<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 {
public:
    vector<vector<int>> twoSum(vector<int>& nums, long long target2, int k) {
        vector<vector<int>> ans;
        int n = nums.size();
        int i = k+1, j = n-1;
        while(i<j) {
            if(nums[i]+nums[j] > target2) {j--;}
            else if(nums[i]+nums[j] < target2) {i++;}
            else {ans.push_back({nums[i],nums[j]}); i++; j--;}
        }
        return ans;
    }
    vector<vector<int>> threeSum(vector<int>& nums, long long target3, int j) {
        vector<vector<int>> ans;
        int n = nums.size();
        for(int i=j+1; i<n; i++) {
            long long target2 = target3 - nums[i];
            auto p = twoSum(nums, target2, i);
            for(auto it : p) {
                it.insert(it.begin(),nums[i]);
                ans.push_back(it);
            }
        }
        return ans;
    }

    vector<vector<int>> fourSum(vector<int>& nums, int target4) {
        set<vector<int>> ans;
        int n = nums.size();
        sort(nums.begin(),nums.end());
        for(int i=0; i<n; i++) {
            long long target3 = target4 - nums[i];
            auto p = threeSum(nums, target3, i);
            for(auto it : p) {
                it.insert(it.begin(),nums[i]);
                ans.insert(it);
            }
        }
        vector<vector<int>> v;
        for(auto it : ans) {v.push_back(it);}
        return v;
    }
};
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