308248: CF1488G. Painting Numbers

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

G. Painting Numberstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard output

You are given $n$ integers, each integer is from $1$ to $n$, all of them are pairwise distinct. You have to paint them red and blue (each integer should have exactly one color).

The cost of painting is the number of pairs $(x, y)$ such that $y \bmod x = 0$, $y$ is red and $x$ is blue.

For each $k \in [1, n]$, calculate the maximum cost of painting if exactly $k$ integers should have a red color.

Input

The first line contains one integer $n$ ($2 \le n \le 10^5$).

Output

For each $k \in [1,n]$ print one integer — the maximum cost of painting, if exactly $k$ integers should be red.

ExamplesInput
6
Output
3 5 6 6 5 0
Input
2
Output
1 0
Input
11
Output
3 6 9 11 12 13 14 14 13 10 0

Input

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