{"problem":{"name":"J. Time Limit","description":{"content":"In CCPC contests, you will get \"Time Limit Exceeded\" when your program tried to run during too much time. Setting suitable time limit for problems is vital to a contest. Mr. Bread is preparing proble","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":2000,"memory_limit":524288},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF10222J"},"statements":[{"statement_type":"Markdown","content":"In CCPC contests, you will get \"Time Limit Exceeded\" when your program tried to run during too much time. Setting suitable time limit for problems is vital to a contest.\n\nMr. Bread is preparing problems for a coming contest with his friends. For each problem, there will be a \"Main Correct Solution\" denotes the standard solution program written by the author. There will also be several \"Correct Solutions\" denote solution programs intended to pass.\n\nAssume there are $n$ programs in total, labeled by $1, 2, \\\\dots, n$. The $1$-th program denotes the \"Main Correct Solution\" while others are \"Correct Solutions\". The $i$-th program runs in $a_i$ seconds.\n\nAccording to the rules in Mr. Bread's mind, the time limit $x$ should meet all the rules below:\n\nPlease write a program to find the time limit $x$.\n\nThe first line of the input contains an integer $T (1 <= T <= 10)$, denoting the number of test cases.\n\nIn each test case, there is one integer $n (2 <= n <= 10)$ in the first line, denoting the number of programs.\n\nIn the second line, there are $n$ integers $a_1, a_2,..., a_n (1 <= a_i <= 10)$.\n\nFor each test case, print a single line containing an integer, denoting the value of $x$.\n\n## Input\n\nThe first line of the input contains an integer $T (1 <= T <= 10)$, denoting the number of test cases.In each test case, there is one integer $n (2 <= n <= 10)$ in the first line, denoting the number of programs.In the second line, there are $n$ integers $a_1, a_2,..., a_n (1 <= a_i <= 10)$.\n\n## Output\n\nFor each test case, print a single line containing an integer, denoting the value of $x$.\n\n[samples]","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"**Definitions**  \nLet $ P, Q \\in \\mathbb{R}^2 $ be two fixed pivot points.  \nLet $ A = \\{A_1, A_2, \\dots, A_n\\} \\subset \\mathbb{R}^2 $ be a set of $ n $ distinct points, none lying on line $ \\overleftrightarrow{PQ} $.  \n\nFor any point $ A_i \\in A $, define the **orientation** relative to triangle $ \\triangle PQA_j $ as:  \n$ A_i $ is **inside** $ \\triangle PQA_j $ (excluding boundary) if it lies in the interior of the triangle formed by $ P, Q, A_j $.  \n\nA **nested triangle sequence** is a strictly increasing sequence of indices $ v_1 < v_2 < \\dots < v_k $ such that for all $ i \\geq 2 $, point $ A_{v_i} $ lies strictly inside triangle $ \\triangle P Q A_{v_{i-1}} $.  \n\n**Constraints**  \n1. $ 1 \\leq T \\leq 1000 $  \n2. For each test case:  \n   - $ 1 \\leq n \\leq 10^5 $  \n   - Coordinates of $ P, Q, A_i \\in [-10^9, 10^9] $  \n   - All points distinct; no $ A_i $ lies on line $ \\overleftrightarrow{PQ} $  \n   - Sum of $ n $ over all test cases $ \\leq 10^6 $  \n\n**Objective**  \nFind the **maximum length** $ k $ of a nested triangle sequence $ v_1, v_2, \\dots, v_k $, and among all such sequences of maximum length, return the **lexicographically smallest** one.  \n\nLexicographic minimality: For two sequences $ \\mathbf{v} = (v_1, \\dots, v_k) $ and $ \\mathbf{u} = (u_1, \\dots, u_k) $, $ \\mathbf{v} < \\mathbf{u} $ iff there exists $ i \\in \\{1, \\dots, k\\} $ such that $ v_j = u_j $ for all $ j < i $ and $ v_i < u_i $.","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF10222J","tags":[],"sample_group":[],"created_at":"2026-03-03 11:00:39"}}