{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eYou are given an integer $$$n$$$. In one move, you can either multiply $$$n$$$ by two or divide $$$n$$$ by $$$6$$$ (if it is divisible by $$$6$$$ without the remainder).\u003c/p\u003e\u003cp\u003eYour task is to find the minimum number of moves needed to obtain $$$1$$$ from $$$n$$$ or determine if it\u0027s impossible to do that.\u003c/p\u003e\u003cp\u003eYou have to answer $$$t$$$ independent test cases.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line of the input contains one integer $$$t$$$ ($$$1 \\le t \\le 2 \\cdot 10^4$$$) — the number of test cases. Then $$$t$$$ test cases follow. \u003c/p\u003e\u003cp\u003eThe only line of the test case contains one integer $$$n$$$ ($$$1 \\le n \\le 10^9$$$).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eFor each test case, print the answer — the minimum number of moves needed to obtain $$$1$$$ from $$$n$$$ if it\u0027s possible to do that or \u003cspan class\u003d\"tex-font-style-tt\"\u003e-1\u003c/span\u003e if it\u0027s impossible to obtain $$$1$$$ from $$$n$$$.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e7\n1\n2\n3\n12\n12345\n15116544\n387420489\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0\n-1\n2\n-1\n-1\n12\n36\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eConsider the sixth test case of the example. The answer can be obtained by the following sequence of moves from the given integer $$$15116544$$$:\u003c/p\u003e\u003col\u003e \u003cli\u003e Divide by $$$6$$$ and get $$$2519424$$$; \u003c/li\u003e\u003cli\u003e divide by $$$6$$$ and get $$$419904$$$; \u003c/li\u003e\u003cli\u003e divide by $$$6$$$ and get $$$69984$$$; \u003c/li\u003e\u003cli\u003e divide by $$$6$$$ and get $$$11664$$$; \u003c/li\u003e\u003cli\u003e multiply by $$$2$$$ and get $$$23328$$$; \u003c/li\u003e\u003cli\u003e divide by $$$6$$$ and get $$$3888$$$; \u003c/li\u003e\u003cli\u003e divide by $$$6$$$ and get $$$648$$$; \u003c/li\u003e\u003cli\u003e divide by $$$6$$$ and get $$$108$$$; \u003c/li\u003e\u003cli\u003e multiply by $$$2$$$ and get $$$216$$$; \u003c/li\u003e\u003cli\u003e divide by $$$6$$$ and get $$$36$$$; \u003c/li\u003e\u003cli\u003e divide by $$$6$$$ and get $$$6$$$; \u003c/li\u003e\u003cli\u003e divide by $$$6$$$ and get $$$1$$$. \u003c/li\u003e\u003c/ol\u003e"}}]}