<p>Given an integer array nums, return all the triplets <code>[nums[i], nums[j], nums[k]]</code> such that <code>i != j</code>, <code>i != k</code>, and <code>j != k</code>, and <code>nums[i] + nums[j] + nums[k] == 0</code>.</p>

<p>Notice that the solution set must not contain duplicate triplets.</p>

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

<pre>
<strong>Input:</strong> nums = [-1,0,1,2,-1,-4]
<strong>Output:</strong> [[-1,-1,2],[-1,0,1]]
<strong>Explanation:</strong> 
nums[0] + nums[1] + nums[2] = (-1) + 0 + 1 = 0.
nums[1] + nums[2] + nums[4] = 0 + 1 + (-1) = 0.
nums[0] + nums[3] + nums[4] = (-1) + 2 + (-1) = 0.
The distinct triplets are [-1,0,1] and [-1,-1,2].
Notice that the order of the output and the order of the triplets does not matter.
</pre>

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

<pre>
<strong>Input:</strong> nums = [0,1,1]
<strong>Output:</strong> []
<strong>Explanation:</strong> The only possible triplet does not sum up to 0.
</pre>

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

<pre>
<strong>Input:</strong> nums = [0,0,0]
<strong>Output:</strong> [[0,0,0]]
<strong>Explanation:</strong> The only possible triplet sums up to 0.
</pre>

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

<ul>
	<li><code>3 &lt;= nums.length &lt;= 3000</code></li>
	<li><code>-10<sup>5</sup> &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution:
    def threeSum(self, nums: list[int]) -> list[list[int]]:
        negative_numbers, positive_numbers, zeroes = [], [], []
        for num in nums:
            if num > 0:
                positive_numbers.append(num)
            elif num < 0:
                negative_numbers.append(num)
            else:
                zeroes.append(num)

        triplets = set()

        negative_numbers_set = set(negative_numbers)
        positive_numbers_set = set(positive_numbers)

        if zeroes:
            for negative_number in negative_numbers_set:
                if -negative_number in positive_numbers_set:
                    triplets.add((negative_number, 0, -negative_number))

        if len(zeroes) >= 3:
            triplets.add((0, 0, 0))

        for i in range(len(negative_numbers)):
            for j in range(i + 1, len(negative_numbers)):
                target = -(negative_numbers[i] + negative_numbers[j])
                if target in positive_numbers_set:
                    triplet = sorted([negative_numbers[i], negative_numbers[j], target])

                    triplets.add(tuple(triplet))

        for i in range(len(positive_numbers)):
            for j in range(i + 1, len(positive_numbers)):
                target = -(positive_numbers[i] + positive_numbers[j])
                if target in negative_numbers_set:
                    triplet = sorted([positive_numbers[i], positive_numbers[j], target])
                    triplets.add(tuple(triplet))

        return triplets
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