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: Runtime Error)

private val scanner = java.util.Scanner(System.`in`)

private fun readInts(n: Int) = Array(n) { scanner.nextInt() }
private fun readLongs(n: Int) = Array(n) { scanner.nextLong() }
private fun readLineInts() = readLine()!!.split(" ").map { it.toInt() }.toTypedArray()
private fun readLineLongs() = readLine()!!.split(" ").map { it.toLong() }.toTypedArray()

fun main(args: Array<String>) {
    val (N, M) = readLineInts()
    val ab = (0 until N).map { readInts(2) }.toTypedArray()

    fun dfs(loc: Int, gone: Set<Int>): Int = if (gone.size == N-1) {
        1
    } else {
        val clock = ab.filter { it[0] == loc && it[1] !in gone }.map { dfs(it[1], gone.plus(loc)) }.sum()
        val reversed = ab.filter { it[1] == loc && it[0] !in gone }.map { dfs(it[0], gone.plus(loc)) }.sum()

        clock + reversed
    }

    println(dfs(1, setOf()))
}