Tesla is planning on constructing a town next to its newest factory. There are multiple rites and maximizing the land utilization is the primary concern. Each potential site is organized in an mn grid. The grid is organized like a checker board, where the black squares are electrified and the white squares are not. The square at coordinate (0,0) is always black. The ground on which the potential towns are to be constructed is not perfect and some squares cannot be used for construction. You have an indicator matrix A, where A[i][j] is 0 if the square cannot be used for construction, and 1 otherwise. The houses that will be constructed are rectangular and take up exactly two squares (one black and one white). For any potential site to be considered, all usable space (Ai][j]=1) should be covered by houses. You will design an algorithm that can determine if, for a potential site, all the usable squares can be covered by houses. Also, from your solution, you should be able to determine how the houses are placed. 4.2. (2 points) Justify that your algorithm is correct. 44. ( 2 points) Give an algorithm that can returns an array of tuples of pairs {(i,j),(u,v)} that correspond to the placement of the houses given a solution to your algorithm from 4.1