To give credit where credit is due: This problem was taken from the ACMICPC-Northwest Regional Programming Contest. Thank you problem writers.

You are helping an archaeologist decipher some runes. He knows that this ancient society used a Base 10 system, and that they never start a number with a leading zero. He's figured out most of the digits as well as a few operators, but he needs your help to figure out the rest.

The professor will give you a simple math expression, of the form

```
[number][op][number]=[number]
```

He has converted all of the runes he knows into digits. The only operators he knows are addition (`+`),subtraction(`-`), and multiplication (`*`), so those are the only ones that will appear. Each number will be in the range from -1000000 to 1000000, and will consist of only the digits 0-9, possibly a leading -, and maybe a few ?s. If there are ?s in an expression, they represent a digit rune that the professor doesn't know (never an operator, and never a leading -). All of the ?s in an expression will represent the same digit (0-9), and it won't be one of the other given digits in the expression. No number will begin with a 0 unless the number itself is  0, therefore 00 would not be a valid number. 

Given an expression, figure out the value of the rune represented by the question mark. If more than one digit works, give the lowest one. If no digit works, well, that's bad news for the professor - it means that he's got some of his runes wrong. output -1 in that case.

Complete the method to solve the expression to find the value of the unknown rune. The method takes a string as a paramater repressenting the expression and will return an int value representing the unknown rune or -1 if no such rune exists.

~~~if:php
**Most of the time, the professor will be able to figure out most of the runes himself, but sometimes, there may be exactly 1 rune present in the expression that the professor cannot figure out (resulting in all question marks where the digits are in the expression) so be careful ;)**
~~~

```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 solve_runes(runes):\n    massV = []                \n    massV_ind = []\n    massD1 = []\n    massD2 = []                # more lists to the god of lists!!!!!!!!!!!\n    massD1_ind = []\n    massD2_ind = []\n    ex = []\n    mat = []\n\n    expr, value = runes.split(\'=\')\n\n    if expr.find(\'*\',1) != -1:\n        ind = expr.index(\'*\',1)\n        dig_1 = expr[:ind]\n        dig_2 = expr[ind+1:]\n        sign = \'*\'\n    elif expr.find(\'+\',1) != -1:\n        ind = expr.index(\'+\',1)\n        dig_1 = expr[:ind]\n        dig_2 = expr[ind+1:]\n        sign = \'+\'\n    else:\n        ind = expr.index(\'-\',1)\n        dig_1 = expr[:ind]\n        dig_2 = expr[ind+1:]\n        sign = \'-\'\n\n\n\n    for i in range(len(value)):\n        if value[i] == "?":\n            massV_ind.append(value.index(value[i],i))\n            massV.append(\'0\')\n        else:\n            massV.append(value[i])\n\n    for i in range(len(dig_1)):\n        if dig_1[i] == "?":\n            massD1_ind.append(dig_1.index(dig_1[i],i))\n            massD1.append(\'0\')\n        else:\n            massD1.append(dig_1[i])\n    \n    for i in range(len(dig_2)):\n        if dig_2[i] == "?":\n            massD2_ind.append(dig_2.index(dig_2[i],i))\n            massD2.append(\'0\')\n        else:\n            massD2.append(dig_2[i])\n\n    for i in range(0,10):\n        for q in range(len(massD1_ind)):\n            massD1[massD1_ind[q]] = str(i)\n        for w in range(len(massD2_ind)):\n            massD2[massD2_ind[w]] = str(i)\n        for e in range(len(massV_ind)):\n            massV[massV_ind[e]] = str(i)\n\n        d1 = int(\'\'.join(massD1))\n        d2 = int(\'\'.join(massD2))\n        val = int(\'\'.join(massV))\n\n        if sign == \'*\':\n            if d1 * d2 == val:\n                ex.append(i)\n\n        if sign == \'-\':\n            if d1 - d2 == val:\n                ex.append(i)\n\n        if sign == \'+\':\n            if d1 + d2 == val:\n                ex.append(i)\n\n                                                # hate\n    if dig_1[0] == \'-\':\n        if 1 in massD1_ind:\n            if len(massD1)>1:                 \n                if 0 in ex:\n                    ex.remove(0)\n    else:\n        if 0 in massD1_ind:\n            if len(massD1)>1:\n                if 0 in ex:\n                    ex.remove(0)\n                                                # minuses                    \n    if dig_2[0] == \'-\':\n        if 1 in massD2_ind:\n            if len(massD2)>1:               \n                if 0 in ex:\n                    ex.remove(0)\n    else:\n        if 0 in massD2_ind:\n            if len(massD2)>1:\n                if 0 in ex:\n                    ex.remove(0)\n\n    if value[0] == \'-\':\n        if 1 in massV_ind:\n            if len(massV)>1:\n                if 0 in ex:\n                    ex.remove(0)\n    else:\n        if 0 in massV_ind:\n            if len(massV)>1:\n                if 0 in ex:\n                    ex.remove(0)\n\n\n    for i in runes:\n        if i in \'1234567890\':\n            mat.append(int(i))\n    mat = set(mat)\n\n    if len(ex) == 0:\n        return -1\n    else:\n        for i in ex:\n            if i in mat:\n                continue\n            else:                         # rofl-master\n                return i                  # 3 hours\n    return -1                             # ------   o,o   -------    -_-'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'solve_runes'
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: 9626