Given n positive integers. Your task is to select a maximum number of integers so that there are no two numbers a, b in which a is divisible by b.

Input

• Line 1: n (1 ≤ n ≤ 200).
• Line 2: n positive integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁹).

Output

• Line 1: k, the maximum number of integers that can be selected.
• Line 2: k selected integers.

Example

Input
8
1 2 3 5 6 8 7 9
Output
5
5 6 8 7 9
Input
4
2 3 2 3
Output
2
2 3