CF1392I Kevin and Grid

As Kevin is in BigMan's house, suddenly a trap sends him onto a grid with $ n $ rows and $ m $ columns. BigMan's trap is configured by two arrays: an array $ a_1,a_2,\ldots,a_n $ and an array $ b_1,b_2,\ldots,b_m $ . In the $ i $ -th row there is a heater which heats the row by $ a_i $ degrees, and in the $ j $ -th column there is a heater which heats the column by $ b_j $ degrees, so that the temperature of cell $ (i,j) $ is $ a_i+b_j $ . Fortunately, Kevin has a suit with one parameter $ x $ and two modes: - heat resistance. In this mode suit can stand all temperatures greater or equal to $ x $ , but freezes as soon as reaches a cell with temperature less than $ x $ . - cold resistance. In this mode suit can stand all temperatures less than $ x $ , but will burn as soon as reaches a cell with temperature at least $ x $ . Once Kevin lands on a cell the suit automatically turns to cold resistance mode if the cell has temperature less than $ x $ , or to heat resistance mode otherwise, and cannot change after that. We say that two cells are adjacent if they share an edge. Let a path be a sequence $ c_1,c_2,\ldots,c_k $ of cells such that $ c_i $ and $ c_{i+1} $ are adjacent for $ 1 \leq i \leq k-1 $ . We say that two cells are connected if there is a path between the two cells consisting only of cells that Kevin can step on. A connected component is a maximal set of pairwise connected cells. We say that a connected component is good if Kevin can escape the grid starting from it — when it contains at least one border cell of the grid, and that it's bad otherwise. To evaluate the situation, Kevin gives a score of $ 1 $ to each good component and a score of $ 2 $ for each bad component. The final score will be the difference between the total score of components with temperatures bigger than or equal to $ x $ and the score of components with temperatures smaller than $ x $ . There are $ q $ possible values of $ x $ that Kevin can use, and for each of them Kevin wants to know the final score. Help Kevin defeat BigMan!

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In the first example, the score for components with temperature smaller than $ 5 $ is $ 1+2 $ , and the score for components with temperature at least $ 5 $ is $ 2 $ . Thus, the final score is $ 2-3=-1 $ .