355. Numbers Painting
Time limit per test: 0.25
second(s)
Memory limit: 65536
kilobytes
input: standard
output: standard
Dr. Vasechkin wants to paint all numbers from 1 to
N in such a way that if number
A is divisible by number
B, numbers
A and
B have different colors.
Help Dr. Vasechkin to find such a painting, where the number of the colors used is minimal.
Input
The input contains integer number
N (
).
Output
Write the number of the colors
M in the desired painting in the first line of the output. In the second line of the output write the desired painting of numbers from 1 to
N. The used colors should be represented by numbers from 1 to
M. If there are several solutions, choose any of them.
Example(s)
sample input

sample output

12

4
1 2 2 3 2 3 2 4 3 3 2 4
