<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:
    long long dist(int x1, int x2, int y1, int y2){
        return (x1-x2)*(x1-x2)+(y1-y2)*(y1-y2);
    }
    double minAreaFreeRect(vector<vector<int>>& p) {
        unordered_map<long long, vector<vector<int>>> m;
        for(int i = 0; i<p.size(); i++){
            for(int j = i+1; j<p.size(); j++){
                long long center = ((long long)(p[i][0]+p[j][0])<<16)+
                (p[i][1]+p[j][1]);
                m[center].push_back({p[i][0], p[i][1], p[j][0], p[j][1]});
            }
        }
        long long res = 0;
        for(auto it = m.begin(); it!= m.end(); it++){
            for(auto i = 0; i<it->second.size(); i++){
                for(auto j = i+1; j<it->second.size(); j++){
                    auto p1 = it->second[i]; auto p2 = it->second[j];
                    if(((p1[0]-p2[0])*(p1[0]-p2[2])+(p1[1]-p2[1])*(p1[1]-p2[3]))==0){
                        auto s1 = dist(p1[0], p2[0], p1[1], p2[1]);
                        auto s2 = dist(p1[0], p2[2], p1[1], p2[3]);
                        if(res==0||res>s1*s2) res = s1*s2;
                    }
                }
            }
        }
        return sqrt(res);
    }
};
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