| James and Wilson are the best of buddies. And, conveniently enough, they both | |
| work at Corpro Corp! Every day, they have the opportunity to eat lunch | |
| together, while talking about how well their favourite sports teams are doing | |
| and how strict their managers are. However, their work obligations can often | |
| get in the way of that. | |
| At Corpro Corp, each workday is 80,000,000 milliseconds long, and the company | |
| uses the phrase "time **t**" to refer to the moment in time **t** milliseconds | |
| after the start of the workday. All employees arrive at time 0, and leave at | |
| time 80,000,000. | |
| On a certain day, James gets invited to **J** optional meetings. The **i**th | |
| of these meetings starts at time **Ai** and ends at time **Bi**. Similarly, | |
| Wilson gets invited to **W** optional meetings, with the **i**th one starting | |
| at time **Ci** and ending at time **Di**. All **J**+**W** meetings might | |
| arbitrarily overlap with one another. | |
| Both James and Wilson may choose to accept any subset of their invitations, | |
| possibly none of them or all of them. The meetings are all conducted | |
| virtually, making it possible to attend multiple meetings at the same time — | |
| as such, two invitations may be accepted even if their time ranges overlap. | |
| As it turns out, James and Wilson actually hate having lunch together, but | |
| they feel obligated to do so if they're able to. Eating lunch takes exactly | |
| **L** milliseconds, and so the two friends will meet up for lunch if there's a | |
| consecutive interval of at least **L** milliseconds within their work hours | |
| during which neither of them is taking part in any meetings. | |
| Less surprisingly, James and Wilson hate attending meetings. If James accepts | |
| **x** of his **J** invitations, and Wilson accepts **y** of his **W** | |
| invitations, then the combined inconvenience they experience is max(**x**, | |
| **y**). Determine whether or not it's possible for them to avoid having to eat | |
| lunch together — and, if so, determine the minimum combined inconvenience they | |
| must incur to do so. | |
| ### Input | |
| Input begins with an integer **T**, the number of days James and Wilson go to | |
| work. For each day, there is first a line containing the space-separated | |
| integers **J**, **W**, and **L**. | |
| Then, **J** lines follow, the **i**th of which contains the space-separated | |
| integers **Ai** and **Bi**. | |
| Then, **W** lines follow, the **i**th of which contains the space-separated | |
| integers **Ci** and **Di**. | |
| ### Output | |
| For the **i**th day, print a line containing "Case #**i**: " followed by the | |
| minimum combined inconvenience James and Wilson must experience, or | |
| "Lunchtime" if they cannot avoid having lunch together. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 20 | |
| 0 ≤ **J**, **W** ≤ 3000 | |
| 1 ≤ **L** ≤ 100,000,000 | |
| 0 ≤ **Ai** < **Bi** ≤ 80,000,000 | |
| 0 ≤ **Ci** < **Di** ≤ 80,000,000 | |
| ### Explanation of Sample | |
| In the first case, James can attend the meeting from time 40,000,000 to | |
| 70,000,000, and Wilson can attend the meeting from time 10,000,000 to time | |
| 21,000,000. They each attend one meeting, so the combined inconvenience is 1. | |