{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eA binary string is a non-empty sequence of $$$0$$$\u0027s and $$$1$$$\u0027s, e.g., \u003cspan class\u003d\"tex-font-style-tt\"\u003e010110\u003c/span\u003e, \u003cspan class\u003d\"tex-font-style-tt\"\u003e1\u003c/span\u003e, \u003cspan class\u003d\"tex-font-style-tt\"\u003e11101\u003c/span\u003e, etc. The edit distance of two binary strings $$$S$$$ and $$$T$$$, denoted by $$$edit(S, T)$$$, is the minimum number of single-character edit (insert, delete, or substitute) to modify $$$S$$$ into $$$T$$$. For example, the edit distance of \u003cspan class\u003d\"tex-font-style-tt\"\u003e0011\u003c/span\u003e and \u003cspan class\u003d\"tex-font-style-tt\"\u003e1100\u003c/span\u003e is $$$4$$$, i.e. \u003cspan class\u003d\"tex-font-style-tt\"\u003e0011\u003c/span\u003e $$$\\rightarrow$$$ \u003cspan class\u003d\"tex-font-style-tt\"\u003e011\u003c/span\u003e $$$\\rightarrow$$$ \u003cspan class\u003d\"tex-font-style-tt\"\u003e11\u003c/span\u003e $$$\\rightarrow$$$ \u003cspan class\u003d\"tex-font-style-tt\"\u003e110\u003c/span\u003e $$$\\rightarrow$$$ \u003cspan class\u003d\"tex-font-style-tt\"\u003e1100\u003c/span\u003e. The edit distance of \u003cspan class\u003d\"tex-font-style-tt\"\u003e1100101\u003c/span\u003e and \u003cspan class\u003d\"tex-font-style-tt\"\u003e1110100\u003c/span\u003e is $$$2$$$, i.e. \u003cspan class\u003d\"tex-font-style-tt\"\u003e1100101\u003c/span\u003e $$$\\rightarrow$$$ \u003cspan class\u003d\"tex-font-style-tt\"\u003e1110101\u003c/span\u003e $$$\\rightarrow$$$ \u003cspan class\u003d\"tex-font-style-tt\"\u003e1110100\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eAyu has a binary string $$$S$$$. She wants to find a binary string with the same length as $$$S$$$ that maximizes the edit distance with $$$S$$$. Formally, she wants to find a binary string $$$T_{max}$$$ such that $$$|S| \u003d |T_{max}|$$$ and $$$edit(S, T_{max}) \\geq edit(S, T\u0027)$$$ for all binary string $$$T\u0027$$$ satisfying $$$|S| \u003d |T\u0027|$$$.\u003c/p\u003e\u003cp\u003eShe needs your help! However, since she wants to make your task easier, you are allowed to return any binary string $$$T$$$ with the same length as $$$S$$$ such that the edit distance of $$$S$$$ and $$$T$$$ is more than half the length of $$$S$$$. Formally, you must return a binary string $$$T$$$ such that $$$|S| \u003d |T|$$$ and $$$edit(S, T) \u0026gt; \\frac{|S|}{2}$$$.\u003c/p\u003e\u003cp\u003eOf course, you can still return $$$T_{max}$$$ if you want, since it can be proven that $$$edit(S, T_{max}) \u0026gt; \\frac{|S|}{2}$$$ for any binary string $$$S$$$. This also proves that there exists a solution for any binary string $$$S$$$. If there is more than one valid solution, you can output any of them.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eInput contains a binary string $$$S$$$ ($$$1 \\le |S| \\le 2000$$$).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eOutput in a line a binary string $$$T$$$ with the same length as $$$S$$$ that satisfies $$$edit(S, T) \u0026gt; \\frac{|S|}{2}$$$.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e0011\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1100\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e1100101\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0011010\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003e\u003cspan class\u003d\"tex-font-style-it\"\u003eExplanation for the sample input/output #1\u003c/span\u003e\u003c/p\u003e\u003cp\u003eAs illustrated in the example above, the edit distance of \u003cspan class\u003d\"tex-font-style-tt\"\u003e0011\u003c/span\u003e and \u003cspan class\u003d\"tex-font-style-tt\"\u003e1100\u003c/span\u003e is $$$4$$$. Since $$$4 \u0026gt; \\frac{4}{2}$$$, \u003cspan class\u003d\"tex-font-style-tt\"\u003e1100\u003c/span\u003e is one of the valid output for this sample.\u003c/p\u003e"}}]}