## Problem Implement `analyze(matrix, nums)` and return `[max_square_area, lis_length]`. ### Part A: Maximal Square `matrix` is a rectangular grid containing only `0` and `1`. Return the area of the largest axis-aligned square containing only `1` values. Return `0` for an empty matrix. ### Part B: Longest Increasing Subsequence `nums` is an integer array. Return the length of its longest strictly increasing subsequence. A subsequence preserves order but need not be contiguous. Return `0` for an empty array. ## Constraints - At most 500 rows and 500 columns in `matrix` - `0 <= len(nums) <= 200,000` - `-10^9 <= nums[i] <= 10^9` ## Example For ```text matrix = [[1,0,1,0,0], [1,0,1,1,1], [1,1,1,1,1], [1,0,0,1,0]] nums = [10,9,2,5,3,7,101,18] ``` return `[4, 4]`. ## Clarifications The square result is area, not side length. Equal values cannot both extend a strictly increasing subsequence. ## Hint For the square, relate a cell to three neighboring subproblems. For the subsequence, maintain the smallest possible tail value for each achievable length. ## Interview Follow-ups - Present brute-force and optimal approaches for both parts. - Reduce maximal-square auxiliary space to one row. - Reconstruct one longest increasing subsequence.