VNOI Marathon 08

Numbers

In a website for mathematical lovers, there is a puzzle as following: given N positive integers, you have to color each number so that each number is not divided by a number that has the same color and the number of used colors is minimized.

Finding this puzzle interesting, Bom asks for your help to solve it! Write a program that help Bom solve this puzzle.

Input

• Line 1: a positive integer N.
• Line 2: N positive integers a₁, a₂, a₃, ..., a_n.

Output

• Line 1: a positive integer K that is the minimum number of used color.
• In the i^th line of the next K lines, write a number c_i indicating how many numbers of color i following by c_i numbers of color i.

Constraints

• N belongs to [1, 50000]
• a_i belongs to [1, 10⁶]

Note

If there are several ways to color the numbers, print any of them.

Example

Input
10
24 7 42 8 2 16 22 21 33 11	

Output
3
3 7 2 11 
4 8 22 21 33 
3 24 42 16