{"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\u003eTwo neighbours, Alan and Bob, live in the city, where there are three buildings only: a cinema, a shop and the house, where they live. The rest is a big asphalt square. \u003c/p\u003e\u003cp\u003eOnce they went to the cinema, and the film impressed them so deeply, that when they left the cinema, they did not want to stop discussing it.\u003c/p\u003e\u003cp\u003eBob wants to get home, but Alan has to go to the shop first, and only then go home. So, they agreed to cover some distance together discussing the film (their common path might pass through the shop, or they might walk circles around the cinema together), and then to part each other\u0027s company and go each his own way. After they part, they will start thinking about their daily pursuits; and even if they meet again, they won\u0027t be able to go on with the discussion. Thus, Bob\u0027s path will be a continuous curve, having the cinema and the house as its ends. Alan\u0027s path — a continuous curve, going through the shop, and having the cinema and the house as its ends.\u003c/p\u003e\u003cp\u003eThe film ended late, that\u0027s why the whole distance covered by Alan should not differ from the shortest one by more than \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003et\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e\u003c/span\u003e, and the distance covered by Bob should not differ from the shortest one by more than \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003et\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eFind the maximum distance that Alan and Bob will cover together, discussing the film.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains two integers: \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003et\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003et\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e0 ≤ \u003ci\u003et\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003et\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e ≤ 100\u003c/span\u003e). The second line contains the cinema\u0027s coordinates, the third one — the house\u0027s, and the last line — the shop\u0027s. \u003c/p\u003e\u003cp\u003eAll the coordinates are given in meters, are integer, and do not exceed 100 in absolute magnitude. No two given places are in the same building.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eIn the only line output one number — the maximum distance that Alan and Bob will cover together, discussing the film. Output the answer accurate to not less than 4 decimal places.\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\u003e0 2\n0 0\n4 0\n-3 0\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1.0000000000\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","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\u003e0 0\n0 0\n2 0\n1 0\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2.0000000000\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}