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)

use std::cmp::{max, min};
use std::collections::{HashMap, HashSet, VecDeque};
use std::io::{stdin, Read};
use std::str::FromStr;

// https://qiita.com/tubo28/items/e6076e9040da57368845
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

#[allow(dead_code)]
fn main() {
    let n = read::<usize>();
    let m = read::<usize>();
    let ab = (0..m)
        .map(|_| (read::<usize>(), read::<usize>()))
        .collect::<Vec<_>>();
    let mut t = vec![vec![0; n]; n];
    for (a, b) in ab {
        t[a - 1][b - 1] = 1;
        t[b - 1][a - 1] = 1;
    }

    let mut node = vec![0; n];
    let ans = visit(0, &t, &mut node, n + 1, 1);
    println!("{}", ans);

    fn visit(i: usize, t: &Vec<Vec<i32>>, node: &mut Vec<i32>, prev: usize, count: usize) -> usize {
        if node[i] == 1 {
            return 0;
        }
        if count == node.len() {
            return 1;
        }

        node[i] = 1;
        let mut ans = 0;
        for (j, &x) in t[i].iter().enumerate() {
            if x == 1 {
                ans += visit(j, t, node, i, count + 1);
            }
        }
        node[i] = 0;
        ans
    }
}