{"trustable":false,"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":"MD","content":"\u003cimg src\u003d\"http://boca.dpi.ufv.br/imgmaratona/capybarapainter.png\" alt\u003d\"Capybara painter\" width\u003d\"200\" align\u003d\"right\"\u003e\nCansado de verificar se os parênteses estão balanceados ou corrigir seu balanceamento? Nessa questão eles já estão balanceados, você só precisa colori-los! Aliás, nem isso: só precisa contar de quantas maneiras podem ser coloridos.\n\nRelembre que em uma sequência de parênteses balanceados, para cada abre parênteses há um correspondente fecha parênteses e os pares de parênteses correspondentes estão aninhados. Por exemplo, \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e()(())\u003c/span\u003e\" e \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e()\u003c/span\u003e\" são sequências de parênteses balanceados, enquanto \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e(()\u003c/span\u003e\" e \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e)(()\u003c/span\u003e\" não são.\n \nA figura abaixo ilustra o balanceamento de \"\u003cspan class\u003d\"tex-font-style-tt\"\u003e()(())\u003c/span\u003e\", colorindo os pares de parênteses correspondentes.\n\n\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/a6b8d63ccf43a76ac950f6a9f1b9407e?v\u003d1713590299\" style\u003d\"max-width: 60.0%;max-height: 60.0%;\"\u003e \u003c/center\u003e\n\nMas nesta questão não queremos colorir parênteses correspondentes. Queremos colorir uma sequência de parêntese balanceados com as seguintes restrições:\n\u003cul\u003e\n\u003cli\u003ecada parêntese é colorido de azul, ou de vermelho, ou não é colorido\u003c/li\u003e\n\u003cli\u003enenhum parentese colorido está ao lado de outro da mesma cor\u003c/li\u003e\n\u003cli\u003epara cada par de parênteses correspondentes, exatamente um deles é colorido\u003c/li\u003e\n\u003c/ul\u003e\n\nCalcule o número de maneiras de colorir os parênteses obedecendo as restrições acima. Duas maneiras de colorir são diferentes se elas diferem na cor de pelo menos um parêntese. Como o número de maneiras pode ser muito grande, escreve o resultado mod \u003cspan class\u003d\"tex-span\"\u003e1000000007\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e + 7\u003c/span\u003e)"}},{"title":"Entrada","value":{"format":"MD","content":"A entrada contém um string \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003es\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e2 ≤ |\u003ci\u003es\u003c/i\u003e| ≤ 800\u003c/span\u003e) com uma sequência corretamente balanceada de parêntese."}},{"title":"Saída","value":{"format":"MD","content":"Escreva o número de maneiras de colorir os parênteses da entrada seguindo as restrições acima. O resultado deve ser escrito mod \u003cspan class\u003d\"tex-span\"\u003e1000000007\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e + 7\u003c/span\u003e)."}},{"title":"Exemplos","value":{"format":"MD","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(())\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e12\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"MD","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(()())\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e40\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"MD","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()\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Nota","value":{"format":"MD","content":"Abaixo, 2 das 12 formas de colorir os parênteses do primeiro exemplo.\n\n\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/4399a47b86d784c277acf53b136c6401?v\u003d1713590299\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/7a03d539d1d681eee4497cfa5c1ed684?v\u003d1713590299\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e\n\nAs duas maneiras mostradas abaixo estão incorretas e não são contadas.\n\n\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/6e03de2eb570c8a20504c3d70355d50c?v\u003d1713590299\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/3fa44dba87152fc9c3181c54c2c20497?v\u003d1713590299\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e "}}]}