{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"livecodebench","formal_name":"LiveCodeBench","introduction":"競技プログラミングの新しい問題を継続的に収集し、コードに関する能力を評価するベンチマークです。初期release_v1は400問で、問題の出題元と公開日時、データセットの版を区別して扱います。\n\nLiveCodeBench continuously collects new competitive-programming problems to evaluate coding capabilities. Its initial release_v1 contains 400 problems, with source platform, contest date, and dataset version tracked explicitly.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://livecodebench.github.io/","indexing_mode":"noindex"},"task_id":"91797717-9c39-5445-91ee-5c9ef3e12617","task_key":"release~5fv1--test--1899~5fD","task_revision_id":"1","upstream_id":"1899_D","short_description":"D. Yarik and Musical Notes","config":"release_v1","split":"test","body":"{\"contest_date\":\"2023-10-17T00:00:00\",\"contest_id\":\"1899\",\"difficulty\":\"hard\",\"platform\":\"codeforces\",\"question_content\":\"Yarik is a big fan of many kinds of music. But Yarik loves not only listening to music but also writing it. He likes electronic music most of all, so he has created his own system of music notes, which, in his opinion, is best for it.\\n\\nSince Yarik also likes informatics, in his system notes are denoted by integers of $2^k$, where $k \\\\ge 1$ — a positive integer. But, as you know, you can't use just notes to write music, so Yarik uses combinations of two notes. The combination of two notes $(a, b)$, where $a = 2^k$ and $b = 2^l$, he denotes by the integer $a^b$.\\n\\nFor example, if $a = 8 = 2^3$, $b = 4 = 2^2$, then the combination $(a, b)$ is denoted by the integer $a^b = 8^4 = 4096$. Note that different combinations can have the same notation, e.g., the combination $(64, 2)$ is also denoted by the integer $4096 = 64^2$.\\n\\nYarik has already chosen $n$ notes that he wants to use in his new melody. However, since their integers can be very large, he has written them down as an array $a$ of length $n$, then the note $i$ is $b_i = 2^{a_i}$. The integers in array $a$ can be repeated.\\n\\nThe melody will consist of several combinations of two notes. Yarik was wondering how many pairs of notes $b_i, b_j$ $(i < j)$ exist such that the combination $(b_i, b_j)$ is equal to the combination $(b_j, b_i)$. In other words, he wants to count the number of pairs $(i, j)$ $(i < j)$ such that $b_i^{b_j} = b_j^{b_i}$. Help him find the number of such pairs.\\n\\nInput\\n\\nThe first line of the input contains one integer $t$ ($1 \\\\le t \\\\le 10^4$) — the number of test cases.\\n\\nThe first line of each test case contains one integer $n$ ($1 \\\\leq n \\\\leq 2 \\\\cdot 10^5$) — the length of the arrays.\\n\\nThe next line contains $n$ integers $a_1, a_2, \\\\dots, a_n$ ($1 \\\\leq a_i \\\\leq 10^9$) — array $a$.\\n\\nIt is guaranteed that the sum of $n$ over all test cases does not exceed $2 \\\\cdot 10^5$.\\n\\nOutput\\n\\nFor each test case, output the number of pairs that satisfy the given condition.Sample Input 1:\\n5\\n\\n1\\n\\n2\\n\\n4\\n\\n3 1 3 2\\n\\n2\\n\\n1000 1000\\n\\n3\\n\\n1 1 1\\n\\n19\\n\\n2 4 1 6 2 8 5 4 2 10 5 10 8 7 4 3 2 6 10\\n\\n\\n\\nSample Output 1:\\n\\n0\\n2\\n1\\n3\\n19\\n\",\"question_title\":\"D. Yarik and Musical Notes\",\"starter_code\":\"\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://livecodebench.github.io/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}