201152: [AtCoder]ARC115 C - ℕ Coloring

Problem Statement

Given is an integer $N$. Among the sequences of $N$ positive integers $A_1, A_2, \ldots, A_N$ satisfying the following condition, print one that minimizes the maximum value in the sequence.

• If $i$ divides $j$, $A_i \neq A_j$ $(1 \leq i < j \leq N)$.

Constraints

• $1 \leq N \leq 10^5$

Input

Input is given from Standard Input in the following format:

$N$

Output

Print a line containing the elements of your sequence, with spaces in between.

If there are multiple valid solutions, any of them will be accepted.

$A_1$ $A_2$ $\ldots$ $A_N$ 

Sample Input 1

4

Sample Output 1

1 2 2 3

This solution satisfies all of the following conditions:

• $A_1 \neq A_2$
• $A_1 \neq A_3$
• $A_1 \neq A_4$
• $A_2 \neq A_4$

Additionally, there is no sequence satisfying these conditions where the maximum value in the sequence is $2$ or less, so this is a valid solution.