C. Ehab and a Special Coloring Problemtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou'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 if their greatest common divisor is 1.InputThe only line contains the integer n (2 \le n \le 10^5).OutputPrint 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.ExamplesInput
4
Output
1 2 1 Input
3
Output
2 1NoteIn 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.
4

1 2 1 
['constructive algorithms', 'number theory', '*1300']