{"problem":{"name":"H. Ancient Wisdom","description":{"content":"David and Aram had the following conversation: David: \"_Aram, you're pretty old._\" Aram: \"_I'm not THAT old. If you cube your age and then multiply by $C$, you'd get exactly my age squared._\" Lucca","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":1000,"memory_limit":1048576},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF10236H"},"statements":[{"statement_type":"Markdown","content":"David and Aram had the following conversation:\n\nDavid: \"_Aram, you're pretty old._\"\n\nAram: \"_I'm not THAT old. If you cube your age and then multiply by $C$, you'd get exactly my age squared._\"\n\nLucca overheard this conversation but isn't sure if he caught the right value for $C$. Help Lucca figure out how young David could be, assuming he heard correctly. \n\nAs everyone knows, ages are positive integers.\n\nInput is a single integer, what Lucca thought he heard for the value of $C$ $(1 <= C < 2^(63))$. \n\nOutput the minimum age David could be.\n\nThe average computer can do roughly $10^8$ elementary operations in one second. If you submit a program that tries to do more than $10^9$ operations, you shouldn't be surprised if your program gets a Time Limit Exceeded verdict! \n\n## Input\n\nInput is a single integer, what Lucca thought he heard for the value of $C$ $(1 <= C < 2^(63))$. \n\n## Output\n\nOutput the minimum age David could be.\n\n[samples]\n\n## Note\n\nThe average computer can do roughly $10^8$ elementary operations in one second. If you submit a program that tries to do more than $10^9$ operations, you shouldn't be surprised if your program gets a Time Limit Exceeded verdict!","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"Let $ C \\in \\mathbb{Z}^+ $ with $ 1 \\leq C < 2^{63} $.  \nFind the minimum positive integer $ d $ such that there exists a positive integer $ a $ satisfying:  \n$$\nC \\cdot d^3 = a^2\n$$","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF10236H","tags":[],"sample_group":[],"created_at":"2026-03-03 11:00:39"}}