Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Vasily the Bear and Sequence

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVasily the bear has got a sequence of positive integers *a*_{1}, *a*_{2}, ..., *a*_{n}. Vasily the Bear wants to write out several numbers on a piece of paper so that the beauty of the numbers he wrote out was maximum.

The beauty of the written out numbers *b*_{1}, *b*_{2}, ..., *b*_{k} is such maximum non-negative integer *v*, that number *b*_{1} *and* *b*_{2} *and* ... *and* *b*_{k} is divisible by number 2^{v} without a remainder. If such number *v* doesn't exist (that is, for any non-negative integer *v*, number *b*_{1} *and* *b*_{2} *and* ... *and* *b*_{k} is divisible by 2^{v} without a remainder), the beauty of the written out numbers equals -1.

Tell the bear which numbers he should write out so that the beauty of the written out numbers is maximum. If there are multiple ways to write out the numbers, you need to choose the one where the bear writes out as many numbers as possible.

Here expression *x* *and* *y* means applying the bitwise AND operation to numbers *x* and *y*. In programming languages C++ and Java this operation is represented by "&", in Pascal — by "and".

Input

The first line contains integer *n* (1 ≤ *n* ≤ 10^{5}). The second line contains *n* space-separated integers *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{1} < *a*_{2} < ... < *a*_{n} ≤ 10^{9}).

Output

In the first line print a single integer *k* (*k* > 0), showing how many numbers to write out. In the second line print *k* integers *b*_{1}, *b*_{2}, ..., *b*_{k} — the numbers to write out. You are allowed to print numbers *b*_{1}, *b*_{2}, ..., *b*_{k} in any order, but all of them must be distinct. If there are multiple ways to write out the numbers, choose the one with the maximum number of numbers to write out. If there still are multiple ways, you are allowed to print any of them.

Examples

Input

5

1 2 3 4 5

Output

2

4 5

Input

3

1 2 4

Output

1

4

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jan/20/2020 08:13:33 (e1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|