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