{"trustable":true,"prependHtml":"\u003cstyle type\u003d\"text/css\"\u003e\n div.illustration {\n float: right;\n padding-left: 20px;\n }\n div.illustration .illustration {\n width: 100%;\n border-radius: 4px;\n }\n pre {\n display: block;\n margin: 0 0 10px;\n font-size: 13px;\n line-height: 1.42857143;\n color: #333;\n word-break: break-all;\n word-wrap: break-word;\n }\n\u003c/style\u003e\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027\\\\[\u0027, right: \u0027\\\\]\u0027, display: true}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\n \u003cdiv style\u003d\"width:30.00%\" class\u003d\"illustration\"\u003e\n \u003cimg src\u003d\"CDN_BASE_URL/a53fbfa434d79fee514d70ba5305b3ad?v\u003d1715887360\" alt\u003d\"/problems/brackets/file/statement/en/img-0001.png\" class\u003d\"illustration\"\u003e\n\n \n \u003c/div\u003eA bracket sequence consisting of ‘(’ and ‘)’ is defined\n to be \u003ci class\u003d\"it\"\u003evalid\u003c/i\u003e as follows:\n\n \u003col class\u003d\"enumerate\"\u003e\n \u003cli\u003e\n \u003cp\u003eAn empty sequence is valid.\u003c/p\u003e\n \u003c/li\u003e\n\n \u003cli\u003e\n \u003cp\u003eIf \u003cspan class\u003d\"tex2jax_process\"\u003e$X$\u003c/span\u003e is a valid\n bracket sequence, then \u003cspan class\u003d\"tex2jax_process\"\u003e$(X)$\u003c/span\u003e is a valid bracket\n sequence.\u003c/p\u003e\n \u003c/li\u003e\n\n \u003cli\u003e\n \u003cp\u003eIf \u003cspan class\u003d\"tex2jax_process\"\u003e$X$\u003c/span\u003e and\n \u003cspan class\u003d\"tex2jax_process\"\u003e$Y$\u003c/span\u003e are valid bracket\n sequences, then the concatenation of \u003cspan class\u003d\"tex2jax_process\"\u003e$X$\u003c/span\u003e and \u003cspan class\u003d\"tex2jax_process\"\u003e$Y$\u003c/span\u003e, \u003cspan class\u003d\"tex2jax_process\"\u003e$Z\u003dXY$\u003c/span\u003e, is a valid bracket\n sequence.\u003c/p\u003e\n \u003c/li\u003e\n \u003c/ol\u003e\n\n \u003cp\u003eFor example, “(())”, “()()”, and “(()())()” are all valid\n bracket sequences, while “(” and “())” are invalid bracket\n sequences.\u003c/p\u003e\n\n \u003cp\u003eYou get a bracket sequence from the professor of length\n \u003cspan class\u003d\"tex2jax_process\"\u003e$n$\u003c/span\u003e. However, it might not\n be valid at the moment. The professor asks you to check if it\n is possible to make the sequence valid by performing \u003ci class\u003d\"it\"\u003eat most one\u003c/i\u003e segment inversion operation. That is, you\n may choose two 1-based indices \u003cspan class\u003d\"tex2jax_process\"\u003e$l$\u003c/span\u003e and \u003cspan class\u003d\"tex2jax_process\"\u003e$r$\u003c/span\u003e (\u003cspan class\u003d\"tex2jax_process\"\u003e$1~\n \\leq ~ l~ \\leq ~ r~ \\leq ~ n$\u003c/span\u003e) and invert each bracket\n with an index in the closed interval \u003cspan class\u003d\"tex2jax_process\"\u003e$[l,r]$\u003c/span\u003e. After the inversion, a left\n bracket ‘(’ becomes a right bracket ‘)’, and a right bracket\n ‘)’ becomes a left bracket ‘(’.\u003c/p\u003e\n\n \u003cp\u003eYou can make “())(” valid by inverting the segment\n \u003cspan class\u003d\"tex2jax_process\"\u003e$[3,4]$\u003c/span\u003e. You can make\n “()))” valid by inverting the segment \u003cspan class\u003d\"tex2jax_process\"\u003e$[3,3]$\u003c/span\u003e, or alternatively by inverting\n the segment \u003cspan class\u003d\"tex2jax_process\"\u003e$[2,2]$\u003c/span\u003e.\n However, there does not exist a segment you can invert to make\n “)))(” valid.\u003c/p\u003e\n\n \u003ch2\u003eInput\u003c/h2\u003e\n\n \u003cp\u003eThe input consists of one line containing between\n \u003cspan class\u003d\"tex2jax_process\"\u003e$1$\u003c/span\u003e and \u003cspan class\u003d\"tex2jax_process\"\u003e$5\\, 000$\u003c/span\u003e brackets.\u003c/p\u003e\n\n \u003ch2\u003eOutput\u003c/h2\u003e\n\n \u003cp\u003eOutput “possible” if you can make the bracket sequence valid\n by performing at most one segment inversion, or “impossible”\n otherwise.\u003c/p\u003e\n\n \u003ch2\u003eSample 1\u003c/h2\u003e\u003cbody\u003e\u003ctable class\u003d\"vjudge_sample\"\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\u003e()))\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003epossible\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/body\u003e\n\n \u003ch2\u003eSample 2\u003c/h2\u003e\u003cbody\u003e\u003ctable class\u003d\"vjudge_sample\"\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\u003e)))(\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eimpossible\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/body\u003e\n\n \u003ch2\u003eSample 3\u003c/h2\u003e\u003cbody\u003e\u003ctable class\u003d\"vjudge_sample\"\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\u003e()\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003epossible\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/body\u003e\n "}}]}