<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>

struct point {
    int x, y;
};

class Solution {
public:
    double minAreaFreeRect(vector<vector<int>>& points) {
        unordered_map<long, vector<pair<point, point>>> m;
        int n = ssize(points);
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                int x1 = points[i][0], y1 = points[i][1];
                int x2 = points[j][0], y2 = points[j][1];
                long center = ((long)(x1 + x2) << 32) + (y1 + y2);
                m[center].push_back({{x1, y1}, {x2, y2}});
            }
        }

        double min_area = INT_MAX;
        for (const auto& [center, p] : m) {
            for (int i = 0; i < ssize(p); i++) {
                for (int j = i + 1; j < ssize(p); j++) {
                    auto [p1, p2] = p[i];
                    auto [x1, y1] = p1;

                    auto [p3, p4] = p[j];
                    auto [x3, y3] = p3;
                    auto [x4, y4] = p4;

                    if ((x1 - x3) * (x1 - x4) + (y1 - y3) * (y1 - y4) != 0) continue;
                    double a = sqrt((long)(x1 - x3) * (x1 - x3) + (long)(y1 - y3) * (y1 - y3));
                    double b = sqrt((long)(x1 - x4) * (x1 - x4) + (long)(y1 - y4) * (y1 - y4));

                    min_area = min(min_area, a * b);
                }
            }
        }

        if (min_area < INT_MAX) return min_area;
        return 0;
    }
};
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