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 (1.14.1) (judge verdict: Accepted)

package main

import (
	"fmt"
)

var graph = make([][]bool, 8)

func dfs(v, N int, visited []bool) int {
	allVisited := true

	for i := 0; i < N; i++ {
		if visited[i] == false {
			allVisited = false
		}
	}

	if allVisited {
		return 1
	}

	var num int

	for i := 0; i < N; i++ {
		if graph[v][i] == false {
			continue
		}
		if visited[i] {
			continue
		}

		visited[i] = true
		num += dfs(i, N, visited)
		visited[i] = false
	}

	return num
}

func main() {
	var (
		N, M, A, B int
	)
	fmt.Scan(&N, &M)
	for i := 0; i < 8; i++ {
		graph[i] = make([]bool, 8)
	}
	for i := 0; i < M; i++ {
		fmt.Scan(&A, &B)
		graph[A-1][B-1], graph[B-1][A-1] = true, true
	}
	visited := make([]bool, 8)
	visited[0] = true

	fmt.Println(dfs(0, N, visited))
}