401579: GYM100495 K Wolf and sheep

A sheep lives on an infinite field. The sheep wants to eat some grass. Grass only exists in one place. That place is a circle defined by a center point (G_x, G_y) and a radius G_r.

The sheep would gladly eat all the grass. But if you read the title of this task you noticed that there is also a wolf on that field. The wolf wants to eat the sheep, but we don't want that to happen.

The wolf is tied to a pole at position (W_x, W_y) with a rope of length W_r.

Find the area of grass that the sheep can eat without being eaten by the wolf. We can assume that the sheep starts in a safe location.

The first line contains the number of test cases T (1 ≤ T ≤ 10000).

Each test case consists of 2 lines. The first line contains integers G_x, G_y and G_r. The second line contains integers W_x, W_y and W_r. ( - 10⁵ ≤ G_x, G_y, W_x, W_y ≤ 10⁵, 1 ≤ G_r, W_r ≤ 10⁵)

For each test case output one line containing “Case #tc: A”, where tc is the number of the test case (starting from 1) and A is the area of grass that the sheep can eat safely with a maximum absolute or relative error of 10^- 6.

2
0 0 5
0 10 5
0 0 5
5 0 5

Case #1: 78.53981634
Case #2: 47.83057387