Školjka

%V0 Let $A = (a_{ij})$, where $i,j = 1,2,\ldots,n$, be a square matrix with all $a_{ij}$ non-negative integers. For each $i,j$ such that $a_{ij} = 0$, the sum of the elements in the $i$th row and the $j$th column is at least $n$. Prove that the sum of all the elements in the matrix is at least $\frac {n^2}{2}$.