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 (1.42.0) (judge verdict: Accepted)

use proconio::input;
use std::cmp::Ordering;
use std::fmt::Debug;
use std::mem::swap;
use proconio::marker::Usize1;

fn next_permutation<T>(mut v: Vec<T>) -> Option<Vec<T>>
    where T: Ord + Debug {
    let mut t = Vec::new();
    t.push(v.pop().unwrap());
    while let Some(mut lst) = v.pop() {
        if lst.cmp(t.last().unwrap()) != Ordering::Less {
            t.push(lst);
            continue;
        }
        t.sort();
        for i in 0..t.len() {
            if t[i] > lst {
                swap(&mut t[i], &mut lst);
                break;
            }
        }
        v.push(lst);
        return Some(v.into_iter().chain(t).collect::<Vec<T>>());
    }
    None
}

fn main()
{
    input! {
    n:usize,
    m:usize,
    edge:[(Usize1,Usize1);m],
    }
    let mut v = (0..n).collect::<Vec<usize>>();

    let mut ans = 0;
    loop {
        let mut exist = true;
        for i in 0..n - 1 {
            let (x, y) = (v[i], v[i + 1]);
            if let Some(_) = edge.iter()
                .find(|&t| (t.0, t.1) == (x, y) || (t.1, t.0) == (x, y)) {
                continue;
            } else {
                exist = false;
                break;
            }
        }
        if exist {
            ans += 1;
        }
        if let Some(nxt) = next_permutation(v) {
            v = nxt;
            if v[0] > 0 {
                break;
            }
        } else {
            break;
        }
    }
    println!("{}", ans);
}