| It's time to settle things once and for all. Your boomerang crew has decided | |
| to challenge their rivals to a boomerang crew battle! | |
| Your crew has **N** members with strengths **A1..N**, while the opposing crew | |
| has **M** members with strengths **B1..M**. The crew battle will proceed as | |
| follows: | |
| 1. Each crew will arrange its members in a line, in some order. | |
| 2. A throwing contest will take place between the first person in your line, and the first person in your opponents' line. | |
| 3. Whoever loses the contest (see below for details) will leave their line permanently, while the winner will stay at the front of their line. | |
| 4. If one of the lines has become empty, that crew loses and the crew battle concludes. | |
| 5. Otherwise, back to step 2. | |
| However, you're not about to play fair with your enemies — you've got the | |
| following 3 things going for you: | |
| 1. You will decide the initial ordering of members for _both_ crews (in step 1 of the crew battle). | |
| 2. When a member of your crew with strength **S** competes in a throwing contest, they'll throw their boomerang a distance of **S** feet. On the other hand, due to a bit of subtle poisoning you've done in advance, your enemies will get tired after each throw. In particular, when a member of the rival crew with strength **S** competes in a throwing contest, such that they've already competed in (and won) **C** throwing contests previously, they'll throw their boomerang a distance of max{**S** \- **C*****D**, 1} feet (where **D** is a set constant). | |
| 3. In each throwing contest, your crew's member will win if their throw distance is greater than _or equal_ to their opponent's. | |
| Despite these advantages, it's possible that you'll still be unable to emerge | |
| victorious. However, whether or not you do, you'd like to maximize the number | |
| of throwing contests that members of your crew win over the course of the crew | |
| battle (given that you choose optimal initial orderings for both lines). | |
| ### Input | |
| Input begins with an integer **T**, the number of battles. For each battle, | |
| there are three lines. The first line contains the space-separated integers | |
| **N**, **M**, and **D**. The second line contains the **N** space-separated | |
| integers **A1** to **AN**. The third line contains the **M** space-separated | |
| integers **B1** to **BM**. | |
| ### Output | |
| For the **i**th battle, print a line containing "Case #**i**: " followed by | |
| the maximum number of throwing contests that your crew can win. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 75 | |
| 1 ≤ **N**, **M** ≤ 100,000 | |
| 1 ≤ **Ai**, **Bi**, **D** ≤ 1,000,000,000 | |
| ### Explanation of Sample | |
| In the first battle, your single member cannot beat theirs. In the second | |
| battle, they can (just barely). In the fourth battle, one solution is to | |
| arrange their crew as [35, 25, 5] and your crew as [10, 20, 30] to emerge | |
| victorious (in which case, 5 throwing contests will occur, of which your crew | |
| will win the last three). | |