below:

First, select the path connecting vertices 1 and 3, and remove a blue edge 1-2. Then, span a new red edge 1-3.

Next, select the path connecting vertices 2 and 3, and remove a blue edge 2-3. Then, span a new red edge 2-3.

Sample Input 2

5
1 2
2 3
3 4
4 5
3 4
2 4
1 4
1 5

Sample Output 2

YES

Sample Input 3

6
1 2
3 5
4 6
1 6
5 1
5 3
1 4
2 6
4 3
5 6

Sample Output 3

NO

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")

#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>

using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
 
typedef long long ll;
typedef long double ld;
typedef complex<ld> cd;

typedef pair<int, int> pi;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pd;

typedef vector<int> vi;
typedef vector<ld> vd;
typedef vector<ll> vl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;

template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;

#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define F0R(i, a) for (int i = 0; i < (a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= (a); i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)
#define trav(a, x) for (auto& a : x)

#define mp make_pair
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound

#define sz(x) (int)x.size()
#define beg(x) x.begin()
#define en(x) x.end()
#define all(x) beg(x), en(x)
#define resz resize

const int MOD = 1000000007;
const ll INF = 1e18;
const int MX = 100001;
const ld PI = 4*atan((ld)1);

template<class T> void ckmin(T &a, T b) { a = min(a, b); }
template<class T> void ckmax(T &a, T b) { a = max(a, b); }

namespace io {
    // TYPE ID (StackOverflow)
    
    template<class T> struct like_array : is_array<T>{};
    template<class T, size_t N> struct like_array<array<T,N>> : true_type{};
    template<class T> struct like_array<vector<T>> : true_type{};
    template<class T> bool is_like_array(const T& a) { return like_array<T>::value; }

    // I/O 
    
    void setIn(string s) { freopen(s.c_str(),"r",stdin); }
    void setOut(string s) { freopen(s.c_str(),"w",stdout); }
    void setIO(string s = "") {
        ios_base::sync_with_stdio(0); cin.tie(0);
        if (sz(s)) { setIn(s+".in"), setOut(s+".out"); }
    }
    
    // INPUT 
    
    template<class T> void re(T& x) { cin >> x; }
    template<class Arg, class... Args> void re(Arg& first, Args&... rest);
    void re(double& x) { string t; re(t); x = stod(t); }
    void re(ld& x) { string t; re(t); x = stold(t); }
    
    template<class T> void re(complex<T>& x);
    template<class T1, class T2> void re(pair<T1,T2>& p);
    template<class T> void re(vector<T>& a);
    template<class T, size_t SZ> void re(array<T,SZ>& a);
    
    template<class Arg, class... Args> void re(Arg& first, Args&... rest) { re(first); re(rest...); }
    template<class T> void re(complex<T>& x) { T a,b; re(a,b); x = cd(a,b); }
    template<class T1, class T2> void re(pair<T1,T2>& p) { re(p.f,p.s); }
    template<class T> void re(vector<T>& a) { F0R(i,sz(a)) re(a[i]); }
    template<class T, size_t SZ> void re(array<T,SZ>& a) { F0R(i,SZ) re(a[i]); }
    
    // OUTPUT 
    
    template<class T1, class T2> ostream& operator<<(ostream& os, const pair<T1,T2>& a) {
        os << '{' << a.f << ", " << a.s << '}'; return os;
    }
    template<class T> ostream& printArray(ostream& os, const T& a, int SZ) {
        os << '{';
        F0R(i,SZ) {
            if (i) {
                os << ", ";
                if (is_like_array(a[i])) cout << "\n";
            }
            os << a[i];
        }
        os << '}';
        return os;
    }
    template<class T, size_t SZ> ostream& operator<<(ostream& os, const array<T,SZ>& a) {
        return printArray(os,a,SZ);
    }
    template<class T> ostream& operator<<(ostream& os, const vector<T>& a) {
        return printArray(os,a,sz(a));
    }
    template<class T> ostream& operator<<(ostream& os, const set<T>& a) {
        os << vector<T>(all(a)); return os;
    }
    template<class T1, class T2> ostream& operator<<(ostream& os, const map<T1,T2>& a) {
        os << vector<pair<T1,T2>>(all(a)); return os;
    }
    
    template<class T> void pr(const T& x) { cout << x << '\n'; }
    template<class Arg, class... Args> void pr(const Arg& first, const Args&... rest) { 
        cout << first << ' '; pr(rest...); 
    }
}

using namespace io;

int N; // while two equivalent edges
multiset<int> adj[MX];
set<pi> posi;

void ins(pi x) {
    if (x.f > x.s) swap(x.f,x.s);
    if (adj[x.f].count(x.s)) posi.insert(x);
    adj[x.f].insert(x.s), adj[x.s].insert(x.f);
}

void del(pi x) {
    if (x.f > x.s) swap(x.f,x.s);
    if (posi.count(x)) posi.erase(x);
    adj[x.f].erase(adj[x.f].find(x.s)), adj[x.s].erase(adj[x.s].find(x.f));
}

int main() {
    // you should actually read the stuff at the bottom
    setIO(); re(N); 
    F0R(i,2*(N-1)) {
        int a, b; re(a,b);
        ins({a,b});
    }
    // pr(sz(posi)); exit(0);
    F0R(i,N-1) {
        if (!sz(posi)) {
            pr("NO");
            exit(0);
        }
        auto a = *posi.begin(); del(a); del(a);
        if (sz(adj[a.f]) < sz(adj[a.s])) swap(a.f,a.s);
        auto b = vi(all(adj[a.s]));
        trav(x,b) {
            del({a.s,x});
            ins({a.f,x});
        }
    }
    pr("YES");
    // you should actually read the stuff at the bottom
}

/* stuff you should look for
    * int overflow, array bounds
    * special cases (n=1?), set tle
    * do smth instead of nothing and stay organized
*/