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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

function main(lines) {
  const [N, M] = na();
  
  // 頂点情報構築
  const nodes = Array(N+1).fill(0).map(() => new Set());
  for (let i = 1; i <= M; i++) {
    const [a, b] = na();
    nodes[a].add(b);
    nodes[b].add(a);
  }

  // ルート探索
  let ans = 0;
  searchRoute(nodes[1], [1]);

  // 探索再帰関数
  function searchRoute(node, passed) {
    if (passed.length == N) return ++ans;
    for (let n of node) {
      if (passed.includes(n)) continue;
      searchRoute(nodes[n], passed.concat(n));
    }
  }
  
  return ans;
}


const lines = require("fs").readFileSync("/dev/stdin", "utf8").trim().split("\n");

let lineCount = 0;
const s = () => lines[lineCount++];
const n = () => Number(s());
const b = () => BigInt(s());
const sa = () => s().split(' ');
const na = () => sa().map(Number);
const ba = () => sa().map(BigInt);

const ans = main(lines);
console.log( ans );