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         def cal(operands, operaters):\n             for opt in operaters:\n                 op2, op1 = operands.pop(-1), operands.pop(-1)\n                 if opt==\'+\':\n                     ret = op1+op2\n                 elif opt==\'-\':\n                     ret = op1-op2\n                 elif opt==\'*\':\n                     ret = op1*op2\n                 elif opt==\'/\' and op2!=0:\n                     ret = op1/op2\n                 else:\n                     return float(\'-inf\')\n                 operands.append(ret)\n             \n             return operands[0] if abs(operands[0]-24)>0.0000001 else 24\n         \n         def comb(arr):\n             if len(arr)==1:\n                 return [arr]\n             ret = []\n             for i in range(len(arr)):\n                 if i-1>=0 and arr[i]==arr[i-1]:\n                     continue\n                 for remain in comb(arr[:i]+arr[i+1:]):\n                     ret.append([arr[i]]+remain)\n             return ret\n         \n         def genopt(n):\n             if n==0:\n                 return [\'\']\n             ret = []\n             for i in \'+-*/\':\n                 for res in genopt(n-1):\n                     ret.append(i+res)\n             return ret\n         \n         nums.sort()\n         ops = comb(nums)\n         opts = genopt(3)\n         for op in ops:\n             for opt in opts:\n                 if cal(op[:], opt)==24:\n                     return True\n                 \n         def base(a, b):\n             return set([a+b,a-b,b-a,a*b]+([a/b] if b!=0 else[])+([b/a] if a!=0 else[]))\n             \n         for i in range(4):\n             for j in range(i+1, 4):\n                 a, b = nums[i], nums[j]\n                 remain = nums[:i]+nums[i+1:j]+nums[j+1:4]\n                 for x in base(a, b):\n                     for y in base(remain[0], remain[1]):\n                         if 24 in base(x, y):\n                             return True\n                 \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: 14378