{"problem":{"name":"Unicyclic Graph Counting","description":{"content":"Snuke has come up with the following problem. > You are given a sequence $d$ of length $N$. Find the number of the undirected graphs with $N$ vertices labeled $1,2,...,N$ satisfying the following con","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"asaporo2_f"},"statements":[{"statement_type":"Markdown","content":"Snuke has come up with the following problem.\n\n> You are given a sequence $d$ of length $N$. Find the number of the undirected graphs with $N$ vertices labeled $1,2,...,N$ satisfying the following conditions, modulo $10^{9} + 7$:\n> \n> *   The graph is simple and connected.\n> *   The degree of Vertex $i$ is $d_i$.\n\n**When $2 \\leq N, 1 \\leq d_i \\leq N-1, {\\rm Σ} d_i = 2(N-1)$,** it can be proved that the answer to the problem is $\\frac{(N-2)!}{(d_{1} -1)!(d_{2} - 1)! ... (d_{N}-1)!}$.\nSnuke is wondering what the answer is **when $3 \\leq N, 1 \\leq d_i \\leq N-1, { \\rm Σ} d_i = 2N$.** Solve the problem under this condition for him.\n\n## Constraints\n\n*   $3 \\leq N \\leq 300$\n*   $1 \\leq d_i \\leq N-1$\n*   ${ \\rm Σ} d_i = 2N$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$d_1$ $d_2$ $...$ $d_{N}$\n\n## Partial Scores\n\n*   In the test set worth $200$ points, $N \\leq 5$.\n*   In the test set worth another $200$ points, $N \\leq 18$.\n*   In the test set worth another $300$ points, $N \\leq 50$.\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"asaporo2_f","tags":[],"sample_group":[["5\n1 2 2 3 2","6\n\n*   There are six graphs as shown below:\n\n![image](https://atcoder.jp/img/asaporo2/51367cdb21c64bfb07113b300921d52c.png)"],["16\n2 1 3 1 2 1 4 1 1 2 1 1 3 2 4 3","555275958\n\n*   Be sure to find the answer modulo $10^{9} + 7$."]],"created_at":"2026-03-03 11:01:14"}}