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)

fn main() {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    let v: Vec<i32> = s
        .trim()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect();
    let n = v[0];
    let m = v[1];

    let mut neighbor: Vec<Vec<i32>> = vec![Vec::new(); 8];

    for _i in 0..m {
        s = String::new();
        std::io::stdin().read_line(&mut s).ok();
        let v: Vec<i32> = s
            .trim()
            .split_whitespace()
            .map(|e| e.parse().ok().unwrap())
            .collect();
        let a = v[0] - 1;
        let b = v[1] - 1;

        neighbor[a as usize].push(b);
        neighbor[b as usize].push(a);
    }

    let mut check = vec![false; n as usize];

    println!("{}", cnt(0, &neighbor, &mut check));
}

fn cnt(v: i32, neighbor: &Vec<Vec<i32>>, check: &mut Vec<bool>) -> i32 {
    check[v as usize] = true;

    let mut ret = 0;

    let mut stuck = true;
    for u in neighbor[v as usize].iter() {
        if !check[*u as usize] {
            stuck = false;
            ret += cnt(*u, neighbor, check);
        }
    }

    if stuck {
        ret = 1;
        for b in check.iter() {
            if !b {
                ret = 0;
            }
        }
    }

    check[v as usize] = false;

    ret
}