Problem: 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.

Examples

Input

3
1 2
2 3
1 3
3 2


Output

YES


Input

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


Output

YES


Input

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


Output

NO

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
map<pair<int,int>,int>mp;
multiset<int> des[100010];
pair<int,int> st[10000100];int top,js;
bool erz[100010];
int main()
{
	//freopen("in.txt","r",stdin);
	int n;scanf("%d",&n);
	for (int i=1;i<n;i++)
	{
		int u,v;scanf("%d%d",&u,&v);
		des[u].insert(v);des[v].insert(u);
		mp[make_pair(min(u,v),max(u,v))]++;
	}
	for (int i=1;i<n;i++)
	{
		int u,v;scanf("%d%d",&u,&v);
		des[u].insert(v);des[v].insert(u);
		mp[make_pair(min(u,v),max(u,v))]++;
	}
	for (map<pair<int,int>,int>::iterator it=mp.begin();it!=mp.end();it++) if (it->second>=2) st[++top]=it->first;
	//cerr<<top<<endl;
	while (top)
	{
		int u=st[top].first,v=st[top].second;top--;
		if ((erz[u])||(erz[v])) continue;js++;if (mp[make_pair(min(u,v),max(u,v))]>2) assert(0);
		des[u].erase(v);des[v].erase(u);
		if (des[u].size()<des[v].size()) swap(u,v);
		erz[v]=true;
		for (multiset<int>::iterator it=des[v].begin();it!=des[v].end();it++) if (!erz[*it])
		{
			if (u==*it) assert(0);
			des[u].insert(*it);des[*it].insert(u);
			mp[make_pair(min(u,*it),max(u,*it))]++;
			if (mp[make_pair(min(u,*it),max(u,*it))]>=2) st[++top]=make_pair(min(u,*it),max(u,*it));
		}
	}
	//for (map<pair<int,int>,int>::iterator it=mp.begin();it!=mp.end();it++)
	//if ((it->second>=2)&&(!erz[it->first.first])&&(!erz[it->first.second])) assert(0);
	
	//cerr<<js<<' '<<top<<endl;
	puts((js==n-1)?"YES":"NO");
}