{"problem":{"name":"H. Hour for a Run","description":{"content":"The complete problemset is available on http://maratona.ime.usp.br/primfase19/provas/competicao/maratona_en.pdf ","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":1000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF10234H"},"statements":[{"statement_type":"Markdown","content":"The complete problemset is available on http://maratona.ime.usp.br/primfase19/provas/competicao/maratona_en.pdf\n\n[samples]","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"**Definitions**  \nLet $ n \\in \\mathbb{Z} $ be the number of lanterns.  \nLet $ X = (x_1, x_2, \\dots, x_n) $ be a strictly increasing sequence of lantern coordinates, where $ 0 \\le x_1 < x_2 < \\dots < x_n \\le 10^{18} $.\n\n**Constraints**  \n$ 3 \\le n \\le 3000 $\n\n**Objective**  \nFind the maximum size $ k $ of a subsequence $ (x_{i_1}, x_{i_2}, \\dots, x_{i_k}) $ with $ i_1 < i_2 < \\dots < i_k $ such that:  \n$$\nx_{i_2} - x_{i_1} = x_{i_3} - x_{i_2} = \\dots = x_{i_k} - x_{i_{k-1}}\n$$  \n(i.e., the selected lanterns form an arithmetic progression).  \nIf $ k < 3 $, any selection is valid — but we seek the *maximum* such $ k $.","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF10234H","tags":[],"sample_group":[],"created_at":"2026-03-03 11:00:39"}}