Gargoyles can trace their history back many thousands of years to ancient Egypt, Greece, and Rome. Terra cotta waterspouts were formed in the shapes of animals such as lions and birds to serve the physical function of running the
rainwater away from the walls and foundations of buildings, and the spiritual function of protecting from evil forces.
Have you ever dreamed of creating your own castle with a lot of beautiful gargoyles on the walls? To your knowledge,
the speed of water coming out of each gargoyle should be identical, so an elaborately designed water system is required.
The water system consists of a huge reservoir and several interconnecting water pipes. Pipes cannot save water, so the total incoming and outgoing speed of water should be equal at each connection.
All the water from gargoyles flows into the reservoir, which is located at the bottom of the castle. Some pipes are connecting the reservoir, but water can only go from the reservoir to pipes, but never from pipes back to the reservoir. A micro-processor is installed inside each pipe, so the speed of water could easily be controlled. However, the microprocessors consume electricity. The exact cost in each pipe is proportional to the speed of water. If the cost constant in the i-th pipe is ci, the electricity cost in that pipe is civi, where vi is the speed of water in that pipe. Write a program to find the optimal configuration of the water system (i.e. the water speed in each pipe) of your dream castle, so that the total cost is minimized. It is always possible to build a water system.

The input consists of several test cases. The first line of each case contains three integers n, m and k (1 ≤ n ≤ 25, 1 ≤ m ≤ 50, 1 ≤ k ≤ 1000), the number of gargoyles, the number of pipe connections and the number of pipes. The following k lines each contains five integers a, b, l, u, c (0 ≤ a, b ≤ n + m, 0 ≤ l ≤ u ≤ 100, 1 ≤ c ≤ 100), describing each pipe. a and b
are the incoming and outgoing vertex number (reservoir is 0, gargoyles are numbered 1 to n, pipe connections are numbered n + 1 to n + m), lower-bound and upper-bound of water speed, and the cost constant. No pipe connects two identical vertices. For every pipe, the incoming vertex will never be a gargoyle, and the outgoing vertex will never be the reservoir. For every pair of vertices, there could be at most one pipe connecting them (if a pipe is going from a to b, no pipes can go from a to b, or from b to a). The last test case is followed by a single zero, which should not be processed.

For each test case, print the case number and minimal cost to two decimal places.

3 1 4
0 4 8 15 5
4 1 2 5 2
4 2 1 6 1
4 3 3 7 2
0

Case 1: 60.00

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A famous mobile communication company is planning to build a new set of base stations. According to the previous investigation, n places are chosen as the possible new locations to build those new stations. However, the condition of each position varies much, so the costs to built a station at different places are different. The cost to build a new station at the ith place is P_i (1<=i<=n).

When complete building, two places which both have stations can communicate with each other.

Besides, according to the marketing department, the company has received m requirements. The ith requirement is represented by three integers A_i, B_i and C_i, which means if place A_i and B_i can communicate with each other, the company will get C_i profit.

Now, the company wants to maximize the profits, so maybe just part of the possible locations will be chosen to build new stations. The boss wants to know the maximum profits.

Multiple test cases (no more than 20), for each test case:
The first line has two integers n (0<n<=5000) and m (0<m<=50000).
The second line has n integers, P1 through Pn, describes the cost of each location.
Next m line, each line contains three integers, A_i, B_i and C_i, describes the ith requirement.

One integer each case, the maximum profit of the company.

5 5
1 2 3 4 5
1 2 3
2 3 4
1 3 3
1 4 2
4 5 3

4

liulibo

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