For a given two numbers your mission is to derive a function that evaluates whether two given numbers are **abundant**, **deficient** or **perfect** and whether together they are **amicable**.



### Abundant Numbers
An abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself.

The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16 (> 12).

### Deficient Numbers
A deficient number is a number for which the sum of its proper divisors is less than the number itself.

The first few deficient numbers are: 1, 2, 3, 4, 5, 7, 8, 9.

### Perfect Numbers
A perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself. 

The first perfect number is 6, because 1, 2, and 3 are its proper positive divisors, and 1 + 2 + 3 = 6.

### Amicable Numbers
Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number. (A proper divisor of a number is a positive factor of that number other than the number itself. For example, the proper divisors of 6 are 1, 2, and 3.)

For example, the smallest pair of amicable numbers is (220, 284); for the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.

### The Function

For a given two numbers, derive function `deficientlyAbundantAmicableNumbers(num1, num2)` which returns a string with first and second word either abundant or deficient depending on whether `num1` or `num2` are abundant, deficient or perfect. The string should finish with either amicable or not amicable depending on the relationship between `num1` and `num2`.

e.g. `deficientlyAbundantAmicableNumbers(220, 284)` returns `"abundant deficient amicable"` as 220 is an abundant number, 284 is a deficient number and amicable because 220 and 284 are an amicable number pair. 





See Part 1 - [Excessively Abundant Numbers](http://www.codewars.com/kata/56a75b91688b49ad94000015)

See Part 2 - [The Most Amicable of Numbers](http://www.codewars.com/kata/56b5ebaa26fd54188b000018)

```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 sum_of_divisors(number):\n    divisors = [1]\n    i = 2\n    while i < number//i:\n        if not number%i:\n            divisors.append(i)\n            divisors.append(number//i)\n        i += 1\n    if i**2==number: divisors.append(i)\n    return sum(divisors)\n\ndef is_perfect(number):\n    return number == sum_of_divisors(number)\n\ndef is_amicable(number_1, number_2):\n    return number_2 == sum_of_divisors(number_1)\n    \ndef deficiently_abundant_amicable_numbers(n1,n2):\n    perfect_1 = "perfect" if is_perfect(n1) else False\n    if not perfect_1: perfect_1 = "abundant" if n1 < sum_of_divisors(n1) else "deficient"\n    perfect_2 = "perfect" if is_perfect(n2) else False\n    if not perfect_2: perfect_2 = "abundant" if n2 < sum_of_divisors(n2) else "deficient"\n    amicable = "amicable" if is_amicable(n1,n2) and not (is_perfect(n1) and is_perfect(n2)) else "not amicable"\n    return perfect_1 + " " + perfect_2 + " " + amicable\n\nprint(deficiently_abundant_amicable_numbers(4,6))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'deficiently_abundant_amicable_numbers'
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: 6002