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`.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "def categorize_study(p_value, requirements):\n    p=p_value*2**(6-requirements)\n    return 'Fine' if p<0.05 and requirements>0 else 'Needs review' if p<0.15 else 'Pants on fire'"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'categorize_study'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5356