Given is a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1, 2, \dots, N$, and the $i$-th edge connects Vertices $A_i$ and $B_i$.

Find the minimum possible number of connected components in the graph after removing zero or more edges so that the following condition will be satisfied:

Condition:
For every pair of vertices $(a, b)$ such that $1 \le a < b \le N$, if Vertices $a$ and $b$ belong to the same connected component, there is an edge that directly connects Vertices $a$ and $b$.

Input is given from Standard Input in the following format:

```
$N$ $M$
$A_1$ $B_1$
$\vdots$
$A_M$ $B_M$
```

Print the answer.

-   All values in input are integers.
-   $1 \le N \le 18$
-   $0 \le M \le \frac{N(N - 1)}{2}$
-   $1 \le A_i < B_i \le N$
-   $(A_i, B_i) \neq (A_j, B_j)$ for $i \neq j$.

2

Without removing edges, the pair (2,3) violates the condition. Removing one of the edges disconnects Vertices 2 and 3, satisfying the condition.