Log Timestamp Counting

roblox Given a series of log entries, each with a timestamp. Your task is to design a system to efficiently count the number of log entries within a given time interval. Additionally, the system should support operation in a distributed environment. Function Requirements: Initialize the log system. Add a log entry to the system, where each entry includes a timestamp. Query the total number of log entries recorded within a specified start and end time. The query implementation should efficiently operate in a distributed system. Input/Output Example: Example 1: Input: init add 1622530800 add 1622534400 add 1622538000 query 1622530800 1622538000 Output: 3 Constraints: Timestamps are non-negative integers. Each request is on a separate line: init for initializing the log system, add <timestamp> for adding a log timestamp, query <start> <end> for querying the number of logs in a specified time span. Assume that in a single machine implementation, data synchronization across distributed systems occurs automatically after each add operation. Example Input init add 1622530800 add 1622534400 add 1622538000 query 1622530800 1622538000