{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eGiven $$$K$$$, construct two non-empty \u003cspan class\u003d\"tex-font-style-bf\"\u003ebinary\u003c/span\u003e strings $$$S$$$ and $$$T$$$ of length \u003cspan class\u003d\"tex-font-style-bf\"\u003eat most 8848\u003c/span\u003e such that they have exactly $$$K$$$ different longest common subsequences. More formally, if $$$L$$$ is the length of the longest common subsequence of $$$S$$$ and $$$T$$$, there should exist exactly $$$K$$$ distinct binary strings of length $$$L$$$ which are subsequences of both $$$S$$$ and $$$T$$$.\u003c/p\u003e\u003cp\u003eIt is guaranteed that under the constraints of this problem such strings always exist.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe only line of input contains a single integer $$$K$$$ ($$$1 \\le K \\le 10^9$$$).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint non-empty binary strings $$$S$$$ and $$$T$$$ on separate lines. The length of each of them should not exceed $$$8848$$$. They can have different lengths.\u003c/p\u003e\u003cp\u003eIf there is more than one solution, you can print any one of them.\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\u003e1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1111\n00\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","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\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e10\n01\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","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\u003e3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e010\n1001\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","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\u003e100\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e10001000001011100001010100011\n11000010001010101001010011100\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\u003eIn the first example, the longest common subsequence of \u003cspan class\u003d\"tex-font-style-tt\"\u003e1111\u003c/span\u003e and \u003cspan class\u003d\"tex-font-style-tt\"\u003e00\u003c/span\u003e has length $$$0$$$, and there exists only one string of length $$$0$$$ which is a subsequence of both of them\u0026nbsp;— the empty string.\u003c/p\u003e\u003cp\u003eIn the second example, the length of the longest common subsequence of strings \u003cspan class\u003d\"tex-font-style-tt\"\u003e10\u003c/span\u003e and \u003cspan class\u003d\"tex-font-style-tt\"\u003e01\u003c/span\u003e is $$$1$$$, and there are $$$2$$$ strings of length $$$1$$$ which are subsequences of both $$$S$$$ and $$$T$$$: \u003cspan class\u003d\"tex-font-style-tt\"\u003e0\u003c/span\u003e and \u003cspan class\u003d\"tex-font-style-tt\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eIn the second example, the length of the longest common subsequence of strings \u003cspan class\u003d\"tex-font-style-tt\"\u003e010\u003c/span\u003e and \u003cspan class\u003d\"tex-font-style-tt\"\u003e1001\u003c/span\u003e is $$$2$$$, and there are $$$3$$$ strings of length $$$2$$$ which are subsequences of both $$$S$$$ and $$$T$$$: \u003cspan class\u003d\"tex-font-style-tt\"\u003e00\u003c/span\u003e, \u003cspan class\u003d\"tex-font-style-tt\"\u003e01\u003c/span\u003e, and \u003cspan class\u003d\"tex-font-style-tt\"\u003e10\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eIt would be disrespectful to make strings longer than Everest...\u003c/p\u003e"}}]}