EXERCISE 12. The United States of Algorithmica (for short: USA) comprise 2" states, but the exact value of n is unknown. The flag of USA is blue; it has n +1 rows, each (except the first one) with 2n-1 red stars and 2n-1 white stars. The first row contains just a sequence of 2 red stars. The second row starts with 2n-1 red stars followed by 2n-1 white stars. The third row starts with a sequence of 2n2 red stars followed by 2n-2 white stars, again 2n2 red stars, and finally 2n-2 white stars. This continues in the same way, so the last row contains an alternating sequence of red and white stars starting with a red one. Once there was a big argument between the states how to program the flag, which led (temporarily) to a separation of the country into the Iterative States of Algorithmica (for short: ISA) and the Recursive States of Algorithmica (for short: RSA). (i) Specify a sequential algorithm used in ISA that takes n as input and produces the flag of USA. (ii) Specify a recursive algorithm used in RSA that takes n as input and produces the flag of USA. (iii) For both algorithms determine the order of magnitude for the number of steps required to produce the flag