{"trustable":true,"prependHtml":"\u003cstyle type\u003d\"text/css\"\u003e\n #problem-body \u003e pre {\n display: block;\n padding: 9.5px;\n margin: 0 0 10px;\n font-size: 13px;\n line-height: 1.42857143;\n word-break: break-all;\n word-wrap: break-word;\n color: #333;\n background: rgba(255, 255, 255, 0.5);\n border: 1px solid #ccc;\n border-radius: 6px;\n }\n\u003c/style\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv id\u003d\"problem-body\"\u003e\n\t\u003cp\u003eYou are given the coordinates of 4*K+5 points on a plane such that no three of them are collinear. You need to select five points from these : a central point O and four arm points A, B, C, D such that:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eRays from the centre to the arm points divide the plane into four regions containing an equal number of points \u003c/li\u003e\r\n\u003cli\u003eNone of the four central angles is a reflex angle \u003c/li\u003e\r\n\u003cli\u003e Sum of absolute values of the cotangents of the central angles is as low as possible \u003c/li\u003e\r\n\u003c/ul\u003e\r\n\r\n\u003cp\u003eIf it is possible to choose points satisfying this condition, output the lowest possible value for the sum of absolute values of the cotangents of the central angles. Otherwise report that it is not possible.\u003c/p\u003e\r\n\u003ch3\u003eInput\u003c/h3\u003e\r\n\u003cp\u003eThe first line of input contains T(\u0026lt;\u003d4), the number of test cases. Following this are the descriptions of the T test cases.\u003c/p\u003e\r\n\u003cp\u003eThe first line in the description of each test case gives K(\u0026lt;\u003d100). Following this are 4*K+5 lines giving the x and y coordinates of each point separated by a space (0\u0026lt;\u003dx, y\u0026lt;\u003d10\u003csup\u003e6\u003c/sup\u003e)\u003c/p\u003e\r\n\u003ch3\u003eOutput\u003c/h3\u003e\r\n\u003cp\u003eFor each test case output in a different line the minimum sum of absolute values of the cotangents of the central angles, with six digits after the decimal point. If the division cannot be done in the manner explained, print Impossible\u003c/p\u003e\r\n\u003ch3\u003eExample\u003c/h3\u003e\r\n\u003cdiv\u003e\u003ctable class\u003d\"vjudge_sample\"\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\u003e2\n0\n0 0\n0 1\n1 1\n1 0\n2 3\n0\n0 0\n2 0\n0 1\n2 1\n1 2\n\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4.500000\nImpossible\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e"}}]}