no one has been able to solve this problem and the editorial is not clear. could anyone please give a better explanation. i.e what is the state of the dp ? and how to move from one state to another ?

problem name : "therectangularcitydiv1" problem link: https://community.topcoder.com/stat?c=problem_statement&pm=14901&rd=17158

editorial: https://www.topcoder.com/blog/single-round-match-734-editorials/