CF290F.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?

佩佳是一名缺乏经验的编程竞赛选手。最近，他遇到了如下问题：

给定一个包含 $n$ 个节点和 $m$ 条边的无向图。你的任务是判断该图是否包含一条哈密顿路径（Hamiltonian path）。

佩佳迅速编写了一段自认为无 bug 的代码来解决这个问题。随后，佩佳决定将该题作为愚人节比赛的题目。不幸的是，佩佳可能犯了错误，他的算法很可能是不正确的。但难道这就能成为不提交该题而让比赛留空的理由吗？

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).

第一行包含两个整数 $n$ 和 $m$（$1 \leq n \leq 20$；$0 \leq m \leq 400$）。接下来的 $m$ 行每行包含一对整数 $v_i$、$u_i$（$1 \leq v_i, u_i \leq n$）。

Follow the format of Petya's code output.

遵循 Petya 代码输出的格式。