On an infinite plane, a robot initially stands at (0, 0) and faces north.  The robot can receive one of three instructions:

"G": go straight 1 unit;
"L": turn 90 degrees to the left;
"R": turn 90 degress to the right.

The robot performs the instructions given in order, and repeats them forever.
Return true if and only if there exists a circle in the plane such that the robot never leaves the circle.
 
Example 1:
Input: "GGLLGG"
Output: true
Explanation: 
The robot moves from (0,0) to (0,2), turns 180 degrees, and then returns to (0,0).
When repeating these instructions, the robot remains in the circle of radius 2 centered at the origin.

Example 2:
Input: "GG"
Output: false
Explanation: 
The robot moves north indefinitely.

Example 3:
Input: "GL"
Output: true
Explanation: 
The robot moves from (0, 0) -> (0, 1) -> (-1, 1) -> (-1, 0) -> (0, 0) -> ...

 
Note:

1 <= instructions.length <= 100
instructions[i] is in {'G', 'L', 'R'}

```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 isRobotBounded(self, instructions: str) -> bool:\n      # loop through all the commands in the arr\n      # scenario the direction is not facing the same\n\n        def is_infinite_loop(command):\n            # iterate over all the commands \n            # direction 0: NameError\n            # x and y coordinates, if x and 0 is (0, 0) return True\n            direction = [(0, 1), (1, 0), (0, -1), (-1, 0)]\n            d_index = 0\n            x, y = 0, 0\n            for move in command:\n                if move == 'G':\n                    x += direction[d_index][0]\n                    y += direction[d_index][1]\n                elif move == 'R':\n                    d_index = (d_index + 1) % 4\n                elif move == 'L':\n                    d_index = (d_index + 3) % 4\n            # if back at origin\n            # print(d_index)\n            if x == y == 0:\n                return True\n            if (x != 0 or y != 0) and d_index != 0:\n                return True\n            return False\n\n        return is_infinite_loop(instructions)\n\n# class Solution:\n#     def isRobotBounded(self, instructions: str) -> bool:\n#         L_occurances = instructions.count('L')\n#         R_occurances = instructions.count('R')\n#         difference = L_occurances - R_occurances\n        \n#         if difference % 4 == 0:\n#             # check if loop otherwise return False too\n#             directions = [(0, 1), (1, 0), (0, -1), (-1, 0)] # N, E, S, W\n#             d = 0                                           # start at North index\n#             point = [0, 0]\n#             for instruction in instructions:\n#                 if instruction == 'G':\n#                     point[0] += directions[d][0]\n#                     point[1] += directions[d][1]\n#                 elif instruction == 'L':\n#                     d = (d + 3) % 4\n#                 elif instruction == 'R':\n#                     d = (d + 1) % 4\n#             return True if point == [0, 0] else False\n#         else:\n#             return True\n        \n        \n#         # return True if L_occurances - R_occurances != 0 else False\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'isRobotBounded'
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: 5544