{"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\"\u003eOne day, Y_UME got an integer $N$ and an interesting program which is shown below:\u003cbr\u003e\u003cbr\u003e\u003ccenter\u003e\u003cimg style\u003d\"max-width:100%;\" src\u003d\"CDN_BASE_URL/534aa1d8a73f5772136c2e5e301cc6c5?v\u003d1714189898\"\u003e\u003c/center\u003e\u003cbr\u003e\u003cbr\u003eY_UME wants to play with this program. Firstly, he randomly generates an integer $n \\in [1, N]$ in equal probability. And then he randomly generates a permutation of length $n$ in equal probability. Afterwards, he runs the interesting program(function calculate()) with this permutation as a parameter and then gets a returning value. Please output the expectation of this value modulo $998244353$.\u003cbr\u003e\u003cbr\u003eA permutation of length $n$ is an array of length $n$ consisting of integers only $\\in [1, n]$ which are pairwise different.\u003cbr\u003e\u003cbr\u003eAn inversion pair in a permutation $p$ is a pair of indices $(i, j)$ such that $i \u0026gt; j$ and $p_i \u0026lt; p_j$. For example, a permutation $[4, 1, 3, 2]$ contains $4$ inversions: $(2, 1), (3, 1), (4, 1), (4, 3)$.\u003cbr\u003e\u003cbr\u003eIn mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements. Note that empty subsequence is also a subsequence of original sequence.\u003cbr\u003e\u003cbr\u003eRefer to \u003cb\u003ehttps://en.wikipedia.org/wiki/Subsequence\u003c/b\u003e for better understanding.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"There are multiple test cases.\u003cbr\u003e\u003cbr\u003eEach case starts with a line containing one integer $N(1 \\leq N \\leq 3000)$.\u003cbr\u003e\u003cbr\u003eIt is guaranteed that the sum of $N$s in all test cases is no larger than $5 \\times 10^4$."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, output one line containing an integer denoting the answer."}},{"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\u003e1\r\n2\r\n3\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0\r\n332748118\r\n554580197\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}