<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:
    double distance(vector<int> p1,vector<int> p2){
        return (double)(p1[0]-p2[0])*(double)(p1[0]-p2[0])+(double)(p1[1]-p2[1])*(double)(p1[1]-p2[1]);
    }
    double minAreaFreeRect(vector<vector<int>>& points) {
        int n=points.size();
        unordered_map<int,vector<pair<pair<int,int>,pair<int,int>>>> ump;
        for(int i=0;i<n;i++){
            for(int j=i+1;j<n;j++){
                int dist=distance(points[i],points[j]);
                ump[dist].push_back({{points[i][0],points[i][1]},{points[j][0],points[j][1]}});
            }
        }
        double minarea=INT_MAX;
        for(auto m:ump){
            if(m.second.size()>1){
                for(int i=0;i<m.second.size();i++){
                    for(int j=i+1;j<m.second.size();j++){
                        double mpxi=(double)(m.second[i].first.first+m.second[i].second.first)/2;
                        double mpxj=(double)(m.second[j].first.first+m.second[j].second.first)/2;
                        if(mpxi!=mpxj) continue;
                        double mpyi=(double)(m.second[i].first.second+m.second[i].second.second)/2;
                        double mpyj=(double)(m.second[j].first.second+m.second[j].second.second)/2;
                        if(mpyi==mpyj){
                            vector<int> p1={m.second[i].first.first,m.second[i].first.second};
                            vector<int> p2={m.second[j].first.first,m.second[j].first.second};
                            vector<int> p3={m.second[j].second.first,m.second[j].second.second};
                            double area=sqrt(distance(p1,p2))*sqrt(distance(p1,p3));
                            minarea=min(minarea,area);
                        }

                    }
                }
            }
        }
        if(minarea==INT_MAX) return 0.0;
        return minarea;
    }
};
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