Design dynamic connectivity with alive nodes

Design a data structure to maintain an undirected graph of N nodes, where each node has a boolean 'alive' flag. Support the following operations efficiently for up to 100,000 operations: ( 1) activate(i) / deactivate(i) to toggle a node's alive status; ( 2) connect(u, v) that adds an edge only if both endpoints are currently alive; ( 3) disconnect(u, v) to remove an existing edge; ( 4) isConnected(u, v) that returns whether u and v are in the same connected component considering only alive nodes; and ( 5) countComponents() over alive nodes. Describe data structures, time/space complexities, and how you would handle deletions and node deactivations (e.g., lazy deletion vs. fully dynamic connectivity). Discuss any concurrency considerations if these operations are called from multiple threads.