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1153 - Internet Bandwidth
 PDF (English) Statistics Forum
 Time Limit: 2 second(s) Memory Limit: 32 MB

On the Internet, machines (nodes) are richly interconnected, and many paths may exist between a given pair of nodes. The total message-carrying capacity (bandwidth) between two given nodes is the maximal amount of data per unit time that can be transmitted from one node to the other. Using a technique called packet switching; this data can be transmitted along several paths at the same time.

For example, the following figure shows a network with four nodes (shown as circles), with a total of five connections among them. Every connection is labeled with a bandwidth that represents its data-carrying capacity per unit time.

In our example, the bandwidth between node 1 and node 4 is 25, which might be thought of as the sum of the bandwidths 10 along the path 1-2-4, 10 along the path 1-3-4, and 5 along the path 1-2-3-4. No other combination of paths between nodes 1 and 4 provides a larger bandwidth.

You must write a program that computes the bandwidth between two given nodes in a network, given the individual bandwidths of all the connections in the network. In this problem, assume that the bandwidth of a connection is always the same in both directions (which is not necessarily true in the real world).

# Input

Input starts with an integer T (≤ 30), denoting the number of test cases.

Every description starts with a line containing an integer n (2 ≤ n ≤ 100), which is the number of nodes in the network. The nodes are numbered from 1 to n. The next line contains three numbers s, t, and c. The numbers s and t are the source and destination nodes, and the number c (c ≤ 5000, s ≠ t) is the total number of connections in the network. Following this are c lines describing the connections. Each of these lines contains three integers: the first two are the numbers of the connected nodes, and the third number is the bandwidth of the connection. The bandwidth is a non-negative number not greater than 1000.

There might be more than one connection between a pair of nodes, but a node cannot be connected to itself. All connections are bi-directional, i.e. data can be transmitted in both directions along a connection, but the sum of the amount of data transmitted in both directions must be less than the bandwidth.

# Output

For each case of input, print the case number and the total bandwidth between the source node s and the destination node t.

# Output for Sample Input

2

4

1 4 5

1 2 20

1 3 10

2 3 5

2 4 10

3 4 20

4

1 4 2

1 4 20

1 4 20

Case 1: 25

Case 2: 40

Special Thanks: Jane Alam Jan (Solution, Dataset)
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