{"problem":{"name":"Select Half","description":{"content":"Given is an integer sequence $A_1, ..., A_N$ of length $N$. We will choose exactly $\\left\\lfloor \\frac{N}{2} \\right\\rfloor$ elements from this sequence so that no two adjacent elements are chosen. Fin","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc162_f"},"statements":[{"statement_type":"Markdown","content":"Given is an integer sequence $A_1, ..., A_N$ of length $N$.\nWe will choose exactly $\\left\\lfloor \\frac{N}{2} \\right\\rfloor$ elements from this sequence so that no two adjacent elements are chosen.\nFind the maximum possible sum of the chosen elements.\nHere $\\lfloor x \\rfloor$ denotes the greatest integer not greater than $x$.\n\n## Constraints\n\n*   $2 \\leq N \\leq 2\\times 10^5$\n*   $|A_i|\\leq 10^9$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$A_1$ $...$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc162_f","tags":[],"sample_group":[["6\n1 2 3 4 5 6","12\n\nChoosing $2$, $4$, and $6$ makes the sum $12$, which is the maximum possible value."],["5\n-1000 -100 -10 0 10","0\n\nChoosing $-10$ and $10$ makes the sum $0$, which is the maximum possible value."],["10\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000","5000000000\n\nWatch out for overflow."],["27\n18 -28 18 28 -45 90 -45 23 -53 60 28 -74 -71 35 -26 -62 49 -77 57 24 -70 -93 69 -99 59 57 -49","295"]],"created_at":"2026-03-03 11:01:13"}}