Given the number n, return a string which shows the minimum number of moves to complete the tower of Hanoi consisting of n layers.
Tower of Hanoi : https://en.wikipedia.org/wiki/Tower_of_Hanoi

Example - 2 layered Tower of Hanoi 

Input: n=2

Start
[[2, 1], [], []]

Goal
[[], [], [2, 1]]

Expected Output : '[[2, 1], [], []]\n[[2], [1], []]\n[[], [1], [2]]\n[[], [], [2, 1]]'

```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 Hanoi_Solution(n):\n    # Establish base cases\n    if n == 0:\n        return([[],[],[]])\n    if n == 1:\n        return([[[1],[],[]],[[],[],[1]]])\n    # Setup recursion\n    else:\n        L = len(Hanoi_Solution(n-1))\n        # Move from [[n,..,1],[],[]] to [n,[n-1,...,1],[]] \n        first_half = Hanoi_Solution(n-1)    \n        for i in range(L):\n            # Insert the new number at the beginning in the previous solution\n            first_half[i][0].insert(0,n)\n            # Switch the last two positions in each move\n            temp_1 = first_half[i][2]\n            first_half[i][2] = first_half[i][1]\n            first_half[i][1] = temp_1\n        # Move from [[],[n-1,...,1],[n]] to [[],[],[n,...,1]]\n        second_half = Hanoi_Solution(n-1)\n        for i in range(L):\n            # Insert the new number at the end in the previous solution\n            second_half[i][2].insert(0,n)\n            # Switch the first two positions in each move\n            temp_2 = second_half[i][1]\n            second_half[i][1] = second_half[i][0]\n            second_half[i][0] = temp_2\n        # Join the two halves into a single solution of length 2**n\n        for i in second_half:\n            first_half.append(i)\n        return(first_half)\n\n# Print the solution in the string format suggested\ndef hanoiArray(n):\n    return((''.join(str(i)+'\\n' for i in Hanoi_Solution(n)))[:-1])"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'hanoiArray'
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: 8207