{"trustable":true,"prependHtml":"\u003cstyle type\u003d\"text/css\"\u003e\n section pre {\n display: block;\n padding: 9.5px;\n margin: 0 0 10px;\n font-size: 13px;\n line-height: 1.42857143;\n word-break: break-all;\n word-wrap: break-word;\n color: #333;\n background: rgba(255, 255, 255, 0.5);\n border: 1px solid #ccc;\n border-radius: 6px;\n }\n\u003c/style\u003e\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027\\\\(\u0027, right: \u0027\\\\)\u0027, display: false},\n {left: \u0027\\\\[\u0027, right: \u0027\\\\]\u0027, display: true}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"Problem Statement","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003eYou are given an integer \u003cvar\u003e\\(N\\)\u003c/var\u003e. Find the number of strings of length \u003cvar\u003e\\(N\\)\u003c/var\u003e that satisfy the following conditions, modulo \u003cvar\u003e\\(10^9+7\\)\u003c/var\u003e:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eThe string does not contain characters other than \u003ccode\u003eA\u003c/code\u003e, \u003ccode\u003eC\u003c/code\u003e, \u003ccode\u003eG\u003c/code\u003e and \u003ccode\u003eT\u003c/code\u003e.\u003c/li\u003e\r\n\u003cli\u003eThe string does not contain \u003ccode\u003eAGC\u003c/code\u003e as a substring.\u003c/li\u003e\r\n\u003cli\u003eThe condition above cannot be violated by swapping two adjacent characters once.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Notes","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003eA substring of a string \u003cvar\u003e\\(T\\)\u003c/var\u003e is a string obtained by removing zero or more characters from the beginning and the end of \u003cvar\u003e\\(T\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003cp\u003eFor example, the substrings of \u003ccode\u003eATCODER\u003c/code\u003e include \u003ccode\u003eTCO\u003c/code\u003e, \u003ccode\u003eAT\u003c/code\u003e, \u003ccode\u003eCODER\u003c/code\u003e, \u003ccode\u003eATCODER\u003c/code\u003e and \u003ccode\u003e\u003c/code\u003e (the empty string), but not \u003ccode\u003eAC\u003c/code\u003e.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Constraints","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cul\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(3 \\leq N \\leq 100\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Input","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003eInput is given from Standard Input in the following format:\u003c/p\u003e\r\n\u003cpre\u003e\u003cvar\u003e\\(N\\)\u003c/var\u003e\r\n\u003c/pre\u003e\r\n\r\n\u003c/section\u003e\r\n"}},{"title":"Output","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003ePrint the number of strings of length \u003cvar\u003e\\(N\\)\u003c/var\u003e that satisfy the following conditions, modulo \u003cvar\u003e\\(10^9+7\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 1","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\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e61\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003cp\u003eThere are \u003cvar\u003e\\(4^3 \u003d 64\\)\u003c/var\u003e strings of length \u003cvar\u003e\\(3\\)\u003c/var\u003e that do not contain characters other than \u003ccode\u003eA\u003c/code\u003e, \u003ccode\u003eC\u003c/code\u003e, \u003ccode\u003eG\u003c/code\u003e and \u003ccode\u003eT\u003c/code\u003e. Among them, only \u003ccode\u003eAGC\u003c/code\u003e, \u003ccode\u003eACG\u003c/code\u003e and \u003ccode\u003eGAC\u003c/code\u003e violate the condition, so the answer is \u003cvar\u003e\\(64 - 3 \u003d 61\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 2","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\u003e4\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e230\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 3","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\u003e100\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e388130742\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003cp\u003eBe sure to print the number of strings modulo \u003cvar\u003e\\(10^9+7\\)\u003c/var\u003e.\u003c/p\u003e\u003c/section\u003e\r\n"}}]}