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:
Determine the maximum total money that can be earned!
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 an integer representing the maximum total money that can be earned.
3 3 1 10 4 2 8 1 9 4 8 2
27
3 3 2 5 9 4 1 3 1 2 8 7
17
3 4 3 5 9 10 1 1 3 1 5 2 5 7 2
19
In the first example, the following is a sequence of operations of one optimal strategy:
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:
So the total money earned is $$$8+9=17$$$.
In the third example, the following is a sequence of operations of one optimal strategy:
So the total money earned is $$$10+9=19$$$.
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