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: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

var g [][]bool
var n, m int

func main() {
	sc.Split(bufio.ScanWords)
	n, m = nextInt(), nextInt()
	g = make([][]bool, n)
	for i := 0; i < n; i++ {
		g[i] = make([]bool, n)
	}
	for i := 0; i < m; i++ {
		a, b := nextInt()-1, nextInt()-1
		g[a][b] = true
		g[b][a] = true
	}

	visted := make([]bool, n)
	visted[0] = true
	fmt.Println(dfs(0, visted))
}

func dfs(v int, visted []bool) int {
	can := true
	for i := 0; i < n; i++ {
		if !visted[i] {
			can = false
		}
	}

	if can {
		return 1
	}

	ret := 0

	for i := 0; i < n; i++ {
		if !g[v][i] {
			continue
		}

		if visted[i] {
			continue
		}

		visted[i] = true
		ret += dfs(i, visted)
		visted[i] = false
	}

	return ret
}