Rectangles can be constructed out of smaller squares. Given a supply of unit squares (1×1 in size), how many unique rectangles can be constructed?

The input file **DATA2.txt** will contain 5 lines, each an integer 1 ≤ `N` ≤ 1000 representing the number of unit squares available.

The output file **OUT2.txt** will contain 5 lines, each being the number of unique rectangles that can be constructed from *up to N* unit squares (not all squares have to be used for some of the rectangles).

*Note:* A rectangle is unique if another rectangle that had previously been constructed can’t be rotated to look the same way. That is, 2×3 and 3×2 are considered to be the same.

Sample Input (first 2 shown):

```
2
6
```

Sample Output (first 2 shown):

```
2
8
```