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Contest: Task: Related: TaskD TaskF

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