{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"hlce","formal_name":"Humanity's Last Code Exam","introduction":"Humanity's Last Code Exam evaluates problem solving and code generation using ICPC World Finals and IOI problems. The project describes 235 problems; this import selects its public ICPC dataset of 146 problems.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://humanity-s-last-code-exam.github.io/website/","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"ddc39977-a30f-5537-b3c3-093a2839188d","task_key":"ICPC~2dWorld~2dFinals--examples--2013~5fD","task_revision_id":"3","upstream_id":"2013_D","short_description":"Factors","config":"ICPC-World-Finals","split":"examples","body":"{\"platform\":\"atcoder\",\"question_content\":\"### Problem Breakdown\\n\\nThe fundamental theorem of arithmetic states that every integer greater than 1 can be uniquely represented as a product of one or more primes. While unique, several arrangements of the prime factors may be possible. For example:\\n\\n- \\\\(10 = 2 \\\\cdot 5\\\\)\\n  - \\\\(= 5 \\\\cdot 2\\\\)\\n- \\\\(20 = 2 \\\\cdot 2 \\\\cdot 5\\\\)\\n  - \\\\(= 2 \\\\cdot 5 \\\\cdot 2\\\\)\\n  - \\\\(= 5 \\\\cdot 2 \\\\cdot 2\\\\)\\n\\nLet \\\\(f(k)\\\\) be the number of different arrangements of the prime factors of \\\\(k\\\\). So \\\\(f(10) = 2\\\\) and \\\\(f(20) = 3\\\\).\\n\\nGiven a positive number \\\\(n\\\\), there always exists at least one number \\\\(k\\\\) such that \\\\(f(k) = n\\\\). We want to know the smallest such \\\\(k\\\\).\\n\\n### Input\\n\\nThe input consists of at most 1000 test cases, each on a separate line. Each test case is a positive integer \\\\(n < 2^{63}\\\\).\\n\\n### Output\\n\\nFor each test case, display its number \\\\(n\\\\) and the smallest number \\\\(k > 1\\\\) such that \\\\(f(k) = n\\\\). The numbers in the input are chosen such that \\\\(k < 2^{63}\\\\).\\n\\n### Sample Input 1\\n\\n```\\n1\\n2\\n3\\n105\\n```\\n\\n### Sample Output 1\\n\\n```\\n1 2\\n2 6\\n3 12\\n105 720\\n```\",\"question_title\":\"Factors\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://humanity-s-last-code-exam.github.io/website/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}