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.

-----Output-----
Print the number of the different paths that start from vertex 1 and visit all the vertices exactly once.

-----Sample Input-----
3 3
1 2
1 3
2 3

-----Sample Output-----
2

The given graph is shown in the following figure:
The following two paths satisfy the condition:

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