As a member of the editorial board of the prestigous scientific Journal _Proceedings of the National Academy of Sciences_, you've decided to go back and review how well old articles you've published stand up to modern publication best practices. Specifically, you'd like to re-evaluate old findings in light of recent literature about ["researcher degrees of freedom"](http://journals.sagepub.com/doi/full/10.1177/0956797611417632).

You want to categorize all the old articles into three groups: "Fine", "Needs review" and "Pants on fire".

In order to categorize them you've enlisted an army of unpaid grad students to review and give you two data points from each study: (1) the p-value behind the paper's primary conclusions, and (2) the number of recommended author requirements to limit researcher degrees of freedom the authors satisfied:

    * Authors must decide the rule for terminating data collection before data collection begins and report this rule in the article.
    * Authors must collect at least 20 observations per cell or else provide a compelling cost-of-data-collection justification. 
    * Authors must list all variables collected in a study.
    * Authors must report all experimental conditions, including failed manipulations.
    * If observations are eliminated, authors must also report what the statistical results are if those observations are included.
    * If an analysis includes a covariate, authors must report the statistical results of the analysis without the covariate.
    
Your army of tenure-hungry grad students will give you the p-value as a float between `1.0` and `0.0` exclusive, and the number of author requirements satisfied as an integer from `0` through `6` inclusive.

You've decided to write a function, `categorize_study()` to automatically categorize each study based on these two inputs using the completely scientifically legitimate "bs-factor". The bs-factor for a particular paper is calculated as follows:

 * bs-factor when the authors satisfy all six requirements is 1
 * bs-factor when the authors satisfy only five requirements is 2
 * bs-factor when the authors satisfy only four requirements is 4
 * bs-factor when the authors satisfy only three requirements is 8...

Your function should multiply the p-value by the bs-factor and use that product to return one of the following strings:

 * product is less than 0.05: "Fine"
 * product is 0.05 to 0.15: "Needs review"
 * product is 0.15 or higher: "Pants on fire"
 
You've also decided that all studies meeting _none_ of the author requirements that would have been categorized as "Fine" should instead be categorized as "Needs review".

For example:

`categorize_study(0.01, 3)` should return `"Needs review"` because the p-value times the bs-factor is `0.08`.

`categorize_study(0.04, 6)` should return `"Fine"` because the p-value times the bs-factor is only `0.04`.

`categorize_study(0.0001, 0)` should return `"Needs review"` even though the p-value times the bs-factor is only `0.0064`.

`categorize_study(0.012, 0)` should return `"Pants on fire"` because the p-value times the bs-factor is `0.768`.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.