Alice and Bob take turns playing a game, with Alice starting first.
Initially, there is a number N on the chalkboard.  On each player's turn, that player makes a move consisting of:

Choosing any x with 0 < x < N and N % x == 0.
Replacing the number N on the chalkboard with N - x.

Also, if a player cannot make a move, they lose the game.
Return True if and only if Alice wins the game, assuming both players play optimally.
 



Example 1:
Input: 2
Output: true
Explanation: Alice chooses 1, and Bob has no more moves.


Example 2:
Input: 3
Output: false
Explanation: Alice chooses 1, Bob chooses 1, and Alice has no more moves.

 
Note:

1 <= N <= 1000

```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 divisorGame(self, N: int) -> bool:\n        \n        def divisors(N):\n            if N == 1:\n                return [1]\n            \n            res = []\n            for n in range(1, int(N**0.5)+1):\n                if N % n == 0:\n                    res.append(n)\n            return res\n        \n        # Initial conditions\n        table = {\n            1 : False,\n            2 : True,\n            3 : False\n        }\n        \n        def compute(i):\n            if i in table:\n                return table[i]\n            \n            divs = divisors(i)\n            next_nums = [i-d for d in divs]\n            \n            for n in next_nums:\n                status = compute(n)\n                \n                if status == False:\n                    table[i] = True\n                    return True\n            table[i] = False\n            return False\n        \n        \n#         for n in range(3, N+1):\n#             divs = divisors(n)\n            \n#             for d in divs:\n#                 next_num = n - d\n#                 if table[next_num] == False:\n#                     # We want the next number to be a losing number\n#                     table[n] = True\n#                     break\n#             if n not in table:\n#                 # If all next numbers are winning, then this is a losing number\n#                 table[n] = False\n\n        return compute(N)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'divisorGame'
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: 6188