Hint

You could use a 2D segment tree. https://cp-algorithms.com/data_structures/segment_tree.html

For each rectangle, let's define $$$x_1, x_2, y_1, y_2$$$ as:

• $$$x$$$ coordinate of top-left corner
• $$$x$$$ coordinate of top-right corner
• $$$y$$$ coordinate of top-left corner
• $$$y$$$ coordinate of bottom-left corner

consecutively.

Obviously if a point $$$i$$$ is inside the rectangle, the condition $$$x_1 ≤ x_i ≤ x_2$$$ and $$$y_1 ≤ y_i ≤ y_2$$$ must be satisfied.

To solve the problem, sort all points based on their $$$x$$$ coordinate first. Let $$$A$$$ denote the array of $$$y$$$ coordinate of all the points(after have been sorted).

For rectangle $$$j$$$, use binary search to find all points with $$$x$$$ coordinate lie within the range $$$[x_1, x_2]$$$. Assume the points we found is the range $$$[l_j, r_j]$$$, the problem turns into finding how many elements smaller or equal to $$$y_2$$$ and bigger or equal to $$$y_1$$$ in range $$$[l_j, r_j]$$$ of array $$$A$$$. This problem can be solved with Segment Tree or Fenwick Tree easily. In order to calculate the answer easier, we can see that the answer is equal to the difference between the number of elements smaller or equal to $$$y_2$$$ and the number of elements smaller than $$$y_1$$$.