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 ans = 0


func dfs(nodeID int, graph [][]int, visited []bool) {

  var _ans = true
  for i := 0; i < len(visited); i++ {
    if (!visited[i]) {
      _ans = false
    }
  }
  if (_ans) {
    ans++
  }

  for nextNodeID := 0; nextNodeID < len(graph[nodeID]); nextNodeID++ {

    if graph[nodeID][nextNodeID] == 0 {
      continue
    }

    if visited[nextNodeID] {
      continue
    }

		visited[nextNodeID] = true
    dfs(nextNodeID, graph, visited)
    visited[nextNodeID] = false
  }
}


func main () {
  var n, m int
  fmt.Scanf("%d %d", &n, &m)

  graph := 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)
    s--; t--
    graph[s][t] = 1
    graph[t][s] = 1
  }

  visited := make([]bool, n)
  visited[0] = true

  dfs(0, graph, visited)
  fmt.Println(ans)
}