{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eSasha loves physics. Sasha has no friends. Whether these facts are connected or not, Sasha is very upset about his lack of friends. So he tried to impress Vadim with an experiment.\u003c/div\u003e\u003c/div\u003e\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eSasha lives on a plane with a Cartesian coordinate system. He took a convex polygon with \u003ci\u003en\u003c/i\u003e vertices numbered from 1 to \u003ci\u003en\u003c/i\u003e, where the \u003ci\u003ei\u003c/i\u003e-th vertex has coordinates (\u003ci\u003ex\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e), and poured juice inside the polygon, filling it to the brim. Then he brought it to Vadim to demonstrate an experiment. Turns out, Vadim doesn’t like physics and doesn’t care about Sasha’s experiments. So he poked a hole in one of the sides of the polygon (but not in one of its vertices!), the hole is a point with coordinates (\u003ci\u003ex\u003c/i\u003e\u003csub\u003e0\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub\u003e0\u003c/sub\u003e). All the excess juice poured out of the polygon due to the gravity (gravity is pointed in the direction of decrease of coordinate \u003ci\u003ey\u003c/i\u003e). But Vadim wasn’t satisfied yet, so he started rotating the polygon slowly by angles \u003ci\u003eα\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e around the center of the coordinate system, spilling even more juice.\u003c/div\u003e\u003c/div\u003e\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eYou witnessed it all, but no one could stop Vadim. At least you can reassure Sasha by telling him how much exactly juice remained before and after every rotation. We hope you are a good person, and you’ll succeed at calming Sasha down.\u003c/div\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eThe first line contains one integer \u003ci\u003en\u003c/i\u003e\u0026nbsp;— the amount of vertices (3 ≤ \u003ci\u003en\u003c/i\u003e ≤ 10\u003csup\u003e5\u003c/sup\u003e).\u003c/div\u003e\u003c/div\u003e\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eNext \u003ci\u003en\u003c/i\u003e lines contain two numbers \u003ci\u003ex\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e each, separated with a space\u0026nbsp;— coordinates of vertices in counter-clockwise order (−10\u003csup\u003e5\u003c/sup\u003e ≤ \u003ci\u003ex\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 10\u003csup\u003e5\u003c/sup\u003e). Coordinates are given with exactly three digits after the decimal point.\u003c/div\u003e\u003c/div\u003e\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eThe (\u003ci\u003en\u003c/i\u003e+2)-th line contain two numbers \u003ci\u003ex\u003c/i\u003e\u003csub\u003e0\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub\u003e0\u003c/sub\u003e each, separated with a space\u0026nbsp;— coordinates of the hole (−10\u003csup\u003e5\u003c/sup\u003e ≤ \u003ci\u003ex\u003c/i\u003e\u003csub\u003e0\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub\u003e0\u003c/sub\u003e ≤ 10\u003csup\u003e5\u003c/sup\u003e). Coordinates are given with exactly three digits after the decimal point.\u003c/div\u003e\u003c/div\u003e\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eThe (\u003ci\u003en\u003c/i\u003e+3)-th line contains an integer \u003ci\u003eq\u003c/i\u003e\u0026nbsp;— the amount of rotations (0 ≤ \u003ci\u003eq\u003c/i\u003e ≤ 10\u003csup\u003e5\u003c/sup\u003e).\u003c/div\u003e\u003c/div\u003e\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eThe last \u003ci\u003eq\u003c/i\u003e lines contain one number \u003ci\u003eα\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e each\u0026nbsp;— angles of rotations in the order they were performed, counter-clockwise, in degerees (−360 ≤ \u003ci\u003eα\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 360, rotation by −\u003ci\u003ex\u003c/i\u003e counter-clockwise is the same as rotation by \u003ci\u003ex\u003c/i\u003e clockwise). The angles are given with exactly three digits after the decimal point.\u003c/div\u003e\u003c/div\u003e\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eIt is guaranteed that the polygon is convex, no three vertices lay on the same line, and that the hole is located exactly on the polygon’s side, but not in one of the vertices.\u003c/div\u003e\u003c/div\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eOutput \u003ci\u003eq\u003c/i\u003e + 1 lines. The first line should contain the area of juice remaining after Vadim poked the hole. Each of next \u003ci\u003eq\u003c/i\u003e lines should contain the remaining area of juice after each rotation.\u003c/div\u003e\u003c/div\u003e\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eThe answer is considered correct if absolute or relative error of each number doesn’t exceed 10\u003csup\u003e−4\u003c/sup\u003e.\u003c/div\u003e\u003c/div\u003e"}},{"title":"Sample","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3\r\n-2.000 1.000\r\n1.000 -2.000\r\n4.000 1.000\r\n1.000 1.000\r\n4\r\n45.000\r\n45.000\r\n45.000\r\n45.000\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e9.000000000\r\n6.750000000\r\n4.500000000\r\n2.250000000\r\n0.000000000\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Notes","value":{"format":"HTML","content":"\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eIllustration of the example\u003c/div\u003e\u003c/div\u003e\u003cimg src\u003d\"CDN_BASE_URL/dd8623f17e9bb27c45c7bba7ad83de5d?v\u003d1715938872\" border\u003d\"0\" alt\u003d\"Problem illustration\" align\u003d\"RIGHT\" class\u003d\"problem_raimage\"\u003e"}}]}