• محدودیت زمان: ۱ ثانیه
• محدودیت حافظه: ۲۵۶ مگابایت

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Some planet exist in the Shekami Way Galaxy. These planets all have the same size and they are completely spherical. Creatures that are living on each of these planets are called $Shamirium$. Each of these planets have infinite amount of delicious foods like $Pesteh$, $Pashmak$ and $Baghali$ $Polo$ $Ba$ $Mahicheh$ and also lots of drinks like $Pinacolada$ , $Ab$ $Havij$ $Bastani$ and $\dots$ and non of these drinks are alcoholic! None of these planets have mountains, valleys nor long departments. All of the Shamiriums in the Shekami way galaxy are friends with each other and they are very kind persons and they never fight with each other except for the FOODs!

However they have foods enough for supplying thousands of years for their own residents. But they still jealous at other planets foods! After they produce the foods, they need some place in their planet to store them so that the people on the other planets can’t see their foods. During all of the galaxy’s history, Shamiriums are only eating foods so their technology has not improved since they invented the telescope – even they use the telescope for seeing the other planets foods! So they are searching for blind spots so that their garner is far from the other planets site seeing. It is possible that some of the planets don’t have any blind spots to build their garner. Your task is to calculate total area of blind spots of all planets.

ورودی

First line of the input contains an integer $T(1 \le T \le 200)$, the number of test cases to follow. Each test case start with an integer $N (2 ≤ N ≤ 50)$ indicating the number of planets and $R (0 < R ≤ 1000)$ an integer indicating radios of planets. Following N lines contain positive pairs of integers $xi , yi (|xi| , |yi| ≤ 1,000,000)$ indicating the coordinates of the $i$’th planet. Of course planets do not intersect, so it is guaranteed that input is valid.

خروجی

For each test case output “Case #X: A” (quotations for clarify) which X is number of the test case and A is the answer as described above with exactly three decimal digits.

مثال‌ها

ورودی نمونه ۱

1
2 2
1 1
100 100

خروجی نمونه ۱

Case #1: 50.265