| 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. |
|
|
|
|
