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;

fn main() {
    let stdin = std::io::stdin();

    let mut buf = String::new();
    stdin.read_line(&mut buf).ok();
    let (n, _m) = to_pair(&buf);

    let graph: Vec<_> = stdin.lock().lines().map(|l| to_pair(&l.unwrap())).collect();

    let mut matrix: Vec<u8> = vec![0; n as usize];
    for e in graph {
        matrix[e.0 as usize - 1] |= 1 << e.1 - 1;
        matrix[e.1 as usize - 1] |= 1 << e.0 - 1;
    }

    let mut seq: Vec<u32> = (0..n).rev().collect();
    let ans = generate(seq.len() - 1, seq.as_mut_slice(), &matrix); // 末尾以外の順列を生成
    println!("{}", ans);
}

fn to_pair(s: &str) -> (u32, u32) {
    let v: Vec<_> = s.split_whitespace().map(|w| w.parse().unwrap()).collect();
    let (l, r) = (v[0], v[1]);
    (l, r)
}

// Heap のアルゴリズム。thx to うぃきぺ
fn generate(n: usize, a: &mut[u32], mat: &[u8]) -> u64 {
    let mut tmp: u32;
    if n == 1 {
        let mut b = true;
        for i in 0..a.len()-1 {
            if mat[a[i] as usize] & (1 << a[i+1]) == 0 {
                b = false;
                break;
            }
        }
        return if b { 1 } else { 0 };
    } else {
        let mut ret: u64 = 0;
        for i in 0..n {
            ret += generate(n-1, a, mat);
            if n & 1 == 0 {
                tmp = a[i];
                a[i] = a[n - 1];
                a[n - 1] = tmp;
            } else {
                tmp = a[0];
                a[0] = a[n - 1];
                a[n - 1] = tmp;
            }
        }
        return ret;
    }
}