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;

fn main() {
    let mut s = String::new();
    io::stdin().read_line(&mut s).ok();
    let nm: Vec<_> = s.trim().split(' ').map(|x| x.parse().unwrap()).collect();

    let mut xs = vec![vec![false; nm[0]]; nm[0]];

    for _ in 0..nm[1] {
        let mut s = String::new();
        io::stdin().read_line(&mut s).ok();
        let ab: Vec<usize> = s.trim().split(' ').map(|x| x.parse().unwrap()).collect();

        xs[ab[0] - 1][ab[1] - 1] = true;
        xs[ab[1] - 1][ab[0] - 1] = true;
    }
    let mut ts = vec![false; nm[0]];

    println!("{}", rec(&xs, nm[0], 0, &mut ts));
}

fn rec(xs: &Vec<Vec<bool>>, n: usize, idx: usize, ts: &mut Vec<bool>) -> u64 {
    ts[idx] = true;
    let mut f = true;
    for i in 0..n {
        f = f && ts[i];
    }

    if f {
        1
    }
    else {
        let mut res = 0;
        for (i, &x) in xs[idx].iter().enumerate() {

            if x && !ts[i] {
                res += rec(xs, n, i, ts);
                ts[i] = false;
            }
        }
        res
    }
}