Hi everyone! Here’s a fun problem: Construct an n*m binary matrix such that all the 1-cells form a single 4-connected component, while maximizing the number of 4-connected components formed by the 0-cells. Two cells are considered adjacent if they share an edge. Is there an O(nm) construction with a provably tight upper bound on the number of zero-components? What is the tightest upper bound you can establish, and what are the best achievable time and space complexities for the construction?