Disrupting the microwave shop industry and ripping consumers off since 2011.

Christmas is quickly approaching, so Nathan needs to buy gifts for each of his ~N~ friends! He will give out ~T~ possible types of gifts, and because he is in a very festive mood, each friend will receive each type of gift.

However, Nathan has not bought any of the gifts yet! He looks online and finds ~S~ gift shops; each shop sells exactly one of each type of gift at varying prices. Since Nathan wants to make a minimal number of trips, he will visit only ~N~ of the ~S~ shops.

Unfortunately for Nathan, the shopkeepers are not in a very festive mood. Before he visits any shop, the shopkeepers can work together to adjust the prices of their gifts. In particular, the price of the ~j^\text{th}~ type of gift at all of the ~N~ shops that he chooses will become the maximum price of the ~j^\text{th}~ type of gift at those ~N~ shops.

Nathan would like to know the minimum cost of buying gifts for all of his friends. Can you help him?

Constraints

~1 \le N \le S~

~1 \le T~

Subtask	Points	~S~	~T~
1	5	~S \le 1\,000~	~T = 1~
2	15	~S \le 1\,000~	~T = 2~
3	20	~S \le 15~	~T \le 5~
4	60	~S \le 30~	~T \le 5~

All prices will be a positive integer no greater than ~10^6~.

Input Specification

The first line will contain three space-separated integers, ~S~, ~N~, and ~T~.

~S~ lines of input follow. The ~i^\text{th}~ line will contain ~T~ space-separated integers; the ~j^\text{th}~ integer represents the price of a gift of type ~j~ from shop ~i~.

Output Specification

Output a single integer, the minimum cost to buy gifts for all of Nathan's friends.

Sample Input

5 3 3
2 4 3
1 5 2
3 1 3
6 2 1
4 3 2

Sample Output

33

Explanation for Sample Output

Nathan can go to shops ~1~, ~3~, and ~5~. The prices for gifts of type ~1~, ~2~, and ~3~ are ~4~, ~4~, and ~3~, respectively. The total cost of buying ~3~ of each type of gift is therefore ~33~.