Please, I want to solve this HW in boring detail

Please solve the following problem as a CSP. Futoshiki is a Japanese logic puzzle that is very simple, but can be quite challenging. You are given an n x n grid, and must place the numbers 1, ... n in the grid such that every row and column has exactly one of each. Additionally, the assignment must satisfy the inequalities placed between some adjacent squares. Below is an instance of this problem, for size n = 4. Some of the squares have known values, such that the puzzle has a unique solution. Note also that inequalities apply only to the two adjacent squares, and do not directly constrain other squares in the row or column 1,1 1,2 1,3 1.4 A 2,3 2,1 2.2 2,4 V 3.2 3,1 3,3 3 A 4,1 4,2 4,3 2 Let's formulate this puzzle as a CSP. We will use 42 variables, one for each cell, with Xij as the variable for the cell in the ith row and jth column (each cell contains its i, j label in the top left corner). The only unary constraints will be those assigning the known initial values to their respective squares (e.g. X34 = 3). (a) Complete the formulation of the CSP using only binary constraints (in addition to the unary constraints specified above. In particular, describe the domains of the variables, and all binary constraints you think are necessary. You do not need to enumerate them all, just describe them using concise mathematical notation. You are not permitted to use n-ary constraints where n> 3. [1.5 mark] (b) After enforcing unary constraints, consider the binary constraints involving X14 and X24. Enforce arc consistency on just these constraints and state the resulting domains for the two variables. [0.5 mark]