*This kata is based on [Project Euler Problem #349](https://projecteuler.net/problem=349). You may want to start with solving [this kata](https://www.codewars.com/kata/langtons-ant) first.*

---

[Langton's ant](https://en.wikipedia.org/wiki/Langton%27s_ant) moves on a regular grid of squares that are coloured either black or white.
The ant is always oriented in one of the cardinal directions (left, right, up or down) and moves  according to the following rules:
- if it is on a black square, it flips the colour of the square to white, rotates 90 degrees counterclockwise and moves forward one square.
- if it is on a white square, it flips the colour of the square to black, rotates 90 degrees clockwise and moves forward one square.

Starting with a grid that is **entirely white**, how many squares are black after `n` moves of the ant?

**Note:** `n` will go as high as 10^(20)

---

## My other katas

If you enjoyed this kata then please try [my other katas](https://www.codewars.com/collections/katas-created-by-anter69)! :-)

#### *Translations are welcome!*

```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 langtons_ant(n):\n    grid = [[0]]\n    column = 0\n    row = 0\n    direction = 0\n    move = {\n        0: (-1, 0),\n        1: ( 0, 1),\n        2: ( 1, 0),\n        3: ( 0,-1),\n        }\n    rows = len(grid)\n    cols = len(grid[0])\n    ap = (row, column)\n    dir = direction\n    n_black = 0\n    \n    max_simple_range = 11000\n    n_black_highway_ref = []\n    ref = 0\n    \n    for i in range(1, n + 1):        \n        if (grid[ap[0]][ap[1]]) == 1:\n            grid[ap[0]][ap[1]] = 0\n            dir = (dir + 1) % 4\n            n_black -= 1\n        else:\n            grid[ap[0]][ap[1]] = 1\n            dir = (dir - 1) % 4\n            n_black += 1\n        ap = (ap[0] + move[dir][0], ap[1] + move[dir][1])\n        \n        if ap[0] >= rows:\n            grid = grid + ([[0]*cols])\n            rows += 1\n        elif ap[0] < 0:\n            grid = ([[0]*cols]) + grid\n            rows += 1\n            ap = (0, ap[1])\n            \n        if ap[1] >= cols:\n            for j, r in enumerate(grid):\n                grid[j] = r + [0]\n            cols += 1\n        elif ap[1] < 0:\n            for j, r in enumerate(grid):\n                grid[j] = [0] + r\n            cols += 1\n            \n            ap = (ap[0], 0)\n            \n        if i >= max_simple_range:\n            if i == max_simple_range:\n                ref = n_black\n            n_black_highway_ref.append(n_black - ref)\n            \n            if i == (max_simple_range + 104):\n                break\n    \n    if n > (max_simple_range + 104):\n        n_black += (n_black_highway_ref[-1] * (((n - max_simple_range) // 104) - 1))        \n        n_black += (n_black_highway_ref[((n - max_simple_range) % 104)]) \n    return n_black'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'langtons_ant'
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: 6458