Given a string s of '(' , ')' and lowercase English characters. 
Your task is to remove the minimum number of parentheses ( '(' or ')', in any positions ) so that the resulting parentheses string is valid and return any valid string.
Formally, a parentheses string is valid if and only if:

It is the empty string, contains only lowercase characters, or
It can be written as AB (A concatenated with B), where A and B are valid strings, or
It can be written as (A), where A is a valid string.

 
Example 1:
Input: s = "lee(t(c)o)de)"
Output: "lee(t(c)o)de"
Explanation: "lee(t(co)de)" , "lee(t(c)ode)" would also be accepted.

Example 2:
Input: s = "a)b(c)d"
Output: "ab(c)d"

Example 3:
Input: s = "))(("
Output: ""
Explanation: An empty string is also valid.

Example 4:
Input: s = "(a(b(c)d)"
Output: "a(b(c)d)"

 
Constraints:

1 <= s.length <= 10^5
s[i] is one of  '(' , ')' and lowercase English letters.

```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 = "class Solution:\n    def minRemoveToMakeValid(self, s: str) -> str:\n        # ())()\n        # (()\n        # (()()\n        # ()(()\n        \n        # Strategy: If sum over string at any point is negative, remove close paren immediately\n        #           Keep track of open parens in string. If sum returns to 0, forget parens and restart, since this is valid so far.\n        #           At the end remove (sum of string) parens from beginning.\n        \n        # s = lee(t(c)o)de)\n        # total = 0\n        # new_s = \n        # recent_opens = []\n        \n        total = 0\n        new_s = ''\n        recent_opens = []  # List of indices in new_s of open parens\n        for char in s:\n            if char == '(':\n                total += 1\n                new_s = ''.join((new_s, char))\n\n                recent_opens.append(len(new_s) - 1)\n            elif char == ')':\n                total -= 1\n\n                if total >= 0:\n                    new_s = ''.join((new_s, char))\n                    recent_opens.pop()\n                    \n                else:\n                    total = 0\n                    \n            else:\n                new_s = ''.join((new_s, char))     \n\n        # Remove extra open parens, if any\n        if total > 0:\n            for count, index in enumerate(recent_opens):\n                total -= 1\n                \n                new_s = ''.join((new_s[:index - count], new_s[index - count + 1:]))\n                \n                if total <= 0:\n                    break\n                    \n        return new_s"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'minRemoveToMakeValid'
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: 5845