Maximum Overlap of Axis-Aligned Rectangles on a Grid

Maximum Overlap of Axis-Aligned Rectangles on a Grid You are given an n x n integer grid indexed from 0 to n - 1 in both dimensions. Initially, every cell is 0. You are given q inclusive rectangle queries. Each query is represented by four integers [r1, c1, r2, c2], where: 0 <= r1 <= r2 < n 0 <= c1 <= c2 < n For each query, increment every cell (r, c) satisfying r1 <= r <= r2 and c1 <= c <= c2 by 1. Return the maximum number of rectangles covering any cell after all queries are applied. Input Format n q r1 c1 r2 c2 r1 c1 r2 c2 ... Output Format One integer: the maximum value in the grid. Constraints 1 <= n <= 2000 1 <= q <= 200000 Every rectangle lies within the grid. Example Input: 4 3 0 0 1 2 1 1 3 3 2 0 2 2 Output: 3 Explanation: some cells, including cells in the intersection of the three rectangles, are covered multiple times; the maximum coverage is 3. Example Input 1 1 0 0 0 0 Output 1