Happy number service (sum of squares of digits until reaches 1) + scaling

Coding: Happy Number Service Implement a function/service: given a positive integer n, repeatedly: Replace n with the sum of squares of its digits. Repeat. Return true if the process eventually reaches 1; return false if it falls into a cycle that never reaches 1. I/O Input: a positive integer n Output: true/false Constraints Assume 64-bit integer input (e.g., 1 <= n <= 10^18). Examples Input: 19 → Output: true (19 → 82 → 68 → 100 → 1) Input: 2 → Output: false Follow-up (Scaling) If this service must handle billions of requests per second, how would you optimize it? Explain why values quickly collapse into a small range (e.g., < 1000). How to exploit that with precomputation/caching (e.g., preload results for a bounded range). Cache sizing, update strategy, and concurrency considerations. Example Input 19 Output true