You are given a set S containing n distinct positive integers .

Please find a subset of S which has the maximum size while satisfying the following constraint:

The binary representations of any two numbers in this subset must have at least two different bits.

If there are multiple valid subsets, please output any one of them.

输入描述:

The input contains only two lines.

The first line contains an integer N denoting the size of S.
The second line contains N positive integers  denoting the members of set S.

* 

* 

* all  are distinct

输出描述:

You should output two lines.

The first line contains one integer m denoting the size of the subset you found.

The second line contains m positive integers denoting the member of this subset.

5
3 1 4 2 5

3
4 1 2

3 (112) and 1 (012) has only 1 different bit so they can not be in the set together. 4 (1002) and 1 (0012) has 2 different bits so they can be in the set together.
Following unordered pairs are allowed to be in the set together: <1, 2>, <1, 4>, <2, 4>, <2, 5>, <3, 4>, <3, 5>. Thus the maximum set is of size 3 ({1, 2, 4}).