Description

One day , DD gets several beads , he wants to make these beads a necklace . But not every bead can link to each other;every bead should link to some particular bead(s). Now , DD wants to know how many kinds of necklace he can make.

Input

It consists of multi-case .

Every case start with two integers N,M ( 1<=N<=18,M<=N*N )

The followed M lines contains two integers a,b ( 1<=a,b<=N ) which means the ath bead and the bth bead are able to be linked.

Output

An integer , which means the number of kinds that the necklace could be.

Sample

Input

3 3
1 2
1 3
2 3

Output

2