For better current execution, multiple$-$granularity locking $($MGL$)$ introduces three new types of locks, IS$,$ IX$,$ and SIX. Consider the following tree of objects, where each node contains all its children. Note that some nodes have been locked by other transactions and the types of locks are given nearby.

Suppose Transaction T$1$ needs to read object p$1.$ What lock$($s$)$ on which node$($s$)$ does it need to acquire? For each lock, specify if it will be granted.

Suppose Transaction T$1$ needs to read p$3$ and write object r$6$ instead. What lock$($s$)$ on which node$($s$)$ does it need to acquire? For each lock, specify if it will be granted.