CF906C.Party

Arseny likes to organize parties and invite people to it. However, not only friends come to his parties, but friends of his friends, friends of friends of his friends and so on. That's why some of Arseny's guests can be unknown to him. He decided to fix this issue using the following procedure.

At each step he selects one of his guests A, who pairwise introduces all of his friends to each other. After this action any two friends of A become friends. This process is run until all pairs of guests are friends.

Arseny doesn't want to spend much time doing it, so he wants to finish this process using the minimum number of steps. Help Arseny to do it.

阿尔谢尼喜欢举办派对并邀请朋友们参加。然而，来到他派对的不仅有他的朋友，还有他朋友的朋友、他朋友的朋友的朋友，等等。因此，阿尔谢尼的一些客人可能彼此并不相识。他决定通过以下过程来解决这一问题。

在每一步中，他从自己的客人中选出一人 $A$，令 $A$ 将其所有朋友两两相互介绍。经过此操作后，$A$ 的任意两位朋友之间都会成为朋友。该过程持续进行，直至所有客人两两之间均为朋友为止。

阿尔谢尼不希望在此过程中花费过多时间，因此他希望以最少的步数完成这一过程。请帮助阿尔谢尼实现这一目标。

The first line contains two integers n and m (1 ≤ n ≤ 22; ) — the number of guests at the party (including Arseny) and the number of pairs of people which are friends.

Each of the next m lines contains two integers u and v (1 ≤ u, v ≤ n; u ≠ v), which means that people with numbers u and v are friends initially. It's guaranteed that each pair of friends is described not more than once and the graph of friendship is connected.

第一行包含两个整数 $n$ 和 $m$（$1 \leq n \leq 22$；），分别表示聚会上的宾客人数（包括阿尔谢尼）以及初始时互为朋友的人对数量。

接下来的 $m$ 行中，每行包含两个整数 $u$ 和 $v$（$1 \leq u, v \leq n$；$u \neq v$），表示编号为 $u$ 和 $v$ 的两人初始时是朋友。保证每对朋友至多被描述一次，且朋友关系图是连通的。

In the first line print the minimum number of steps required to make all pairs of guests friends.

In the second line print the ids of guests, who are selected at each step.

If there are multiple solutions, you can output any of them.

第一行输出使所有宾客对成为朋友所需的最少步数。

第二行输出每一步所选择的宾客编号。

若存在多种解法，输出任意一种即可。

In the first test case there is no guest who is friend of all other guests, so at least two steps are required to perform the task. After second guest pairwise introduces all his friends, only pairs of guests (4, 1) and (4, 2) are not friends. Guest 3 or 5 can introduce them.

In the second test case guest number 1 is a friend of all guests, so he can pairwise introduce all guests in one step.

在第一个测试用例中，不存在一位宾客是其余所有宾客的朋友，因此至少需要两步才能完成任务。在第二位宾客将其所有朋友两两介绍之后，仅有宾客对 (4, 1) 和 (4, 2) 尚未成为朋友。宾客 3 或 5 可以将他们互相介绍。

在第二个测试用例中，宾客 1 是所有宾客的朋友，因此他可以在一步之内将所有宾客两两介绍。