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::{Read, stdin};
use std::str::FromStr;

fn main() {
    let n: usize = read();
    let m: usize = read();
    let mut edge: Vec<Vec<usize>> = vec![Vec::new(); n];
    for _i in 0..m {
        let ai: usize = read();
        let bi: usize = read();
        edge[ai - 1].push(bi - 1);
        edge[bi - 1].push(ai - 1);
    }
    let visited: [bool; 8] = [false; 8];
    println!("{}", dfs(0, n, &visited, &edge, 0));
}

fn dfs(i: usize, n: usize, visited: &[bool; 8], edge: &Vec<Vec<usize>>, mut cnt: i32) -> i32 {
    let mut u_visited = *visited;
    u_visited[i] = true;
    if is_all_visited(n, u_visited) {
        cnt += 1;
    } else {
        for j in &edge[i] {
            if u_visited[*j] == false {
                cnt = dfs(*j, n, &u_visited, &edge, cnt);
                u_visited[*j] = false;
            }
        }
    }
    cnt
}

fn is_all_visited(n: usize, visited: [bool; 8]) -> bool {
    let mut flag: bool = true;
    for i in 0..n {
        if !visited[i] {
            flag = false;
        }
    }
    flag
}

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")
}