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: Wrong Answer)

fn main() {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let v: Vec<usize> = s.trim().split(' ').map(|x| x.parse().unwrap()).collect();

    let mut g: Vec<Vec<usize>> = vec![Vec::new(); v[1]];
    for i in 0..v[1] {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        g[i] = s.trim().split(' ').map(|x| x.parse().unwrap()).collect();
    }

    static mut c: usize = 0;

    let mut b: Vec<bool> = vec![false; v[1]];
    let mut q: Vec<usize> = vec![0; v[1]];
    fn rec(i: usize, z: usize, b: &mut Vec<bool>, q: &mut Vec<usize>, g: &Vec<Vec<usize>>) {
        if i >= z {
            let mut x = true;
            for j in 1..q.len() {
                let a = std::cmp::min(q[j-1]+1, q[j]+1);
                let d = std::cmp::max(q[j-1]+1, q[j]+1);
                if !g.contains(&vec![a, d]) {x = false; break;}
            }
            if x {unsafe {c += 1;}}
        }
        else {
            for j in 1..z {
                if !b[j] {
                    b[j] = true;
                    q[i] = j;
                    rec(i+1, z, b, q, g);
                    b[j] = false;
                }
            }
        }
    }
    rec(1, v[1], &mut b, &mut q, &g);

    unsafe {println!("{}", c);}
}