Saw this on LC discussion and have no idea how to approach. https://leetcode.com/discuss/interview-question/5365200/Amazon-OA

Everyone I know has stopped Competitive Programming after getting a Job which made me sad. Is there no passion for Competitive Programming? Do people really solve all these problems in hopes of getting a better Job. Do Jobs even require you to be CM or IM for the hiring process? It's weird to me since I always did this for fun

Question here: https://www.codechef.com/practice/course/4-star-difficulty-problems/DIFF1900/problems/SEGDIV?tab=statement

I'm intrigued about this submission over here: https://www.codechef.com/viewsolution/82916450

I have no idea why it works. The poster also just left out the proof part and simply wrote, "It's difficult to prove it". Is there any proof of this or is just conveniently satisfies for the given question's constraints? (n <= 500)