looking for functional programming expert ( racket, scheme )

“[login to view URL]” to Gradescope. You may NOT use any of Scheme’s imperative features (assignment/loops) or anything else not covered in class. You should use Racket ([login to view URL]) for your implementation. For all problems, you can assume all inputs obey the types as specified in a problem. Testing and Auto Grading We will use the Gradescope Autograder feature to grade the assignment. So it is important to start from the code template “[login to view URL]” on Canvas, which only has dummy implementationsbut is nevertheless useful since it obeys a few important requirements for auto grading, such as file name, function names etc one of the example problem is we define Church number n as λf n: (fn z), where (fn z) represents the n-fold composition of function f applied to z (i.e., f(f(: : : (f z))) where f is repeated for n times). a) (5pt) Implement a function funPower, which takes a function f, an integer n and returns the function fn. For example, ((funPower sqrt 2) 16) should return 2. b) (5pt) Implement a function encode, which takes a natural number n and returns the church encoding of n. For example, (encode 2) should return 2 (i.e., the function λf: λz: f (f z)). c) (5pt) Implement a function decode, which takes n (the church encoding of some natural number n) and returns n. For example, (decode (encode 2)) should return 2. d) (5pt) Implement a function MULT, which takes two church numbers n1, n2 and returns the church number of n1 × n2 (i.e., n1 × n2). For example, (decode (MULT (encode 2) (encode 3))) should be 6.