You will be given an array of positive integers. The array should be sorted by the amount of distinct perfect squares and reversed, that can be generated from each number permuting its digits.

E.g.: ```arr = [715, 112, 136, 169, 144]``` 
``` 
Number   Perfect Squares w/ its Digits   Amount
 715                -                       0
 112               121                      1
 136               361                      1
 169           169, 196, 961                3
 144             144, 441                   2
``` 
So the output will have the following order:
```[169, 144, 112, 136, 715]``` 

When we have two or more numbers with the same amount of perfect squares in their permutations, we sorted by their values.

In the example given above, we can see that 112 and 136 both generate a perfect square. So 112 comes first.

Examples for this kata:
```python
sort_by_perfsq([715, 112, 136, 169, 144]) == [169, 144, 112, 136, 715]
# number of perfect squares:                   3    2    1    1    0
``` 
We may have in the array numbers that belongs to the same set of permutations.
```python
sort_by_perfsq([234, 61, 16, 441, 144, 728]) == [144, 441, 16, 61, 234, 728]
# number of perfect squares:                      2    2    1   0   0    0
```

Features of the random tests:
~~~if:ruby,python
- Number of tests: 80
- Arrays between 4 and 20 elements
- Integers having from 1 to 7 digits included
~~~
~~~if:js
- Number of tests: 30
- Arrays between 4 and 16 elements
- Integers having from 1 to 7 digits included
~~~

Enjoy it!!

```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 collections import defaultdict\nSQUARES = [x**2 for x in range(1, 3163)]\nDIGITS  = defaultdict(int)\nfor sqr in SQUARES:\n    DIGITS[''.join(sorted(str(sqr)))] += 1\n\ndef sort_by_perfsq(arr):\n    return sorted(arr, key=lambda n: (-DIGITS[''.join(sorted(str(n)))], n))"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'sort_by_perfsq'
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: 5802