On a blackboard, a binary non$-$empty tree is drawn with distinct keys at the vertices. Moreover, this tree is simultaneously a Max$-$Heap and a Binary Search Tree. How many vertices can this tree have? Pick all options.

Question options:

$1$

$2$

$3$

$4$

$5$

$10$

Any positive integer

Any positive even number

Any positive odd number

$2$k for any integer non$-$negative k