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        table = dict()\n        res  = self.helper(N, 0, table)\n        return res\n        \n        \n    def helper(self, N:int, numRds: int, ht: dict) -> bool:\n        soln = False\n        \n        # Bob wins base case\n        if N == 1 and numRds % 2 == 0: return False \n        \n        # Alice wins base case\n        if N == 1 and numRds % 2 != 0: return True\n        \n        # Check to see if the current N values has been processed\n        if ht.get(N, None) != None: \n            a = 5\n            return ht[N]\n        \n        # Obtain list of factors\n        fact = findFactors(N)\n        \n        # If not in the table process N against all of its factors\n        ht[N] = False        # Base case to ensure no false positives\n        for num in fact:\n            ht[N] = ht[N] or self.helper(N - num, numRds + 1, ht)\n            \n        return ht[N]\n        \n        \n        \ndef findFactors(num: int) -> list:\n    res = []\n    for val in range(1, num):\n        if num % val == 0: res.append(val)        \n    return res'
_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: 5972