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)

#![allow(unused_imports)]
use std::io::{ self, Write };
use std::str::FromStr;
use std::cmp::{ min, max };
use std::collections::{ BinaryHeap, VecDeque };

macro_rules! trace {
    ($var:expr) => ({
        let _ = writeln!(&mut std::io::stderr(), ">>> {} = {:?}", stringify!($var), $var);
    })
}
macro_rules! swap { ($a:expr, $b:expr) => ({ let t = $b; $b = $a; $a = t; }) }
struct Permutation { n: usize, idx: usize }
impl Permutation {
    fn new(n: usize) -> Permutation {
        Permutation { n: n, idx: 0 }
    }
}
impl Iterator for Permutation {
    type Item = Vec<usize>;
    fn next(&mut self) -> Option<Vec<usize>> {
        let mut r = vec![0; self.n];
        let mut idx = self.idx;
        for k in 1..self.n {
            r[k] = idx % (k + 1);
            idx /= k + 1;
        }
        if idx > 0 { return None }
        r.reverse();
        let mut b = vec![true; self.n];
        b[r[0]] = false;
        for k in 1..self.n {
            let mut count = 0;
            for j in 0..self.n {
                if b[j] {
                    if count == r[k] {
                        r[k] = j;
                        b[j] = false;
                        break;
                    }
                    count += 1;
                }
            }
        }
        self.idx += 1;
        return Some(r)
    }
}

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.cin();

    let mut table = vec![vec![false; n]; n];

    let m: usize = sc.cin();
    for _ in 0..m {
        let u: usize = sc.cin();
        let v: usize = sc.cin();
        table[u - 1][v - 1] = true;
        table[v - 1][u - 1] = true;
    }

    let mut ans = 0;
    for a in Permutation::new(n - 1) {
        if !table[0][a[0] + 1] { continue; }
        let mut ok = true;
        for i in 0..(a.len() - 1) {
            if !table[a[i] + 1][a[i + 1] + 1] {
                ok = false;
                break;
            }
        }
        if ok {
            ans += 1;
        }
    }

    println!("{}", ans);

}

#[allow(dead_code)]
struct Scanner { stdin: io::Stdin, buffer: VecDeque<String>, }
#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner { Scanner { stdin: io::stdin(), buffer: VecDeque::new() } }
    fn reserve(&mut self) {
        while self.buffer.len() == 0 {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
    }
    fn cin<T: FromStr>(&mut self) -> T {
        self.reserve();
        match self.buffer.pop_front().unwrap().parse::<T>() {
            Ok(a) => a,
            Err(_) => panic!("parse err")
        }
    }
    fn get_char(&mut self) -> char {
        self.reserve();
        let head = self.buffer[0].chars().nth(0).unwrap();
        let tail = String::from( &self.buffer[0][1..] );
        if tail.len()>0 { self.buffer[0]=tail } else { self.buffer.pop_front(); }
        head
    }
}