A12594. Ehab and a Special Coloring Problem

You're given an integer $n$ . For every integer $i$ from $2$ to $n$ , assign a positive integer $a_i$ such that the following conditions hold:

- For any pair of integers $(i,j)$ , if $i$ and $j$ are coprime, $a_i \neq a_j$ .
- The maximal value of all $a_i$ should be minimized (that is, as small as possible).

A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is $1$ .

The only line contains the integer $n$ ( $2 \le n \le 10^5$ ).

Print $n-1$ integers, $a_2$ , $a_3$ , $\ldots$ , $a_n$ ( $1 \leq a_i \leq n$ ).

If there are multiple solutions, print any of them.

In the first example, notice that $3$ and $4$ are coprime, so $a_3 \neq a_4$ . Also, notice that $a=[1,2,3]$ satisfies the first condition, but it's not a correct answer because its maximal value is $3$ .