You have a sequence of n integers, and each integer is coloured either red or green. You need to find the largest sum of a subsequence of the input sequence, but under the restriction that two integers that are consecutive in the original sequence can only both be included if they are different colours. Note that this sequence can include both positive and negative integers. (a) Consider the greedy algorithm that considers the integers from left to right, and takes each positive integer in turn as long as it is not forbidden under the rules. Give and demonstrate a counterexample to show that this greedy algorithm does not always work. Give a recurrence that will compute the largest possible sum allowed from the sequence of numbers, where number i has value v_i and colour c_i. Include all cases needed to compute the recurrence. Also give the parameter values that correspond to the needed overall answer (how the recurrence would need to be initially called)