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 Rust (1.15.1) (judge verdict: Accepted)

pub fn read1<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

pub fn readn<T: std::str::FromStr>(delimiter: &str) -> Vec<T> {
    let s = read1::<String>();
    s.split(delimiter).map(|e| e.parse().ok().unwrap()).collect::<Vec<T>>()
}

fn main() {
    let nm = readn::<usize>(" ");
    let n = nm[0];
    let m = nm[1];
    let mut visited = vec![0; n];
    let mut edge = vec![Vec::new(); n];

    for _ in 0..m {
        let ab = readn::<usize>(" ");
        edge[ab[0] - 1].push(ab[1] - 1);
        edge[ab[1] - 1].push(ab[0] - 1);
    }

    println!("{}", dfs(0, 0, n, &mut visited, &edge));
}

fn dfs(node: usize, num: usize, n: usize, visited: &mut Vec<usize>, edge: &Vec<Vec<usize>>) -> usize {
    if num + 1 == n {
        return 1;
    }

    let mut v = (*visited).clone();
    let mut path = 0;
    v[node] = 1;

    for &b in (*edge[node]).iter() {
        if visited[b] == 0 {
            path += dfs(b, num + 1, n, &mut v, edge);
        }
    }

    path
}