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:

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

Note

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

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

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

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

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

Digital Wallet

Examples