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	$S\le 1000$	$T=1$
2	15	$S\le 1000$	$T=2$
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 $33$.