{"raw_statement":[{"iden":"problem statement","content":"Takahashi has an unbiased six-sided die and a positive integer $R$ less than $10^9$. Each time the die is cast, it shows one of the numbers $1,2,3,4,5,6$ with equal probability, independently of the outcomes of the other trials.\nTakahashi will perform the following procedure. Initially, $C=0$.\n\n1.  Cast the die and increment $C$ by $1$.\n2.  Let $X$ be the sum of the numbers shown so far. If $X-R$ is a multiple of $10^9$, quit the procedure.\n3.  Go back to step 1.\n\nFind the expected value of $C$ at the end of the procedure, modulo $998244353$."},{"iden":"notes","content":"Under the constraints of this problem, it can be shown that the expected value of $C$ is represented as an irreducible fraction $p/q$, and there is a unique integer $x\\ (0\\leq x\\lt998244353)$ such that $xq \\equiv p\\pmod{998244353}$. Print this $x$."},{"iden":"constraints","content":"*   $0\\lt R\\lt10^9$\n*   $R$ is an integer."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$R$"},{"iden":"sample input 1","content":"1"},{"iden":"sample output 1","content":"291034221\n\nThe expected value of $C$ at the end of the procedure is approximately $833333333.619047619$, and $291034221$ when represented modulo $998244353$."},{"iden":"sample input 2","content":"720357616"},{"iden":"sample output 2","content":"153778832"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}