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::*;
use std::str::FromStr;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn dfs(cn: usize, map: &Vec<Vec<usize>>, cnt: &mut usize, is_done: &mut Vec<bool>) {
    if is_done[cn] {
        return;
    }

    is_done[cn] = true;
    if is_done.iter().all(|&x| x == true) {
        *cnt += 1;
    }
    for i in &map[cn] {
        if is_done[*i] == true {
            continue;
        }
        let mut copy_done = is_done.clone();
        dfs(*i, map, cnt, &mut copy_done);
    }
}

fn main() {
    let n: usize = read();
    let m: usize = read();
    let mut map: Vec<Vec<usize>> = vec![vec![]; n + 1];

    for _ in 0..m {
        let a: usize = read();
        let b: usize = read();
        map[a].push(b);
        map[b].push(a);
    }
    let mut ans = 0;
    let mut is_done = vec![false; n + 1];
    is_done[0] = true;

    dfs(1, &map, &mut ans, &mut is_done);
    println!("{}", ans);
}