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 v5.12) (judge verdict: Runtime Error)

'use strict';

function visitedAll(visited) {
  let flag = true;
  for (let vis of visited) {
    if (vis !== 1) {
      flag = false;
    }
  }
  return flag;
}

function dfs(v, N, graph, visited) {
  if (visitedAll(visited)) {
    count++;
  }


  for (let i = 0; i < N; i++) {
    if (graph[v][i] === 1 && visited[i] === 0) {
      visited[i] = 1;
      dfs(i, N, graph, visited);
      visited[i] = 0;
    }
  }

  return count;

}

function main(input) {
  const tmp = input.split('\n');
  const NM = tmp.shift().split(' ').map((elem) => parseInt(elem, 10));
  const N = NM[0];
  const M = NM[1];

  let graph = Array(N).fill(0).map((elem) => Array(N).fill(0));
  for (let line of tmp) {
    const splited = line.split(' ').map((elem) => parseInt(elem, 10));
    const a = splited[0];
    const b = splited[1];

    graph[a - 1][b - 1] = 1;
    graph[b - 1][a - 1] = 1;
  }
  let visited = Array(N).fill(0);
  visited[0] = 1;
  console.log(dfs(0, N, graph, visited));
}
let count = 0;
main(require('fs').readFileSync('/dev/stdin', 'utf8'));