B"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: 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 <= q i <= q 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! The first line contains three integers n , m , q ( 1 <= q n,m,q <= q 10^5 ) xe2 x80 x93 the number of rows, columns, and the number of possible values for x respectively. The second line contains n "...