You are given a set of size $m$ with integer elements between $0$ and $2^{n}-1$ inclusive. Let's build an undirected graph on these integers in the following way: connect two integers $x$ and $y$ with an edge if and only if $x \& y = 0$. Here $\&$ is the bitwise AND operation. Count the number of connected components in that graph.

Input

In the first line of input there are two integers $n$ and $m$ ($0 \le n \le 22$, $1 \le m \le 2^{n}$).

In the second line there are $m$ integers $a_1, a_2, \ldots, a_m$ ($0 \le a_{i} \lt 2^{n}$) — the elements of the set. All $a_{i}$ are distinct.

Output

Print the number of connected components.

Note

Graph from first sample:

Graph from second sample: