{"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\u003eSnuke received an integer sequence \u003cvar\u003e\\(a\\)\u003c/var\u003e of length \u003cvar\u003e\\(2N-1\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003cp\u003eHe arbitrarily permuted the elements in \u003cvar\u003e\\(a\\)\u003c/var\u003e, then used it to construct a new integer sequence \u003cvar\u003e\\(b\\)\u003c/var\u003e of length \u003cvar\u003e\\(N\\)\u003c/var\u003e, as follows:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(b_1 \u003d\\)\u003c/var\u003e the median of \u003cvar\u003e\\((a_1)\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(b_2 \u003d\\)\u003c/var\u003e the median of \u003cvar\u003e\\((a_1, a_2, a_3)\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(b_3 \u003d\\)\u003c/var\u003e the median of \u003cvar\u003e\\((a_1, a_2, a_3, a_4, a_5)\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(:\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(b_N \u003d\\)\u003c/var\u003e the median of \u003cvar\u003e\\((a_1, a_2, a_3, ..., a_{2N-1})\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cp\u003eHow many different sequences can be obtained as \u003cvar\u003e\\(b\\)\u003c/var\u003e? Find the count modulo \u003cvar\u003e\\(10^{9} + 7\\)\u003c/var\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\\(1 ≤ N ≤ 50\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 ≤ a_i ≤ 2N-1\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(a_i\\)\u003c/var\u003e are integers.\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\u003cvar\u003e\\(a_1\\)\u003c/var\u003e \u003cvar\u003e\\(a_2\\)\u003c/var\u003e \u003cvar\u003e\\(...\\)\u003c/var\u003e \u003cvar\u003e\\(a_{2N-1}\\)\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 answer.\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\u003e2\r\n1 3 2\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\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 three sequences that can be obtained as \u003cvar\u003e\\(b\\)\u003c/var\u003e: \u003cvar\u003e\\((1,2)\\)\u003c/var\u003e, \u003cvar\u003e\\((2,2)\\)\u003c/var\u003e and \u003cvar\u003e\\((3,2)\\)\u003c/var\u003e. Each of these can be constructed from \u003cvar\u003e\\((1,2,3)\\)\u003c/var\u003e, \u003cvar\u003e\\((2,1,3)\\)\u003c/var\u003e and \u003cvar\u003e\\((3,1,2)\\)\u003c/var\u003e, respectively.\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\n1 3 2 3 2 4 3\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e16\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\u003e15\r\n1 5 9 11 1 19 17 18 20 1 14 3 3 8 19 15 16 29 10 2 4 13 6 12 7 15 16 1 1\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e911828634\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\u003ePrint the count modulo \u003cvar\u003e\\(10^{9} + 7\\)\u003c/var\u003e.\u003c/p\u003e\u003c/section\u003e\r\n"}}]}