# Happy birthday

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 672    Accepted Submission(s): 302

Problem Description
Today is Gorwin’s birthday. So her mother want to realize her a wish. Gorwin says that she wants to eat many cakes. Thus, her mother takes her to a cake garden.

The garden is splited into n*m grids. In each grids, there is a cake. The weight of cake in the i-th row j-th column is

When Gorwin reachs a grid, she can eat up the cake in that grid or just leave it alone. However she can’t eat part of the cake. But Gorwin’s belly is not very large, so she can eat at most K kilos cake. Now, Gorwin has stood in the top-left grid and look at the map of the garden, she want to find a route which can lead her to eat most cake. But the map is so complicated. So she wants you to help her.

Input
Multiple test cases (about 15), every case gives n, m, K in a single line.

In the next n lines, the i-th line contains m integers

Please process to the end of file.

[Technical Specification]

All inputs are integers.

1<=n,m,K<=100 1<=

Output
For each case, output an integer in an single line indicates the maximum weight of cake Gorwin can eat.

Sample Input
1 1 2
3
2 3 100
1 2 3
4 5 6

Sample Output
0
16

Hint

In the first case, Gorwin can’t eat part of cake, so she can’t eat any cake.

In the second case, Gorwin walks though below route (1,1)->(2,1)->(2,2)->(2,3). When she passes a grid, she eats up the cake in that grid. Thus the total amount cake she eats is 1+4+5+6=16.

Source

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01 背包，二维而已

01背包对于第i个物品的状态是只能由 i-1得到 （所以倒着循环，在计算i-1状态的时候总保证i的状态已经写出来了，可以省一维空间）