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)

#[macro_use]
pub mod basic_stdin {
use std::str::FromStr;

pub fn read<T: FromStr>() -> T {
    use std::io::stdin;
    use std::io::Read;

    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed reading char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed parsing")
}

}

#[macro_export]
macro_rules! test_function {
    (func = $func:expr, $($input:expr => $output:expr),* $(,)*) => {
        $(
            assert_eq!($func(std::io::Cursor::new($input)) , $output);
        )*
    };
}

#[macro_export]
macro_rules! input_macro {
    (string = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    (reader = $s:expr, $($r:tt)*) => {
        let reader = std::io::BufReader::new($s);
        let mut bytes = std::io::Read::bytes(reader);
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[macro_export]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
    ($iter:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[macro_export]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

type Graph = Vec<Vec<usize>>;

fn main() {
    let stdin = std::io::stdin();
    let ret = solve(stdin.lock());

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

fn dfs(graph: &Graph, visit: &mut Vec<bool>, start: usize, c: usize) -> usize {
    let mut count = c;
    if visit[start] {
        return count;
    }

    visit[start] = true;

    if visit.iter().all(|&x| x) {
        count += 1;
    }

    for new_start in &graph[start] {
        count = dfs(graph, visit, *new_start, count);
    }

    visit[start] = false;

    return count;
}

fn solve<T: std::io::Read>(reader: T) -> usize {
    input_macro! {
        reader = reader,
        n: usize,
        m: usize,
        edges: [(usize1, usize1); m],
    }

    let mut graph = Graph::with_capacity(n);
    for _ in 0..n {
        graph.push(Vec::new());
    }
    for e in edges {
        graph[e.0].push(e.1);
        graph[e.1].push(e.0);
    }

    let mut visit: Vec<bool> = Vec::with_capacity(n);
    visit.resize(n, false);

    let ans = dfs(&graph, &mut visit, 0, 0);
    ans
}

#[cfg(test)]
mod tests {

    #[test]
    fn test_solve_function() {
        atcorder::test_function! {
            func = super::solve,
            "3 3 1 2 1 3 2 3" => 2,
            "7 7 1 3 2 7 3 4 4 5 4 6 5 6 6 7" => 1,
        }
    }
}