-- Define the root CTE to find nodes with no parent

WITH root AS ( SELECT DISTINCT N FROM BST WHERE P IS NULL ),

-- Define the inner_node CTE to find nodes that are parents of other nodes -- but are not classified as roots

inner_node AS ( SELECT DISTINCT P FROM BST
WHERE P NOT IN (SELECT N FROM root) ),

-- Define the leaf CTE to find nodes that are not parents of any nodes -- and have a parent (i.e., P is not NULL)

leaf AS ( SELECT DISTINCT N FROM BST WHERE N NOT IN (SELECT P FROM inner_node) AND P IS NOT NULL )

-- Combine results from all three CTEs and classify nodes as 'Root', 'Inner', or 'Leaf'

SELECT N, 'Root' FROM root

UNION ALL

SELECT P, 'Inner' FROM inner_node

UNION ALL

SELECT N, 'Leaf' FROM leaf

-- Order the final result by node value ORDER BY 1;