You have 4 cards each containing a number from 1 to 9.  You need to judge whether they could operated through *, /, +, -, (, ) to get the value of 24.


Example 1:

Input: [4, 1, 8, 7]
Output: True
Explanation: (8-4) * (7-1) = 24



Example 2:

Input: [1, 2, 1, 2]
Output: False



Note:

The division operator / represents real division, not integer division.  For example, 4 / (1 - 2/3) = 12.
Every operation done is between two numbers.  In particular, we cannot use - as a unary operator.  For example, with [1, 1, 1, 1] as input, the expression -1 - 1 - 1 - 1 is not allowed.
You cannot concatenate numbers together.  For example, if the input is [1, 2, 1, 2], we cannot write this as 12 + 12.

```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(object):\n     def judgePoint24(self, nums):\n         """\n         :type nums: List[int]\n         :rtype: bool\n         """\n         n = len(nums)\n         if n == 1:\n             return abs(nums[0] - 24) < 0.0001\n \n         for i in range(n - 1):\n             for j in range(i + 1, n):\n                 remainder = nums[:i] + nums[i + 1:j] + nums[j + 1:]\n \n                 if self.judgePoint24(remainder + [nums[i] + nums[j]]):\n                     return True\n                 if self.judgePoint24(remainder + [nums[i] - nums[j]]):\n                     return True\n                 if self.judgePoint24(remainder + [nums[j] - nums[i]]):\n                     return True\n                 if self.judgePoint24(remainder + [nums[i] * nums[j]]):\n                     return True\n                 if nums[j] != 0 and self.judgePoint24(remainder + [nums[i] / nums[j]]):\n                     return True\n                 if nums[i] != 0 and self.judgePoint24(remainder + [nums[j] / nums[i]]):\n                     return True\n \n         return False'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'judgePoint24'
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: 7278