F. Kate and imperfectiontime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputKate has a set S of n integers \{1, \dots, n\} . She thinks that imperfection of a subset M \subseteq S is equal to the maximum of gcd(a, b) over all pairs (a, b) such that both a and b are in M and a \neq b. Kate is a very neat girl and for each k \in \{2, \dots, n\} she wants to find a subset that has the smallest imperfection among all subsets in S of size k. There can be more than one subset with the smallest imperfection and the same size, but you don't need to worry about it. Kate wants to find all the subsets herself, but she needs your help to find the smallest possible imperfection for each size k, will name it I_k. Please, help Kate to find I_2, I_3, ..., I_n.InputThe first and only line in the input consists of only one integer n (2\le n \le 5 \cdot 10^5)  — the size of the given set S.OutputOutput contains only one line that includes n - 1 integers: I_2, I_3, ..., I_n.ExamplesInput
2
Output
1 Input
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1 1 NoteFirst sample: answer is 1, because gcd(1, 2) = 1.Second sample: there are subsets of S with sizes 2, 3 with imperfection equal to 1. For example, \{2,3\} and \{1, 2, 3\}.
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1 
['greedy', 'implementation', 'math', 'number theory', 'sortings', 'two pointers', '*2200']