The postorder traversal of a binary tree is $$8,9,6,7,4,5,2,3,1.$$ The inorder traversal of the same tree is $$8,6,9,4,7,2,5,1,3.$$ The height of a tree is the length of the longest path from the root to any leaf. The height of the binary tree above is ______.

Consider a binary tree $$T$$ that has $$200$$ leaf nodes. Then, the number of nodes in $$T$$ that have exactly two children are ________.

While inserting the elements $$71, 65, 84, 69, 67, 83$$ in an empty binary search tree $$(BST)$$ in the sequence shown, the element in the lowest level is

Consider a complete binary tree where the left and the right sub-trees of the root are max-heaps. The lower bound for the number of operations to convert the tree to a heap is