Spider tree P98714

A spider mom plans to buy a tree (an undirected and connected graph with no cycles) for its progeny. The spider mom has $n$ kids, and wants a tree with $8n$ vertices that can be divided into $n$ subtrees with exactly eight vertices each (one subtree for each kid, with one vertex for each of its eight legs), only by removing $n - 1$ edges. Let us call such a tree a spider tree.

Given a tree with $8n$ vertices, is it a spider tree?

Input

Input consists of several cases, each with $n$ followed by $8n - 1$ pairs $x$ $y$ indicating an edge between $x$ and $y$. Assume $1 \le n \le 10^4$, that the given graph is indeed a tree, and that vertices are numbered starting from zero.

Output

For every tree, tell if it is a spider tree or not.