Illustrate the following sequence of disjoint set operations using union-by-rank and path compression. First perform a MAKESET on each of 1, 2, ..., 12. Then (a) UNION(1, 2), UNION(3, 4), UNION (5, 6), UNION (7, 8), UNION (9, 10), UNION (11, 12) (b) UNION (1, 5), UNION (3, 7), UNION (9, 11) (c) UNION(8, 12) (d) UNION(1, 3) Show the forest after each step (a)-(d)