<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>>
    fourSum(vector<int> & vals, int const target)
    {
        size_t const sz{ vals.size() };
        vector<vector<int>> tmp;
        tmp.reserve(sz);
        sort(begin(vals), end(vals));
        unordered_map<int64_t, size_t> m;
        m.reserve(sz);
        for(size_t d{ 0 }; d < sz; ++d)
        {
            auto const val_d{ vals[d] };
            m[target - val_d] = d;
        }
        int64_t const max_rhs{ target - vals.back() };
        for(size_t a{ 0 }; a < sz; ++a)
        {
            int64_t const val_a{ vals[a] };
            for(size_t b{ a + 1 }; b < sz; ++b)
            {
                int64_t const val_b{ vals[b] };
                for(size_t c{ b + 1 }; c < sz; ++c)
                {
                    int64_t const val_c{ vals[c] };
                    int64_t const conjugate{ val_a + val_b + val_c };
                    auto got{ m.find(conjugate) };
                    if(got == end(m))
                    {
                        continue;
                    }
                    auto const d{ got->second };
                    if(d <= a || d <= b || d <= c)
                    {
                        continue;
                    }
                    int64_t const val_d{ vals[d] };
                    tmp.push_back({ static_cast<int>(val_a),
                                    static_cast<int>(val_b),
                                    static_cast<int>(val_c),
                                    static_cast<int>(val_d) });
                }
            }    
        }
        return filter(tmp);
    }

    vector<vector<int>>
    filter(vector<vector<int>> const & vals)
    {
        set<vector<int>> tmp{ begin(vals), end(vals) };
        return { begin(tmp), end(tmp) };
    }
};
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