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 (n, m) = {
        let v = read_vec::<usize>();
        (v[0], v[1])
    };
    let mut g: Vec<Vec<usize>> = Vec::new();
    let mut seen: Vec<bool> = Vec::new();
    for _ in 0..n {
        g.push(Vec::new());
        seen.push(false);
    }
    for _ in 0..m {
        let (a, b) = {
            let v = read_vec::<usize>();
            (v[0]-1, v[1]-1)
        };
        g[a].push(b);
        g[b].push(a);
    }

    seen[0] = true;
    let ret = dfs(0, 100, &g, &mut seen);
    println!("{}", ret);
}

fn dfs(c: usize, p: usize, g: &Vec<Vec<usize>>, seen: &mut Vec<bool>) -> usize {
    let mut all_visited = true;
    for i in 0..seen.len() {
        if seen[i] == false {
            all_visited = false;
        }
    }
    if all_visited {
        return 1;
    }

    let mut ret = 0;
    for &n in &g[c] {
        if n == p { continue; }
        if seen[n] { continue; }
        seen[n] = true;
        ret += dfs(n, c, g, seen);
        seen[n] = false;
    }
    return ret;
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}