Assume the role of a Distributed Systems Engineer. You are tasked with designing a custom key-value store that utilizes the Raft consensus algorithm for high availability. Explain the theoretical underpinnings of the Leader Election and Log Replication phases of Raft. Specifically, answer the following: 1. How does Raft guarantee safety (the property that if a server has applied a log entry at a given index to its state machine, no other server will ever apply a different log entry for the same index)? 2. Describe a detailed implementation plan for handling leader failures during a network partition. 3. Discuss how you would optimize log compaction to prevent infinite log growth in your Go implementation without compromising the ability to restore state for new followers. 4. Analyze the impact of log replication latency on the system's write throughput and propose mechanisms to mitigate this.