{"problem":{"name":"Counting Subsets","description":{"content":"Given a positive integer $N$, find the number, modulo $998244353$, of subsets $S$ of ${1, 2, \\ldots, N}$ that satisfy the following condition. *   Every positive integer at most $N$ can be represente","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc143_f"},"statements":[{"statement_type":"Markdown","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.\n\n## Constraints\n\n*   $1 \\leq N \\leq 1500$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc143_f","tags":[],"sample_group":[["3","2\n\nThe subsets ${1,2}$ and ${1,2,3}$ satisfy the condition."],["5","5"],["1000","742952024"]],"created_at":"2026-03-03 11:01:14"}}