$(3+3$ Points$)$ Suppose there is a Binary Min$-$Heap with exactly $5$ nodes, containing items with priorities $6,10,1,8,5$ a$.$ Show every possible binary min$-$heap that could match this description. For each, draw the appropriate tree and the array representation. b$.$ For one of your answers to part $($a$),$ show what happens with $4$ deleteMin operations. Clearly indicate which heap you are starting with and show the heap after each deleteMin. You can just draw the tree $($not the array$)$ after each step. $(4$ Points Draw a valid AVL tree and give two keys to be inserted on the left subtree of this tree. The second insertion should cause a violation of the height invariant at the root, fixing this violation must require a double rotation. $(5$ Points$)$ Draw all the rotations that you must perform and the final AVL tree after the following elements are inserted in the given order starting from an empty tree. $1,10,5,7,3,13,6,4,8,9$ Draw all intermediate trees. All height factors must be clearly indicated at every step.