You are given a list of $n$ integers, $a_1, a_2, \dots, a_n$. Your task is to pick two numbers $a_i$ and $a_j$ ($1 \leq i < j \leq n$) from the list such that the product $a_i \cdot a_j$ has the maximum number of 1 bits in its binary representation.

Input

The first line contains a single integer $n$, the size of the list. The second line contains $n$ integers $a_1, a_2, \dots, a_n$, the elements of the list.

Output

On the first line, print a single integer: the maximum number of 1 bits in the product.

On the second line, print two integers, the values $a_i$ and $a_j$, such that their product has the maximum number of 1 bits in its binary representation. If there are multiple valid answers, print any of them.

Constraints

• $2 \leq n \leq 10^4$
• $1 \leq a_i \leq 10^9$

Example

Input:

5
2 3 7 10 15

Output:

4
3 15