Suppose we have 10 elements in a set. we begin with all the elements in their singleton sets. consider the following sequence of operations: a. union(1,2) /* assume that 1 is the root */b. m = find(1)c. union(3,4) /*assume that 3 is the root */d. n = find(4)e. union(m, n)f. m = find(1)g. union(m,5)h. union(6,7) /*assume that 6 is the root */i. m = find(6)j. union(m,8)k. union(9,10) /*assume that 9 is the root */l. m = find(10)m. n = find(4)n. n = find(2)o. union(m, n)p. m = find(10)q. n = find(8)r. union(m, n)show the resulting trees after steps e, g, j, o, r for the following two strategies: i. union by sizeii. union by size and path compression