Review the Longest Increasing Subsequence problem and the dynamic solution explained in the lectures, given the instance S$=[4,6,2,8,7,5],$ do what is required: Build the "brute force" tree $($with bound$)$ when the analysis is in the order s$\_1,$s$\_2,...,$s$\_$n$,$ use black font when the sequence is a valid increasing subsequence and red font otherwise. $(0\mathrm{.}4$ points$)$ Draw the corresponding DAG for the instance. $(0\mathrm{.}1$ point$)$ Given the dynamic programming $($bottom$-$up$)$ approach explained in the lectures, show the table with the corresponding saved solutions for the subproblems of the given instance $(0\mathrm{.}1$ point$)$ Write the corresponding solution for each subproblem. To obtain the points it is mandatory to specify max$\{1,...\}$ indicating which LIS$[$X$]$ is analyzed and then their values. Exclude any LIS$[$X$]$ that is not valid in the calculation