Minimum Number of Days to Disconnect Island

Given an m×n binary grid of land (1) and water (0), return the minimum number of single-cell land-to-water removals needed to make the grid "disconnected" (zero or multiple islands). The core challenge is detecting initial connectivity and whether the island contains a critical land cell (an articulation point) whose removal splits it (answer 1); if not (and more than one land cell) the answer is 2 (m,n ≤ 30).