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 (1.42.0) (judge verdict: Accepted)

use proconio::{fastout, input};
use std::io::*;
use std::str::FromStr;

use std::cmp::{max, min};
use std::collections::{BinaryHeap, HashMap, HashSet, VecDeque};

fn main() {
    input! {
        n: usize,
        m: usize,
        ab: [(usize, usize); m],
    }

    let mut map = HashMap::new();
    for i in 0..ab.len() {
        let current = map.entry(ab[i].0).or_insert(vec![]);
        current.push(ab[i].1);
        let current = map.entry(ab[i].1).or_insert(vec![]);
        current.push(ab[i].0);
    }
    let mut done = vec![0; n + 1];
    let mut cnt = 0;
    dfs(1, &mut done, &map, 0, &mut cnt);
    println!("{}", cnt);
}

fn dfs(
    cn: usize,
    done: &mut Vec<usize>,
    map: &HashMap<usize, Vec<usize>>,
    pn: usize,
    cnt: &mut usize,
) {
    if done[cn] != 0 {
        return;
    }
    done[cn] = 1;
    done[0] += 1;
    if done[0] == map.len() {
        *cnt += 1;
    }
    for i in map.get(&cn).unwrap() {
        if pn == *i {
            continue;
        }
        if done[*i] != 0 {
            continue;
        }
        let mut donec = done.clone();
        dfs(*i, &mut donec, map, cn, cnt);
    }
}