{"problem":{"name":"Replace by Average","description":{"content":"Given is a sequence of $N$ positive integers $A = (A_1, A_2, \\ldots, A_N)$. You can do the following operation on this sequence any number of times. *   Choose integers $i, j, k$ such that $1\\leq i <","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc130_f"},"statements":[{"statement_type":"Markdown","content":"Given is a sequence of $N$ positive integers $A = (A_1, A_2, \\ldots, A_N)$.\nYou can do the following operation on this sequence any number of times.\n\n*   Choose integers $i, j, k$ such that $1\\leq i < j < k \\leq N$ and $j = \\frac{i+k}{2}$. Replace $A_j$ with $\\lfloor\\frac{A_i+A_k}{2}\\rfloor$.\n\nFind the minimum possible value of $\\sum_{i=1}^N A_i$ after the operations.\n\n## Constraints\n\n*   $3\\leq N\\leq 3\\times 10^5$\n*   $1\\leq A_i\\leq 10^{12}$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $\\ldots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc130_f","tags":[],"sample_group":[["5\n2 2 5 5 4","13\n\nThe following operations achieves $\\sum_{i=1}^N A_i = 13$.\n\n*   Do the operation with $(i,j,k) = (1,3,5)$. The sequence $A$ is now $(2,2,3,5,4)$.\n*   Do the operation with $(i,j,k) = (3,4,5)$. The sequence $A$ is now $(2,2,3,3,4)$.\n*   Do the operation with $(i,j,k) = (2,3,4)$. The sequence $A$ is now $(2,2,2,3,4)$."],["5\n3 1 4 1 5","11"],["3\n3 1 3","7"],["3\n3 5 3","9"]],"created_at":"2026-03-03 11:01:13"}}