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;

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 next_permutation<T: std::cmp::PartialOrd>(arr: &mut std::vec::Vec<T>) -> bool {
    let mut i = arr.len() - 1;
    while i > 0 && arr[i - 1] >= arr[i] {
        i -= 1;
    }
    if i <= 0 {
        return false;
    }

    let mut j = arr.len() - 1;
    while arr[j] <= arr[i - 1] {
        j -= 1;
    }
    arr.swap(i - 1, j);

    arr[i..].reverse();

    return true;
}

#[derive(Debug)]
struct App {
    // input
    n: i32,
    m: i32,
    a: Vec<(i32, i32)>,
}

impl App {
    fn input() -> App {
        let n: i32 = read();
        let m: i32 = read();
        return App {
            n: n,
            m: m,
            a: (0..m).map(|_| (read::<i32>() - 1, read::<i32>() - 1)).collect(),
        };
    }

    fn solve(&mut self) {
        let mut mat = vec![vec![false; self.n as usize]; self.n as usize];
        for &(u, v) in &self.a {
            mat[u as usize][v as usize] = true;
            mat[v as usize][u as usize] = true;
        }

        let mut a: Vec<i32> = (0..self.n).collect();
        let mut ans = 0;
        loop {
            if a[0] == 0 {
                let mut ite = a.windows(2).map(|e| mat[e[0] as usize][e[1] as usize]);
                if ite.all(|f| f) {
                    ans += 1;
                }
            }

            if !next_permutation(&mut a) {
                break;
            }
        }

        println!("{}", ans);
    }
}

fn main() {
    let mut app = App::input();
    app.solve();
}