49 empty cups are arranged in a 7×7 square. Each cup can hold up to 50 marbles.

Every time you add marbles to a cup you must add the same number of marbles to the adjacent cups.
Similarly, every time you remove marbles from a cup you must remove the same number of marbles from the adjacent cups. The central cup has 4 neighbors.

What is the largest number of marbles you can have in the center cup when all of the other cups are empty?