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)]
#![allow(dead_code)]

use std::thread;
use std::io::{ self, Read };
use std::fmt;
use std::iter::Iterator;
use std::cmp::*;
use std::collections::*;
use std::str::*;

#[derive(Default)]
struct Input {
    buf: Vec<String>
}

impl Input {
    fn new() -> Input {
        Input { buf: Vec::new() }
    }

    fn read<T: FromStr>(&mut self) -> T 
    where <T as FromStr>::Err: fmt::Debug {
        self.next().unwrap().parse::<T>().unwrap()
    }

    fn read_bytes(&mut self) -> Vec<u8> {
        self.next().unwrap().into_bytes()
    }

    fn read_n<T: FromStr>(&mut self, n: usize) -> Vec<T>
    where <T as FromStr>::Err: fmt::Debug {
        let mut v = Vec::new();
        for _ in 0..n { v.push(self.read::<T>()); }
        v
    }
}

impl Iterator for Input {
    type Item = String;
    fn next(&mut self) -> Option<String> {
        while self.buf.is_empty() {
            let mut s = String::new();
            let _res = io::stdin().read_line(&mut s);
            self.buf = s.split_whitespace().map(|s| s.to_owned()).collect::<Vec<_>>();
            self.buf.reverse();
        }
        self.buf.pop()
    }
}

fn dfs(u: usize, c:usize, e: &[Vec<i64>], s: &mut [bool]) -> i64 {
    if s[u] { return 0; }
    if c == e.len() - 1 { return 1; }
    s[u] = true;
    let mut y = 0;
    for v in 1..e.len() {
        if e[u][v] > 0 { y += dfs(v, c + 1, e, s); }
    }
    s[u] = false;
    y
}

fn run() {
    let mut ip = Input::new();
    let n = ip.read::<usize>();
    let m = ip.read::<usize>();
    let mut e = vec![vec![0; n + 1]; n + 1];
    for _ in 0..m {
        let u = ip.read::<usize>();
        let v = ip.read::<usize>();
        e[u][v] = 1;
        e[v][u] = 1;
    }
    let mut s = vec![false; n + 1];
    let y = dfs(1, 1, &e, &mut s);
    println!("{}", y);
}

fn main() {
    let _ = thread::Builder::new()
        .stack_size(10 * 1024 * 1024)
        .spawn(run).unwrap()
        .join();
}