{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eNeko is playing with his toys on the backyard of Aki\u0027s house. Aki decided to play a prank on him, by secretly putting catnip into Neko\u0027s toys. Unfortunately, he went overboard and put an entire bag of catnip into the toys...\u003c/p\u003e\u003cp\u003eIt took Neko an entire day to turn back to normal. Neko reported to Aki that he saw a lot of weird things, including a \u003ca href\u003d\"https://en.wikipedia.org/wiki/Trie\"\u003etrie\u003c/a\u003e of all correct bracket sequences of length $$$2n$$$.\u003c/p\u003e\u003cp\u003eThe definition of correct bracket sequence is as follows:\u003c/p\u003e\u003cul\u003e \u003cli\u003e The empty sequence is a correct bracket sequence, \u003c/li\u003e\u003cli\u003e If $$$s$$$ is a correct bracket sequence, then $$$(\\,s\\,)$$$ is a correct bracket sequence, \u003c/li\u003e\u003cli\u003e If $$$s$$$ and $$$t$$$ are a correct bracket sequence, then $$$st$$$ is also a correct bracket sequence. \u003c/li\u003e\u003c/ul\u003e\u003cp\u003eFor example, the strings \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e(())\u003c/span\u003e\", \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e()()\u003c/span\u003e\" form a correct bracket sequence, while \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e)(\u003c/span\u003e\" and \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e((\u003c/span\u003e\" not.\u003c/p\u003e\u003cp\u003eAki then came up with an interesting problem: What is the size of the maximum matching (the largest set of edges such that there are no two edges with a common vertex) in this trie? Since the answer can be quite large, print it modulo $$$10^9 + 7$$$.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe only line contains a single integer $$$n$$$ ($$$1 \\le n \\le 1000$$$).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint exactly one integer\u0026nbsp;— the size of the maximum matching in the trie. Since the answer can be quite large, print it modulo $$$10^9 + 7$$$.\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\u003e1\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\u003e3\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\u003e9\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\u003eThe pictures below illustrate tries in the first two examples (for clarity, the round brackets are replaced with angle brackets). The maximum matching is highlighted with blue.\u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/6e3593cf0d0ec4166901b6b5370f4547?v\u003d1714753035\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e\u0026nbsp;\u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/46aacaf50ec5a4d252d145add5475169?v\u003d1714753035\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e"}}]}