In this kata, we will check is an array is (hyper)rectangular.  
A rectangular array is an N-dimensional array with fixed sized within one dimension. Its sizes can be repsented like A1xA2xA3...xAN. That means a N-dimensional array has N sizes. The 'As' are the hyperrectangular properties of an array.

You should implement a functions that returns a N-tuple with the arrays hyperrectangular properties or None if the array is not hyperrectangular.
```
hyperrectangularity_properties(arr)
```
## Note
An empty array IS rectagular and has one dimension of length 0
```
hyperrectangularity_properties([]) == (0,)
```
## Example
```
1D array
hyperrectangularity_properties([1,2,3]) == (3,)

2D arrays  

hyperrectangularity_properties(
                                [[0,1,2],
                                 [3,4,5],           
                                 [6,7,8]] ) == (3,3)                              
hyperrectangularity_properties(
                                [[0,1,2],
                                 [3,4,5]] ) == (2,3)
hyperrectangularity_properties( 
                                [[0,1,2],
                                 [3,4]  ] ) == None
3D arrays  
hyperrectangularity_properties(  
                                [
                                 [ [0], [2] ],
                                 [ [0], [2] ],  
                                 [ [0], [2] ]
                                              ] ) == (3,2,1)    
hyperrectangularity_properties(  
                                [
                                   [[0],[2]],
                                   [[0],[2,2]],   
                                   [[0],[2]]
                                              ] )  ==  None 
hyperrectangularity_properties(
                                [[ [], [], [] ]]
                                                ) ==  (1,3,0) 
```
### Heterogeneous Arrays can appear too
```
hyperrectangularity_properties(      
                                [[0,1,2],
                                 3,   
                                 [[4],5,6]] ) ==  None
hyperrectangularity_properties(      
                                [1,
                                 [1,2],   
                                 [[3],[4,[5]],[6]]
                                                  ] ) ==  None
                                                  hyperrectangularity_properties(
                                [[ [], [] ], [] ]
                                                  ) ==  None
hyperrectangularity_properties(
                                [ 1, [], [2, [3]] ]
                                                  ) ==  None
```
The first property shows the length of the outer layer. The second of the layer one step deeper and so on. The function should handle higher dimensions too.


## Input
##### N-dimensional array of integers

## Expected Ouput
##### An N-tuple with the hyperrectangularity properties

```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 itertools import chain\n\ndef hyperrectangularity_properties(arr):\n    hr, arr = [], [arr]\n    while 1:\n        check = sum(isinstance(v, int) for v in arr)        # Check homogeneity\n        if check or not arr:                                # some int are present or empty array (edge case)\n            if check == len(arr): return tuple(hr)          # only int: found the bottom of the tree\n            break\n            \n        l = set(map(len,arr))\n        if len(l) > 1: break                                # invalid if different length found\n        hr.append(l.pop())\n        arr = list(chain.from_iterable(arr))                # get the "lower level"'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'hyperrectangularity_properties'
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: 6140