Anna’s garden is a grid of \(n \times m\) squares. She wants to have trees in some of these squares, but she wants the total number of trees in each column and in each row to be an odd number (not necessarily the same, they just all need to be odd). Show that it is possible only if \(m\) and \(n\) are both even or both odd and calculate in how many different ways she can place the trees in the grid.