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 $a <= b <= c$ and $a dot.op b dot.op c = i$. 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.*
The only line contains a single integer $n$ $(1 <= n <= 2 dot.op 10^3)$.
For all $i$ from $1$ to $n$, print $t_i$.
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 $7$: $(1, 1, 7)$.
## Input
The only line contains a single integer $n$ $(1 <= n <= 2 dot.op 10^3)$.
## Output
For all $i$ from $1$ to $n$, print $t_i$.
[samples]
## 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 $7$: $(1, 1, 7)$.
**Definitions**
Let $ n \in \mathbb{Z} $ with $ 1 \leq n \leq 2 \cdot 10^3 $.
For each $ i \in \{1, 2, \dots, n\} $, define $ t_i $ as the number of unordered triples $ (a, b, c) \in \mathbb{Z}^3 $ such that:
- $ 1 \leq a \leq b \leq c $,
- $ a \cdot b \cdot c = i $.
**Objective**
Compute and output $ t_i $ for all $ i = 1, 2, \dots, n $.