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::str::FromStr;
use std::fmt::Debug;
use std::cmp;
#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

#[allow(dead_code)]
fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

fn enum_pats(n: usize, v: &Vec<Vec<bool>>, cur_stat: &mut Vec<bool>, cur_pos: usize) -> usize{

    if cur_stat.iter().all(|x| *x){
        return 1;
    }

    let mut ans = 0;
    for i in 0..n{
        if v[cur_pos][i] && !cur_stat[i]{
            cur_stat[i] = true;
            ans += enum_pats(n, v, cur_stat, i);
            cur_stat[i] = false;
        }
    }

    return ans;
}

fn main(){
    let line = read_as_vec::<usize>();
    let (n, m) = (line[0], line[1]);

    let mut v: Vec<Vec<bool>> = vec![vec![false;n];n];

    for _ in 0..m{
        let line = read_as_vec::<usize>();
        let (a, b) = (line[0]-1, line[1]-1);
        v[a][b] = true;
        v[b][a] = true;
    }

    let mut tmp = vec![false;n];
    tmp[0] = true;
    println!("{}", enum_pats(n, &mut v, &mut tmp, 0));
}