One-stroke Path

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: $N$ $M$ $a_1$ $b_1$ $a_2$ $b_2$ $:$ $a_M$ $b_M$ [samples]