B - Star or Not

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.

5
1 4
2 4
3 4
4 5

Yes

The given graph is a star.

4
2 4
1 4
2 3

No

The given graph is not a star.

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

Yes