| In the ever-popular role-playing game _Dungeons & Dragons_, or _D&D_, some | |
| wizards enhance their skills by training as geometers, specialist spellcasters | |
| who rely on the inherent magical properties of geometric forms. | |
| Unlike low-level wizards who may be able to fight only a single zombie at a | |
| time, you, the budding geometer, are ready and able to fight medium-sized | |
| hordes! | |
| There are **N** zombies on an infinite 2D plane, with the _i_th one at | |
| coordinates (**Xi**, **Yi**). You have two spells at your disposal, but you | |
| can only cast each one once. | |
| You'll first cast the function-spell `Move(x, y, r, dx, dy)`. Each of its five | |
| parameters can be any real number, though `r` must be positive. Upon | |
| performing this spell, each zombie initially within the circle centered at | |
| coordinates (`x`, `y`) and having radius `r` will have its coordinates | |
| translated by (`dx`, `dy`). In other words, it will have `dx` added to its | |
| x-coordinate, and `dy` added to its y-coordinate. Zombies on the border of the | |
| circle are also affected. | |
| You'll then cast the function-spell `Destroy(x, y)`. Each of its two | |
| parameters can be any real number. Upon performing this spell, each zombie | |
| currently within the axis-aligned square centered at coordinates (`x`, `y`) | |
| and having side-length **R** will be destroyed. Zombies on the border of the | |
| square are also affected. | |
|   | |
| What's the largest number of zombies that can be destroyed by this combination | |
| of function-spells? | |
| ### Input | |
| Input begins with an integer **T**, the number of zombie hordes you fight. For | |
| each case, there is first a line containing two space-separated integers, | |
| **N** and **R**. Then, **N** lines follow, the _i_th of which contains 2 | |
| space-separated integers, **Xi** and **Yi**. | |
| ### Output | |
| For the _i_th case, print a line containing "Case #**i**: " followed by the | |
| maximum number of zombies you can slay with your spells. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 50 | |
| 1 ≤ **N** ≤ 50 | |
| 0 ≤ **Xi**, **Yi** ≤ 1,000,000,000 | |
| 1 ≤ **R** ≤ 1,000,000,000 | |
| It is guaranteed that no two zombies are initially at the same point, though | |
| zombies may later be moved such that there are multiple at the same | |
| coordinates. | |
| ### Explanation of Sample | |
| In the first case (shown in the pictures above), one optimal strategy is to | |
| first cast `Move(2.5, 4.5, 2.2, 3, -1)`, moving 4 zombies, and then cast | |
| `Destroy(5.5, 2.5)`, destroying 6 zombies. | |