<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 a rectangle formed from these points, with sides parallel to the X and Y axes</em>. If there is not any such rectangle, return <code>0</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/03/rec1.JPG" style="width: 500px; height: 447px;" />
<pre>
<strong>Input:</strong> points = [[1,1],[1,3],[3,1],[3,3],[2,2]]
<strong>Output:</strong> 4
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/03/rec2.JPG" style="width: 500px; height: 477px;" />
<pre>
<strong>Input:</strong> points = [[1,1],[1,3],[3,1],[3,3],[4,1],[4,3]]
<strong>Output:</strong> 2
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= points.length &lt;= 500</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: 
    # Grouping axis with HashMap. Key is axis-pair (2 y coordinates), value is previous x-coordinate. If lookup is successful, we know there is a valid rectangle.
    def minAreaRect(self, points: List[List[int]]) -> int:
        n = len(points)
        nx = len(set([x for x,y in points]))
        ny = len(set([y for x,y in points]))
        if nx == n or ny == n: # no two points share same x or y
            return 0
        
        x_to_y = collections.defaultdict(list)
        # group points by axis 
        for x, y in points:
            x_to_y[x].append(y) 
        
        # b/c we want minimum, only need last-seen x axis for the same (y1, y2) pair
        lastX = {} 
        res = float('inf')
        for x in sorted(x_to_y): # sorted by key (axis)
            x_to_y[x].sort()
            for i in range(len(x_to_y[x])): # iter y pairs in current x-axis
                for j in range(i):
                    y1, y2 = x_to_y[x][i], x_to_y[x][j] # y1 > y2
                    Y_pair = (y1, y2)
                    if Y_pair in lastX:
                        area = (x - lastX[Y_pair]) * abs(y1 - y2)
                        res = min(res, area)
                    lastX[Y_pair] = x
        return res if res < float('inf') else 0
        
21200