{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003eFirst we define:\u003cbr\u003e(1) $lcm(a,b)$, the least common multiple of two integers $a$ and $b$, is the smallest positive integer that is divisible by both $a$ and $b$. for example, $lcm(2,3)\u003d6$ and $lcm(4,6)\u003d12$.\u003cbr\u003e(2) $gcd(a,b)$, the greatest common divisor of two integers $a$ and $b$, is the largest positive integer that divides both $a$ and $b$ without a remainder, $gcd(2,3)\u003d1$ and $gcd(4,6)\u003d2$.\u003cbr\u003e(3) $[exp]$, $exp$ is a logical expression, if the result of $exp$ is $true$, then $[exp]\u003d1$, else $[exp]\u003d0$. for example, $[1+2\\geq 3]\u003d1$ and $[1+2\\geq 4]\u003d0$.\u003cbr\u003e\u003cbr\u003eNow Stilwell wants to calculate such a problem:\u003cbr\u003e$$F(n)\u003d\\sum_{i\u003d1}^n\\sum_{j\u003d1}^n~[~lcm(i,j)+gcd(i,j)\\geq n~] \\\\\\\\S(n)\u003d\\sum_{i\u003d1}^nF(i)$$\u003cbr\u003eFind $S(n)~mod~258280327$.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line of the input contains a single number $T$, the number of test cases.\u003cbr\u003eNext $T$ lines, each line contains a positive integer $n$.\u003cbr\u003e$T\\leq 10^5$, $n\\leq 10^6$."}},{"title":"Output","value":{"format":"HTML","content":"$T$ lines, find $S(n)~mod~258280327$."}},{"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\u003e8\r\n1\r\n2\r\n3\r\n4\r\n10\r\n100\r\n233\r\n11037\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\r\n5\r\n13\r\n26\r\n289\r\n296582\r\n3928449\r\n213582482\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}