Suppose we insert the following numbers into an initially empty 2-3 tree, in the given order:...

  

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Suppose we insert the following numbers into an initially empty 2-3 tree, in the given order: 9, 15, 4, 3:6, 13, 2, 11; 7, 1, 16, 12; 14, 8, 10, 5. (a) Draw a picture of the 2-3 tree after each insertion: you do not have to write down the "guides" at each node - just draw the tree structure and the keys at the leaves. (b) Suppose that now a split operation is performed, which splits the tree into two trees: one containing those numbers < 8, and the other containing those numbers > 8. Show the resulting trees (again, please omit the "guides"). Suppose we insert the following numbers into an initially empty 2-3 tree, in the given order: 9, 15, 4, 3:6, 13, 2, 11; 7, 1, 16, 12; 14, 8, 10, 5. (a) Draw a picture of the 2-3 tree after each insertion: you do not have to write down the "guides" at each node - just draw the tree structure and the keys at the leaves. (b) Suppose that now a split operation is performed, which splits the tree into two trees: one containing those numbers < 8, and the other containing those numbers > 8. Show the resulting trees (again, please omit the "guides").