Coding decimal numbers with factorials is a way of writing out numbers 
in a base system that depends on factorials, rather than powers of numbers.

In this system, the last digit is always `0` and is in base 0!. The digit before that is either `0 or 1` and is in base 1!.  The digit before that is either `0, 1, or 2` and is in base 2!, etc.
More generally, the nth-to-last digit is always `0, 1, 2, ..., n` and is in base n!.

Read more about it at: http://en.wikipedia.org/wiki/Factorial_number_system


## Example

The decimal number `463` is encoded as `"341010"`, because:

463 = 3×5! + 4×4! + 1×3! + 0×2! + 1×1! + 0×0!


If we are limited to digits `0..9`, the biggest number we can encode is 10!-1 (= 3628799). So we extend `0..9` with letters `A..Z`. With these 36 digits we can now encode numbers up to 36!-1 (= 3.72 × 10^(41))


## Task

We will need two functions. The first one will receive a decimal number and return a string with the factorial representation.

~~~if:java
**Note:** the input number is at most a long.
~~~

The second one will receive a string with a factorial representation and produce the decimal representation.

Given numbers will always be positive.

```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 = "base='0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'\nfact = lambda n: fact(n-1)*n if n else 1\n\ndef dec2FactString(nb, i=1):\n    return dec2FactString(nb//i,i+1) + base[nb%i] if nb else ''\n\ndef factString2Dec(string):\n    return fact(len(string)-1)*base.index(string[0]) + factString2Dec(string[1:]) if len(string) else 0\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'dec2FactString'
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: 5892