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)

fun main(args: Array<String>) {
    val (n, m) = readLine()!!.split(' ').map(String::toInt)
    val ab = mutableListOf<Pair<Int, Int>>()
    for (i in 1..m) {
        val (a, b) = readLine()!!.split(' ').map(String::toInt)
        ab.add(Pair(a, b))
    }

    val a = Permutation((2..n).toList().toTypedArray())
    var count = 0
    do {
        val list = a.target!!.toMutableList()
        list.add(0, 1)

        var containFlg = true
        for (i in 1 until n) {
            containFlg = ab.any {
                (list[i - 1] == it.first && list[i] == it.second)
                        || (list[i - 1] == it.second && list[i] == it.first)
            }
            if (!containFlg) break
        }
        if (containFlg) count++
    } while (a.next())

    println(count)
}

class Permutation<T> private constructor(private val baseIndex: Int, private var index: Int, val target: Array<T>?) {
    private var subPermutation: Permutation<T>? = null

    constructor(objs: Array<T>) : this(0, 0, objs.clone())

    init {
        if (target == null || target.isEmpty()) {
            throw IllegalArgumentException()
        }

        if (this.index < this.target.size - 1) {
            this.subPermutation = Permutation(this.baseIndex + 1, this.index + 1, this.target)
        }
    }

    operator fun next(): Boolean {
        if (this.subPermutation == null) {
            return false
        }
        val result = this.subPermutation!!.next()
        if (result) {
            return true
        }
        this.swap(this.baseIndex, this.index)
        ++this.index
        if (this.target!!.size <= this.index) {
            this.index = this.baseIndex
            return false
        }
        this.swap(this.index, this.baseIndex)
        return true
    }

    private fun swap(index1: Int, index2: Int) {
        val tmp = this.target!![index1]
        this.target[index1] = this.target[index2]
        this.target[index2] = tmp
    }
}