Description:
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 Format:
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 $$$a_1, a_2, \ldots, a_m$$$ ($$$0 \le a_{i} < 2^{n}$$$) — the elements of the set. All $$$a_{i}$$$ are distinct.
Output Format:
Print the number of connected components.
Note:
Graph from first sample:
Graph from second sample: