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 n int
var used [8][8]bool
var g [8][8]int

func dfs(start, depth int) int {
	if depth == n-1 {
		return 1
	}

	ans := 0
	// skip i = 0 as we don't want to go back to the start
	for i := 1; i < n; i++ {
		if g[start][i] != 1 || used[start][i] {
			continue
		}
		used[start][i] = true
		ans += dfs(i, depth+1)
	}
	return ans
}

func main() {
	var m int
	fmt.Scan(&n, &m)
	var a, b int
	for i := 0; i < m; i++ {
		fmt.Scan(&a, &b)
		g[a-1][b-1] = 1
		g[b-1][a-1] = 1
	}

	ans := dfs(1, 0)
	fmt.Println(ans)
}