| Thanks to his tireless hard work, Wilson has been promoted and now gets to |
| drive his moving company's trucks! No, he can't believe it either. |
|
|
| The moving company services a region that has **N** towns, with **M** roads |
| running amongst them. The _i_th road connects two different towns **Ai** and |
| **Bi**, requires **Gi** litres of gas to drive along, and can be traversed in |
| either direction. There may be multiple roads running directly between any |
| given pair of towns. |
|
|
| Today, Wilson has been scheduled to transport **K** families' belongings. The |
| _i_th family is moving from town **Si** to a different town **Di**. Wilson and |
| his truck will be starting off the day at the company headquarters in town 1. |
| For each family, he'll need to drive to their starting town by following a |
| sequence of roads, load his truck there, and at some point later, arrive at |
| their destination town to unload their belongings. His truck is large enough |
| to fit at most 2 families' sets of belongings at a time, meaning that he |
| doesn't necessarily need to deliver each load immediately after picking it up. |
|
|
| However, Wilson has been instructed that the **K** families must be helped |
| strictly in order. In particular, if i < j, then the _i_th family's belongings |
| must be loaded before the _j_th family's belongings are loaded, and the _i_th |
| family's belongings must be delivered before the _j_th family's belongings are |
| delivered. |
|
|
| Although Wilson's wages are higher than ever, he does have to pay for the |
| truck's gas out of his own pocket, so it's in his best interest to get the job |
| done while burning through as little of it as possible. Of course, he'll still |
| need to be careful to follow his company's strict rules regarding the relative |
| order of the families' loads and unloads, to avoid getting fired. That being |
| said, it's a possibility for it to be impossible to even complete all of the |
| requested moves, in which case Wilson will simply call it a day and stay home |
| instead. |
|
|
| ### Input |
|
|
| Input begins with an integer **T**, the number of sets of families Wilson |
| needs to move. |
|
|
| For each case, there is first a line containing three space-separated |
| integers, **N**, **M**, and **K**. |
|
|
| Then, **M** lines follow, the _i_th of which contains 3 space-separated |
| integers, **Ai**, **Bi**, and **Gi**. |
|
|
| Then, **K** lines follow, the _i_th of which contains 2 space-separated |
| integers, **Si** and **Di**. |
|
|
| ### Output |
|
|
| For the _i_th case, print a line containing "Case #**i**: " followed by the |
| minimum amount of gas required for Wilson to validly complete his delivery |
| schedule, or -1 if it can't be done. |
|
|
| ### Constraints |
|
|
| 1 ≤ **T** ≤ 100 |
| 2 ≤ **N** ≤ 100 |
| 1 ≤ **M** ≤ 5,000 |
| 1 ≤ **K** ≤ 5,000 |
| 1 ≤ **Ai**, **Bi** ≤ **N**, **Ai** ≠ **Bi** |
| 1 ≤ **Si**, **Di** ≤ **N**, **Si** ≠ **Di** |
| 1 ≤ **Gi** ≤ 1,000 |
|
|
| ### Explanation of Sample |
|
|
| In the first case, Wilson drives to town 2, and then drives the first family's |
| belongings back to town 1. That's 8 litres gas so far. Then Wilson drives to |
| city 3 (11 more litres of gas), picks up the remaining belongings, and drives |
| them all to town 2 (7 litres of gas). A grand total of 8 + 11 + 7 = 26 litres |
| of gas. |
|
|
| In the fourth case, Wilson can't reach town 4 in order to complete the 2nd and |
| 3rd families' moves. |
|
|
|
|
