{"problem":{"name":"Frog Jump","description":{"content":"There is an infinitely large pond, which we consider as a number line. In this pond, there are $N$ lotuses floating at coordinates $0$, $1$, $2$, ..., $N-2$ and $N-1$. On the lotus at coordinate $i$, ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc128_f"},"statements":[{"statement_type":"Markdown","content":"There is an infinitely large pond, which we consider as a number line. In this pond, there are $N$ lotuses floating at coordinates $0$, $1$, $2$, ..., $N-2$ and $N-1$. On the lotus at coordinate $i$, an integer $s_i$ is written.\nYou are standing on the lotus at coordinate $0$. You will play a game that proceeds as follows:\n\n*   $1$. Choose positive integers $A$ and $B$. Your score is initially $0$.\n*   $2$. Let $x$ be your current coordinate, and $y = x+A$. The lotus at coordinate $x$ disappears, and you move to coordinate $y$.\n    *   If $y = N-1$, the game ends.\n    *   If $y \\neq N-1$ and there is a lotus floating at coordinate $y$, your score increases by $s_y$.\n    *   If $y \\neq N-1$ and there is no lotus floating at coordinate $y$, you drown. Your score decreases by $10^{100}$ points, and the game ends.\n*   $3$. Let $x$ be your current coordinate, and $y = x-B$. The lotus at coordinate $x$ disappears, and you move to coordinate $y$.\n    *   If $y = N-1$, the game ends.\n    *   If $y \\neq N-1$ and there is a lotus floating at coordinate $y$, your score increases by $s_y$.\n    *   If $y \\neq N-1$ and there is no lotus floating at coordinate $y$, you drown. Your score decreases by $10^{100}$ points, and the game ends.\n*   $4$. Go back to step $2$.\n\nYou want to end the game with as high a score as possible. What is the score obtained by the optimal choice of $A$ and $B$?\n\n## Constraints\n\n*   $3 \\leq N \\leq 10^5$\n*   $-10^9 \\leq s_i \\leq 10^9$\n*   $s_0=s_{N-1}=0$\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$s_0$ $s_1$ $......$ $s_{N-1}$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc128_f","tags":[],"sample_group":[["5\n0 2 5 1 0","3\n\nIf you choose $A = 3$ and $B = 2$, the game proceeds as follows:\n\n*   Move to coordinate $0 + 3 = 3$. Your score increases by $s_3 = 1$.\n*   Move to coordinate $3 - 2 = 1$. Your score increases by $s_1 = 2$.\n*   Move to coordinate $1 + 3 = 4$. The game ends with a score of $3$.\n\nThere is no way to end the game with a score of $4$ or higher, so the answer is $3$. Note that you cannot land the lotus at coordinate $2$ without drowning later."],["6\n0 10 -7 -4 -13 0","0\n\nThe optimal strategy here is to land the final lotus immediately by choosing $A = 5$ (the value of $B$ does not matter)."],["11\n0 -4 0 -99 31 14 -15 -39 43 18 0","59"]],"created_at":"2026-03-03 11:01:14"}}