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)

use std::io::stdin;

fn main(){
    let (n, m) = nm();
    let edges = read_edges(n, m);
    println!("{}", solve(&edges));
}

fn _solve(node: usize, edges: &Vec<Vec<i64>>, mut visited: &mut Vec<bool>) -> i64{
    if visited.iter().fold(true, |acc, &x|{acc && x}) {1}
    else{
        let mut ans = 0;
        for next in edges[node].iter(){
            if !visited[*next as usize]{
                visited[*next as usize] = true;
                ans += _solve(*next as usize, edges, visited);
                visited[*next as usize] = false;
            }
        }
        ans
    }
}

fn solve(edges: &Vec<Vec<i64>>) -> i64{
    let mut v: Vec<bool> = Vec::new();
    for _ in 0..edges.len(){v.push(false)}
    v[0] = true;
    _solve(0, edges, &mut v)
}

fn read_edges(n: i64, m: i64)->Vec<Vec<i64>>{
    let mut edges: Vec<Vec<i64>> = Vec::new();
    for _ in 0..n{edges.push(Vec::new())}
    for _ in 0..m{
        let (a, b) = nm();
        edges[(a-1) as usize].push(b-1);
        edges[(b-1) as usize].push(a-1);
    }
    edges
}

#[allow(dead_code)]
fn getline() -> String {
    let mut s = String::new();
    match stdin().read_line(&mut s){
        Ok(_) => {s.trim().to_string()}
        Err(_) => String::new()
    }
}

#[allow(dead_code)]
fn getvec() -> Vec<i64>{
    let line = getline();
    line.split_whitespace().map(|x| x.parse().unwrap()).collect()
}

fn nm() -> (i64, i64){
    let temp: Vec<i64> = getvec();
    (temp[0], temp[1])
}