Question 181
Find the largest positive integer $m$ such that there is a way to color some of the cells red in a $70 \times 70$ grid, satisfying the following two conditions:
(1) There do not exist two red cells such that the number of red cells in the row they belong to and the number of red cells in the column they belong to are the same;
(2) There are at least 2 rows each containing exactly $m$ red cells.
(1) There do not exist two red cells such that the number of red cells in the row they belong to and the number of red cells in the column they belong to are the same;
(2) There are at least 2 rows each containing exactly $m$ red cells.