{"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\"\u003eIn number theory, Euler\u0027s totient function $\\varphi(n)$ counts the positive integers up to a given integer $n$ that are relatively prime to $n$. It can be defined more formally as the number of integers $k$ in the range $1\\leq k\\leq n$ for which the greatest common divisor $\\gcd(n, k)$ is equal to $1$.\u003cbr\u003eFor example, $\\varphi(9) \u003d 6$ because $1, 2, 4, 5, 7$ and $8$ are coprime with $9$. As another example, $\\varphi(1) \u003d 1$ since for $n \u003d 1$ the only integer in the range from $1$ to $n$ is $1$ itself, and $\\gcd(1, 1) \u003d 1$.\u003cbr\u003eA composite number is a positive integer that can be formed by multiplying together two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than $1$ and itself. So obviously $1$ and all prime numbers are not composite number.\u003cbr\u003eIn this problem, given integer $k$, your task is to find the $k$-th smallest positive integer $n$, that $\\varphi(n)$ is a composite number.\u003cbr\u003e\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line of the input contains an integer $T(1\\leq T\\leq100000)$, denoting the number of test cases.\u003cbr\u003eIn each test case, there is only one integer $k(1\\leq k\\leq 10^9)$.\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"For each test case, print a single line containing an integer, denoting the answer.\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\u003e2\r\n1\r\n2\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e5\r\n7\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}