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 (
	"bufio"
	"fmt"
	"os"
)

func main() {
	N, M := ReadInt(), ReadInt()
	graph := make([][]bool, N)
	for i := 0; i < N; i++ {
		graph[i] = make([]bool, N)
	}
	for i := 0; i < M; i++ {
		a, b := ReadInt()-1, ReadInt()-1
		graph[a][b] = true
		graph[b][a] = true
	}

	order := make([]int, N-1)
	for i := 0; i < N-1; i++ {
		order[i] = i + 1
	}

	ans := 0
	for {
		ok := true
		origin := 0
		for _, dest := range order {
			if !graph[origin][dest] {
				ok = false
				break
			}
			origin = dest
		}
		if ok {
			ans++
		}
		if !NextPermutation(order) {
			break
		}
	}
	fmt.Println(ans)
}

func NextPermutation(xs []int) bool {
	k := len(xs) - 2
	for ; k >= 0 && xs[k] >= xs[k+1]; k-- {
	}
	if k < 0 {
		return false
	}
	l := len(xs) - 1
	for ; xs[k] > xs[l]; l-- {
	}
	xs[k], xs[l] = xs[l], xs[k]
	for l, r := k+1, len(xs)-1; l < r; {
		xs[l], xs[r] = xs[r], xs[l]
		l++
		r--
	}
	return true
}

var reader = bufio.NewReader(os.Stdin)

func Scan(a ...interface{}) {
	if _, err := fmt.Fscan(reader, a...); err != nil {
		panic(err)
	}
}
func ReadInt() (i int) { Scan(&i); return }