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(non_snake_case,unused_imports)]
use std::io::Read;
use std::cmp::max;
use std::cmp::min;
use std::str::FromStr;

fn check(N:usize,E:&Vec<Vec<usize>>,i:usize,done:usize) -> usize{
    if done == ((1<<N) -1){
        return 1;
    }
    let mut ans = 0;
    for &j in &E[i]{
        if done>>j &1 == 1 { continue; }
        ans += check(N,&E,j,done | 1<<j);
    }
    ans
}

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    let N:usize = iter.next().unwrap().parse().unwrap();
    let M:usize = iter.next().unwrap().parse().unwrap();
    let mut AB = Vec::new();
    let mut E = Vec::new();
    for _ in 0..N{
        E.push(Vec::new());
    }
    for i in 0..M{
        AB.push((iter.next().unwrap().parse::<usize>().unwrap(),
                 iter.next().unwrap().parse::<usize>().unwrap()));
        E[AB[i].0-1].push(AB[i].1-1);
        E[AB[i].1-1].push(AB[i].0-1);
    }
    println!("{}",check(N,&E,0,1));
}