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::io::Read;

fn main() {
    let mut stdin = io::stdin();
    let mut lines = String::new();
    let _ = stdin.read_to_string(&mut lines);
    let vec = lines.lines().collect::<Vec<&str>>();
    let firstline = vec[0].split(' ').collect::<Vec<&str>>();
    let n :usize = firstline[0].trim().parse().unwrap();
    let m :usize = firstline[1].trim().parse().unwrap();
    let mut hens :Vec<(usize,usize)> = Vec::new();
    for i in 0..m {
        let thisline = vec[i+1].split(' ').collect::<Vec<&str>>();
        let a :usize = thisline[0].trim().parse().unwrap();
        let b :usize = thisline[1].trim().parse().unwrap();
        hens.push((a-1,b-1));
    }
    let hens = hens;
    let mut dp : Vec<usize> = vec![0;n*(1<<n)];
    dp[1*n+0] = 1;
    for i in 2..(1<<n) {
        for j in 0..n {
            if (1<<j) & i == 0 {continue;}
            for &(a,b) in &hens {
                let tail = if a == j {
                    b
                } else if b == j {
                    a
                } else {
                    n
                };
                if tail == n {continue;}
                dp[i*n+j] += dp[(i^(1<<j))*n+tail];
            }
        }
    }
    let mut fin = 0;
    for i in 0..n {
        fin += dp[((1<<n)-1)*n+i];
    }
    println!("{}",fin);
}