C - ℕ Coloring /

### 問題文

• ij の約数ならば、A_i \neq A_j (1 \leq i < j \leq N)

### 制約

• 1 \leq N \leq 10^5

### 入力

N


### 出力

A_1 A_2 \ldots A_N


### 入力例 1

4


### 出力例 1

1 2 2 3


この出力は以下の条件をすべて満たします。

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

また、登場する値の最大値が 2 以下である数列であって、これらの条件をすべて満たすものは存在しないので、この出力は適当です。

Score : 500 points

### 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.