{"raw_statement":[{"iden":"problem statement","content":"You are given an integer $N$. We call a rooted tree $T$ satisfying the following conditions a **BFS-ordered tree**.\n\n*   $T$ is a rooted tree with $N$ vertices numbered from $1$ to $N$.\n*   The root is vertex $1$.\n*   Let vertex $p_i$ be the parent of each vertex $i$ ($2 \\leq i \\leq N$). Then, $p_2 \\leq p_3 \\leq \\cdots \\leq p_N$ holds.\n\nFor each $d=1,2,\\ldots,(N-1)$, find the number, modulo $998244353$, of BFS-ordered trees $T$ satisfying the following condition.\n\n*   The distance between vertices $(N-1)$ and $N$ in $T$ is exactly $d$. More precisely, when considering $T$ as an undirected tree and the path connecting vertices $(N-1)$ and $N$, the number of edges in that path is exactly $d$."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 10^6$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$"},{"iden":"sample input 1","content":"2"},{"iden":"sample output 1","content":"1"},{"iden":"sample input 2","content":"3"},{"iden":"sample output 2","content":"1\n1"},{"iden":"sample input 3","content":"4"},{"iden":"sample output 3","content":"2\n2\n1"},{"iden":"sample input 4","content":"5"},{"iden":"sample output 4","content":"5\n5\n3\n1"},{"iden":"sample input 5","content":"20"},{"iden":"sample output 5","content":"477638700\n477638700\n178405156\n178405139\n109639972\n108787985\n86366256\n69212603\n43976909\n22930595\n9698374\n3355343\n947052\n215710\n38814\n5324\n524\n33\n1"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}