{"raw_statement":[{"iden":"problem statement","content":"Let $S(n)$ denote the sum of the digits in the decimal notation of $n$. For example, $S(101) = 1 + 0 + 1 = 2$.\nGiven an integer $N$, determine if $S(N)$ divides $N$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 10^9$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$"},{"iden":"sample input 1","content":"12"},{"iden":"sample output 1","content":"Yes\n\nIn this input, $N=12$. As $S(12) = 1 + 2 = 3$, $S(N)$ divides $N$."},{"iden":"sample input 2","content":"101"},{"iden":"sample output 2","content":"No\n\nAs $S(101) = 1 + 0 + 1 = 2$, $S(N)$ does not divide $N$."},{"iden":"sample input 3","content":"999999999"},{"iden":"sample output 3","content":"Yes"}],"translated_statement":[{"iden":"problem statement","content":"设 $S(n)$ 表示 $n$ 的十进制表示中各位数字之和。例如，$S(101) = 1 + 0 + 1 = 2$。\n给定一个整数 $N$，判断 $S(N)$ 是否能整除 $N$。"},{"iden":"constraints","content":"*   $1 \\leq N \\leq 10^9$"},{"iden":"input","content":"输入从标准输入给出，格式如下：\n\n$N$"},{"iden":"sample input 1","content":"12"},{"iden":"sample output 1","content":"Yes\n\n在该输入中，$N=12$。由于 $S(12) = 1 + 2 = 3$，$S(N)$ 能整除 $N$。"},{"iden":"sample input 2","content":"101"},{"iden":"sample output 2","content":"No\n\n由于 $S(101) = 1 + 0 + 1 = 2$，$S(N)$ 不能整除 $N$。"},{"iden":"sample input 3","content":"999999999"},{"iden":"sample output 3","content":"Yes"}],"sample_group":[],"show_order":["default"],"formal_statement":"### Definitions\n- For $n\\in\\mathbb{Z}_{\\ge 0}$ with decimal expansion $n=\\sum_{i=0}^{k} d_i 10^i$, where $k\\in\\mathbb{Z}_{\\ge 0}$ and $d_i\\in\\{0,1,\\dots,9\\}$, define\n$$\nS(n)=\\sum_{i=0}^{k} d_i .\n$$\n\n### Given\n- $N\\in\\mathbb{Z}_{\\ge 0}$.\n\n### Objective\n- Determine whether $S(N)\\mid N$, i.e.\n$$\n\\exists q\\in\\mathbb{Z}\\ \\text{such that}\\ N=q\\,S(N).\n$$","simple_statement":null,"has_page_source":true}