Which of these statements is not true about an $AVL$ tree $T$ containing $n$ nodes?
- Rotations may be required during key insertion to keep $T$ balanced.
- The height of $T$ cannot exceed $1.5$ * $\log 2^{n}$ . And It is possible to insert nodes into $T$ in $O$$\left ( \lg n \right )$ asymptotic algorithmic complexity.
- The number of interior nodes in $T$ cannot exceed the number of leaves in $T$.
- If each node in $T$ is augmented with an integer showing the size of that node’s sub-tree, then $T$ can be used to perform order statistic searches in $O$$\left ( \lg n \right )$ asymptotic algorithmic complexity.