Max Pooling with Argmax Coordinates

Problem: Implement 2D Max Pooling and Return Argmax Coordinates Given an integer matrix grid of size H x W, a pooling window size kH x kW, and strides sH, sW. Implement 2D max pooling: for every valid window, output the maximum value inside that window. As a follow-up, for each window, also output the coordinate (row, col) of the maximum value in the original matrix grid. Coordinates are 0-indexed. If there are multiple cells with the same maximum value in a window, return the lexicographically smallest coordinate: smallest row first, then smallest col. No padding is used. Only windows fully contained in the matrix are considered. Output Size outH = floor((H - kH) / sH) + 1 outW = floor((W - kW) / sW) + 1 It is guaranteed that H >= kH and W >= kW. Input Format H W kH kW sH sW grid[0][0] grid[0][1] ... grid[0][W-1] ... grid[H-1][0] ... grid[H-1][W-1] Output Format First print: outH outW Then print outH rows, each containing outW integers: the max-pooled values. Then print outH rows, each containing outW coordinates in the format (r,c): the argmax coordinates in the original matrix. Constraints 1 <= H, W <= 500 1 <= kH <= H 1 <= kW <= W 1 <= sH, sW <= 500 -10^9 <= grid[i][j] <= 10^9 Example Input: 4 4 2 2 2 2 1 3 2 4 5 6 1 2 7 8 9 0 1 2 3 4 Output: 2 2 6 4 8 9 (1,1) (0,3) (2,1) (2,2) Example Input 4 4 2 2 2 2 1 3 2 4 5 6 1 2 7 8 9 0 1 2 3 4 Output 2 2 6 4 8 9 (1,1) (0,3) (2,1) (2,2)