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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

int num[8], n, ans = 0;
bool r[8][8], flg[8];

void saiki(int a) {
  int i;
  if(a == n) {
    bool b = true;
    for(i = 1; i < n; ++i) if(!r[num[i - 1]][num[i]]) b = false;
    if(b) ++ans;
    return;
  }
  for(i = 1; i < n; ++i) if(flg[i]) {
    num[a] = i, flg[i] = false;
    saiki(a + 1);
    flg[i] = true;
  }
}

int main(void) {
  int i, m, j, x, y;
  scanf("%d%d", &n, &m);
  for(i = 0; i < n; ++i) for(j = 0; j < n; ++j) r[i][j] = false;
  for(i = 0; i < n; ++i) flg[i] = true;
  for(i = 0; i < m; ++i) {
    scanf("%d%d", &x, &y);
    x--, y--;
    r[x][y] = r[y][x] = true;
  }
  num[0] = 0;
  saiki(1);
  printf("%d", ans);
  return 0;
}