Problem Statement

You are given a tree with $N$ vertices and $N-1$ edges.
The vertices are numbered $1,2,\dots ,N$. The $i$-th edge connects Vertex a_iai and Vertex b_ibi.
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 10^53≤N≤105
• 1 \leq a_i \lt b_i \leq N1≤ai<bi≤N
• The given graph is a tree.

$N$a_1a1b_1b1$⋮$a_{N-1}aN−1b_{N-1}bN−1