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        #nums=[2,6,2,2,7]\n        nums.sort()\n        \n        quotient = []   # *3\n        remainder = []\n        ret = 0\n        \n        for num in nums:\n            quotient.append(num//3*3)\n            remainder.append(num%3)\n            ret += num\n        \n        #print(nums)\n        #print(quotient)\n        #print(remainder)\n        \n        remainder_sum = ret%3\n        #print(remainder_sum)\n        if remainder_sum == 0:\n            return ret\n        elif remainder_sum == 1:\n            # compare min remainder 1 and 2\n            remainder1 = 0\n            remainder1_count = 0\n            remainder2 = 0\n            remainder2_count = 0\n            for i in range(len(nums)):\n                if remainder[i] == 1:\n                    if remainder1_count >= 1:\n                        continue\n                    remainder1_count += 1\n                    remainder1 += nums[i]\n                if remainder[i] == 2:\n                    if remainder2_count >= 2:\n                        continue\n                    remainder2_count += 1\n                    remainder2 += nums[i]    \n                if remainder2_count >= 1 and remainder1_count >= 2:\n                    break\n                \n            if remainder2_count == 2 and remainder1_count == 1:\n                return ret - min(remainder1, remainder2)\n            elif remainder2_count == 2:\n                return ret - remainder2\n            elif remainder1_count == 1:\n                return ret - remainder1\n            else:\n                return 0\n        else:\n            # compare min remainder 1 and 2\n            remainder1 = 0\n            remainder1_count = 0\n            remainder2 = 0\n            remainder2_count = 0\n            for i in range(len(nums)):\n                if remainder[i] == 1:\n                    if remainder1_count >= 2:\n                        continue\n                    remainder1_count += 1\n                    remainder1 += nums[i]\n                if remainder[i] == 2:\n                    if remainder2_count >= 1:\n                        continue\n                    remainder2_count += 1\n                    remainder2 += nums[i]    \n                if remainder2_count >= 1 and remainder1_count >= 2:\n                    break\n                \n            if remainder2_count == 1 and remainder1_count == 2:\n                return ret - min(remainder1, remainder2)\n            elif remainder2_count == 1:\n                return ret - remainder2\n            elif remainder1_count == 2:\n                return ret - remainder1\n            else:\n                return 0\n                \n            return 0\n            \n        return 0'
_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: 6242