{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eA growing number of people accept nowadays the theory of strings and\r\nsuperstrings and of the mirror world. One of the most interesting objects of\r\nstudy within this theory is circular strings. They can be used for traveling\r\nbetween worlds: flying through the ring of such a string, an observer finds\r\nhimself in the mirror world, which can have entirely different stars, galaxies,\r\nand, possibly, life. The traveler can return to his world by flying backward\r\nthrough the same or any other circular string. Unfortunately, superstrings are\r\nunstable. Gradually losing their energy, they contract and eventually explode\r\nwhen their diameter decreases to the diameter of an elementary particle. Which\r\nmeans that a travel to the mirror world is potentially dangerous.\r\n\u003c/div\u003e\u003c/div\u003e\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eCircular strings also have a practical application. They can be used to draw\r\nany regular polygon without ruler or compasses. For this, a string should be\r\nmade to oscillate exactly in a plane at one of its resonance frequencies. In\r\nthis situation, several points of the string stay fixed. According to the\r\ntheory, these points are vertices of the required polygon. Physicists have just\r\nmade such an experiment and now ask you to analyze the results.\u003c/div\u003e\u003c/div\u003e\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eYou are given \u003ci\u003en\u003c/i\u003e pairs of real numbers. The physicists claim that these are\r\nthe coordinates of vertices of a nondegenerate \u003ci\u003en\u003c/i\u003e-gon written in the traversal\r\norder.\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 the integer \u003ci\u003en\u003c/i\u003e (3 ≤ \u003ci\u003en\u003c/i\u003e ≤ 100). The \u003ci\u003ei\u003c/i\u003e-th\r\nof the following \u003ci\u003en\u003c/i\u003e lines contains real numbers \u003ci\u003ex\u003csub\u003ei\u003c/sub\u003e\u003c/i\u003e and \u003ci\u003ey\u003csub\u003ei\u003c/sub\u003e\u003c/i\u003e separated with\r\na space (0 ≤ \u003ci\u003ex\u003csub\u003ei\u003c/sub\u003e\u003c/i\u003e, \u003ci\u003ey\u003csub\u003ei\u003c/sub\u003e\u003c/i\u003e ≤ 1); these numbers are the coordinates of the\r\n\u003ci\u003ei\u003c/i\u003e-th point. The coordinates of different points may coincide, but it is\r\nguaranteed that there exists at least one pair of points at a distance of at\r\nleast 0.3. The coordinates are given with accuracy of at least 10\u003csup\u003e−10\u003c/sup\u003e.\u003c/div\u003e\u003c/div\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eIf the experiment didn\u0027t produce vertices of a regular \u003ci\u003en\u003c/i\u003e-gon in\r\nthe traversal order, output “NO”. Otherwise,\r\noutput “YES”. It is guaranteed that in the case of the negative\r\nanswer the coordinates of the points can\u0027t be changed by less than 10\u003csup\u003e−5\u003c/sup\u003e so\r\nthat they become the coordinates of vertices of a regular \u003ci\u003en\u003c/i\u003e-gon written in\r\nthe traversal order.\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\u003e4\r\n0 0\r\n1 0\r\n1 1\r\n0 1\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eYES\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003cbr\u003e\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\n0 0\r\n1 0\r\n0.5 1\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eNO\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}