Let n be an even positive integer. Write the numbers
1;2; ... ,n^2 in the squares of an nxn grid so that the
1st row, from left to right, is
1, 2, 3, ,...n and each row represents the continuation of the previous.

Color the numbers so that half of them
in each row and in each column are red and the other
half are black.

Prove that for each coloring, the sum of the red numbers equals to the sum of the black numbers.