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::input;

fn proc_r(depth: usize, node: usize, n: usize, m: &mut [bool; 8], v: &Vec<Vec<usize>> ) -> usize {
	if depth == n {
		return 1;
	}
	let mut ret = 0;
	for i in 0..v[node].len() {
		if !m[v[node][i]] {
			m[v[node][i]] = true;
			ret += proc_r(depth+1, v[node][i], n, m, v);
			m[v[node][i]] = false;
		}
	}
	return ret;
}

fn main() {
	input!(n: usize);
	input!(m: usize);

	let mut v: Vec<Vec<usize>> = vec![vec![]; n];
	for _i in 0..m {
		input!(a: usize);
		input!(b: usize);
		v[a-1].push(b-1);
		v[b-1].push(a-1);
	}

	let mut m: [bool; 8] = [false; 8];
	m[0] = true;
	println!("{}", proc_r(1, 0, n, &mut m, &v));
}