{"raw_statement":[{"iden":"problem statement","content":"We have a rooted tree with $N$ vertices numbered $1$ to $N$. Vertex $1$ is the root of the tree, and the parent of vertex $i\\ (2\\leq i)$ is vertex $p_i$.\nEach vertex has a color: black or white. Initially, all vertices are white.\nIn this rooted tree, vertex $i$ is said to be _good_ when all vertices on the simple path connecting vertices $1$ and $i$ (including vertices $1$ and $i$) are black, and _bad_ otherwise.\nUntil all vertices are black, let us repeat the following operation: choose one vertex from the bad vertices uniformly at random, and repaint the chosen vertex black.\nFind the expected value of the number of times we perform the operation, modulo $998244353$.\nThe definition of the expected value modulo $998244353$It can be proved that the sought expected value is always a rational number. Additionally, when that value is represented as an irreducible fraction $\\frac{P}{Q}$, it can also be proved that $Q \\not \\equiv 0 \\pmod{998244353}$. Therefore, there is a unique integer $R$ such that $R \\times Q \\equiv P \\pmod{998244353}$ and $0 \\leq R < 998244353$. Find this $R$."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq p_i < i$\n*   All values in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$\n$p_2$ $p_3$ $\\dots$ $p_{N}$"},{"iden":"sample input 1","content":"4\n1 1 3"},{"iden":"sample output 1","content":"831870300\n\nConsider a case where the first three operations have chosen vertices $1$, $2$, and $4$ in this order. Then, vertices $1$ and $2$ are good, but vertex $4$ is still bad since vertex $3$, an ancestor of vertex $4$, is white. Thus, the fourth operation will choose vertex $3$ or $4$ uniformly at random.\nThe expected value of the number of times we perform the operation is $\\displaystyle \\frac{35}{6}$."},{"iden":"sample input 2","content":"15\n1 2 1 1 4 5 3 3 5 10 3 6 3 13"},{"iden":"sample output 2","content":"515759610"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}