Consider the following SQL query which finds the name and number of departments with employees making less than 80,000 USD and work on ProjectX: SELECT Dnumber, Dname FROM DEPARTMENT D, EMPLOYEE E, WORKS_ON W, PROJECT P WHERE E.Salary<80000 AND D.Dnumber=E.Dno AND E.SSN=W.ESSN AND W.PNO=P.Pnumber AND P.Pname=ProjectX For the query above, write a corresponding relational algebra query. Transform your query into a more efficient form (use heuristic rules). Show how the query tree is optimized by the heuristic query optimization algorithm, one step at a time. Use a drawing tool (of your choice) to draw your initial trees and the resulting trees after each optimization step. You may also use pen and paper and scan your work in if you wish. For each transformation cite the heuristic rule used.