{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eMartian spy satellites have taken a photo of an area on the dark \r\nside of the Moon. In this photo, only a lot of light points are \r\nseen in the dark. The Martian general suggests that the points are secret \r\nobjects at lunar military bases. He wants to know how many \r\nbases there are on the Moon. The Martians suppose that the bases \r\nare seen at the photo as clusters of light points and satisfy the following property:\r\nthe distance between any two objects at the same base is strictly less\r\nthan the distance from any object at this base to any object at any other base.\r\nThe area on the photo can be assumed flat, and the distance \r\nbetween objects having in the photo coordinates (\u003ci\u003eA\u003c/i\u003e, \u003ci\u003eB\u003c/i\u003e) and \r\n(\u003ci\u003eС\u003c/i\u003e, \u003ci\u003eD\u003c/i\u003e) is assumed to be \r\nsqrt((\u003ci\u003eA\u003c/i\u003e – \u003ci\u003eC\u003c/i\u003e)\u003csup\u003e2\u003c/sup\u003e + (\u003ci\u003eB\u003c/i\u003e – \u003ci\u003eD\u003c/i\u003e)\u003csup\u003e2\u003c/sup\u003e).\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 input contains several tests separated by an empty line.\r\nThe first line of each test contains the number of objects on the \r\nphoto \u003ci\u003eN\u003c/i\u003e. The next \u003ci\u003eN\u003c/i\u003e lines contain coordinates of \r\nthe objects, two integers separated by a space per line. Absolute values \r\nof all coordinates do not exceed 10\u003csup\u003e4\u003c/sup\u003e. \r\nAfter the last test there is an empty line and the number 0.\r\nThe sum of all \u003ci\u003eN\u003c/i\u003e in the input does not exceed 5 000, \r\nthe sum of all \u003ci\u003eN\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e does not exceed 400 000, \r\nand the sum of all \u003ci\u003eN\u003c/i\u003e\u003csup\u003e3\u003c/sup\u003e does not exceed 250 000 000.\r\n\u003c/div\u003e\u003c/div\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cdiv class\u003d\"problem_par\"\u003e\u003cdiv class\u003d\"problem_par_normal\"\u003eFor each test, you should output all possible numbers of bases \r\non the photo in the form of a line of length \u003ci\u003eN\u003c/i\u003e consisting of zeros and ones. For example, the line 110 means that there may be one or two bases on the photo, and the line 011 means that there may be two or three bases.\r\n\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\n-1 -1\r\n1 1\r\n1 -1\r\n-1 1\r\n\r\n4\r\n1 0\r\n2 4\r\n1 1\r\n0 1\r\n\r\n0\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1001\r\n1101\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}