{"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\u003eBarney lives in country USC (United States of Charzeh). USC has \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e cities numbered from \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e through \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e - 1\u003c/span\u003e roads between them. Cities and roads of USC form a rooted tree (Barney\u0027s not sure why it is rooted). Root of the tree is the city number \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e. Thus if one will start his journey from city \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e, he can visit any city he wants by following roads.\u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/629ac8bbfb62f83a34e1167339bc62e6?v\u003d1713961682\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e\u003cp\u003eSome girl has stolen Barney\u0027s heart, and Barney wants to find her. He starts looking for in the root of the tree and (since he is Barney Stinson not a random guy), he uses a \u003cspan class\u003d\"tex-font-style-it\"\u003erandom DFS\u003c/span\u003e to search in the cities. A pseudo code of this algorithm is as follows:\u003c/p\u003e\u003cpre class\u003d\"verbatim\"\u003e\u003cbr\u003elet starting_time be an array of length n\u003cbr\u003ecurrent_time \u003d 0\u003cbr\u003edfs(v):\u003cbr\u003e\tcurrent_time \u003d current_time + 1\u003cbr\u003e\tstarting_time[v] \u003d current_time\u003cbr\u003e\tshuffle children[v] randomly (each permutation with equal possibility)\u003cbr\u003e\t// children[v] is vector of children cities of city v\u003cbr\u003e\tfor u in children[v]:\u003cbr\u003e\t\tdfs(u)\u003cbr\u003e\u003c/pre\u003e\u003cp\u003eAs told before, Barney will start his journey in the root of the tree (equivalent to call \u003cspan class\u003d\"tex-font-style-tt\"\u003edfs(1)\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eNow Barney needs to pack a backpack and so he wants to know more about his upcoming journey: for every city \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e, Barney wants to know the expected value of \u003cspan class\u003d\"tex-font-style-tt\"\u003estarting_time[i]\u003c/span\u003e. He\u0027s a friend of Jon Snow and knows nothing, that\u0027s why he asked for your help.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line of input contains a single integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003en\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e5\u003c/sup\u003e\u003c/span\u003e)\u0026nbsp;— the number of cities in USC.\u003c/p\u003e\u003cp\u003eThe second line contains \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e - 1\u003c/span\u003e integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, \u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e3\u003c/sub\u003e, ..., \u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ep\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e \u0026lt; \u003ci\u003ei\u003c/i\u003e\u003c/span\u003e), where \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\u003c/span\u003e is the number of the parent city of city number \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e in the tree, meaning there is a road between cities numbered \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\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e in USC.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eIn the first and only line of output print \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e numbers, where \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th number is the expected value of \u003cspan class\u003d\"tex-font-style-tt\"\u003estarting_time[i]\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eYour answer for each city will be considered correct if its absolute or relative error does not exceed \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e - 6\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\u003e7\n1 2 1 1 4 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1.0 4.0 5.0 3.5 4.5 5.0 5.0 \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\u003e12\n1 1 2 2 4 4 3 3 1 10 8\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1.0 5.0 5.5 6.5 7.5 8.0 8.0 7.0 7.5 6.5 7.5 8.0 \n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}