Qiz on heaps question

We have a binary heap on n elements and wish to insert n more elements (not necessarily one after another) into this heap. The total time required for this is

O(logN)

O(N)

O(NlogN)

O(N^2)

according to me the answer should be O(NlogN) as
2^h elements i.e. n elements can be inserted at height h , with complexity logn , which makes it is n * logn

Yes, I also think it should be n log n

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