Source

This problem is moved from Long Long OJ (Copyright by Codeforces). All rights reserved.

Adapted from: https://codeforces.com/contest/988/problem/D

Problem Description

There are $n$ distinct points on a coordinate line, the coordinate of $i$-th point equals to $x_i$. 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 $x_{i_1}, x_{i_2}, \ldots, x_{i_m}$ such that for each pair $x_{i_j}$, $x_{i_k}$ it is true that $|x_{i_j} - x_{i_k}| = 2^d$ where $d$ is some non-negative integer number (not necessarily the same for each pair of points).

Input Format

The first line contains one integer $n$.

The second line contains $n$ pairwise distinct integers $x_1, x_2, \ldots, x_n$.

Output Format

In the first line print an positive interger $m$, indicating the maximum possible number of points in a subset that satisfies the conditions described above.

In the second line print $m$ positive integers, indicating the coordinates of points in the subset you have chosen.

If there are multiple answers, print any of them.

Samples

6
3 5 4 7 10 12

3
7 3 5

5
-1 2 5 8 11

1
8

Sample 1 Explanation

In the first example the answer is $[7,3,5]$. Note that $|7-3|=4=2^2$, $|7-5|=2=2^1$ and $|3-5|=2=2^1$.

Although the answer $[4,3,5]$ is also considered correct, You can't find a subset having more points satisfying the required property.

Data Range

For $50\%$ of the test cases, $n \le 20$.

For $100\%$ of the test cases, $1 \le n \le 2 \times 10^5$, $-10^9 \le x_i \le 10^9$.