Problem Name — "Group Photo"

There are $$$N$$$ people, each with a unique height. The height of the $$$i^{th}$$$ person is $$$i (1 \leq i \leq N)$$$. The $$$i^{th}$$$ person will smile in the photo if at least $$$A[i]$$$ people in the photo are shorter than him and at most $$$B[i]$$$ people in the photo are taller than him.

Find the largest group such that everyone will smile in the photo of this group. A group is a collection of randomly selected people from the given $$$N$$$ people.

Constraints:

• $$$1 \leq N \leq 10^5$$$

• $$$0 \leq A[i], B[i] \leq N$$$

I cannot come up with a better solution for this. Any help would be greatly appreciated, thanks!