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::{BufRead, Write, stdin, stdout};
use std::collections::BTreeSet;

fn generate<M: FnMut(&mut Vec<u16>)>(n: usize, a: &mut Vec<u16>, cb: &mut M) {
    if n == 1 {
        cb(a);
    } else {
        for i in 0..n - 1 {
            generate(n - 1, a, cb);

            if n % 2 == 0 {
                a.swap(i, n - 1);
            } else {
                a.swap(0, n - 1);
            }
        }
        generate(n - 1, a, cb);
    }
}

fn solve<R: BufRead, W: Write>(mut input: R, mut output: W) {
    let mut s = String::new();
    input.read_line(&mut s).unwrap();
    let mut split = s.split_whitespace();
    let n: u16 = split.next().unwrap().parse().unwrap();
    let m: u16 = split.next().unwrap().parse().unwrap();
    let ab: BTreeSet<(u16, u16)> = (0..m)
        .map(|_| {
            let mut s = String::new();
            input.read_line(&mut s).unwrap();
            let mut split = s.split_whitespace();
            let a: u16 = split.next().unwrap().parse().unwrap();
            let b: u16 = split.next().unwrap().parse().unwrap();
            (a - 1, b - 1)
        })
        .collect();
    let mut count = 0u16;
    let mut perm: Vec<u16> = (0..n).collect();
    generate(perm.len(),
             &mut perm,
             &mut |perm| if perm[0] == 0 &&
                            perm.windows(2)
                 .map(|arr| ab.contains(&(arr[0], arr[1])) || ab.contains(&(arr[1], arr[0])))
                 .all(|x| x) {
                 count += 1;
             });
    writeln!(output, "{}", count).unwrap();
}

fn main() {
    let stdin = stdin();
    solve(stdin.lock(), stdout());
}

#[cfg(test)]
mod tests {
    fn test(input: &str, output: &str) {
        let mut v = Vec::<u8>::new();
        ::solve(input.as_bytes(), &mut v);
        assert_eq!(String::from_utf8(v).unwrap(), output);
    }
    #[test]
    fn case1() {
        test("3 3
1 2
1 3
2 3\n",
             "2\n");
    }
    #[test]
    fn case2() {
        test("7 7
1 3
2 7
3 4
4 5
4 6
5 6
6 7\n",
             "1\n");
    }
}