(10 points) Write the pseudocode for an algorithm, we call it MAX, that receives as input an array A[ij] of positive numbers and returns the index for largest number in A[ij]. You should assume that ij and that there may be repeated numbers in the array. You must use loops (i.e.,. "while" or "for") but you may not use recursion. (20 points) Prove that your pseudocode in Question 1 is indeed correct by: (a) Indicating the invariant (b) Proving the initialization case (c) Proving the maintenance case (d) Proving the termination case