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 parse_terms(string):\n    poly, add = [], ""\n    for i in string:\n        if i == "+" and len(add) != 0:\n            poly.append(add)\n            #poly.append("+")\n            add = ""\n        elif i == "-" and len(add) != 0:\n            poly.append(add)\n            #poly.append("+")\n            add = "-"\n        else: \n            add = add + i\n    poly.append(add)\n    return poly\n\n\ndef parse_coef(term):\n    numbers = "1234567890"\n    coef, end = "", 0\n    \n    if term == "+":\n        return False, 0, term\n    else:\n        for i in range(len(term)):\n            if term[i] in numbers+"-":\n                coef = coef + term[i]\n            else: \n                end = i\n                break\n        \n    if coef == "":\n        return True, 1, term\n    elif coef == "-":\n        return True, -1, term[1:]\n    else:\n        return True, int(coef), term[end:]\n    \n    \ndef simplify(poly):\n    print(poly)\n    if poly[0] == "+":\n        poly = poly.replace("+", "", 1)\n        print(poly)\n        \n    coeff = []\n    poly = parse_terms(poly)\n    print(poly)\n    \n    for i in range(len(poly)):\n        if_term, coef, term = parse_coef(poly[i])\n        if if_term:\n            coeff.append(coef)\n            poly[i] = "".join(sorted(term))\n            \n\n    for i in range(len(poly)-1):\n        for j in range(i+1, len(poly)):\n            if poly[i] == poly[j] and coeff[i] != 0:\n                coeff[i] = coeff[i] + coeff[j]\n                coeff[j] = 0\n            \n            \n    poly = [[poly[i], coeff[i], len(poly[i])] for i in range(len(poly))]\n    poly.sort(key= lambda poly: poly[0])    \n    poly.sort(key= lambda poly: poly[2])\n    print(poly)\n    \n    \n    for i in range(len(poly)):\n        if poly[i][1] == 1:\n            pass\n        elif poly[i][1] == -1:\n            poly[i][0] = "-" + poly[i][0]\n        elif poly[i][1] == 0:\n            poly[i][0] = ""            \n        else:\n            poly[i][0] = str(poly[i][1]) + poly[i][0]\n    \n    output = [i[0] for i in poly if i[0] != ""] \n    send = ""\n    for i in range(len(output) - 1):\n        if output[i+1][0] == "-":\n            send = send + output[i]\n        else: \n            send = send + output[i] + "+"\n    send = send + output[-1]\n    \n    print(send)\n    return send\n    \n'
_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: 8573