D. Digital Wallet
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

There are $$$N$$$ arrays, each array has $$$M$$$ positive integer elements The $$$j$$$-th element of the $$$i$$$-th array is $$$A_{i,j}$$$.

Initially, Chaneka's digital wallet contains $$$0$$$ money. Given an integer $$$K$$$. Chaneka will do $$$M-K+1$$$ operations. In the $$$p$$$-th operation, Chaneka does the following procedure:

  1. Choose any array. Let's say Chaneka chooses the $$$x$$$-th array.
  2. Choose an index $$$y$$$ in that array such that $$$p \leq y \leq p+K-1$$$.
  3. Add the value of $$$A_{x, y}$$$ to the total money in the wallet.
  4. Change the value of $$$A_{x, y}$$$ into $$$0$$$.

Determine the maximum total money that can be earned!

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.

Examples
Input
3 3 1
10 4 2
8 1 9
4 8 2
Output
27
Input
3 3 2
5 9 4
1 3 1
2 8 7
Output
17
Input
3 4 3
5 9 10 1
1 3 1 5
2 5 7 2
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 $$$10+9=19$$$.