CF11D.A Simple Task

Given a simple graph, output the number of simple cycles in it. A simple cycle is a cycle with no repeated vertices or edges.

给定一个简单图，输出其中简单环的数量。简单环是指不包含重复顶点或重复边的环。

The first line of input contains two integers n and m (1 ≤ n ≤ 19, 0 ≤ m) – respectively the number of vertices and edges of the graph. Each of the subsequent m lines contains two integers a and b, (1 ≤ a, b ≤ n, a ≠ b) indicating that vertices a and b are connected by an undirected edge. There is no more than one edge connecting any pair of vertices.

输入的第一行包含两个整数 $n$ 和 $m$（$1 ≤ n ≤ 19$，$0 ≤ m$），分别表示图的顶点数和边数。接下来的 $m$ 行中，每行包含两个整数 $a$ 和 $b$（$1 ≤ a,\,b ≤ n$，$a ≠ b$），表示顶点 $a$ 和 $b$ 之间存在一条无向边。任意一对顶点之间至多只有一条边。

Output the number of cycles in the given graph.

输出给定图中环的数量。

The example graph is a clique and contains four cycles of length 3 and three cycles of length 4.

示例图是一个团，包含四个长度为 3 的环和三个长度为 4 的环。