CN-TST 2012 Problem 11

Given two integers $m,n$ which are greater than $1$ . $r,s$ are two given positive real numbers such that $r<s$ . For all $a_{ij}\ge 0$ which are not all zeroes,find the maximal value of the expression $$f=\frac{(\sum_{j=1}^{n}(\sum_{i=1}^{m}a_{ij}^s)^{\frac{r}{s}})^{\frac{1}{r}}}{(\sum_{i=1}^{m})\sum_{j=1}^{n}a_{ij}^r)^{\frac{s}{r}})^{\frac{1}{s}}}.$$