Land area

A city is divided into $N \times M$ cells, and the price of every cell is known. You have $K$ money. Buy a rectangular plot of maximum area (number of cells) whose total price does not exceed $K$. If there are several such plots, choose the cheapest.

The first line contains $N$, $M$, $K$ ($1 \le N, M \le 100$, $0$). Each of the next lines contains integers — the cell prices ().

A single line with two numbers: the area of the plot and its price. If no cell can be bought, print 0 0.

Choose the top and bottom rows ($O(N^2)$ pairs) — the price of every column over these rows comes from column prefix sums in $O(1)$. Prices are non-negative, so two pointers work over the columns: for every right border find the leftmost border with sum $\le K$. In total $$.