You are given a weighted 2-banded graph, which is a undirected graph G (V, E) with 2n vertices. Each vertex is labeled as (i) where i = 1 or i-2, and J-1, .. , n. There is an edge between (j) to (i, j + 1) for every i = 1, 2 and J-1, . . . , n-1. There is also an edge between (1.3) and (2,j) for all possible j's. Below is such a graph for n = 4. Furthermore, each vertex has a weight, which is a positive integer. 2,2 2,3 2,4 An independent set W is a subset of V, such that for any two vertices u,vE W, there is no edge between u and v in the graph G. The total weight of a set W is the sum of the weights of all vertices in W; the total weight of the empty set is 0. There are many possible independent sets in G; the independent set with the largest total weight is the marimum independent set Give a O(n) dynamic programming algorithm that, given a weighted two-banded graph outputs the weight of its maximum independent set (it is not necessary to find the maximum independent set, just compute the weight