Problem:
Score : 300 points

Problem Statement

You are given an undirected unweighted graph with N vertices and M edges that contains neither self-loops nor double edges.

Here, a self-loop is an edge where a_i = b_i (1≤i≤M), and double edges are two edges where (a_i,b_i)=(a_j,b_j) or (a_i,b_i)=(b_j,a_j) (1≤i<j≤M).

How many different paths start from vertex 1 and visit all the vertices exactly once?

Here, the endpoints of a path are considered visited.

For example, let us assume that the following undirected graph shown in Figure 1 is given.

Figure 1: an example of an undirected graph

The following path shown in Figure 2 satisfies the condition.

Figure 2: an example of a path that satisfies the condition

However, the following path shown in Figure 3 does not satisfy the condition, because it does not visit all the vertices.

Figure 3: an example of a path that does not satisfy the condition

Neither the following path shown in Figure 4, because it does not start from vertex 1.

Figure 4: another example of a path that does not satisfy the condition

Constraints

2≦N≦8

0≦M≦N(N-1)/2

1≦a_i<b_i≦N

The given graph contains neither self-loops nor double edges.

Input

The input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print the number of the different paths that start from vertex 1 and visit all the vertices exactly once.

Sample Input 1

3 3
1 2
1 3
2 3

Sample Output 1

2

The given graph is shown in the following figure:

The following two paths satisfy the condition:

Sample Input 2

7 7
1 3
2 7
3 4
4 5
4 6
5 6
6 7

Sample Output 2

1

This test case is the same as the one described in the problem statement.

Solution in Go (1.6) (judge verdict: Wrong Answer)

package main

import "fmt"

var e [][]int
var n, m int

func printEdge(e [][]int) {
	for i := 1; i < n+1; i++ {
		fmt.Printf("%d: ", i)
		for _, v := range e[i] {
			fmt.Printf("%d ", v)
		}
		fmt.Println()
	}
}

func dfs(v int, visited []bool, count int) (bool, int) {
	if visited[v] {
		return false, 0
	}
	// visited[v] = true
	// fmt.Println(v, visited, num, count)

	comp := true
	for i := 0; i < n; i++ {
		if !visited[i] {
			comp = false
			break
		}
	}

	if comp {
		return true, 0
	}

	for _, ne := range e[v] {
		// fmt.Printf("ne=%d\n", ne)
		visited[v] = true
		if cmp, _ := dfs(ne, visited, count); cmp {
			count++
		}
		visited[v] = false
	}
	return true, count
}

func main() {
	fmt.Scan(&n, &m)

	e = make([][]int, n+1)
	for i := 1; i < n+1; i++ {
		e[i] = make([]int, 0)
	}
	for i := 0; i < m; i++ {
		var a, b int
		fmt.Scan(&a, &b)
		e[a] = append(e[a], b)
		e[b] = append(e[b], a)
	}
	// printEdge(e)

	visited := make([]bool, n+1)
	_, count := dfs(1, visited, 0)
	fmt.Println(count)
}