{"raw_statement":[{"iden":"statement","content":"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 (Gx, Gy) and a radius Gr.\n\nThe 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.\n\nThe wolf is tied to a pole at position (Wx, Wy) with a rope of length Wr.\n\nFind 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.\n\nThe first line contains the number of test cases T (1 ≤ T ≤ 10000). \n\nEach test case consists of 2 lines. The first line contains integers Gx, Gy and Gr. The second line contains integers Wx, Wy and Wr. ( - 105 ≤ Gx, Gy, Wx, Wy ≤ 105, 1 ≤ Gr, Wr ≤ 105)\n\nFor 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*.\n\n"},{"iden":"input","content":"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 Gx, Gy and Gr. The second line contains integers Wx, Wy and Wr. ( - 105 ≤ Gx, Gy, Wx, Wy ≤ 105, 1 ≤ Gr, Wr ≤ 105)"},{"iden":"output","content":"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*."},{"iden":"examples","content":"Input20 0 50 10 50 0 55 0 5OutputCase #1: 78.53981634Case #2: 47.83057387"}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ T \\in \\mathbb{Z} $ be the number of test cases.  \nFor each test case $ k \\in \\{1, \\dots, T\\} $:  \n- Let $ C_G = (G_x, G_y) \\in \\mathbb{R}^2 $ be the center of the grass circle with radius $ G_r \\in \\mathbb{R}^+ $.  \n- Let $ C_W = (W_x, W_y) \\in \\mathbb{R}^2 $ be the center of the wolf's reach circle with radius $ W_r \\in \\mathbb{R}^+ $.  \n\n**Constraints**  \n1. $ 1 \\le T \\le 10000 $  \n2. $ -10^5 \\le G_x, G_y, W_x, W_y \\le 10^5 $  \n3. $ 1 \\le G_r, W_r \\le 10^5 $  \n\n**Objective**  \nFor each test case $ k $, compute the area of the grass circle $ C_G $ that lies outside the wolf's reach circle $ C_W $:  \n$$\nA_k = \\text{Area}(C_G \\setminus C_W)\n$$  \nThat is, the area of the disk centered at $ C_G $ with radius $ G_r $, minus the area of its intersection with the disk centered at $ C_W $ with radius $ W_r $.","simple_statement":"A sheep can eat grass inside a circle centered at (Gx, Gy) with radius Gr.  \nA wolf is tied to a point (Wx, Wy) with a rope of length Wr.  \nThe wolf can reach any point within its circle.  \n\nFind the area of grass the sheep can eat without entering the wolf’s reach.  \n\nInput:  \n- First line: T (number of test cases)  \n- Next T pairs of lines:  \n  - Line 1: Gx, Gy, Gr (grass circle)  \n  - Line 2: Wx, Wy, Wr (wolf circle)  \n\nOutput:  \nFor each test case, print “Case #tc: A” where A is the safe grass area with error ≤ 1e-6.","has_page_source":false}