# Task
 A robot is standing at the `(0, 0)` point of the Cartesian plane and is oriented towards the vertical (y) axis in the direction of increasing y values (in other words, he's facing up, or north). The robot executes several commands each of which is a single positive integer. When the robot is given a positive integer K it moves K squares forward and then turns 90 degrees clockwise.

 The commands are such that both of the robot's coordinates stay non-negative.

 Your task is to determine if there is a square that the robot visits at least twice after executing all the commands.

# Example

 For `a = [4, 4, 3, 2, 2, 3]`, the output should be `true`.

 The path of the robot looks like this:

 ![](https://codefightsuserpics.s3.amazonaws.com/tasks/robotWalk/img/path.png?_tm=1486563151922)

 The point `(4, 3)` is visited twice, so the answer is `true`.

# Input/Output


 - `[input]` integer array a

  An array of positive integers, each number representing a command.

  Constraints:
  
  `3 ≤ a.length ≤ 100`
  
  `1 ≤ a[i] ≤ 10000`


 - `[output]` a boolean value

  `true` if there is a square that the robot visits at least twice, `false` otherwise.

```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 = 'from math import gcd\nfrom functools import reduce\nfrom itertools import cycle\n\ndef robot_walk(a):\n    g = reduce(gcd, a)\n    a = [x//g for x in a]\n    it = cycle([1j, 1, -1j, -1])\n    seen = {0}\n    pos = 0\n    for x in a:\n        d = next(it)\n        for i in range(x):\n            pos += d\n            if pos in seen:\n                return True\n            seen.add(pos)\n    return False'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'robot_walk'
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: 6792