Consider the join R ≤R.a=S.b S, given the following information about the relations to be joined. The cost metric is the number of page I/Os unless otherwise noted, and the cost of writing out the result should be uniformly ignored. Relation R contains 200,000 tuples and has 20 tuples per page. Relation S contains 4,000,000 tuples and also has 20 tuples per page. Attribute a of relation R is the primary key for R. Both relations are stored as simple heap files (un-ordered files). Each tuple of R joins with exactly 20 tuples of S. 1,002 buffer pages are available. 1. What is the cost of joining R and S using a page-oriented simple nested loops join? 2. What is the cost of joining R and S using a block nested loops join? 3. What is the cost of joining R and S using a sort-merge join? 4. What is the cost of joining R and S using a hash join? What is the cost of joining R and S using a hash join if the size of the buffer is 52 pages. 5. What would be the lowest possible I/O cost for joining R and S using any join algorithm, and how much buffer space would be needed to achieve this cost? Explain briefly.