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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Monad
main=do
 [n,m]<-map read.words<$>getLine
 ed<-replicateM m (map ((\n->n-1).read).words<$>getLine)
 print(f n ed [(0,take n (repeat 0))] 0)
  where f _ _ [] ans = ans
        f n ed ((ve,arc):st) ans = f n ed ((g ve arc ed)++st) (if (sum arc)==(n-1) then (ans+1) else ans)
        g ve arc [] = []
        g ve arc ([a,b]:ed) | ve==a = if (arc!!b)==0 then ((h ve b arc):(g ve arc ed)) else (g ve arc ed)
                            | ve==b = if (arc!!a)==0 then ((h ve a arc):(g ve arc ed)) else (g ve arc ed)
                            |otherwise = g ve arc ed
        h ve a arc = (a,(take ve arc)++(1:(drop (ve+1) arc)))