{"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\"\u003eWe can rewrite a binary string (i.e. strings where only $0$ or $1$ is included) $s$ as $kp+p\u0027$. $p\u0027$ is a prefix of $p$ ($p\u0027$ could be empty). $+p\u0027$ means concatenating $p\u0027$ to the last of $kp$. $kp$ means concatenating $k$ copies of $p$, where $p$ is the unit of $s$. \u003cbr\u003e\u003cbr\u003eThe unit of a binary string $s$ is when ignoring $p\u0027$, the non-empty string $p$ which makes $k$ maximal.\u003cbr\u003e\u003cbr\u003eWe define $v(s)$ as the value of $s$, which is $k$ in the previous statement. For example, $v(01001001)\u003d2$, because $01001001$ could be written as $2(010)+(01)$, and $v(11111)\u003d5$ since $11111$ could be written as $5(1)$ and $p\u0027$ is empty . \u003cbr\u003e\u003cbr\u003eNow given $n$, your task is to calculate the sum of the value of all binary strings whose length is exactly $n$. As the answer could be very large, just output the answer modulo $998244353$.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line contains a single positive integer $T\\ (1\\le T\\le 100)$, indicating that there are $T$ test cases.\u003cbr\u003e\u003cbr\u003eEach test case contains a single positive integer $n\\ (1\\le n \\le 10^{9})$ in one line.\u003cbr\u003e\u003cbr\u003eIt is guaranteed that $\\sum n\\le 10^{10}$."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, print an integer indicating the answer modulo $998244353$ in a single line."}},{"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\u003e5\r\n1\r\n2\r\n3\r\n114\r\n514\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2\r\n6\r\n12\r\n954037435\r\n530871613\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":"For n\u003d3,\u003cbr\u003ev(000)+v(001)+v(010)+v(011)+v(100)+v(101)+v(110)+v(111)\u003cbr\u003e\u003d3+1+1+1+1+1+1+3\u003cbr\u003e\u003d12\u003cbr\u003e"}}]}