{"raw_statement":[{"iden":"problem statement","content":"Given is a directed tree with $N$ vertices numbered $1$ through $N$.\nVertex $1$ is the root of the tree. For each integer $i$ such that $2 \\leq i \\leq N$, there is a directed edge from Vertex $p_i$ to $i$.\nLet $a$ be the permutation of $(1, \\ldots, N)$, and $a_i$ be the $i$\\-th element of $a$.\nAmong the $N!$ sequences that can be $a$, find the number of sequences that satisfy the following condition, modulo $998244353$.\n\n*   Condition: For every integer $i$ such that $1 \\leq i \\leq N$, Vertex $i$ is unreachable from Vertex $a_i$ by traversing **one or more** edges."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $1 \\leq N \\leq 2000$\n*   $1 \\leq p_i < i$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$p_{2}$ $\\cdots$ $p_N$"},{"iden":"sample input 1","content":"4\n1 1 3"},{"iden":"sample output 1","content":"4"},{"iden":"sample input 2","content":"30\n1 1 3 1 5 1 1 1 8 9 7 3 11 11 15 14 4 10 11 12 1 10 13 11 7 23 8 12 18"},{"iden":"sample output 2","content":"746746186\n\n*   Remember to print the count modulo $998244353$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}