Codeforces Round 632 (Div. 2) |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

greedy

implementation

math

number theory

sortings

two pointers

*2200

No tag edit access

The problem statement has recently been changed. View the changes.

×
F. Kate and imperfection

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard 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 $$$I_2$$$, $$$I_3$$$, ..., $$$I_n$$$.

Input

The 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 $$$S$$$.

Output

Output contains only one line that includes $$$n - 1$$$ integers: $$$I_2$$$, $$$I_3$$$, ..., $$$I_n$$$.

Examples

Input

2

Output

1

Input

3

Output

1 1

Note

First 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 $$$\{1, 2, 3\}$$$.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jun/24/2024 10:14:29 (i2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|