Migrated from Lutece 9 Headache about the Floor

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Description

Zplinti1 has a room whose floor is a square. He wants to decorate the floor using a tile. The tile is a regular polygon with $N$ sides, and each side has a length $M$.

It is guaranteed that the diameter of the circumscribed circle of the tile is shorter than the side of the floor.

Some of you may already realize, that some place of the floor may not be covered by the tile, no matter how zplinti1 puts the tile on the floor (He will never break the tile into pieces!) Zplinti1 get a headache about the problem. He wants to know the total area that cannot be covered.

Since the floor is in the room, no part of the tile may get stretched outside the floor, because there are walls around the room, it is a house not a yard!

Input

The first line of input contains a number $T$ ($T\leq 100$), indicating the number of test cases. For each case, there are two integers $N$ and $M$.($3\leq N\leq 8$, $1\leq M\leq 100$)

Output

For each case, output Case #i: first. ($i$ is the number of the test case, from $1$ to $T$). Then output the total area with precision of six decimal places.

Samples

3
3 1
4 2
5 3

Case #1: 0.000000
Case #2: 0.000000
Case #3: 1.747450

Note

The circumscribed circle of a polygon is the minimum such circle, that all the vertices of the polygon lie on the circle.

Resources

The 11th UESTC Programming Contest Final