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 Kotlin (1.0.0) (judge verdict: Accepted)


var visited = mutableListOf<Boolean>()
var pathList = Array(100) {arrayOfNulls<Boolean>(100)}
var n = 0
var m = 0

fun main(args: Array<String>) {

    val total = readLine()?.split(" ").orEmpty()
    n = total[0].toInt()
    m = total[1].toInt()

   var k = 0
   while(k < 100){
       var l = 0
       while(l < 100){
            pathList[k][l] = false
            l++
        }
       k++
    }

    var i = 0
    while(i < m){
        var path = readLine()?.split(" ").orEmpty()
            pathList[path[0].toInt() - 1][path[1].toInt() - 1] = true
            pathList[path[1].toInt() - 1][path[0].toInt() - 1] = true
        i++
    }


    for(j in 1 .. n){
        visited.add(false)
    }
    //----------------------------------------------------------

    println(dfs(0,0))

    //----------------------------------------------------------


}

fun dfs( now: Int, depth: Int): Int {
    if (visited[now]) {
        return 0
    }
    if (depth == n - 1) {
        return 1
    }
    visited[now] = true
    var totalPaths = 0

    for (h in 0 until n) {
        if (pathList[now][h]!!) {
            totalPaths += dfs(h, depth + 1)
        }
    }
    visited[now] = false
    return totalPaths
}