There is a Binary Search Tree with $12$ nodes. Each node has a distinct value between $1$ and $12.$ The root has value $9,$ and its left child has value $5.$ How many possible Binary Search Trees could this be$?$ Recall that in a BST$,$ if a node has value x$,$ then all nodes in its left subtree have value $<=$ x$,$ and all nodes in its right subtree have value $>=$ x$.$