<p>You are given an array of points in the <strong>X-Y</strong> plane <code>points</code> where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code>.</p>

<p>Return <em>the minimum area of any rectangle formed from these points, with sides <strong>not necessarily parallel</strong> to the X and Y axes</em>. If there is not any such rectangle, return <code>0</code>.</p>

<p>Answers within <code>10<sup>-5</sup></code> of the actual answer will be accepted.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/21/1a.png" style="width: 398px; height: 400px;" />
<pre>
<strong>Input:</strong> points = [[1,2],[2,1],[1,0],[0,1]]
<strong>Output:</strong> 2.00000
<strong>Explanation:</strong> The minimum area rectangle occurs at [1,2],[2,1],[1,0],[0,1], with an area of 2.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/22/2.png" style="width: 400px; height: 251px;" />
<pre>
<strong>Input:</strong> points = [[0,1],[2,1],[1,1],[1,0],[2,0]]
<strong>Output:</strong> 1.00000
<strong>Explanation:</strong> The minimum area rectangle occurs at [1,0],[1,1],[2,1],[2,0], with an area of 1.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/22/3.png" style="width: 383px; height: 400px;" />
<pre>
<strong>Input:</strong> points = [[0,3],[1,2],[3,1],[1,3],[2,1]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> There is no possible rectangle to form from these points.
</pre>

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

<ul>
	<li><code>1 &lt;= points.length &lt;= 50</code></li>
	<li><code>points[i].length == 2</code></li>
	<li><code>0 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 4 * 10<sup>4</sup></code></li>
	<li>All the given points are <strong>unique</strong>.</li>
</ul>

class Solution {
public:
    size_t d2(int x1, int y1, int x2, int y2) {
        return (x1 - x2) * (x1 - x2) + (y1 - y2)*(y1 - y2);
    }
    double minAreaFreeRect(vector<vector<int>>& ps, size_t res = 0) {
        unordered_map<size_t, unordered_map<size_t, vector<vector<int>>>> m;
        for (auto i = 0; i < ps.size(); i++)
            for(auto j = i+1; j<ps.size(); j++) {
                auto center = ((size_t)(ps[i][0] + ps[j][0]) << 16) + ps[i][1] + ps[j][1];
                auto len = d2(ps[i][0], ps[i][1], ps[j][0], ps[j][1]);
                m[center][len].push_back({ps[i][0], ps[i][1], ps[j][0], ps[j][1]});
            }

        for (auto it_c = begin(m); it_c!= end(m); ++it_c)
            for (auto it_l = begin(it_c->second); it_l != end(it_c->second); ++it_l)
            for(auto i = 0;  i < it_l->second.size(); i++)
                for(auto j = i+1; j < it_l->second.size(); j++) {
                    auto& p1 = it_l->second[i], &p2 = it_l->second[j];
                auto area = d2(p1[0], p1[1], p2[0], p2[1]) * d2(p1[0], p1[1], p2[2], p2[3]);
                    if(res == 0 || res > area) res = area;

                }
            return sqrt(res);
    }
};
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