{"raw_statement":[{"iden":"problem statement","content":"Given a positive integer $N$, find the number, modulo $998244353$, of subsets $S$ of ${1, 2, \\ldots, N}$ that satisfy the following condition.\n\n*   Every positive integer at most $N$ can be represented as the sum of some distinct elements of $S$, and there are at most two such representations."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 1500$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$"},{"iden":"sample input 1","content":"3"},{"iden":"sample output 1","content":"2\n\nThe subsets ${1,2}$ and ${1,2,3}$ satisfy the condition."},{"iden":"sample input 2","content":"5"},{"iden":"sample output 2","content":"5"},{"iden":"sample input 3","content":"1000"},{"iden":"sample output 3","content":"742952024"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}