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::prelude::*;

fn input<T>() -> T
where
    T: std::str::FromStr,
{
    let stdin = std::io::stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}

fn main() {
    let n: usize = input();
    let m: usize = input();
    let ab: Vec<(usize, usize)> = (0..m)
        .map(|_| {
            let a = input();
            let b = input();
            (a, b)
        })
        .collect();

    let mut path = vec![vec![]; n + 1];
    for &(a, b) in &ab {
        path[a].push(b);
        path[b].push(a);
    }

    let mut v = vec![false; n + 1];
    v[0] = true;
    v[1] = true;
    println!("{}", dfs(1, &mut v, &path));
}

fn dfs(cur: usize, visited: &mut Vec<bool>, path: &Vec<Vec<usize>>) -> i64 {
    let mut temp = 0;
    for &next in &path[cur] {
        if !visited[next] {
            temp += 1;
        }
    }

    if temp == 0 {
        if visited.iter().all(|&b| b) {
            1
        } else {
            0
        }
    } else {
        let mut ans = 0;
        for &next in &path[cur] {
            if !visited[next] {
                visited[next] = true;
                ans += dfs(next, visited, path);
                visited[next] = false;
            }
        }
        ans
    }
}