Yuta gives Rikka a chess board of size $n \times m$.
As we all know, on a chess board, every cell is either black or white and every two cells that share a side have different colors.
Rikka can choose any rectangle formed by board squares and perform an inversion, every white cell becomes black, and vice versa.
Rikka wants to turn all cells into the same color, please tell Rikka the minimal number of inversions she need to achieve her goal.