Design and implement a thread-safe, fixed-capacity producer–consumer buffer supporting multiple producers and consumers. Provide put(item) that blocks when full and take() that blocks when empty; preserve FIFO order; allow a configurable capacity N; add shutdown() to unblock waiting threads and reject new puts; and support timeouts for put and take. Explain how you prevent race conditions, deadlocks, and lost wakeups; discuss fairness and performance trade-offs; and analyze time and space complexity. If time permits, compare a lock-based design (mutex + condition variables) to a lock-free approach.