Greg and Grid

Recently, Greg got a grid with $n$ rows and $m$ columns. Rows are indexed from $1$ to $n$ and columns are indexed from $1$ to $m$. The cell $ ( i , j )$ is the cell of intersection of row $i$ and column $j$. Each cell has a number written on it. The number written on cell $( i , j )$ is equal to $(i+j)$. Now, Greg wants to select some cells from the grid, such that for every pair of selecte