<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 minAreaFreeRect(vector<vector<int>>& a) {
        double area = INT_MAX;
        int n = a.size();
        unordered_map<string,vector<pair<int,int>>> mp;
        for(int i=0;i<n;i++)
        {
            for(int j=i+1;j<n;j++)
            {
                long dis = (a[i][0] - a[j][0]) * (a[i][0]-a[j][0]) + (a[i][1]-a[j][1])* (a[i][1]-a[j][1]);
                int mx = (a[i][0]+a[j][0]);
                int my = (a[i][1]+a[j][1]);
                string key = to_string(dis)+" "+to_string(mx)+" "+to_string(my);

                mp[key].push_back({i,j});
            }
        }
        
        for(auto el: mp)
        {
            for(int i=0;i<el.second.size();i++)
            {
                for(int j=i+1;j<el.second.size();j++)
                {
                    auto p = el.second[i].first;
                    auto q = el.second[j].first;
                    auto r = el.second[j].second;
                    int x1 = a[p][0];
                    int y1 = a[p][1];
                    int x2 = a[q][0];
                    int y2 = a[q][1];
                    int x3 = a[r][0];
                    int y3 = a[r][1];
                    double d1 = sqrt(1ll*(x1-x2)*(x1-x2) + (y1-y2)*(y1-y2));
                    double d2 = sqrt(1ll*(x1-x3)*(x1-x3) + (y1-y3)*(y1-y3));
                    double ar = d1*d2;
                    area = min(area,ar);
                }
            }
        }
        return area==INT_MAX?0.0:area;

    }
};
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