A1. Product of Triples (Easy Version)
time limit per test
15 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Many great mathematicians have sequences named after them. Timmy is a great mathematician, so he created a sequence called $$$t$$$, but he needs help to compute its values. Let $$$t_i$$$ be the number of unordered triples $$$(a, b, c)$$$ where $$$a \leq b \leq c$$$ and $$$a \cdot b \cdot c = i$$$. For all $$$i$$$ from $$$1$$$ to $$$n$$$, find and print $$$t_i$$$.

Please see the announcement to see how to abuse these constraints.

If you're using Python, please submit as PyPy rather than Python itself.

Input

The only line contains a single integer $$$n$$$ $$$(1 \leq n \leq 2 \cdot 10^3)$$$.

Output

For all $$$i$$$ from $$$1$$$ to $$$n$$$, print $$$t_i$$$.

Example
Input
10
Output
1
1
1
2
1
2
1
3
2
2
Note

There are $$$3$$$ triples that have product $$$8$$$: $$$(1, 1, 8)$$$, $$$(1, 2, 4)$$$, and $$$(2, 2, 2)$$$. However, there is only $$$1$$$ triple that has product $$$7$$$: $$$(1, 1, 7)$$$.