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 (
	"fmt"
)

var pathNum = 0
var visited []int
var VISIT = 1
var UNVISITED = 0

func isAllVisited() bool {
	for _, v := range visited {
		if v == UNVISITED {
			return false
		}
	}

	return true
}

func dfs(v int, graph [][]int) {
	if isAllVisited() {
		pathNum++
		return
	}

	for i, adjecent := range graph[v] {
		if adjecent == 1 && visited[i] == UNVISITED {
			visited[i] = VISIT
			dfs(i, graph)
			visited[i] = UNVISITED
		}
	}
}

func main() {
	var N, M int
	fmt.Scanf("%d %d", &N, &M)

	graph := make([][]int, N)
	visited = make([]int, N)
	for i := 0; i < N; i++ {
		graph[i] = make([]int, N)
	}

	var s, t int
	for i := 0; i < M; i++ {
		fmt.Scanf("%d %d", &s, &t)
		graph[s-1][t-1] = 1
		graph[t-1][s-1] = 1
	}

	visited[0] = VISIT
	dfs(0, graph)
	fmt.Println(pathNum)
}