Blue and Red Tree

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

inputFormat

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}

outputFormat

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

样例

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

YES