Problem 1 Write a iterative function that finds the n-th integer of the Fibonacci sequence. Then build a minimal program (main function) to test it. That is, write the fib() solution as a separate function and call it in your main() function to test it. For reference see Fibonacci number. INPUT OUTPUT (0, 2) (1, 3) (2, 5) 5 INPUT: OUTPUT: (0, 2) (1, 3) (2, 5) (3, 8) (4, 13) 13 INPUT: OUTPUT: (0, 2) 6765 (1, 3) (2, 5) (3, 8) (4, 13) (5, 21) (6, 34) (7, 55) (8, 89) (9, 144) (10, 233) Note, the first number in the pair is the iteration count (i) and the second number is the value of the (i+2)-th Fibonacci value. Problem 2 Write a recursive function that finds the n-th integer of the Fibonacci sequence. Then build a minimal program to test it. For reference see Fibonacci number. To check for recursion, please have the Fibonacci function print out its input as shown in the examples below: INPUT: OUTPUT: fib(5) fib(4) fib(3) fib(2) fib(1) fib(0) fib(1) fib(2) fib(1) fib(0) fib(3) fib(2) fib(1) INPUT: OUTPUT: fib(7) fib(6) fib(5) fib(4) fib(3) fib(2) fib(1) fib(0) fib(1) fib(2) fib(1) fib(0) fib(3) 13 Problem 3 In this problem, you need to print the pattern of the following form containing the numbers from 1 to n: 4 4 4 4 4 4 4 4 3 3 3 3 3 4 4 3 2 2 2 3 4 4 3 2 1 2 3 4 4 3 2 2 2 3 4 4 3 3 3 3 3 4 4 4 4 4 4 4 4 Example when n=4. INPUT Input contains a single integer n. CONSTRAINTS 1