Problem 3. [Category: Stable matching] We have talked about stable matching problem with examples of hospital and medical students matching problems and Gale-Shapley algorithm for the n hospitals and n students setting. In this problem, we will switch to the opposite sex marriage stable matching problem that we can apply Gale-Shapley algorithm. Given n men and n women, we want to find a stable matching set so that men and women would be paired as couples and no unstable pairs. Given the preference list (Figure 1) of the men and women as follows, please follow Gale-Shapley algorithm (start with men's side) writing out the stable matching set found by the algorithm. You don't need to write down every step of the algorithm. [20 points ] Men's Preference Profile Women's Preference Profile