Consider the following sequence of keys 5, 13, 10, 9, 8, 12, 20, 11, 4, 3, 16, 7. (a) Construct a heap by inserting the above keys one after the other, using algorithm Insert seen in class. (b) Assuming the above keys are stored in that order in an array H from position 1 to 12, execute the linear-time algorithm BottomUpHeap seen in class to obtain a valid heap. In both cases you are to draw the final heap as a complete binary tree and write its standard array implementation