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 Data.Array.IO
import Data.List
import Data.IORef
import Data.Array

all_ord::Int -> [[Int]]
all_ord n = map (1:) (permutations [2..n])

main::IO()
main= do
  nmc<-getLine
  let n:m:[]=map read (words nmc)::[Int]
  con<-newArray ((1,1),(n,n)) False
  ptr<-newIORef con
  create_edge ptr m
  st_ar<-freeze con
  print (solver st_ar n)


create_edge::IORef (IOArray (Int,Int) Bool) -> Int -> IO()
create_edge _ 0 = return ()
create_edge pt n = do
  abc<-getLine
  let a:b:[]=map read (words abc) ::[Int]
  ar<-readIORef pt
  writeArray ar (a,b) True
  writeArray ar (b,a) True
  create_edge  pt (n-1)

solver::(Array (Int,Int) Bool) -> Int -> Int
solver ar n = length (filter (check ar) (all_ord n))

check::(Array (Int,Int) Bool) -> [Int] -> Bool
check _  []       =True
check _  (_:[])   =True
check ar (a:b:xs) =(ar!(a,b))&& (check ar (b:xs))