Sending email

There are n SMTP servers connected by network cables. Each of the m cables connects two com- puters and has a certain latency measured in milliseconds required to send an email message. What is the shortest time required to send a message from server S to server T along a sequence of cables? Assume that there is no delay incurred at any of the servers. Input The first line of input gives the number of cases, N. N test cases follow. Each one starts with a line containing n (2 ≤ n ≤ 20000), m (0 ≤ m ≤ 50000), S (0 ≤ S < n) and T (0 ≤ T < n). S ̸= T. The next m lines will each contain 3 integers: 2 different servers (in the range [0, n − 1]) that are connected by a bidirectional cable and the latency, w, along this cable (0 ≤ w ≤ 10000). Output For each test case, output the line ‘Case #x:’ followed by the number of milliseconds required to send a message from S to T . Print ‘unreachable’ if there is no route from S to T . Sample Input 3 2101 0 1 100 3320 0 1 100 0 2 200 1 2 50 2001 Sample Output Case #1: 100 Case #2: 150 Case #3: unreachable “A new internet watchdog is creating a stir in Springfield. Mr. X, if that is his real name, has come up with a sensational scoop.” Kent Brockman