Problem Statement

You are given a tree with N vertices and N-1 edges.
The vertices are numbered $1,2,\ldots,N$. The i-th edge connects Vertex a_i and Vertex b_i.
Determine whether this tree is a star.
Here, a star is a tree where there is a vertex directly connected to all other vertices.

Input

Input is given from Standard Input in the following format:
N
a_1 b_1
$\vdots$
a_{N-1} b_{N-1}

Output

If the given graph is a star, print Yes; otherwise, print No.

Constraints

• $3 \leq N \leq 10^5$
• $1 \leq a_i \lt b_i \leq N$
• The given graph is a tree.

Sample Input 1

5
1 4
2 4
3 4
4 5

Sample Output 1

Yes

The given graph is a star.

Sample Input 2

4
2 4
1 4
2 3

Sample Output 2

No

The given graph is not a star.

Sample Input 3

10
9 10
3 10
4 10
8 10
1 10
2 10
7 10
6 10
5 10

Sample Output 3

Yes

见题面 Input 部分

见题面 Output 部分