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: Wrong Answer)

#![allow(unused_mut)]
#![allow(non_snake_case)]
#![allow(unused_imports)]
use std::collections::HashSet;
use std::collections::HashMap;
use std::collections::BTreeSet;
use std::collections::VecDeque;
use std::cmp::{max, min};

// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

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

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

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

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

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

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

fn  all_used(used: &Vec<bool>) -> bool {
    for i in used {
        if !i {
            return false
        }
    }
    true
}

fn dfs(a: usize, mut used: Vec<bool>, hm: HashMap<usize, HashSet<usize>>) -> i64 {
    if used[a] {
        0
    } else {
        used[a] = true;
        if all_used(&used) {
            1
        } else {
            let mut sum = 0;
            for hs in hm[&a].clone() {
                sum += dfs(hs, used.clone(), hm.clone());
            }
            sum
        }
    }
}

fn main() {
    input! {
        n: usize,
        m: usize,
        abs: [(usize1, usize1); m],
    }
    let mut hms = HashMap::new();
    for ab in abs {
        if hms.contains_key(&ab.0) {
            let hs: &mut HashSet<usize> = hms.get_mut(&ab.0).unwrap();
            hs.insert(ab.1);
        } else {
            let mut hs = HashSet::new();
            hs.insert(ab.1);
            hms.insert(ab.0, hs);
        }
        if hms.contains_key(&ab.1) {
            let hs: &mut HashSet<usize> = hms.get_mut(&ab.1).unwrap();
            hs.insert(ab.0);
        } else {
            let mut hs = HashSet::new();
            hs.insert(ab.0);
            hms.insert(ab.1, hs);
        }
    }
    ///println!("{:?}", hms);
    let mut used = vec![false; n];
    let x = dfs(1, used, hms);
    println!("{:?}", x);
}