Plates

Dr. Patel has N stacks of plates. Each stack contains K plates. Each plate has a positive beauty value, describing how beautiful it looks.

Dr. Patel would like to take exactly P plates to use for dinner tonight. If he would like to take a plate in a stack, he must also take all of the plates above it in that stack as well.

Help Dr. Patel pick the P plates that would maximize the total sum of beauty values.

The first line of the input gives the number of test cases, T. T test cases follow. Each test case begins with a line containing the three integers N, K and P. Then, N lines follow. The i-th line contains K integers, describing the beauty values of each stack of plates from top to bottom.

For each test case, output one line containing Case #x: y, where x is the test case number (starting from 1) and y is the maximum total sum of beauty values that Dr. Patel could pick.

• 1 ≤ T ≤ 100.
• 1 ≤ K ≤ 30.
• 1 ≤ P ≤ N * K.
• The beauty values are between 1 and 100, inclusive.

In Sample Case #1, Dr. Patel needs to pick P = 5 plates:

• He can pick the top 3 plates from the first stack (10 + 10 + 100 = 120).
• He can pick the top 2 plates from the second stack (80 + 50 = 130) .

In total, the sum of beauty values is 250.

In Sample Case #2, Dr. Patel needs to pick P = 3 plates:

• He can pick the top 2 plates from the first stack (80 + 80 = 160).
• He can pick no plates from the second stack.
• He can pick the top plate from the third stack (20).

In total, the sum of beauty values is 180.