P7: Given is the following algorithm to determine the maximal value in an array A[1..N]. You may assume that all values in array A[1..N] are positive. Algorithm FIND-MAX (A[1N]) : MAX =0 FOR i in [1N]: if A[i]> MAX: MAX=A[i] return MAX Prove the correctness of this algorithm with the following loop invariant: "Prior to the i-th iteration, MAX holds the maximal value of all array elements A[1] to A[i1]. " As shown in the lecture, the proof should have three parts: (1) Initialization, (2) Maintenance, and (3) Termination