{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eThe Minister for education is coming! Naturally, nobody wants to perform poorly in front of such a honored guest. However, two hours before the arrival it turned out that one of the classes has a malfunctioning lightbulb — for some reason it doesn\u0027t get enough energy. The solution was found quickly: all we\u0027ve got to do is to change the location of the lightbulb so that it got the maximum amount of energy.\u003c/p\u003e\u003cp\u003eEverybody knows that the power of the lightbulb equals \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/b2d7205d6760a21b5528d96953ce669d?v\u003d1715207325\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e, where \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eC\u003c/i\u003e\u003c/span\u003e is some constant value and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003er\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e is the Euclidean distance from the bulb to the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th generator. Consequently, our task is to minimize \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/6acdc2134172b48f7bc488f9f1c09145?v\u003d1715207325\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e. Of course, we know the positions of all generators.\u003c/p\u003e\u003cp\u003eThe bulb should be on the ceiling of the class. The ceiling of the class is in the form of a strictly convex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e-gon (the class itself has the form of a right prism with a strictly convex \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e-gon at the bottom). Help to find the optimum location for the bulb. Assume that all generators are in the plane of the class ceiling. Consider that the plane of the class ceiling has some Cartesian coordinate system introduced.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(2 ≤ \u003ci\u003en\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e)\u003c/span\u003e — the number of generators. Each of the next \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e lines contains a pair of integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e, representing the coordinates of the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th generator in the plane of the class ceiling. It\u0027s guaranteed that no two generators have the same location.\u003c/p\u003e\u003cp\u003eThe next line contains integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e(3 ≤ \u003ci\u003em\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e)\u003c/span\u003e — the number of vertexes in the convex polygon that describes the ceiling of the class. Each of the following \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e lines contains a pair of integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003eq\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e, representing the coordinates of the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th point of the polygon in the clockwise order. It\u0027s guaranteed that the polygon is strictly convex.\u003c/p\u003e\u003cp\u003eThe absolute value of all the coordinates don\u0027t exceed \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e6\u003c/sup\u003e\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint a single real number — the minimum value of the sum of squares of distances from the generators to the point of the lightbulb\u0027s optimal position. The answer will be considered valid if its absolute or relative error doesn\u0027t exceed \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e - 4\u003c/sup\u003e\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Examples","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\n3 2\n3 4\n5 4\n5 2\n4\n3 3\n4 4\n5 3\n4 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e8.00000000\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eWe\u0027ll define a strictly convex polygon as a convex polygon with the following property: no three vertices of the polygon lie on the same line.\u003c/p\u003e"}}]}