# Practice on Toph

Participate in exhilarating programming contests, solve unique algorithm and data structure challenges and be a part of an awesome community.

# Divine Tree

By Nobel_ruettt · Limits 3s, 512 MB

One day Thor gave Nabil Bin Masterchief a rooted tree consisting of n vertices. Unfortunately, During the fight with Hela, his tree was shattered and he doesn't remember all it's edges. He only managed to restore m edges of the initial tree.

Now as a good friend of Nabil, you have to count the number of distinct trees of size n with vertex 1 as root which contain all of the m edges.

## Input

The first line of the input contains two integers n and m (1 ≤ n ≤ 13,** 0 ≤ m < n**) — the number of vertices and the number of edges remembered by Nabil respectively.

Each of the next m lines contains two integers Ui and Vi (1 ≤Ui,Vi n, Ui Vi) — the numbers of vertices connected by the i-th edge. It's guaranteed that this set of edges is a subset of edges of some tree. Same edge will not be given more than once in input.

## Output

Print a single integer — the number of trees of size n that contain all of the m edges.

## Samples

InputOutput
5 2
4 1
4 2


15

InputOutput
3 1
2 1
2


Two rooted trees are considered to be distinct if there exists an edge that occur in one of them and doesn't occur in the other one.

### Statistics

63% Solution Ratio

YouKnowWhoEarliest, Aug '19

YouKnowWhoFastest, 0.0s

YouKnowWhoLightest, 131 kB

ovis96Shortest, 545B