{"trustable":true,"prependHtml":"\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 async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003e I spin it again and again,and throw it away \u0026#xc;finally.\u003cbr\u003e So now I have a row of n ball,named from 1 to n,each ball is white initially.\u003cbr\u003e At each step I randomly chose a interval [l, r] and paint all ball in this interval to black.\u003cbr\u003e It means every \u003cimg style\u003d\"max-width:100%;\" src\u003d\"CDN_BASE_URL/cce96627fc255f3af482b9a3d457f3da?v\u003d1715741734\"\u003e interval have a equal chance of being chosen.\u003cbr\u003e And I\u0027ll stop if all ball are black.What is the expected steps before I stop?\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":" The first line contains integer T(1\u0026lt;\u003dT\u0026lt;\u003d50). Denoting the number of the test cases.\u003cbr\u003e Then T lines follows, each line contains an integer n (1\u0026lt;\u003dn\u0026lt;\u003d50)."}},{"title":"Output","value":{"format":"HTML","content":"For each test cases,print the answer in a line.\u003cbr\u003ePrint the answer rounded to 15 decimal places.\u003cbr\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\u003e3\r\n1\r\n2\r\n3\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1.000000000000000\r\n2.000000000000000\r\n2.900000000000000\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Hint","value":{"format":"HTML","content":"\u003cbr\u003e不建议使用long double\u003cbr\u003e"}}]}