(15 pts) Consider the problem count-evens, defined as follows: Input: a list of integers. Output: the...

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(15 pts) Consider the problem count-evens, defined as follows: Input: a list of integers. Output: the number of even integers in the list. For example, (count-evens (1 4 3 7 8)) should return the value 2 because the list contains two even numbers. a) Describe a recursive strategy for solving this problem in Racket without using any helper functions or parameters other than the input list. Describe your algorithm clearly in English. Be sure to describe how you would break the problem down into sub-problems, and how each sub-problem would be solved. b) Now suppose that the input list can be nested. For example, you can call (count-evens (1 (23) (4 (5 6)))). How would you modify your strategy from part a) to provide a correct algorithm for nested lists? (15 pts) Consider the problem count-evens, defined as follows: Input: a list of integers. Output: the number of even integers in the list. For example, (count-evens (1 4 3 7 8)) should return the value 2 because the list contains two even numbers. a) Describe a recursive strategy for solving this problem in Racket without using any helper functions or parameters other than the input list. Describe your algorithm clearly in English. Be sure to describe how you would break the problem down into sub-problems, and how each sub-problem would be solved. b) Now suppose that the input list can be nested. For example, you can call (count-evens (1 (23) (4 (5 6)))). How would you modify your strategy from part a) to provide a correct algorithm for nested lists?