A8885 | Greedy Petya

Petya is an unexperienced programming contestant. Recently he has come across the following problem:

You are given a non-directed graph which consists of $n$ nodes and $m$ edges. Your task is to determine whether the graph contains a Hamiltonian path.

Petya wrote a quick bug-free code which he believes solves this problem. After that Petya decided to give this problem for April Fools Day contest. Unfortunately, Petya might have made a mistake, and it's quite possible that his algorithm is wrong. But this isn't a good excuse to leave the contest without submitting this problem, is it?

The first line contains two integers $n,m$ $(1<=n<=20; 0<=m<=400)$ . Next $m$ lines contain pairs of integers $v_{i},u_{i}$ $(1<=v_{i},u_{i}<=n)$ .

Follow the format of Petya's code output.