<p>You are given a 2D integer array <code>rectangles</code> where <code>rectangles[i] = [l<sub>i</sub>, h<sub>i</sub>]</code> indicates that <code>i<sup>th</sup></code> rectangle has a length of <code>l<sub>i</sub></code> and a height of <code>h<sub>i</sub></code>. You are also given a 2D integer array <code>points</code> where <code>points[j] = [x<sub>j</sub>, y<sub>j</sub>]</code> is a point with coordinates <code>(x<sub>j</sub>, y<sub>j</sub>)</code>.</p>

<p>The <code>i<sup>th</sup></code> rectangle has its <strong>bottom-left corner</strong> point at the coordinates <code>(0, 0)</code> and its <strong>top-right corner</strong> point at <code>(l<sub>i</sub>, h<sub>i</sub>)</code>.</p>

<p>Return<em> an integer array </em><code>count</code><em> of length </em><code>points.length</code><em> where </em><code>count[j]</code><em> is the number of rectangles that <strong>contain</strong> the </em><code>j<sup>th</sup></code><em> point.</em></p>

<p>The <code>i<sup>th</sup></code> rectangle <strong>contains</strong> the <code>j<sup>th</sup></code> point if <code>0 &lt;= x<sub>j</sub> &lt;= l<sub>i</sub></code> and <code>0 &lt;= y<sub>j</sub> &lt;= h<sub>i</sub></code>. Note that points that lie on the <strong>edges</strong> of a rectangle are also considered to be contained by that rectangle.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/03/02/example1.png" style="width: 300px; height: 509px;" />
<pre>
<strong>Input:</strong> rectangles = [[1,2],[2,3],[2,5]], points = [[2,1],[1,4]]
<strong>Output:</strong> [2,1]
<strong>Explanation:</strong> 
The first rectangle contains no points.
The second rectangle contains only the point (2, 1).
The third rectangle contains the points (2, 1) and (1, 4).
The number of rectangles that contain the point (2, 1) is 2.
The number of rectangles that contain the point (1, 4) is 1.
Therefore, we return [2, 1].
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/03/02/example2.png" style="width: 300px; height: 312px;" />
<pre>
<strong>Input:</strong> rectangles = [[1,1],[2,2],[3,3]], points = [[1,3],[1,1]]
<strong>Output:</strong> [1,3]
<strong>Explanation:
</strong>The first rectangle contains only the point (1, 1).
The second rectangle contains only the point (1, 1).
The third rectangle contains the points (1, 3) and (1, 1).
The number of rectangles that contain the point (1, 3) is 1.
The number of rectangles that contain the point (1, 1) is 3.
Therefore, we return [1, 3].
</pre>

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

<ul>
	<li><code>1 &lt;= rectangles.length, points.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>rectangles[i].length == points[j].length == 2</code></li>
	<li><code>1 &lt;= l<sub>i</sub>, x<sub>j</sub> &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= h<sub>i</sub>, y<sub>j</sub> &lt;= 100</code></li>
	<li>All the <code>rectangles</code> are <strong>unique</strong>.</li>
	<li>All the <code>points</code> are <strong>unique</strong>.</li>
</ul>

from bisect import bisect_left

class Solution:
    def countRectangles(self, rectangles: List[List[int]], points: List[List[int]]) -> List[int]:
        # Dictionary to store lists of lengths for each height
        height_to_lengths = [[] for _ in range(101)]
        
        # Group rectangles by height
        for l, h in rectangles:
            height_to_lengths[h].append(l)
        
        # Sort each height's length list
        for h in range(101):
            height_to_lengths[h].sort()
        
        # Function to count how many rectangles contain a point
        result = []
        for x, y in points:
            count = 0
            # Check for heights >= y
            for h in range(y, 101):
                lengths = height_to_lengths[h]
                if lengths:
                    # Use binary search to find how many lengths are >= x
                    idx = bisect_left(lengths, x)
                    count += len(lengths) - idx
            result.append(count)
        
        return result

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