Digital Wallet

Description:

Input:

The first line contains three integers $$$N$$$, $$$M$$$, and $$$K$$$ ($$$1 \leq N \leq 10$$$; $$$1 \leq M \leq 10^5$$$; $$$1 \leq K \leq \min(10, M)$$$) — the number of arrays, the size of each array, and the constant that describes the operation constraints.

The $$$i$$$-th of the next $$$N$$$ lines contains $$$M$$$ integers $$$A_{i,1}, A_{i,2}, \ldots, A_{i,M}$$$ ($$$1 \leq A_{i,j} \leq 10^6$$$) — the elements of the $$$i$$$-th array.

Output:

Output an integer representing the maximum total money that can be earned.

Sample Input:

3 3 1
10 4 2
8 1 9
4 8 2

Sample Output:

27

Sample Input:

3 3 2
5 9 4
1 3 1
2 8 7

Sample Output:

17

Sample Input:

3 4 3
5 9 10 1
1 3 1 5
2 5 7 2

Sample Output:

19

Note:

In the first example, the following is a sequence of operations of one optimal strategy:

1. Choosing element $$$A_{1, 1}$$$ with a value of $$$10$$$.
2. Choosing element $$$A_{3, 2}$$$ with a value of $$$8$$$.
3. Choosing element $$$A_{2, 3}$$$ with a value of $$$9$$$.

So the total money earned is $$$10+8+9=27$$$.

In the second example, the following is a sequence of operations of one optimal strategy:

1. Choosing element $$$A_{3, 2}$$$ with a value of $$$8$$$.
2. Choosing element $$$A_{1, 2}$$$ with a value of $$$9$$$.

So the total money earned is $$$8+9=17$$$.

In the third example, the following is a sequence of operations of one optimal strategy:

1. Choosing element $$$A_{1, 3}$$$ with a value of $$$10$$$.
2. Choosing element $$$A_{1, 2}$$$ with a value of $$$9$$$.

So the total money earned is $$$10+9=19$$$.