CF988D.Points and Powers of Two

普及/提高-

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题目描述

There are nn distinct points on a coordinate line, the coordinate of ii -th point equals to xix_i . Choose a subset of the given set of points such that the distance between each pair of points in a subset is an integral power of two. It is necessary to consider each pair of points, not only adjacent. Note that any subset containing one element satisfies the condition above. Among all these subsets, choose a subset with maximum possible size.

In other words, you have to choose the maximum possible number of points xi1,xi2,,ximx_{i_1}, x_{i_2}, \dots, x_{i_m} such that for each pair xijx_{i_j} , xikx_{i_k} it is true that xijxik=2d|x_{i_j} - x_{i_k}| = 2^d where dd is some non-negative integer number (not necessarily the same for each pair of points).

输入格式

The first line contains one integer nn ( 1n21051 \le n \le 2 \cdot 10^5 ) — the number of points.

The second line contains nn pairwise distinct integers x1,x2,,xnx_1, x_2, \dots, x_n ( 109xi109-10^9 \le x_i \le 10^9 ) — the coordinates of points.

输出格式

In the first line print mm — the maximum possible number of points in a subset that satisfies the conditions described above.

In the second line print mm integers — the coordinates of points in the subset you have chosen.

If there are multiple answers, print any of them.

输入输出样例

  • 输入#1

    6
    3 5 4 7 10 12
    

    输出#1

    3
    7 3 5
  • 输入#2

    5
    -1 2 5 8 11
    

    输出#2

    1
    8
    

说明/提示

In the first example the answer is [7,3,5][7, 3, 5] . Note, that 73=4=22|7-3|=4=2^2 , 75=2=21|7-5|=2=2^1 and 35=2=21|3-5|=2=2^1 . You can't find a subset having more points satisfying the required property.

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