<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 solve(vector<int>& a, vector<int> b) {
        return (b[0]-a[0])* (b[0]-a[0]) + (b[1] - a[1]) * (b[1] - a[1]);
    }

    double minAreaFreeRect(vector<vector<int>>& points) {
        map<string, vector<vector<int>>> map;
        int n = points.size();
        for(int i =0; i < n; i++) {
            for(int j = i+1; j < n; j++) {
                long long dist = solve(points[i], points[j]);
                double centerX = (double) (points[i][0] + points[j][0])/2;
                double centerY = (double) (points[i][1] + points[j][1])/2;
                string key = "" + to_string(dist) + "+" + to_string(centerX) + "+"+ to_string(centerY);
                map[key].push_back({i,j});
            }
        }
        double res= INT_MAX;
        for(auto pair : map) {
            string key = pair.first;
            auto arr = pair.second;
            for(int i =0; i < arr.size(); i++) {
                for(int j = i +1; j < arr.size(); j++) {
                    
                    auto p1 = arr[i][0];
                    auto p2 = arr[j][0];
                    auto p3 = arr[j][1];
                    if(p1 == p2 || p1 == p3) continue;
                    if(arr[i][1] == p2 || arr[i][1] == p3) continue;
                    double len1 = sqrt(solve(points[p1], points[p2]));
                    double len2 = sqrt(solve(points[p1], points[p3]));
                    // cout << len1 << " " << len2 << endl;
                    cout << len1 * len2 << ": " << p1 << " " <<  p2 << " " << arr[i][1] << " " << p3 <<endl;
                    res=min(res,len1 * len2);
                }
            }
        }
        return res == INT_MAX ? 0 : res;
    }
};
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