Luxury burrow#7480
Tired of adventures, the hobbit Bilbo decided to build a new burrow. The hill where Bilbo plans to purchase a plot has a rectangular shape and can be represented as a table with rows and columns (rows and columns are numbered starting from one: row is the topmost, and column is the leftmost). Each cell of the table corresponds to a square plot of land measuring 1 \times 1 meter.
Hobbits prefer neat and simple shapes, so Bilbo is determined to buy a rectangular plot with sides parallel to the edges of the hill. Formally, he selects four integers x_1, x_2, y_1, y_2~(x_1 \le x_2,~ y_1 \le y_2) and purchases all cells satisfying x_1 \le x \le x_2 and y_1 \le y \le y_2.
His recent adventures brought Bilbo so much gold that the cost of the land doesn't worry him much. However, he deeply cares about his reputation — so he wants the minimum cell cost in the chosen plot to be as high as possible. Additionally, Bilbo values spaciousness, so the area of the plot must be at least . If there are multiple plots with the same minimum cell cost, Bilbo will choose the one with the largest area.
Help the hobbit choose the most suitable plot.
The first line contains three integers , , and k~(1 \le n, m \le 1000, 1 \le k \le n \cdot m) — the number of rows, columns, and the minimum acceptable area of the plot, respectively.
The next lines each contain integers — the costs of the cells. The -th number in the -th line corresponds to the cost of the cell at coordinates . All costs are integers between and 10^9, inclusive.
Print two integers:
the maximum possible minimum cell cost of the plot,
the maximum possible area of such a plot (among all plots with that maximum minimum cost).
Example 1
Example 2
Example 3