{"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\"\u003eThere are two sequences $h_1\\sim h_n$ and $c_1\\sim c_n$. $h_1\\sim h_n$ is a permutation of $1\\sim n$. particularly, $h_0\u003dh_{n+1}\u003d0$.\u003cbr\u003e\u003cbr\u003e We define the expression $[condition]$ is 1 when $condition$ is True,is 0 when $condition$ is False.\u003cbr\u003e\u003cbr\u003e Define the function $f(h)\u003d\\sum_{i\u003d1}^{n}{c_i[h_i\u0026gt;h_{i-1}~~and~~h_i\u0026gt;h_{i+1}]}$\u003cbr\u003e\u003cbr\u003e Bo have gotten the value of $c_1\\sim c_n$, and he wants to know the expected value of $f(h)$.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"This problem has multi test cases(no more than $12$).\u003cbr\u003e\u003cbr\u003e For each test case, the first line contains a non-negative integer $n(1\\leq n\\leq1000)$, second line contains $n$ non-negative integer $c_i(0\\leq c_i\\leq 1000)$."}},{"title":"Output","value":{"format":"HTML","content":"For each test cases print a decimal - the expectation of $f(h)$.\u003cbr\u003e \u003cbr\u003e If the absolute error between your answer and the standard answer is no more than $10^{-4}$, your solution will be accepted."}},{"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\u003e4\r\n3 2 4 5\r\n5\r\n3 5 99 32 12\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e6.000000\r\n52.833333\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}