When we attended middle school were asked to simplify mathematical expressions like "3x-yx+2xy-x" (or usually bigger), and that was easy-peasy ("2x+xy"). But tell that to your pc and we'll see! 

Write a function: `simplify`, that takes a string in input, representing a *multilinear non-constant polynomial in integers coefficients* (like `"3x-zx+2xy-x"`), and returns another string as output where the same expression has been simplified in the following way ( `->` means application of `simplify`):

- All possible sums and subtraction of equivalent monomials ("xy==yx") has been done, e.g.: `"cb+cba" -> "bc+abc"`, `"2xy-yx" -> "xy"`, `"-a+5ab+3a-c-2a" -> "-c+5ab"`

- All monomials appears in order of increasing number of variables, e.g.: `"-abc+3a+2ac" -> "3a+2ac-abc"`, `"xyz-xz" -> "-xz+xyz"`
 
- If two monomials have the same number of variables, they appears in lexicographic order, e.g.: `"a+ca-ab" -> "a-ab+ac"`, `"xzy+zby" ->"byz+xyz"`
  
- There is no leading `+` sign if the first coefficient is positive, e.g.: `"-y+x" -> "x-y"`, but no restrictions for `-`:  `"y-x" ->"-x+y"`

---

__N.B.__ to keep it simplest, the string in input is restricted to represent only *multilinear non-constant polynomials*, so you won't find something like `-3+yx^2'. **Multilinear** means in this context: **of degree 1 on each variable**.

**Warning**: the string in input can contain arbitrary variables represented by lowercase characters in the english alphabet.

__Good Work :)__

```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 simplify(poly):\n    # I\'m feeling verbose today\n    \n    # get 3 parts (even if non-existent) of each term: (+/-, coefficient, variables)\n    import re\n    matches = re.findall(r\'([+\\-]?)(\\d*)([a-z]+)\', poly)\n    \n    # get the int equivalent of coefficient (including sign) and the sorted variables (for later comparison)\n    expanded = [[int(i[0] + (i[1] if i[1] != "" else "1")), \'\'.join(sorted(i[2]))] for i in matches]\n    \n    # get the unique variables from above list. Sort them first by length, then alphabetically\n    variables = sorted(list(set(i[1] for i in expanded)), key=lambda x: (len(x), x))\n    \n    # get the sum of coefficients (located in expanded) for each variable\n    coefficients = {v:sum(i[0] for i in expanded if i[1] == v) for v in variables}\n    \n    # clean-up: join them with + signs, remove \'1\' coefficients, and change \'+-\' to \'-\'\n    return \'+\'.join(str(coefficients[v]) + v for v in variables if coefficients[v] != 0).replace(\'1\',\'\').replace(\'+-\',\'-\')'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'simplify'
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: 42027