{"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 has come up with the following problem.\u003c/p\u003e\r\n\u003cblockquote\u003e\r\n\u003cp\u003eYou are given a sequence \u003cvar\u003e\\(d\\)\u003c/var\u003e of length \u003cvar\u003e\\(N\\)\u003c/var\u003e.\r\nFind the number of the undirected graphs with \u003cvar\u003e\\(N\\)\u003c/var\u003e vertices labeled \u003cvar\u003e\\(1,2,...,N\\)\u003c/var\u003e satisfying the following conditions, modulo \u003cvar\u003e\\(10^{9} + 7\\)\u003c/var\u003e:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eThe graph is simple and connected.\u003c/li\u003e\r\n\u003cli\u003eThe degree of Vertex \u003cvar\u003e\\(i\\)\u003c/var\u003e is \u003cvar\u003e\\(d_i\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003c/blockquote\u003e\r\n\u003cp\u003e\u003cstrong\u003eWhen \u003cvar\u003e\\(2 \\leq N, 1 \\leq d_i \\leq N-1, {\\rm Σ} d_i \u003d 2(N-1)\\)\u003c/var\u003e,\u003c/strong\u003e it can be proved that the answer to the problem is \u003cvar\u003e\\(\\frac{(N-2)!}{(d_{1} -1)!(d_{2} - 1)! ... (d_{N}-1)!}\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003cp\u003eSnuke is wondering what the answer is \u003cstrong\u003ewhen \u003cvar\u003e\\(3 \\leq N, 1 \\leq d_i \\leq N-1, { \\rm Σ} d_i \u003d 2N\\)\u003c/var\u003e.\u003c/strong\u003e\r\nSolve the problem under this condition for him.\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 300\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 \\leq d_i \\leq N-1\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\({ \\rm Σ} d_i \u003d 2N\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Partial Scores","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eIn the test set worth \u003cvar\u003e\\(200\\)\u003c/var\u003e points, \u003cvar\u003e\\(N \\leq 5\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003cli\u003eIn the test set worth another \u003cvar\u003e\\(200\\)\u003c/var\u003e points, \u003cvar\u003e\\(N \\leq 18\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003cli\u003eIn the test set worth another \u003cvar\u003e\\(300\\)\u003c/var\u003e points, \u003cvar\u003e\\(N \\leq 50\\)\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\u003cvar\u003e\\(d_1\\)\u003c/var\u003e \u003cvar\u003e\\(d_2\\)\u003c/var\u003e \u003cvar\u003e\\(...\\)\u003c/var\u003e \u003cvar\u003e\\(d_{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 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\u003e5\r\n1 2 2 3 2\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e6\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\u003cul\u003e\r\n\u003cli\u003eThere are six graphs as shown below:\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cdiv style\u003d\"text-align: center;\"\u003e\r\n\u003cimg alt\u003d\"51367cdb21c64bfb07113b300921d52c.png\" src\u003d\"CDN_BASE_URL/b9c7134722a0a85d6dc96dd966895ff4?v\u003d1725737028\"\u003e\r\n\u003c/div\u003e\r\n\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\u003e16\r\n2 1 3 1 2 1 4 1 1 2 1 1 3 2 4 3\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e555275958\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\u003cul\u003e\r\n\u003cli\u003eBe sure to find the answer modulo \u003cvar\u003e\\(10^{9} + 7\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003c/ul\u003e\u003c/section\u003e\r\n"}}]}