a. In nucleotide-based alignment, one algorithm to update scores in comparing two nucleotide sequences is shown below (8 is gap penalty; vi and wj are two nucleotides being compared; u is a constant): Si-1.j S = max [ s -8 i.j i.j-1 S ] i-1,j-1 + 1, if vi= wj i-1, j-1 - , otherwise When performing an alignment of two AA sequences, a scoring matrix is used, which provides the likelihoods (costs) of switching from on AA to another AA. PAM or BLOSUM are well- known such matrices. Suppose, a gap penalty is 8 and that a scoring matrix, D[20][20] is given. As shown above, show the core of the dynamic programming for the for loops that update the scores with respect to the AA score matrix D.