{"raw_statement":[{"iden":"background","content":"![](https://cdn.luogu.com.cn/upload/image_hosting/9pyd7oxa.png)\n\nIn the middle of night."},{"iden":"statement","content":"定义函数 $f(n) = \\displaystyle\\sum_{i = 1}^n \\sum_{j = 1}^n \\sum_{k = 1}^n [i + j + k = n] \\operatorname{lcm}(i, \\gcd(j, k))$\n\n给定 $n$，对于所有 $1 \\leq i \\leq n$，**求出所有** $f(i) \\bmod 998244353$ 的值。"},{"iden":"input","content":"一行，一个整数 $n$。"},{"iden":"output","content":"一行，$n$ 个整数，表示所有 $f(i) \\bmod 998244353$ 的值。"},{"iden":"note","content":"**【数据范围】**\n\n$$\n\\def\\or{\\operatorname{or}}\n%\\def\\arrayscretch{1.5}\n\\def\\arraystretch{1.5}\n\\begin{array}{|c|c|c|}\\hline\n\\textbf{测试点编号}&n= &\\textbf{Points}\\cr\\hline\n\\sf1&100&10 \\operatorname{pts}\\cr\\hline\n\\sf2&10^3&10 \\operatorname{pts}\\cr\\hline\n\\sf3&10^4&20 \\operatorname{pts}\\cr\\hline\n\\sf4&10^5&20 \\operatorname{pts}\\cr\\hline\n\\sf5&/&40 \\operatorname{pts}\\cr\\hline\n\\end{array}\n$$\n对于 $100\\%$ 的数据，$1 \\leq n \\leq 10^6$。"}],"translated_statement":null,"sample_group":[["10","0 0 1 4 11 20 42 60 100 134"]],"show_order":[],"formal_statement":null,"simple_statement":null,"has_page_source":false}