{"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\"\u003eChiaki has a sequence $A\u003d\\{a_1,a_2,\\dots,a_n\\}$. Let $\\mathbf{RMQ}(A, l, r)$ be the minimum $i$ ($l \\le i \\le r$) such that $a_i$ is the maximum value in $a_l, a_{l+1}, \\dots, a_{r}$.\u003cbr\u003e\u003cbr\u003eTwo sequences $A$ and $B$ are called \\textit{RMQ Similar}, if they have the same length $n$ and for every $1 \\le l \\le r \\le n$, $\\mathbf{RMQ}(A, l, r) \u003d \\mathbf{RMQ}(B, l, r)$.\u003cbr\u003e\u003cbr\u003eFor a given the sequence $A\u003d\\{a_1,a_2,\\dots,a_n\\}$, define the weight of a sequence $B\u003d\\{b_1,b_2,\\dots,b_n\\}$ be $\\sum\\limits_{i\u003d1}^{n} b_i$ (i.e. the sum of all elements in $B$) if sequence $B$ and sequence $A$ are RMQ Similar, or $0$ otherwise. If each element of $B$ is a real number chosen independently and uniformly at random between $0$ and $1$, find the expected weight of $B$.\u003cbr\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"There are multiple test cases. The first line of input contains an integer $T$, indicating the number of test cases. For each test case:\u003cbr\u003eThe first line contains an integer $n$ ($1 \\le n \\le 10^6$) -- the length of the sequence.\u003cbr\u003eThe second line contains $n$ integers $a_1, a_2, \\dots, a_n$ ($1 \\le a_i \\le n$) denoting the sequence.\u003cbr\u003eIt is guaranteed that the sum of all n does not exceed $3 \\times 10^6$."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, output the answer as a value of a rational number modulo $10^9 + 7$.\u003cbr\u003eFormally, it is guaranteed that under given constraints the probability is always a rational number $\\frac{p}{q}$ ($p$ and $q$ are integer and coprime, $q$ is positive), such that $q$ is not divisible by $10^9 + 7$. Output such integer a between $0$ and $10^9 + 6$ that $p - aq$ is divisible by $10^9 + 7$.\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\n3\r\n1 2 3\r\n3\r\n1 2 1\r\n5\r\n1 2 3 2 1\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e250000002\r\n500000004\r\n125000001\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}