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