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Quick Summary

Track the formation of contiguous house segments on a number line as positions are added sequentially.
After each insertion, determine and record the length of the longest currently formed block.
Input guarantees prevent simultaneous bridging of two separate segments in a single step.

What This Tests

Dynamic interval state management
Efficient lookup and update strategies using hash maps
Boundary endpoint tracking optimization
Sequential processing with running aggregates

Common Patterns

Hashing

Union Find

Test Cases

Input

Output

Expected