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)

fn main(){
    let mut sc = Scanner::new();
    while sc.read() {
        let n = sc.next();
        let m = sc.next();
        let mut graph = vec![vec![]; n];
        for _ in 0..m {
            let a = sc.next::<usize>() - 1;
            let b = sc.next::<usize>() - 1;
            graph[a].push(b);
            graph[b].push(a);
        }
        let mut flg = vec![false; n];
        println!("{}", rec(0, &mut flg, &graph));
    }
}

fn rec(v: usize, flg: &mut Vec<bool>, graph: &Vec<Vec<usize>>) -> i32 {
    flg[v] = true;
    let mut end = true;
    for f in flg.iter() {
        end &= *f;
    }
    let res = if end {
        1
    } else {
        let mut s = 0;
        for w in graph[v].iter() {
            if !flg[*w] {
                s += rec(*w, flg, graph);
            }
        }
        s
    };
    flg[v] = false;
    res
}

#[allow(dead_code)]
struct Scanner {
    buf: Vec<u8>, i: usize, next: Option<String>,
}

#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner {
        Scanner { buf: vec![], i: 0, next: None, }
    }

    fn next<T: std::str::FromStr>(&mut self) -> T {
        self.wrapped::<T>().unwrap()
    }

    fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        let mut res = Vec::<T>::with_capacity(n);
        for _ in 0..n { res.push(self.next()) }
        res
    }

    fn wrapped<T: std::str::FromStr>(&mut self) -> Option<T> {
        self.read();
        self.next.take().and_then(|s| s.parse::<T>().ok())
    }

    fn read(&mut self) -> bool {
        if self.next.is_some() { return true }
        let mut s = String::with_capacity(16);
        while let Some(c) = self.get_char() {
            if !c.is_whitespace() { s.push(c); }
            else if !s.is_empty() { break; }
        }
        self.next = if !s.is_empty() { Some(s) } else { None };
        self.next.is_some()
    }

    fn get_char(&mut self) -> Option<char> {
        if self.i >= self.buf.len() {
            use std::io::BufRead;
            let reader = std::io::stdin();
            let mut buffer = reader.lock();
            let len = match buffer.fill_buf() {
                Ok(bytes) => {
                    self.buf.resize(bytes.len(), b'\0');
                    self.buf.copy_from_slice(bytes);
                    Some(bytes.len())
                },
                Err(_) => None,
            };
            self.i = 0;
            if len.is_some() { buffer.consume(len.unwrap()); }
            if len.is_none() || len.unwrap() == 0 { return None }
        }
        self.i += 1;
        Some(self.buf[self.i - 1] as char)
    }
}