# Fourier transformations are hard. Fouriest transformations are harder.

This Kata is based on the SMBC Comic on fourier transformations.

A fourier transformation on a number is one that converts the number to a base in which it has more `4`s ( `10` in base `6` is `14`, which has `1` four as opposed to none, hence, fourier in base `6` ).

A number's fouriest transformation converts it to the base in which it has the most `4`s.  
For example: `35353` is the fouriest in base `6`: `431401`.

This kata requires you to create a method `fouriest` that takes a number and makes it the fouriest, telling us in which base this happened, as follows:

```python
fouriest(number) -> "{number} is the fouriest ({fouriest_representation}) in base {base}"
```

## Important notes

* For this kata we don't care about digits greater than `9` ( only `0` to `9` ), so we will represent all digits greater than `9` as `'x'`: `10` in base `11` is `'x'`, `119` in base `20` is `'5x'`, `118` in base `20` is also `'5x'`

* When a number has several fouriest representations, we want the one with the LOWEST base

```if:haskell,javascript
* Numbers below `9` will not be tested
```

```if:javascript
* A `BigNumber` library has been provided; documentation is [here](https://mikemcl.github.io/bignumber.js/)
```

## Examples

```python
"30 is the fouriest (42) in base 7"
"15 is the fouriest (14) in base 11"
```

```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 fouriest(i):\n    highscore = 0\n    winner = 5\n    for base in range(5, i-3, 1):\n        fours = 0\n        n = i\n        while n > 0:\n            if n % base == 4:\n                fours += 1\n            n //= base\n        if fours > highscore:\n            highscore = fours\n            winner = base\n        elif 4*base**(highscore) > i:\n            break\n    n = i\n    result = ""\n    while n > 0:\n        result = str(n % winner) + result if n % winner < 10 else "x" + result\n        n //= winner\n    return "{} is the fouriest ({}) in base {}".format(i, result, winner)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'fouriest'
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: 5740