<p>Given an array <code>nums</code> of <code>n</code> integers, return <em>an array of all the <strong>unique</strong> quadruplets</em> <code>[nums[a], nums[b], nums[c], nums[d]]</code> such that:</p>

<ul>
	<li><code>0 &lt;= a, b, c, d&nbsp;&lt; n</code></li>
	<li><code>a</code>, <code>b</code>, <code>c</code>, and <code>d</code> are <strong>distinct</strong>.</li>
	<li><code>nums[a] + nums[b] + nums[c] + nums[d] == target</code></li>
</ul>

<p>You may return the answer in <strong>any order</strong>.</p>

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

<pre>
<strong>Input:</strong> nums = [1,0,-1,0,-2,2], target = 0
<strong>Output:</strong> [[-2,-1,1,2],[-2,0,0,2],[-1,0,0,1]]
</pre>

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

<pre>
<strong>Input:</strong> nums = [2,2,2,2,2], target = 8
<strong>Output:</strong> [[2,2,2,2]]
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 200</code></li>
	<li><code>-10<sup>9</sup> &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>-10<sup>9</sup> &lt;= target &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:
    def fourSum(self, nums: List[int], target: int) -> List[List[int]]:
        def findNsum(nums, target, N, result, results):
            if len(nums) < N or N < 2 or target < nums[0]*N or target > nums[-1]*N:  # early termination
                return
            if N == 2: # two pointers solve sorted 2-sum problem
                l,r = 0,len(nums)-1
                while l < r:
                    s = nums[l] + nums[r]
                    if s == target:
                        results.append(result + [nums[l], nums[r]])
                        l += 1
                        while l < r and nums[l] == nums[l-1]:
                            l += 1
                    elif s < target:
                        l += 1
                    else:
                        r -= 1
            else: # recursively reduce N
                for i in range(len(nums)-N+1):
                    if i == 0 or (i > 0 and nums[i-1] != nums[i]):
                        findNsum(nums[i+1:], target-nums[i], N-1, result+[nums[i]], results)

        results = []
        findNsum(sorted(nums), target, 4, [], results)
        return results
16300