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::collections::HashSet;
use std::io::{stdin, Read};

macro_rules! parse {
    ($it: ident) => {
        $it.next().unwrap().parse().unwrap()
    };
    ($it: ident,2) => {
        (parse!($it), parse!($it))
    };
    ($it: ident,3) => {
        (parse!($it), parse!($it), parse!($it))
    };
    ($it: ident,4) => {
        (parse!($it), parse!($it), parse!($it), parse!($it))
    };
    ($it: ident, $n: expr) => {
        (&mut $it).take($n).map(|e| e.parse().unwrap()).collect();
    };
}
fn perm_part<T: Clone>(n: usize, v: &mut [T], all: &mut Vec<Vec<T>>) {
    if n == 1 {
        all.push(v.to_vec());
        return;
    }
    for i in 0..n {
        perm_part(n - 1, v, all);
        if n % 2 == 0 {
            v.swap(i, n - 1);
        } else {
            v.swap(0, n - 1);
        }
    }
}

pub fn perm<T: Clone>(v: &Vec<T>) -> Vec<Vec<T>> {
    let mut v = v.clone();
    let mut all = vec![];
    perm_part(v.len(), &mut v, &mut all);
    all
}

fn solve(s: &str) {
    let mut it = s.split_whitespace();
    let (n, m) = parse!(it, 2);
    let mut g: Vec<HashSet<usize>> = vec![HashSet::new(); n];
    for _ in 0..m {
        let (a, b): (usize, usize) = parse!(it, 2);
        g[a - 1].insert(b - 1);
        g[b - 1].insert(a - 1);
    }
    let a: Vec<usize> = (1..n).collect();
    let mut ret = 0;
    for p in perm(&a) {
        let mut ok = true;
        if !g[0].contains(&p[0]) {
            ok = false;
        }
        for i in (0..(n - 2)) {
            if !g[p[i]].contains(&p[i + 1]) {
                ok = false;
                break;
            }
        }
        ret += ok as usize;
    }
    println!("{}", ret);
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    solve(&s);
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_input() {
        let s = "
        ";
        solve(s);
    }
}