# Does Heapsort work in time o(n log n) in the best case?

Is it possible for Heapsort to work in time $o(n\log n)$ on certain inputs?

For example in case of Insertion sort it is possible, however when it comes to Quickssort it is not possible. What about Heapsort? I tried to find an input array such that Heapsort will be working in $o(n\log n)$.

I ask you is it possible? Some permutation? The same elements?

Theorem 1: Heapsort requires that at least $\frac{1}{2} n \lg n - O(n)$ data moves for any heap composed of distinct keys.
Theorem 3: The average number of data moves required to Heapsort a random permutation of $n$ distinct keys is $\sim n \lg n$.