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)

#[test]
fn test_solve() {
    assert_eq!(solve("3 3\n1 2\n1 3\n2 3\n"), "2\n");
    assert_eq!(solve("7 7\n1 3\n2 7\n3 4\n4 5\n4 6\n5 6\n6 7\n"), "1\n");
}
fn solve(src: &str) -> String {
    let mut sc = Scanner::from_str(src);

    let n: usize = sc.read();
    let m: usize = sc.read();
    let mut cnd = vec![vec![false; n]; n];
    for _ in 0..m {
        let a: usize = sc.read();
        let b: usize = sc.read();
        cnd[a - 1][b - 1] = true;
        cnd[b - 1][a - 1] = true;
    }
    let mut s = 0;
    let mut prm: Vec<_> = (0..n).collect();
    while {
        if prm[0] == 0 && (0..n - 1).all(|i| cnd[prm[i]][prm[i + 1]]) {
            s += 1;
        };
        next_permutation(&mut prm)
    } {}

    format!("{}\n", s)
}

fn next_permutation<T: Ord>(v: &mut [T]) -> bool {
    let len = v.len();
    if len <= 1 {
        return false;
    }
    let mut i = len - 1;
    loop {
        let i1 = i;
        i -= 1;
        if v[i] < v[i1] {
            let mut i2 = len - 1;
            while v[i] >= v[i2] {
                i2 -= 1;
            }
            v.swap(i, i2);
            for j in 0..(len - i1) >> 1 {
                v.swap(i1 + j, len - j - 1);
            }
            return true;
        }
        if i == 0 {
            v.reverse();
            return false;
        }
    }
}

fn main() {
    let mut buf = String::new();
    use std::io;
    use std::io::{Read, Write};
    io::stdin().read_to_string(&mut buf).unwrap();
    io::stdout().write_all(solve(&buf).as_bytes()).unwrap();
}

struct Scanner<'a>(std::str::SplitWhitespace<'a>);
impl<'a> Scanner<'a> {
    fn from_str(src: &str) -> Scanner {
        Scanner(src.split_whitespace())
    }
    fn get(&mut self) -> &str {
        self.0.next().unwrap()
    }
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.get().parse().ok().unwrap()
    }
}