Problem E: Class Schedule
At Fred Hacker's school, there are T × C classes,
divided into C catagories of T classes each. The day begins with
all the category 1 classes being taught simultaneously. These all end
at the same time, and then all the category 2 classes are taught, etc.
Fred has to take exactly one class in each category. His goal
is to choose the set of classes that will minimize the amount of
``energy'' required to carry out his daily schedule.
The energy requirement of a schedule is the sum of the energy
requirement of the classes themselves, and energy consumed
by moving from one class to the next through the schedule.
More specifically, taking the jth class in the ith category uses
Eij units of energy. The rooms where classes take place are
located at integer positions (ranging from 0 to L) along a single
hallway. The jth class in the ith category is located at position
Pij. Fred starts the day at position 0, moves from class to
class, according to his chosen schedule, and finally exits
at location L. Moving a distance d uses d units of energy.
The first line of the input is Z ≤ 20 the number of test cases.
This is followed by Z test cases. Each test case begins with three
space-separated integers: C, T, and L. Each of the following
C× T lines gives, respectively, the location and energy
consumption of a class. The first T lines represent the classes of
category 1, the next T lines represent the classes of category 2,
and so on. No two classes in the same category will have the same
1 ≤ C ≤ 25
1 ≤ T ≤ 1000
1 ≤ L ≤ 1,000,000
1 ≤ Eij ≤ 1,000,000
0 ≤ Pij ≤ L
3 2 5
Explanation of Sample Input
Fred must take 3 classes every day, and for each he has 2 choices. The
hall has length 5. His first possible class is located at position 2 and
will take 1 unit of energy each day, etc.
For each input instance, the output will be a single integer on a line
by itself which is the minimum possible energy of a schedule
satisfying the constraints.
Output for Sample Input
Explanation of Sample Output
Here is one way to obtain the minimum energy:
Go to the class at location 2. Energy used: 3
Next, go to the class at location 4. Energy used: 6
Then go to the class at location 3. Energy used: 9
Finally, leave the school at location 5. Energy used: 11