{"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\u003eThis is yet another problem on regular bracket sequences.\u003c/p\u003e\u003cp\u003eA bracket sequence is called regular, if by inserting \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e+\u003c/span\u003e\" and \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e1\u003c/span\u003e\" into it we get a correct mathematical expression. For example, sequences \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e(())()\u003c/span\u003e\", \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e()\u003c/span\u003e\" and \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e(()(()))\u003c/span\u003e\" are regular, while \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e)(\u003c/span\u003e\", \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e(()\u003c/span\u003e\" and \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e(()))(\u003c/span\u003e\" are not. You have a pattern of a bracket sequence that consists of characters \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e(\u003c/span\u003e\", \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e)\u003c/span\u003e\" and \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e?\u003c/span\u003e\". You have to replace each character \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e?\u003c/span\u003e\" with a bracket so, that you get a regular bracket sequence.\u003c/p\u003e\u003cp\u003eFor each character \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e?\u003c/span\u003e\" the cost of its replacement with \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e(\u003c/span\u003e\" and \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e)\u003c/span\u003e\" is given. Among all the possible variants your should choose the cheapest.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains a non-empty pattern of even length, consisting of characters \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e(\u003c/span\u003e\", \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e)\u003c/span\u003e\" and \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e?\u003c/span\u003e\". Its length doesn\u0027t exceed \u003cspan class\u003d\"tex-span\"\u003e5·10\u003csup class\u003d\"upper-index\"\u003e4\u003c/sup\u003e\u003c/span\u003e. Then there follow \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e lines, where \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003em\u003c/i\u003e\u003c/span\u003e is the number of characters \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e?\u003c/span\u003e\" in the pattern. Each line contains two integer numbers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003eb\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e6\u003c/sup\u003e\u003c/span\u003e), where \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e is the cost of replacing the \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/span\u003e-th character \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e?\u003c/span\u003e\" with an opening bracket, and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003eb\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e — with a closing one.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint the cost of the optimal regular bracket sequence in the first line, and the required sequence in the second.\u003c/p\u003e\u003cp\u003ePrint \u003cspan class\u003d\"tex-font-style-tt\"\u003e-1\u003c/span\u003e, if there is no answer. If the answer is not unique, print any 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\u003e(??)\n1 2\n2 8\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4\n()()\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}