We have an array with string digits that occurrs more than once, for example, ```arr = ['1', '2', '2', '2', '3', '3']```. How many different string numbers can be generated taking the 6 elements at a time?

We present the list of them below in an unsorted way:
``` 
['223213', '312322', '223312', '222133', '312223', '223321', '223231', '132223', '132322', '223132', '322321', '322312', '231322', '222313', '221233', '213322', '122323', '321322', '221332', '133222', '123232', '323221', '222331', '132232', '321232', '212323', '232213', '232132', '331222', '232312', '332212', '213223', '123322', '322231', '321223', '231232', '233221', '231223', '213232', '312232', '233122', '322132', '223123', '322123', '232231', '323122', '323212', '122233', '212233', '123223', '332221', '122332', '221323', '332122', '232123', '212332', '232321', '322213', '233212', '313222']
``` 
There are ```60``` different numbers and ```122233``` is the lowest one and ```332221``` the highest of all of them.

Given an array, ```arr```, with string digits (from '0' to '9'), you should give the exact amount of different numbers that may be generated with the lowest and highest value but both converted into integer values, using all the digits given in the array for each generated string number.

The function will be called as ```proc_arr()```.
```python
proc_arr(['1', '2', '2', '3', '2', '3']) == [60, 122233, 332221]
```

If the digit '0' is present in the given array will produce string numbers with leading zeroes, that will not be not taken in account when they are converted to integers.
```python
proc_arr(['1','2','3','0','5','1','1','3']) == [3360, 1112335, 53321110]
```
You will never receive an array with only one digit repeated n times.

Features of the random tests:
```
Low performance tests:
Number of tests: 100
Arrays of length between 6 and 10

Higher performance tests:
Number of tests: 100
Arrays of length between 30 and 100
```

```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 = 'from functools import reduce\nfrom math import factorial as fac\nfrom operator import mul\n\ndef proc_arr(lst):\n    stg = "".join(sorted(lst))\n    p = fac(len(stg)) // reduce(mul, (fac(stg.count(d)) for d in set(stg)))\n    return [p, int(stg), int(stg[::-1])]'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'proc_arr'
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: 6281