#905 Divisor Chains

Statement

Statement language

Let $S(n)$ be the set of all positive divisors of a positive integer $n$ .

Define $f(n)$ as the number of nonempty subsets of $S(n)$ such that, for every two distinct elements $a,b$ in the subset, either $a$ divides $b$ or divides .

You are given a positive integer $N$ . Compute all values $f(1),f(2),\cdots,f(N)$ .

Input

The input is given in the following format:

$N$

Output

Print exactly $N$ lines.

The $n$ -th line must contain $f(n)$ , for $1\le n\le N$ .

Constraints

$1\le N\le 100\,000$ .

Subtasks

#	Score	Constraints
1	20	$N\le 20$ .
2	30	$N\le 2\,000$ .
3	50	No additional constraints.

Samples

Sample 1

Input

6

Output

Sample 2

Input

1

Output

1