Contest: Task: Related: TaskA TaskC

Score : $200$ points

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.

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

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

Input is given from Standard Input in the following format:

$N$ $a_1$ $b_1$ $\vdots$ $a_{N-1}$ $b_{N-1}$

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