题目描述
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
输入格式
见题面
输出格式
见题面
样例输入
5
1 2
2 3
3 4
4 5
3 4
2 4
1 4
1 5
样例输出
YES