A number is simply made up of digits.  
The number 1256 is made up of the digits 1, 2, 5, and 6.  
For 1256 there are 24 distinct permutations of the digits:  
1256, 1265, 1625, 1652, 1562, 1526, 2156, 2165, 2615, 2651, 2561, 2516,   
5126, 5162, 5216, 5261, 5621, 5612, 6125, 6152, 6251, 6215, 6521, 6512.
  
Your goal is to write a program that takes a number, n, and returns the average value of all distinct permutations of the digits in n.  Your answer should be rounded to the nearest integer. For the example above the return value would be 3889. * 
  
  n will never be negative
  
A few examples:
```python
permutation_average(2)
return 2

permutation_average(25)
>>> 25 + 52 = 77
>>> 77 / 2 = 38.5
return 39 *

permutation_average(20)
>>> 20 + 02 = 22
>>> 22 / 2 = 11
return 11

permutation_average(737)
>>> 737 + 377 + 773 = 1887
>>> 1887 / 3 = 629
return 629

```

Note: Your program should be able to handle numbers up to 6 digits long
~~~if:python
\* Python version 3 and above uses Banker Rounding so the expected values for those tests would be 3888 and 38 respectively
~~~
~~~if-not:python
\* ignore these marks, they're for Python only
~~~

```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 permutation_average(n):\n    digits = [int(i) for i in str(n)]\n    length = len(str(n))\n    \n    def factorial(n): \n        if n is 1 or n is 0:\n            return 1\n        else:\n            return n * factorial(n-1)\n\n    averager = factorial(length) #denominator of the average\n\n    def get_coefficient(width): #after adding up all the digits, a pattern is seen dependent on\n        coefficient = 0  #the number of digits there are. This exploits that\n        if width <= 1:\n            coefficient = 1\n        else:\n            for x in range(width):\n                coefficient += factorial(width-1)*(10**x)\n\n        return coefficient\n\n    total = 0\n    for index in digits:  #just multiplying the same coefficient (ironically enough) with every digit\n        multiplier = get_coefficient(length)\n        total += multiplier * index\n\n    average = total/float(averager)\n    avg = int(round(average, 0))\n    return avg'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'permutation_average'
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: 6112