{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":" Mr.\u0026nbsp;Nod is an astrologist and has defined a new constellation. He took two photos of the constellation to foretell a future of his friend. The constellation consists of \u003ci\u003en\u003c/i\u003e stars. The shape of the constellation in these photos are the same, but the angle of them are different because these photos were taken on a different day. He foretells a future by the difference of the angle of them. Your job is to write a program to calculate the difference of the angle of two constellation. \u003cbr\u003e\u003cdiv align\u003d\"left\" style\u003d\"margin-top: 1.0em;\"\u003e\u003cb\u003eInput\u003c/b\u003e\u003c/div\u003eThe input is given in the following format: \u003cpre\u003e\u003ci\u003en\u003c/i\u003e\n\u003ci\u003ex\u003c/i\u003e\u003csub\u003e1,1\u003c/sub\u003e \u003ci\u003ey\u003c/i\u003e\u003csub\u003e1,1\u003c/sub\u003e\n...\n\u003ci\u003ex\u003c/i\u003e\u003csub\u003e1,\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e \u003ci\u003ey\u003c/i\u003e\u003csub\u003e1,\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\n\u003ci\u003ex\u003c/i\u003e\u003csub\u003e2,1\u003c/sub\u003e \u003ci\u003ey\u003c/i\u003e\u003csub\u003e2,1\u003c/sub\u003e\n...\n\u003ci\u003ex\u003c/i\u003e\u003csub\u003e2,\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e \u003ci\u003ey\u003c/i\u003e\u003csub\u003e2,\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\n\u003c/pre\u003e The first line of the input contains a positive integer \u003ci\u003en\u003c/i\u003e (\u003ci\u003en\u003c/i\u003e ≤ 1000). The next \u003ci\u003en\u003c/i\u003e lines contain two real numbers \u003ci\u003ex\u003c/i\u003e\u003csub\u003e1,\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e and \u003ci\u003ey\u003c/i\u003e\u003csub\u003e1,\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e (|x\u003csub\u003e1,\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e|, |y\u003csub\u003e1,\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e| ≤ 100), where (\u003ci\u003ex\u003c/i\u003e\u003csub\u003e1,\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub\u003e1,\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e) denotes the coordinates of the \u003ci\u003ei\u003c/i\u003e-th star of the constellation in the first photo. The next \u003ci\u003en\u003c/i\u003e lines contain two real numbers \u003ci\u003ex\u003c/i\u003e\u003csub\u003e2,\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e and \u003ci\u003ey\u003c/i\u003e\u003csub\u003e2,\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e (|x\u003csub\u003e2,\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e|, |y\u003csub\u003e2,\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e| ≤ 100), where (\u003ci\u003ex\u003c/i\u003e\u003csub\u003e2,\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub\u003e2,\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e) denotes the coordinates of the \u003ci\u003ei\u003c/i\u003e-th star of the constellation in the second photo. Note that the ordering of the stars does \u003ci\u003enot\u003c/i\u003e matter for the sameness. It is guaranteed that distance between every pair of stars in each photo is larger than 10\u003csup\u003e-5\u003c/sup\u003e. \u003cbr\u003e\u003cdiv align\u003d\"left\" style\u003d\"margin-top: 1.0em;\"\u003e\u003cb\u003eOutput\u003c/b\u003e\u003c/div\u003eYou should print a non-negative real number which is the difference of the angle of the constellation in the first photo and in the second photo. The difference should be in radian, and should not be negative. If there are two or more solutions, you should print the smallest one, i.e. your solution should be an angle between 0 and \u003ci\u003epi\u003c/i\u003e radians, inclusive. The difference may be printed with any number of digits after decimal point, provided the absolute error does not exceed 10\u003csup\u003e-7\u003c/sup\u003e. \u003cbr\u003e"}},{"title":"Sample 1","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\n0.0 0.0\n1.0 1.0\n0.0 1.0\n3.0 3.0\n2.0 2.0\n3.0 2.0\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3.14159265359\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}