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Contest: Task: Related: TaskA TaskC

Score : $200$ points

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.

Notes

For the definition of a tree, see Tree (graph theory) - Wikipedia.

Constraints

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

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.

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