Given an array nums of integers, we need to find the maximum possible sum of elements of the array such that it is divisible by three.


 
Example 1:
Input: nums = [3,6,5,1,8]
Output: 18
Explanation: Pick numbers 3, 6, 1 and 8 their sum is 18 (maximum sum divisible by 3).
Example 2:
Input: nums = [4]
Output: 0
Explanation: Since 4 is not divisible by 3, do not pick any number.

Example 3:
Input: nums = [1,2,3,4,4]
Output: 12
Explanation: Pick numbers 1, 3, 4 and 4 their sum is 12 (maximum sum divisible by 3).

 
Constraints:

1 <= nums.length <= 4 * 10^4
1 <= nums[i] <= 10^4

```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 maxSumDivThree(self, nums: List[int]) -> int:\n        ans = 0\n        next_nums = []\n        nums1, nums2 = [], []\n        nums.sort(reverse=True)\n        for n in nums:\n            val = n % 3\n            if val == 0:\n                ans += n\n            elif val == 1:\n                nums1.append(n)\n            else:\n                nums2.append(n)\n\n        if len(nums1) < len(nums2):\n            small = nums1\n            big = nums2\n        else:\n            small = nums2\n            big = nums1\n\n        mod = (len(big) - len(small)) % 3\n        val1, val2 = 0, 0\n        if mod == 0:\n            val1 = sum(big) + sum(small)\n        else:\n            val1 = sum(small) + sum(big[:-mod])\n            if len(big) >= 3 and 3 - mod <= len(small):\n                val2 = sum(small[:-(3 - mod)]) + sum(big)\n\n        return ans + max(val1, val2)\n\n    def traversal(self, nums1, nums2, idx1, idx2, curr_val, visited):\n        if idx1 == len(nums1) and idx2 == len(nums2):\n            return curr_val, True\n\n        if (idx1, idx2, curr_val) in visited:\n            return visited[(idx1, idx2, curr_val)], False\n\n        if idx1 + 1 <= len(nums1) and idx2 + 1 <= len(nums2):\n            val, ret = self.traversal(\n                nums1,\n                nums2,\n                idx1 + 1,\n                idx2 + 1,\n                curr_val + nums1[idx1] + nums2[idx2],\n                visited\n            )\n            if ret:\n                return val, True\n            max_val = max(max_val, val)\n\n        max_val = curr_val\n        if idx2 + 3 <= len(nums2):\n            s = nums2[idx2] + nums2[idx2 + 1] + nums2[idx2 + 2]\n            val, ret = self.traversal(\n                nums1,\n                nums2,\n                idx1,\n                idx2 + 3,\n                curr_val + s,\n                visited\n            )\n            if ret:\n                return val, True\n            max_val = max(max_val, val)\n\n        if idx1 + 3 <= len(nums1):\n            s = nums1[idx1] + nums1[idx1 + 1] + nums1[idx1 + 2]\n            val, ret = self.traversal(\n                nums1,\n                nums2,\n                idx1 + 3,\n                idx2,\n                curr_val + s,\n                visited\n            )\n            if ret:\n                return val, True\n            max_val = max(max_val, val)\n\n        visited[(idx1, idx2, curr_val)] = max_val\n        return max_val, True\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'maxSumDivThree'
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: 6154