TwoTurtledoves | Topcoder Archive

Problem Statement

I give my true love presents every day. On day 1, I give her one Type 1 present. On day 2, I give her two Type 2 presents, followed by one Type 1 present. On day 3, I give her three Type 3 presents, followed by two Type 2 presents, followed by one Type 1 present. This pattern continues day after day. Soon I begin to wonder, what type of present will be the 100th present that I give my true love? The 1000th? The 1000000th?

For example, the 10th present that I give my true love is the Type 1 present on day 3.

Write a method that takes an int n and returns the type of the nth present that I give my true love. Note that n is one-based, so n=1 refers to the very first present I give her (the Type 1 present on day 1).

Definition

Class:: TwoTurtledoves
Method:: presentType
Parameters:: int
Returns:: int
Method signature:: int presentType(int n)
(be sure your method is public)

Notes

Unlike the poseur in the popular Christmas song, I do not stop giving my true love presents after the 12th day.

Constraints

n is between 1 and 1000000000, inclusive.

Examples

```
10
```
```
Returns: 1
```
The example above.
```
12
```
```
Returns: 4
```
The second of four Type 4 presents on Day 4.
```
399
```
```
Returns: 11
```
```
123456
```
```
Returns: 65
```
```
1000000000
```
```
Returns: 1704
```

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