{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003e--- \u003cem\u003eNothing personal, but I don\u0027t believe in your ways of cutting the cake. \u003c/em\u003e --- \u003cem\u003eYou\u0027d better believed. \u003c/em\u003e --- \u003cem\u003eThan prove it. \u003c/em\u003e --- \u003cem\u003eI\u0027m not so cool, but my notebook never lies to me. \u003c/em\u003e --- \u003cem\u003eI can\u0027t see a backpack on you. \u003c/em\u003e --- \u003cem\u003eDamn it, haven\u0027t I taken it?.. Joke, surely I have.\u003c/em\u003e\u003c/p\u003e\n\n\u003cp\u003eReminding that the cake cutting plan contains the following information: The cake is represented as regular \u003cstrong\u003eN\u003c/strong\u003e-gon with center at point \u003cstrong\u003e(0, 0)\u003c/strong\u003e and one of the vertices at point \u003cstrong\u003e(1, 0)\u003c/strong\u003e. Whole cake is cut into \u003cstrong\u003eN+1\u003c/strong\u003e pieces. Each of those pieces is convex polygons.\u003c/p\u003e\n\n\u003cp\u003eCheck if all the pieces are convex polygons without three vertices on one line, in counterclockwise pass order. Check if all the pieces have equal square. Check if all the pieces have equal length of the outer border, i.e. the part of the border that reproduces the initial cake border. Check if is possible to join all the pieces together, so they will form the full cake.\u003c/p\u003e\n\n\u003cp\u003e\u003ch2\u003eInput\u003c/h2\u003e\u003c/p\u003e\n\n\u003cp\u003eIn the fi\u001crst line is given number \u003cstrong\u003eN\u003c/strong\u003e (\u003cstrong\u003e3\u003c/strong\u003e ≤ \u003cstrong\u003eN\u003c/strong\u003e ≤ \u003cstrong\u003e100\u003c/strong\u003e) --- number of the cake vertices. Then the description of \u003cstrong\u003eN+1\u003c/strong\u003e pieces is given. The description of one piece is started with number \u003cstrong\u003eK_i\u003c/strong\u003e (\u003cstrong\u003e3\u003c/strong\u003e ≤ \u003cstrong\u003eK_i\u003c/strong\u003e ≤ \u003cstrong\u003e100\u003c/strong\u003e) --- number of the vertices in the piece. Next \u003cstrong\u003eK_i\u003c/strong\u003e number of the vertices in the piece. Next lines contain those vertices listed in random order, given by two coordinates \u003cstrong\u003ex_i\u003c/strong\u003e and \u003cstrong\u003ey_i\u003c/strong\u003e (\u003cstrong\u003e-100\u003c/strong\u003e ≤ \u003cstrong\u003ex_i\u003c/strong\u003e, \u003cstrong\u003ey_i\u003c/strong\u003e ≤ \u003cstrong\u003e100\u003c/strong\u003e). Àll the coordiantes are real numbers with not more than \u003cstrong\u003e15\u003c/strong\u003e decimal places.\u003c/p\u003e\n\n\u003cp\u003e\u003ch2\u003eOutput\u003c/h2\u003e\u003c/p\u003e\n\n\u003cp\u003ePrint \"\u003cstrong\u003eYes\u003c/strong\u003e\", in case the description matches the correct cake cutting, otherwise --- \"\u003cstrong\u003eNo\u003c/strong\u003e\". It\u0027s guaranteed that in case the answer is\"\u003cstrong\u003eNo\u003c/strong\u003e\" parameters which provide this answer are not less than \u003cstrong\u003e10^\\{-6\\\u003c/strong\u003e}.\u003c/p\u003e\n\n"}},{"title":"Example","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\n3\n0.000000000000 0.000000000000\n1.000000000000 0.000000000000\n-0.125000000000 0.649519052838\n4\n0.000000000000 0.000000000000\n-0.125000000000 0.649519052838\n-0.500000000000 0.866025403784\n-0.500000000000 0.000000000000\n4\n0.000000000000 0.000000000000\n-0.500000000000 0.000000000000\n-0.500000000000 -0.866025403784\n-0.125000000000 -0.649519052838\n3\n0.000000000000 0.000000000000\n-0.125000000000 -0.649519052838\n1.000000000000 -0.000000000000\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eYes\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}