<p>Given an integer array <code>nums</code>, return <em>the <strong>maximum possible sum </strong>of elements of the array such that it is divisible by three</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,6,5,1,8]
<strong>Output:</strong> 18
<strong>Explanation:</strong> Pick numbers 3, 6, 1 and 8 their sum is 18 (maximum sum divisible by 3).</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [4]
<strong>Output:</strong> 0
<strong>Explanation:</strong> Since 4 is not divisible by 3, do not pick any number.
</pre>

<p><strong class="example">Example 3:</strong></p>

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

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 4 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution:
    def maxSumDivThree(self, nums: List[int]) -> int:
        total_sum = sum(nums)
        remainder_one = []
        remainder_two = []

        for num in nums:
            if num % 3 == 1:
                remainder_one.append(num)
            elif num % 3 == 2:
                remainder_two.append(num)

        remainder_one.sort()
        remainder_two.sort()

        if total_sum % 3 == 0:
            return total_sum
        elif total_sum % 3 == 1:
            remove_one_or_two = min(
                remainder_one[0] if len(remainder_one) > 0 else float('inf'),
                sum(remainder_two[:2]) if len(remainder_two) >= 2 else float('inf')
            )
        else:  # total_sum % 3 == 2
            remove_one_or_two = min(
                remainder_two[0] if len(remainder_two) > 0 else float('inf'),
                sum(remainder_one[:2]) if len(remainder_one) >= 2 else float('inf')
            )

        return total_sum - remove_one_or_two
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