A robot on an infinite grid starts at point (0, 0) and faces north.  The robot can receive one of three possible types of commands:

-2: turn left 90 degrees
-1: turn right 90 degrees
1 <= x <= 9: move forward x units

Some of the grid squares are obstacles. 
The i-th obstacle is at grid point (obstacles[i][0], obstacles[i][1])
If the robot would try to move onto them, the robot stays on the previous grid square instead (but still continues following the rest of the route.)
Return the square of the maximum Euclidean distance that the robot will be from the origin.
 
Example 1:
Input: commands = [4,-1,3], obstacles = []
Output: 25
Explanation: robot will go to (3, 4)


Example 2:
Input: commands = [4,-1,4,-2,4], obstacles = [[2,4]]
Output: 65
Explanation: robot will be stuck at (1, 4) before turning left and going to (1, 8)


 
Note:

0 <= commands.length <= 10000
0 <= obstacles.length <= 10000
-30000 <= obstacle[i][0] <= 30000
-30000 <= obstacle[i][1] <= 30000
The answer is guaranteed to be less than 2 ^ 31.

```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 robotSim(self, commands: List[int], obstacles: List[List[int]]) -> int:\n        x, y = 0, 0   #current position of robot\n        dx, dy = 0, 1   #direction of robot\n        obs = {tuple(i) for i in obstacles}   #create set of obstacles for faster access\n        maxdist = 0   #store max distance after each command\n        \n        for step in commands:\n            if 0 < step < 10:\n                for i in range(step):\n                    x, y = x+dx, y+dy   #take each step individually\n                    if (x,y) in obs:   #take one step back if on an obstacle\n                        x, y = x-dx, y-dy\n                        break\n            elif step == -2:   #change direction | move left\n                dx, dy = -dy, dx\n            elif step == -1:   #change direction | move right\n                dx, dy = dy, -dx\n            \n            maxdist = max(maxdist, x**2 + y**2)\n        \n        return maxdist'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'robotSim'
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: 5646