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 = "\n# 1262. Greatest Sum Divisible by Three\n\n# Explanation: seen[i] means the current maximum possible sum that sum % 3 = i\n# Complexity: Time O(N), Space O(1)\n\nclass Solution1:\n    def maxSumDivThree(self, nums: List[int]) -> int:\n        seen = [0, 0, 0]\n        for a in nums:\n            for i in seen[:]: # 这里必须用 [:] 否则 下一次迭代会使用更新后的值 计算结果不对\n                seen[(i + a) % 3] = max(seen[(i + a) % 3], i + a)\n                # print(a, i, seen)\n        return seen[0]\n    \n# Divide the whole list into three parts: mod_0, mod_1, mod_2.\n# Think about the sum of the original list, if it mods 3 == 0, then we can just return the sum.\n# If tot_sum % 3 == 1, then we should remove one smallest element from mod_1 or two smallest ones from mod_2.\n# If tot_sum % 3 == 2, then we should remove one smallest element from mod_2 or two smallest ones from mod_1.\n\nclass Solution: # （没明白。。）\n    def maxSumDivThree(self, nums: List[int]) -> int:\n        mod_1, mod_2,res,remove = [], [], 0, float('inf')\n        for i in nums:\n            if i % 3 == 0: res += i\n            if i % 3 == 1: mod_1 += [i]\n            if i % 3 == 2: mod_2 += [i]\n        mod_1.sort(reverse = True)\n        mod_2.sort(reverse = True)\n        tmp = sum(mod_1) + sum(mod_2)\n        if tmp % 3 == 0:\n            return res + tmp\n        elif tmp% 3 == 1:\n            if len(mod_1): \n                remove = min(remove, mod_1[-1])\n            if len(mod_2) > 1: \n                remove = min(mod_2[-1] + mod_2[-2], remove)\n        elif tmp % 3 == 2:\n            if len(mod_2): \n                remove = min(remove, mod_2[-1])\n            if len(mod_1) > 1: \n                remove = min(mod_1[-1] + mod_1[-2], remove)\n        return res + tmp - remove"
_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: 6196