{"trustable":true,"prependHtml":"\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 async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003eConsider words of length 3n over alphabet {A, B, C} . Denote the number of occurences of A in a word a as A(a) , analogously let the number of occurences of B be denoted as B(a), and the number of occurenced of C as C(a) . \u003cbr\u003e\u003cbr\u003eLet us call the word w regular if the following conditions are satisfied: \u003cbr\u003e\u003cbr\u003eA(w)\u003dB(w)\u003dC(w) ; \u003cbr\u003eif c is a prefix of w , then A(c)\u0026gt;\u003d B(c) \u0026gt;\u003d C(c) . \u003cbr\u003eFor example, if n \u003d 2 there are 5 regular words: AABBCC , AABCBC , ABABCC , ABACBC and ABCABC . \u003cbr\u003e\u003cbr\u003eRegular words in some sense generalize regular brackets sequences (if we consider two-letter alphabet and put similar conditions on regular words, they represent regular brackets sequences). \u003cbr\u003e\u003cbr\u003eGiven n , find the number of regular words. \u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"There are mutiple cases in the input file. \u003cbr\u003e\u003cbr\u003eEach case contains n (0 \u0026lt;\u003d n \u0026lt;\u003d 60 ). \u003cbr\u003e\u003cbr\u003eThere is an empty line after each case."}},{"title":"Output","value":{"format":"HTML","content":"Output the number of regular words of length 3n . \u003cbr\u003e\u003cbr\u003eThere should be am empty line after each case. "}},{"title":"Sample","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\r\n\r\n3\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e5\r\n\r\n42\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}