A Simple Task

题意翻译

求简单无向图的环数

题目描述

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

输入输出格式

输入格式


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.

输出格式


Output the number of cycles in the given graph.

输入输出样例

输入样例 #1

4 6
1 2
1 3
1 4
2 3
2 4
3 4

输出样例 #1

7

说明

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